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FEDERAL RESERVE BANK OF ST. LOUIS JUNE 1977 Treasury Bill Futures Market and Market Expectations of Interest Rates Energy Resources and Potential G N P .... rLE*RQ£K Vol. 5 9 , No. 6 ,0 The Treasury Bill Futures Market and Market Expectations of Interest Rates* ALBERT E. BURGER, RICHARD W. LANG, and ROBERT H. RASCHE CON OM ISTS and other analysts seek to measure expectations of future interest rates because such ex pectations have important effects on economic behav ior. Changes in expectations can lead to changes in economic activity, both at the level of the individual firm or consumer, and at the level of the national economy. For example, interest rate expectations enter into investment decisions of firms, portfolio de cisions of financial intermediaries and other investors, and borrowing decisions of state and local govern ments. If these groups alter their expectations of the future level of interest rates, changes in investment, portfolio, and borrowing decisions will occur which affect not only each group individually, but which also affect the level of economic activity in the econ omy as a whole. Consequently, policymakers and researchers have been interested in measuring market expectations of interest rates — first, to understand the behavior of economic units in individual markets, and second, to monitor changes in expectations which result from policy actions, in order to judge the im pact which the policy may have on the economy. actions would be made much easier if market expec tations of future interest rates were readily observable. A considerable amount of economic research has been devoted to formulating measures of market ex pectations of interest rates, since data on expectations are not directly observable unless survey methods are used. Efforts at measurement have taken the form of everything from “informed judgement” to elaborate econometric models. Another means of obtaining an estimate of the level of short-term interest rates ex pected to prevail at some future date has become available since early 1976. This method employs the yield quotations of the futures market in U.S. Treas ury bills. These quotations, which are available on a daily basis, embody market expectations of future short-term interest rates. This paper focuses on the information about market expectations which can be obtained from yields on Treasury bill futures contracts. THE ROLE OF THE TREASURY RILL FUTURES MARKET For example, consider the discussion surrounding the recently aborted Federal income tax rebate. The argument for such a policy was that it would stimu late consumer spending, and thus stimulate aggre gate output and employment. However, there was considerable concern that the policy would cause an upward revision of short-term interest rate expecta tions if there were general agreement that the Treas ury would have to increase its borrowing substantially during the second half of 1977 to finance the in creased deficit. Under such circumstances, much, if not all, of the alleged stimulus that would be pro vided by the tax rebate could be offset by the negative impact of higher interest rate expectations on firms’ decisions to invest in real capital. Such a negative effect arises because the higher the expected level of future interest rates, the less profitable the income stream associated with each particular investment project. T he examination of such effects of policy T he futures market in three-month U.S. Treasury bills was opened on the International Monetary Mar ket of the Chicago Mercantile Exchange in January 1976, soon after the opening of a mortgage futures market on the Chicago Board of Trade in October 1975.1 Both of these futures markets in financial in struments operate in essentially the same way as the traditional commodity futures markets. Futures trad ing in financial instruments allows the separation of the risk of unexpected interest rate movements from other types of risk. Futures contracts can be used to hedge against interest rate movements in order to protect actual or expected cash positions of market participants. Profits are thereby protected in much the same way as hedging in commodity futures mar kets protects against price fluctuations of a particular commodity. Speculation is facilitated by the existence of futures markets, which allow the assumption of “The authors gratefully acknowledge the assistance of Ms. Jeanne Rickey and the Statistical Department of the Chicago Mercantile Exchange for providing data used in this paper. 'F o r details on the Treasury bill futures market, see the ac companying section: “Characteristics of the Treasury Bill Futures Market.” 2 Digitized forPage FRASER JUNE FEDERAL RESERVE BANK OF ST. LOUIS 1977 Characteristics of the Treasury Bill Futures Market The Treasury bill futures market began active trad ing on January 6, 1976, in contracts of three-month (thirteen-week) U.S. Treasury bills for delivery in March, June, September, and December. Originally, there were only four contracts traded, the latest being for delivery only one year in the future. But in July 1976 the number of contracts was increased to six, the latest being for delivery eighteen months in the future. The size of each contract is $1 million, in terms of the face value at maturity. Thus, a sale of eight futures contracts of March 1978 Treasury bills is a sale of $8 million of thirteen-week Treasury bills to be deliv ered in March 1978 at an agreed upon price. Simi larly, a purchase of eight futures contracts of March 1978 Treasury bills is a purchase of $8 million of thirteen-week Treasury bills to be delivered in March 1978 at an agreed upon price. If held to delivery, a futures contract is settled on the business day follow ing the last day of trading in the delivery month.1 Futures trading terminates on the second business day following the Treasury auction of three-month bills in the third week of the delivery month. For example, March 1978 Treasury bill futures contracts are deliv ered in the third week of March, with the delivered 1Details on the Treasury bill futures market are contained in Chicago Mercantile Exchange, Opportunities in Interest Rates: Treasury Bill Futures (Chicago, 1976), and Inter national Monetary Market Division, International Mone tary Market Year Book 1975-76 (Chicago, 1976). Con tract information was also provided by the Statistical Department of the Chicago Mercantile Exchange. interest-rate risk by individuals willing to bear such risk in return for the possibility of making a profit.2 Futures Markets, Information, and Market Expectations Trading in futures markets provides information to the cash market about the commodity being traded.3 Prices of futures contracts for delivery of a 2For a discussion of the futures markets and the roles of hedg ing and speculation, see Thomas A. Hieronymus, Economics of Futures Trading: For Commercial and Personal Profit, 2nd ed. (New York: Commodity Research Bureau, Inc., i9 7 7 ). Uses of the Treasury bill futures market in terms of hedg ing and speculation are basically the same as those of the mortgage futures market. In addition, a discussion of the costs and benefits of the Treasury bill futures market would be essentially the same as a discussion of the costs and bene fits of the mortgage futures market. For such analyses of the mortgage futures market, see Neil A. Stevens, “A Mortgage Futures Market: Its Development, Uses, Benefits, and Costs,” this Review (April 1976), pp. 12-19. 3For a discussion of the effect of futures trading on information in spot markets, see Charles C. Cox, “Futures Trading and Market Information,” Journal of Political Economy ( Decem ber 1976), pp. 1215-37. Treasury bills maturing at the end of three months (the third week of June 1978). Although the size of a single contract is $1 million, a person interested in buying or selling a contract can trade in this futures market on margin. The minimum initial margin is $1,500 per contract, and the commis sion for executing an order is $60 per contract. By off setting an initial buy or sell order prior to the delivery date, it is possible to trade in Treasury bill futures contracts with far less money than the $1 million face value of each contract. Prices in the Treasury bill market are quoted on a discount basis, that is, at a price lower than the face value, and prices in the Treasury bill futures market are also quoted on a discount basis. The interest earned on a Treasury bill, if held to maturity, is the difference between the purchase price and the face value (or par price). Prices in the Treasury bill futures market are quoted in terms of the IMM (International Monetary Market) Index, which represents the difference be tween the Treasury bill yield (discount) on an annual basis and 100 (face value or par).2 For example, Table I shows the futures price and yield quotations for Treasury bills on March 14, 1977, as published