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3 Is Money Irrelevant? 18 The October Crash: Some Evidence on the Cascade Theory 34 The Competitive Nature o f State Spending on the Promotion of Manufacturing Exports 43 Money Demand and Inflation in Switzerland: An Application of the Pascal Lag Technique 53 The Effect of Monetary Policy on Short-Tterm Interest Rates THE FEDERAL J RESERVE JZk RANK of ST. LOUIS 1 Federal Reserve Bank of St. Louis Review M ay/June 1988 In T h is I s s u e . . . In the first article in this Review, “ Is M oney Irrelevant?” Gerald P. Dwyer, Jr. and R. W. Hafer examine w hether the stock o f m oney in the econom y is largely irrelevant for the future path o f important m acroeconom ic measures, such as inflation, incom e and real output. Long-standing propositions suggest that changes in m oney growth affect the long-run rate o f increase o f variables such as nominal GNP and the price level but do not affect the long-run rate o f in crease o f real GNP. In particular, an increase in the annual growth o f m oney by one percentage point per year should be associated with a one percentage point increase in the rate o f increase o f nominal GNP and the price level. Basic econom ic theory, however, provides some reasons w hy these relationships do not hold exactly over short periods o f time. Dwyer and Hafer examine these propositions using data across 62 countries from 1979 to 1984, using the fiveyear period to examine the long-run effects and two individual years, 1979 and 1984, to see w hether the relationships actually are looser over shorter periods. The authors find a clear one-for-one association o f the m oney stock with nominal GNP and the price level for the five-year period. In any given year, though, the association o f the m oney stock with nominal GNP and the price level is weak at best. In no case, however, do they find evidence o f a reliable relationship between m oney and real GNP. The authors conclude that attempts to use the long-run relationships to explain the data over short periods are quite likely to be disappointing. Furthermore, such attempts may produce mis leading conclusions about the importance o f the m oney stock in influencing nominal GNP and the price level. * * * Recently, a number of official investigating agencies have released reports about the October 1987 crash in stock prices. The report o f the Presidential Task Force on Market Mechanisms (the Brady Commission) has received the most public attention; the legislative and regulatory stock market reforms that have been proposed recently are based primarily on its recommendations. The Brady report suggests that the interaction o f index arbitrage and portfolio insurance trading strategies caused a “ downward cascade” in stock prices on October 19. In the second article in this Review, “The October Crash: Some Evi dence on the Cascade Theory,” G. J. Santoni analyzes this claim using minuteby-minute data on the prices o f stocks from October 15 to October 23, 1987. Santoni notes that the cascade theory advanced in the Brady report relies on notions that stock traders behave mechanically, are insensitive to price and execute trades without regard to transaction costs. However, not only are these notions inconsistent with econom ic theory, the data analyzed by Santoni do not support the view that the trading strategies caused the crash in stock prices. History, the author argues, indicates that legislative reforms following a financial panic have done little to reduce the frequency or severity of subsequent panics. Santoni concludes that the reforms advanced by the proponents o f the cascade theory are unlikely to alter this historical pattern. * * * 2 The internationalization o f the U.S. econom y has forced state governments to becom e increasingly aware o f the importance o f international business activity in sustaining the level and growth o f econom ic activity in their own states. In recent years, state governments have devoted more resources to prom ote man ufactured exports by firms located within their states. Previous research indicates a positive relationship between exports from a state and its promotional expenditures. In the third article in this Review, “The Competitive Nature o f State Spending on the Prom otion o f Manufacturing Ex ports,” Cletus C. Coughlin examines the related issue o f w hether a state’s ex ports are affected by the prom otional expenditures o f other states. The author finds some evidence that exports from one state are affected negatively by the promotional expenditures o f other states; however, data limitations and the sensitivity o f results to different measures o f prom otional expenditures by other states preclude a definitive conclusion. * * * In 1973, the Swiss National Bank ceased pegging the exchange rate o f the Swiss franc to the U.S. dollar. Since then, the m onetary authority has focused on reducing inflation. M oney dem and estimates help to gauge the effect o f m one tary growth on inflation. Hence, they are important in the formulation o f monetaiy targets in Switzerland. In the fourth article in this issue, “ M oney Demand and Inflation in Switzer land: An Application o f the Pascal Lag Technique,” Tobias F. Rotheli develops a flexible m odel o f price-level adjustment to estimate Swiss m oney demand. This econom etric specification allows the estimation o f m oney dem and elasticities and the dynamic response o f the price level to a change in the supply o f or d e mand for real m oney balances. The results corroborate the skepticism toward the use o f the partial-adjustment hypothesis or Koyck lag for the price-level adjustment: it takes approximately one and one-half years for the adjustment speed o f the price level to reach its maximum. Moreover, the Koyck lag overesti mates the half-time o f the price-level adjustment by 90 percent. Additional find ings on the dem and for m oney indicate that, if no structural shifts occur, M l growth o f between 1 percent and 3 percent per year is consistent with a stable price level in Switzerland. * * * In the final article in the Review, Daniel L. Thornton investigates the respon siveness o f interest rates to changes in monetary policy. Analysts often argue, Thornton notes, that changes in monetary policy initially affect the econom y through a “liquidity effect” on interest rates. For example, an expansionary m onetary policy is said to depress market interest rates initially. Applying three reduced-form m ethodologies com m only found in the literature to the same m onthly data set, the author finds no evidence o f a strong, statistically signi ficant, inverse relationship between monetary changes and interest rates. He finds that the strongest and most consistent negative relationship is between interest rates and nonborrowed reserves. Even in this case, however, the effect is weak and short-lived. FEDERAL RESERVE BANK OF ST. LOUIS 3 Gerald P. Dwyer, Jr., and R. W. Hafer Gerald P. Dwyer, Jr., an associate professor of economics at the University of Houston, is a visiting scholar at the Federal Reserve Bank of St. Louis. Ft. W. Hafer is a research officer at the Federal Reserve Bank of St. Louis. Nancy D. Juen provided research assistance. Is Money Irrelevant? M ANY economists recently have been claim ing that m oney has little or no effect on inflation and econom ic activity. For example, Lyle E. Gramley, past governor of the Federal Reserve Board, has been quoted as saying “ the relationship be tween growth o f the econom y and the growth o f the m oney supply is just no longer there.” 1Mean while, even a noted monetarist such as Beryl W. Sprinkel, the current chairman o f the Council o f Econom ic Advisers, says: “ It’s a problem. Nobody knows where w e are going. These recent statements are hardly novel, nor have they changed all that much over the years. In 1971, Federal Reserve Board Governor A ndrew F. Brimmer noted that it has “ not [been] dem on strated convincingly that the relationship between the m oney supply and econom ic activity is espe cially close.”3 cussion o f h ow changes in the growth o f the m oney supply affect the econom y in the long run. Following this, w e use cross-sectional data based on a large number o f countries to see h ow w ell the offered theory holds up to the facts. W e also illus trate that the connection between changes in m oney growth and econom ic activity is quite loose over short time periods. The upshot o f our find ings is that, even today, one cannot dismiss the proposition that, in the long run, increases in the growth o f the m oney supply w ill increase inflation and have no lasting effect on real econom ic activ ity. SOME BASIC PROPOSITIONS The overriding question seems to be how w ell m oney growth predicts econom ic activity over some horizon. In this paper w e offer a brief dis The basic propositions discussed are derived from the quantity theory. Basically, this theory states that, in the long run, changes in money growth are reflected one-for-one in nominal in com e growth and inflation but have no impact on the output o f real goods.4 'See Kilborn (1986). 3Quoted in Francis (1972). 2lbid. Among other things, monetarism is characterized by the proposition that there is a direct and proportional linkage be tween changes in the growth of the money supply and nominal economic variables, like inflation and nominal income growth. In addition, money growth changes have no influence on real economic activity. The effects on nominal income and inflation hold in the long run, a point discussed later in this article. See Brunner (1968), who coined the term monetarist, for a discus sion of these and other issues. “Many economists who would not call themselves quantity theorists or monetarists probably would subscribe to the follow ing propositions. MAY/JUNE 1988 4 Money and Nominal Incom e Going back at least to living Fisher (1911) and Arthur C. Pigou (1917), the first proposition is: P ro p o sitio n I : Changes in the money supply are associated with changes in spending and nominal income. This proposition results from an analysis o f the demand for and the supply of money, which can be discussed conveniently in terms o f the quantity equation, (1) M = kY, w here M is the nominal quantity o f money, k is households’ and firms’ desired ratio o f m oney to income, and Y is nominal income. In the first in stance, M can be interpreted as the quantity o f m oney dem anded by firms and households. If the amount o f m oney households and firms want to hold relative to incom e is constant, equation 1 simply says that an increase in nominal incom e w ill increase the quantity o f m oney dem anded — a plausible statement.3 Saying anything about the effects o f changes in the m oney supply on incom e requires a supposi tion about the relationship between the quantity o f m oney dem anded and supplied. At least over longer periods o f time, the quantity o f m oney de m anded and the quantity supplied are the same.6 Under this supposition, equation 1 says that the quantity o f m oney supplied equals households' and firms’ desired ratio o f m oney to incom e multi plied by nominal income. If the quantity o f m oney supplied increases, either k, the desired ratio of m oney to income, or Y, nominal income, must increase. What actually happens if the quantity o f m oney in an econom y suddenly increases? The addi tional m oney w ill be held: it is a rare person w ho bum s money. Assuming that nominal incom e and households' and firms’ desired ratio o f m oney to incom e initially are unaffected, firms and house holds momentarily are holding more m oney than they want to hold. What w ill they do? They w ill spend some o f it . To the extent the additional 5Actually, a lot of evidence is consistent with it as well. A good summary is provided by Laidler (1977). 6This difference between the quantities of money demanded and supplied is contingent on a simple specification of equation 1. In a fully-specified model of the demand for money with all adjustment costs and state variables included, the quantity of money demanded always equals the quantity of money sup plied. FEDERAL RESERVE BANK OF ST. LOUIS m oney is spent on final goods and services, Gross National Product (the dollar value o f such spend ing) increases. Because Gross National Product also is a measure o f nominal income, an increase in the quantity o f m oney supplied increases both spending and income. A strong corollaiy o f this first proposition is: P ro p o sitio n l a : An increase in the growth rate o f money will be matched by an equal increase in the growth rate o f nom inal income. When the quantity equation is written in terms o f the growth rates o f money, the desired ratio o f money to income, and income, it becomes (2) M = k + Y, where the dots over variables indicate their growth rates. If the growth rate o f k, firms' and house holds’ desired ratio o f m oney to income, is inde pendent o f changes in the growth rate o f the m oney supply, then changes in the growth o f the m oney supply must be m atched one-for-one by changes in the growth o f nominal income. In other words, holding k constant, a 1 percentage point increase in m oney growth is associated with a 1 percentage point increase in nominal incom e growth. This proposition is a long-run proposition. Sup pose, for example, that the growth rate o f the m oney supply has been 10 percent per year for a long time and the growth rate o f k is 4 percent. Then, from equation (2), the growth rate o f nom i nal incom e is 6 percent. If the growth rate o f the m oney supply increases from 10 to 15 percent, the growth rate o f nominal incom e w ill not increase from 6 percent to 11 percent immediately. It will be some time before the increase in spending oc curs and the econom y com pletely adjusts to the changed circumstances. The speed w ith which firms and households increase their spending after an increase in the m oney supply is affected by other things in the econom y.7Eventually the econom y w ill adjust, but as the data w e present below indicate, the adjustment period may exceed one year. 'Interest rates and expectations about future inflation are two such factors. Gavin and Dewald (1987, pp. 22-24) present some interesting evidence for 39 countries consistent with the importance of changes in expected inflation. 5 W hile nominal incom e growth clearly is o f some interest, the breakdown o f nominal incom e growth into real growth and inflation is perhaps even more informative about the state o f the econ omy. By definition, nominal incom e is the price level times real income. In terms o f growth rates, the growth rate o f nominal incom e equals the rate o f increase o f prices plus the growth rate o f real income, or (3) Y = P + y, where P is the rate o f increase o f the price level (the inflation rate), a n d y is the growth rate o f real income. As equation 3 indicates, nominal income growth o f 5 percent per year could occur with no inflation and real incom e growing at 5 percent per year. On the other hand, inflation could be 25 per cent per year with real incom e falling 20 percent per year. Clearly, any given growth rate o f nominal incom e can be associated with quite different inflation rates and real incom e growth rates. Money and Real Income A second proposition, pointed out forcefully by David Hume (1752), is: P ro p o sitio n I I : Changes in the money supply are not associated with permanent changes in real income. With respect to real incom e growth, changes in the growth o f m oney w ill have no effect. The basis for this proposition is quite simple. Real incom e and output, the quantity o f goods and services produced, are the same thing. Over long periods o f time, the quantity of goods and services produced in an econom y is determ ined by the quantity of resources applied to producing goods and ser vices, including land, labor and capital, as w ell as technology, workers' skills and knowledge. Under most circumstances, m oney plays a ve iy m inor role in the long run. Large changes in the growth o f the m oney supply, for example a change from 0 to 1,000 percent per year, can sufficiently disrupt an econom y that real incom e falls. Small changes, however, are unlikely to have such an effect.8 “Changes in the money supply can be related to changes in real income. Indeed, many economists argue that, in one way or another, changes in the money supply are positively related to short-run changes in real income. This relationship is used to explain the changes in real income associated with business fluctuations. Money and Inflation The third proposition is about inflation: P ro p o sitio n I I I : An increase in the growth rate o f money, oth er things the same, will be matched by an equal increase in the rate o f inflation. This proposition is derived from the two earlier ones. If changes in the growth rate o f the m oney supply are associated one-for-one with changes in nominal incom e growth, then changes in the growth o f the m oney supply must change real incom e growth or the inflation rate. The combina tion o f the two propositions above implies that, in the long run, only the inflation rate is affected. Consequently, if the growth rate o f m oney in creases by 1 percentage point per year, then the inflation rate eventually must increase 1 percent age point per year as well. This one-for-one relationship between the growth o f the m oney supply and the inflation rate is the result o f a relationship between m oney and spending w hich takes time to be played out, com bined with the lack o f a long-run relationship be tween m oney and real income. It w ou ld be sur prising if this third proposition held each month, quarter or year. The length o f the period over which it does apply is examined below. THE DATA These propositions can be examined in a variety o f ways. One approach is to look at data for a spe cific country over a long time span, say, 100 years. Another approach, the one adopted here, is to use data across a large number of countries for a shorter time period. Because the propositions are, as Robert Lucas has noted, “ characteristics o f steady states [that is, long-run equilibria], ... the ideal experiment for testing them w ou ld be a com parison o f long-term average behavior across econom ies w ith different m onetary policies but similar in other respects.”9 The specific data set that w e use includes data on nominal income, real income, the price level and the m oney stock for 62 countries. Incom e and the associated price indexes are calculated using 9Lucas (1980), p. 1006. This approach has been used by, among others, Schwartz (1973), Lothian (1985) and Lucas (1986). MAY/JUNE 1988 6 either Gross National Product (GNP) or Gross D o mestic Product (GDP).10Nominal and real GNP are used if they are available and the price level is measured by the GNP deflator; otherwise, nominal and real GDP are used and the price level is m ea sured by the GDP deflator." The countries and the data are presented in the appendix. The “long-term ” growth rates for the econom ic variables used are averages o f annual growth rates for five years, 1979 to 1984.12The ‘'short-term” growth rates are annual growth rates for individ ual years. The focus on the recent period is delib erate: the relevance o f m oney in recent years has been challenged. Therefore, a key issue is w hether the propositions discussed above are supported by the data from the past few years. MONEY; INCOME AND INFLATION Table 1 Income and Inflation Regressions: 1979 to 1984 Coefficient estimates Dependent variable Growth rate of nominal income Growth rate of real income Inflation rate Constant Growth rate of money 1.592 (1.128) 2.613 (0.366) -1 .3 5 4 (1.055) 1.007 (0.027) -0 .0 1 8 (0.009) 1.031 (0.025) R2 0.96 0.07 0.96 NOTE: The symbol R2 is the fraction of variation explained. Standard errors of the estimated coefficients are reported in parentheses. The Long-Run Evidence indicates a one-for-one correspondence between the two, consistent with proposition I. The first proposition states that there is a oneto-one relationship between m oney growth and the growth o f nominal income. To see if this is true, the long-run growth rates o f m oney and in com e for the countries in our sample are shown in figure l . 13The scatter of points indicates that the data are consistent with this proposition. As the figure shows, there is a w ide diversity in experi ence across countries. For 1979 to 1984, average m oney growth rates range from about 2 percent per year for Switzerland to 220 percent per year for Bolivia. The growth rate o f nominal incom e also varies substantially, from about 5 percent per year for the United Arab Emirates to about 200 percent per year for Bolivia. M ore important, the points tend to lie on the reference line in the figure, which has a slope o f one. This clustering of incom e and m oney growth rates along the line To examine this proposition another way, w e present a simple regression using the data in figure 1 in the first line o f table 1. This regression is the estimated straight line w hich best fits the data for nominal incom e growth and m oney growth.14 The regression is consistent with our observations about the graph. The estimated coefficient for m oney growth is 1.007, which indicates that an increase in m oney growth o f 1 percentage point per year is associated with an increase in nominal incom e growth o f almost exactly 1 percentage point per year. In addition, the statistic measuring the fraction o f variation explained, the R-, shows that 96 percent o f the variation in the nominal incom e growth rates is explained by m oney growth. This corroborates the graphic evidence that m oney and nominal incom e growth are closely linked. ,0GNP is defined as the current market value of all final goods and services produced by labor and property supplied by residents of the country. GDP is the current market value of all final goods and services produced by labor and property lo cated in the country. 14The estimation technique used is ordinary least squares, which defines the “ best” straight line as the one which minimizes the total sum of squared deviations of the dependent variable from the estimated line. The numbers in parentheses in the table are the standard errors of the estimated coefficients. These statis tics are useful for testing hypotheses about the estimated coefficients. For example, suppose one wishes to determine whether the estimated coefficient is statistically different from zero. One need only divide the estimated coefficient by its standard error. If the resulting value — known as a t-statistic — exceeds some predetermined value, say 2, then the coefficient is said to be significantly different from zero. Another way of evaluating these regression results is to test whether the coeffi cient equals one. To test the hypothesis that an estimated coefficient is equal to one, the estimated coefficient minus one is divided by the reported standard error. A t-statistic less than 2 means that the hypothesis that the estimate equals one cannot be rejected. "T he deflator simply is calculated as the ratio of nominal income to real income; for example, the GNP deflator is nominal GNP divided by real GNP. 12Although one may quibble whether five years is long enough to be long run, it seems to be long enough for transitory distur bances to average out. 13The propositions imply that the slope of the reference line should be one for nominal income growth and inflation. They do not imply that the lines pass through the origin, but they are drawn through the origin for convenience. FEDERAL RESERVE BANK OF ST. LOUIS 7 Chart 1 Growth in Nominal GNP and Growth in Money: 1979 to 1984 Nominal GNP (Percent) Nominal GNP (Percent) Money (Percent) The second proposition concerns the indepen dence o f m oney and real incom e growth in the long run. Figure 2 shows the countries’ average m oney growth and real incom e growth rates for 1979 to 1984. In this figure, the reference line is drawn at the average real incom e growth rate across the countries. This line has a slope o f zero, as im plied by the second proposition. The data plotted in this graph suggest little relationship between the two. Some countries with extremely high m oney growth rates have low or even nega tive growth rates o f real income. Bolivia, for exam ple, has a 220 percent average annual growth rate of m oney even though real incom e over the period declines at an average annual rate o f about 2 per cent. Also, Israel’s m oney growth is about 152 per cent, but real incom e growth is only 2 percent per year. In contrast, other countries have relatively low m oney growth and fast real incom e growth. Singa pore, for instance, has an average real incom e growth o f 8.6 percent over the five years and a 9 percent average m oney growth rate. This is below the average m oney growth o f 23 percent for all the countries, but w ell above the average real growth o f 2.2 percent per year. This second proposition also can be examined by regressing real incom e growth on money growth; the result is presented in the m iddle row o f table 1. The estimated coefficient on m oney growth is negative, suggesting that a faster expan sion in the m oney supply lowers real incom e growth in the long run. Although an increase in m oney growth is associated with an increase in nom inal incom e growth, the evidence suggests an increase in m oney growth is associated with a decrease in real incom e growth.15 The final proposition concerns the relationship between m oney growth and inflation. Is a 1 percentage-point increase in the growth rate of m oney reflected in a 1 percentage-point increase in the rate o f inflation? Figure 3 shows m oney growth and inflation rates across the countries. The visual evidence supports a one-for-one corre- ,5ln a regression without Bolivia, the estimated coefficient of money growth is still negative, -0 .0 1 4 , but is no longer statisti cally different from zero. MAY/JUNE 1988 8 Chart 2 Growth in Real GNP and Growth in Money: 1979 to 1984 Real GNP (Percent) Real GNP (Percent) 12 12 10 10 . 