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Review Vol. 69, No. 1 January 1987 5 Does U.S. M on ey Growth Determ ine M oney Growth in Other Nations? 15 Ik\ R eform and Investment: H ow Big an Im pact? T h e Review is p u b lis h e d 10 tim e s p e r y e a r b y th e R e se a rch a n d P u b lic I n f o r m a t io n D e p a r tm e n t o f th e F e d e ra l R eserve R a n k o f St. L o u is . S in g le -c o p y s u b s c rip tio n s a re a v a ila b le to th e p u b lic f r e e o f c h a rg e . M a il re q u e s ts f o r s u b s c rip tio n s , b a c k issues, o r a d d re s s c h a n g e s to : R e se a rch a n d P u b lic In f o r m a t io n D e p a rtm e n t, F e d e ra l R eserve R a n k o f St. Ix ju is , P.O. R o \ 442, St. L o u is , M is s o u r i 63166. T h e vie w s e x p re s s e d a re th o s e o f th e in d iv id u a l a u th o r s a n d d o n o t n e c e s s a rily r e fle c t o ff ic ia l p o s itio n s o f th e F e d e ra l R eserve R a n k o f St. L o u is o r th e F e d e ra l R eserve S yste m . A r tic le s h e r e in m a y be r e p r in t e d p r o v id e d th e s o u rc e is c re d ite d . P lease p r o v id e th e R a n k's R e s e a rc h a n d P u b lic In f o r m a t io n D e p a r tm e n t w ith a c o p y o f r e p r in t e d m a te ria l. Federal Reserve Bank of St. Louis Review January 1987 In This Issue . . . There have been few studies o f the relationship between m oney growth rates across countries. Yet assessing the impact of, say, the U.S. m oney growth rate on other nations’ m oney growth rates is important because o f its implication about the transmission o f monetary-induced inflation between countries. In the first article o f this Review, "Does U.S. M oney Growth Determine M oney Growth in Other Nations?” Richard G. Sheehan reviews the potential relation ships between two countries' m oney growth rates under fixed and flexible exchange rate regimes. A standard m odel suggests that increases in U.S. m oney growth should have produced increases in foreign m oney growth under fixed exchange rates. If foreign monetary authorities took full advantage o f the insulat ing properties o f flexible exchange rates, however, U.S. and foreign m oney growth should be independent. Using the Haugh test for independence, Sheehan finds that U.S. and foreign m oney growth rates generally w ere related under fixed exchange rates; moreover, m oney growth in many countries has been indepen dent o f U.S. m oney growth during the floating exchange rate period. The recent Tax Reform Act o f 1986 has drawn significant criticism for its treatment o f capital investment incentives. M any economists have argued that the new tax system w ill lead eventually to a sharp reduction o f productive capital in the United States. In the second article in this Review, “Tax Reform and Investment: H ow Big an Im pact?” Steven M. Fazzari analyzes several m ajor changes in the tax system that affect corporate capital spending incentives. Fazzari considers h ow investment tax credits, tax depreciation schedules and the corporate tax rate affect the after tax cost o f capital for a variety o f asset classes. The recent changes in these aspects of the tax system are discussed in an integrated framework that illustrates their combined effect on the cost o f capital. The author concludes that the after-tax cost o f capital will rise as a result o f tax reform, which w ill reduce the long-run capital stock in the United States. H ow big the reduction w ill be, however, is uncertain. Fazzari shows that, under plausible assumptions, the changes need not be as dramatic as many analysts predict. 3 JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS Does U.S. Money Growth Determine Money Growth in Other Nations? Richard G. Sheehan T HE money-inflation relationship has been exam ined extensively for a variety o f economies resulting in a consensus that m oney growth has had a significant and positive impact on inflation.1A related, but little studied issue, is the relationship between m oney growth rates across countries. This issue is important for assessing the extent to which inflation pressures have been transmitted from country to country. In this paper w e attempt to ascertain w hether U.S. m oney growth has had identifiable impacts on m oney growth in other industrial countries. W e first consider w hy U.S. m oney growth might exert effects on foreign m oney growth under both fixed and flexible exchange rate regimes. W e then present some empirical evi dence on the significance o f this relationship. If, for example, U.S. m oney growth influences the actions o f foreign central banks and, therefore, foreign m oney growth, it also influences foreign inflation. Thus, rapid U.S. m oney growth may lead both to a higher U.S. inflation rate and to higher inflation rates around the world. In other words, focusing solely on the U.S. impacts o f rapid U.S. m oney growth could substantially understate its total effects.2 PREVIOUS STUDIES OF MONETARY LINKAGES Richard G. Sheehan is an economist at the Federal Reserve Bank of St. Louis. Sandra Graham provided research assistance. 'For example, see Cuddington (1981), DyReyes, Starleaf and Wang (1980), Genberg and Swoboda (1977), Gutierrez-Camara and Hup (1983), Laidler (1976), Mills and Wood (1978), Mixon, Pratt and Wallace (1980), Pearce (1983), Swoboda (1977) and Wahlroos (1985). 2We ignore the possible existence of a direct relationship from U.S. money growth to foreign inflation. For theoretical arguments on the existence of such an effect, see Aukrust (1977) and Bordo and Choudhri (1982). Since the money-inflation relationship has been ex amined in detail elsewhere, this article focuses solely on the link between U.S. and foreign m oney growth rates. This latter relationship has received compara tively little attention. Feige and Johannes (1982) used causality tests to examine the U.S. money-foreign m oney relationship during the fixed exchange rate period. They found m ixed results; U.S. m oney growth influenced m oney growth in Australia, France and Germany but had no impact in Norway or Sweden. Batten and Ott (1985) used a small structural m odel to examine this relationship during the floating ex change rate period. They found that U.S. money growth influenced m oney growth rates in Canada, Germany, Japan, the Netherlands and possibly the United Kingdom; m oney growth rates in France, Italy and Switzerland, however, w ere unaffected by U.S. 5 FEDERAL RESERVE BANK OF ST. LOUIS m oney growth. In a study spanning both fixed and floating exchange rate periods, Sheehan (1983) found significant cross-country differences, with U.S. m oney growth (M l) influencing Australian and German m oney growth but having no discernable impact on m oney growth in Canada, Italy, Japan and the United Kingdom.3 Here, w e re-examine the U.S. moneyforeign m oney relationship using a com m on m ethod ology to analyze the fixed vs. floating exchange rate periods, extending the analysis to a broader group of countries and updating the analysis through 1985. WHY SHOULD U.S. AND FOREIGN MONEY GROWTH BE RELATED? THEORETICAL ISSUES The theoretical relationship between U.S. and for eign m oney growth may differ substantially depend ing upon the exchange rate regime. Fixed Exchange Rate Regime For a fixed exchange rate system, traditional models o f the monetary approach to the balance o f payments predict that if the United States is the reserve currency country, an increase in the U.S. m oney supply leads to increased m oney stocks in other open econom ies.4 To see why, consider the sequence o f events that typically follows an increase in U.S. m oney growth. Initially, the increase causes an excess supply o f U.S. m oney and an excess U.S. dem and for goods and capital. This excess dem and results in simultaneous inflows o f goods and services to the United States and outflows o f funds from the United States to the foreign economy. Attempts to convert some o f these dollars to foreign assets result in a low er exchange rate (the price o f the dollar in terms o f the foreign currency) in the absence o f any intervention by the monetary p o li cymakers. To maintain the exchange rate, the foreign monetary authority, and perhaps the Federal Reserve as well, must purchase dollars with foreign assets. The foreign central bank affects these purchases by in- JANUARY 1987 creasing its ow n monetary base and, as a result, its own m oney stock.5 There is a potentially important qualification, h ow ever, to this traditional approach to the transmission mechanism from U.S. m oney growth to foreign m oney growth under fixed exchange rates. M cKinnon (1982) has advanced the so-called currency substitution ar gument based on desired shifts in asset holdings be tween U.S. and foreign-denom inated assets. Assume preferences shift from holding foreign-denom inated assets to holding dollar-denom inated assets, perhaps in response to changes in perceived long-run produc tivity growth. Simply to accomm odate these changes and prevent exchange rate changes under fixed ex change rates, the Federal Reserve w ould have to in crease the U.S. m oney stock, or the foreign monetary authority w ould have to decrease the foreign m oney stock, or some combination o f the two. Thus, in this case, the U.S. and foreign m oney stocks w ou ld move generally in opposite directions.6 W hether this nega tive currency substitution effect is sufficiently large enough or occurs frequently enough to offset or over come entirely the traditional positive effect is an em pirical question.7 Floating Exchange Rate Regime In the traditional m odel o f floating exchange rates, the foreign econom y is insulated from U.S. m oney growth because the foreign monetary authority is not comm itted to buying (or selling) dollars at any fixed rate. Floating exchange rates, therefore, enable foreign monetary policymakers to base their policy actions on variables other than the exchange rate. An increase in the U.S. m oney supply, assuming dem and constant, simply leads to an excess supply o f dollars, a higher rate o f U.S. inflation and downward pressure on the exchange rate. Thus, if monetary policymakers fully take advantage o f the insulating properties o f floating 5The foreign monetary base and money stock would not increase if these purchases were sterilized by foreign monetary authorities. See Batten and Ott (1984) for a detailed discussion of the ability of foreign monetary authorities to sterilize. 3For results for individual countries, see Layton (1983) and Pearce (1983). “For example, see Barro (1984), pp. 536-39, Frenkel (1986) or Swoboda (1977). This statement assumes fiscal policy is devoted to other goals. A typical assumption is that monetary policy is better suited to deal with exchange rate fluctuations, while fiscal policy is better suited to other objectives. See Frenkel and Mussa (1981). 6 FRASER Digitized for 6ln theory, zero correlation also could occur if only the U.S. money or foreign money stock changed. In practice, however, it is generally assumed that both the U.S. and the foreign monetary authority would alter their money stocks. 7See the debate by McKinnon and others (1984) and the references cited there for alternative views on the importance of the currency substitution argument. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS MONEY GROWTH DATA Table 1 Correlation Coefficients of U.S. and Foreign Money Growth Rates Fixed exchange rate Belgium Canada1 France Germany Italy Japan Netherlands Switzerland United Kingdom .238 .398 .304 .139 .209 .083 -.0 5 7 .391 Floating exchange rate .168 .374 .034 .194 .138 .110 .157 -.1 0 3 .105 'The floating exchange rate period for the tests of independence for Canada begin in 111/1973 to maintain comparability with the other countries, even though Canada switched to floating exchange rates in 111/1970. Beginning the floating rate period earlier for Canada does not alter the results. exchange rates, changes in the U.S. m oney growth rate may have permanent impacts on the foreign exchange rate, but no effect on the foreign m oney growth. Even during the floating exchange rate period, h ow ever, there is considerable evidence that monetary policy actions have attempted, in part, to manipulate the exchange rate.8 Moreover, many countries have attempted to keep their exchange rate movement within some w ider or narrower range in order to achieve some “target rates.”9Attempts to manage ex change rates, however, lead inevitably to some loss of monetary independence.10 To determine the impact o f U.S. on foreign m oney growth, w e focus on the m ajor w orld traders for which m oney data are available: Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Switzerland and the United Kingdom.11 Since this group includes the major countries that have adopted floating ex change rates, w e can determine w hether the switch from fixed to floating exchange rates altered the U.S.foreign m oney growth relationship. These countries also have the most active foreign exchange markets; thus, they may have substantial capital mobility as well. Table 1 compares the correlation coefficients o f U.S. m oney (M l) growth and foreign m oney (M l) growth for the fixed and floating exchange rate periods.12The fixed exchange rate sample period runs from 1/1960 to II/1971, w hile the floating exchange rate period runs from III/1973 to IV/1985. The intervening period is viewed as transitional and thus is not considered in the analysis.13 In general, the correlation coefficients suggest that movements in U.S. M l growth are partially reflected in movements in foreign m oney growth. In addition, the correlations generally are larger for the fixed exchange rate period than for the floating exchange rate period. For example, the correlation coefficient between U.S. and U.K. m oney growth rates is .391 during the fixed rate period but declines to .105 under floating ex capital mobility also may reduce the insulating ability of floating exchange rates. "T his set of countries is the so-called Group of 10 plus Switzerland. Sweden is excluded due to lack of data. 8For example, see Batten and Ott (1985) and Wickham (1985). See also Federal Reserve Bank of New York’s regular summary of "Foreign Exchange Operations,” e.g. (1986). 9The International Monetary Fund (IMF) classifies countries by type of exchange rate regime. For example, see IMF (1985). See Heller (1978) for an alternative classification procedure. While the period since 1973 is generally acknowledged to be one of floating ex change rates, in fact, relatively few countries are classified as “floaters.” For example, as of December 1983, the IMF classified just nine countries as having independently managed floating ex change rates. 10The ability of floating exchange rates to insulate foreign money growth from U.S. money growth, however, may be even less com plete than suggested by this discussion, even when foreign mone tary authorities allow the exchange rate to fluctuate. As with fixed exchange rates, currency substitution may result in a negative correlation between U.S. and foreign money growth. In addition, ,2Given seasonally unadjusted data with trend, we use the second difference, that is: A(ln M, - In Mt_4). The change from one year ago removes seasonality, while first differencing the result removes any remaining trend. The sample ends in IV/1984 for Switzerland due to a break in the data and in 111/1985 for Italy since that is the most recent available. In addition, Canadian data for the fixed exchange rate period is omitted due to breaks in the data. Other breaks in the data — Canada in IV/1981, France in IV/1977, Germany in 1/1968 and the United Kingdom in 11/1975 and IV/1980 — appear to be relatively unimportant. ,3The Smithsonian Agreement in 1971 replaced the Bretton Woods fixed exchange rate system. It was not until 1973, however, when the Smithsonian Agreement broke down, that exchange rates were allowed to fluctuate freely. This practice of omitting the period from 111/1971 to 11/1973 follows Mixon, Pratt and Wallace (1980). Studies of the floating exchange rate period generally begin after mid-1973. For example, see Batten and Ott (1985). Studies of the fixed exchange rate period generally end before mid-1971. For example, see Feige and Johannes (1982). 7 JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS C hart 1 M o n e y G ro w th in the United States a n d G erm an y 1961 63 65 67 69 71 change rates. This finding is consistent with the ability and willingness o f countries to conduct independent monetary policy under floating exchange rates. Differ ences among foreign countries should also be noted. For some countries including France and the United Kingdom, the correlation is quite strong during the fixed-rate period; for others, such as the Netherlands and Switzerland, the relationship is much weaker. To further illustrate the relationship between U.S. and foreign m oney growth rates, charts 1 to 3 present the annualized m oney (M l) growth rates for Germany, Italy and the United Kingdom relative to U.S. money growth for the period 1/1960 through IV/1985. These countries are chosen to reflect a diversity o f monetary Digitized for 8 FRASER 73 75 77 79 81 83 1985 behavior, both between countries and over time within a country.14 For Germany there appears to be a regular associa tion w ith U.S. m oney growth throughout the period. In contrast, the Italian m oney growth rates bear little resemblance to U.S. rates until mid-1981. For the United Kingdom, there appears to be a close relation ship w ith U.S. m oney growth until 1971. After that, the "N either the graphs nor the correlations allow us to investigate the causes for the diversity of money growth rates in detail. An examina tion of the causes of this diversity, while an interesting topic for further research, is tangential to the goal of this paper. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS rates diverge substantially. The charts also suggest that the period may be divided into the fixed and floating exchange rate regimes, and there are no other obvious breaks in the data. ARE U.S. AND FOREIGN MONEY GROWTH INDEPENDENT?: RESULTS USING THE HAUGH TECHNIQUE The simple correlations and graphical analysis dis cussed above are generally not sufficient to discover many statistical regularities, in particular, lagged rela tionships. To find w hether such statistical regularity exists requires m ore refined techniques. T o investi gate this issue, a statistical technique developed by Haugh (1976) was used to test for independence o f U.S. and foreign m oney growth rates. Although the Haugh technique previously has been used to consider ques tions o f causality, it is used here only to test indepen dence.15 The direction o f causality is assumed to run from U.S. to foreign m oney growth.16 For example, if U.S. and Belgian m oney growth are statistically depen dent, this result is interpreted as im plying that U.S. m oney growth causes Belgian m oney growth. The Haugh procedure ascertains statistical inde pendence between two series based on their crosscorrelations. In particular, it considers both the con temporaneous correlation between U.S. and foreign m oney growth and the correlations between these series across time. For example, the contemporaneous correlation between tw o series, X and Y, can be defined as rxv(0), w hile the correlation between X in one period and Y in the following period can be defined as rX¥(11and the correlation between X in one period and Y in the preceding period as rxv( —1). Haugh’s test statistic for small samples is m N2 2 (N - | k | )- fXY(k)2, k = —m w here N is the number o f observations, m is the maximum lag (and lead) length and r is the estimated cross-correlation coefficient. Thus, this statistic is based on the cross-correlations from X with Y lagged m periods to X w ith Y led m periods (or equivalently, Y with X lagged m periods). Haugh has demonstrated that this statistic follows a x 2 distribution with 2m + 1 degrees o f freedom (the number o f cross-correlation coefficients calculated). In the statistical results reported below, w e vaiy m, the maximum lag (and lead) length. In all cases, h ow ever, the maximum lag length is relatively short. The rationale for short lags is quite simple. If exchange markets are efficient, any adjustment o f foreign to U.S. m oney growth, either to avoid exchange rate changes or to accomm odate currency substitution or mobile capital flows, should occur relatively quickly. This hypothesis implies that longer lags and the corre sponding cross-correlations should be insignificant, which is supported by the empirical results. EMPIRICAL RESULTS 15For example, see Feige and Johannes (1982). 16Granger causality relies on time precedence in regression analysis. As Sims (1972) has admitted, it is a sophisticated version of post hoc, ergo propter hoc. Simply stated, regressing X on lags of Y is assumed to reveal if Y preceded — and thus “ Granger-caused” — X. Zellner (1979) reviews the methodological criticisms of this ap proach. The Haugh technique tests only for the independence of two series. The direction of causation can then be tested, subject to the timing problems discussed by Zellner. Alternately, the direction of causation can simply be assumed. The assumed lack of causality running from foreign money growth to U.S. money growth should not be troubling for the smaller foreign countries examined. For Ger many and Japan, in particular, one might argue that causality may run in both directions. To date, however, there is no evidence in the U.S. reaction function literature to support the hypothesis that U.S. money growth is influenced by any foreign money growth rate. The Haugh technique is also not without its limitations. In particu lar, it requires filtered data as discussed below, and the results may be sensitive to the choice of filter employed. See footnote 17. In addition, since the Haugh technique uses cross-correlations rather than regression analysis, it is not possible to hold other factors constant. This limitation is discussed by Schwert (1979). Table 1 presents the significance levels for the Haugh statistic for alternative values o f m in both the fixed and floating exchange rate periods.17 For the fixed exchange rate period and for each value o f m, the null hypothesis o f independence between U.S. and foreign m oney growth can be rejected for four o f the eight countries using a 10 percent significance level.18 17The Haugh technique requires stationarity in both series. Given seasonally unadjusted data, all variables were converted to log differences, then time series techniques were used to obtain white noise residuals. The filters employed are available upon request. The results are basically unchanged when using Sims’ (1972) filter. ''Canada had to be dropped from the fixed exchange rate period because of a break in the data. In addition, Canada had fixed exchange rates only for the 111/1962 to 11/1970 period. 