by The Wall Street Journal. The March 1977 futures price at the close of trading (the settlement price) was 95.39, so that the interest rate (yield on a discount basis) on the March 1977 contract was 4.61 percent (100 — 95.39). -Opportunities in Interest Rates, pp. 27-29. commodity at a future date provide market partici pants with information as to the expected pattern of future spot prices of this commodity. This is because information relating to the future state of the market for a particular commodity is utilized by market par ticipants when determining the price at which they are willing to buy or sell futures contracts. If a trader projects that a commodity’s price will be different in the future than at the present time, he will buy or sell contracts for delivery of the com modity at some future date as if his projection were correct. Any trader who has better information about future spot prices than other market participants (or feels that he does) can attempt to make profits by trading on this information, with the result that such information is quickly incorporated into the prices of futures contracts. Thus, the interaction of all traders in the futures market provides price quotations which embody the market’s expectations of the future spot prices that will prevail on various delivery dates. Page 3 FEDERAL RESERVE BANK OF ST. LOUIS In the case of the futures market in Treasury bills, the yields on futures contracts indicate the pattern of interest rates expected by market participants to pre vail in certain months in the future, given currently available information. Any expectation of future in terest rates, however arrived at, utilizes information about the current and expected values of variables that are thought to influence the behavior of interest rates. Such variables include measures of the current and future state of the economy, the supply and de mand for credit, and the course of monetary and fiscal policy. The futures market in Treasury bills serves the role of a processor of this information. As new information about the course of key factors influencing interest rates becomes available, it is rapidly reflected in futures market prices.4 The expected interest rate for any date in the future which is embodied in the yield on current futures contracts is not necessarily the interest rate that will prevail at that future date. Market partici pants in the futures market do not have a crystal ball that foretells the future perfectly. Their decisions to buy or sell contracts are based on the information available at th e presen t tim e. As new information be comes available, market participants may very well revise their expectations. The effect of new informa tion — such as a change in the announced monetary targets, new budget projections, revised projections of the strength of economic activity, new pricing policies by O PEC, and so on — is reflected in changes in the prices of (and yields on) futures contracts. Consequendy, ch an g es in market expectations can be identified by shifts in the pattern of yields on futures contracts (futures rates). Sharp declines or increases in futures rates can be identified as changes in the ex pected level of future interest rates. Thus, a compari son of the quotations on futures contracts at two dif ferent points in time provides information on whether 4This discussion does not imply that the Treasury bill futures market satisfies the “efficient market” hypothesis. In an “effi cient market”, all available information is utilized immediately by traders (and potential traders), new information is avail able to everyone at the same time, and new information is immediately incorporated into market prices and yields. The discussion in the paper implies only that some of the avail able information is utilized by traders (or potential traders), and that new information which is utilized is quickly reflected in futures prices. This allows for information costs and imperfect information among market participants. For a general discus sion of the “efficient market” model, see Oldrich A. Vasicek and John A. McQuown, “The Efficient Market Model,” Fi nancial Analysts Journal ( September - October 1972), pp. 7184. For a theoretical treatment, see Eugene F. Fama, “Effi cient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance (May 1970), pp. 383-417; or Richard Roll, The Behavior of Interest Rates: An Application of the Efficient Market Model to U.S. Treasury Bills (New York: Basic Books, Inc., 1970). 4 Digitized forPage FRASER JUNE 1977 market expectations have changed with regard to the future level of short-term rates. One implication of this is that it may be possible to assess the effect of a change in monetary or fiscal policy on market expectations of future short-term interest rates. Futures Rates and Expected Spot Rates One way of looking at the price and yield quota tions on Treasury bill futures contracts in Table I is to interpret the yields on each futures contract as a market estimate of the three-month Treasury bill rate that is currently expected to prevail in each delivery month. Thus, the market’s expectation on March 14, 1977, was that the three-month bill rate would be 5.23 percent in June of this year, and would increase another 126 basis points by December to 6.49 percent. In comparison, the three-month bill rate on March 14, 1977, for currently traded three-month bills, was about 4.57 percent. However, such use of the Treasury bill futures rates is subject to some reservations. The main ques tion is whether the futures rates are unbiased esti mates of the market’s expectations of future interest rates. According to the “normal backwardation” argument of Keynes and Hicks, futures p rices are downward-biased estimates of expected future spot prices.5 This implies that even if future spot prices are expected to remain the same as the current spot price, the futures price will be below the expected spot price by an amount equal to a risk premium. This premium is considered to be a return to specu lators for assuming the risk of possible future price fluctuations, and is larger for delivery dates which extend further into the future. This implies, in turn, that the price of the futures contract will tend to rise (the yield will fall) as the delivery date ap proaches, provided there is no change in market expectations. In terms of futures markets in Treasury bills, the theory of “normal backwardation” implies that yields on futures contracts are u piv ard -biased estimates of expected future interest rates (since prices and yields of securities are inversely related). Accordingly, the interest rate on three-month Treasury bills expected to prevail as of some future delivery date is less than the yield quoted on the futures contract for that 5John Maynard Keynes, A Treatise on Money: The Applied Theory of Money, vol. II (New York: Harcourt, Brace and Company, 1930), pp. 142-47; and J. R. Hicks, Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory, 2nd ed. (Oxford: Clarendon Press, 1946), pp. 136-39. FEDERAL RESERVE BANK OF ST. LOUIS JUNE 1977 Table 1 FUTURES Delivery M onth P R IC E S FOR U .S. T R E A S U R Y BILLS O N Price O pen High Low C lo se * MARCH 14, 1977 Y ie ld ** Change* * ( Discount) Yield C h an ge * March 19 77 9 5 .3 7 95.4 0 9 5 .3 7 95.39 + -01 4.61 — .01 June 1 9 7 7 94.7 3 94.84 94.71 9 4 .7 7 + .03 5.23 — .03 September 1 9 7 7 94.1 0 94.1 6 94.05 94.1 0 + .01 5.90 — .01 December 1 97 7 93.52 93.5 6 93.4 6 93.51 — .01 93.05 9 3 .1 7 93.04 93.13 .01 .08 6.49 March 1978 + + 6.87 - .08 June 1978 92.6 6 92.75 92.6 6 92.6 6 7.34 ♦Closing price is the settlement price. ♦♦Based on the closing (or settlement) price. Price and yield changes are the changes from the previous day. Source: The Wall Street Journal, March 15, 1977 delivery date.6 In addition, if yields on futures con tracts are higher for later delivery dates than for earlier delivery dates, it is not certain that the ex pected future spot rate is higher for the later deliv ery dates than for the earlier delivery dates. This is because a larger risk premium is included in the yield associated with the later delivery dates. Only if the difference between the yields for an earlier and later delivery date exceed the difference between their risk premia can one conclude that the expected future spot rate is higher for the later delivery date. One implication of this line of reasoning is that gradual declines in futures rates cannot necessarily be identified as declines in market expectations of future spot rates, since the yields on futures contracts tend to fall as the delivery date approaches. How ever, sharp declines indicate a change in expectations, as do increases in futures rates, provided the risk premia are constant or change very little (which is generally assumed by the theory). If these risk premia could be easily estimated, market expectations of future interest rates could be estimated from quotations on futures contracts. Unfor tunately, this is not the case. In addition, other ana lysts dispute the “normal backwardation” argument and claim that futures prices are u n b iased estimates of expected future spot prices.7 The issues surround8Hicks used the “normal backwardation” argument of the futures market in his development of the liquidity preference theory of the term structure of interest rates. See Hicks, Value and Capital, Chapters XI and XIII. In the literature on the term structure, market expectations of future interest rates have been examined using the implied forward rates which are embodied in the yield curve. These implied for ward rates are theoretically equivalent to futures rates. 