2 111 •• 0 • » • • V- .» -2 - -2 Not Shown Israel Bolivia . • M RGNP 152 220 2.3 - 2 .3 100 110 -4 -8 10 20 30 40 50 60 70 80 90 Money (Percent) Chart 3 Inflation Rate and Growth in Money: 1979 to 1984 I n fla tio n ( P e r c e n t ) FEDERAL RESERVE BANK OF ST. LOUIS I n fla tio n (P e r c e n t ) Money (Percent) 120 9 spondence: the points clearly are clustered around the reference line, indicating that coun tries with higher m oney growth on average simi larly have higher rates o f inflation. which data for all 62 countries are available. The other is 1979, the beginning o f the period. H ow w ell do these long-run propositions fare in each year? The data shown in figure 3 also support this proposition w hen used in a regression o f inflation on m oney growth. Reported in the last line in ta ble 1, the regression results are consistent with a one-for-one link between money growth rates and inflation. The estimated coefficient o f 1.031 indi cates that an increase in the growth rate o f money by 1 percentage point is associated with a similar increase in the inflation rate. Figure 4 shows the data for nominal incom e and m oney growth for 1984; the association here ap pears somewhat looser than shown in figure 1. For instance, in 1984, Peru’s m oney growth rate o f 116 percent is associated w ith 128 percent growth in nominal income, w hile Iceland’s money growth rate o f 107 percent is associated with only a 33 percent rate o f increase in nominal income. While these two countries offer convenient examples, the variety of incom e growth rates associated with a given m oney growth rate is sufficiently large to make the point. For example, 35 percent m oney growth is associated with nominal incom e growth rates ranging from 5 percent to 70 percent.17 To recap the evidence, the data are generally consistent with the propositions set forth above. The data from 62 countries for 1979 to 1984 show that, holding other things constant: (1) there is a one-for-one connection between m oney growth and nominal incom e growth; (2) there is little sys tematic relationship between m oney growth and real incom e growth; and (3) there is a one-for-one connection between m oney growth and inflation. These results are not specific to this particular sample o f countries or time period: evidence based on a smaller set o f countries (40) for the period 1981-86 supports these same conclusions.16 The Short-Term Evidence Given the evidence above, w hy then has the relevance o f m oney com e under such strong criti cism in recent years? Perhaps one reason is that attempts to apply these long-run propositions to shorter time spans have led to disappointing results and erroneous rejection o f the proposi tions. As Milton Friedman (1986) recently reiter ated, the "tim e delay between changes in the quantity o f m oney and in other magnitudes are long and variable’ and depend a great deal on surrounding circumstances.” Tw o single years from the period suffice to illus trate the errors in attempting to use longer-run relationships to explain shorter-run outcomes. One year chosen is 1984, the most recent year for 16The evidence based on the 40 countries with five-year average data through 1986 is similar. A regression of nominal GNP growth on money growth has a coefficient of 0.970 with a standard error of 0.020; a regression of real GNP growth on money growth has a coefficient of -0 .0 1 2 with a standard error of .015; and a regression of the inflation rate on money growth has a coefficient of 0.965 with a standard error of 0.025. The perception that the link between money and incom e is looser in 1984 than for the five-year period running from 1979 to 1984 is corroborated by a simple regression. The first row of table 2 presents regression results using data for 1984. The regression o f incom e growth on money growth, unlike its companion equation in table 1, indicates that a 1 percentage-point increase in m oney growth is not associated w ith a like in crease in incom e growth. Rather, nominal income growth increases by about three-fourths o f a per centage point. This illustrates the point that the one-for-one proposition concerning incom e and m oney growth does not necessarily hold over shorter periods.18 Figure 5 shows the relationship between nom i nal incom e and m oney growth rates for 1979. The looseness o f the shorter-run association between growth rates o f m oney and nominal incom e again is evident. On the one hand, Israel and Zaire have nominal incom e growth rates o f 92 percent and 103 percent and m oney growth rates o f 0 and m i nus 2 percent, respectively. On the other hand, Haiti and Tanzania both have nominal incom e growth o f about 11 percent and m oney growth percent and 21 percent; Zaire, 38 percent and 68 percent; and Tanzania, 35 percent and 15 percent. "The large outliers in figure 4 are Bolivia, Brazil and Israel. Are these countries responsible for the regression result in table 2? Deleting them and re-estimating the income-money equation produces an estimated coefficient of money growth of 0.689, again different from unity. '7For example, Denmark has 35 percent money growth and 9 percent nominal income growth; Ecuador, 36 percent money growth and a 45 percent income growth rate; Bangladesh, 34 MAY/JUNE 1988 10 Chart 4 Growth in Nominal GNP and Growth in Money: 1984 Nominal GNP (Percent) Nominal GNP (Percent) Money (Percent) rates near 54 percent. Clearly, the link between m oney and incom e growth rates is much more variable on a one-year basis than over a span o f five years. Table 2 Income and Inflation Regressions: 1979 and 1984 Coefficient estimates Dependent variable Constant Growth rate of money R2 1984 Growth rate of nominal income Growth rate of real income Inflation rate 7.191 (3.093) 3.198 (0.407) 3.277 (1.06) Growth rate of nominal income Growth rate of real income Inflation rate 13.181 (3.542) 3.889 (0.726) 9.256 (3.483) 0.756 (0.013) -0 .0 0 2 (0.002) 0.764 (0.013) 0.98 0.532 (0.134) 0.037 (0.027) 0.457 (0.131) 0.21 0.03 0.98 1979 0.03 0.17 NOTE: The symbol R2 is the fraction of variation explained. Standard errors of the estimated coefficients are reported in parentheses. FEDERAL RESERVE BANK OF ST. LOUIS The regression in table 2 for 1979 confirms that the short-run relationship between m oney and incom e is less reliable than the long-run relation ship. The coefficient on m oney growth is only 0.53, far below unity. Moreover, the R2w hich is 98 per cent in 1984, is only 21 percent for 1979. This dra matic switch in results indicates that using m oney growth to predict nominal incom e for a period as brief as one year is likely to be associated with large errors. Such short-term inaccuracy, however, does not obviate the underlying, long-run proposi tion supported by the evidence presented earlier. Real incom e and m oney growth for 1984 are presented in figure 6. The figure suggests no discernable pattern. This is consistent with the p rop osition that real incom e growth is independent of m oney growth, even over a period as brief as a year. The associated regression in table 2 corrobo rates this: the estimated coefficient o f m oney growth is not different from zero. Moreover, 11 Chart 5 Grow th in Nom inal GNP and Grow th in Money: 1979 Nominal GNP (Percent) Nominal GNP (Percent) Money (Percent) Chart 6 Growth in Real GNP and Growth in Money: 1984 Real GNP (Percent) Real GNP (Percent) 12 10 12 % %• • • • • 2 0 -2 10 - • • - Not Shown Brazil Israel Bolivia J____ L -10 0 10 20 30 J____ L 40 50 60 Money (Percent) M rg ' n p 199 349 1793 4.4 1.7 - 0 .9 100 110 -4 J____ L 70 80 90 120 MAY/JUNE 1988 12 Chart 7 G row th in Real GNP and Grow th in Money: 1979 Real GNP (Percent) 12 Real GNP (Percent) 12 10 10 8 6 4 2 2 0 0 -2 -2 -4 -6 United Arab Emirates J____ I____ L -10 -4 N ot S how n 10 20 30 40 50 60 70 M RG*NP 9 25 1 1 1 1 80 90 100 110 -6 -8 120 Money (Percent) m oney growth explains a mere 3 percent o f the total variation in real incom e growth.'9 A similar story unfolds using the data from 1979, which are plotted in figure 7. Austria and Peru provide a taste o f this diversity. Austria has real incom e growth o f 5 percent with a m oney growth rate o f minus 9 percent. In stark contrast, Peru has real incom e growth o f about 4 percent with a m oney growth rate o f 70 percent. The regression in table 2 again points to no reliable relationship between m oney growth and real incom e growth: the estimated coefficient is roughly zero. The data for 1979, like the data for 1984, are consistent with the proposition that the variation o f real incom e growth is largely independent o f m oney growth. As w ould be expected based on the results for nominal and real incom e for these two years, the relationship between m oney growth and inflation is quite loose in any single year. Figure 8 shows inflation and m oney growth for 1984. The graph does not suggest the one-for-one relationship 19With Bolivia, Brazil and Israel deleted, the estimated coefficient of money growth is - 0.004, which does not alter our conclu sion. FEDERAL RESERVE BANK OF ST. LOUIS found with the data for the five-year period. The relevant regression in table 2 is consistent with this observation. The regression reveals that, in 1984, a 1 percentage-point increase in the growth rate o f m oney is associated w ith about a threequarters o f a percentage-point increase in in flation. Although significant and positive, the asso ciation obviously is not one-for-one. The m oney growth and inflation data for 1979, presented in figure 9, show that 1984 is not abnor mal. If anything, figure 9 reveals even greater vari ety in the combinations o f inflation and m oney growth than the data for 1984 reveal. This observa tion is corroborated by the results o f the regres sion in table 2. In contrast to 1984, the data for 1979 show a weak link between m oney growth and inflation. Not only is the R2o f the equation lo w — only 17 percent o f the variation in inflation is ex plained by m oney growth — but the estimated coefficient on m oney growth again is w ell below unity. 13 Chart 8 Inflation Rate and Growth in Money: 1984 Inflation (Percent) Inflation (Percent) Money (Percent) Chart 9 Inflation Rate and Growth in Money: 1979 Inflation (Percent) Inflation (Percent) Money (Percent) MAY/JUNE 1988 14 The evidence in this section indicates that m oney’s relevance cannot be judged accurately over shorter-run periods o f one month, one quar ter or even one year. Over such short-run periods, an increase in m oney growth may result in a sub stantial rise in the growth o f nominal incom e — the evidence from 1984 — or show little effect on nominal incom e — the 1979 result. Similar results hold when assessing the short-run association between m oney growth and inflation. CONCLUSION Is m oney irrelevant? The short-run linkages between the growth rates o f money, incom e (both nominal and real) and prices are, as w e have shown, quite loose. In anv particular year, higher m oney growth is not associated with an equal increase in nominal incom e or inflation. Even so, propositions about the importance o f m oney in determining inflation in the longer run have not faded. Viewed in the proper time perspective, a higher growth rate o f the m oney supply is associ ated with a higher inflation rate. Attempts to use the longer-run relationships between m oney growth and either nominal incom e growth or in flation for explaining short-run outcomes are likely to prove disappointing. M oney’s relevance w ill be substantially misjudged if attention is fo cused on the short run. FEDERAL RESERVE BANK OF ST. LOUIS REFERENCES Brunner, Karl. “ The Role of Money and Monetary Policy,” this Review (July 1968), pp. 9-24. Fisher, Irving. 1911). The Purchasing Power of Money (Macmillan, Francis, Darryl R. “ Has Monetarism Failed? — The Record Examined," this Review (March 1972), pp. 32-38. Friedman, Milton. “ M1 's Hot Streak Gave Keynesians a Bad Idea," Wall Street Journal, September 18, 1986. Gavin, William T., and William G. Dewald. “ Velocity Uncer tainty: An Historical Perspective,” United States Department of State, Bureau of Economic and Business Affairs Working Paper 87/4 (November 1987). Hume, David. “ Of Money,” in Writings on Economics, edited by Eugene Rotwein (University of Wisconsin Press, 1970). Reprint of selected essays from Political Discourses, 1752. Kilborn, Peter T. “ Monetarism Falls From Grace,” New York Times, July 3,1986. Laidler, David E. W. The Demand for Money: Theories and Evidence, 2nd ed. (Dun-Donnelley, 1977). Lothian, James R. “ Equilibrium Relationships Between Money and Other Economic Variables," American Economic Review (September 1985), pp. 828-35. Lucas, Robert E., Jr. “Adaptive Behavior and Economic The ory,” Journal of Business (October 1986), Part 2, pp. S40126. _________ “Two Illustrations of the Quantity Theory of Money,” American Economic Review (December 1980), pp. 1005-14. Pigou, Arthur C. “ The Value of Money,” Quarterly Journal of Economics (November 1917), pp. 38-65. Schwartz, Anna J. “ Secular Price Change in Historical Per spective,” Journal of Money, Credit and Banking (February 1973), Part 2, pp. 243-69. 15 D a ta A Ap Xp e n d ix Data for 1979- 84 country United States United Kingdom Austria Belgium Denmark France Germany Italy Norway Switzerland Canada Japan Finland Greece Iceland Ireland Australia New Zealand South Africa Bolivia Brazil Chile Colombia Costa Rica Dominican Republic Ecuador El Salvador Guatemala Haiti Honduras Mexico Panama Paraguay Peru Uruguay Venezuela Cyprus Israel Jordan Syrian Arab Republic United Arab Emirates Bangladesh Burma Sri Lanka India Korea Malaysia Nepal Pakistan Philippines Singapore Thailand Burundi Zaire Kenya Malawi Morocco Nigeria Tanzania Zambia Papua New Guinea Hungary Money Growth 7.5% 11.8 7.1 3.0 15.4 10.9 4.7 13.0 13.6 2.1 10.7 4.0 12.1 18.9 64.9 8.7 8.9 8.9 30.5 220.3 98.0 18.2 24.3 37.1 14.1 25.2 8.2 3.4 4.8 9.2 45.0 4.8 14.6 67.6 29.2 15.3 14.9 152.0 13.5 23.4 7.2 18.2 12.8 16.8 15.6 15.8 9.5 14.3 13.2 12.3 9.2 8.0 9.9 61.8 7.4 11.2 9.5 14.7 15.9 11.0 5.0 8.7 Inflation 6.5% 9.5 5.3 5.5 8.4 10.3 3.7 19.5 10.2 4.6 7.7 2.2 9.5 20.4 60.4 13.0 9.6 11.8 14.9 205.9 126.5 18.9 23.5 36.0 10.7 25.5 10.7 6.8 9.8 7.1 52.3 5.2 15.7 81.1 41.3 12.9 10.0 170.3 7.0 10.0 1.6 11.4 2.6 18.0 8.8 10.7 4.2 8.4 9.1 18.4 5.3 6.3 8.8 53.2 10.0 13.5 8.3 9.8 15.0 12.5 5.6 5.5 Real Income Growth 1.8% 0.7 1.6 1.0 1.5 1.5 1.1 1.8 3.2 1.5 1.9 3.9 3.4 1.1 - 1 .4 2.3 2.5 2.4 2.5 - 2 .3 1.5 0.6 2.4 0.3 3.2 2.2 - 4 .0 - 0 .3 0.4 0.7 2.7 4.8 3.7 - 0 .3 - 1 .9 - 1 .7 5.5 2.3 7.3 3.7 3.1 3.3 6.0 5.1 5.5 5.8 6.9 2.8 6.7 0.8 8.6 5.5 2.9 1.2 2.9 1.0 2.7 - 2 .9 0.6 0.6 0.3 1.9 Nominal Income Growth 8.5% 10.2 6.9 6.6 10.1 12.0 4.9 21.7 13.6 6.2 9.8 6.1 13.1 21.6 58.1 15.6 12.4 14.4 17.8 198.9 129.9 19.6 26.5 36.4 14.3 28.3 6.3 6.5 10.2 7.9 56.4 10.3 20.0 80.6 38.6 10.9 16.1 176.6 14.8 14.1 4.7 15.2 8.7 24.0 14.8 17.1 11.4 11.4 16.5 19.3 14.3 12.2 12.0 55.1 13.2 14.6 11.2 6.6 15.7 13.1 5.9 7.5 MAY/JUNE 1988 16 Data for 1979 Country Money Growth United States United Kingdom Austria Belgium Denmark France Germany Italy Norway Switzerland Canada Japan Finland Greece Iceland Ireland Australia New Zealand South Africa Bolivia Brazil Chile Colombia Costa Rica Dominican Republic Ecuador El Salvador Guatemala Haiti Honduras Mexico Panama Paraguay Peru Uruguay Venezuela Cyprus Israel Jordan Syrian Arab Republic United Arab Emirates Bangladesh Burma Sri Lanka India Korea Malaysia Nepal Pakistan Philippines Singapore Thailand Burundi Zaire Kenya Malawi Morocco Nigeria Tanzania Zambia Papua New Guinea Hungary FEDERAL RESERVE BANK OF ST. LOUIS 6.7% 9.1 - 9 .0 2.5 9.9 11.8 2.9 23.7 7.6 -1 .9 1.4 3.0 22.5 16.3 46.3 8.1 15.4 3.4 20.7 11.1 74.9 64.5 24.8 10.7 30.7 27.4 21.5 10.7 54.3 13.6 33.7 22.5 24.4 70.3 71.6 8.9 28.5 0.0 25.7 16.2 8.5 25.4 11.1 29.7 12.2 20.7 17.2 15.2 20.4 11.2 15.8 16.6 7.8 - 2 .4 16.5 -3 .4 12.4 20.5 52.9 30.2 9.2 10.0 Inflation 8.8% 14.5 4.1 4.6 7.6 10.1 4.0 15.9 6.6 2.0 10.0 3.0 8.3 18.6 39.3 13.7 8.2 13.8 15.1 19.7 56.8 46.3 24.0 9.1 11.1 16.1 13.9 8.6 2.9 9.6 20.2 9.2 20.6 78.3 75.5 21.3 13.0 84.6 14.1 15.5 5.4 12.9 5.6 15.4 15.6 19.9 12.1 10.0 5.5 15.2 5.2 11.6 20.3 102.1 6.2 4.5 7.6 16.8 10.6 21.9 15.5 5.5 Real Income Growth 2.5% 2.2 4.7 1.7 3.5 3.2 3.9 4.9 5.1 2.5 3.7 5.3 7.3 3.7 5.0 3.1 4.7 2.7 3.2 0.2 6.4 8.3 5.4 4.9 4.5 5.3 -1 .7 4.7 7.6 6.3 9.2 4.5 10.7 4.3 6.2 1.3 10.3 3.8 4.4 4.2 25.0 4.6 5.2 6.4 - 4 .8 7.4 9.3 2.4 4.9 6.9 9.4 6.1 2.0 0.3 3.9 3.3 4.5 3.9 1.2 -3 .1 0.0 2.7 Nominal Income Growth 11.5% 17.1 9.0 6.3 11.4 13.7 8.1 21.6 12.0 4.5 14.1 8.5 16.3 23.0 46.3 17.2 13.2 16.8 18.8 19.9 66.8 58.4 30.7 14.5 16.1 22.3 11.9 13.7 10.7 16.5 31.2 14.2 33.5 85.9 86.3 22.9 24.6 91.7 19.1 20.3 31.8 18.1 11.1 22.8 10.0 28.8 22.5 12.6 10.6 23.2 15.1 18.4 22.7 102.6 10.4 8.0 12.5 21.4 12.0 18.2 15.5 8.4 17 Data for 1984 Country United States United Kingdom Austria Belgium Denmark France Germany Italy Norway Switzerland Canada Japan Finland Greece Iceland Ireland Australia New Zealand South Africa Bolivia Brazil Chile Colombia Costa Rica Dominican Republic Ecuador El Salvador Guatemala Haiti Honduras Mexico Panama Paraguay Peru Uruguay Venezuela Cyprus Israel Jordan Syrian Arab Republic United Arab Emirates Bangladesh Burma Sri Lanka India Korea Malaysia Nepal Pakistan Philippines Singapore Thailand Burundi Zaire Kenya Malawi Morocco Nigeria Tanzania Zambia Papua New Guinea Hungary Money Growth 5.9% 15.4 3.5 0.3 34.7 8.9 5.9 12.4 24.4 0.1 19.9 6.9 16.4 20.2 107.4 9.6 8.2 9.8 41.2 1793.3 198.5 13.1 24.1 17.6 48.4 35.6 18.3 4.3 19.2 3.8 60.0 2.3 29.4 116.0 48.4 23.8 4.4 348.5 1.0 25.0 - 2 .6 33.6 15.5 14.1 18.5 0.5 - 0 .6 13.2 5.2 3.5 3.0 14.1 6.4 38.3 14.1 20.7 7.6 8.2 34.6 9.4 20.9 4.8 Inflation 3.9% 4.1 4.8 5.5 5.7 7.5 2.0 10.2 6.4 2.9 3.8 1.2 9.2 20.3 29.0 7.7 7.0 5.6 12.0 1345.7 214.3 14.3 22.2 19.4 24.5 39.2 12.3 4.2 11.1 4.2 61.8 4.8 26.9 117.2 61.5 21.6 8.9 391.3 3.9 6.7 -5 .0 16.4 1.9 21.5 6.4 3.9 6.1 5.0 9.6 49.8 0.7 1.3 12.4 64.0 10.0 13.7 9.1 15.6 11.9 19.5 7.6 6.3 Real Income Growth 6.4% 2.2 2.0 1.9 3.5 1.4 3.3 3.5 5.7 2.0 5.1 5.1 3.3 2.7 2.7 3.2 6.9 6.6 5.1 -0 .9 4.4 6.3 3.4 8.0 0.4 4.2 2.3 0.5 0.3 2.8 3.7 - 0 .4 3.1 4.8 -1 .5 -1 .4 7.5 1.7 1.5 - 3 .6 3.3 4.2 5.6 4.1 3.8 8.6 7.8 7.8 5.3 -7 .1 8.2 5.5 3.2 2.7 0.4 4.5 2.2 - 5 .5 2.5 - 1 .3 2.2 2.7 Nominal Income Growth 10.5% 6.4 6.9 7.4 9.3 8.9 5.3 14.1 12.5 5.0 9.1 6.4 12.8 23.6 32.6 11.1 14.4 12.6 17.7 1332.5 228.2 21.5 26.3 29.0 25.0 45.0 14.8 4.6 11.5 7.1 67.7 4.4 30.8 127.5 59.1 20.0 17.0 399.5 5.4 2.8 - 1 .9 21.3 7.6 26.4 10.5 12.9 14.4 13.1 15.5 39.2 9.0 6.9 16.0 68.4 10.4 18.8 11.5 9.2 14.7 17.9 10.0 9.2 MAY/JUNE 1988 18 G. J. Santoni G. J. Santoni is a senior economist at the Federal Reserve Bank of St. Louis. Thomas A. Poiimann provided research assistance. The October Crash: Some Evidence on the Cascade Theory “I t ’s the nearest thing to a meltdown that I ever want to see.” John J. Phelan, Jr., Chairman o f the N ew York Stock Exchange HE record one-day decline in stock prices on October 19,1987, stripped roughly 22 percent from stock values. More disconcerting, however, w ere the speed o f the adjustment, the tumultuous trad ing activity in financial markets and the uncer tainty that prevailed during the week o f October 19. These aspects o f the crash bore a surprising resemblance to previous financial panics that many thought w ere historical artifacts outm oded by m odern regulatory and surveillance systems as w ell as by advances in the financial sophistication o f market participants. The crash shocked this com placency and reawakened considerable inter est in financial panics and their causes. As with its 1929 predecessor, the list o f popular explanations for the panic o f 1987 runs the gamut from the purely econom ic and financial to the frailties inherent in human nature (see opposite page). Recently, a number of more-or-less official 1See, for example, the Report of the Presidential Task Force on Market Mechanisms (1988); U.S. General Accounting Office (1988); U.S. Commodity Futures Trading Commission (1988); and the report of Miller, Hawke, Malkiel and Scholes (1987). FEDERAL RESERVE BANK OF ST. LOUIS investigating agencies have released reports about the October panic.1Generally speaking, these re ports do not attempt to identify the reason for the decline in stock prices. Rather, they focus on the factors that characterized it as a panic: the sharp ness o f the decline on October 19 and the tum ultu ous trading activity that occurred on this day and during the follow ing week. Virtually all o f the reports agree that the inability of the N ew York and other cash market exchanges to process the unprecedented volum e o f trades quickly contributed im portantly to the market turmoil. They disagree widely, however, about the reasons for the sharpness o f the decline. The Brady Commission Report attributes the downward “ cascade” in stock prices to pro gram m ed trading — m ore specifically, to the trad ing strategies known as index arbitrage and portfo- 19 Some Popular Notions Regarding the Crash of ’87 “Wall Street has supplanted Las Vegas, Atlan tic City, Monte Carlo and Disneyland as the place where dreams are made, where castles appear in the clouds. It was Pinocchio’s Plea sure Island, where children (and the adults whose bodies they inhabited) could do and have whatever they wanted, w henever they wanted it. But now it’s m orning and the binge seems to be over. Many have hangovers. Many have worse. The jackasses are clearly identifiable. And the rest o f us, w ho pretended not to notice, are left with the job o f cleaning up the mess.” Robert B. Reich, New York Times (October 22,1987) “ People are beginning to see that the five-year bull market o f the Eighties was a new Gatsby age, com plete with the materialism and eu phoric excesses o f all speculative eras. Like the Jazz Age o f F. Scott Fitzgerald's . . the years combined the romance o f wealth and youth with the slightly sinister aura o f secret under standings.” William Glaberson, New York Times (December 13,1987) “W e've been through quite a few years in which w e felt w e had reached the millennium, which was high rewards and no risk. W e are now understanding that that is not the case.” Peter G. Peterson, New York Times (December 13,1987) “Ultimately, w e w ill view this period as one in which w e made a very important mistake. What w e did was divorce our financial system from reality." Martin Lipton, New York Times (December 13,1987) “Investors knew that stocks w ere overpriced by any traditional valuation measure such as price/eamings ratios and price to book value. They also knew that the combination o f pro gram trading and portfolio insurance could send prices plummeting." Anise C. Wallace, New York Times (November 3,1987) “On Monday, October 19, Wall Street’s leg endary herd instincts, now em bedded in digital code and am plified by hundreds o f computers, helped turn a sell-off into a panic." David E. Sanger, New York Times (December 15,1987) "Futures and options are like barnacles on a ship. They take their life from the pricing of stocks and bonds. W hen the barnacles start steering the ship, you get into trouble, as w e saw last week.” Marshall Front, Christian Science M o n ito r (October 30,1987) “ One trader’s gain is another’s loss, and the costs o f feeding computers and brokers are a social waste.” Louis Lowenstien, New York Times (May 11, 1988). "W e probably w ould have had only a 100- to 150-point drop if it hadn’t been for computers.’ Frederick Ruopp, Christian Science M o n ito r (October 30, 1987) “This [restrictions on programm ed trading] w ill make it a market where the individual in vestor can tread without fear o f the computers.” Edward A. Greene, New York Times (Novem ber 3, 1987). “ In m y mind, w e should start by banning index option arbitrage and then proceed with other reforms which will restore public con fidence in the financial markets. The public has every reason to believe that the present game is rigged. It is. Many w ould be better off in a ca sino since there people expect to lose but have a good meal and a good time w hile they're d o ing it.” Donald Regan, U.S. Senate Hearing, Committee on Banking, Housing and Urban Affairs (May 24,1988, pp. 76-77). MAY/JUNE 1988 20 The Trading Strategies Portfolio insurance is an investment strategy that attempts to insure a return for large portfo lios above some acceptable minimum. For ex ample, if the acceptable minimum return is 8 percent and the portfolio is currently returning 13 percent, the portfolio’s managers may want to decrease the share o f the portfolio held in bonds and cash, which are safe but yield rela tively low returns, and increase the share o f the portfolio held in higher-yielding stock. This increases the expected return o f the portfolio but exposes it to more risk. On the other hand, a stock price decline that reduced the return o f the portfolio to, say, 10 percent puts the return close to the minimum. In this event, the man agers may want to reduce the risk exposure o f the portfolio. This can be accom plished by re ducing the share o f the portfolio held in stock and increasing the shares held in cash and bonds.' This strategy results in stock purchases when stock prices rise significantly and stock sales when stock prices decline significantly.2Ini tially, these portfolio adjustments typically are 'See Miller, Hawke, Malkiel and Scholes (1987), p. 12. 2The purpose of this paper is not to evaluate the wisdom of these trading strategies. Rather, it is to evaluate the proposi tion that they contributed importantly to the panic. made by trading in stock index futures, because the transaction cost for large baskets o f stock are low er in futures than in the cash market.3 Inde\ arbitrage is a trading strategy based on simultaneous trades o f stock index futures and the corresponding basket o f stocks in the cash market. This trading strategy attempts to profit from typically small and short-lived price dis crepancies for the same group o f stocks in the cash and futures markets. Cash and futures prices for the same stock or group o f stocks typically differ. The difference — called the basis — results from the “cost of carrying” stocks over the time interval spanned by the futures contract. These costs depend on the relevant interest rate and the dividends the stocks are expected to pay during the interval. On occasion, the observed basis may diverge from the cost o f carry. If so, arbitrageurs can expect to profit if simultaneous trades can be placed in the two markets — purchasing the relatively low -priced instrument and selling the relatively high-priced instrument. These trades move the basis back to the cost o f carry. $500 lower than trading the equivalent basket of stocks in the cash market. See Miller, Hawke, Malkiel and Scholes (1987), p. 11, and U.S. General Accounting Office (1988), p. 20 . 3For example, the transaction costs of trading one futures contract based on the Standard and Poor’s 500 are about lio insurance (see above for a discussion o f these strategies).2This conclusion, however, is ques tioned seriously in reports filed by the Com m odity Futures Trading Commission (CFTC) and Chicago Mercantile Exchange (C M E )3These reports attrib ute the swift decline in stock prices to a massive revision in investors' perceptions o f the funda mental determinants o f stock prices.4Further more, since different rules govern trading in the cash and futures markets, a careful analysis o f the effect o f these different rules may better explain the evidence advanced by the Brady Commission in support o f the cascade theory.5 2See the Report of the Presidential Task Force on Market Mecha nisms (1988), pp. v, 15, 21, 29, 30 and 34-36. 4See U.S. Commodity Futures Trading Commission (1988), p. ix; and Miller, Hawke, Malkiel and Scholes (1987), p. 6. 3See U.S. Commodity Futures Trading Commission (1988), pp. iv, v, viii and 38-138 (especially p. 137); and Miller, Hawke, Malkiel and Scholes (1987), pp. 6, 8,1 0-11 , 41-43 and 55-56. sSee Miller, Hawke, Malkiel and Scholes (1987), pp. 21-23, 25, 37 and 49-50. FEDERAL RESERVE BANK OF ST. LOUIS This paper examines minute-by-minute price data gathered from the cash and futures market for stocks from October 15-23 to determine if the data are best explained by the cascade theory or the different trading rules in the tw o markets. Resolving this issue is important because o f the legislative and regulatory proposals spawned by the October panic. For example, the regulatory 21 proposals advanced by the Brady Commission include: (1) One agency to coordinate regulatory issues that have an impact across all financial markets; (2) Unified clearing systems across related financial markets; (3) Consistent margin requirements in the cash and futures markets; (4) Circuit breaker mechanisms (such as price limits and coordinated trading halts); and (5) Integrated information systems across re lated financial markets.6 Proposals 3 and 4 clearly reflect the Com m ission’s belief that programm ed trading contributed sig nificantly to the panic. Furthermore, the action taken by the New York Stock Exchange (NYSE) to restrict use o f its Designated Order Turnaround (DOT) system by program traders suggests that the officials o f this exchange also subscribe to the Brady Com m ission’s explanation.7This belief was reaffirmed more recently. Beginning February 4, 1988, the NYSE has denied use o f the DOT system to program traders whenever the Dow Jones In dustrial Average moves up or dow n by more than 50 points from its previous day’s close. THE CASCADE THEORY The Brady Commission suggests that the stock market panic is best explained by the “ cascade theoiy.” This theoiy argues that "mechanical, price-insensitive selling” by institutions using portfolio insurance strategies contributed signifi cantly to the break in stock prices.8In an effort to liquidate the equity exposure o f their portfolios quickly, these institutions sold stock index futures contracts in the Chicago market. Such sales lo w ered the price o f the futures contracts relative to the price o f the equivalent basket o f stocks in the N ew York cash market. The decline in the futures price relative to the cash price induced index arbi trageurs to purchase futures contracts in the Chi cago market (which, in their view, were under valued) and sell (short) the underlying stocks in 6Report of the Presidential Task Force on Market Mechanisms (1988), p. vii. 7The DOT System is a high-speed, order-routing system that program traders use to execute simultaneous trades in the cash and futures markets. 8Report of the Presidential Task Force on Market Mechanisms (1988), p. v. 9/£>/d., pp. 15, 17, 21, 30-36 and 69. It is apparent that our knowledge of stock market panics has advanced considerably the N ew York market (which, in their view, were overvalued relative to futures). Thus, index arbi trage transmitted the selling pressure from the Chicago futures market to the N ew York cash mar ket causing cash prices in N ew York to decline. The story does not end here. According to the theory, the decline in cash prices triggered a fur ther selling wave in the Chicago market by portfo lio insurers that index arbitrageurs, again, trans mitted to the N ew York market. This process was repeated time after time causing a “ downward cascade” in stock prices.11 The Brady Commission suggests that support for the cascade theoiy can be found bv examining the behavior o f the spread (the basis) between the price o f stock index futures contracts and the cash prices o f the shares underlying the contracts."1 The basis is normally positive. Stock index futures prices generally exceed cash prices because the net costs o f carrying stock forward (interest cost less expected dividends) are typically positive." During the panic, however, the basis turned nega tive. The Commission suggests that this observa tion is consistent with the cascade theoiy. Chart 1 plots both the price o f the December Standard and Poor’s 500 futures contract and the Standard and Poor's index o f 500 comm on stocks. The latter represents the cash price o f the stocks underlying the futures contract. The data cover half-hour intervals during October 15-23, 1987. Chart 2 plots the basis — the difference between the two prices shown in chart 1. As one can see, the basis fell below zero in the late afternoon of October 16 and, with a few exceptions, remained negative for the rest o f the week. In the Brady Com m ission’s view, this evidence provides im por tant support for the cascade theory. THERE IS LESS TO THE CASCADE THEORY THAN MEETS THE EYE The Negative Basis As mentioned, proponents o f the cascade theory suggest that their theory is supported by the negain the 58 years since the 1929 crash. “ Black Tuesday” was caused by a downward price “ spiral.” “ Bloody Monday" was a “ cascade.” 