9 FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 C hart 2 M o n ey G row th in the United States and Italy 1961 63 65 67 69 71 The countries rejecting independence vary, however, based on the value o f m. The French and Japanese results reject independence for m = 0 but not for higher values; the results for Belgium and the Nether lands, however, cannot reject independence for m = 0 but can for higher values. The null hypothesis o f independence o f foreign m oney growth from U.S. m oney growth cannot be rejected for any value o f m only for Italy and Switzerland. What do these results mean? If foreign money growth responds to U.S. m oney growth within one quarter, the Haugh test should reject independence for m = 0. Higher order values for m may not be able to reject independence, however, because the pow er o f the test declines for higher values o f m w hen the true Digitized for 10FRASER 73 75 77 79 81 83 1985 relationship exists only at short lags.19 Alternately, if foreign m oney growth responds with a lag (or w ith a lead if foreign monetary authorities anticipate U.S. policy actions and change their policy in advance), the contemporaneous correlation w ould suggest inde pendence, w hile higher values o f m w ould capture the true dependence.20 Thus, a rejection o f the null hy ,9Consider a simple, albeit extreme, example: r(0) = .4, r(i) = 0 for i + 0 and N = 50. For m = 0, the Haugh statistic is significant at the 1 percent level. For m = 2, the Haugh statistic is insignificant even at the 10 percent level. “ Consider another simple example: r(1) = .4, r(i) = 0 for i =£ 1 and N = 50. For m = 0, the Haugh statistic is clearly insignificant. For m = 1, the statistic is significant at the 5 percent level, while for m = 2, it is again insignificant. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS C ha rt 3 M o n e y G ro w th in the United States and the United Kingdom 19 6 1 63 65 67 69 71 pothesis at any value o f m should be considered evidence o f non-independence. Using this criterion, foreign m oney growth “ de pends” on U.S. m oney growth at the 10 percent signifi cance level during the fixed-rate period for six o f the eight countries considered. In addition, in all cases in w hich the null hypothesis o f independence is re jected, the correlations are positive. These correla tions are consistent with the traditional channel o f influence from U.S. m oney growth to foreign m oney growth. They are not consistent, however, with the currency substitution hypothesis. These results also are generally consistent with Feige and Johannes’ (1982) results that U.S. m oney growth influenced for eign money growth in most countries. 73 75 77 79 81 83 1985 The failure to reject the null hypothesis o f indepen dence for Italian and Swiss m oney growth, however, appears at odds with traditional theory. Tw o possible explanations exist for this result. First, Italy and Switz erland’s rates may, in fact, have been floating during the period. This rationale, however, conflicts with an examination o f the exchange rate data and classifica tions o f exchange rate regimes such as the IM F’s which suggest that exchange rates w ere fixed. Alternately, the insignificant results may be due to the relatively low pow er o f the Haugh test.21 With a 21See Schwert (1979). 11 FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 Table 2 Tests of Independence of U.S. and Foreign Money Growth Rates Haugh Statistic — Significance Levels Fixed exchange rate Floating exchange rate Country m = 0 m = 1 m = 2 m = 0 m = 1 m = 2 Belgium Canada1 France Germany Italy Japan Netherlands Switzerland United Kingdom .2767 .0329 .0880 .0352 .0175 .2437 .0539 .2396 .9854 .0013 .2118 .0127 .4247 .1664 .0585 .2627 .0123 .2620 .0005 .2674 .2452 .0612 .4921 .0448 .3599 .0029 .5891 .1521 .3322 .1831 .2406 .6460 .1183 .4303 .0205 .1741 .3505 .3280 .0310 .5715 .5944 .4467 .4203 .0242 .4003 .4032 .5399 .0040 .7516 .8088 .6836 T h e floating exchange rate period for the tests of independence for Canada begin in 111/1973 to maintain comparability with the other countries, even though Canada switched to floating exchange rates in 111/1970. Beginning the floating rate period earlier for Canada does not alter the results. significance level o f 10 percent, the probability o f re jecting a true null hypothesis is set at 10 percent, while the probability o f correctly rejecting a false null hy pothesis — the pow er o f the test — generally is un known. Although Italian and Swiss m oney growth, in fact, may depend on U.S. m oney growth, w e may be unable to correctly reject the false null hypothesis of independence.22 Floating Exchange Rate P erio d The floating exchange rate results differ substan tially from the fixed- rate results. W e can reject the null hypothesis o f independence only for Canada and Ja pan. In both cases, the correlation is positive, again inconsistent with the currency substitution hypothe sis. These results are consistent with Batten and Ott’s (1985) finding that some countries — including Can ada and Japan — have not fully availed themselves o f the insulating properties o f floating exchange rates. icy response to U.S. m oney growth. For example, for eign m onetary authorities may change foreign m oney growth in response to changes in their real interest rate, and their real rate may change in response to U.S. m oney growth or a host o f other factors, including a change in foreign m oney demand.23 Results Using German Money Growth in Place o f U.S. Money Growth To test further the importance o f cross-national monetary linkages, w e repeated the tests in table 2 for the European econom ies using German rather than U.S. m oney growth as the reference point. Under fixed exchange rates, the traditional theory w ou ld allow a relationship between, say, German and Swiss m oney growth only to the extent that both are correlated with U.S. m oney growth since both are pegged to the dollar. Using the Haugh test, it is impossible to determine w hether this dependence is due to discretionary p o l ,,f\ third possible explanation of the insignificant Italian and Swiss results is that the positive correlation associated with the traditional channel and the negative impact associated with currency substitu tion may be offsetting. Of course, it then is necessary to explain why currency substitution should vary systematically with U.S. money growth. Digitized 12 for FRASER ?3lt may be preferable to run the Haugh test not on money growth (rh) but on money growth in excess of money demand growth. Assuming money demand growth can be approximated by income growth (y), we should examine the relationships of rh-y between the United States and foreign countries. Unfortunately, quarterly gross national product data (or gross domestic product data) are unavailable for some or all of the period for Belgium, France, the Netherlands and Switzerland. With one exception, the results for rh-y were basically unaltered for the subset of countries with available data. The only exception was the floating exchange rate result for the United Kingdom, which was significant (at m = 0) and negative. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS Table 3 Tests of Independence of German and Other Nations’ Money Growth Rates Haugh Statistic — Significance Levels Fixed exchange rate Belgium France Italy Netherlands Switzerland United Kingdom o II E Country Floating exchange rate m = 1 m = 2 m = 0 m = 1 m = 2 .3768 .4576 .9345 .4553 .2564 .0380 .6623 .5745 .8499 .5809 .4738 .1340 .7872 .6809 .8934 .7392 .7659 .0524 .1817 .6969 .8164 .0121 .0273 .0578 .5797 .6734 .7850 .0323 .1814 .0992 .0911 .8333 .5034 .0677 .0736 .0750 The results in table 3 suggest that the null hypothe sis o f independence can be rejected during the fixed exchange rate period only for Germany and the United Kingdom. This result likely reflects the com m on im pact o f U.S. m oney growth on both German and U.K. m oney growth, since these two countries w ere the most closely correlated with U.S. m oney growth. The correlation again is positive, which again refutes the currency substitution hypothesis. The inability to re ject the null hypothesis o f independence for other countries reflects their low er correlations w ith U.S. m oney growth. land and the United Kingdom have responded to German m oney growth using the 10 percent level of significance. Given EMS procedures for maintaining exchange rates within narrow bounds, the results should not be too surprising. The only possible sur prise is the Swiss and U.K. results, since Switzerland and the United Kingdom are not part o f the EMS.24The empirical evidence, however, suggests that they have behaved as if they were. Under floating exchange rates, German m oney growth may have an impact on other nations’ m oney growth that it w ould not have had under the Bretton W oods system. Floating exchange rates, in fact, could mean a different system o f pegging for some countries rather than truly floating rates. For example, other nations may choose to peg their exchange rate to the deutsche mark rather than the dollar. The current European Monetary System (EMS) form ed in 1979 reflects a m ovem ent in that direction. To the extent that other nations peg to the mark, the traditional analysis on the relation between the dollar and other currencies w ou ld then hold between the mark and those currencies. Clearly, during the floating ex change rate period, based on the results in table 2, any relation between German m oney growth and other nations' m oney growth cannot be attributed to com mon response to U.S. m oney growth. The results here both support and extend previous results by Batten and Ott (1985), Feige and Johannes (1982) and Sheehan (1983). Feige and Johannes fo cused exclusively on the fixed exchange rate period. Batten and Ott, using a different m ethodology, con sidered only the floating rate period. Here,, a com m on technique was used to consider the impact o f U.S. m oney growth on foreign m oney growth for both the fixed and floating exchange rate periods. Under fixed exchange rates, U.S. m oney growth had a significant impact on foreign m oney growth in most countries, as predicted by the textbook m odel o f fixed exchange rates. There was no evidence o f negative correlation im plied by the currency substitution hypothesis. The floating exchange results in table 3 indicate that m oney growth in Belgium, the Netherlands, Switzer CONCLUSIONS During the floating exchange rate period, the effect o f U.S. m oney growth was less pervasive, influencing 24Although Switzerland is not part of the EMS, it has admitted being influenced by the exchange rate with respect to the mark. See Schiltknecht (1983). 