7For discussions of the issues involved and some empirical evidence in support of normal backwardation, see Hendrik S. Houthakker, “Normal Backwardation,” in Value, Capital, and Growth: Papers in Honour of Sir John Hicks, ed. James N. Wolfe (Edinburgh: Edinburgh University Press, 1958), Chap ter 7, and “Can Speculators Forecast Prices?” The Review of Economics and Statistics (May 1957), pp. 143-51. For evi dence against the theory of normal backwardation, see Lester ing this question of unbiasedness are not within the scope of this paper, but some observations on the matter can be made. Even if futures rates are biased estimates of mar ket expectations, the bias will not be very large, judging from the estimates of risk premia embodied in the yield curve.8 Furthermore, the bias, if it exists, is expected by most theorists to be consistent over time, rather than being subject to large fluctuations. Consequently, even though futures rates may not be entirely accurate as point estimates of market expec tations, it may be possible to make rough estimates of expected future interest rates. Trading Volume Another issue bearing on the usefulness of the futures rates involves the amount of trading which occurs in each contract. Generally, it is thought that the larger the amount of trading in a security, the more representative the price and yield quotations G. Telser, “Futures Trading and the Storage of Cotton and Wheat,” Journal of Political Economy (June 1958), pp. 23355. Telser argues that prices of futures contracts are solely market expectations of future spot rates and contain no risk premia. 8Since such premia in the Treasury bill futures market will be, at most, for three-month bills eighteen months in the future, the bias in the yields on futures contracts will not be very large. This is due to the fact that the premia, according to the liquidity preference theory, increase with term-to-maturity for such Treasury bills. Thus, the premia associated with three-month bills to be issued six months from today are expected to be smaller than the premia associated with threemonth bills to be issued one year from today. Estimates of these premia have generally been less than 50 basis points. See J. Huston McCulloch, “An Estimate of the Liquidity Premium,” Journal of Political Economy (February 1975), pp. 95-119; Roll, The Behavior of Interest Rates, p p . 98-99; and Edward J. Kane and Burton G. Malkiel, “The Term Structure of Interest Rates: An Analysis of a Survey of Interest-Rate Expectations,” The Review of Economics and Sta tistics (August 1967), pp. 345-55. The existence of a bias in the futures rates can be tested by investigating whether, with constant expectations, the prices of futures contracts rise (yields fall) as the delivery date approaches. Page 5 FEDERAL RESERVE BANK OF ST. LOUIS JUNE 1977 Table II AVERAGE D A IL Y T R A D I N G V O L U M E BY M O N T H Contract Delivery Month Month Traded January 1976 February 1976 March 1976 April 1976 May 1976 June 1976 July 1976 August 1976 September 1976 October 1976 November 1976 December 1976 January 1977 February 1977 March 1977 April 1977 March 1976 June 1976 128.95 58.89 27.46 36.79 41.53 182.39 141.76 92.00 26.47 Septembe r December 1976 1976 18.11 21.74 71.17 120.43 224.45 230.14 242.43 60.73 19.67 4.88 12.71 29.83 39.00 84.60 87.55 258.57 273.50 185.43 119.71 59.30 31.88 ............. ...... ...... ...................................... ................... .................. September December June March June March September 1977 1977 1977 19 77 1978 1978 1978 Total All (Issues) 188.72 134.86 7.84 5.00 17.37 27.36 43.05 68.64 107.62 290.71 345.65 236.43 216.67 79.32 36.59 318.69 306.19 7.58 10.45 18.43 11.50 39.81 160.57 315.40 294.81 398.48 415.05 350.91 232.65 7.71 2.32 4.00 27.71 67.75 122.95 301.33 242.26 386.04 518.45 6.05 2.41 3.10 15.19 20.35 36.90 74.71 88.05 174.09 523.25 2.00 4.29 22.55 17.67 35.14 17.21 50.74 172.10 3.86 8.26 27.13 75.75 27.67 42.85 426.00 381.97 576.24 419.09 361.62 618.19 831.00 740.64 1030.19 850.16 1053.17 1565.05 Source: International Monetary Market Division of Chicago Mercantile Exchange will be of the market value of the security.0 In the case of Treasury bill futures contracts, this suggests that contracts with low trading volume are not rep resentative of the market value of these contracts, and, hence, are not representative of market expecta tions. However, the issue is more complicated than this. As can be seen from Table II, trading in any par ticular futures contract is low when it is first traded, increases over time, but then is again low as its delivery date approaches. For example, trading in the futures contract for delivery in March 1977 can be examined by reading down the appropriate column in Table II. This issue was first traded in March 1976, and the average daily volume of trading was only 7.84 contracts. By November 1976, trading in creased to over 345 contracts per day. But after January 1977, with less than two months to the delivery date, trading declined below 100 contracts per day. As the delivery date approaches, trading volume generally declines because there is greater certainty as to what the spot rate will be on the delivery date. That is, traders tend to agree as to the future market value of three-month Treasury bills (their expecta tions become homogeneous) when the delivery date is near. Consequently, there is less risk of interest rate fluctuations to be hedged against and less likeli hood that profits can be made from trading, so that less trading occurs. In this case, the futures rates do 9This line of reasoning underlies, in part, the construction of the Treasury Department’s yield curves, which give greater weight to the yields of some actively traded issues. Page 6 reflect the market valuation of the contracts, even though there is little trading. However, a lack of trading may also be indicative of a case where market participants have ill-defined expectations of future interest rates and their expec tations are so diffuse that traders’ bid or asked prices are not matched up with each other. In this case, there is little trading because there is great uncertainty as to the range in which the future spot rate will fall. It is possible that this case applies to the futures rates associated with contracts for deliv ery in fifteen to eighteen months, such as the March 1978 contract which was first traded in September 1976 (T ab le I I ) . On the other hand, when market participants have well-defined but heterogeneous expectations of future spot rates, trading activity is likely to be large. In this case, traders tend to agree as to the range in which the future spot rate will fall, but disagree as to the exact value. Market participants perceive that there is greater risk of interest rate fluctuations to be hedged against, and that profits can be made from trading. Bid and asked prices on contracts for the delivery date match up over a larger number of traders, and trading volume is larger. Therefore, the extent to which the yields on futures contracts for particular delivery dates accurately reflect the market value of these contracts, and market expec tations of future interest rates, depends upon the distribution of the expectations of traders. It is not simply a matter of the amount of trading in each contract. FEDERAL RESERVE BANK OF ST. LOUIS The volume of trading also reflects on the Treasury bill futures market as a whole. The volume of trading in futures contracts compares quite favorably with the volume of trading in the spot market for Treasury bills. The total volume of trading in the Treasury bill futures market was relatively light during the first two months of trading after its opening on January 6, 1976. But beginning in March 1976, trading in creased substantially to an average daily volume of about 318 contracts (T ab le I I ) . W ith each contract representing $1 million of three-month bills, this trading represented the daily exchange of $318 mil lion of Treasury securities in the futures market. In contrast, the average daily volume of trading by se curities dealers in the spot market for all outstanding Treasury bills (approximately forty different issues) was $6.76 billion during March 1976. These figures average