10Report of the Presidential Task Force on Market Mechanisms (1988), pp. 111.1—III.26, especially III.16-111.22. "S ee Figlewski (1984), pp. 658-60; Burns (1979), pp. 31-57; Cornell and French (1983), pp. 2-4; Modest and Sundaresan (1983), pp. 22-23; Santoni (1987), pp. 23-25; Schwarz, Hill and Schneeweis (1986), pp. 326-46; Working (1977); Kawaller, Koch and Koch (1987), p. 1311. MAY/JUNE 1988 22 Chart 1 Cash and December Futures S&P 500 Index S&P 500 Index 300 300 Cash 275 275 250 250 225 225 \ 200 j Futures i 200 \ * u I 175 175 15 16 19 20 21 October 1987 * Futures market closed Chart 2 Basis = December Futures-Cash October 1987 ^Futures market closed FEDERAL RESERVE BANK OF ST. LOUIS 22 23 23 Table 1 Calculating the Basis Panel A Assumptions: D, = $1.00 g = 5.0% E,Dt+1 = D,(1+g) = $1.05 r = 11% (1) P, = E,D,+,/( r - g ) = S1.05/.06 = $17.50 (2) E,P,+1 = P,(1 + r) - E,Dt+1 = $17.50(1.11) - $1.05 = $18.38 (3) B = E,Pt+I - P, = $18.38 - $17.50 = $ .88 Panel B Assumptions: Same as A except g' = 3.0% (1) P \ = E,D',+1/ ( r - g ') = $1.03/,08 = $12.88 (2) E,P'1+) = P',(1 + r) - E,D',+, = $12.88(1.11) - $1.03 = $13.27 (3) B' = E,P',t1 - P', = $13.27 - $12.88 = $ .39 where: D, = the current dividend E,Dt+1 = the expected dividend at year end P, = the current share price g = the expected growth rate in dividends r = the relevant long-term interest rate tive basis observed on the afternoon o f October 16 and on subsequent trading days during the week o f October 19. However, a negative basis does not necessarily support the cascade theory. Panel A o f table 1 calculates the current price of a stock, P„ assuming that the currently obseived dividend, D„ is $1; the long-term interest rate, r, is 11 percent and the expected growth rate in divi dends, g, is 5 percent.1- Under these assumptions, the current price o f the stock is $17,501 = $1.05/ .11 — .05]). In addition, panel A calculates the ex pected price o f the stock one year from now, E,PI+1. This expected price is the amount to which P, 2See Brealey (1983), pp. 67-72. w ould grow if invested at r less the dividend ex pected at the end o f the year, E,DI+I.13This amount is $18,381 = $17.50[1.11] - $1.05). Assuming that arbitrageurs are rational and that transaction costs are veiy low, the basis between the price o f a fu tures contract dated to mature in one year and the current cash price o f the stock is the difference between the expected price o f the stock one year from now and its current price, $.88( = $18.38 -$17.50). Panel B performs similar calculations assuming that the expected growth rate in dividends, g, falls from 5 percent to 3 percent, while everything else ,3The example assumes that the yield curve is flat. MAY/JUNE 1988 24 remains constant. Notice that this results in a decline in the current price o f the stock from $17.50 to $12.88, a reduction o f about 30 percent. Furthermore, since the expected price o f the stock one year from now falls to $13.27, the basis falls to $.39( = $13.27 —$12.88). Other things the same, a decline in the expected growth rate o f dividends causes a decline in the current price, the futures price and the basis. For reasons discussed later, futures prices typically respond to new informa tion more rapidly than indexes o f cash market prices. This was particularly so during the crash. In terms o f our example, if the futures price d e clines im m ediately to $13.27 but cash prices adjust less quickly, the observed basis may be negative during the adjustment period. In short, there is no need for a special theory, like the cascade theory, to explain the behavior of the basis during the week o f October 19.14 Irrational Price-Insensitive Traders Stock prices declined throughout the day o f October 19,1987. The decline was particularly sharp in the afternoon (see chart 1). At about 1:30 p.m. EST, the price o f a Decem ber S&.P 500 futures contract was about 15 points low er than the cash prices o f the stocks underlying the contract (that is, the basis was — 15 points, see chart 2). This means that liquidating the basket o f stocks under lying the S&.P 500 through futures market sales was about $7,500 more costly (before transaction costs) than liquidating the same basket in the cash market.15Yet, according to the cascade theory, portfolio insurers continued to liquidate in the futures market. In the words o f the Brady Com mission, this apparently anomalous behavior was the result o f "mechanical price-insensitive selling." Put m ore bluntly, the theory attributes the obser vation to irrationality on the part o f portfolio man agers who, by most accounts — including those of the Brady Commission — are credited with being highly sophisticated financial experts. The Missing Arbs The cascade theory depends on index arbitrage activity to transmit selling pressure from the fu tures to the cash market. Yet, by all accounts, in 14See, in addition, Malkiel (1988), pp. 5-6. ,sThe value of a S&P 500 futures contract is $500 times the level of the index. Consequently, if the cash market index is about 255 and the futures market index is about 240 as they were at 1:30 p.m. EST on October 19, the value of the basis: B = $500(240) - $500(255) = -$7 ,5 00 . FEDERAL RESERVE BANK OF ST. LOUIS dex arbitrage virtually ceased about 1:30 p.m. EST on October 19.ui Cash market prices, however, fell sharply between 1:30 and the market's close. The S&P 500 index lost about 30 points during this time, w hile the D ow fell by m ore than 300 points. Furthermore, index arbitrage was severely re stricted in subsequent trading days because the NYSE lim ited use o f its DOT system by arbitra geurs. However, this did not prevent a further sharp decline in stock prices on October 26. Foreign Markets and Previous Panics The cascade theory fails to explain w hy stock market panics in foreign markets occurred at the same time as the U.S. panic. Programmed trading is virtually nonexistent in overseas markets. Yet these markets crashed as quickly and by as much as the U.S. market. Between October 16 and 23, for example, the U.K. stock market declined 22 per cent, the German and Japanese markets fell 12 percent, the French market fell 10 percent and the U.S. market declined 13 percent. What's more, program m ed trading dates back no further than 1982 when stock index futures contracts began trading. U.S. stock market panics have a much longer history. Since the cascade theory does not explain these other panics, there is some reason to be skeptical about its usefulness in explaining the latest U.S. panic. AN ALTERNATIVE EXPLANATION: EFFICIENT MARKETS A long-standing proposition in both econom ics and finance is that stock prices are form ed in ef ficient markets.17This means that all o f the rele vant information currently known about interest rates, dividends and the future prospects for firms (the fundamentals) is contained in current stock prices. Stock prices change only w hen new infor mation regarding the fundamentals is obtained by someone. N ew information, by definition, cannot be predicted ahead o f its arrival; because the news is just as likely to be good as it is to be bad, jumps in stock prices cannot be predicted in advance. If the efficient markets hypothesis is correct, past price changes contain no useful information 16See the Report of the Presidential Task Force on Market Mecha nisms (1988), pp. vi, 32 and 40; U.S. General Accounting Office (1988), pp. 43 and 45-46; U.S. Commodity Futures Trading Commission (1988), pp. vi and 46. ,7See Brealey and Meyers (1984), pp. 266-81; Malkiel (1981), pp. 171-79; Brealey (1983), pp. 15-18; Leroy (1982) and Fama (1970). 25 about future price changes. With some added assumptions, this can be translated into a useful empirical proposition. If transaction costs are low, the expected return to holding stock is constant and the volatility of stock prices does not change during the time period examined, the efficient market hypothesis implies that observed changes in stock prices w ill be uncorrelated. The sequence o f price changes are unrelated; they behave as random variables. This is sometimes called “weak form efficiency.” This im plication contrasts sharply with a cen tral implication o f the cascade theory. The cascade theory suggests that price changes in both the cash and futures markets are positively correlated with their own past. This follows from the theory’s circularity which attributes sharp price declines to im m ediately preceding sharp declines. The behavior of U.S. stock prices generally con forms to the efficient markets hypothesis in the sense that past changes in stock prices contain no useful information about future changes.'* H ow ever, when data on stock price indexes are ob served at very high frequency (intra-day but not day-to-day), changes in the level o f cash market indexes are correlated and appear to lag changes in futures prices.19This behavior appears to favor the cascade theory. When differences in the “market-making” techniques em ployed in the cash and futures markets are taken into account, however, intra-day data from both markets reject the cascade theory, while, on the whole, they are consistent with the efficient markets hypothesis.20 Market-Making in the Cash Market Trading on the NYSE is conducted by members w ho trade within an auction framework at posts manned by specialists.21Specialists' activities are concentrated on a particular group o f stocks that are traded at a particular post. One o f the main functions o f a specialist is to execute limit orders for other members o f the Exchange. A limit order is an order to buy (sell) a specified number o f shares o f a given stock when and if the price o f the stock falls (rises) to some specified level. The spe 18Malkiel (1981), Brealey (1983) and Fama (1970). ,9See Perry (1985); Atchison, Butler and Simonds (1987) and Harris (1988). “ See Grossman and Miller (1988) for a discussion of why trad ing rules many differ across the markets. cialist maintains a book in which these orders are recorded and to which only he has access. The ability to place a limit order with a specialist frees the broker w ho places the order from having to wait at the post for a price movement that may never occur. For example, suppose the information con tained in the specialist's book for shares o f XYZ corporation is summarized in figure l . 22The de mand curve aggregates the purchase orders that have been placed with the specialist. These in clude bids o f $97/h for 400 shares, $9:,/4 for 300 shares, etc. The supply curve aggregates the spe cialist’s sell orders o f 100 shares at $10Vk, 200 shares at $10V4, etc. Brokers, standing at the post, trade XYZ shares with each other and the special ist. At any time, a broker may request a quote from the specialist who, given the information in figure 1, w ould respond “$97/x for 400, 100 at $10V«.” This indicates that the specialist has buy orders for 400 shares at $97/s and sell orders for 100 shares at $10Vs. If the buy and sell orders o f the other bro kers at the post are in balance at the current price, trading in XYZ shares w ill occur w ithin the price range o f $97/« bid and $10V« ask.-' Suppose, however, that a broker has a market buy order for 300 shares that he is unable to cross with a broker w ith sell orders for 300 shares at the quoted spread (in this case, at an ask price o f $10Vs or less). Since the specialist’s quote indi cates that he will sell 100 shares at $10 Vx, the bro ker w ill respond "Take it.” The broker has pur chased 100 shares from the specialist at $10Vx. Since the broker must buy another 200 shares, he w ill ask for a further quote. If nothing further has occurred, the specialist will quote "$ 9 7/x for 400, 200 at $10V4.” The broker w ill respond “Take it.” The broker has satisfied the market buy order for 300 shares o f XYZ. He purchased 100 shares at $10Vx and 200 shares at $ 1 0 '/4. Of course, the bro ker could have acquired 300 shares im m ediately bv offering to pay a price o f $10'/4 but the cost w ould have been greater. Instead, it pays the bro ker to try to "walk up" the supply curve by execut ing a number of trades rather than jumping di rectly to the price that w ill get him 300 shares in 21Of course, the NYSE is not the only cash market for stocks, but it is a major market. Because of its relative size, the discussion focuses on this market. 22For purposes of exposition, the figure and discussion ignore the effect of “ stops” and “stop loss orders” on the book. 23See Stoll (1985), Shultz (1946), pp. 119-44 and The New York Stock Exchange Market (1979), pp. 14-21 and pp. 30-31. MAY/JUNE 1988 26 Figure 1 An Illustration of Limit Order Supply and Demand P r i c e ........ .......... ................. Limit Order Supply 105/s J 10V2 % 10 10V4 10V8 10 9VS 93/4 Limit Order Demand J____I____I____I____I____1 1 2 3 4 5 6 7 8 I 9 Quantity (in hundreds) one trade.24Similar reasoning applies to situations in which excess market sell orders exist at the quoted spread. Notice that this process o f “walking u p” the supply curve or “walking d ow n ” the demand curve can generate a sequence o f recorded trans action prices that run in the same direction. The larger the excess o f market buy (or sell) orders is relative to the size of the specialist’s limit orders at various prices, the longer the sequence o f re corded transaction prices that run in the same direction and the greater the likelihood that re 24Under NYSE rules, public orders have precedence over spe cialists’ orders at the same price. See Stoll (1985), p. 7. FEDERAL RESERVE BANK OF ST. LOUIS corded price changes over the time interval are correlated. This situation is particularly likely to arise during panics when large order imbalances develop at quoted prices. Specialist Rule 104 Specialists are required bv rule SR 104 to main tain a “fair and orderly” market. M ore specifically, the rule states that (t]he maintenance of a fair and orderly market im plies the maintenance of price continuity with rea- 27 sonable depth, and the minimizing of the effects of temporary disparity between supply and demand. In connection with the maintenance of a fair and orderly market, it is commonly desirable that a . . . specialist engage to a reasonable degree under exist ing circumstances in dealings for his own account when lack of price continuity, lack of depth, or dis parity between supply and demand exists or is rea sonably to be anticipated.-5 For example, rule SR 104 requires the specialist to buy shares for his ow n account to assist the maintenance o f an orderly market if, in his estima tion, sell orders tem porarily exceed buy orders at the existing market price and conversely. If these imbalances are truly temporary, the trades re quired by SR 104 w ill be profitable for the special ist; evidence indicates that specialists typically sell on up ticks in price and buy on down ticks.21' If large order imbalances develop that threaten the orderliness o f the market, the specialist may insti tute an opening delay or trading halt. The special ist needs the approval o f a floor official or governor to do this and to establish a new opening price.27 The effect o f SR 104 is to smooth what w ould otherwise be abrupt movements in stock prices, at least over short periods o f time (a few minutes). Rather than allowing the price to move directly to some new level, specialist trading temporarily retards the movement. This can generate a se quence o f correlated price changes. Market-Making in the Futures Market Trading in futures markets is governed by CFTC rules that require all trades o f futures contracts to be executed openly and com petitively by “ open outcry.” In particular, the trading arena, or pit, has no single auctioneer through whom all trades are funneled. Rather, the pit is com posed o f many traders w ho call out their bids and offers to each other. The traders are not required to stabilize the market. They may at any time take any side o f a transaction even though this might add to an im balance o f buy and sell orders at the quoted price, and they may leave the pit (refuse to trade) at any time. At the time o f the crash, there was no rule 25Report of the Presidential Task Force on Market Mechanisms (1988), p. vi-7. Rule 104 is taken seriously. See pp. vi-9. “ See Stoll (1985), pp. 35-36. 27lt was the application of SR 104 that resulted in the opening delays and trading halts that occurred during the week of October 19. For stocks included in the S&P 500, these delays and halts averaged 51 minutes on October 19 and 78 minutes on October 20. See U.S. General Accounting Office (1988), p. 56. regarding limit moves in the price o f the Standard and Poor’s futures contract. These rules contain no requirement to smooth out movements in the price. Traders are free to move the price im m ediately to a new level. Unlike the cash market, there are no trading rules in fu tures markets that are likely to result in correlated price changes. Furthermore, since there w ere no rules that retarded price changes in the futures market, futures prices w ere free to adjust more quickly than cash prices so changes in futures prices may lead changes in cash prices. Different Instruments It is important to note that different instruments are traded in the cash and futures markets. Stock index futures contracts are agreements between a seller (short position) and a buyer (long position) to a cash settlement based on the change in a stock index’s value between the date the contract is entered by the two parties and some future date.2” The instrument underlying the futures con tract is a large basket o f different stocks, that is, the stocks contained in the Major Market Index, the Value Line Index, the S&P 500 Index, etc. No such instrument is traded in the cash market, where purchasing or selling 500 different stocks, for example, requires as many different transac tions and can only be executed at significantly higher costs.23 The different instruments traded in the cash and futures markets have a further implication for the relationship between observed price changes between the two markets. The cash market prices shown in chart 1, as w ell as those examined by the Brady Commission, are measured by an index. The index is an average o f the prices o f all the stocks included in the index. When the index is obseived at a veiy high frequency (say, minute-byminute), some o f the stocks included in the index may not have traded during the interval between obseivations. If not, the level o f cash prices mea sured by the index includes some prices from previous observations. In other words, the index 28See Schwarz, Hill and Schneeweis (1986), p. 9. «For example, the cost of trading one futures contract based on the Standard and Poor’s 500 is about $500 lower than trading the equivalent basket of stocks in the cash market. See Miller, Hawke, Malkiel and Scholes (1987), p. 11, and U.S. General Accounting Office (1988), p. 20. MAY/JUNE 1988 28 play positively correlated changes as shown in the table. Table 2 Stale Prices and Correlated Changes in a Price Index: A Simple Example Period Share prices ________ ________ A B C Index1 $10 $20 $30 100 9 9 9 20 18 18 30 30 27 98.33 95.00 90.00 Change in index THE DIFFERENT IMPLICATIONS -1 .6 7 -3 .3 3 -5 .0 0 (A + B + C)/3 'Index = ------------------ x 100 $20.00 includes some "stale" prices. The term used to describe this phenom enon is “nonsynchronous trading." Typically, nonsynchronous trading does not create a serious measurement problem. Under normal conditions, a buy or sell order is executed in about two minutes on the NYSE. On October 16 and during the w eek o f October 19, however, the time required to execute orders rose markedly.'" On those days, the index contained a considerable number of stale prices.31The subsequent piece meal adjustment o f these stale prices for individ ual stocks could explain correlated changes in the level o f the cash market index. This is shown in the table 2 example. The example assumes that the index is a simple average o f the prices o f three stocks (A, B and C) divided by the average price in period zero and m ultiplied by 100. The initial prices (in period zero) are equilibrium prices (i.e., they contain all currently available relevant infor mation). Then, new information becom es available in period 1 that eventually w ill cause a 10 percent decline in all stock prices. If there is nonsynchro nous trading, the revisions w ill occur piecemeal for each o f the stocks. One example o f this is shown in the table: the price o f stock A falls in period 1, the price o f stock B falls in period 2, etc. If the index is reported in each period, it w ill dis “ See U.S. General Accounting Office (1988), p. 73. 3'See Harris (1988); Report of the Presidential Task Force on Market Mechanisms (1988), p. 30; Miller, Hawke, Malkiel and Scholes (1987), pp. 21-22 and 34-35; U.S. Commodity Futures Trading Commission (1988), pp. v, 15 and B-1 through B-9. FEDERAL RESERVE BANK OF ST. LOUIS The stale price problem is not relevant for fu tures market prices; futures prices are actual prices. As a result, changes in futures prices w ill appear to lead changes in the cash market index if the index contains a substantial number of stale prices. The central feature o f the cascade theory is that declines in cash and futures prices reinforced each other and led to further declines in both markets. The theory suggests that declines in the price o f stock index futures contracts caused a decline in the cash prices o f the underlying stocks, and this drop caused a further decline in the prices o f index futures contracts. If the theory is correct, changes in cash prices w ill be positively correlated with past changes in the price o f index futures and conversely. The cascade theory fur ther implies that price changes in each market are positively correlated with their ow n past changes. This follows from the circularity o f the theory which attributes sharp declines in stock prices to im m ediately preceding sharp declines. Finally, since the cascade theory contends that this spe cific behavior caused the panic, these correlations should be observed during the panic, but not at other times. The efficient markets hypothesis suggests that market-making in the cash market and nonsynchronous trading could produce intra-day cash market price changes that are correlated. Further more, the hypothesis suggests that changes in futures prices may lead changes in cash prices. These implications are similar to the implications o f the cascade theory. The two differ, however, in three important respects. Unlike the cascade the ory, the efficient markets hypothesis suggests that: (1) Changes in the price o f stock index futures contracts are uncorrelated, (2) Changes in cash prices do not lead changes in futures prices, and (3) Relationships that exist across the two mar kets are not unique to the panic. 29 TESTING THE TWO THEORIES These theories are tested using minute-byminute data on the level o f the Standard and Poor’s 500 index (S&P 500) and the price o f the December 1987 Standard and Poor’s 500 index futures contract (S&P 500 Futures). The level o f the S&P 500 index represents the cash price o f the stocks underlying the S&.P 500 futures contract. All tests are conducted using first differences o f the natural logs o f the levels. This transformation o f the data approximates one-minute percentage changes (expressed in decimals) in cash and fu tures market prices. The data cover the trading days immediately before, during and after the panic: October 16, 19 and 20.32 A few comments about the data are important. The NYSE^, on which the great bulk o f the stocks included in the S&P 500 index are traded, was open from 9:30 a.m. to 4:00 p.m. EST on the above days. The CME, which trades the S&P 500 futures contract, was open from 9:30 a.m. to 4:15 p.m. EST on October 16 and 19; on October 20, however, trading in the S&P 500 futures contract was halted from 12:15 p.m. to 1:05 p.m. EST. All tests reported here e*elude the period on October 20 w hen trad ing in the futures market was halted. Were Changes in Stock Prices Correlated? Table 3 presents the results o f a test (called a Box-Pierce test) based on the estimated autocorre lations o f percentage changes in cash market prices. This test is designed to determine whether the data are significantly correlated, that is, whether current changes in cash market prices are related to their ow n past changes. Both theo ries discussed in this paper suggest that intra-day, high-frequency cash market price changes w ill be positively correlated, although the reasons for the positive correlation are considerably different. As a result, these data do not help discriminate be tween the two theories. If the data prove inconsis tent with this implication, however, neither theoiy performs w ell in explaining the behavior o f cash market prices. The data in table 3 indicate that minute-tominute changes in the S&P 500 Index are signifi cantly correlated. Furthermore, the correlations are positive at least over the initial lag.33 Table 3 Cash Market (Autocorrelation Coefficients and Box-Pierce Statistics for First Differences of Logs of the Minute-by-Minute S&P 500 Index) Panel A: October 16,1987 (9:30 a.m. - 4:00 p.m. EST) To lag Autocorrelation coefficient Box-Pierce statistic’ 1 2 3 6 12 18 24 .570* .530* .385* .178* -.1 4 8 -.2 0 8 - .072 112.09 209.00 260.14 333.81 352.51 406.39 462.80 Panel B: October 19 ,19 8 7 (9:30 a.m. - 4:00 p.m. EST) To lag 1 2 3 6 12 18 24 Autocorrelation coefficient .342* .397* .406* .264* .231* .124 .054 Box-Pierce statistic’ 37.78 88.69 141.93 237.78 345.66 385.52 396.34 Panel C: October 2 0 ,19 8 7 (9:30 a.m. - 4:00 p.m. EST) To lag 1 2 3 6 12 18 24 Autocorrelation coefficient .535* .561* .590* .521* .311* .324* .250 Box-Pierce statistic’ 84.15 176.68 279.02 548.61 845.55 1026.74 1155.57 ’Critical value for 24 lags is 33.20. A Box-Pierce statistic in excess of this indicates significant autocorrelation. 'Exceeds two standard errors Table 4 presents the results o f the same test for the Decem ber S&P 500 futures contract. The ef ficient markets hypothesis and the absence of specialist traders suggest that these changes are not correlated. Conversely, the cascade theory 32Minute-by-minute price data were also examined for October 15 and 21-23. In each case, the qualitative results were the same as those presented here. “ These correlations are analyzed further below. MAY/JUNE 1988 30 predicts that percentage changes in the futures price will be positively correlated. Table 4 Futures Market (Autocorrelation Coefficients and Box-Pierce Statistics for First Differences of Logs of the Minute-by-Minute Price of the December S&P 500 Futures Contract) Panel A: October 16,1987 (9:30 a.m. - 4:15 p.m. EST) To lag Autocorrelation coefficient Box-Pierce statistic1 1 2 3 6 12 18 24 .090 .035 - .047 - .020 -.0 2 0 .017 - .044 2.89 3.33 4.12 8.25 16.02 19.10 22.29 Panel B: October 19,1987 (9:30 a.m. - 11:00 a.m. EST) To lag Autocorrelation coefficient Box-Pierce statistic' 1 2 3 6 12 18 24 - .309* .140 .005 -.1 3 1 .110 .043 - .020 8.49 10.24 10.24 15.41 18.95 21.69 23.13 Panel C: October 19 ,19 8 7 (11:00 a .m .- 4 : 1 5 p.m. EST) To lag Autocorrelation coefficient Box-Pierce statistic1 1 2 3 6 12 18 24 - .072 .090 - .004 .091 .020 .073 .000 1.63 4.17 4.18 7.21 9.60 14.95 22.37 Panel D: October 2 0 ,19 8 7 (9:30 a.m. - 4:15 p.m. EST) To lag Autocorrelation coefficient Box-Pierce statistic1 1 2 3 6 12 18 24 .029 .022 .042 .046 -.0 7 1 .033 - .035 .26 .41 .95 4.22 9.28 11.81 17.62 ’Critical value for 24 lags is 33.20. A Box-Pierce statistic in excess of this value indicates significant autocorrelation. 'Exceeds two standard errors FEDERAL RESERVE BANK OF ST. LOUIS The data presented in table 4 are consistent w ith the efficient markets hypothesis, not the cas cade theoiy. None o f the test statistics for October 16 (panel A), October 20 (panel D) and for the bulk o f the trading day on October 19 (panel C) indicate significant correlations at conventional signifi cance levels. These price changes are serially un correlated.34Data for the first 90 minutes o f trading on October 19 (panel B) are an exception. During this period, changes in the futures price w ere sig nificantly correlated with the change the previous minute. This correlation, however, is negative, not positive as the cascade theory implies.35Thus, the evidence presented in table 4 is inconsistent with the cascade theoiy, while, on the whole, it con forms to the efficient markets hypothesis. Is the Cash Market Efficient? The table 3 results indicate that intra-dav changes in cash market prices are correlated. Put another wav, past price changes contain some information about future changes for the next few minutes. Is this information useful in the sense that it can be profitably exploited by traders? If so, it w ou ld suggest that cash market traders do not incorporate information efficiently. This, o f course, w ould provide evidence against the efficient mar kets hypothesis. In part, the answer to this question depends on the length o f the time period over which the price changes are related. If the time period is short, shorter than the time required to execute a trans action, the information contained in past price changes cannot be exploited profitably and the cash market is efficient. Table 5 helps answer this question. The table 5 data are estimates o f the length o f the lagged rela tionship between current and past cash market price changes for October 16,19 and 20. The esti mates w ere obtained by regressing the contem po raneous minute-to-minute price change on the 15 previous minute-to-minute price changes. Ini tially, this specification was identified as the unre stricted model. To determine w hether the esti- "T he same result was obtained when data for October 15 and 21-23 were examined. 35This puzzling result for the first 90 minutes of trading on Octo ber 19 may be due to the fact that many stocks had not yet opened for trading on the NYSE and the rumors at that time that the SEC would call a trading halt. See Miller, Hawke, Malkiel and Scholes (1987), wire report summary. 