13 FEDERAL RESERVE BANK OF ST. LOUIS only a relatively small number o f countries. This find ing is consistent with Batten and Ott’s results that some countries have not fully availed themselves o f the insulating properties o f floating exchange rates. Further buttressing these results, w hen German m oney growth replaced U.S. m oney growth, some European countries’ m oney growth rates w ere shown to be related to German m oney growth during the floating rate period, a finding consistent w ith EMS institutional arrangements as w ell as Batten and Ott’s results. The results presented here should be considered suggestive rather than definitive for two reasons. First, the finding o f dependence between U.S. and foreign m oney growth may be the result of com m on response to some third variable rather than a deliberate re sponse o f foreign central banks to U.S. m oney growth. And second, the Haugh test has relatively low power. Nevertheless, the results suggest that U.S. m oney growth had wide-ranging impacts on foreign money growth rates during the fixed exchange rate period and that these impacts have becom e much narrower during the floating-rate period. JANUARY 1987 Frenkel, Jacob A. “ International Interdependence and the Con straints on Macroeconomic Policies,” in R. W. Hafer, ed., How Open Is the U.S. Economy? (Lexington Books, 1986), pp. 171-205. Frenkel, Jacob A., and Michael L. Mussa. “ Monetary and Fiscal Policies in an Open Economy,” American Economic Review (May 1981), pp. 253-58. Gutierrez-Camara, Jose L., and Hans-Joachim Hup. “ The Interac tion Between Floating Exchange Rates, Money, and Prices — An Empirical Analysis,” Weltwirtschaftliches Archiv (1983), pp. 4 0 1 28. Haugh, Larry D. “ Checking the Independence of Two CovarianceStationary Time Series: A Univariate Residual Cross-Correlation Approach,” Journal of the American Statistical Association (June 1976), pp. 378-85. Heller, H. Robert. “ Determinants of Exchange Rate Practices,” Journal o f Money, Credit, and Banking (August 1978), pp. 308-21. International Monetary Fund. Annual Report on Exchange Arrange ments and Exchange Restrictions 1985. Laidler, David. “ Inflation — Alternative Explanations and Policies: Tests on Data Drawn from Six Countries,” Carnegie-Rochester Conference Series on Public Policy (1976), pp. 251-306. Layton, Allan P. “ Is U.S. Monetary Growth a Leading Indicator of Australian Money Growth?” Economic Record (June 1983), pp. 180-85. McKinnon, Ronald I. “ Currency Substitution and Instability in the World Dollar Standard,” American Economic Review (June 1982), pp. 320-33. McKinnon, Ronald I., and others. “ International Influences on the U.S. Economy: Summary of an Exchange,” American Economic Review (December 1984), pp. 1132-34. REFERENCES Aukrust, Odd. “ Inflation in the Open Economy: A Norwegian Model,” in Lawrence B. Krause and Walter S. Salant, eds., World wide Inflation: Theory and Recent Experience (The Brookings Insti tution, 1977), pp. 107-66. Barro, Robert J. Macroeconomics (John Wiley & Sons, 1984). Batten, Dallas S., and Mack Ott. “The Interrelationship of Monetary Policies under Floating Exchange Rates,” Journal of Money, Credit, and Banking (February 1985), pp. 103-10. ________ _ “ What Can Central Banks Do About the Value of the Dollar?” this Review (May 1984), pp. 16-26. Bordo, Michael D., and Ehsan U. Choudhri. “ The Link Between Money and Prices in an Open Economy: The Canadian Evidence from 1971 to 1980,” this Review (August/September 1982), pp. 13-23. Cuddington, John T. “ Money, Income, and Causality in the United Kingdom: An Empirical Reexamination,” Journal of Money, Credit, and Banking (August 1981), pp. 342-51. DyReyes, Felix R., Jr., Dennis R. Starleaf, and George H. Wang. “Tests of the Direction of Causation between Money and Income in Six Countries,” Southern Economic Journal (October 1980), pp. 477-87. Federal Reserve Bank of New York. “Treasury and Federal Re serve Foreign Exchange Operations,” Quarterly Review (Summer 1986), pp. 47-51. Feige, Edgar L., and James M. Johannes. “Was the United States Responsible for Worldwide Inflation Under the Regime of Fixed Exchange Rates?” Kyklos (1982, Fasc. 2), pp. 263-77. Digitized for 14FRASER Mills, Terry C., and Geoffrey E. Wood. “ Money-lncome Relation ships and the Exchange Rate Regime,” this Review (August 1978), pp. 22-27. Mixon, J. Wilson, Jr., Leila J. Pratt, and Myles S. Wallace. “ Moneylncome Causality in the U.K.: Fixed and Flexible Exchange Rates,” Southern Economic Journal (July 1980), pp. 201-09. Pearce, Douglas K. “The Transmission of Inflation between the United S ta te s an d C anada: An Empirical A nalysis,” Journal of Macroeconomics (Summer 1983), pp. 265-79. Schiltknecht, Kurt. “ Switzerland — The Pursuit of Monetary Objec tives," in Paul Meek, ed., Central Bank Views on Monetary Target ing (Federal Reserve Bank of New York, 1983), pp. 72-79. Schwert, G. William. “Tests of Causality: The Message in the Inno vations,” Carnegie-Rochester Conference Series on Public Policy (1979), pp. 55-96. Sheehan, Richard G. “ Money-lncome Causality: Results for Six Countries,” Journal of Macroeconomics (Fall 1983), pp. 473-94. Sims, Christopher A. “ Money, Income and Causality,” American Economic Review (September 1972), pp. 540-52. Swoboda, Alexander K. “ Monetary Approaches to Worldwide Infla tion,” in Lawrence B. Krause and Walter S. Salant, eds., World wide Inflation: Theory and Recent Experience (The Brookings Insti tution, 1977), pp. 9-62. Wahlroos, Bjorn. “ Money and Prices in a Small Economy,” Scandanavian Journal o f Economics (IV:1985), pp. 605-24. Wickham, Peter. “The Choice of Exchange Rate Regime in Devel oping Countries: A Survey of the Literature,” Staff Papers, Interna tional Monetary Fund (June 1985), pp. 248-88. Zellner, Arnold. “ Causality and Econometrics,” Carnegie-Rochester Conference Series on Public Policy (1979), pp. 9-54. FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 Tax Reform and Investment: How Big an Impact? Steven M. Fazzari T HE U.S. Congress has recently passed historic legislation that revises the fundamental structure of U.S. incom e tax law. Promoters o f this legislation hope that the new tax system w ill encourage m ore produc tive use o f econom ic resources and faster econom ic growth. Economists disagree very little about the gen eral objectives o f tax reform. The new law, however, has drawn significant criticism, primarily because of its treatment o f capital investment. The new law weak ens or eliminates many tax initiatives originally de signed to stimulate investment. This article analyzes the effect o f tax reform on investment and the U.S. capital stock. It discusses the channels through which changes in the corporate incom e tax rate, the investment tax credit and the rules for deducting depreciation expense from taxable incom e affect the cost o f capital and a firm ’s invest ment decisions. Furthermore, this article assesses how the increase in corporate taxes affects invest ment. First, however, the next section presents some capital theory concepts that provide a framework for understanding tax effects on investment. SOME BASIC CONCEPTS IN CAPITAL THEORY A firm invests to maintain and expand its stock o f productive capital. Most econom ic models o f invest- Steven Fazzari, an assistant professor of economics at Washington University in St. Louis, is a visiting scholar at the Federal Resen/e Bank of St. Louis. The author thanks Rosemarie Mueller for research assis tance, and Laurence H. Meyer, Joel Prakken and Chris Varvares for providing data and helpful comments. ment begin with the equation: , v ["Change in 1 (1) Investment = I . , . , + Depreciation. [Desired CapitalJ Over the long run, the amount o f depreciation is determined primarily by the size o f the capital stock in place. To explain investment, therefore, one must un derstand h ow firms choose their desired stock o f capital.1 W e begin by analyzing the investment decisions o f a representative firm that maximizes its expected earn ings over time to increase the wealth o f its sharehold ers. The firm faces constraints on its choices. Some of these constraints, like the firm ’s technology, are deter m ined by past investment decisions and the long term developm ent o f the economy; other constraints are market-determined, such as interest rates and the availability o f funds to finance investment spending. The tax system imposes another constraint on the firm ’s behavior. To understand its role in investment decisions, w e must first see h ow firms w ould make investment decisions in the absence o f corporate taxation. 'Equation 1 explains gross investment. Some studies consider the change in desired capital alone, or net investment. The response of investment and the actual capital stock to changes in the desired capital stock will not be immediate; there may be long lags between investment decisions, orders, expenditures and delivery. Estimates of these lags are necessary to predict the timing of investment arising from a change in desired capital. These transitional issues are beyond the scope of this article. The analysis here focuses on the long-run changes in the capital stock caused by the new tax law. For further discussion of short-run adjustments, see Jorgenson’s (1971) survey article. 15 JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS Investment Decisions without Corporate Taxation W hen considering capital expenditure, a firm w ill compare the revenue that the new investment w ill produce over its useful life with the costs o f purchas ing and using the new capital. Because capital goods are durable, they contribute to production over a number o f years. It w ould be incorrect, therefore, to charge the full purchase price o f a capital good against revenue in the year it is purchased. Rather, the cost o f a capital asset over a year is its opportunity cost; this is simply what the firm gives up by holding it for a year. In the absence o f tax effects, the opportunity cost o f an investment has tw o components: interest expense and depreciation.2 Suppose a firm uses its ow n funds to finance an investment expenditure. The firm gives up the op por tunity to earn interest on these funds. If the firm borrows from others to finance its investment, then it must pay interest to its creditor. W hether the firm uses its ow n funds or borrows from others, some measure o f interest expense enters the cost o f capital. Actually, only the real interest rate affects the firm ’s cost o f capital. Assume that capital goods prices rise at the same rate as the general price level. If the interest rate w ere equal to the inflation rate, the firm w ou ld not sacrifice any purchasing pow er by holding capital assets instead o f financial assets. Only the portion o f interest that exceeds what is necessary to offset ex pected inflation, real interest, represents a sacrifice for firms that hold capital rather than financial assets. Let i denote the nominal interest rate and t t " denote the expected inflation rate. Then the real expected inter est rate can be closely approximated by i — Tre. These concepts lead to a natural characterization o f the w ay firms determine their desired