out to a daily volume of roughly $64 million for each Treasury bill futures market issue (five issues were traded in March 1976), compared to about $169 million for each outstanding Treasury bill issue in March 1976. MARKET EXPECTATIONS OF SHORT-TERM INTEREST RATES SINCE JANUARY 1976 The pattern of yields on Treasury bill futures con tracts since the initiation of trading on the Interna tional Monetary Market is shown on a daily basis in Chart I. Examining the movement of these yields provides some insight into the adjustment of market expectations of future short-term interest rates to new information about the state of the economy and the future supply of and demand for credit. The chart shows that die yields on all of the futures contracts being traded during any particular time period follow the same pattern of movement to a remarkable degree. During the first quarter of 1976, market expecta tions of the future level of the three-month Treasury bill rate increased as the economy experienced a 9.2 percent annual rate of growth in Real Gross National Product (G N P ). W ith the economy growing at such a rapid pace, market participants apparently antici pated a continuation of this upswing in economic activity during the remainder of the year, although not at so fast a pace. This expected strength in eco nomic activity was translated into anticipations of increased demands for short-term credit, with a con sequent rise in interest rates. During March 1976, the yield on the September 1976 futures contract was generally above 6.50 percent, while the currently JUNE 1977 traded three-month Treasury bill yielded about 5 percent. The yields on futures contracts declined during April 1976, but by May yields had returned to roughly the same levels as were recorded in March (C hart I ) . During most of April 1976, newly available data indicated moderating pressures on the credit market and expectations of future levels of interest rates were revised downward. For example, the yields on the September 1976 futures contract during April were close to 6 percent, down from about 6.5 percent in March. Data on the money stock ( M l ) that became available in the first half of April showed that the money stock had grown at a 2.9 percent rate over the first quarter of 1976, well below the FO M C ’s an nounced target ranges for M l growth.10 Most market participants apparently did not anticipate any nearterm tightening in monetary policy actions, and viewed the growth of money as being consistent with a continued gradual reduction of the longer-run infla tionary impact of policy actions. The preliminary GNP data available in mid-April continued to show a slowing in inflation and a strong surge in real output growth. Business loan demand at commercial banks remained weak and Treasury financing requirements were running well below earlier estimates. Beginning in late April 1976, however, there were several developments that acted to change market expectations. On April 22, market participants became aware that there had been a very sharp surge in M l in early April (money stock data is reported with a one-week lag ). Data available in May indicated that the money stock was rising very rapidly, ex panding at nearly a 17 percent annual rate in April and then at a 5.7 percent rate in May. On May 3 it was announced that the FO M C had voted at its April meeting to lower the upper band on the long-run growth of M l from 7V2 to 7 percent.11 The Federal Reserve moved to a more restrictive policy, and this was made apparent to market participants by a steady rise in the Federal funds rate from about 4.78 per cent in the week ended April 23 to 5.02 percent in the week ended May 14. Then, at its May 18 meet ing, the FO M C voted to adopt a Federal funds range of 5 - 5 % percent, compared to a 4% - 5% percent range at the April meeting. By the week ended May 28, the Federal funds rate had risen to an average of 10Albert E. Burger and Douglas R. Mudd, “The FOMC in 1976: Progress Against Inflation,” this Review (March 1977), pp. 2-17. 11Ibid. Rates of growth of the money stock used in this paper are the originally reported figures, not the subsequently re vised figures. Page 7 ’■ ti p OQ <t> 00 Y i e l d s o n T r e a s u r y Bi ll F u t u r e s C o n t r a c t s 11 Ja n u a ry 1976 - April 1977 L I A ll y i e l d s a r e o n a d i s c o u n t b a s is. S o u r c e : In t e r n a t io n a l M o n e t a r y M a r k e t D iv is io n FEDERAL RESERVE BANK OF ST. LOUIS 5.50 percent. As this new information about the course of monetary developments became available, market anticipations of future levels of interest rates returned by late May to about the same level as was recorded in March 1976. The expected increase in credit demand failed to appear, GNP growth remained moderate, the inflation rate declined, and the unemployment rate increased during the summer of 1976. Growth of the money stock fell to about a 3 percent rate from May to September. Yields on futures contracts and the spot rate on three-month bills both declined slowly from late May until early October,12 when the yields on futures contracts fell quite sharply. This sharp decline was reversed in late October when yields increased almost to their early September levels. This reversal in expected yields was also associated with incoming monetary data that indicated a sharp surge in the rate of growth of the money stock. From September to October, M l increased at a 15.5 percent annual rate. Indicators of the strength of economic activity con tinued to decline during the last quarter of 1976, as did the rate of inflation, and market interest rates on all types of securities continued to decline. In the last half of November, market expectations of future interest rates declined sharply. After the surge in M l growth during October, the money stock was little changed during November. But the Federal funds rate declined from about 5 percent in early November to about 4.75 percent in early December, which, in turn, was interpreted by market partici pants as indicating that the Federal Reserve had adopted a somewhat less restrictive policy. During November, yields on futures contracts fell 50 basis points or more. W ith pessimism about the “pause” in the economy mounting, yields on futures contracts for Treasury bills continued to fluctuate around these lower levels until the end of the year. The increase in expected future interest rates in early January 1977 coincided with the new Adminis tration’s announcement of a stimulative fiscal pack age. At the same time, data on the economic indi cators for November were revised upward and a strong showing of some of the indicators for Decem ber was reported. Furthermore, monetary actions were no longer moving toward a further reduction in the 12Under the “normal backwardation” hypothesis, this gradual decline in futures rates may not reflect a gradual decline in market expectations of future spot rates. Instead, such a gradual decline over time is consistent with constant market expectations of future spot rates, since if “normal backwarda tion” holds, futures rates tend to fall (futures prices rise) as the contract delivery date approaches. JUNE 1977 Federal funds rate, contrary to the initial expectations of many market analysts. As a result, yields on futures contracts increased to their levels of mid-October through early November. From early January through March 1977, yields on futures contracts were relatively stable. During April, when the Administration’s rebate program was can celled and the energy program was announced, fu tures rates fluctuated sharply. As new information on the state of the economy and on future supplies and demands for credit becomes available to market par ticipants, the expected future interest rates that are embodied in the yields on future contracts for U.S. Treasury bills will be revised. Movements in the levels of these yields will, therefore, provide a significant indicator of revisions of market expectations of future short-term interest rates. SUMMARY AND CONCLUSIONS The Treasury bill futures market provides a means for hedging against interest-rate risk. Speculators are allowed the opportunity of making profits in this market in return for bearing the risk of future interest rate fluctuations. In addition, futures markets provide information about the expected future pattern of prices. In doing so, indications of changes in market expectations of future short-term interest rates can be obtained. Although exact estimates of the expected level of future spot rates may not be obtainable from futures rates without adjusting for a risk premium, an approximation of the level is possible. If it can be shown that futures rates are unbiased estimates of expected future interest rates, the data from the Treasury bill futures market could be very useful in a number of ways. Policymakers would be able to readily assess the effects of policy changes on market expectations