31 Table 5 Estimated Lag Lengths in the Cash Market_________________ Panel A: October 16,1987 (9:30 a.m. - 4:00 p.m. EST) ALNC, = -.0 0 3 + .401 ALNC,_, + .343ALNC,_2 (1.19) (7.80)* (6.51)* R2 = .41 DW = 2.00 Panel B: October 19,1987 (9:30 a.m. - 4:00 p.m. EST) ALNC, = -.0 1 6 + .123ALNC,_, + .228ALNC,_2 + .242ALNC,_3 + .112ALNC,_4 (2.46)* (2.20)* (4.14)* (4.39)* (1.99)* R2 = .26 DW = 2.01 Panel C: October 20,19 8 7 (9:30 a.m. - 4:00 p.m. EST) ALNC, = -.0 0 1 + .107ALNC,., + ,173ALNC,_2 + ,258ALNC,_3 + .174ALNC,_, + .153ALNC,_5 (.132) (1.82) (2.98)* (4.52)* (2.99)* (2.60)* R2 = .48 DW = 2.02 ‘ Statistically significant at the 5 percent level mated coefficients are sensitive to the lag length and to identify statistically redundant lags, the lag structure was successively shortened by one lag. At each stage, the t-statistic for the coefficient o f the most distant lag was examined. If the test indi cated the coefficient was statistically insignificant, that lag was dropped and the equation was reesti mated with one less lag. This process was re peated until the test rejected the hypothesis that the estimated coefficient o f the most distant re maining lag was zero.311 The estimates shown in table 5 indicate that the lags ranged from about two minutes on October 16 to five minutes on October 20.37 It requires about two minutes to execute a trade on the NYSE under normal trading conditions. During the panic, exe cution times ranged from about 10 to 75 minutes at times.38 In view of this, the lags estimated in table 5 do not appear to be long enough to reject 36See Anderson (1971), pp. 223 and 275-76. It is possible that this test may reject some lags that are, in fact, significant if taken as a group. To control for this, F-tests were run with the lag length in the unrestricted model set at 15. The number of lags in the restricted model was set at 12 to determine if the three omitted lags were significant. The lags in the restricted model was then reduced to nine and the test repeated, etc. the efficient markets hypothesis: also, since they varied over the period, it is doubtful that past price changes contained information that could be exploited by traders. Did Stock Price Changes Reinforce Each Other Across Markets? The central feature o f the cascade theory can be tested by determining w hether past price changes in the futures market help explain current price changes in the cash market and conversely. This is done by regressing the change in cash prices on past changes in cash prices: then, past changes in futures prices are added to the estimated regres sion equation to see if they improve the equation's explanatory power. An F-test is conducted to de termine w hether the addition o f the futures mar ket data significantly increases the cash price equation’s coefficient o f determination (R2). The problem that the probability of rejecting the null hypothesis (the estimated coefficient is zero) when it is true rises as the lag length is reduced. Consequently, the true lag lengths may be shorter than those estimated in table 5. See Batten and Thorn ton (1983), pp. 22-23, and Anderson (1971), pp. 30-43. “ U.S. Government Accounting Office (1988), p. 73. 37The lag had declined to about three minutes by October 23. The method used in this paper to estimate lag length has the MAY/JUNE 1988 32 Table 6 Granger Tests Day Lags F-statistic Futures - * Cash F-statistic Cash - » Futures October 16 October 19 October 20 2 4 5 17.61* 4.46* 2.59* .76 1.57 .67 ‘ Statistically significant at the 5 percent level test is then reversed, with the change in futures prices as the dependent variable. The results o f this test are presented in table 6 for each o f the trading days examined in this pa per. The lag length em ployed on each day is the one identified by the table 5 test.39The results for cash market prices show that the addition o f past changes in futures prices improve the regression estimates; this suggests that price changes in the futures market preceded those in the cash market. This result is consistent with both the cascade theory and the efficient markets hypothesis. Fur thermore, it is not unique to the panic; it has been observed for intra-day price data during other periods as well.411 Other table 6 results, however, are inconsistent with the cascade theory. The inclusion o f past changes in cash prices in the regressions that estimate the change in futures prices does not sig nificantly improve the estimates. This rejects the notion that past changes in cash prices help ex plain changes in futures prices. This finding is inconsistent with the central feature o f the cas cade theory, w hich suggests the panic was caused by declines in cash and futures prices that became larger as they tumbled over each other on the way down. CONCLUSION This paper has examined the cascade theory, which has been advanced as an explanation o f the October 1987 stock market panic. The theory relies on the notion that stock traders behave “mechani cally,” are “ insensitive to price,” and execute 39Hsiao (1981) uses a similar method. These lag lengths apply to the cash market. Analysis of the futures market suggests that the appropriate lag for this market is zero. wSee Kawaller, Koch and Koch (1987). FEDERAL RESERVE BANK OF ST. LOUIS transactions in markets without regard to transac tion costs. These assertions are inconsistent with the behavior o f wealth-m axim izing individuals. Not only are the theoretical underpinnings o f the cascade theory weak, the data do not support the theory. Instead, the observed relationships that do exist between the markets are not unique to the crash and can be explained by a theory that relies on wealth m aximizing behavior. Almost 60 years later, the cause o f the “ Great Crash” in October 1929 is still being debated. Those with even longer m emories know that there is little agreement about what caused the stock market panic in 1907. Although financial reforms follow ed each o f these panics, history indicates that the reforms have done little to reduce the frequency or severity o f panics. Without a reliable theoretical guide to the mechanics o f a panic, any reform is no more than a “ shot in the dark.” The evidence presented in this paper suggests that the reforms advanced by proponents o f the cascade theory are unlikely to alter this historical pattern. REFERENCES Anderson, Theodore W. The Statistical Analysis of Time Series (John Wiley and Sons, Inc., 1971). Atchison, Michael D., Kirt C. Butler, and Richard R. Simonds. “ Nonsynchronous Security Trading and Market Index Auto correlation,” Journal of Finance (March 1987), pp. 111-18. Batten, Dallas S., and Daniel L. Thornton. “Polynomial Distrib uted Lags and the Estimation of the St. Louis Equation,” this Review (April 1983), pp. 13-25. Brealey, R. A. An Introduction to Risk and Return from Common Stocks (The MIT Press, 1983). Brealey, Richard, and Stewart Meyers. Finance (McGraw-Hill, 1984). Principles of Corporate Burns, Joseph M. A Treatise on Markets: Spot, Futures, and Options (American Enterprise Institute, 1979), pp. 31-55. Cornell, Bradford, and Kenneth R. French. “ The Pricing of Stock Index Futures,” Journal of Futures Markets (Spring 1983), pp. 1-14. Fama, Eugene F. “ Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal o f Finance, Papers and Proceedings (May 1970), pp. 383-417. Figlewski, Stephen. “ Hedging Performance and Basis Risk in Stock Index Futures,” Journal of Finance (July 1984), pp. 657-69. Grossman, Sanford J., and Merton H. Miller. “ Liquidity and Market Structure,” Princeton University Financial Research Center Memorandum No. 88 (March 1988). 33 Harris, Lawrence. “ Nonsynchronous Trading and the S&P 500 Stock-Futures Basis in October 1987” (University of Southern California Working Paper, processed January 11,1988). Perry, Philip R. “ Portfolio Serial Correlation and Nonsynchro nous Trading,” Journal of Financial and Quantitative Analysis (December 1985), pp. 517-23. Hsiao, Cheng. “Autoregressive Modelling and Money-lncome Causality Detection,” Journal of Monetary Economics (Janu ary 1981), pp. 85-106. Report of the Presidential Task Force on Market Mechanisms (U.S. Government Printing Office, January 1988). Kawaller, Ira G., Paul D. Koch, and Timothy W. Koch. "The Temporal Price Relationship Between S&P 500 Futures and the S&P 500 Index,” Journal of Finance (December 1987), pp. 1309-29. Leroy, Stephen F. “ Expectations Models of Asset Prices: A Survey of Theory,” Journal of Finance (March 1982), pp. 185217. Malkiel, Burton G. “ The Brady Commission Report," Princeton University Financial Research Center Memorandum No. 92 (May 1988). _________A Random Walk Down Wall Street (W. W. Norton and Company, 1981). Miller, Merton H., John D. Hawke, Jr., Burton Malkiel, and Myron Scholes. Preliminary Report o f the Committee of Inquiry Appointed by the Chicago Mercantile Exchange to Examine the Events Surrounding October 19, 1987 (December 22, 1987). Modest, David M., and Mahadevan Sundaresan. “ The Rela tionship Between Spot and Futures Prices in Stock Index Futures Markets: Some Preliminary Evidence,” Journal of Futures Markets (Spring 1983), pp. 15-41. Santoni, G. J. "Has Programmed Trading Made Stock Prices More Volatile?” this Review (May 1987), pp. 18-29. Schwarz, Edward W., Joanne M. Hill, and Thomas Schneeweis. Financial Futures (Dow Jones-lrwin, 1986). Shultz, Birl E. The Securities Market and How It Works (Harper and Brothers, 1946). Stoll, Hans R. The Stock Exchange Specialist System: An Economic Analysis. Monograph Series in Finance and Eco nomics (Salomon Brothers Center for the Study of Financial Institutions, New York University, 1985). The New York Stock Exchange Market (New York Stock Ex change, June 1979). U.S. Commodity Futures Trading Commission. Final Report on Stock Index Futures and Cash Market Activity During October 1987 (U.S. Commodity Futures Trading Commission, January 1988). U.S. General Accounting Office. Financial Markets: Preliminary Observations on the October 1987 Crash (U.S. General Ac counting Office, January 1988). Working, Holbrook. Selected Writings of Holbrook Working (Chicago Board of Trade, 1977). MAY/JUNE 1988 34 Cletus C. Coughlin Cletus C. Coughlin is a senior economist at the Federal Reserve Bank of St. Louis. Thomas A. Pollmann provided research assistance. The Competitive Nature of State Spending on the Promotion of Manufacturing Exports T J L HE expansion o f jobs and incomes is a lead ing priority o f state governments. An increasingly popular view is that econom ic growth can be stim ulated by increasing the amount o f manufactured goods that are sold by firms in a state to con sumers and producer's in foreign countries. To accomplish this, many states have devoted more resources to the prom otion o f manufactured ex ports abroad. Very little, however, is known about the effects o f this econom ic developm ent effort. Research by Coughlin and Cartwright (1987) found a positive relationship between a state’s exports and its promotional expenditures. A re lated issue, the focus o f this study, is whether a state’s exports are affected by the prom otional expenditures o f other states.1Are the effects o f a state’s prom otional efforts being counteracted by the expenditures o f other states? On the other hand, are the prom otional expenditures o f other 1A similar issue arises as states compete for foreign direct investment. This issue is illustrated in an anecdote from Prestowitz (1988). The author, then a Department of Commerce specialist on U.S.-Japanese trade, was asked to brief a group of Kentucky congressmen on Japan. The briefing occurred shortly after Toyota had announced its plans to build an as sembly plant in Kentucky, and the congressmen were hoping to attract Japanese parts suppliers with various incentives. Prestowitz asked whether they realized that for every Japa nese plant that opened in Kentucky, an American one in Michi gan was likely to close. “ We’re not the congressmen from Michigan,” was their reply. While one might question Presto- FEDERAL RESERVE BANK OF ST. LOUIS states increasing export dem and overall, thereby increasing a state’s exports? This paper begins with an overview o f state ex port prom otion expenditures and programs. The subsequent analysis consists o f developing and estimating a m odel o f state-manufactured exports for 1980 that includes standard international trade variables as w ell as export prom otion expendi tures.2A summary o f the primary results com pletes the study. STATE GOVERNMENT EXPORT PROMOTION Manufactured exports are an important source o f jobs for many state economies. In 1984, the most recent year o f estimates in the Annual Survey o f Manufactures, more than 500,000 jobs in Califor- witz’s assertion about the effects on Michigan of attracting a parts supplier to Kentucky, the motivation of the Kentucky congressmen is clear. Their goal is to stimulate economic activity in Kentucky with, at most, minimal regard for its conse quences elsewhere. 2While some of the data in this study are available for more recent years than 1980, the more recent data are not as com plete. For example, more states supplied figures for export promotion in 1980 than in recent years. A second reason for using 1980 is a desire to compare the current results using the export equation with previous research. 35 nia, 5.5 percent o f private-sector employment, w ere due to manufactured exports. Though Cali fornia led the nation in the number o f jobs in volved, numerous states w ere relatively more d e pendent on manufactured exports for jobs. The percentage o f private-sector em ploym ent due to manufactured exports exceeded 7 percent for Connecticut and 6 percent for Indiana, Massachu setts, Michigan, Ohio and Washington.3 Not surprisingly, states have tried to increase their manufactured exports.4 State governments provide resources for trade missions and catalog shows. Many maintain overseas offices to provide basic information to potential foreign customers about goods and services available from state firms. The information available through some state governments (for example, N ew York) has been expanded by the developm ent o f com puter ized information systems concerning trade oppor tunities. Some state governments (for example, Illinois and Arkansas) are also becom ing increas ingly involved in providing financial assistance to exporters. Finally, a number o f states are either developing their own export trading companies (for example, N ew York/ N ew Jersey and Virginia) or assisting private firms using export trading companies. Due to the alleged cost disadvantages faced by small firms, these state services tend to be geared to small rather than large businesses. Before 1980, evidence on state export prom o tional expenditures is scarce. Albaum (1968) re ported sketchy budget information on 36 states (16 o f which had no specific budget) for 1967. The most com plete budgetaiy data for all states was com piled by Berry and Mussen (1980), w ho re ported state export prom otion expenditures of approximately $18.9 m illion during 1980. These expenditures reflected an average state expendi ture o f $377,111. Due to the complexity o f allocating state budget expenditures to export promotion, these figures are likely to represent a low er bound. For example, although the figures include the salaries o f per sonnel explicitly tied to export promotion, the salaries o f state government officials such as gover nors w ho spend much time and effort prom oting exports are not included in these figures. One might also include the salaries o f personnel at state universities involved in export prom otion as w ell as the costs associated with providing finan cial assistance to exporters. Given the small size of the reported state expenditures, these omissions could be relatively important. Table 1 presents the state export prom otion data used in this analysis. Export promotion, w hich is a very small share o f a state’s total ex penditures, ranged from zero for Utah to more than $1.8 million for Ohio. Illinois, Virginia and Maryland joined Ohio in spending more than $1 million to prom ote exports. To take into account the differences among states in terms o f their populations, the export prom otion figures in table 1 are also presented on a per capita basis. The median expenditure is slightly in excess o f 5 cents. On a per capita basis, Alaska is far and away the leading state. Alaska’s expenditure o f 93 cents per resident is more than 2 1/2 times the per capita expenditure o f Montana, the second-leading state. Although neither Alaska (13) nor Montana (18) w ere among the leading states on a total expenditures basis, those that were, w ere also among the leading states on a per capita basis. Ohio, Illinois, Virginia and Maryland w ere ranked 6, 12, 4 and 3, respectively, on a per capita basis. The limited evidence, which mixes expenditures to attract foreign direct investment with export promotion, suggests that export prom otion ex penditures are increasing rapidly. Berry and Mus sen (1980) reported that average state expendi tures for the prom otion o f international business increased by a factor of four between 1976 and 1980 for a sample o f 25 states that supplied ade quate data. Figures from the National Association o f State Development Agencies (1986) indicate that such expenditures increased by two-thirds be tween 1984 and 1986. A MODEL OF STATE EXPORTS In this section, a m odel o f state exports is pre sented and estimated. The m odel incorporates the standard variables used in international trade studies along with export prom otion variables. The empirical results shed some light on the effect o f a state's promotional expenditures on its ex- 3Between 1980 and 1984, the relative importance of manufac tured exports for jobs declined; however, recent increases in U.S. exports suggest that this decline has been reversed. 4Barovick (1984) and Ouida (1984) can be consulted for details about the proliferation of export activities. MAY/JUNE 1988 36 Table 1 1980 State Export Promotion Expenditures Total State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York N o rth C a ro lin a North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Export Promotion $ 273,750 372,500 107,200 175,000 234,224 1 2 0 ,1 2 0 75,000 30,000 458,280 310,050 107,250 47,500 1,527,060 752,042 240,273 70,000 576,810 25,000 90,740 1,287,319 45,000 682,000 188,000 150,000 729,000 277,632 195,711 5,000 2 0 ,0 0 0 315,000 70,000 845,000 503,500 99,960 1,832,800 247,604 361,767 263,285 11,250 1 0 0 ,0 0 0 139,200 193,644 739,794 0 6,825 1,487,187 333,000 35,773 82,500 15,000 Per Capita Rank 19 13 32 27 23 30 37 43 12 17 31 40 2 7 22 38/39 10 44 35 4 41 9 26 28 8 18 24 49 45 16 38/39 5 11 34 1 21 14 20 47 33 29 25 6 50 48 3 15 42 36 46 Export Promotion $.0709 .9306 .0395 .0767 .0 1 0 0 .0417 .0242 .0504 .0478 .0575 .1 1 1 2 .0048 .1349 .1379 .0826 .0297 .1584 .0060 .0807 .3070 .0079 .0738 .0462 .0599 .1487 .3542 .1251 .0063 .0218 .0429 .0542 .0484 .0861 .1533 .1704 .0826 .1382 .0223 .0 1 2 0 .0326 .2024 .0427 .0523 .0 0 0 0 .0133 .2795 .0810 .0186 .0176 .0320 Rank 22 1 34 20 45 33 38 27 29 24 14 49 12 11 16 37 7 48 19 3 46 21 30 23 9 2 13 47 40 31 25 28 15 8 6 17 10 39 44 35 5 32 26 50 43 4 18 41 42 36 SOURCE: Berry and Mussen (1980) in Export Development and Foreign Investment: The Role of the States and Its Linkage to Federal Action. FEDERAL RESERVE BANK OF ST. LOUIS 37 ports as well as the effect o f export prom otion by other states on a selected state. The Heckscher-Ohlin approach to international trade, developed by two Swedish economists, Eli Heckscher and Bertil Ohlin, highlights the im por tance o f a country’s productive resources in deter mining its pattern o f international trade .5 Goods are traded internationally because o f differences in production costs. These differences depend on the proportions in which factors o f production exist in different countries (that is, the relative factor endowments) and how the factors are used in producing different goods (that is, the relative factor intensities). An example can be used to illustrate the Heckscher-Ohlin theory. Assume two countries, the United States and Mexico, two factors o f pro duction, capital and labor, and two goods, air planes and cloth. In a two-factor world, a country is capital-abundant (labor-abundant) if it is en dow ed with a higher (lower) ratio o f capital to labor than the other country. Assume the United States is capital-abundant and Mexico is laborabundant. In a two-good world, a product is capital-intensive if its production requires a rela tively higher ratio o f capital to labor than the other good. Assume airplanes are capital-intensive and cloth is labor-intensive. The Heckscher-Ohlin the ory predicts that a country w ill export the good that uses its abundant factor intensively and im port the other good. The reason for this trade pat tern hinges on the relative production costs. A country should be able to produce the good that uses relatively larger amounts o f its abundant resource at a low er cost. Thus, the United States should export airplanes to M exico and import cloth from Mexico. The Heckscher-Ohlin approach allows for pre dictions about trade patterns based on knowledge o f countries’ factor supplies. Since the services o f factors o f production are em bodied in exports and imports, international trade may be view ed as the Additional details on the Heckscher-Ohlin theory can be found in Krugman and Obstfeld (1988) or any other introductory international trade text. 6Unless noted otherwise, the data were taken from various issues of the Annual Survey of Manufactures. 'The bulk of cross-industry studies have found physical capital to be a scarce factor (Baldwin, 1971; Branson and Junz, 1971; Sailors, Thomas and Luciani, 1977; Stern and Maskus, 1981); however, the deficiencies of these studies have been high lighted by Learner and Bowen’s (1981) demonstration that inferences about factor abundance were not strictly justified and by Aw’s (1983) identification of the highly restrictive condi tions that are necessary to justify the inferences. Research by exchange o f the seivices o f the country’s abundant factor for the services o f the country's scarce fac tor. In the example, the United States exports the services o f its abundant factor, capital, and im ports the services o f its scarce factor, labor. A comm on summary statement is that capital is a source o f comparative advantage for the United States, w hile labor is a source o f comparative disadvantage. The preceding idea can be applied to regions within a country. In Coughlin and Fabel (forth coming), a Heckscher-Ohlin approach was devel oped to examine the export perform ance o f indi vidual states. The international exports o f a state (EX) are defined as the value o f manufactured di rect exports for 1980.6A state’s endowm ent o f manufacturing resources determines its interna tional competitiveness. Relying upon a standard Heckscher-Ohlin framework, a three-factor model w ith physical capital (K), human capital (H) and labor (L) is used. Thus, a state’s exports are related to its relative endow m ent o f these manufacturing resources. A state with larger amounts that are sources o f U.S. comparative advantage (disadvan tage) w ill have more (less) exports. W hether physical capital is a source o f U.S. com parative advantage has been a controversial topic since Leontief’s (1954) surprising finding that the U.S. exported labor-intensive rather than capitalintensive goods. This continuing controversy is irrelevant for the current research .7 To reflect the controversy, the expected impact o f physical capi tal, measured by the gross book value o f a state’s depreciable manufacturing assets, is uncertain .8 Stern and Maskus (1981), as w ell as many others, have concluded that human capital is a source of U.S. comparative advantage. Thus, increases in a state’s endowm ent o f human capital, ceteris pari bus, are expected to be related positively to state export performance. The calculation o f a state’s endowm ent o f human capital, following Hufbauer (1970), attributes the difference between a state’s Bowen (1983) and by Coughlin and Fabel (forthcoming), which were designed to avoid the criticisms of cross-industry studies, suggests that physical capital is a source of U.S. comparative advantage. 8The use of the gross book value of depreciable assets as a measure of physical capital is not ideal. As Browne et al. (1980) have indicated, this measure is derived from accounting practices rather than economics. Consequently, it might not be a good measure of productive capacity. This problem is parti ally mitigated by the cross-section nature of the current analy sis because relative productive capacity rather than absolute capacity is of primary importance. MAY/JUNE 1988 38 average annual pay in manufacturing and the median pay o f persons with zero to eight years of education as a return to human capital." This re turn is m ultiplied by the number o f manufacturing em ployees to generate a measure o f total returns to human capital in manufacturing. A state’s en dowm ent o f human capital is the capitalized (at 1 0 percent) value o f these total returns. A standard research finding reconfirm ed re cently by Stern and Maskus (1981) is that labor, measured as the number o f manufacturing em ployees in a state, is a relatively scarce factor in the United States. If this factor is a source o f U.S. comparative disadvantage, then increases in a state’s endowm ent o f labor, holding physical and human capital constant, should be related nega tively to the state’s exports. In addition to a state’s endowm ent o f physical capital, human capital and labor, export prom o tion expenditures are expected to affect manufac turing exports from a state positively. The export prom otion figures cited in table 1 encompass ex penditures for the prom otion o f manufactured and agricultural goods. Since this study focuses on manufactured exports, the use o f total export prom otion expenditures might introduce some error into the estimations. Unfortunately, the mag nitude o f agricultural export prom otion at the state level is unknown. Beriy and Mussen (1980) reported that the De partment o f Agriculture in 26 states received funds for export prom otion. Since agricultural exports could be prom oted by other administrative units, agricultural export prom otion is not necessarily restricted to these states. To approximate total expenditures for manufacturing export promotion, total export prom otion expenditures were multi 9This calculation of human capital has been used frequently in international trade studies. It should be noted that the differ ence between average annual pay in manufacturing and the pay of persons with zero to eight years of education might not be entirely a return to human capital. For example, the market power of unions might increase wages in manufacturing; how ever, the inclusion of a state unionization variable did not affect the impact of human capital and was not statistically significant. ,0Two other adjustments to total export promotion expenditures were examined; these adjustments did not alter the empirical results. Total export promotion expenditures were multiplied by: ( 1 ) the percentage of a state’s population that did not live on farms; and (2 ) the ratio of manufacturing employees to the sum of manufacturing and total agricultural employees. Total export promotion expenditures were found in Berry and Mus sen (1980). The adjustment factors to develop estimates of manufacturing export promotion expenditures were taken from the Statistical Abstract of the United States (farm population figures) and the Census of Agriculture (agricultural employment figures). FEDERAL RESERVE BANK OF ST. LOUIS plied by the ratio o f manufacturing em ployees to the sum o f manufacturing and full-time agricul tural employees. This new measure is designated as PROM.'" Estimation Results Assuming a linear function, the preceding m odel can be represented as (1) EX = d„ + d,K + d,H + d.L + d4PROM + e, where the d's are the parameters to be estimated and e is the disturbance term. The m odel was estimated using generalized least squares because the residuals using ordinary least squares indi cated heteroscedasticity." The results, w hich w ere also reported in Coughlin and Cartwright (1987), are listed under variant #1 in table 2. 12 The results indicate that both physical and human capital are positive, statistically significant determinants of state manufacturing exports. The remaining endowm ent variable, labor, is not statistically significant. For present purposes, the positive impact of export prom otion expenditures is the key result; however, the statistical significance o f this variable hinges on whether a 5 percent or 10 percent significance level is chosen .13 The point estimate indicates that manufacturing exports, on average w ill increase by .432 for a one-unit increase in manufacturing export prom otion expenditures. Since export prom otion expenditures are mea sured in thousands o f dollars and exports are measured in millions o f dollars, an increase in export prom otion expenditures o f $ 1 0 0 0 is esti mated to increase exports by $432,000. This estimate seems much too large and, in fact, there are reasons to think the estimate is biased "Following Glejser (1969), the weights for the observations are determined by a two-step procedure. First, the residuals from an ordinary least squares regression of equation 1 are gener ated. Second, the inverses of the weights are generated by a linear function using total state employment as the determinant of the absolute value of the residuals from the first step. See Fom byet al. (1984), pp. 180-82, for details. 12Since Washington was uncharacteristic in the sense that the actual value of exports was exceptionally large relative to its predicted value, it was dropped from the estimation. 13lt should be noted that export promotion expenditures likely have important investment aspects. The results of current export promotion expenditures will not necessarily occur imme diately. Consequently, export promotion expenditures in 1980 will affect exports in future periods as well as the current pe riod, and exports in 1980 were likely affected by previous export promotion expenditures. Because of absence of suffic ient time-series data on export promotion, this lag structure could not be estimated. 