capital stock and their corresponding investment decisions. N ew investment increases a firm ’s output. Economists call this increment to output during a year the marginal prod uct o f capital (MPK). The revenue gained from investing in another unit o f capital, the value o f the marginal product o f capital, is P X MPK, where P represents the firm ’s output price. The opportunity cost o f a unit o f capital, is its price, Pc, m ultiplied by the sum o f the real interest rate and the depreciation rate (i — tt' + d). The insert on the opposite page provides an example calculation o f this cost. If the value o f the marginal product o f capital, P X MPK, exceeds the opportunity cost o f investment, Pc(i — 7re + d), the firm can increase its profit by making the investment. On the other hand, if P X MPK is less than Pc(i — tt' + d), the investment is not profitable. To maximize its profits, the firm w ill invest up to the point at which the revenues and costs from additional capital are equal, or, (2) P x MPK = Pc(i - tt' + d). The firm ’s desired capital stock is reached w hen the last unit o f capital purchased satisfies equation 2. This is a fundamental result in capital theory. It divides the determinants o f a firm ’s desired capital stock into technical (MPK and d) and market factors (P, Pc, i). Changes in these factors alter a firm ’s desired capital stock, and, as equation 1 shows, changes in the de sired capital stock along w ith depreciation determine investment.3 TAX REFORM AND THE COST OF CAPITAL Of course, equation 2 is strictly valid only in the absence o f corporate taxation. But the analysis under lying it helps to explain h ow the new tax law w ill affect capital spending. The changes necessary to incorpo rate corporate taxation into equation 2 are summa rized in the insert on page 18. The key issue consid ered here is h ow tax reform has changed the after-tax cost o f capital. W e shall analyze three changes o f particular importance: the repeal o f the investment tax credit, the change in depreciation rules and the cut in the corporate tax rate. Repeal o f Investment Tax Credits In 1963, the E con om ic Report o f the President stated that " ... it is essential to our em ploym ent and growth 2Rather than analyzing the cost of holding a capital asset year by year, we could compute the present value of the costs over the life of the asset. This would be subtracted from the present value of the revenues generated by the asset to give the net present value. To maximize its shareholders’ wealth, the firm would invest in any project with a positive net present value. This procedure is more complicated than the year-by-year analysis presented in the text. It leads to equivalent results, however, assuming that the firm takes the rate of depreciation and the real rate of interest as constant over the life of the asset. Digitized 16 for FRASER 3ln general, the marginal product of capital in equation 2 will depend on the input of other factors of production along with the capital input. These other factors, labor in particular, are not considered here. For further discussion of this issue, see the Economic Report of the President (1987), pp. 90-93. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS Calculating the Cost of Capital: An Example Consider an example o f h ow the real interest rate and the depreciation rate affect the cost o f an in vestment project. Suppose a firm buys a machine for $100,000 at the beginning o f a year. It finances the purchase by borrowing from a bank at a real interest rate o f 5 percent. The value o f the machine depreciates by 20 percent over the year in real terms. At the end o f the year, the firm must pay $5,000 to the bank in interest and it has a machine that is n ow worth $80,000, rather than $100,000, because o f w ear and tear and obsolescence. The real cost to the firm o f using the machine for a year is $25,000, or 25 percent, o f the original investment. objectives as w ell as to our international competitive stance that w e stimulate more rapid expansion and m odernization o f Am erica’s productive facilities. ”4 One policy designed to achieve this goal was the investment tax credit, first instituted in 1962. This tax subsidy allowed firms to reduce their taxes by a per centage o f their spending on certain kinds o f capital equipment. To integrate this into the capital theory summarized by equation 2, suppose that the revenues from capital investment are taxed at a rate t and the only allowable deduction for capital costs is the investment tax credit at a rate o f k. Then, the after-tax cost o f purchasing a unit o f capital is the price paid (Pc) minus the invest ment tax credit amount (kPJ. The after-tax benefit o f investment is (1 —t) m ultiplied by the value o f the marginal product o f capital. This changes equation 2 to (3) Pc x M P K (l- t ) = (Pc-kP„) (i-TT' + d) = Pc( l —k) (i —Tr' + d). The investment tax credit reduces the after-tax cost of capital on the right-hand side o f equation 3, increasing the desired capital stock and investment. The new tax bill, by eliminating this subsidy, directly increases a firm’s cost o f capital, reduces the corporate sector’s desired capital stock and depresses investment. “See pages xvi-xvii of the report. If the firm finances the investment through inter nal funds then, with a 5 percent real return, it gives up the opportunity to have a financial asset worth $105,000 at the end o f the year. Instead, the firm buys the machine, which is worth $80,000 at yearend. The cost o f capital is $105,000 — $80,000 = $25,000, the same result obtained w hen the pur chase was financed by borrowing. This investment w ill be worthwhile if it generates at least $25,000 in new revenue for the firm after other costs, such as maintenance and insurance, are deducted. Depreciation Rules: Some Theory As capital wears out over time, its value declines, im posing a cost on the firm that should be deducted from its taxable income. A problem arises, however, w hen this concept is put into practice: h ow should depreciation costs be determ ined for tax purposes? From an econom ic perspective, depreciation is the change in the market value o f a capital asset. But market value w ou ld be costly for firms to measure and the IRS to verify. As an alternative, the tax code pro vides schedules prescribing the percentage o f an as set’s purchase price that can be deducted from each year’s taxable income. Changes in these rules lead to changes in the after-tax cost o f capital faced by firms. W hile all depreciation schedules allow deductions that eventually equal the total historical cost o f an asset, the earlier these deductions occur, the more valuable they are. Thus, the after-tax cost o f capital is reduced by depreciation schedules that concentrate deductions over a shorter period. Also, “accelerated” depreciation, which permits firms to write off a greater proportion o f the asset’s cost early in its life, reduces the cost o f capital relative to “ straight lin e” methods that divide the deductions evenly over the asset’s service life.5 To evaluate the importance o f changing 5See Ott (1984) for a discussion of depreciation methods and an analysis of the effects of changes in the depreciation rules that occurred in 1981 and 1982. 17 JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS The Effect of Corporate Taxes on the Desired Capital Stock Equation In the absence o f corporate taxation, firms choose their capital stock to satisfy equation 2: P x MPK — Pc (i Tre + d). With a proportional tax on corporate incom e at rate t and an investment tax credit at rate k, the equation becomes: P x M P K (l- t ) = Pc (1 —k) (i - it* P x MPK (1 —t) = Pc (1 — k — tz) (i - ire + d). Finally, recognizing the tax deductibility o f nominal depreciation rules, one must compare the present values o f the tax saving over time under the old and new tax laws. An example o f h ow these present values are com puted is given in the insert on page 20. Consider h ow the deductibility o f depreciation af fects the cost o f capital. The tax saving w ill equal the present value of depreciation deductions per dollar o f investment (z), m ultiplied by the corporate incom e tax rate (t) and the cost o f a unit o f capital (Pc). Thus, the tax deductibility o f depreciation reduces the after-tax cost o f a unit o f capital by tzPc. This changes the equation that determines the desired capital stock to = Pc (1 - k -tz ) (i - tt" + d) + d). The right-hand side o f equation 4 represents the effec tive cost o f capital after accounting for the investment tax credit and depreciation deductions. A reduction in z, the present value o f depreciation deductions, in creases the cost o f capital. Changes in Depreciation Rules Due to Tax Reform The tax acts o f 1981 and 1982 instituted the Acceler ated Cost Recovery System (ACRS) that increased the tax benefit from depreciation deductions and reduced the cost o f capital. The new tax law changes these rules. Digitized for 18FRASER where L is the firm ’s marginal proportion o f invest ment financed by debt. Rearranging this equation yields: (1 —t) Including tax deductions for depreciation allow ances with a present value o f z gives: tt' P x MPK (1 —t) = Pc (1 —k —tz) (i-TT' + d -tL i), (1 — k — tz) (P/Pc) x MPK = ---------------- (i - ir* + d - tLi). + d). (4) P x MPK (1 —t) = (Pc - kPc - tzPc) (i - interest expenses gives: The right side o f this equation gives the taxadjusted cost o f capital in equation 6. The calcula tions in table 2 are based on this formula. See the text for further explanation. The figures in table 1 compare the present values o f depreciation allowances for several representative as set classes over a range o f pre-tax interest rates. For equipment purchases, the new tax law changes the present value o f depreciation deductions in several ways. First, the service lives for some assets w ere lengthened. For example, cars and light trucks had their tax service lives extended from three to five years. This reduces the present value o f their depreciation allowance, as shown in table 1, because it extends the time between a capital purchase and the tax saving. For many other assets, however, tax service lives were unchanged. Office, com puting and accounting equip ment, for example, kept its five-year depreciation p e riod. On average, equipm ent service lives w ere ex tended to 6.0 years from their 4.6-year average under ACRS.6 On the other hand, the n ew law allows a more accelerated depreciation schedule (firms m ay use a 200 percent, rather than a 150 percent, declining bal ance depreciation method). This allows a greater pro portion o f the total deduction in the earlier years. By itself, this change w ould increase the present value o f 6The average service life estimates used in this article are weighted averages over the different classes of assets. The weights reflect the proportion of total assets in each class. The author thanks Joel Prakken of Laurence H. Meyer and Associates for providing these estimates. FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 Table 1 Present Value of Depreciation Allowances Per Dollar of Investment Pre-Tax Interest Rate 5 percent 10 percent 15 