of future interest rates. Econ omists and other researchers would have o b serv a b le values for market expectations of interest rates, in stead of having to use proxy variables for such ex pected rates. Analyses of the portfolio behavior of financial intermediaries, investment decisions of firms, and the term structure of interest rates are among the many areas of research which would be aided by the use of such data. In addition, analysts who fore cast interest rates would be able to compare their estimates of future interest rates against the market’s expectations. Since market expectations of interest rates are an important factor in many economic rela tionships, the information on expectations contained in the Treasury bill futures market will be of increas ing interest to businessmen, financial managers, pol icymakers, and other economic analysts. Page 9 Energy Resources and Potential GNP ROBERT H. RASCHE and JOHN A. TATOM X H E dramatic change in supply conditions for energy resources since 1973 had a substantial effect on the productive capabilities of the U.S. economy. Higher prices of energy resources, relative to the prices of labor and capital resources, resulted in a loss of economic capacity and higher output prices. It has been estimated that four to five percentage points of both the higher price level and reduction in national output in 1974 were due to the increased scarcity of energy resources entailed by the quadrupling of O PEC petroleum prices.1 The loss of national output because of energy mar ket developments was a permanent loss. The energy price revision reduced the effective supply of re sources available. Thus, the rate of output achievable by fully utilizing the nation’s resources, the “potential” output of the economy, was lowered. Conventional methods of measuring the economy’s potential have focused primarily upon the availability and productivity of la b o r resources. More recently such efforts have also attempted to account for the availability and productivity of ca p ita l resources. Es timates of potential output which consider the rela tionship of only capital and labor resources to national output are not well suited to the task of accounting for the effects of changes in the availability or cost of energy resources. Nevertheless, the Council of Eco nomic Advisers (C E A ) has recently pointed to evi dence which indicates that a permanent drop in the productivity of U.S. capital and labor resources may have occurred after 1973. The CEA suggests that this drop is due to the higher cost of energy resources.2 A direct route to estimating potential output, which accounts for the supplies of labor, capital, and energy resources under conditions of full utilization, is pos sible. Such an approach shows that a preoccupation with the supply of energy resources in measuring po tential output is not important prior to 1973. Only !See Robert H. Rasche and John A. Tatom, “The Effects of the New Energy Regime on Economic Capacity, Production, and Prices,” this Review (May 1977), pp. 2-12. 2See Council of Economic Advisers, Economic Report of the President, 1977, pp. 55-56. Page 10 small year-to-year changes in the relative scarcity of energy occurred before 1973. The effect of such changes was minor and capable of being captured by the trend growth of productivity of labor and capital. However, such a direct approach also demonstrates the fundamental importance of accounting for energy in measuring potential output after 1973. W hen energy is included in the production relationship link ing resources to output, the effect of the increased scarcity of energy is seen to be of the magnitude of our earlier estimates which were based upon eco nomic theory and more indirect evidence. Aside from clarifying the recent performance of the U.S. economy relative to its potential, estimates of potential output which account for energy resources have important implications for economic and social prospects. Potential output measures which do not include the loss due to the change in the world energy market overstate the gains in output achievable by full utilization of resources. Consequently, such meas ures, in addition to endorsing impossible short-term growth possibilities, foster an inflationary bias in ef forts to achieve an unattainable potential output. Also, unrealistically high estimates of potential output im ply corresponding overestimates of the tax revenues associated with full resource utilization. Thus, federal budget planning tends to have a greater bias toward deficits. THE DEVELOPMENT OF MEASURES OF POTENTIAL GNP The Original CEA Estimates The notion of potential GNP, the output rate pro duced when the economy fully utilizes its resources, was first developed by the Council of Economic Ad visers in 1962.3 The original estimates of potential GNP were based on three simple statistical approaches 3See Council of Economic Advisers, Economic Report o f the President, 1962, pp. 49-56, and Arthur M. Okun, “Potential GNP: Its Measurement and Significance,” American Statisti cal Association, 1962 Proceedings of the Economic Statistics Section, pp. 98-104, also reprinted in his The Political Econ omy of Prosperity, (Washington, D.C.: Brookings Institution, 1970). FEDERAL RESERVE BANK OF ST. LOUIS JUNE 1977 C h o rt I " O l d C E A ” P o te n tia l G N P a n d A c t u a l O u t p u t L a te st d a t a p lotted : 1 9 7 6 S o u r c e s : U .S. D e p a rtm e n t o f C o m m e rc e a n d C o u n c il of E c o n o m ic A d v is e r s developed by Okun that related the unemployment rate to actual real GNP. The estimates assumed that full utilization of resources occurs when the unemploy ment rate for the civilian labor force is four percent, that is, the economy operated at its potential in mid1955. The original estimates assumed that potential output grew at an annual trend rate of about 4.5 per cent from 1947 to 1953, and at about a 3.5 percent rate from 1953 to 1962.4 The original estimates achieved widespread recog nition. The simple device of relating departures of the unemployment rate from four percent to the “gap” between actual and potential output facilitated the popular discussion of both economic goals, such as full employment and growth, and fiscal policy. W ith regard to the latter, the notion of a high-employment Federal budget was developed and used to indicate the state of the budget deficit or surplus under high-employment economic conditions as well as the magnitude of fiscal efforts required to move the economy to a four percent unemployment rate. Since these original estimates, the CEA has recog nized that various forces, particularly demographic 4See Okun, “Potential GNP,” pp. 101-02. factors, can change the trend rate of growth of re sources and, hence, potential output. Consequently, the CEA has from time to time adjusted the trend rate of growth used to update their data series for potential output. From 1952 through 1962, the CEA uses the 3.5 percent trend rate of growth derived by Okun. This trend rate was raised to 3.75 percent for the period from 1962 through 1968 and further increased to four percent from 1969 through 1975. Because of a slow down in the rate of growth of the labor force, the CEA reduced the trend rate of growth of potential GNP after 1975 to 3.75 percent. This series is referred to below as the “old” CEA estimate and is shown in Chart I along with actual GNP.5 Okun indicated in his original work that his analysis skipped over important links between changes in the unemployment rate and output, and in an often quoted passage he concluded: Still, I shall feel much more satisfied with the esti mation of potential output when our data and our analysis have advanced to the point where the esti 5For a full description of the old estimate see the note in U.S. Department of Commerce, Bureau of Economic Analysis, Business Conditions Digest (September 1976), p. 95 and the discussion in issues of the CEA Economic Report since 1962. Page 11 FEDERAL RESERVE BANK OF ST. LOUIS mation can proceed step-by-step and where the cap ital factor can be taken explicitly into account.6 Since 1962 several studies have attempted to improve upon the original work. The major efforts attempted to account for capital resources and for the interaction between actual output and prospective potential out put. The major development has been to use an ap proach based upon an aggregate production function.7 However, until recently no serious problems have been detected with the old CEA estimates.8 The “New” CEA Potential Output Series More recently, studies of potential output have in dicated some major departures from old estimates. In addition to the slowdown in the long-term growth of the labor force pointed out by the CEA in the fall 1976 revision of the growth trend, a study by Data Resources, Inc., suggests a further slowdown since 1973 because of a substantial decline in the growth of the capital stock.9 More importantly, the CEA itself has pointed out an apparent slowdown in productivity growth since 1966. Clark has developed a new poten tial output series for the CEA which is based, to an extent, on production function estimates rather than simple trends.10 These new estimates imply a growth rate of potential output of about 3.5 percent in the 6Okun, “Potential GNP,” p. 104. 