39 Table 2 Export Promotion Variants of 1980 State Export Functions Dependent Variable: EX' GLS Parameter Estimates (t-ratios)' ' In n o n o n n o n t Variables Variant #1 Variant # 2 Variant # 3 Variant # 4 Variant # 5 Intercept -8 .5 0 3 (-0 .1 5 ) 9.259* (3.81) 39.173(2.19) 7.730 (0.60) 0.432 (1.65) -4.281 (-0 .0 7 ) 12.677* (3.88) 42.654(2.39) 5.922 (0.41) 0.354 (1.36) 23.343 (0.32) 11.994* (3.78) 52.735(2.13) 3.895 (0 .0 2 ) 0.436(1.72) -5 4 .7 2 5 (-0 .9 8 ) 9.330* (3.99) 37.632(2.18) 12.633 (0.89) - 0 .0 0 1 - (0 .0 0 ) 14.388* (2.36) -5 6 .8 3 7 (-1 .0 4 ) 9.476* (4.12) 37.054(2.18) 13.408 (0.96) -0 .1 1 9 (-0 .3 6 ) K' H' L' PROM' RP-Census' RP-Cluster' TP-Census' 24.651* (2 .6 6 ) -0 .6 4 6 (-0 .6 9 ) TP-Cluster' -1 .2 9 7 (-0 .8 3 ) * statistically significant at the .05 level (two-sided) a statistically significant at the .05 level (one-sided) ’ The variables are defined in the text and are measured as follows: EX - millions of dollars; K and H hundred millions of dollars; L - ten thousands of employees; PROM - thousands of dollars; TP-Census and TP-Cluster - numerator is in millions of dollars and denominator is the number of states; and RP-Census and RP-Cluster - numerator and denominator are in cents per capita. upward. First, as m entioned previously, the re ported state budget expenditures on export pro motion are likely a low er bound. To the extent these figures are understated, the coefficient esti mate will be overstated. For example, if the export prom otion expenditures are understated by 50 percent, the coefficient estimate should be halved. Second, the m odel does not control for either pri vate or other governmental export prom otion ex penditures. To the extent that these other export prom otion expenditures are correlated with state expenditures, the coefficient estimate is biased upward. Finally, due to the lack o f data, there is no lag structure in the m odel. Consequently, w hile export prom otion expenditures and exports are positively related, the point estimate is likely unreliable. Cross-State Effects Attention can now be focused upon w hether there are externalities associated with export pro motion. If these externalities exist, they could be positive or negative. Export prom otion expendi tures by other states might increase export de mand generally and produce additional exports from the state in question. On the other hand, perhaps a substitution effect exists; increases in export prom otion expenditures by one state will reduce the exports o f other states . 14 In this case, a state may be forced into prom otional efforts as an act o f self-defense. Ascertaining the existence o f externalities is neither easy nor straightforward. The preceding 14Even though a state’s exports may be affected adversely by the export promotion expenditures of competitive states, the state may not necessarily incur short-run employment losses because the export demand reduction could be offset by in creased domestic demand. MAY/JUNE 1988 40 paragraph focuses on the notion o f competitive export goods; however, the dependent variable is total state exports. Given this aggregation, the idea o f competitive exports must be transformed into competitive states. For example, it is difficult to envision h ow export prom otion by South Carolina w ould affect Alaska; it is not difficult, however, to envision h ow export prom otion by South Carolina w ould affect North Carolina. The notion o f com petitive states was developed in two ways. First, states w ere view ed as competitive if they belong to the same census region . 15 Since geography is a key feature o f this categorization, an attempt to clas sify states on the basis o f certain econom ic charac teristics was made. The results reported in variant # 1 in table 2 reflect the fact that states have differ ent sources o f comparative advantage. Competitive states should be those states w hose sources of comparative advantage (that is, resource en dow ments) are similar. A cluster analysis was per form ed that grouped states into seven clusters based on their ratios o f physical capital to labor and human capital to labor . 111 After the states w ere grouped, the next step was to construct reasonable variables to test for exter nalities. There are numerous reasonable candi dates. The difficulty arises because o f the necessity o f scaling the prom otional expenditures o f com petitive states. For example, assume two groups o f states, one containing five states and the other three states. The goal o f the regression analysis is to indicate the impact upon a mem ber of a group when prom otional expenditures by another m em 15The nine census regions are as follows: New England — Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island and Vermont; Middle Atlantic — New Jersey, New York and Pennsylvania; East North Central — Illinois, Indiana, Michigan, Ohio and Wisconsin; West North Central — Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota and South Dakota; South Atlantic — Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia and West Virginia; East South Central — Alabama, Kentucky Mississippi and Tennessee; West South Central — Arkansas, Louisiana, Oklahoma and Texas; Mountain — Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah and Wyoming; and Pacific — Alaska, California, Hawaii, Oregon and Washington. 16The clusters were generated using the CLUSTER procedure in SAS. The purpose of cluster analysis is to group objects such that those in a given cluster tend to be similar to each other in some sense while those in different clusters tend to be dissimi lar. In the present case, states with similar ratios of physical capital to labor and human capital to labor were grouped to gether. The procedure, described on pages 423 and 424 in the SAS User's Guide: Statistics (1982), begins with each observa tion (i.e., state) as a cluster by itself. Next, the two closest clusters are combined to form a new cluster. This merging continues until only one cluster remains. There are different clustering algorithms with the distinguishing feature being how FEDERAL RESERVE BANK OF ST. LOUIS ber (or members) increase. It seems reasonable that the larger the group the smaller the impact on any individual m em ber o f increased expendi tures by another member. The effect is lessened because it is spread over more states. A straightfor ward approach is to divide the total prom otional expenditures o f competitors by the number o f competitors. These variables are designated as TPCensus and TP-Cluster. The existence o f a positive impact o f a region’s export prom otional expendi tures w ill be revealed by a positive sign for the TP variables, w hile a negative impact w ill be revealed by a negative sign. Another approach to test for externalities is to use a state’s spending on export prom otion rela tive to the spending o f its competitors. Scaling the promotional expenditures o f a state relative to its competitors is accom plished by dividing both expenditures by their respective populations .17 These variables are designated as RP-Census and RP-Cluster. If a region's per capita export prom o tion expenditures increase, ceteris paribus, then the ratio o f state to region per capita export pro m otion expenditures w ill decline. Consequently, the existence o f a positive impact o f a regions’s export prom otion expenditures w ill be revealed by a negative sign for the RP variables, w hile a nega tive impact w ill be revealed by a positive sign. Variants # 2 and #3 in table 2 highlight the effect o f adding TP-Census and TP-Cluster to the basic model, w hile variants # 4 and #5 highlight the effect o f adding RP-Census and RP-Cluster. The the difference between two clusters is measured. In Ward’s method, which was the specific algorithm used, the distance between two clusters is the sum of squares between the two clusters over all clusters. At each step, the within-cluster sum of squares is minimized over all the possibilities obtainable by merging two clusters from the previous step. This method was used to reduce the original 49 clusters until there were the following seven groups: (1) California, New York, Connecticut and New Jersey; (2) Arizona, Missouri, Oklahoma, Utah, Wis consin, Massachusetts, Minnesota, Colorado, Oregon, Penn sylvania, Maryland and Nevada; (3) Indiana, Delaware, Ohio, Illinois, Washington and Michigan; (4) Alabama, Idaho, North Dakota, Hawaii, Kentucky, Iowa and New Mexico; (5) Florida, Tennessee, Georgia, Kansas, Virginia, New Hampshire and Rhode Island; (6 ) Arkansas, Maine, South Carolina, Missis sippi, Nebraska, North Carolina, Vermont and South Dakota; and (7) Texas, West Virginia, Wyoming, Alaska, Louisiana and Montana. ,7The ratio of state to region per capita export promotion expend itures was selected rather than the ratio of region to state because of Utah’s zero value for export promotion. This com plicates the interpretation of the variable, but was unavoidable. 41 only unqualified conclusion is that there is no substantial impact on the statistical results for the factor endowm ent variables. The remaining con clusions must be qualified. The results, w hile similar for both groupings of competitive states, are sensitive to which m ethod is used to control for externalities. The results for each variant indicate that increases in prom o tional expenditures by competitors, ceteris p a ri bus, are associated w ith a reduction in a state’s exports; however, the results are not strong. Total prom otional expenditures divided by the number o f competitors in variants #2 and #3 is not a sta tistically significant determinant o f state exports, w hile state per capita prom otional expenditures divided by competitors' per capita promotional expenditures in variants # 4 and #5 is a statisti cally significant determinant. In addition, the im pact o f adding the variable to control for external ities has different effects on the export prom otion variable (PROM). The t-ratios are roughly similar in variants #2 and #3 compared to variant #1. In fact, in variant #3 PROM is statistically significant. On the other hand, in variants #4 and #5 the tratio for PROM is virtually zero. SUMMARY The results, which should be viewed as tentative because o f the acknowledged data limitation, highlight the effects o f export prom otion expendi tures. Using two groupings o f competitive states, statistical evidence was found that exports from a state are affected adversely by the promotional expenditures o f other states; however, another reasonable variable designed to capture this effect was statistically insignificant. Thus, definitive con clusions about the effects o f export prom otion expenditures are not possible. Nonetheless, one suggestion does emerge. In light o f the large in creases in expenditures and the increasing use o f financial incentives to prom ote state exports, the competitive and efficiency aspects o f export pro m otion expenditures and programs deserve addi tional scrutiny.'" At this point, the lack o f timeseries data is the major obstacle. Aw, Bee-Yan. “The Interpretation of Cross-Section Regression Tests of the Heckscher-Ohlin Theorem With Many Goods and Factors," Journal of International Economics (February 1983), pp. 163-67. Baldwin, Robert E. "Determinants of the Commodity Structure of U.S. Trade,” American Economic Review (March 1971), pp. 126-46. Barovick, Richard. “ State Governments Broaden Range of Export Expansion Activities,” Business America (October 1, 1984), pp. 16-18. Berry, Willard M., and William A. Mussen. “ Part I — A Report,” in Export Development and Foreign Investment: The Role of the States and Its Linkage to Federal Action (Committee on International Trade and Foreign Relations, National Gover nors' Association, 1980). Bowen, Harry P. “ Changes in the International Distribution of Resources and Their Impact on U.S. Comparative Advan tage,” Review of Economics and Statistics (August 1983), pp. 402-14. Boyd, John H. “ Eximbank Lending: A Federal Program That Costs Too Much,” Federal Resen/e Bank of Minneapolis Quarterly Review (Winter 1982), pp. 1-17. Branson, William H., and Helen B. Junz. “Trends in U.S. Trade and Comparative Advantage,” Brookings Papers on Economic Activity (1971:2), pp. 285-345. Browne, Lynn E., P. Mieszkowski, and R.F. Syron. “ Regional Investment Patterns,” New England Economic Review (July/ August 1980), pp. 5-23. Coughlin, Cletus C., and Phillip A. Cartwright. “ An Examination of State Foreign Export Promotion and Manufacturing Ex ports,” Journal of Regional Science (August 1987), pp. 4 3 949. Coughlin, Cletus C., and Oliver Fabel. “ State Factor Endow ments and Exports: An Alternative to Cross-Industry Studies," Review of Economics and Statistics, forthcoming. Fomby, Thomas B., R. Carter Hill, and Stanley R. Johnson. Advanced Econometric Methods (Springer-Verlag, 1984). Glejser, H. “A New Test for Heteroscedasticity,” Journal of the American Statistical Association (1969), pp. 316-23. Hufbauer, Gary C. "The Impact of National Characteristics and Technology on the Commodity Composition of Trade in Manufactured Goods," in Raymond Vernon, ed., The Technol ogy Factor in International Trade (National Bureau of Eco nomic Research, 1970), pp. 145-231. Krugman, Paul R., and Maurice Obstfeld. International Eco nomics: Theory and Policy (Scott, Foresman and Company, 1988). Learner, Edward E., and Harry P. Bowen. “ Cross-Section Tests of the Heckscher-Ohlin Theorem: Comment," American Economic Review (December 1981), pp. 1040-43. Leontief, Wassily W. “ Domestic Production and Foreign Trade; the American Capital Position Re-examined,” Economia Internazionale (February 1954), pp. 3-32. REFERENCES National Association of State Development Agencies. Export Program Database (NASDA, 1986). State Albaum, Gerald. State Government Promotion of International Business (University of Arizona, Division of Economic and Business Research, 1968). Ouida, Herbert. “ XPORT: Port Authority ETC Simplifies and Expands Export Operations,” Business America (March 19, 1984), pp. 8-12. 18ln a recent cost-benefit analysis of the Export-lmport Bank of the United States, Boyd (1982) concluded that for 1976-80 the annual costs exceeded the benefits by an average of $ 2 0 0 million. MAY/JUNE 1988 42 Prestowitz, Clyde V., Jr. Trading Places: How We Allowed Japan to Take the Lead (Basic Books, Inc., 1988). U.S. Department of Agriculture. 1982 Census of Agriculture — Geographic Area Series — Volume 1, Part 51 (GPO, 1984). Sailors, J.W., R.W. Thomas, and S. Luciani. “ Sources of Comparative Advantage of the United States,” Economia Internazionale (May-August 1977), pp. 282-94. U.S. Department of Commerce, Bureau of the Census. Sun/ey of Manufactures (GPO, various years). SAS User's Guide: Statistics, 1982 Edition (SAS Institute, 1982). Stern, Robert M., and Keith E. Maskus. “ Determinants of the Structure of U.S. Foreign Trade, 1958-76," Journal of Interna tional Economics (May 1981), pp. 207-24. http://fraser.stlouisfed.org/ FEDERAL RESERVE BANK OF ST. LOUIS Federal Reserve Bank of St. Louis Annual _________ 1980 Census of Population — Volume 1, Character istics of the Population — Part 1, United States Summary (GPO, December 1983). ----------------Statistical Abstract of the United States (GPO, various years). 43 Tobias F. Rotheli Tobias F. Rotheli, an economist at the Swiss National Bank in Zurich, was a visiting scholar at the Federal Reserve Bank of St. Louis. Laura A. Prives provided research assistance. Money Demand and Inflation in Switzerland: An Application of the Pascal Lag Technique I n 1973, thi! Swiss National Bank ceased pegging the Swiss franc to the U.S. dollar. In so doing, the Swiss monetary authorities gained control over the domestic m oney stock. This article describes the role o f m oney dem and estimates in the new monetary policy. It then assesses this foundation o f policy by developing a statistical m odel for m oney demand tailored to the current exchange rate and monetary control regime. SWISS MONETARY POLICY Under the Bretton W oods system, Switzerland was one o f many countries to experience the transmission of U.S. inflation to its economy. Be cause the Swiss National Bank pegged the ex change rate o f the Swiss franc against the U.S. dol 'This does not mean that inflation is not a monetary phenome non. Under fixed exchange rates, inflation in a particular coun try is not caused by the money growth of that country, but by the combined money growth of all countries participating in this monetary arrangement. In such an environment, a small coun try is a price taker, with virtually no influence on the world price level. When the exogeneous price level rises, domestic resi dents restore their real balances by accumulating foreign lar, there was a close connection between U.S. and Swiss inflation. Arbitrage saw to it that changes in the dollar prices o f internationally traded goods w ere matched by proportional changes in corre sponding Swiss franc prices. Competition caused the prices o f Swiss domestic goods to keep pace with the prices o f internationally traded goods. Meanwhile, the public adjusted the Swiss money stock to the rising price level, in order to hold real m oney balances at the desired level . 1 The Determination o f Monetary Targets The beginning o f 1973 marked a change in the monetary regime. With the transition to flexible exchange rates, the Swiss m onetary authorities exchange (dollars) through current account surpluses. These earnings are then converted to domestic currency (Swiss francs) by the central bank (the Swiss National Bank) which is ready to make any transaction at the given exchange rate. MAY/JUNE 1988 44 Monetary Targets and Monetary Growth At the end o f 1974, the Swiss National Bank (SNB) announced the first monetary target.' Until 1978 M l targets w ere used. These targets w ere translated into operational targets for the monetary base. To accomplish this, a dynamic m odel forecasting the m ultiplier (the ratio be tween M l and the base) was developed.- The policy was im plem ented mainly through for eign exchange purchases and sales. The actual course o f the m oney stock did not always follow its announced path. The table at right shows the targeted and effective m oney growth rates up to 1986. The Swiss National Bank tried, mainly in the seventies, to dampen erratic movements o f the exchange rate. In 1978, for example, the Swiss franc appreciated strongly against the dollar; as a result, Swiss exports o f goods and services, approximately 40 percent o f gross national income, declined. To prevent further appreciation o f the Swiss franc, the monetary authority expanded the m oney supply far beyond the target .3 The monetary target for 1978 was abandoned in September. There was no target for 1979, and since 1980 targets for the adjusted monetary base have been used .4 W hile exchange rate considerations led to marked deviations from the projected m oney path, these deviations w ere neutralized in the long run. On average, over the 11 years for which targets w ere announced, the annual 'Kohli and Rich (1986) provide a survey of the Swiss experi ment of monetary control. For a comparison of U.S. and Swiss experience with monetary targeting, see Rich (1987). 2See Buttler et al (1979) on the multiplier model. 3See Niehans (1984), chapters 11 and 13, for an in-depth could determine domestic m oney growth and inflation independently. Monetary targets played a central role in the implementation o f the new policy (see shaded insert above). The Swiss National Bank relied strongly on m oney dem and estimates in establish ing those targets. An early econom etric study of Swiss m oney demand was published by Schelbert in 1967. In later research, Vital (1978), Kohli (1985), and Kohli and Rich (1986) pooled data from the fixed and the flexible exchange rate period in their FEDERAL RESERVE BANK OF ST. LOUIS money growth was only 0.14 percent higher than the targeted value. Monetary Growth: Targeted and Effective Target Variable1 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 Target2 Effective2 4.4 7.7 5.5 16.2 M, M, M, M, 6 — — — M0 M0 M0 M0 M0 M0 M0 43 —0 .6 3 - 0 .5 6 5 5 4 3 3 3 3 2 2 .6 3.6 2.5 2 .2 2 .0 This table is updated from Kohli and Rich (1986). 'M, covers currency outside the federal government and the commercial banks, as well as demand deposits of Swiss nonbanks with the postal giro system and the commercial banks. M0 stands for the adjusted monetary base (deposits of private sector with the SNB and outstanding bank notes less the month-end bulge in SNB credit to the commercial banks). 2Average of monthly year-on-year rates of change. 3The target for 1980 was defined as the average percentage increase in M 0 over the level of November 1979. For each month of 1980, the percentage increase over the level of November 1979 was calculated. The monthly growth rates were in turn compounded in order to obtain annualized rates. The effective rate of - 0 . 6 percent represents the average of the annualized growth rates. treatment of the relation between the money supply and real exchange rate fluctuations. "Rich and Beguelin (1985) give detailed information on both M 1 and base targeting and reasons for the transition to the latter. samples. According to these studies the deflated monetary aggregates (from the m onetary base to M3) can be w ell explained by two variables: the interest rate and national income. The long-run goal o f Swiss monetary policy is price level stability. In order to achieve this goal, the nominal m oney stock has to increase by as much as the growth in the demand for real m oney balances. This is where the m oney dem and esti mates enter the policy-making process. Since in terest rate changes are hardly predictable, they are 45 not taken into consideration when formulating the m onetaiy target. This leaves the incom e elasticity o f m oney dem and as the decisive coefficient. M ul tiplying the incom e elasticity by the expected growth o f real incom e provides an estimate o f the growth o f the m oney supply consistent with a stable price level. The statistical findings indicate that the income elasticities o f the demand for base m oney and M l are close to unity. This leads to the rule o f thumb that price level stability can be achieved if money growth is equal to the growth o f real income. The growth potential o f the Swiss real incom e is esti mated to be around 2 percent per year .2 Accord ingly, the Swiss m onetaiy targets have been gradu ally low ered over time to 2 percent in 1986. Monetary Regime and Money Demand Estimation With the change to flexible exchange rates, the estimation o f the m oney dem and function must be reconsidered. Under the current regime of m onetaiy control, the nominal m oney supply is exogenous. Consequently, price level movements must bring aggregate real m oney balances in line with the desired level. The Chow m oney demand specification, the one most w idely used in Swiss m oney dem and estimates, does not adequately capture this adjustment process .3 This problem appears in empirical findings: Her! (1986) reports that the explanatory pow er o f a Chow specifica tion decreases substantially w hen the sample contains data only from the flexible-exchange-rate period. The present article develops a m odel o f price level adjustment to estimate Swiss m oney demand for the period from 1/1973 to IV/1986. Since w e are interested in accurate measurements o f the in com e and interest rate elasticities, an estimation procedure is chosen that considers a broad range o f dynamic adjustments o f the price level. 2For an up-to-date study of the Swiss potential real income growth, see Buttler, Ettlin and Ruoss (1987). 3Chow (1966) introduced the following adjustment specification for money demand estimates: Mrl —M„_, = (3(Mf, —Mr,_,) 0<(J«1, where Mr denotes real money balances, and M?is the long-run money demand. Laidler (1985), pp. 111-12, points out that this “ real adjustment” version coincides with a price adjustment version based on the partial-adjustment hypothesis only if the money supply is invariant over time. ESTIMATING THE MONEY DEMAND FUNCTION FOR THE FLEXIBLE-EXCHANGE-RATE PERIOD We start with a long-run demand for money function: (1 ) M? = f(Z), where M '1denotes real m oney balances demanded, and Z is a set o f variables, usually including a mea sure o f real incom e and one or more interest rates. Equilibrium requires that equation 2 holds: (2) M/P* = M;! The nominal m oney stock, M, is exogenous. There fore, this equation determines the equilibrium price level P*. The actual price level, P, does not always equal P*. Laidler (1985) elaborates: When a flexible price economy is pushed off its long-run demand-for-money function, it moves back by way of the influence of price level changes on the stock of real balances. If the price level is perfectly flexible, such adjustment is instantane ous, and only a long-run aggregate demand-formoney function is observable. However, if prices move less than instantaneously, we would observe the economy moving slowly to equilibrium over time by way of price level changes influencing the quantity of real balances.4 To illustrate this point, consider the following experiment: W e start with the price level in equi librium (at P*). Now, the quantity o f m oney is in creased. At the prevailing price level, real balances are above their equilibrium value, w hich induces people to increase their spending and investment. In an econom y close to full employment, the in creased dem and will drive up prices. In this process, existing contracts are renegoti ated over time. Hence, the price level does not jump to the new equilibrium (Pf) immediately; instead, it adjusts gradually. Figure la shows two possible shapes o f this adjustment process .5 In its 4Laidler (1985), p. 111. 5The notion that the real money stock can deviate from the desired money stock and that this discrepancy is only slowly diminished through price level changes has recently been called the “ buffer stock concept” of money. Laidler (1987) gives a description of buffer stock money and the transmission mechanism. MAY/JUNE 1988 46 Figure 1a Figure 1b Adjustment Paths of the Price Level Lag Weights for the Price Level Adjustment w.i general form, the adjustment process can be w rit ten as 00 (3) P, = 2 w, p;_,, i= 0 00 with w, = 2 i= 1 . 0 Figure lb shows the pattern o f lag weights (w,l that correspond to the two adjustment paths in figure l a .8 The lag weights are also called the speed of adjustment since they measure the adjustment o f the price level per unit o f time. The Kovck lag, the simplest case, is denoted by the solid line. It can be derived from a partial-adjustment hypothesis which states that the gap between P, and P* is closed by a constant fraction ((3) per unit o f time. This implies that the adjustment speed o f the price level is highest at the beginning and dim in ishes steadily thereafter. Because o f its simplicity, this adjustment specification has been the most popular form o f capturing the dynamic aspects o f m oney dem and .7 Equations 2 and 3 ensure that a constant growth rate of money eventually leads to a rate of inflation equal to the rate of money growth 'See Thornton (1985) for a concise overview of applications of the partial-adjustment hypothesis in money demand estimates. FEDERAL RESERVE BANK OF ST. LOUIS Laidler questions the application o f the partial adjustment hypothesis to the behavior o f the price level. He writes: [Wit; would have to argue that it is possible to capture in one simple parameter (3 the entire transmission mechanism whereby the price level responds to discrepancies between the supply and demand for nominal money. This might be possible, though it seems implausible to say the least.8 Laidler concludes that if w e are suspicious o f the validity of the p artial-adjustm ent hypothesis, then w e must also be suspicious o f all other parameters (for example, incom e and interest rate elasticities) estimated w ith a partial-adjustment specification. Estimates for Switzerland suggest that the re sponse o f the price level to changes in the m oney stock resembles the pattern shown by the dashed line in figures la and l b .3 This adjustment is char acterized by a slowly increasing adjustment speed in the initial stage o f the process; it takes time for the price level movem ent to build momentum. To get accurate estimates o f incom e and interest rate elasticities, it is therefore worthwhile to consider a 8Laidler (1985), p. 111. ... , _ 9See Wasserfallen (1985) and Zenger (1985). 47 w id er range o f possible lag patterns than just the Kovck specification. plest case, the geom etric lag . 13 Equation 4 can be written as The Pascal Lag Technique (4')P, = (1 - X ) The Pascal lag distribution is a flexible instru ment for capturing the dynamic adjustment pro cess discussed above. Solow (1960) suggested that the W; in equation 3 can be represented by the Pascal distribution. Applied to the case at hand, this specification takes the form: 0° 141 P, = (1 —X)' The first part on the right-hand side contains ex ogenous variables as far back as the sample period runs. The second term contains values that go back to infinity. This second term, however, can be written as 2 (r + ! - 1 ) V P,*_,+ e„ i= 0 1 00 (1 where r is a positive integer, \ is a parameter to be estimated, and e, denotes an error term. The com bination term in parentheses after the summation sign is a scalar value that depends on r and i. Kmenta (1986) presents an instructive graphical example o f h ow the shape o f the lag changes with different values o f r.’