percent Previous law New law Previous law New law Previous law New law Cars and light trucks .971 .947 .943 .900 .918 .857 Office, computing and accounting equipment .948 .947 .901 .900 .858 .857 Communications equipment .948 .923 .901 .857 .858 .800 Equipment average .952 .935 .908 .877 .868 .827 Business structures .815 .626 .682 .431 .583 .319 Asset Class NOTE: The present value is computed by discounting the depreciation allowances for each asset at the after-tax interest rate. Thus, the discount rate is 1 - 0.46 times the interest rate shown for the old law and 1 - 0.34 times the interest rate for the new law. Further details about the depreciation flows are given in the appendix. depreciation deductions, thus partly offsetting the negative impact o f extending service lives. Finally, by reducing the corporate tax rate, the new tax law increases the after-tax discount rate firms use to calculate the present value o f their depreciation deductions at a given nominal interest rate. By itself, this reduces the present value o f a particular sequence o f depreciation deductions. As table 1 shows, on net these changes cause the present value o f depreciation allowances to decline under the new tax law. The effects for equipm ent Eire m odest on average. The new law has a much more significant impact on business structures. The ACRS system adopted in 1981 allowed firms to depreciate business structures over 19 years with an accelerated m ethod (175 percent declining balance). The new law requires straight line depreciation over 31.5 years. As the bottom row o f table 1 shows, this significantly reduces the present value o f depreciation allowances for structures. Changes in the Corporate Tax Rate The new tax law cuts the top corporate incom e tax rate from 46 percent to 34 percent. By itself, it might seem that this w ou ld stimulate investment, because it allows firms to keep a larger proportion o f the profits earned from new capital. The analysis that led to equations 2 through 4 shows that this may not be the case. Although a cut in the corporate incom e tax rate increases the after-tax revenues gained from new in vestment, it also decreases the value o f tax deductions generated by capital costs. Thus, the net effect on investment of a low er corporate tax rate is ambiguous. It depends on the extent to w hich capital costs are taxdeductible. Let us consider this point in more detail. The cost of capital per dollar o f investment is reduced by the corporate tax rate times the present value o f deprecia tion allowances (tz). The low er the corporate tax rate, the low er the value o f this deduction, and the higher the after-tax cost o f capital. Thus, considering this channel alone, low ering the corporate tax rate actually reduces the incentive to invest. Another primary com ponent o f capital cost is real interest earnings foregone by investing in fixed capital. In the absence o f corporate taxation, this cost was essentially the same w hether firms financed their in vestment w ith internal funds or external borrowing. This is no longer true w hen w e introduce the corpo rate incom e tax. Nominal interest paid on debt is taxdeductible, but foregone interest on internal funds is not. This gives debt financing a tax advantage over internal financing.7 The tax saving from interest de ductions is the corporate tax rate (t), m ultiplied by the proportion o f the investment financed with debt (L), m ultiplied by the nominal interest rate (i). This amount is subtracted from the real interest rate in the 7See Brealey and Myers (1984) for a clear summary of this idea. 19 FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 The Present Value of Depreciation Deductions To correctly evaluate the cost o f a capital asset, a firm must take into account the tax savings that result from depreciation deductions. These sav ings, however, occur over time after the asset is purchased. The further in the future a tax deduc tion occurs, the low er its "present value,” because the firm loses the opportunity to earn interest on the tax saving. Suppose a firm buys a com puter for $100,000 in 1987. The new tax law allows the firm to write off this cost over five years. The deductions for each year are given in the first column o f the accompany ing table. The $20,000 deduction the firm gets in 1987 is worth the same amount as any other cost it incurs in 1987, so it is not discounted. The firm will obtain a $32,000 deduction in 1988. The present value o f this deduction is the amount o f m oney the firm w ould need in 1987 to get $32,000 in 1988. Assume the pre-tax interest rate is 10 per cent and the corporate tax rate is 34 percent, as specified in the new tax law. Then, the after-tax interest rate is 6.6 percent = (1 — .34) X 10 percent. The amount o f m oney needed in 1987 to have $32,000 aftertax in 1988 is $32,000/1.066 = $30,019. This is the present, or “ discounted” value o f a $32,000 depreciation deduction in 1987. The divisor 1.066 is called the “discount factor.” The longer the firm must wait for depreciation deductions, the greater the discount factor, and the low er the present value. For example, the $19,200 depreciation in 1989 from the hypothetical com puter purchase is discounted by (1.066)2 = 1.136. Applying this m ethod to all the depreciation d e ductions yields a total present value o f $89,965 in depreciation deductions from a $100,000 purchase, or about 90 cents for every dollar spent. All the figures in the following table are com puted using this approach. Present Value of Depreciation Deductions from a $100,000 Computer Purchase under the New Tax Law Year Depreciation Deduction Discount Factor Present Value of Deduction 1987 1988 $ 20,000 1.000 $ 20,000 32,000 1.066 30,019 1989 19,200 1.136 16,901 1990 14,400 1.211 11,891 1991 14,400 1.291 11,154 Total $100,000 capital cost in equation 4, w hich n ow becomes: (5) P X M P K (l- t ) = Pc(l —k —tz) (i - it' + d - tLi). As noted previously, the corporate incom e tax rate also affects the revenue side o f the investment deci sion. The effective value o f the marginal product is (1 —t) P X MPK. A low er corporate tax rate stimulates investment through this channel; with low er taxes, firms keep a larger proportion o f the revenues gener ated by new investment. Digitized for 20FRASER $ 89,965 In summary, reducing the corporate tax rate in creases the benefits from n ew capital investment by raising the left side o f equation 5. At the same time, low er corporate tax rates reduce the value o f tax de ductions for depreciation and interest expense. This increases the costs o f new capital on the right side of equation 5. Therefore, this theory cannot predict w hether the low er corporate tax rate w ill stimulate or depress investment. To obtain a m ore definite result, w e must look at the net effects o f changes in the tax law. JANUARY 1987 FEDERAL RESERVE BANK OF ST. LOUIS Table 2 The Effects of Tax Reform on the After-Tax Cost of Capital Investment Category Base Case (Old Tax Law) Base With Repeal of Investment Tax Credit Base With Revised Depreciation Base With 34 Percent Corporate Tax Rate New Tax Law Cars and light trucks 36.1% 39.4% 37.5% 36.2% 39.9% Office, computing and accounting equipment 29.6 34.3 29.6 29.5 33.6 Communications equipment 15.6 18.0 16.1 15.7 18.2 Equipment average 17.1 19.5 17.5 17.2 19.6 Business structures 13.2 13.2 15.4 12.5 13.9 NOTE: These calculations assume a 10 percent nominal interest rate and a 4 percent expected inflation rate. The cost-of-capital formula and additional assumptions are given in the appendix. Net Effects o f Tax Changes on the Cost o f Capital To fully assess the impact o f tax reform on the cost o f capital, w e need a w a y o f combining all the changes into a single measure. The basis for this is the theory summarized in equation 5. By putting all the terms affected by the tax system on the right side o f the equation, w e obtain: (6 ) (P/Pc) (1 — k — t z ) X MPK = --- --------- (i - it ' + d - tLi). The right side o f this equation is the tax-adjusted cost o f capital per dollar o f investment spending. Some representative calculations o f this cost are shown in table 2.® The differences among the cost o f capital estimates for different asset classes are primarily due to different rates o f econom ic depreciation. The first colum n o f table 2 gives cost o f capital estimates based on assumptions that reflect the old “The basic reference for the tax-adjusted cost of capital measure is Hall and Jorgenson (1967). Further details of the calculation are given in the appendix. To make the comparisons shown in table 2, one must make assumptions about the future course of nominal interest rates and expected inflation. The calculations in table 2 assume a nominal interest rate of 10 percent and expected inflation of 4 percent. These assumptions are the same for the old and new tax laws to focus on the results of tax changes alone. Some economists have argued that the tax reform will change interest rates and inflation. This issue is considered later in the article. Also, these calculations do not consider the effects of changes in personal taxes on capital income. See Henderson (1986) for further discus sion of this issue. tax law. The second column shows the effect o f elim i nating the investment tax credit, w hile retaining all other assumptions o f the base case. This has a sig nificant impact on the after-tax cost o f capital for equipment. The average equipm ent cost o f capital rises by 2.4 percentage points w ith the repeal o f the investment tax credit. The credit does not apply to structures.9 On the other hand, the third colum n shows that the effect o f changing the depreciation rules is m ore p ro nounced for the after-tax cost o f business structures. The present value o f depreciation deductions d e clines much m ore for structures than for equipment under the new tax law. Com pared with the base case o f the old tax law, the change in tax depreciation rules raises the after-tax cost o f capital by only 0.4 percent age points for equipment, on the average, w hile raising the cost o f capital by 2.2 percentage points for busi ness structures. The fourth column shows the effect o f lowering the corporate tax rate from 46 percent to 34 percent. This causes a substantial reduction in the cost o f capital for business structures, but leaves the equipment figures virtually unchanged. The analysis in the previous sec tion explains this result. Theoretically, the net effect o f 9ln econometric analysis that uses National Income and Product Accounts (NIPA) data, the investment tax credit for structures is often not set at zero. This is because the NIPA data for structures include asset classes, drilling rigs and air-conditioning equipment, for example, which were eligible for the credit. This is not important, however, for the illustrative calculations in table 2. 