7A few of the major studies are: Edwin Kuh, “Measurement of Potential Output,” American Economic Review (Septem ber 1966), pp. 758-76; Lester C. Thurow and L. D. Taylor, “The Interaction Between the Actual and the Potential Rates of Growth,” The Review of Economics and Statistics (N o vember 1966), pp. 351-60; Stanley W. Black and R. Robert Russell, “An Alternative Estimate of Potential GNP,” The Review of Economics and Statistics (February 1969), pp. 70-76; and Benjamin M. Friedman and Michael L. Wachter, “Unemployment: Okun’s Law, Labor Force, and Productiv ity,” The Review of Economics and Statistics (May 1974), pp. 167-76. 8For example, see the discussion by George M. vonFurstenberg, “Comments on Estimating Potential Output for the U.S. Economy in a Model Framework,” Achieving the Goals of the Employment Act of 1946 — Thirtieth Anniversary Review, U.S. Congress, Joint Economic Committee, 94th Cong. 2nd sess., December 3, 1976, pp. 26-28. He points out that more elaborate “supply-orientecf models” are valuable for improv ing understanding, but estimates from them are not “demon strably more reliable” than the old official estimates. He also notes that the usefulness of the old CEA potential output estimates “would be unaffected by anyone showing, for in stance, that potential is consistently one percent larger or smaller than officially estimated” (p. 2 8 ). 9See Roger Brinner, “Potential Growth to 1980,” Otto Eckstein et. al., Economic Issues and Parameters of the Next 4 Years, (Lexington, Massachusetts: Data Resources, Inc., Economic Study Series, 1977), pp. 9-17. 10See the CEA, Economic Report, 1977, pp. 45-57 and Peter K. Clark, “A New Estimate of Potential GNP,” Council of Economic Advisers, unpublished memorandum, January 27, 1977. Digitized forPage FRASER 12 JUNE 1977 late 1960s and early 1970s. These new estimates are in agreement with projections made in 1972 by William Nordhaus.11 In two respects the new CEA series on poten tial output represents a major departure from the methods used to compute the old series. First, poten tial output now is viewed more as high-employment output rather than being linked to a four percent un employment rate. The new CEA estimates are based on explicit considerations of participation rates and dif ferential high-employment unemployment experiences of different age-sex groups. The high-employment benchmark of a four percent civilian labor force un employment rate in mid-1955 is preserved, but the new series is based on explicit estimates of the revi sion in the high-employment benchmark over time due primarily to changes in the composition of the labor force. The second major departure is an at tempt to account more explicitly for capital resources in the estimation of productivity and potential output. However, the new estimates of the CEA do not take into account a further one-time reduction in produc tivity and potential output which their analysis indi cates occurred in 1974 and which they suggest may be a permanent change due to the energy price shock.12 A comparison of the new and old series is presented in Chart I I for the period 1952-1976. Until 1967, the two CEA potential output series are very similar. The new CEA estimates show potential output to be about one percent lower from 1952 to 1967, but growing at roughly the same rate. After 1967 the new estimates fall short of the old series by a growing amount. By 1976 the new estimate of $1363.6 billion is only 95.9 percent of the old estimate of $1421.2 billion.13 The bulk of the $57.8 billion reduction is attributed to a slowdown in the growth of labor productivity and an increase in the full-employment unemployment rate. As noted above, the CEA has suggested that pro ductivity fell further in 1974, so that by 1976, poten tial output may be $30 billion lower than their own new estimates. These new estimates, like those of D ata Resources, Inc., mentioned above, assume a n See William D. Nordhaus, “The Recent Productivity Slow down,” Brookings Papers on Economic Activity (3 :1 9 7 2 ), pp. 493-545. 12While the Economic Report discusses the new estimates, neither the old nor new series have been published in the monthly publication of the Bureau of Economic Analysis, Business Conditions Digest, since October 1976. 13See CEA, Economic Report, 1977, p. 55. All potential output measures are in constant (1 9 7 2 ) dollars throughout this article. JUNE FEDERAL RESERVE BANK OF ST. LOUIS 1977 C h a rt II R a tio o f " N e w L a te st d a t a plotted: 1 9 7 6 C E A ” to " O l d C E A ” P o te n tia l G N P S o u r c e : C o u n c il o f E c o n o m ic A d v ise rs Cobb-Douglas production function with only labor and capital resources and assume output elasticities of one-third for capital and two-thirds for labor. Thus, neither estimate is able to capture fully changes in productivity of labor and capital resources due to reductions in potential energy usage associated with a higher relative price of energy resources. the E-H study is similar to that used here, the conclu sions are markedly different. These differences result from serious data problems and a specification error in their demand for energy. Since their study has such a similar methodology and reaches such different re sults, a full critique is contained in Appendix I.15 The production-function approach to the estimation of potential output taken in this article accounts explicitly for energy resources. The potential output measures draw heavily upon the recent work involved in the new CEA measures of potential output, specifi cally by using their estimates of the potential labor force and the full-employment unemployment rate. ACCOUNTING FOR ENERGY IN AN AGGREGATE PRODUCTION FUNCTION One recent study, that of Eckstein and Heien (E -H ), has attempted to account for energy effects on poten tial output through the aggregate production func tion.14 The E-H results indicate, however, that in recent years potential output is much higher than the old CEA estimates. W hile the methodology used in 14Albert J. Eckstein and Dale M. Heien, “Estimating Potential Output for the U.S. Economy in a Model Framework,” Achieving the Goals of the Employment Act of 1946 — Thirtieth Anniversary Review, U.S. Congress, Joint Eco nomic Committee, 94th Cong., 2nd sess., December 3, 1976, pp. 1-25. The first step in a production-function approach to measuring potential output is the estimation of an 1“Another study which includes energy price developments in an estimate of potential output is that by Jacques R. Artus, “Measures of Potential Output in Manufacturing for Eight Industrial Countries, 1955-78,” International Mon etary Fund Staff Papers (March, 1977), pp. 1-35. Like Clark’s study he finds an energy price impact using a dummy variable approach instead of explicitly incorporat ing the energy price. Since his study includes seven countries he is forced by data limitations to impose several arbitrary constraints which raise serious questions about the meaningfulness of his coefficient estimates. Relaxing the con straint that the effect is the same across countries, his esti mate of the energy price impact is that U.S. potential manufacturing output fell 2.7 percent in 1974 which is below both Clark's estimate of 4.2 percent for the private business sector and our earlier estimate of five percent which is confirmed below. Ignoring the other constraint problems, it may be noted that his estimate is not significantly different from ours given its relatively large standard error. Page 13 JUNE FEDERAL RESERVE BANK OF ST. LOUIS aggregate production function. The approach taken here follows the usual practice with one major ex ception: energy resources are considered as an inte gral part of the production function. This is in con trast to the usual practice of estimating the functional relationship between output and only labor and capital resources. The latter approach implicitly as sumes that changes in the stock and flow of energy resources are captured by movements in the capital stock and need not be explicitly taken into account. The measure of output for which a production func tion is estimated is the output of the private business sector. Real GNP includes, in addition to the out put of the private business sector, gross output orig inating in the rest of the world, the output of the general government sector, output imputed to owneroccupied dwellings, and output of households and nonprofit institutions. For estimating potential real GNP these components of actual GNP are simply added to potential real output of the private business sector. Actual real output in