° In the simplest case (r = 1 ), the Pascal lag reduces to the Koyck lag. Thus, this technique captures a Koyck-type adjustment while opening the possibility o f tracing a lag pat tern similar to the dashed line in figure lb. The Pascal lag is estimated w ith a maximum likelihood procedure, that searches for the parameter values that m inim ize the residual sum o f squares. It can be estimated in either its autore gressive f o i T n or in its distributed lag form ." In this study, the distributed lag form is chosen because a possible misspecification o f the serial correlation properties o f the residual process can lead to flawed parameter estimates in the autoregressive specification .12 As Maddala and Rao suggest, the order o f the Pascal Lag (r) can be chosen by select ing the specification that maximizes the adjusted R2. The lag technique used here implies an infinite adjustment process. Because o f the finite sample size, this poses a problem. Tw o ways to deal with this issue shall be briefly described for the sim 10Kmenta (1986), p. 537. "S ee Maddala (1977) for a comprehensive treatment of the Pascal lag. Maddala and Rao (1971) give a thorough descrip tion of the estimation methods for the Pascal lag model. t —1 oo 2 VPJV + (1 —X) 2 XJP.V + e,. i= 0 i= t —X) 2 V P,’_, = VEIPJ. i= t Thus, the term X1 E(P0) can be substituted for the infinite part o f the equation. In exchange for avoid ing the problem o f dealing with an infinite series, however, w e face a new problem: the expected value o f P, [E(P0) for t = 0] is not observable. This problem is approached in two ways. First, E(P0) is estimated by including an additional parameter . 14 Second, the actual value o f P0 is used in place of E(P„). The first procedure shall be called “ the m ethod o f free parameters;" the latter shall be called “the m ethod o f determined parameters.” The Specification o f the Model The specification o f the long-run m oney de mand function is (5) m, — p* = a„ + a^v, + ouR, a,>0, a,<0. The estimates are conducted with differenced data. Therefore, no estimate o f the constant (a„) is provided. Low er case letters denote logarithmic variables. The semi-logarithmic specification of m oney demand is the most w idely used in Switz erland. All variables (except the income, y,) are quarterly averages. The price level is represented by the consumer price index. The m oney stock variable is M l, and the incom e variable is the real gross domestic product. R, is the return (in per- ,4With the increasing order of the Pascal lag an increasing num ber of expected initial values must be replaced by new parame ters (see Maddala and Rao, p. 80). That is why a selection criterion (R2) is used that is adjusted for the degrees of free dom. ,2See Maddala and Rao p. 84, and Harvey (1985), chapter 7. ,3Following Maddala, and Maddala and Rao. MAY/JUNE 1988 48 centage points) on three-month Euro-deposits in Swiss francs . '5 Estimation Results Table 1 The first round o f estimates is conducted by using the m ethod o f free parameters. The equilibrium price level in equation 4 is replaced by its determi nants according to equation 5. The following equa tion is then estimated: R= X 1 0.3834 0.4469 0.4443 0.4433 0.9663 0.8677 0.8025 0.7741 3 4 00 2 •I' + j i= + r 2 16) Ap, = II —X)' R2Statistics and \ Estimates for Pascal Lag Estimates of Different Order (r): 1/1973-1V/1986 0 X1(Am,_i — a,Ay,_; — a.AR,^) * E,. Table 1 contains the R2s and the estimates o f X for orders o f the Pascal lag ranging from one to four. The X estimates, which range from 0.77 to 0.97, indicate that the empirical adjustment is rather slow; fast adjustment w ou ld im ply a X close to zero. The lag distribution im plied by the estimates o f X are shown in chart 1. Since the maximum R- is achieved w ith the r = 2 specification, the estimates reject the Koyck lag (r = l ) as the best specification o f the adjustment process. Visible for the optimal case (r = 2 ) is a small adjustment o f the price level within the quarter of the disturbance. In contrast to the Koyck lag, w, reaches its maximum value only six quarters after the disturbance and then slowly decreases. It takes approximately 10 quar ters for the price level to adjust by 50 percent to ward a new equilibrium value. This is much closer to the 12 quarters that both Wasserfallen and Zenger report than the 19 quarters im plied bv the Koyck estimate. Chart 2, the empirical counterpart to figure la , shows the adjustment paths o f the price level im plied by the Pascal lag estimates for r = 1 and r = 2. The chart assumes an increase in the equilibrium price level from one to two in p e riod one. The two adjustment paths show a simi lar response o f the price level only over the first year. ,5Data on the gross domestic product (GDP) are released quar terly. The consumer price index, published monthly, is a better measure of Swiss inflation than the GDP deflator. The nominal GDP, and hence the deflator, are subject to larger revisions than the deflated GDP. The R2s of the estimates decrease substantially when the consumer price index is replaced by the GDP deflator. Although the estimated coefficients remain virtually unchanged when the GDP is deflated with the con sumer price index, the R2s of the estimates decrease. There fore, the officially deflated series for the GDP is used in this study. The interest rate for Euro-deposits in Swiss francs is FEDERAL RESERVE BANK OF ST. LOUIS Table 2 contains the parameter estimates and various statistics for the r = 2 case. The tw o a coef ficients have the expected signs. The interest semi elasticity is very close to the corresponding esti mate reported in Kohli and Rich (1986). The incom e elasticity, however, is substantially smaller than in previous estimates and not significantly different from zero. As the appendix points out, however, using the m ethod o f free parameters im plicitly involves the estimation o f time trends, w hich can affect the reported results. The m ethod o f determ ined parameters is used to generate an alternative set o f estimates. The R 2 criterion again leads to the choice o f the r = 2 case as the best dynamic specification; the results are presented in table 3. The incom e coefficient is 0.83; this time, it is significantly different from zero. The other estimated coefficients are very close to the estimates obtained from the first method. The m ethod o f determ ined parameters depends heavily on the starting values o f the sample period. The m odel is correctly specified only w hen the initial values o f P, are equal (or nearly equal) to the expected values for w hich they are substituted. If this condition is not met, the estimate suffers from m isspecification .’6 This flaw is likely to produce a considered the best indicator for the return on money market instruments in Switzerland. Published domestic rates are applicable to small investors; large investors are able to get Euromarket rates (about half a percentage point more than the domestic rate) even if they deposit their funds with a domestic bank. "T his can be seen with the terminology used in the appendix: while the method of free parameters searches for 7 values that minimize the residual sum of squares, the method of deter mined parameters imposes arbitrary 7 values. 49 Chart 1 Pascal Lag Estimates of Lag Weights for the Price Level Adjustment W | W . i (Q u a rte rs) Chart 2 Pascal Lag Estimates of the Adjustment Path of the Price Level MAY/JUNE 1988 50 Table 2 Table 3 Estimates of Pascal Lag (r=2) Using the Method of Free Parameters: 1/1973-IV/1986 Estimates of Pascal Lag (r=2) Using the Method of Determined Parameters: 1/1973 - 1V/1986 0 .8 6 8 * (53.17) X 0.830* (56.93) 0.393 (0.97) “i 0.830* (2.45) -0 .0 4 2 * (5.45) a2 -0 .0 4 5 * (7.50) R2 0.45 R2 0.41 DW 2.05 DW 1.65 SSR 0.0023 SSR 0.0029 ot, «2 Absolute values of t-statistic in parentheses. * Indicates statistical significance at the 5 percent level. Absolute values of t-statistic in parentheses. * Indicates statistical significance at the 5 percent level. Table 4 Estimates of Pascal Lag (r=2) Using the Method of Determined Parameters Starting Point of Sample Period 74.1 74.2 73.2 73.3 73.4 0.854* (51.19) 0.628* (23.02) 0.715* (14.23) 0.758* (20.60) 0.772* (51.92) 0.628 (1.64) 0.586 (1.54) 1.198* (2.75) 1.553* (4.05) 0.482 (1.44) a 2 —0.043* (6.15) -0 .0 2 3 * (4.77) -0 .0 2 3 * (3.50) -0 .0 3 1 * (5.20) -0 .0 4 4 * (8.56) -0 .0 5 0 * (8.56) R2 0.42 0.18 0.00 0.05 0.30 0.31 0.08 0.31 DW 1.79 0 6 6 0.51* 0.65* 0.96* 1.08* 0.79* 1.75 SSR 0.0027 0.0088 0.0072 0.0050 0.0031 0.0027 0.0035 0.0014 X . * 74.3 74.4 75.1 0.803* (53.37) 0.780* (39.30) 0.892* (76.05) 0.175 (0.44) 0.869* (2 .2 1 ) 0.799* (2.36) - 0 .0 2 2 * (3.01) -0 .0 5 6 * (5.38) Absolute values of t-statistic in parentheses. * Indicates statistical significance at the 5 percent level. p oor fit and significant autocorrelation o f the re siduals. To get a feel for the magnitude o f this problem, the m odel is reestimated with eight new starting points ranging from 1973.2 to 1975.1. Table 4 shows the outcome. The adjusted coefficient o f determination (R2) varies w idely with the starting value o f the estimate. Six estimates show signifi cant autocorrelation o f the residuals. Only two estimates pass a Durbin-Watson test for misspeci FEDERAL RESERVE BANK OF ST. LOUIS fication; these two, with starting points 1973.2 and 1975.1, have the highest R 2s in this series o f esti mates. Finally, the parameter estimates in these two cases are in line with those in tables 2 and 3. Thus, w hile both methods o f applying the Pas cal lag to a relatively small data sample have their limitations, their estimates o f the parameters o f long-run m oney demand, as w ell as the dynamic adjustment process, are consistent. 51 SUMMARY AND CONCLUSIONS Harvey, Andrew C. The Econometric Analysis of Time Series (Philip Allan, 1985). This article deals with the estimation o f money dem and in Switzerland. During the period o f m on etary control since 1973, the public has adjusted real m oney balances to its desired level by means o f price level changes. Thus, the estimation of m oney demand is tantamount to statistically tracking variations in the price level. Heri, Erwin W. Die Geldnachfrage: Theorie und empirische Ergebnisse fur die Schweiz (Springer, 1986). The Pascal lag technique frees the adjustment dynamics from the rigid corset o f the partial ad justment process so frequently used in money dem and studies. The statistical findings show that the partial adjustment process does not accu rately describe h ow the price level adjusts to changes in its determinants. It takes approxi mately one and a half years for the adjustment speed o f the price level to reach its maximum and about one more year before half o f the necessary adjustment is completed. Among the.estimates that pass a test o f misspecification, no incom e coefficient o f m oney demand is statistically significantly different from one. Nev ertheless, all point estimates are less than one. This result suggests that price level stability in Switzerland is more likely to be achieved with an M l growth somewhat less than real income growth. REFERENCES Buttler, H. J., J. F. Gorgerat, H. Schiltknecht, and K. Schiltknecht. “ A Multiplier Model for Controlling the Money Stock,” Journal of Monetary Economics (July 1979), pp. 3 2 741. Kmenta, Jan. Elements of Econometrics (Macmillan, 1986). Kohli, Ulrich. "La demande de monnaie en Suisse,” Bulletin Trimestriel de la Banque Nationale Suisse (June 1985), pp. 64-70. Kohli, Ulrich, and Georg Rich. “ Monetary Control: The Swiss Experience,” Cato Journal (Winter 1986), pp. 911-26. Laidler, David E. W. 1985). The Demand for Money (Harper and Row, _________ “ ‘Buffer Stock Money' and the Transmission Mechanism,” Federal Reserve Bank of Atlanta Economic Review (March/April 1987), pp. 11-23. Maddala, G. S. Econometrics (McGraw-Hill, 1977). Maddala, G. S., and A. S. Rao. “ Maximum Likelihood Estima tion of Solow's and Jorgenson’s Distributed Lag Models,” The Review of Economics and Statistics (February 1971), pp. 8 0 88. Niehans, Jiirg. International Monetary Economics (The Johns Hopkins University Press, 1984). Rich, Georg. “ Swiss and United States Monetary Policy: Has Monetarism Failed?” Federal Reserve Bank of Richmond Economic Review (May/June 1987), pp. 3-16. Rich, Georg, and Jean-Pierre Beguelin. “ Swiss Monetary Policy in the 1970s and 1980s: An Experiment in Pragmatic Monetarism,” in Karl Brunner, ed, Monetary Policy and Mone tary Regimes, Center Symposium Series C-17 (Center for Research in Government Policy and Business, University of Rochester, 1985). Schelbert-Syfrig, Heidi. Empirische Untersuchungen uber die Geldnachfrage in der Schweiz (Polygraphischer Verlag, 1967). Solow, Robert, M. “ On a Family of Lag Distributions,” Econometrica (April 1960), pp. 393-406. Thornton, Daniel, L. "Money Demand Dynamics: Some New Evidence,” this Review (March 1985), pp. 14-23. Vital, Christian. Geldnachfragegieichungen fur die Schweiz (Verlag Industrielle Organisation, 1978). Buttler, H. J., F. Ettlin, and E. Ruoss. “ Empirische Schatzung des Wachstums der potentiellen Produktion in der Schweiz,” Quartalsheft der Schweizerischen Nationalbank (March 1987), pp. 61-71. Wasserfallen, Walter. Makrookonomische Untersuchungen mit Rationaien Erwartungen. Empirische Analysen fur die Schweiz (V e rla g P aul H aup t, 1985). Chow, Gregory C. “ On the Long-Run and Short-Run Demand for Money,” Journal of Political Economy (April 1966) pp. 11131. Zenger, Christian. “ Bestimmungsgrunde der Schweizerischen Konjunktur-und Inflationsentwicklung,” mimeo (Schweizerische Bankgesellschaft, 1985). MAY/JUNE 1988 52 Appendix Implicit Time Trends in the Pascal Lag Estimation Using the Method of Free Parameters This appendix demonstrates that using the m ethod o f free parameters to apply the Pascal lag to a finite sample size implies the estimation o f time trends. The Pascal lag o f order 2 serves as an example. The initial equation for this case is The estimation procedure is not designed to gen erate values o f a, and a 4 that are equal to the cor responding E(Ap) values. Instead, the maximum likelihood procedure w ill find values o f these "free parameters” that m inim ize the sum o f squared residuals: Ap, = 00 (1 + —X)- 2 (i-f- 1 ) X1 (Am,., — a, Ay,_; — ou AR,.,) i= 0 a, = E(Ap„) + 7 ,. a 4 = E( Ap,) + 7 ,. £,. The infinite part o f the equation is om itted by rewriting this equation as Hence, implicitly, the m ethod o f free parameters respecifies the initial equation to Ap, = t —2 (1 -X )- 2 (i + i= 0 A Pt = 1 ) X1 (Am,,, - a, Ayt_, - a 2 AR,_i) 00 (1 - X Ap, = ( 1 -X )- t —2 2 li + i= 0 1 ) X1 (Am,., - a, Ay,., - a, AR,_,) — (t —1 ) X' a, + tX1" 1 a 4 + e,. FEDERAL RESERVE BANK OF ST. LOUIS 1 , ( 1 —t) X1 + 7 2 i= - (t —1 ) X'E(Ap0) + tX— ElAp,) + £,. Using the m ethod o f free parameters means esti mating this equation in the form: (i + )2 + 7 ) X' (Am ,., - a, Ay,., - a 2 AR,_.) 0 , tX'“ ' + et. The term thus added to the basic equation, 7 , (1 —t) X' + 7 , tX'“ ', is a time trend. The form o f this time trend is limited: after a positive or nega tive value at the beginning o f the sample, it eventu ally goes toward zero. The trend parameters, 7 , and 7 ., however, cannot be estimated explicitly. 53 Daniel L. Thornton Daniel L Thornton is a research officer at the Federal Reserve Bank of St. Louis. Rosemarie V. Mueller provided research assis tance. The Effect of Monetary Policy on Short-Term Interest Rates T -■-HE “liquidity effect” plays a central role in Keynesian theoiy of the transmission o f monetary policy. It is based on the notion that the demand for m oney is negatively related to the nominal interest rate.' Other things the same, an exogenous increase in the m oney stock depresses nominal and real interest rates, stimulating aggregate demand. Even though theorists acquiesce to the liquidity effect as a theoretical proposition, it is often chal lenged on efficacy grounds. It is argued that changes in the m oney stock do not leave all other things unchanged. Monetarists, such as Friedman (1968) assert that the liquidity effect is, at best, only temporary; the ultimate effect o f more rapid m oney growth is higher inflation (or, m ore im por tantly, expectations o f higher inflation) and, conse quently, higher nominal interest rates. N ew classi cal economists argue that the real interest rate is determined by basic tastes and technology con siderations, which are slow to change .2 If increases ’ Until fairly recently, most forms of money were non-interestbearing. Consequently, the opportunity cost of holding money was represented by the nominal interest rate. A large portion of M1 now is held in the form of interest-bearing NOW accounts. The opportunity cost of this component of M1 is the spread between market rates and the rate paid on these deposits. Recently, Niehans (1987) has argued convincingly that the description of the rational expectations school as “ new classi cal economics” is a misnomer. He argues that its emphasis on continuous market-clearing constitutes a fundamental break from both classical and neoclassical economics. 2 in the m oney supply primarily affect the market’s expectations o f inflation, nominal interest rates w ill rise immediately. Estimates o f m oney dem and equations, espe cially short-run equations, indicate that m oney dem and is very interest inelastic, suggesting that there is a strong liquidity effect .3 Most other em pirical work, however, has estimated the total ef fect o f changes in monetary policy on interest rates. A w ide range o f m ethodologies have pro duced diverse and sometimes conflicting results. This article is an attempt to consolidate the evi dence on the responsiveness o f interest rates to monetary changes. Various methods for estimating the relationship between interest rates and m one tary impulses are reviewed and then applied to a com m on data set. Also, the analysis im plicitly incorporates the possibility that the m oney stock is endogenous in the sense that the m oney multi plier depends on the interest rate .4 3Many economists, for example Carr and Darby (1981), believe the liquidity effect implied by these equations to be implausibly large. “The interest sensitivity of the multiplier is shown in models of the money supply process. For example in Thornton (1982), the behavioral equations are assumed to be linear; thus, al though the multipliers are not functions of the interest rate per se, they are functions of the interest elasticities of these behav ioral equations. MAY/JUNE 1988 54 THE LIQUIDITY EFFECT The liquidity effect is defined as the interest responsiveness o f the demand for m oney in a sim ple m odel o f liquidity preference where the m oney stock is assumed to be controlled directly and exogenously by the m onetaiy authority .5 For ex ample, consider the following specification o f the demand for nominal m oney (1) Md = L(i, Pv), Lt < 0 , L„, E. > 0, where M, i, v and P denote the nominal money stock, the nominal interest rate, real incom e and the price level, respectively. If the m oney stock is taken as exogenous, M 5 = lYl, the market equilib rium condition is The effect o f an exogenous change in m oney on interest rates given by equation 4 is strictly smaller than the liquidity effect o f equation 3 because o f the incom e and price level effects. According to the Keynesian transmission mechanism, the low er nominal and, at this point real interest rate, stimu lates aggregate dem and and, hence, real income. The rise in real incom e increases the dem and for money, causing interest rates to rise; this mitigates the initial liquidity effect. Equation 4 also incorpo rates the direct price level or the “ Keynes effect” . An increase in the nominal m oney stock causes the price level to rise, which in turn causes the real m oney stock to decline, resulting in an in crease in interest rates .6 P = P(M), P' > 0 If m oney stock changes affect output or prices sufficiently rapidly, then the incom e and price level effects w ill offset, at least in part, the decline in interest rates associated with the liquidity ef fect. Moreover, it may be difficult to find a statisti cally significant negative relationship between changes in the m oney stock and changes in the interest rate if the data are averaged over a long period .7 Indeed, if financial market participants anticipate the rise in incom e or the price level, these effects w ill be reflected in market interest rates immediately; thus the observed change in interest rates associated with a m oney stock change might be small even over short time periods. and The “Fisher Effect” (2) M = L(i, Py). Hence, the liquidity effect is defined as 13) di = (l/L,)dM. W hile the theoretical relevance o f the liquidity effect is acknowledged, analysts generally argue that it may be partially or totally offset quickly by other effects, both direct and indirect, o f m oney stock changes. To see this, assume that the price level is positively related to the m oney stock and real output is negatively related to the interest rate. That is, v = v(i), y ' < 0 . Substituting the above expressions into equation 2 , the effect o f an exogenous change in the money stock on interest rates is 14) di = ( l - L pP'y)dM/(L, + LyPy'). This measure reflects not only the interest sensi tivity o f the dem and for money, Lt, but the direct effect o f m oney stock changes on the price level, LpP'y, and the indirect effect o f interest rates on income, LyPy'. 5Because the liquidity effect usually is discussed in models where the money stock is assumed to be controlled by the monetary authority, it has become synonymous with the inter est responsiveness of money demand. In a model where the money stock is endogenous, it may be more appropriate to think of the liquidity effect in terms of the impact of an exoge nous change in monetary policy on interest rates. This would reflect not only the slope of the money demand function, but the slope of the money supply function as well. 6For notational convenience, equation 1 is written without im posing the usual assumption that L(.) is linear homogenous of degree one in P. FEDERAL RESERVE BANK OF ST. LOUIS In addition to the incom e and price level effects incorporated in equation 4, there is also the possi bility o f the “ Fisher effect.” Fisher (1930) argued that, in the absence o f differences in holding costs, the real, risk-adjusted return on assets should be the same regardless o f the units in which the as sets are expressed. Consequently, the return on physical assets should be the same as the return on credit contracts denom inated in fixed units o f nominal money. This implies that the interest rate on dollar-denom inated contracts w ill reflect the H'his may be one reason why Peek (1982) and Wilcox (1983a), Makin (1983) and Hoffman and Schlagenhauf (1985) obtained different results using similar data and methodologies. All used the biannual Livingston survey data on inflation expectations; however, Makin, Hoffman and Schlagenhauf interpolated the data and estimated a quarterly model, while Peek and Wilcox used biannual data. 55 market’s expectation o f inflation over the duration o f the contract. Hence, if an increase in m oney growth produces expectations o f more rapid in flation, the nominal interest rate w ill rise .8 The existence o f a contemporaneous price expectation effect mitigates and possibly eliminates the liquid ity effect on the nominal interest rates .9 The Effect o f an Endogenous Money Supply Until now, the m oney supply has been assumed to be controlled exogenously by the Federal Re serve. In the m odern financial system, however, the total m oney stock is determ ined not only by the policy actions o f the Federal Reserve, but by the portfolio decisions o f depository institutions and the public. That is, the m oney supply is com posed o f both “inside” and “outside’’ money. Gen erally, there is no sense in which one can measure the effect o f a change in the stock o f endogenous, inside m oney on interest rates .10 Instead, the effect o f monetary changes on the interest rate is m ea sured in terms o f changes in outside money. For example, assume that the m oney supply is endogenous in that the usual m oney m ultiplier is a function o f the interest rate. That is, let the m oney supply be expressed as (5) Ms = m(i)H, m ' > 0, w here H denotes the stock o f “high-powered,” outside m oney and m(i) denotes the usual m oney multiplier. Setting (5) equal to (1) results in the equilibrium condition (6 ) m(i)H = L(i, P(m (i)H )y(i)). Consequently, the effect o f an exogenous change aThe reader should note that there is a somewhat subtle differ ence between equating the liquidity effect to shifts in the stock of money and shifts in the growth rate of money. The problem here is that the Fisher effect, which relates the level of nominal interest rates to the rate of inflation, is fundamentally dynamic. The bridge that links these concepts can be found in the mone tary growth models where, in long-run equilibrium, both the monetary growth rate and the nominal interest rate are con stant. An exogenous increase in the growth rate of money produces a liquidity effect and potentially a Fisher effect. This difference is also reflected in empirical work. For example, compare the approach of Gibson (1970b) with that of Cagan and Gandolfi (1969). 9The outcome depends on a number of factors, including the homogeneity of the demand for real money with respect to the price level. If there is no money illusion, the nominal interest rate must rise point for point with the expected rate of inflation. Consequently, if the inflation consequences of an increase in the growth rate of the money stock are fully anticipated, the nominal rate must rise with the acceleration in money growth. in the stock o f high-powered m oney on the inter est rate is given by (7) di = (1 - LPyP')mdH/(Lj + U Py' + (L„yP' - ljm 'H ). The responsiveness o f interest rates measured by (7) is strictly smaller than that given by (4) for an identical exogenous change in the m oney supply, that is, mdH = dM. The Role o f Monetary Policy Objectives There is an exception where it w ould be appro priate to measure the effect o f monetary changes on interest rates in terms o f the total m oney stock despite the presence o f inside money. This occurs when the monetary authority is targeting the total m oney supply and when it is forecasting and quickly offsetting the effect o f other factors on the supply o f m oney .11 For example, suppose that the Federal Reserve is targeting the total m oney sup ply but controls only H directly. If m w ere to rise, say due to a decrease in the public’s desire to hold currency relative to checkable deposits, the Fed w ould attempt to offset the effect o f the rise in the m oney stock by reducing H. If the Fed anticipated the rise in m and changed H by the appropriate amount immediately, there w ould be no change in the m oney supply or interest rates associated with the change in H. Estimates o f the responsiveness o f interest rates to changes in H w ould be biased downward. If, on the other hand, the Fed does not respond instantaneously, interest rates w ou ld be negatively associated with changes in H. In con trast, assume that there is an exogenous increase in the dem and for money. If the Fed responds 10See Patinkin (1965), pp. 297-301, for a good discussion of this point. Of course, this does not apply to exogenous shifts in the stock of inside money, such as a gold discovery under a gold standard. "S ee Thornton (1984) for a discussion of this point in terms of the issue of debt monetization. Also, see Mishkin (1982) for a discussion of the effects of this form of money stock endoge neity or estimates of the market's response to changes in the money stock. Also, Mishkin (1981) and Robinson (1988) use M2 to measure the responsiveness of interest rates to changes in the money supply. This is odd since changes in M2 are much more likely to be related to factors other than policy changes. MAY/JUNE 1988 56 instantly to offset the effect o f this increase on the m oney stock, interest rates w ill rise while the m oney remains unchanged and the stock o f highpow ered m oney is reduced. If the Fed does not respond instantaneously, both interest rates and the m oney stock w ill initially rise, then interest rates w ill continue to rise as the m oney stock falls. The point here is that whether the total m oney stock or the stock o f high-powered m oney should be used depends on w hether the Fed is trying to control the m oney stock and on h ow rapidly it is responding to other factors that influence money. This observation has implications for empirical work. If the Fed is attempting to control the total m oney stock and if the Fed moves reasonably quickly to offset the effect o f other factors, measur ing the responsiveness o f interest rates in terms of the total m oney supply w ould be appropriate even if day-to-day or week-to-week shocks w ere not offset instantaneously. this instance, the Fed m erely adjusts the m oney stock to shifts in the dem and for or the supply of m oney over w hich it has no control. In the case of exogenous shifts in the m oney supply function, the Fed neutralizes the effect o f such shifts on nominal interest through appropriate open mar ket operations . 