21 FEDERAL RESERVE BANK OF ST. LOUIS a low er corporate tax rate on the cost o f capital is ambiguous. The direction o f change depends on the value o f tax deductions for depreciation. The depreci ation deductions for equipment per dollar o f invest ment are much m ore valuable than those for business structures, because equipm ent write-offs are faster. Thus, low ering the corporate tax rate reduces the value o f equipment depreciation allowances more than business structures allowances. On the other hand, the benefit o f low er corporate taxes — from the reduced proportion of revenues paid in taxes — is the same for both equipment and structures. Thus, low er corporate tax rates benefit structures much m ore than equipment, as the fourth column o f table 2 shows. The aspects o f the tax reform bill that affect the cost o f capital have drawn significant criticism because some analysts view them as anti-growth. The results presented in table 2 provide some support for this view. The last colum n shows the net effect o f the new tax law. All the cost o f capital estimates rise relative to the old law. For equipment, the repeal o f the invest ment tax credit has the most important effect, and some asset classes face higher costs due to changes in the depreciation rules. For business structures, the change in depreciation has a significant impact by itself, but this is offset to a large degree by the benefits o f a low er corporate tax rate. The comparatively m oderate increase in the cost o f capital for business structures is somewhat surpris ing in light o f the strong criticism the new tax treat ment o f structures has drawn. This is probably be cause most analyses focus on the more obvious effect o f less generous structure depreciation. But it is im portant not to ignore the important impact o f low er corporate tax rates.’0 JANUARY 1987 changes in the after-tax cost o f capital. Furthermore, m any economists have argued that tax reform w ill low er the real interest rate. The calculations pre sented in table 2 assume that real interest rates do not change under the new tax law. The Link between Investment and the Cost o f Capital Economists generally agree that the new tax law w ill increase the cost o f capital. The effect o f this increase on investment and the desired capital stock depends on the econom y’s production technology. The key parameter is called the “elasticity o f substitution’’ between capital and other factors o f production. This measures the sensitivity o f firms’ dem and for capital to changes in the cost o f capital. An increase in the cost o f capital induces firms to substitute other factors o f production for capital. This lowers the desired capital stock, and according to equation 1, investment falls. The higher the elasticity o f substitution, the bigger the reduction in the long-run capital stock. Let c„ and c„ represent the cost o f capital under the old and n ew tax laws, respectively. The theory p re dicts that the long-run percentage change in the capi tal stock is given by: (7) Percent Change in Capital = 100 x ((eye,,)’ — 1], where s is the elasticity o f substitution. The assump tions used to derive equation 7 are discussed in the appendix. The higher s is, the greater the long-run reduction in the capital stock w ill be as a result o f tax reform. H ow large an effect w ill changes in the cost o f capital have on U.S. investment and the capital stock? This is not an easy question to answer. Economists have not resolved important technical questions about the sensitivity o f the desired capital stock to The elasticity o f substitution is determ ined by the econom y’s technology. Although not directly observ able, it can be estimated, and a w ide range o f estimates o f s can be found in the econom ics literature. Some researchers have concluded that the elasticity o f sub stitution is close to unity." If this is true, the size o f the desired capital stock w ou ld be very sensitive to changes in the cost o f capital. Thus, even the m odest increase in the cost o f capital shown in table 2 could have a significant long-run impact on the capital stock. 10Of course, this point is relevant only for profitable firms that invest in structures. Firms that invest only to obtain tax losses from fat depreciation allowances will be hurt by the new depreciation rules, but, since they pay no tax, will not be helped by lower tax rates. " I f the elasticity of substitution is equal to one, the economy’s technol ogy can be represented by a Cobb-Douglas production function. Jorgenson (1971) finds empirical support for this case. Also see Chirinko and Eisner (1982) for further discussion. THE IMPACT OF TAX REFORM ON INVESTMENT AND THE CAPITAL STOCK Digitized for22 FRASER FEDERAL RESERVE BANK OF ST. LOUIS With s equal to 1.0 in equation 7 and the cost of capital figures from table 2 w e obtain the following results: Percent Change in Equipment = 100 X [(17.1%/19.6%) - 1] = - 1 2 .8 % Percent Change in Structures = 100 X [(13.2%/13.9%) - 1] = -5.0%. These dramatic results support the views of tax reform critics. A 12.8 percent drop in the stock o f U.S. capital equipment w ould cause a significant reduction in the econom y’s productive potential with a correspond ingly negative impact on future national output and em ployment.12 Other researchers have found that the desired capi tal stock is much less sensitive to changes in the cost o f capital. For example, in an extensive survey o f pre dictions from large econom etric models, Chirinko and Eisner (1982) found estimates o f s as lo w as 0.55 for equipment and 0.16 for structures. Such low values ch a n g e th e p r e d ic t e d e ffe c ts o f tax re fo rm significantly: Percent Change in Equipment = 100 X [(17.1%/19.6% )0S5 - 1] = -7.2% Percent Change in Structures = 100 X [(13.2%/13.9% )0,e - 1] = - 0 .8 % . These results suggest that tax reform could have a more moderate effect on equipment and virtually no effect on structures. Tax Reform, Interest Rates and Investment The analysis up to this point has assumed that the interest rate w ould not be affected by tax reform. Yet, there are w idespread predictions that tax reform w ill 12Some economists have argued that, although investment and the capital stock will fall as a result of tax reform, the projects that are undertaken will be more efficient. Eliminating special tax breaks for certain kinds of investment will encourage firms to carry out more productive projects rather than projects that generate the biggest tax savings. Thus, the fall in investment may benefit the economy by reducing wasteful investment. A complete analysis of this issue is outside the scope of this article. See Batten and Ott (1985), Hender son (1986), and the Economic Report of the President (1987), pp. 86-93, for further discussion. JANUARY 1987 decrease interest rates. The tax reform bill cuts mar ginal personal tax rates sharply, especially for highincom e individuals. Thus, the after-tax returns to sav ing rise, which stimulates saving and low er real interest rates. Furthermore, reduced capital spending lowers the dem and for financing. This also pushes real interest rates lower. One recent study, for example, predicts that the new tax law w ill cause a 1.3 percentage-point decline in the corporate bond yield and a 0.5 percentage-point decline in the inflation rate. Under these circumstances, the real interest rate w ou ld decrease 0.8 percentage points.13 The effects o f low er interest rates are explored in table 3. The first column reproduces results given earlier for the percentage changes in the capital stock assuming no changes in real interest rates due to the n ew tax law. Figures are given for both the high elastic ity o f substitution case (s = 1) and the lo w elasticity case (s = 0.55 for equipment and s = 0.16 for struc tures). The columns show the effects o f a range of assumptions about the decline in the interest rate induced by tax reform. These figures show that even modest reductions in real interest rates from the new tax law can substan tially mitigate the negative impact o f tax reform on investment. The effects on the stock o f producers’ durable equipment are moderate, especially with the low er elasticity o f substitution estimate. Surprisingly, the calculations show that the desired stock o f busi ness structures may even rise with real interest rate reductions in the m iddle o f the relevant range. Thus, the dramatic reductions in the capital stock and in vestment predicted by some critics o f the new tax law represent a worst case, where the elasticity o f substi tution is high and the real rate o f interest does not fall in response to tax changes. The Effects o f Increasing Corporate Tax Burdens The analysis to this point has used conventional capital theoretic concepts to evaluate the impact o f tax reform on investment incentives. Tax policy affects investment decisions by changing the costs and benefits o f individual investment projects. A firm can obtain financing for any profitable project at the pre vailing cost o f capital. Thus, the reduction o f a firm ’s internal funds available to finance investment caused 13These estimates are from Prakken (1986), p. 30. Some economists have argued that the fall in long-term interest rates during 1986 was due, at least in part, to expectations that the new tax law would reduce interest rates. 23 FED ERAL RESERVE BANK OF ST. LOUIS JA N U A R Y 1987 Table 3 Percentage Changes in the Desired Capital Stock Due to Tax Reform Real Interest Rate Reduction (percentage points) Investment Category 0.0 0.5 0.8 1.0 -1 2 .8 - 5.0 -1 0 .5 - 0.8 - 9 .0 2.3 -8 .1 4.8 - 5.5 10.9 - - 5.9 - 0.1 -5 .1 0.4 - 4 .5 0.7 - 3.1 1.7 1.5 High Elasticity Case Equipment (s = 1.00) Structures (s = 1.00) Low Elasticity Case Equipment (s = 0.55) Structures (s = 0.16) 7.2 0.8 NOTE: The variable s represents the elasticity of substitution assumed in each calculation. See the text for further discussion. by the new tax law does not directly affect investment. Firms offset the decline in internal cash flow by bor rowing the necessary funds in external capital mar kets.14 The econom ics literature, however, has iden tified reasons w hy this view may not be valid. The assumption that all desired investment can be financed at the market interest rate ignores the prob lem o f communicating information from borrow er to lender. It is costly for lenders to evaluate the prospec tive returns o f various investment projects because they do not have extensive knowledge o f the particular situations facing potential borrowers. W hile borrow ers w ill provide some relevant information, they have an incentive to present an optimistic view o f their circumstances. Thus, lenders may be willing to finance some investment projects only at interest rates so high that these projects becom e unprofitable. Furthermore, as various studies have shown, when capital market information is costly, some firms may not be able to obtain external financing even at high interest rates.15 In this case, the new tax law could 14An immediate objection that might be raised against this view is that firms must pay interest on external funds, so borrowing appears more costly than internal finance. This is true on the firm’s income statement. But in economic terms, the firm also gives up the oppor tunity to earn interest on internal funds when they are spent on capital accumulation. 