the private business sector depends upon the employment of capital and labor services as well as energy resources. The production function may be written as (1) 1977 the Federal Reserve Board index of capacity utiliza tion times the capital stock in place at the beginning of each period.17 The annual capital stock measure is the constant dollar (1972) net stock of fixed nonresidential equipment and structures.18 A comparable data series on energy use in the private business sec tor could not be found. However, the rate of energy use in the private business sector is presumably that demanded and the demand for energy is determined completely by the production function and the rela tive price of energy. If firms in the private business sector maximize economic profits, they employ energy at a rate where the value of the additional product obtained from employing more energy equals its price. The demand for energy from equation ( 1 ) is (2) E = y Y / - ) \ B where PF is the price of energy and PB is the price of output of the private business sector.19 Equation (2 ) can be used for the energy input in the production function so equation ( 1 ) may be found by estimating i (3) Y = ( A* ert L “ P “ y) l 'y Y = A e " L “ K'i Ey where Y is output, L is labor measured in manhours, K is the effective flow of capital services, E is the flow of energy resources, and t is time. The other terms in equation (1 ) are estimated statistically. The A term is essentially a scaling factor, r is the trend rate of growth of output due to technological change, and a , |3, y are the output elasticities of the respec tive inputs. The estimated production function was re stricted by requiring that the sum of the exponents a , p, y equal unity. The basic implications of such a “Cobb-Douglas” production function are constant re turns to scale and partial elasticities of substitution of unity.18 The output and manhours data for the private busi ness sector are those prepared by the Bureau of Labor Statistics of the U.S. Department of Labor. The effective services of capital are found by multiplying 16Constant returns to scale means that equal proportionate changes in each of the resources employed causes a propor tionate change in output. This is a common assumption em ployed in estimating production functions, especially at such a highly aggregated level. Unit partial elasticities of substitu tion have also been employed in earlier studies, although al ternative production function specifications exist which relax this constraint. Page 14 where A* is another scaling factor and P is the rela tive price of energy (P E/PB). The relative price of energy is measured by the ratio of the wholesale price index for fuel, related products, and power to the implicit price deflator for the output of the private business sector. The credibility of the assumed Cobb-Douglas pro duction function is, of course, purely an empirical matter that can be subjected to statistical testing. The assumption implies relatively high price and output elasticities of demand for energy and unit partial elasticities of substitution between energy and capital 17In a previous paper, “The Effects of the New Energy Re gime,” we discussed the possible biases of the FRB capacity utilization index in recent years as a result of changes in the relative price of energy, when it is viewed as a measure of utilization of economic capacity. In the present context, we need a measure of utilized capital. When this index is viewed as such a measure, there is no reason to believe that the change in the relative price of energy has introduced a systematic measurement bias. 18See John C. Musgrave, “Fixed Nonresidential Business and Residential Capital in the United States, 1925-75,” Survey of Current Business (April 1976), pp. 46-52. 19The marginal product of energy from equation ( 1 ) is y Y /E , so the profit-maximizing employment of energy occurs where PE = (v Y /E ) PB. FEDERAL RESERVE BANK OF ST. LOUIS or labor.20 There is, however, some evidence that these properties apply to the U.S. economy. An output elasticity of demand for energy of unity in the long run for at least the United States, Japan, and Western Europe is supported by a number of studies.21 Using cross-sectional data and the trans-log production func tion, Griffin and Gregory have demonstrated that for nine industrial nations the production function has partial elasticities of substitution of energy for capital and labor that are constant and unity.22 Most impor tantly for the purpose at hand, the assumption of a Cobb-Douglas production function cannot be rejected with the data examined. Recent studies of productivity suggest that in esti mating an aggregate production function it is impor tant to account for qualitative changes in manhours and for productivity differences in capital due to the increasing importance of mandated pollution-abatement capital expenditures.23 Attempts to control for skill differences by including variables for the com position of the labor force by age were unsuccessful except for the 16 - 1 9 age group; a negative effect of the share of the latter group on productivity was not statistically significant when the estimation was ad justed for autoregression. Clark’s gross capital stock data are adjusted for pollution-abatement capital. Use of his series produced results essentially identical to those found using the gross nonresidential stock of business capital (constant 1972 dollars). Thus, no attempt is made to adjust the net nonresidential stock of business capital for pollution-abatement capital.24 JUNE 1977 Table 1 An A ggre gate P ro d u c tio n Function w ith E n e rgy (A n nu al Data 1 9 4 9 -7 5 ) In Y = 1.7134 + (1 1 .7 1 ) .7371 In I + (1 2 .0 1 ) - . 1 3 6 3 In P + (-5 .6 6 ) F S.E. = .96 = .0093 .26 2 9 In K (4.28) .0185 t (9.67) D.W. = p = 1.45 .63 Values in parentheses are t-statistics. the ratio of output to capital and manhours to capital. The hypothesized negative effect of the relative price of energy is statistically significant. The estimates of the output elasticities of the pro duction function, based on the equation in Table I, are presented in the Table II. The output elasticity of the energy resource is 12 percent which is consistent with the Griffin and Gregory estimate of the cost share of energy and energy price elasticity of demand for capital.25 The latter estimates have been used to show that capacity in manufacturing fell five percent in 1974 due to the 45.3 percent rise in the nominal price of energy from the end of 1973 to the end of 1974. The estimate also supports the assumption that the manufacturing result is representative of the effect of the energy price change on the private business sector.26 The estimated standard error of the estimate of y is 2.12 percent.27 20The potential biases introduced by assuming a Cobb-Douglas production function and some indications of their absence are discussed in Appendix II. 21See, for example, Joseph A. Yager and Eleanor B. Steinberg, “Trends in the International Oil Market,” Higher Oil Prices and the World Economy: The Adjustment Problem , ed. Edward R. Fried and Charles L. Schultze (Washington, D.C.; Brookings Institution, 1975), pp. 246-47, and the ref erences cited in their footnote 45. The estimate of the output elasticity of labor in Table I is very close to the usual estimate of labor’s share of income as well as being approximately equal to labor’s average share of cost in the private busi ness sector over the period of estimation. The aver age share of labor in the private business sector over the sample period is 66.37 percent. A test for the differences between the estimated output elastic ity and the sample period average labor share yielded a t-value of 0.2914. Thus, the hypothesis that the esti mated output elasticity of manhours is equal to labor’s share can n ot be rejected. 22See James M. Griffin and Paul R. Gregory, “An Intercountry Translog Model of Energy Substitution Responses,” The American Economic Review (December 1976), pp. 845-57. Since the relative price of energy changed dramati cally in 1974 and 1975, the production function in The production function (3 ) estimated with annual data for the period 1949-75 is given in logarithmic form in Table I. The equation was estimated with the constant-retums-to-scale restriction imposed by taking 23See, for example, Clark, “A New Measure of Potential Output.” 24No doubt pollution-abatement capital investment will be come an increasingly important factor for such studies in the future. Thus, the problems of measuring such investment will also become more pressing. The unimportance of the adjustment now is due only to its small size to date. For example, in Clark’s estimates the pollution-abatement capi tal stock is only about two percent of the gross fixed non residential capital stock by 1975. 25See Griffin and Gregory, “An Intercountry Translog Model,” pp. 849-52. 26See Rasche and Tatom, “The New Energy Regime,” p. 5 and pp. 10-12. 