13 As a result, both the nominal m oney stock and the interest rate are unchanged. In the case o f shifts in the dem and for money, the Fed uses open market operations to accomm odate changes in the dem and for money. The interest rate remains unchanged, but the m oney stock changes. Policy-Related Endogeneity This type o f endogeneity creates severe prob lems for isolating the responsiveness o f interest rates to monetary changes because only the mar ket equilibrium values o f the interest rate are ob served. Since the interest rate is unchanged, de spite changes in the m oney stock, the responsive ness o f interest rates to changes in the m oney stock appears to be nil .14 If the Fed offsets only part o f a dem and shift, however, m oney stock and interest rate changes w ill be positively correlated. If only part o f the exogenous supply shifts are offset, m oney and interest rates w ill be negatively correlated. Consequently, statistical analysis may show a positive, negative or no statistically signifi cant relationship between interest rates and m oney growth, despite the fact that it is precisely because o f the liquidity effect that compensatory open market operations are undertaken. The endogeneity o f the m oney stock discussed above is based upon the econom ic response of depository institutions and the public to changes in nominal interest rates. Another monetary-policy related view holds that the m oney supply is en dogenous w henever the Fed is using short-term interest rates as an intermediate policy target. In If the Fed reacts instantaneously to these shocks, evidence o f the effect o f changes in the m oney stock on interest rates can be obtained with precise knowledge o f the Fed’s interest rate target. Unfortunately, such information is gener ally unavailable .15 Alternatively, a time interval short enough to isolate the response o f the market l2For example during most of the 1960s and the early 1970s, the policy directives of the Federal Open Market Committee to the Trading Desk were stated in terms such as “ maintain the existing degree of credit restraint.” Even when the Fed was targeting the monetary aggregates in the late 1970s and early 1980s, the policy directives often were stated in terms of multi ple monetary aggregates and in loose terms, such as “ run somewhat above the upper limit of the target range." More over, the money growth objectives frequently were conditional on movements of other variables such as the federal funds rate. 14ln terms of a more formal model, let H* be the stock of highpowered money required to hit some target interest rate i*, i.e., H* = L(i*,Py)/m(i*). From this, dH/dPy = LPy/m(i). The change in the equilibrium interest rate associated with a shift in the demand for money is given by di/dPy = - [LPy/(L, - m'H) ] + [m(i)/(L, - m'H)](dH/dPy). Substituting in for dH/dPy, yields di/dPy = 0. To determine w hether the estimated respon siveness o f interest rates is sensitive to the m one tary variable used, alternative measures o f the monetary impulse are used. This is necessary because the Fed often relies on multiple objectives and is not explicit about them .12 Of course, if m' is small, the choice o f a m onetaiy variable will be relatively unimportant. ,3The Fed’s reaction to offset a supply-side shift is referred to as “defensive open market operations.” Stabilizing the normal interest rate will be effective only if the change in the money stock does not give rise to inflationary or deflationary expecta tions. Proponents of this view would argue this will not happen because the Fed is merely accommodating shifts in the de mand for money. FEDERAL RESERVE BANK OF ST. LOUIS 15At times, the Fed’s announced ranges for the federal funds rate were fairly narrow. It is difficult to use these ranges to model this relationship, however, because the relationship between the federal funds rate and the T-bill rate, which is usually used to estimate the responsiveness of interest rates to monetary changes, is itself not very stable. 57 to the Fed’s actions could be used. In the absence o f such detailed information or such a rich data set, it is important to measure the effect o f m one tary changes on interest rates during periods in which the Fed was attempting to exert greater control over the m oney supply.“ and r denote the price level and real interest rate, respectively. Z, and X, are vectors o f variables that influence the dem and for comm odities and money, respectively, and v„ and v2l are stochastic disturbances such that v„ is iid( 0 , cr;), v,, is iid( 0 , &i) and E(v„ v,,) = 0 for all t. The m odel is closed by the Phillips cuive A REVIEW OF METHODOLOGIES (11) P, = Pf + cy* One m ethod o f estimating the responsiveness of interest rates to changes in the m oney stock, used by Cagan and Gandolfi (1969) and more recently by Melvin (1983) and Brown and Santoni (19831, is to regress the change in the nominal interest rate (Ait) on a distributed lag of unanticipated changes in the nominal m oney stock, A M U. That is, the equation where the superscript “e ” denotes the expectation based on information known before period t. Equations 9, 10 and 11 are solved for the real inter est rate. The result is substituted into the Fisher equation, K (8 ) Ai, = a 0 + 2 (ii AM “_i + i= 0 (1 2 ) i, = r, + Trf, where tt denotes the rate o f change in the price level, to yield a quasi-reduced form equation for the nominal interest rate e, is estimated. The random error, e, is assumed to be identically and independently distributed with a mean o f zero and a constant variance, that is, e is iid(0, ct2). This equation is estimated w ith ordi nary least squares (OLS). A second approach used by Peek (1982), Wilcox (1983a), Mehra (1985), Hoffman and Schlagenhauf (1985) and Peek and W ilcox (1987) employs an ISLM, aggregate demand/aggregate supply m odel . ' 7 In this model, com m odity demand is a function of the real interest rate and m oney demand is a func tion o f the nominal interest rate. While specific models differ, the following specification encom passes the essential features. The IS curve is given (13) i, = A„ + A,Z,a2 + A 2X,b3 - A,(M, - Pf) + A ,71° + u,. The responsiveness o f the interest rate to real m oney stock changes, A 3 = [(c + b,)a, + b j 1 > 0 , captures not only the “liquidity effect” (bj, but also the net effect o f all other factors that influence the equilibrium interest rate. (10) (M, —P,) = b„ + b, y* — b,i, + h, X, + v,,. While equations 13 and 8 appear quite different, they are both reduced-form equations. The funda mental differences are that equation 13 is stated in level rather than first-difference form and that it explicitly includes factors, in addition to the m oney stock, that could affect nominal interest rates. The absence o f these factors from equation 8 could be justified by arguing that it is a final-form equation, not simply a reduced-form equation. On the other hand, estimates o f the response o f inter est rates based on equation 8 could be biased if variation in other factors that affect interest rates is not controlled for.'" [Unless otherwise stated, all variables are in loga rithms.) y*denotes the deviation o f real GNP from its “natural rate” (or full em ployment level), and P Another difference is that equation 8 incorpo rates a distributed lag o f unanticipated money, w hile equation 13 uses only the contemporaneous by (9) y* = a„ — a,r, + a2Z, + v„ and the LM curve by 16lt should be noted that Mishkin’s (1981, 1982) approach of using unanticipated money does not circumvent this problem. In this instance, unexpected changes in the money stock due to demand and supply shocks are different, so that the coeffi cient on unexpected money will be different depending on whether the shock emanates from the demand or supply side. Moreover, the effect of an unexpected change in the money supply will be different from the effect of a shock to the money supply. Also, because equation 13 is a quasi-reduced form, the vari ables Z„ X„ Pf, M, or Trfmay be correlated with the error term. Consequently, OLS estimates of these equations may be inconsistent. Of course, the same would be true of equation 8 if the money stock is endogenous. This observation is the basis for Mehra’s (1985) work. 18 "Actually, this approach was used earlier by Sargent (1969, 1972). MAY/JUNE 1988 58 level o f actual money. The structure o f equations 9-12 can be m odified, however, to replace the monetary variable by its unexpected component; a distributed lag o f unanticipated m oney also can be included by appealing to "price-stickiness” or Blinder and Fisher’s (1981) inventory adjustment . 13 A third m ethodology has roots in the rational expectations/efficient market literature .20 Mishkin (1981,1982) and, m ore recently, Hardouvelis (1986) and Robinson (1988) estimate the equation (14) i, - i' = a 0 + a,I, + a,(M t - M“) + ot3(y, - y f) + a 4(ir, - ttH + t),. I, denotes the set o f information that market par ticipants have available to them at the beginning of the period, w hile t), denotes the error term. Mish kin characterizes equation 14 as the “rational ex pectations analog o f the typical m oney dem and relationship found in the literature. ”21 Mishkin derives equation 14 by using the ef ficient market/rational expectations m odel to ar gue that Furthermore, equations 8,13 and 14 are alterna tive representations for the nominal interest rate. Thus, they can be com pared directly using stand ard nested and/or nonnested test procedures. EMPIRICAL ESTIMATES OF THE LIQUIDITY EFFECT The empirical estimates presented here cover the period from 1958.08 to 1987.06. Prior studies have generally used quarterly data w hen estimat ing equations 13 and 14 and m onthly data w hen estimating equation 8 . This study uses monthly observations for all specifications. The month p e riod is short enough that the liquidity effect is less likely to be weakened by subsequent income, price level or inflation-expectations effects. On the other hand, many o f the variables that might reasonably enter equations like 13 are unavailable on a m onthly basis, so that the estimates are subject to a potential omitted-variables bias. The variables used are y = the real value o f the industrial production index, i, —ir = (w, - w?)0 + a>„ TBR = the three-month Treasury bill rate, w here W, is a vector o f variables that reflect the “information relevant to the determination o f short-term interest rates” and w, denotes the error term .22 He then solves a m onetary equilibrium condition for the interest rate in terms o f all the other variables that enter the m oney demand function, that is, variables w hich appear as argu ments in equation 1 . He includes these variables in W„ arguing that they are part o f the relevant infor mation set. Of course, any right-hand-side variable in equation 13 could be considered an element of W, simply by broadening the theoretical frame work. Consequently, equation 14 differs from the other specifications primarily in its explicit and com plete reliance on the efficient markets/rational expectations paradigm. 19For example, see Makin (1983) and Hoffman and Schlagenhauf (1985). “ Dwyer (1981) has an alternative rational expectations frame work where, because the same factors affect both the ex pected inflation rate and the real interest rate, they give rise to a set of cross-equation restrictions that can be tested. 21 Mishkin (1982), p. 6 6 . “ Mishkin (1982), p. 64. 23Cagan and Gandolfi (1969) p. 279, state “ It is hard to deter mine to what extent monetary changes at any particular time are anticipated, but presumably a steady growth rate will sooner or later come to be reflected in a corresponding rise in FEDERAL RESERVE BANK OF ST. LOUIS P = the CPI, M = the M l definition o f the m oney stock, MB = the Federal Reserve Bank o f St. Louis ad justed monetary base, and NBR = the Federal Reserve Bank o f St. Louis ad justed nonborrow ed reserves. Tw o measures o f unanticipated changes in the m oney supply are used here. The first is the change in the growth rate o f money. Cagan and Gandolfi use changes in the growth rate o f m oney to proxy such changes, arguing that the market should respond only to unanticipated changes in the money stock .23 Today, the unanticipated change prices (allowing for the growth rate of real income). Conse quently, changes in the monetary growth rate will tend to pro duce, every time they occur, a response in interest rates .. Gibson (1970a) uses a similar equation based on an analo gous argument; however, Gibson (1970b) regresses first differences of the interest rate on first differences of the money stock. 59 in the growth rate o f m oney typically w ould be obtained by subtracting expected m oney growth, estimated using some time-series method, from actual m oney growth. Nevertheless, because Cagan and Gandolfi’s procedure has been utilized by all w ho have estimated equation 8 , their measure o f unanticipated m oney is used to see if the results are sensitive to the form o f the unantici pated monetary variable. is estimated. The unanticipated monetary variable, MVU, is alternately proxied by A M I, AMB, ANBR, (AM 1 -AM 1 '), (AMB —AMBe) and (A N B R -A N B R ' ) . 25 The unanticipated price (PVU) and incom e (yVu) variables are alternatively measured by AP and Ay or (AP —A P ) and (Ay —Ay * ) .28 This specification, and others w hich follow, include a finite distrib uted lag o f the dependent variable to capture any effect o f past information .27 Additionally, unanticipated m oney is measured by (AM-AMC), where AM e is a time-series represen tation o f past AM. In this instance, the expected values o f M, y and P are obtained by regressing each on a six-month distributed lag o f itself and the other variables, including changes in the Trea sury bill rate .24 OLS estimates o f equation 15 for the period 1959.08-1987.06 and two subperiods, 1959.081973.09 and 1973.10-1987.06, are presented in tables 1-3. The split was made at 1973.09 because (1 ) it marks the well-known break in the demand for money, (2 ) it roughly coincides with the demise o f the Bretton W oods agreement and (3) it also roughly coincides with the beginning o f an era in w hich the Federal Reserve claim ed to pay increas ing attention to the growth rate o f the monetary aggregates .28 The equation is estimated with and without PVUand yVuto determine h ow sensitive the results are to these variables. This study uses three monetary policy variables: M l, the adjusted monetary base (MB), and nonbor row ed reserves (NBR). The m onetary base is used often as a measure o f exogenous monetary policy. NBR is used because some w ou ld argue that it is a better measure o f the exogenous monetary im pulse than MB because depository institutions’ borrowings from the Federal Reserve are related to the interest rate. Also, the Fed used a NBRoperating procedure to control the m oney stock from October 1979 to October 1982. Since the Fed was primarily targeting M l growth during this period, however, unanticipated M l growth may be a better measure o f the exogenous m onetary im pulse during this period. Alternative measures o f the monetary impulse are used to see whether estimates o f the respon siveness o f interest rates to monetary impulses are dependent on the variable used. Initially, the equation 6 (15) ATBR, = ot0 + + m-PV;- + 8 yV“ 2 aATBR, , + |3MVr i= 1 + e, 24This is similar to the multivariate time-series approach of Mish kin (1981) except that a distributed lag of the ATBR is included in all regressions. It is important to include all relevant variables that affect interest rates. Wickens (1982) has argued that if they are not included, the expectations cannot be efficient. Also, there was some experimentation with alternative lag lengths. The lags used here appeared to work well and pro duced white noise residuals. 25When (AM - AMe) is used, AM denotes the annualized first difference of the log of the variable. AM, however, is the first difference of the annualized growth rate of the variable. The same is true for all other variables. 26The unanticipated monetary, price and income variables are matched in the regressions. That is, if AM1 is used as the The results indicate considerable variability in the statistical significance o f the effect o f the m on etary variables on interest rates, both across time and across m onetary variables. During the entire period, there is a small but statistically significant negative effect for three o f the unanticipated m on etary variables. The largest statistically significant negative effect is obtained w hen A M I is used, but there is a statistically significant negative response o f interest rates when the unanticipated growth o f nonborrowed reserves is used, w hether it is m ea sured by ANBR or (ANBR - ANBRe). The results in tables 2 and 3 indicate that the responsiveness o f interest rates to m onetary im pulses is sensitive to the sample period. W hen pre-1974 data are used (table 2) the effect is statis tically significant only w hen the unanticipated change in the growth rate o f nonborrowed re- monetary variable, then AP and Ay are used as the corre sponding unanticipated price and income variables. 27The coefficients on the lagged dependent variable are not reported. In nearly every instance, they were jointly significant at the 5 percent level. 28Hafer and Hein (1982) date the break in money demand at 1973.04, while Lin and Oh (1984) date it at 1972.02. The United States formally broke from the Bretton Woods accord in late 1971. The Federal Reserve Open Market Committee stated a desire to place increased emphasis on the growth of certain monetary aggregates at its January 15,1970 meeting; Congress passed Resolution 133 requiring the Board of Governors to set longrun ranges for the aggregates on March 24, 1975. MAY/JUNE 1988 60 Table 1 Estimates of Equation 15:1959.08 -1987.06 MV“ AM1 AMB ANBR (AM1 - AM19) (A M B -A M B e) (ANBR-ANBR®) Constant .008 (0.28) .008 (0.30) .008 (0.29) .009 (0.30) .008 (0.28) .008 (0.29) .009 (0.31) .009 (0.31) .009 (0.31) .009 (0.31) .009 (0.33) .009 (0.32) MV“ -.0 1 5 * (3.68) -.0 1 6 * (3.79) -.0 0 0 (0.05) yVu 1 PV“ > R2 SEE .003 (1.25) — .014* (1.71) — .254 .5089 .250 .5103 .003 (1.37) .016* (1.85) — .223 .5194 .217 .5214 -.0 0 0 (0.06) -.0 0 5 * (3.49) -.004 * (3.74) -.0 0 7 (1.23) -.0 0 6 (1.04) .014 (1.51) .017 (1.89) -.0 0 9 * (5.41) -.0 1 0 * (5.94) .003 (1.31) — .0 1 1 .251 .5099 (131) — .249 .5107 .008* (2 .8 8 ) — .029* (2.46) — .242 .5129 .219 .5206 .009* (3.16) — .040* (3.36) — .260 .5069 .225 .5186 .008* (2.94) — .033* (3.00) — .320 .4860 .293 .4954 'Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. * Indicates statistical significance at the 5 percent level. serves is measured by (ANBR —ANBRe) and when PVUand yV" are omitted. Even in this case, h ow ever, the strength o f the effect is small. In contrast, there is a statistically significant negative effect during the latter period (table 3) w hen A M I or NBR, in either form, is the monetary variable. These results are interesting because they suggest that the response o f interest rates is stronger during the latter period, when the Fed claims to have paid more attention to m onetary aggregates and w hen Melvin (1983) reports that the effect vanishes. Finally, the coefficient for un 29This result is not too surprising in the case where the unantici pated variables are measured by the difference between actual and expected. It is usually assumed, either explicitly or implic itly, that in the case where the expectation-generating equa tions are jointly estimated with the “ structural” equation, the unanticipated components are mutually orthogonal. (Estimates indicate that this condition is reasonably satisfied for the speci fications used here). When these variables are measured in this way, the regressors of equation 15 are nearly mutually orthogonal. Consequently, the parameter estimates of one are not likely to be affected by the absence of the others. FEDERAL RESERVE BANK OF ST. LOUIS anticipated base growth measured by (AMB — AMB'), is significantly positive during this period. Both quantitatively and qualitatively, the results are similar w hether the unanticipated price or income variables are included. Accounting for the possible effect o f unanticipated inflation or in come growth does not appear to be important in measuring the effect o f unanticipated monetary growth on interest rates .28 The effects o f unantici pated inflation and incom e growth are highly sig nificant for the entire period, but they are much less so during the individual subperiods .30 “ This could be a manifestation of the heteroskedasticity in the data. In general, heteroskedasticity may cause the reported standard errors of the parameters of OLS to be biased, and they can be either too large or too small. 61 Table 2 Estimates of Equation 15:1959.08 -1973.09 MVU Constant AM1 .017 (0 .8 6 ) .017 (0 .8 8 ) .017 (0.87) .017 (0 .8 8 ) .017 (0.87) .017 (0 .8 8 ) .017 (0.89) .017 (0 .8 8 ) .017 (0 .8 8 ) .017 (0 .8 8 ) .017 (0.90) .017 (0.89) AMB ANBR (AM1 - AM1e) (AMB - AMBe) (A N B R -A N B R 6) MV“ yVu 1 .0 0 1 .0 0 1 (0.32) (0.56) — .0 0 1 PV U ' R2 SEE .007 (1.28) — .160 .2544 .162 .2542 .007 ( 1 .2 1 ) — .160 .2545 .162 .2541 .007 (1.19) — .160 .2544 .162 .2541 .017 ( 1 .6 6 ) — .172 .2527 .168 .2533 .013 (1.28) — .161 .2543 .162 .2542 .0 2 2 * (2 .2 0 ) — .198 .2487 .182 .2511 (0.16) .0 0 0 .0 0 1 (0 . 1 0 ) (0.54) — -.0 0 1 (0.30) -.0 0 0 (0 .2 1 ) -.0 0 0 (0.42) .006 (1 .1 0 ) .006 ( 1 .1 1 ) .0 0 1 (0.54) — .0 0 1 (0.37) — .0 0 1 .0 0 2 (0 .2 0 ) (0.82) — .0 0 2 (025) -.0 0 3 (1.82) - .004* (2 .0 2 ) .0 0 2 (1.07) — 'Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. * Indicates statistical significance at the 5 percent level. Because the results could be specific to the form o f equation 15, the equation 36 6 (IB) ATBR, = a 0 + 2 i= aATBR, , 1 + 2 i= frMV;' , + e„ 0 was estimated using the same data for the same periods .31 These results, reported in tables 4—G, are strikingly different from those in tables 1-3. For the entire period (table 4) there is no statistically significant, negative response o f interest rates, even initially, w hen A M I or AMB is used. M ore over, the sum o f the coefficients is significantly positive for both monetary variables. These results are consistent w ith those reported by Cagan and Gandolfi (1969), Brown and Santoni (1983) and Melvin (1983). W hen ANBR is used, however, there 31Cagan and Gandolfi (1969) used 38 lags, Melvin (1983) used 36 and Brown and Santoni (1983) used 24. Because of the long lags involved, it was necessary to delete the first three years from the entire estimation period and from the first sub period when (A M V -A M V e) is used as the monetary variable. is a significant initial negative response o f interest rates for the entire period, and the sum o f the coefficients is negative and significant. The results using the unanticipated monetary variable measured by IAMV —AMV') are consider ably different from those using AMV .32 For both M l and MB, few coefficients are significant and most o f these are positive. Also, w hile the sums o f the coefficients are positive, they are not statistically significant. W hen NBR is used, the initial coef ficient is negative and significant, but the sum o f the coefficients is positive and not significant. Most of the results for the pre-1974 period (table 5) are qualitatively the same as those for the entire period. One exception is for (ANBR —ANBRe), when the initial coefficient is negative but not significant 32OLS estimates of the standard errors of the coefficients are biased downward when unanticipated monetary variables are measured by (A M V -A M V e). Consequently, the reported t-ratios overstate the significance of the effect of unanticipated monetary impulses. See Pagan (1984) p. 234. MAY/JUNE 1988 62 Table 3 Estimates of Equation 15:1973.10-1987.06 MV Constant MVU yVu 1 PV“ ' R2 SEE AM1 -.0 1 5 (0.30) -.0 1 6 (0.30) -.0 1 3 (0.25) -.0 1 4 (0.26) -.0 1 4 (0.26) -.0 1 4 (0.27) - .0 1 4 (0.26) -.0 1 4 (0.26) -.0 1 4 (0.26) -.0 1 4 (0.26) -.0 1 4 (0.27) .014 (0.27) -.022* (3.44) - .0 2 2 * (3.45) .006 (1.17) .027 (1.65) .282 .6708 .274 .6745 -.0 0 2 .006 ( 1 .2 1 ) .227 .6958 — .219 .6996 AMB ANBR (AM1 - AM1e) (A M B -A M B ') (A N B R -A N B R ') (0.16) -.0 0 0 (0.03) - .006* (2.99) - .007* (3.29) -.0 1 3 (1.31) -.0 1 0 ( 1 .0 1 ) .030 ( 1 .6 8 ) .037* (2.07) -.010* (3.53) -.012* (4.15) — — — .028 ( 1 .0 2 ) .005 (0.91) — .0 2 0 .269 .6766 ( 1 .2 2 ) — .269 .6767 .0 1 1 * (178) — .044* (1.99) — .244 .6882 .224 .6973 .0 1 2 * (1.92) — .044* (1.97) — .261 .6805 .240 .6903 .009 (1.50) — .045* (2.16) .314 .6556 .296 .6641 — 'Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. * Indicates statistical significance at the 5 percent level. and the sum o f the coefficients is positive and sig nificant. The results for the post-1973 period (table 6 ) are different when NBR is used. The initial negative response o f interest rates is larger during the post1973 period and is statistically significant regard less o f h ow unanticipated nonborrow ed reserves are measured. The sums o f the coefficients, how ever, are not significantly different from zero. Thus, w hile the magnitude o f the negative effect is larger during this period, it is not permanent. The results for the M l and MB measures are similar to those o f the entire period. Tests o f Alternative Specifications Tables 1-6 show that the results are sensitive to the specification o f the m onetaiy variable and to “ Although not reported here, the results of the J-test applied to the specification given by equation 16 were also inconclusive. FEDERAL RESERVE BANK OF ST. LOUIS the sample period. Consequently, it is important to test which m onetary variable, if any, best ex plains changes in the interest rate. To this end, the specifications w ith alternative m onetary variables are tested against one another using the Davidson and MacKinnon (1981) J-test. In order for the test to favor specification A over specification B con clusively, the information in B must not be signifi cant when specification A is the null hypothesis and the information in specification A must be sig nificant when B is the null. Table 7 presents the test results which, though largely inconclusive, favor M l and NBR when un expected m oney is specified in AMV form. This is due solely to the post-1973 period, however. When the m onetaiy variables are specified in (AMV —AMVn) form, the results tend to favor NBR .33 Table 4 Estimates of Equation 16:1962.08 -1987.06 Lag AM1 A M 1 -A M 1 * Constant -0 .0 3 3 (1.09) -0 .0 0 3 (0.47) 0.037* (5.08) 0.033* (3.66) 0.042* (4.32) 0.030* (2.81) 0.033* (3.01) 0.034* (3.04) 0.032* (2.96) 0.033* (2.90) 0.033* (2.93) 0.036* (3.06) 0.046* (3.83) 0.042’ (3.37) 0.023 (1.83) 0.027* (2.18) 0.032* (2.60) -0 .0 0 6 (0.19) -0 .0 0 5 (0.80) 0.039* (6.24) 0.003 (0.43) 0.005 (0.75) - 0 .0 0 2 (0.25) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 .0 2 1 (1.64) 0.028* (2.27) 0.039* (3.11) 0.045* (3.55) 0 .0 0 1 (0.08) 0.016* (2.25) 0 .0 1 0 (1.38) 0.009 (1.24) 0.007 (1.07) 0.004 (0.51) 0 .0 1 2 (1.72) - 0 .0 0 2 (0.32) - 0 .0 2 0 * (2.92) 0.000 (0 .0 1 ) 0.009 (1.23) -0 .0 1 4 (1-97) 0.009 (1.18) 0.004 (0.57) -0 .0 0 3 (0.44) AMB -.0 2 8 (0.85) 0 .0 2 1 * (2 .0 1 ) 0.052* (3.48) 0.059* (3.19) 0.058* (2.77) 0.039 (1.77) 0.051* (2.26) 0.051* (2.33) 0.044* (2.07) 0.031 (1.43) 0.036 ( 1 .6 8 ) 0.047’ (2.19) 0.047* (2 .2 2 ) 0.055* (2.61) 0.040 (1.90) 0.054* (2.54) 0.045* (2.13) 0.049* (2.31) 0.058* (2.76) 0.064* (3.07) 0.072* (3.43) •Indicates statistical significance at the 5 percent level. ANBR A M B -A M B ' .033 (1.05) - 0 .0 1 0 * (5.73) -0 .0 0 9 * (4.28) -0 .0 0 6 * (2.47) - 0.008* (2 .8 8 ) -0 .0 0 7 * (2.48) - 0 .0 1 1 * (3.29) - 0 .0 1 1 * (2.97) - 0 .0 1 1 * (2.98) - 0 .0 1 1 * (2.69) - 0 .0 1 0 * (2.38) - 0 .0 1 1 ’ (2.63) - 0 .0 1 1 * (2.58) -0 .0 0 7 (1.64) -0 .0 0 9 * (2 .0 2 ) - 0 .0 1 0 * (2.06) -0 .0 0 9 (190) -0 .0 0 9 (1.92) - 0 .0 1 0 * (2.03) - 0 .0 1 1 * (2.37) - 0 .0 1 0 * (2.07) -.0 0 9 (0.28) 0.019 (1.65) 0.033* (2.87) 0.009 (0.75) 0.000 (0 .0 1 ) - 0 .0 1 2 (1.03) 0.026* (2 .2 0 ) 0 .0 2 1 (1.81) -0 .0 0 3 (0.29) - 0 .0 0 2 (0 .2 1 ) 0 .0 1 0 (0.81) 0 .0 2 (1.31) 0.007 (0.58) 0.014 (1.16) 0 .0 0 2 (0.14) 0.023* (1.98) 0.007 (0.60) 0.008 (0.69) 0.003 (0.28) 0.007 (0.60) 0.009 (0.78) 1 Lag A N B R -A N B R * .027 (0.81) - 0 .0 1 1 * (5.56) - 0 .0 0 2 (0.80) 0.003 (1.57) 0 .0 0 1 20 21 22 23 24 (0.26) 0 .0 0 1 (0.67) -0 .0 0 3 ( 1 .2 2 ) -0 .0 0 0 (0.09) - 0 .0 0 1 (0.47) 0.003 (1.54) 0 .0 0 1 25 26 27 28 29 30 (0.35) - 0 .0 0 1 31 (0.33) - 0 .0 0 1 32 (0.39) 0.005* (2.31) 33 0.000 34 (0.14) - 0 .0 0 2 35 (0.98) 0 .0 0 1 36 (0.36) - 0 .0 0 1 Sum of Lags (0 .6 8 ) - 0.037* (2 .8 6 ) 0.032* (2.53) 0.040* (3.13) 0.041* (3.18) 0.031* (2.39) 0.027* (2 .1 2 ) 0.026* (2.08) 0.023 (1.89) 0.023 (192) 0.024* (2 .1 0 ) 0.025* (2.36) 0 .0 2 2 * (2.16) 0.024* (2.40) 0.014 (1.60) 0 .0 2 1 * (2.62) 0.009 (1.30) 0.015* (2.59) AM1 -A M 1 * -0 .0 0 8 (1.18) - 0 .0 1 2 (1.74) 0 .0 0 2 (0.23) 0.004 (0.57) -0 .0 0 6 (0 .8 6 ) - 0 .0 0 1 (0.09) -0 .0 0 6 (0.80) -0 .0 0 8 (1.08) - 0 .0 0 1 (0.19) - 0 .0 0 2 (0.33) -0 .0 0 6 (0 .8 8 ) -0 .0 0 5 (0.65) 0.004 (0.53) -0 .0 0 4 (0.53) 0.007 (0.99) - 0.005 (0.73) AMB 0.065* (3.04) 0.059* (2.76) 0.066’ (3.09) 0.060* (2.77) 0.053* (2.48) 0.053* (2.47) 0.048* (2.23) 0.034 (1.61) 0.036 (1.71) 0.041* (2 .0 0 ) 0.031 (1.57) 0.034 (1.76) 0 .0 2 0 (1.13) 0 .0 2 2 (1.48) (1.30) 0.017 ( 1 .1 2 ) 0.019 (1.54) 0.013 (1-37) .043 (0.94) 1.645* (3.30) 0 .0 1 0 A M B -A M B ' ANBR - 0.003 (0.28) - 0 .0 0 2 (0.14) - 0.008 (179) -0 .0 0 9 (1.93) - 0 .0 1 0 * (2.18) -0 .0 0 9 * (2 .0 2 ) - 0 .0 1 1 * (2.33) -0 .0 0 7 (1.50) -0 .0 0 8 (1.74) -0 .0 0 9 * (2.17) - 0.009* (2.15) -0 .0 0 9 * (2.29) - 0.006 (1.72) -0 .0 0 6 (1.57) -0 .0 0 6 (1.83) -0 .0 0 5 (169) - 0 .0 0 1 (0.49) 0 .0 1 1 (1.03) 0.004 (0.36) 0.008 (0.69) 0 .0 1 2 (1.04) -0 .0 0 6 (0.49) -0 .0 1 7 (1.53) 0 .0 0 1 (0 .1 2 ) 0.004 (0.37) - 0 .0 1 2 (1.08) 0.005 (0.50) -0 .0 0 6 (0.51) -0 .0 0 5 (0.46) 0.000 (0 .0 2 ) 0.004 (0.37) -0 .0 1 3 ( 1 .2 1 ) A N B R -A N B R * 0 .0 0 1 (0.48) -0 .0 0 0 (0.15) - 0 .0 0 2 (0 .8 6 ) - 0 .0 0 0 (0 . 1 1 ) - 0 .0 0 1 (0.40) 0.004* (2.05) -0 .0 0 0 (0.15) - 0 .0 0 2 (0.72) -0 .0 0 0 (0.09) -0 .0 0 0 (0.16) 0.003 (148) 0 .0 0 1 (0.25) (0.57) -0 .0 0 0 (0 .0 2 ) -0 .0 0 0 (0 .2 1 ) 0.004 ( 1 .8 8 ) 0.003 (1.35) - 0.000 (0.17) -0 .3 0 4 * (2.77) (0.09) 0 .0 0 2 (0.62) 0.000 0 .0 0 2 (0 .8 6 ) - AM1 1.075* (3.76) .181 (1.89) .0 0 1 0 .0 0 2 (0.84) -0 .0 0 0 (0.06) F’ R* SEE 2.82’ .37 .4912 2.39* .34 .5025 F-statistic for the joint significance of the monetary variables. 1 .2 2 .24 .5374 0.99 .2 2 .5453 1.65* .28 .5237 1.65* .28 .5237 Table 5 Estimates of Equation 16:1962.08 -1973.09 Lag Constant 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 AM1 A M I - AM1' -.0 2 4 (1.03) .0 1 0 (0.47) 0 .0 1 2 0 .0 1 1 (1.72) 0.003 (0.38) 0.004 (0.39) 0.004 (0.43) 0.009 (0.81) 0.009 (0.79) 0.016 (1.50) 0.026* (2.35) 0.031* (2.62) 0.036* (2.92) 0.048* (3.78) 0.053* (4.12) 0.041* (3.12) 0.035* (2 .6 8 ) 0.023 (1.77) 0.025 (1.93) 0.018 (1.38) 0.030* (2 .2 1 ) 0.045* (3.39) 0.046* (3.41) (1.74) - 0 .0 0 1 (0.15) - 0 .0 0 2 (0.36) -0 .0 0 6 (0.81) 0 .0 0 2 0.23 -0 .0 0 4 (0.58) 0 .0 1 2 (1.67) 0.019* (2.70) 0.007 ( 1 .0 1 ) 0.007 (0 .8 8 ) 0 .0 1 2 (1.64) 0.006 (0.74) - 0.008 (1.08) - 0 .0 0 2 (0.30) -0 .0 0 6 (0.72) 0 .0 0 2 (0.23) -0 .0 0 9 (1.27) 0.005 (0 .6 8 ) 0.018* (2.57) AMB -.0 0 6 (0.23) -0 .0 0 7 (0.84) -0 .0 0 7 (0.58) -0 .0 0 5 (0.38) -0 .0 2 5 (166) -0 .0 0 9 (0.57) 0.003 (0.19) A M B -A M B ' .0 1 0 (043) - 0 .0 0 1 (0.08) - 0 .0 2 2 * (2.38) 0 .0 1 2 (1.26) 0 .0 1 2 (1.27) 0 .0 1 2 0 .0 1 0 (0.71) (1 1 0 ) 0.015 (1.69) 0.006 (0.67) 0.004 (0.43) 0.014 (1.56) 0 .0 2 1 (1.23) 0 .0 2 2 (1.29) 0.019 (1.14) 0.025 (1.49) 0.017 (1.03) 0.023 (1.40) 0.009 (0.53) 0 .0 1 2 (0.72) 0 .0 0 1 (0 . 