15This situation is called “ credit rationing” in the economics literature. Stiglitz and Weiss (1981) present a theoretical model that explains this possibility. This idea is linked to investment theoretically by Greenwald, Stiglitz, and Weiss (1984) and empirically by Fazzari and Athey (1987). Digitized for24 FRASER reduce investment because firms w ould not be able to offset the loss o f internal funds by borrowing. Furthermore, even if lenders are willing to provide funds at favorable market interest rates, firms them selves may be reluctant to use credit markets to re cover investment finance lost under the new tax law. Firms are concerned about their debt-equity ratios and their credit ratings. Thus, they may choose to curtail capital expenditures rather than increase bor rowing. N ew equity issues are a potential source o f funds, but the historical evidence shows that little new investment is financed through new share issue.18 H ow big an impact w ill tax reform have on invest ment through this channel? The investment equation 1 can be m odified to address this question: (8) Investment = Depreciation + Change in Cash Desired + b x m Flow Capital The parameter b represents the size o f the effect o f internal cash flow on investment. Estimation o f b from ,6ln a detailed study of 12 large companies over 10 years, Donaldson and Lorsch (1983), p. 52, show that only 0.5 percent of new funds raised resulted from equity issues. They also find a strong prefer ence for internal investment financing, rather than debt financing. Common and preferred stock issues accounted for only 3.9 percent of the sources of funds for 799 industrial firms reported on the Value Line database in 1984. Greenwald, Stiglitz and Weiss (1984) pro vide a theoretical explanation, based on capital market signaling, for why firms avoid equity finance. FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 historical data shows that cash flow has been posi tively related to equipment investment over the last three decades; cash flow had no significant effect, however, on business structures investment. The de tails o f the estimation are presented in the appendix. stock o f equipment. Different assumptions, however, lead to much smaller changes. Moreover, low er inter est rates caused by tax changes w ill likely offset some o f the rise in after-tax capital costs due to changes in tax rules. These estimates provide one w ay to predict the effect o f increasing corporate taxes w hile reducing personal taxes. Suppose, in the absence o f tax changes, that real equipment investment w ould grow from mid-1986 through 1988 at a 5 percent annual rate. N ow suppose that the new tax act w ill increase corpo rate taxes by $25.2 billion in 1987 and $23.9 billion in 1988.17Then, the estimates o f equation 8 predict a 2.8 percentage-point reduction in equipment investment for 1987 and a 2.1 percentage-point reduction in 1988, relative to the benchmark 5 percent real growth trend. W hile not especially large relative to historical varia tions in equipment investment, these changes are still substantial.18 The 1987 E con om ic Report o f the President predicts that “a somewhat higher overall marginal tax rate on capital incom e w ill m odestly reduce the econom y’s long-run capital intensity” (p. 79). The analysis pre sented in this article supports this view. A middle-ofthe-road forecast indicates that the new tax law alone w ill cause a moderate decline in equipment invest ment, chiefly due to the repeal o f the investment tax credit. The effects on business structure investment w ill likely be small, at least for structure investment motivated by econom ic profits as opposed to tax benefits (see footnote 10). The rollback o f generous depreciation treatment for structures increases their after-tax cost, but the low er corporate tax rate and the potential for low er real interest rates largely offset the depreciation rule change. There is an important qualification to these predic tions. The calculations are based on the assumption that firms absorb the w hole tax increase in reduced cash flow rather than increasing before-tax markups to recover part o f the tax increase through higher prices. This assumption becom es less realistic as the forecast horizon expands further into the future and firms revise their pricing policies to reflect the new tax system. This eventually could reduce or even elim i nate the effect o f higher taxes on corporate cash flow. CONCLUDING REMARKS H ow big an impact w ill tax reform have on invest ment? The analysis presented here shows a rather w ide range o f possibilities. Capital theory implies that the new tax law w ill increase the cost o f capital, especially for producers’ durable equipment invest ment, tending to reduce investment and low er the U.S. capital stock. The size o f this effect, however, is uncer tain. Under some assumptions, the rising cost o f capi tal leads to a dramatic 13 percent long-run fall in the REFERENCES Batten, Dallas S., and Mack Ott. “The President’s Proposed Corpo rate Tax Reforms: A Move Toward Tax Neutrality," this Review (August/September 1985), pp. 5-17. Brealey, Richard, and Stewart Myers. nance (McGraw Hill, 1984). Principles of Corporate Fi Bureau of National Affairs, Inc. “ Conference Report (H Rept. 99841) on HR 3838, T ax Reform Act of 1986,” ' DER No. 183 (September 22,1986). Chirinko, Robert, and Robert Eisner. “The Effects of Tax Parame ters in the Investment Equations in Macroeconomic Econometric Models” in Marshall Blume, Jean Crockett, and Paul Taubman, eds., Economic Activity and Finance (Ballinger Publishinq Com pany, 1982). Clark, Peter. “ Investment in the 1970s: Theory, Performance, and Prediction,” Brookings Papers on Economic Activity (1979) pp. 7 3 124. Donaldson, Gordon, and Jay W. Lorsch. (Basic Books, Inc., 1983). Economic Report of the President. Office, 1963 and 1987). Decision Making at the Top (U.S. Government Printing Fazzari, Steven, and Michael Athey. “Asymmetric Information, Fi nancing Constraints, and Investment,” Review of Economics and Statistics (forthcoming, 1987). l7The 5 percent annual growth rate was the actual growth rate of real producers’ durable equipment investment from the second quarter of 1985 through the second quarter of 1986. It gives a benchmark for equipment investment growth in the absence of tax reform. The estimated changes in corporate taxes were obtained from the con gressional conference committee report on the Tax Reform Act of 1986. See Bureau of National Affairs, Inc. (1986). 18The standard deviation of the producers’ real durable equipment growth rate from 1970 through 1985 was 9.9 percentage points. Greenwald, Bruce, Joseph Stiglitz, and Andrew Weiss. “ Informa tional Imperfections in Capital Markets and Macroeconomic Fluc tuations,” American Economic Review (May 1984), pp. 194-99. Hall, Robert, and Dale Jorgenson. “ Tax Policy and Investment Behavior,” American Economic Review (June 1967), pp. 391-414. Henderson, Yolanda. “ Lessons from Federal Reform of Business Taxes,” New England Economic Review (November/December 1986), pp. 9-25. 25 FEDERAL RESERVE BANK OF ST. LOUIS JANUARY 1987 Jorgenson, Dale. “ Econometric Studies of Investment Behavior: A Survey,” Journal of Economic Literature (1971), pp. 1111-147. Prakken, Joel. “ The Macroeconomics of Tax Reform,’’ presented at the American Council for Capital Formation conference entitled “The Consumption Tax: A Better Alternative?” (September 1986). Ott, Mack. “ Depreciation, Inflation and Investment Incentives: The Effects of the Tax Acts of 1981 and 1982," this Review (November 1984), pp. 17-30. Stiglitz, Joseph, and Andrew Weiss. “ Credit Rationing in Markets with Imperfect Information,” American Economic Review (June 1981), pp. 393-410. Technical Appendix A. Present Value of Depreciation Allowances where The tax service life for cars and light trucks under the old tax law was three years. It has been lengthened to five years under the tax reform act. The tax service lives for office, com puting and accounting equipment, and communications equipment w ere five years un der the old law. Tax reform did not change the depre ciation period for office, computing and accounting equipment, but it extended the service life for com munications equipment to seven years. The tax ser vice lives are based on the Asset Depreciation Range system. See Ott (1984) for further details. Depreciation allowances for equipment w ere com puted using a 150 percent declining balance m ethod under the old tax law and a 200 percent declining balance under the new law. A switch to straight-line depreciation to maximize the deduction is also as sumed. These methods are discussed in detail in Ott (1984). The half-year convention was used that treats all purchases w ithin a year as if they occur at m id year. To com pute the present value, depreciation deduc tions w ere discounted at an after-tax rate obtained by multiplying the nominal interest rate by one minus the appropriate marginal corporate tax rate. k = investment tax credit rate, t = corporate tax rate, z = present value of a one dollar depreciation allowance, L = leverage ratio (debt as a proportion of assets), i = nominal interest rate, d = economic depreciation rate, and tt* = expected inflation rate. A leverage ratio o f 0.306, based on data from the Washington University Macro M odel (WUMM), was used in all the calculations. The capital stock calculations given in the text are based on a constant elasticity o f substitution aggre gate production function. With this technology, the desired capital stock is proportional to c~s where c is the cost o f capital defined above and s is the elasticity o f substitution. These calculations assume that the level o f output and the ratio o f the price o f investment goods to the price o f output are constant. C. Estimated Effect of Cash Flow Changes on Investment The estimated reductions in equipment investment due to low er corporate cash flow caused by tax reform are based on the regression equation: /p y , _ INVE, = 0.0994 K,_, + 0.0174 f \E,c, (0.0153) B. Cost of Capital The cost o f capital calculations in the text are based on the Hall and Jorgenson (1967) formula. The cost o f capital, often called the im plicit capital rental rate, is given by the formula: 1 - k - tz (1 - 0.5 X k) c = 100 X ------------- — -------------[(1 - tL) i - Digitized for26 FRASER it* 4- d], p, E.^c,., + 0.2081 IFIN, + 0.0953 IFIN,., + 0.0136 IFIN,_2, (0.0380) (0.0538) (0.0534) where INVE, = producers’ durable equipment investment at time t in 1982 dollars, K,_, = lagged stock of equipment (as calculated for WUMM), FEDERAL RESERVE BANK OF ST. LOUIS Pt = implicit price deflator for private non-farm output, E, = implicit price deflator for producers' durable equipment, Yt = real private, non-farm output, and IFIN,: internal finance, defined as after-tax corporate profits plus depreciation allowances minus corpo rate dividends, deflated by E,. JANUARY 1987 Standard errors o f the estimated coefficients appear beneath the estimates. The f(*) function represents a 14-quarter, third-degree polynom ial distributed lag. The equation was estimated with a correction for first order autocorrelation o f the residuals, with quarterly data from the third quarter o f 1956 through the second quarter o f 1986. 27
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