1 2 ) 0.003 (0.36) -0 .0 1 3 (1.31) 0.006 (0.59) 0 .0 1 2 0 .0 1 0 (0.70) (0.56) (1 1 0 ) -0 .0 0 3 (0.29) 0 .0 2 1 0 .0 1 0 (1.24) 0.016 (0.92) ( 1 .1 2 ) 0.003 (0.32) 0.014 (1.56) 0 .0 1 0 0 .0 0 1 0 .0 2 1 (0 . 1 2 ) ( 1 .2 1 ) ‘ Indicates statistical significance at the 5 percent level. 0 .0 1 1 (1.23) 0.003 (0.37) ANBR .032 (1.48) -0 .0 0 4 * (2.33) -0 .0 0 8 * (2.70) -0 .0 0 9 * (2.37) - 0 .0 1 1 * (2.60) - 0 .0 1 0 * (2 .1 0 ) - 0 .0 1 2 * (2.42) - 0 .0 1 2 * (2.27) -0 .0 1 3 * (2.48) - 0 .0 1 2 * (2.13) - 0 .0 1 1 (1.95) -0 .0 1 3 * (2 .2 1 ) -0 .0 1 5 * (2.58) -0 .0 1 3 * (2.15) - 0 .0 1 1 (1.80) - 0 .0 1 0 (1.70) -0 .0 0 8 (1.51) - 0 .0 1 1 * (2.14) - 0 .0 1 1 * (2.24) - 0 .0 1 0 * (1.96) -0 .0 0 7 (1.47) Lag A N B R -A N B R .041 (193) -0 .0 0 3 (1.46) - 0 .0 0 1 (0.57) - 0 .0 0 0 (0 .0 2 ) - 0 .0 0 2 (0.98) 0 .0 0 2 20 21 22 23 24 25 (0.99) - 0 .0 0 0 26 (0 .1 2 ) 0 .0 0 2 27 (1 .1 1 ) 0 .0 0 2 (1.15) 0.005* (2.39) 0.004 ( 1 .8 6 ) - 0 .0 0 0 28 29 30 31 (0.04) - 0 .0 0 0 (0.16) 0.004* (2.15) 0.004* (2.15) 0.003 ( 1 .2 1 ) 0.003 (1.57) - 32 33 34 35 36 AM1 0.038* (2.83) 0.034* (2.57) 0.038* (2.94) 0.041* (3.15) 0.040* (3.09) 0.043* (3.40) 0.037* (2.99) 0.025* (2.05) 0.029* (2.43) 0.028* (2.49) 0.034* (3.11) 0 .0 2 1 (1.95) 0.031* (2 .8 6 ) 0.027* (2.61) 0.041* (4.15) 0.030* (3.53) 0.030* (4.80) A M 1 -A M 1 * -0 .0 0 8 (1.15) -0 .0 0 4 (0.58) 0.005 (0.65) -0 .0 0 3 (0.40) -0 .0 0 7 (0.91) 0.004 (0.60) -0 .0 0 4 (0.52) - 0 .0 1 2 (1.63) 0.004 (0.48) -0 .0 0 9 (1.15) 0 .0 1 1 (139) 0 .0 1 1 (1.35) 0 .0 1 1 (129) - 0 .0 1 1 (1.30) 0 .0 0 2 (0 .2 2 ) - 0 .0 0 2 (1.56) 0.014 (1.84) .049 (0.77) 0.582 (1.48) (1.17) 0 .0 1 2 (1.59) 0 .0 1 0 (131) 0 .0 0 2 (0.27) 0.008 (1 . 1 1 ) - 0 .0 2 2 A M B -A M B * (0.14) -0 .0 0 7 (0.80) 0.014 (1.72) 0 .0 2 2 * (2.60) -0 .0 0 9 (1.05) -0 .0 0 9 (0.99) 0 .0 0 0 - 0.007 (0.40) 0.017 ( 1 .0 0 ) 0.027 (1.62) 0.040* (2.45) 0.029 (1.72) 0.025 (1.56) (1.34) 0.009 (0.54) 0.015 (0.95) 0.027 (1.84) 0.028 (1.94) 0.028 (1.97) 0.014 (1 0 2 ) 0.023 (1.84) 0.038* (3.20) 0.026* (2.53) 0.015 (1.93) (0 .0 2 ) 0.003 (0.45) - AMB 0 .0 1 1 (0.18) - 0 .0 1 0 ( 1 .2 0 ) 0.006 (0.77) 0.013 (1.62) - 0 .0 0 2 (0 .2 1 ) 0 .0 0 1 ANBR - 0 .0 1 0 * (2.05) - 0 .0 1 1 * (2.15) -0 .0 0 8 (1.61) -0 .0 0 5 (0.93) -0 .0 0 7 (1.34) -0 .0 0 5 (1.05) -0 .0 0 6 ( 1 .2 0 ) -0 .0 0 3 (0.67) -0 .0 0 4 (1.03) - 0 .0 0 2 (0.50) -0 .0 0 5 (113) -0 .0 0 4 ( 1 .1 1 ) -0 .0 0 5 (1.25) - 0 .0 0 0 (0 . 1 1 ) 0 .0 0 2 (0.48) 0 .0 0 2 A N B R -A N B R ' - 0 .0 0 2 (0 .8 6 ) 0 .0 0 1 (0.40) 0.005* (2.48) 0.006* (2 .8 8 ) - 0 .0 0 2 (1.06) 0 .0 0 2 (0.67) 0 .0 0 1 (0.61) 0.005* (2.08) - 0 .0 0 0 (0 .2 1 ) 0.003 (1.38) 0 .0 0 1 (0.53) 0 .0 0 0 (0.13) 0 .0 0 1 (0.45) 0.005* (2.33) 0.003 (1.29) 0 .0 0 1 (0.61) 0.005* (2.28) (0.31) 0.006* (2.42) - .278* (2.06) .071* (3.12) 1.65* .32 .2351 1.97* .37 .2265 0 .0 0 0 (0 . 1 2 ) 0.003 (1.29) 0.006* (2.76) 0.004* (2 .0 2 ) Sum of Lags F’ R2 SEE 1.078* (3.62) . * .35 .2288 1 8 8 1.38 .27 .2435 'F —statistic for the joint significance of the monetary variables. 1.62* .31 .2362 .1 1 0 1.49 .29 .2400 Table 6 Estimates of Equation 16:1973.10-1987.06 Lag AM1 A M 1 -A M 1 ' Constant -.0 4 6 (0.92) -0 .0 0 8 (0.99) 0.050* (4.58) 0.044* (3.17) 0.055* (3.65) 0.039* (2.37) 0.045* (2.58) 0.042* (2.33) 0.032 (1.94) 0.030 (1.82) 0.031 (1.84) 0.026 (1.54) 0.041 * (2.33) 0.040* (2 .2 0 ) 0.013 (0.71) -.0 5 8 (0.94) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 .0 2 0 ( 1 .1 1 ) 0.028 (1.57) 0.013 (0.71) 0 .0 2 2 ( 1 .2 2 ) 0.036* (2 .0 0 ) 0.044* (2.44) - 0 .0 0 2 (0 .2 0 ) 0.062* (5.44) -0 .0 0 5 (0.40) 0 .0 2 0 (1.53) 0 .0 0 0 (0 .0 1 ) 0.008 (0.58) 0.024 (1.75) 0.006 (0.39) 0.016 (1.15) - 0 .0 0 1 (0 . 1 0 ) 0 .0 0 2 (0.17) 0.014 (1.05) -0 .0 0 3 (0 .2 1 ) -0 .0 3 4 ’ (2.55) 0.005 (0.34) 0 .0 1 2 (0.82) -0 .0 1 4 (0.98) 0 .0 2 0 (1.39) 0 .0 0 2 (0.14) 0.008 (0.57) AMB -.0 2 8 (0.52) 0.039* (2.18) 0.094* (3.69) 0 .1 0 0 * (3.02) 0 .1 1 1 * (2.92) 0.070 (1.73) 0.082* (2 .0 1 ) 0.076 (1.94) 0.060 (1.60) 0.032 (0 .8 6 ) 0.033 (0.89) 0.040 (1.08) 0.047 (1.28) 0.056 (1.55) 0.034 (0.96) 0.053 (1.50) 0.043 ( 1 -2 1 ) 0.059 (1.69) 0.066 (1.94) 0.082* (2.42) 0.091* (2 .6 8 ) A M B -A M B ' .0 0 1 (0 .0 1 ) 0.049 (1.97) 0.029 ( 1 .1 1 ) - 0 .0 0 2 (0.09) 0.030 (1.14) -0 .0 5 2 (1.93) 0.085* (3.11) 0 .0 2 0 (0 .6 6 ) -0 .0 3 3 (1 .1 1 ) -0 .0 0 6 (0 .2 1 ) 0.028 (105) -0 .0 0 5 (0 .2 0 ) 0.014 (0.55) 0.030 (1.17) -0 .0 1 4 (0.56) 0.056* (2.25) 0.026 ( 1 .0 0 ) 0 .0 2 1 (0.83) - 'Indicates statistical significance at the 5 percent level. ANBR 0 .0 1 2 (0.48) 0.041 ( 1 .6 6 ) 0 .0 0 1 (0.04) .0 2 0 (0.36) -0 .0 1 3 * (4.65) - 0 .0 1 0 * (3.04) -0 .0 0 5 (1.43) -0 .0 0 8 (1.97) -0 .0 0 7 (1.53) - 0 .0 1 1 * (2.25) - 0 .0 1 1 * (2.04) - 0 .0 1 0 (1.72) - 0 .0 1 0 (1.62) -0 .0 0 9 (1.43) - 0 .0 1 1 (1.65) - 0 .0 1 0 (1.49) -0 .0 0 5 (0.74) -0 .0 0 8 (1 2 0 ) -0 .0 0 8 (1.15) -0 .0 0 8 (1.13) -0 .0 0 8 (1.08) -0 .0 0 7 (0.94) - 0 .0 1 1 (1.48) -0 .0 0 9 (1.27) 1 Lag A N B R -A N B R ' -.0 2 9 (0.40) -0 .0 1 3 * (3.28) - 0 .0 0 0 (0.06) 0.004 (1.09) 0.004 ( 1 .0 2 ) 0 .0 0 2 20 21 22 23 24 0 .0 0 2 0 .0 2 2 26 (1.18) 0.018 (0.99) (0.55) 0 .0 0 1 27 (0.28) 0 .0 0 0 28 (0 .0 2 ) 0 .0 0 2 29 (0.59) - 0 .0 0 2 30 (0.58) - 0 .0 0 2 31 (0.46) - - 0 .0 0 0 32 (0 .1 0 ) 0.005 (1.26) 33 0 .0 0 2 34 (0.42) -0 .0 0 4 (1.05) - 0 .0 0 1 (0.38) - 0 .0 0 0 (0 . 1 1 ) -0 .0 0 3 (0.70) -0 .0 0 7 (1.77) - 0 .0 0 2 (0.42) 0.032 (1.73) 0.031 (1.65) 0.044* (2.37) 0.039* (2.08) 0.026 (1.35) 25 (0.37) - AM1 35 36 0 .0 1 2 (0.69) 0.014 (0.78) 0.016 (0.93) 0.015 (0.90) 0.014 (0.92) 0.018 (1.19) 0.009 (0.70) 0.015 (1.31) 0.006 (0.57) 0 .0 1 1 (1.26) Sum of Lags F1 R2 SEE 0.986* (2.38) 2.24* .40 .6137 AM1 - AM 1' AMB -0 .0 1 8 (1.29) -0 .0 1 3 (0.96) 0.093* (2 .6 8 ) 0.086* (2.43) 0 .1 0 1 * (2.84) 0.077* (2 .1 2 ) 0.069 ( 1 .8 8 ) 0.067 (1.81) 0.059 (1.57) 0.046 ( 1 .2 1 ) 0.041 (1.06) 0.037 (0.97) 0.024 (0 .6 6 ) 0.028 (0.81) 0.013 (0.41) 0.014 (0.49) 0 .0 0 0 (0 .0 1 ) 0.003 (0 .2 2 ) -0 .0 0 9 (0.65) 0.003 (0 .2 2 ) - 0 .0 1 1 (0.79) -0 .0 0 3 (0 .2 0 ) - 0 .0 0 1 (0.08) 0.003 (0.19) - 0 .0 1 1 (0.87) - 0 .0 0 2 (0.17) 0 .0 1 2 (0.94) 0 .0 0 0 (0 .0 0 ) 0 .0 1 0 - 0 .0 0 2 (0.75) -0 .0 0 3 (0 .2 1 ) 0.017 (1.31) (0.09) 0.009 (0.42) 0.003 (0.19) .115 (1.82) 2.034* (2.33) 1.72* .40 .6595 F-statistic for the joint significance of the monetary variables. 1 .1 0 .24 .6891 A M B -A M B * ANBR 0.003 (0 . 1 2 ) 0.007 (0.29) 0.013 (0.54) -0 .0 0 6 (0.80) -0 .0 0 9 (1.25) - 0 .0 1 0 (1.30) -0 .0 0 9 (1.27) - 0 .0 1 1 (1.49) -0 .0 0 6 (0 .8 6 ) -0 .0 0 8 (1.15) - 0 .0 1 1 (1.60) -0 .0 0 9 (1.44) - 0 .0 1 0 (1.55) -0 .0 0 7 ( 1 .2 0 ) -0 .0 0 7 (1.23) -0 .0 0 7 (1.29) -0 .0 0 7 (1.47) - 0 .0 0 2 (0.53) - 0 .0 1 1 (0.49) 0 .0 2 2 (0.94) 0.032 (1.40) -0 .0 3 2 (1.37) -0 .0 0 8 (0.36) -0 .0 1 8 (0.78) - 0 .0 0 1 (0.03) - 0 .0 2 0 (0.87) 0 .0 2 2 (0.94) - 0 .0 0 1 (0.06) -0 .0 0 7 (0.31) -0 .0 0 7 (0.30) 0.007 (0.33) -0 .0 1 6 (0.69) .289* (2 .0 0 ) 1.16 .30 .7109 A N B R -A N B R ' 0 .0 0 2 (0.26) -0 .0 0 3 (0.83) (0.50) -0 .0 0 3 (0 .8 6 ) -0 .0 0 3 (0.67) -0 .0 0 6 (1.49) -0 .0 0 3 (0 .8 8 ) 0.008 (1.93) -0 .0 0 5 (1.19) -0 .0 0 5 (1.17) - 0 .0 0 2 (0.42) - 0 .0 0 2 (0.55) -0 .0 0 3 (0.62) 0.003 (0 .6 6 ) - 0 .0 0 1 (0.32) -0 .0 0 3 (0.74) 0.004 (0.97) - 0 .0 0 1 (0.30) -0 .0 0 4 (0.73) -0 .2 9 8 (1.74) -.0 4 4 (1.28) 1 .1 0 1 .1 2 0 .0 0 1 .24 .6895 .30 .7149 66 Table 7 Results of the Davidson-MacKinnon J-test Estimation Periods Null/Alternative Hypotheses 1 959.081987.06 AM1/AMB AMB/AM1 AM1/ANBR ANBR/AM1 AMB/ANBR ANBR/AMB (AM1 - AM1 6)/(AMB - AMB6) (A M B -A M B 6)/(AM1 -A M 1 6) (AM1 - AM1 e)/(ANBR - ANBR8) (ANBR - ANBR*)/(AM1 -M 1 -) (AMB - AMB6)/(ANBR - ANBR6) (ANBR - ANBR6)/(AMB - AMB6) 1 959.081973.09 - .8 7 3.78* 3.15* 3.36* 3.59* - .1 2 .33 .31 .18 .04 .03 1.61 2.83* 0.53 3.36* -1 .3 7 3.59* .0 1 6.29* -2 .2 5 * 6 .2 2 * 2 .0 1 * 1 .0 2 3.58* 2.53* 3.03* 3.02* - .5 0 2.72* 1.46 4.15* -.7 5 4.25* 1.73 .2 0 -.8 6 1973.101987.06 'Indicates statistical significance at the 5 percent level. Estimates o f Equation 13 As a further test o f the robustness o f the results to the m odel specification, equations o f the gen eral form o f equation 13 are estimated. This speci fication has been estimated in such diverse ways and with such a w ide array of regressors that an exhaustive evaluation is difficult. Instead, the ap proach here relies on the fact that this specifica tion differs from the others primarily in that it has been estimated in level, rather than firstdifference, form ." Some studies include measures o f expected and unexpected inflation and unan ticipated m oney growth; others include expected inflation, some measure o f incom e growth, and a measure o f the change in the growth rate of money. In the form er studies, inflation expecta tions are generated as they are in the rational ex pectations models; in the latter, they are usually derived from survey data. Furthermore, Mehra (1985) and W ilcox (1983 a,b) measure the change in the m oney supply by the annualized growth rate o f m oney over a shorter period relative to its growth rate over a longer period. tions o f this specification. These equations are 6 (17) TBR, = ct0 + 1 aJBR, ; + (3LIQ, i= l + |xAP, + 5Ay,+ XP, + e, and 6 (18) TBR, = ot0+ 2 aJBR, ,+ P(A M V -A M V '), i= l + jx( AP —A Pe)t + S( Ay —Ay®), + A P ' + e, Consequently, two equations are estimated to capture the essence, if not the exact form, o f varia LIQ is the negative o f the difference between the annualized growth rate o f M l during the last three months and its annualized growth rate over the prior 1 2 months, AP is the change in the growth rate o f the price level and Ay is the change in level o f the industrial production index. Because equa tion 18 includes APf, the estimated standard errors o f AP; from the usual two-step estimator o f equa tion 18 are biased. Consequently, equation 18 is estimated using a full-information, maximumlikelihood (FIML) m ethod used by Mishkin (1981, 1982).33 "O ne exception to this is Peek who, although he specified the equation in level form, appears to have estimated it in firstdifference form. See Peek (1982) p. 986. restrictions. Also, because equation 18 includes a distributed lag of the level of TBR, the equations used to generate these expectations are modified to include the level of interest rates. 35Equation 18 is estimated simultaneously with the equations that generate the expected rates of monetary growth, inflation and real output growth, imposing the implied cross-equation FEDERAL RESERVE BANK OF ST. LOUIS 67 Table 8 Estimates of Equation 17 s a > Constant LIQ AP Ay 1 P’ R2 SEE .040* (3.92) .042* (4.16) .044* (4.23) .970 .5141 .970 .5185 .970 .5264 .975 .2443 .973 .2449 .974 .2420 .944 .6732 .947 .6703 .940 .6947 1 9 6 0 .0 5 - 1987.06 M1 MB NBR -.0 0 3 (0.04) -.0 2 8 (38) .035 (.047) .034* (4.25) .051* (3.53) -.0 0 3 (1.67) -.0 0 4 (0.37) -.0 0 3 (0.27) -.0 0 3 (0.29) .067* (3.38) .077* (3.87) .068* (3.30) 1 9 6 0 .0 5 - 1973.09 M1 MB NBR .145 ( 1 .8 8 ) .156* (2 .0 1 ) .151* (2 .0 1 ) .006 (0 .8 6 ) .0 0 0 (0 .0 2 ) -.0 0 5 (1.93) -.0 1 1 (1-35) -.0 1 1 (1.29) .006 (0.47) .006 (0.48) -.0 1 1 -.0 0 1 (1.29) (0 . 1 0 ) .034* (2.72) .034* (2.70) .032* (2.55) 1 9 7 3 .1 0 - 1987.06 M1 MB NBR -.0 8 5 (0.44) - .1 5 3 (0.79) -.0 4 6 (0.23) .042* (3.27) .091* (3.48) -.0 0 0 (0 .0 1 ) -.0 0 2 (0.09) -.0 0 2 .0 0 1 (0.81) (0.06) .131* (3.34) .144* (3.72) .146* (3.55) .049* (3.04) .052* (3.31) .056* (3.43) ’Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. ’ Indicates statistical significance at the 5 percent level. Table 8 presents estimates o f equation The results indicate that interest rates show no statisti cally significant negative response; however, the coefficient for NBR for the pre-1974 period is nearly significant at the 5 percent level. The signifi cant positive relation between LIQ and the level of the Treasury bill rate during the entire period, when either M l or MB is the monetary variable, is attributable solely to the post-1973 period. The magnitude of the coefficients on AP and Ay and, in the case o f A y its statistical significance, *Som e econometric issues should be addressed because equations are estimated in both level and first-difference form. The issues center around whether the variables on both the left- and right-hand sides of the equations are stationary. If the right-hand-side variables are non-stationary, then the reported standard errors from the level equation will be incorrect even if the left-hand-side variable is stationary. On the other hand, if both the left- and right-hand-side variables are stationary, the reported standard errors from the first-difference specification will be inconsistent because the error term from this equation will be serially correlated. Most tests of macroeconomic timeseries variables, like the ones used here, suggest that they are not stationary in the levels, e.g., Nelson and Plosser (1982); however, these tests are not powerful against the alternative depends on the period. The positive coefficient on P is statistically significant regardless o f the sam ple period; however, the estimated magnitude o f the coefficient is sensitive to the sample period. Table 9 presents estimates o f equation 18. Unan ticipated inflation is significant in all three periods only w hen NBR is the m onetaiy variable. Both unanticipated incom e and inflation are significant during the post-1973 period for all monetary vari ables. Surprisingly, anticipated inflation is signifi- hypothesis that the data are generated by a stationary AR process with close to a unit root. In this instance, estimates of the level equation would be appropriate, though the sample size necessary for appropriate inferences might be large. Because the objective is to see whether the results are sensi tive to the specification of the equation, we are agnostic about whether the level or first-difference specification is “ best.” Because of the lags involved in the construction of LIQ, it was necessary to shorten the estimation period for the first two periods. They begin at 1960.05, rather than 1958.07. MAY/JUNE 1988 68 Table 9 FIML Estimates of Equation 18 for the three periods MV“ Constant A M V-A M V ' AP-AP* > A y -A y *1 AP* .008* (3.26) .0 1 1 * (4.31) .009* (3.65) .069* (5.77) .018 (1.46) .013 (1.03) .0 0 0 .059* (3.54) .061* (3.73) .024 (1.58) 1 9 5 9 .0 8 - 1987.06 M1 MB NBR .060 (0.95) .054 (0.81) .081 (1.24) -.0 0 8 (1.58) .016 (1.94) -.011* (6 .6 8 ) .009 (0.93) .050* (4.51) .039* (3.71) 1 9 5 9 .0 8 - 1973.09 M1 MB NBR .189* (2.69) .183* (2.55) .144* (2.08) .009 (1.62) .003 (0.48) - .003* (2 .1 0 ) .014 (1.49) .013 (1.28) .024* (2.51) (0 .0 0 ) .0 0 1 (0.42) .0 0 2 (1.09) 1 9 7 3 .1 0 - 1987.06 M1 -.1 8 8 (0.91) MB -.0 2 0 NBR (0.08) .193 (1.08) - .027* (3.43) .036* (2.32) -.0 1 5 * (5.60) .105* (6.19) .083* (4.38) .058* (3.13) .0 2 1 * (4.33) .0 2 1 * (4.06) .0 1 0 * (1.92) - .0 3 4 (161) - .0 1 3 (0 .6 8 ) .0 0 0 (0 .0 2 ) 'Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. 'Indicates statistical significance at the 5 percent level. cant only during the pre-1974 period, and then only w hen M l or MB is used. With respect to the responsiveness o f interest rates to m onetary changes, the results are consist ent with those reported in tables 1-6. A significant negative effect is obtained during all three periods only w hen NBR is the m onetary variable. M ore over, the effect is larger during the post-1973 pe riod, when a significant negative effect is also ob tained with M l as the monetary variable. Hence, the results are similar w hether the interest rate is specified in level or first-difference form. The Responsiveness o f Interest Rates and Monetary Control The responsiveness o f interest rates should be greatest during periods when the Federal Reserve 37Cunningham (1987) and Cunningham and Hardouvelis (1987) also use weekly data and proxy changes in prices by the BLS 2 2 -commodity spot price index and income by unemployment claims. They acknowledge the weakness of these proxies and FEDERAL RESERVE BANK OF ST. LOUIS is attempting to control money. Since the Fed was attempting to control M l through a nonborrowedreserves operating procedure from October 1979 to October 1982, more precise estimates o f the responsiveness o f interest rates should be ob tained during this period. The lim ited number of monthly observations prevents using specifica tions w ith a large num ber o f parameters; however, the number of observations can be expanded by em ploying weekly data. The w eekly time period has the added advantage that the responsiveness o f interest rates to m onetary changes is even less likely to be contaminated by incom e and inflation expectations effects. Unfortunately, using weekly data precludes the incom e and price variables .37 Previous results, however, indicate that a statistically significant report no direct evidence consistent with a strong response of interest rates. 69 Table 10 Estimates of Equation 15 Using Monthly Data: 1979.10 - 1982.09 MV“ Constant MV" yVu' PV" R2 SEE AM1 .018 (0.08) - .040* (2.03) -.0 3 8 ( 1 .8 8 ) .007 (0.15) .018 (0.39) -.0 4 1 * (4.98) -.0 4 1 * (4.91) -CD40 (1.09) .017 (0.49) .094 ( 1 .2 2 ) .157* (2.15) - .053* (4.47) - .057* (4.53) .023 (1.13) .086 (1.49) .341 1.2533 — — .300 1.2930 .026 (1.17) .069 (1.06) .238 1.3485 — — .215 1.3682 .039 (0 .8 8 ) .610 .9650 — .576 1.0061 .256 1.3320 .218 1.3661 .398 1.1984 — .323 1.2707 .106 (1.64) .606 .9698 — .545 1.0416 .0 0 2 (0 .0 1 ) AMB .017 (0.07) .008 (0.04) ANBR .006 (0.04) .004 (0 .0 2 ) (AM1-AM16) .063 (0.28) .006 (0.03) (AMB-AMB6) .029 (0.14) .087 (0.40) (ANBR-ANBR6) .109 (0 .6 6 ) .065 (0.37) .029* (1.84) — .0 2 1 (0.79) — — .046* (1.95) — .035* (1.89) — .162* (1.78) .164* (1.78) 'Since the coefficients on these variables are hypothesized to be positive, the significance tests are one-tailed. ’ indicates statistical significance at the 5 percent level. effect is just as likely to show up in relatively sim ple and parsimonious specifications like equation 15. Also, the results indicate that the significance o f the effect is relatively unaffected by the form of the unanticipated m onetaiy variable. Conse quently, specifications like equations 15 and 16 (without the price and incom e variables) can be used to estimate the responsiveness o f interest rates to changes in the money stock with weekly data. Estimates o f equation 15 using monthly data for the period from 1979.10 to 1982.09 are presented in table 10. They are similar to those for the post1973 period. When A M I is the unanticipated m on etary variable, the coefficient is negative and sig nificant at the 5 percent level if unanticipated output and inflation are included, and marginally insignificant if they are not. For MB, the coefficient is positive and statistically significant only if (AMB —AMBe) is used and the other variables are excluded. W hen NBR is used, however, the coef ficient is negative and highly significant regardless o f w hether the other variables are included. Fur thermore, the estimated coefficients are larger than those obtained for the entire post-1973 p e riod, and the adjusted R2 is about twice that o f the other monetary aggregates. These results are in keeping with the nonborrowed-reserves operating procedure used during the period. Nevertheless, the coefficients are small, indicating that a 1 per cent increase in the growth rate o f nonborrowed reserves results in an about four to six basis points decline in the m onthly Treasuiy bill rate .38 Table 11 presents results using weekly data .39 ^See Thornton (1988) for a discussion of the borrowed-reserves operating procedure. 39An equation similar to 16 was also estimated using weekly data. The results are not qualitatively different from those reported in table 1 1 . MAY/JUNE 1988 70 Table 11 Estimates of Equation 15 Using Weekly Data: October 3, 1979-October 6,1982. Monetary Variable AM1 AMB ANBR (AM 1-A M 1s) (AMB-AMB*) (ANBR-ANBR*) Constant - .008 (0.18) -.0 0 8 (0.18) -.0 0 8 (0.18) - .0 0 8 (0.18) -.0 0 8 (0.18) -.0 0 8 (0.18) MVU -.0 0 0 R2 SEE .085 .5843 .084 .5844 .090 .5826 .088 .5831 .084 .5843 .098 .5801 (0.30) -.0 0 0 (0 .1 1 ) -.0 0 0 (0.97) -.0 0 2 (0.82) -.0 0 1 (0.27) -.0 0 1 (1.50) 'Indicates statistical significance at the 5 percent level. There is no statistically significant response of equation 15 without the price and incom e vari ables, regardless o f the monetary variable used. The results suggest that interest rates do not re spond over a period as short as a week, but do respond over a period as long as a m onth .40 interest rates to m onetary changes using alterna tive specifications that have been used in the liter ature and alternative monetary variables. The equations are estimated over the same time peri ods using the same data. Several interesting results emerge from this study. One possible reason for the disparity between the weekly and monthly results is that the data are averages o f daily figures and the averaging process might mask the response o f interest rates when weekly data are used .41 Consequently, the equa tions using weekly data w ere re-estimated with the change in the Treasury bill rate measured by the difference in the Treasury bill rate on consecu tive Wednesdays. Though not reported here, the results are qualitatively the same as those shown in table 11. Consequently, the insignificant re sponse o f interest rates is not due to averaging. First, estimates o f the response o f interest rates are relatively insensitive to the specification em ployed; they are, however, sensitive to the m one tary variable used. A significant negative response o f interest rates is most likely obtained if nonbor row ed reserves is used as the monetary variable. SUMMARY AND CONCLUSIONS This article estimates the responsiveness of 40Hardouvelis (1987) estimates an equation similar to equation 16 using quarterly data for the period 1979.04 to 1982.03 and reports a very large negative and statistically significant effect of unanticipated money on the three-month Treasury bill rate. He finds no significant effect for the 11 quarters prior to 1979.04 or during the 12 quarters after 1982.03. He interprets this as evidence of a strong liquidity effect during the period when the Fed was targeting the money stock. Since he does not adjust for the credit controls during the first and second quarters of 1980, however, his atypically large interest rate response may be due to unusual movements in money and interest rates during these quarters. For example, the money http://fraser.stlouisfed.org/ FEDERAL RESERVE BANK OF ST. LOUIS Federal Reserve Bank of St. Louis Second, a negative an d statistically significant relationship between M l or nonborrow ed reserves and interest rates is more likely to be obtained during periods when the Fed was placing greater emphasis on m onetary aggregates. The most con sistent and statistically significant negative effect is obtained using nonborrow ed reserves, a monetary variable that is likely to reflect the independent actions o f the Federal Reserve. Nevertheless, the fact that there is a significant effect using nonbor- stock decreased at a 5.9 percent annual rate during the first quarter of 1980, while the three-month Treasury bill rate in creased by 316 basis points (measured as Hardouvelis does from the last month of the quarter). The money supply in creased at a 2 1 percent rate during the second quarter of 1980 and the Treasury bill rate declined by 813 basis points. 41The monthly data used here are also averages of daily figures. Mishkin (1982) argues that misleading results about market efficiency can be obtained using averaged data, and reports that he obtained substantially worse fits when he estimated his equations using quarterly averaged data. 71 row ed reserves regardless o f w hether the Fed is concerned about the m oney stock or interest rates is anomolous. Third, estimates o f the responsiveness o f inter est rates are sensitive to the time period chosen. Generally, there is no statistically significant re sponse o f interest rates from 1958.08 to 1973.09 regardless o f the m onetaiy variable used. In con trast, a statistically significant negative effect is obtained using both M l or nonborrow ed reserves after 1973.09. Fourth, the results are sensitive to the periodic ity o f the data. In particular, in the specifications estimated over the period from October 1979 to October 1982, there is a significant negative effect w hen monthly nonborrowed reserves are used, but not when weekly nonborrowed reserves are used. Finally, the evidence shows that even when there is a significant negative response o f interest rates, the measured response is small. REFERENCES Blinder, Alan S., and Stanley Fischer. “ Inventories, Rational Expectations and the Business Cycle,” Journal of Monetary Economics (November 1981), pp. 277-304. Brown, W. W., and G. J. Santoni. “ Monetary Growth and the Timing of Interest Rate Movements,” this Review (August/ September 1983), pp. 16 -25 . Cagan, Phillip. The Channels of Monetary Effects on Interest Rates (NBER, 1972). Cagan, Phillip and Arthur Gandolfi. “The Lag in Monetary Policy as Implied by the Time Pattern of Monetary Effects on Interest Rates,” American Economic Review (May 1969), pp. 277-84. Carr, Jack, and Michael R. Darby. 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First Boston Working Paper 8 6 -2 8 (1986). ----------------“ Monetary Policy and Short-Term Interest Rates: New Evidence on the Liquidity Effect,” Economics Letters (1987) pp. 6 3 -66 . Hoffman, Dennis L., and Don E. Schlagenhauf. “ Real Interest Rates, Anticipated Inflation, and Unanticipated Money: A Multi-Country Study,” Review of Economics and Statistics (May 1985), pp. 284-96. Lin, Kuan-Pin and John S. Oh. “ Stability of the U.S. Short-Run Money Demand Function, 19 59-81,” Journal of Finance (December 1984), pp. 1383-96. Makin, John H. "Real Interest, Money Surprises, Anticipated Inflation and Fiscal Deficits,” Review of Economics and Statis tics (August 1983), pp. 374-84. Mehra, Yash. “ Inflationary Expectations, Money Growth and the Vanishing Liquidity Effect of Money on Interest: A Further Investigation.” Federal Reserve Bank of Richmond Economic Review (March-April 1985), pp. 2 3 -25 . Melvin, Michael. “ The Vanishing Liquidity Effect of Money on Interest: Analysis and Implications for Policy,” Economic Inquiry (April 1983), pp. 188-202. Mishkin, Frederic S. “ Monetary Policy and Long-Term Interest Rates: An Efficient Markets Approach,” Journal of Monetary Economics (January 1981), pp. 2 9 -55 . ----------------“ Monetary Policy and Short-Term Interest Rates: An Efficient Markets-Rational Expectations Approach,” Jour nal of Finance (March 1982), pp. 6 3 -72 . Nelson, Charles R., and Charles I. Plosser. “Trends and Random Walks in Macroeconomic Time Series: Some Evi dence and Implications,” Journal of Monetary Economics (September 1982), pp. 139-62. Niehans, Jurg. “ Classical Monetary Theory, New and Old," Journal of Money, Credit and Banking, (November 1987), pp. 409-24. Pagan, Adrian. "Econometric Issues in the Analysis of Regres sions with Generated Regressors,” International Economic Review (February 1984), pp. 221-47. _________ and Gikas A. Hardouvelis. “Temporal Aggregation, Monetary Policy, and Interest Rates,” Federal Reserve Bank of Atlanta Working Paper 8 7 -0 4 (May 1987). Patinkin, Don. Money, Interest, and Prices, 2nd ed., (Harper and Row, 1965). Davidson, Russell, and James G. MacKinnon. “ Several Tests for Model Specification in the Presence of Alternative Hypoth eses,” Econometrica (May 1981), pp. 781-93. Peek, Joe. “ Interest Rates, Income Taxes, and Anticipated Inflation,” American Economic Review (December 1982), pp 980-91. Dwyer, Gerald P. “Are Expectations of Inflation Rational or Is Variation of the Expected Real Interest Rate Unpredictable?" Journal of Monetary Economics (July 1981), pp. 5 9 -8 4 . Peek, Joe and James A. Wilcox. “ Monetary Policy Regimes and The Reduced Form for Interest Rates,” Journal of Money, Credit and Banking (August 1987), pp. 273-91. Fisher, Irving. 1930). Friedman, Milton. “The Role of Monetary Policy,” American Economic Review (March 1968), pp. 1-17. Robinson, Kenneth J. “ The Effect of Monetary Policy on LongTerm Interest Rates: Further Evidence from an EfficientMarkets Approach,” Federal Reserve Bank of Dallas Eco nomic Review (March 1988), pp. 10-16. Gibson, William E. “The Lag in the Effect of Monetary Policy on Income and Interest Rates,” Quarterly Journal of Eco nomics (May 1970a), pp. 288-300. Sargent, Thomas J. “ Commodity Price Expectations and The Interest Rate,” The Quarterly Journal of Economics (February 1969), pp. 127-40. The Theory of Interest (New York: Macmillan, MAY/JUNE 1988 72 _________ “ Anticipated Inflation and The Nominal Rate of Interest,” The Quarterly Journal of Economics (May 1972), pp. 21 2-2 5. Thornton, Daniel L. “ Simple Analytics of the Money Supply Process and Monetary Control,” this Review (October 1982), pp. 2 2 -3 9 . _________ “ Monetizing the Debt,” this Review (December 1984), pp. 3 0 -4 3 . _________ “The Borrowed-Reserves Operating Procedure: Theory and Evidence,” this Review (January/February 1988), pp. 3 0 -5 4 . FEDERAL RESERVE BANK OF ST. LOUIS Wickens, M.R. “The Efficient Estimation of Econometric Models with Rational Expectations", Review of Economic Studies (1982), pp. 5 5 -6 7 . Wilcox, James A. “ Why Real Interest Rates Were So Low in the 1970s,” American Economic Review (March 1983a), pp. 4 4 -5 3 . _______ “ The Missing Fisher Effect on Nominal Interest Rates in the 1950s," Review of Economics and Statistics (1983b), pp. 64 4-4 7. 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