27Formulas for computing the variance of the restricted paramaters ( a , |3, y ) may be found in Jan Kmenta, Elements o f Econometrics, (New York: The Macmillan Company, 1971), p. 444. Page 15 FEDERAL RESERVE BANK OF ST. LOUIS JUNE Table II 1977 Table III E stim ate s o f O u t p u t E la sticitie s — T he C o b b - D o u g l a s A c c o u n t in g fo r E n e r g y P ro d u c tio n Function W it h o u t E n e r g y (A n nu al Data) Sam ple periods 1 9 4 9 -7 5 1 9 4 9 -7 3 Labor ( a ) 6 4 .9 % Capital (|3) (5 .1 6 % ) (6 .9 3 % ) (y) 12 .0 % 11 .7 % (2 .1 2 % ) (6 .0 8 % ) (3.1) 1 9 4 9 -7 3 : In Y = Energy Time Trend (r) 5 8 .9 % 1.0168 + .6968 In I + .3032 In K (1 5 .1 5 ) (1 2 .4 8 ) (5 .4 3 ) (5 .1 6 % ) (6 .9 3 % ) + 2 3 .1 % 2 9 .4 % 1 .6 % (0 .1 6 % ) .96 .00 8 5 (3.2 ) 1 9 4 9 -7 5 : In Y = 1 .2 % Table I was reestimated over the period ending in 1973 to assess the impact of the large price change on the estimates. The estimates of the output elasticities for the earlier period are also given in Table II. The estimates are practically the same as those for the longer period, especially for energy.28 Thus, it does not appear that the importance of energy resources in the production function estimate is due to the dramatic energy developments which have occurred since 1973. The importance of accounting for energy and its relative price in estimating production relationships is illustrated by the equations in Table III. A standard Cobb-Douglas production function omitting energy is estimated for the two periods 1949-73 and 1949-75. The first equation, for the period prior to the large rise in the relative price of energy, performs about the same as the equation in Table I which includes energy in the production function. W hen 1974 and 1975 are included to estimate the second equation, how ever, the simple production function performs much worse. The standard error of the second equation is more than 50 percent larger than that for the earlier period and almost 50 percent larger than that given in Table I.29 The omission of energy from production function studies prior to 1974 would appear to be a 28The estimated standard error of a is 6.93 percent, so a 95 percent confidence interval for the restricted estimate of labor’s share contains the sample average share of 66.2 per cent for 1949-73. 28For the sake of comparison it may be noted that the stand ard error of the equation in Table I over the shorter period, 1949-73, is .82 percent, about the same as for the first equation in Table III. Also, before the Cochrane-Orcutt adjustment, the coefficients of the Table III equations are not as stable. For example, the manhours coefficient drops significantly from 62 percent for the 1949-73 period to 47 ercent for the 1949-75 period. Such a significant change oes not occur in the production function estimates which include energy, nor was there a noticeable change in the labor share data for 1974-75 in private business sector data. D.W. = p = R2 = S.E. = 1.58 .84 1.0729 + .7048 In L + .29 5 2 In K (9 .7 4 ) (9 .0 2 ) (3 .7 8 ) + (0 .2 1 % ) Values in parentheses are standard errors. 16 Digitized forPage FRASER R2 = S.E. = .0171 t (7.9 6 ) .01 4 6 t (4 .9 8 ) .91 .01 3 5 D .W = p = 1.92 .86 Values in parentheses are t-statistics. minor problem, if indeed it is a problem at all.30 After the dramatic change in energy prices, explicit con sideration of energy resources and the relative price of energy resources is required to obtain stable esti mates of U.S. production relationships.31 AN ESTIMATE OF POTENTIAL OUTPUT The production function estimates can be used to estimate potential output in the U.S. economy when supplemented with assumptions concerning the fullemployment availability of resources. The stock of capital available during a period is essentially the same regardless of whether the economy operates at its potential. The utilization rate of capital, however, varies with economic conditions. Consequently, esti mations of potential output for the private business sector and the economy as a whole requires some es timate of the utilization rate that would prevail at potential output. Quarterly estimates of the Federal Reserve Board index of capacity utilization in manu facturing since 1948 indicate that the 87.7 percent utilization rate of capital achieved in late 1973 has been exceeded in only two prior peak periods, dur ing the Korean W ar and the Vietnam War, when it was about 90 percent. During mid-1955, a bench mark year for original studies of potential output, 30The unimportance of accounting for energy in some earlier estimates of the production function is due to its high corre lation with time trends and capital. For example, from 1948 through 1970 a trend decline of the relative price of energy of 1.33 percent per year accounts for over 95 percent of its variation with a standard error of two percent. 31When the energy price is excluded from the production function, a Chow test on the additional observations, 1974-75, indicates structural change at a one percent sig nificance level. At this significance level, equality of the coefficients of the production function including the energy price cannot be rejected when these observations are added. FEDERAL RESERVE BANK OF ST. LOUIS the index was 87.5 percent. 32 This latter rate is used here as the assumed full-employment capital utiliza tion rate. The flow of manhours at the potential output rate depends upon both the size of the “potential labor force” and the supply of hours per worker at potential output. Clark’s recent study provides annual estimates of the potential civilian labor force. The estimates are based upon the population and labor force participa tion rate of each of eight age-sex groups adjusted for cyclical effects. Clark has also estimated a full-em ployment unemployment rate annually since 1948 which is equivalent to a four percent unemployment rate in 1955. These estimates are based upon the relationship between the unemployment rate for each of the eight age-sex groups and: 1 ) the unemploy ment rate of adult males (age 25-54) and 2) the relative size of the potential group in the potential labor force .33 An annual series for potential civilian employment is obtained by adjusting the potential labor force for the full-employment unemployment rate. Potential employment in the private business sector in each period is the difference between poten tial civilian employment and actual employment out side the private business sector, principally in government. Hours per worker in the private business sector at potential output is estimated in a fairly standard manner.34 Hours per worker varies cyclically as well as secularly. Hours per worker at potential output, adjusted for Clark’s full-employment unemployment rate, is estimated using the postwar relationship in Table IV, which treats hours per worker as a function of the unemployment rate and a time trend. Potential manhours is the product of the estimated potential hours per worker and potential employment in the private business sector. The relative price of energy at potential output is assumed to be the actual relative price. Until 1974 it is conceivable that moving from a smaller output to potential output in any period would have raised this relative price. However, since any change of this type would have probably been quite small given the small variance in this relative price in the postwar period through mid-1973, and since the coefficient of the 32See Richard D. Raddock and Lawrence R. Forest, “New Estimates of Capacity Utilization: Manufacturing and Mate rials,” Federal Reserve Bulletin (November 1976), pp. 892-905. 33See Clark, “A New Measure of Potential GNP,” pp. 14-22. 34For example, see Black and Russell, “An Alternative Estimate of Potential GNP,” pp. 70-76. JUNE 1977 Table IV H o u rs p e r W o r k e r in the P riv ate B u sin e ss Se c to r (A n nu al Data 1 9 4 8 -7 5 ) In H P W = .8125 — .0 0 3 0 U - .0 0 4 0 t (1 6 9 .2 7 ) (3 0 .0 0 ) (4 0 .0 0 ) HPW = U = t — R2 = S.E. = hours per worker unemployment rate time .97 .0062 D.W. = .55 Values in parentheses are t-statistics. relative price is not large, it is unlikely that the as sumption has any noticeable impact on the estimates of potential output. The production function and the assumptions above provide an estimate of potential output in the private business sector .35 Potential real GNP is found by adding the actual component of output outside the private business sector. The annual estimates of poten tial real GNP from 1952 to 1976 are shown in Chart III along with the old CEA series .36 Unlike both the new and old estimates of the Council of Economic Ad visers, the series is not smoothed. The average annual rate of growth of the series from 1952 to 1975 is 3.4 percent. This is slightly lower than the 3.6 percent average rate of growth in the new CEA series or the 3.7 percent in the old series for the same period. The estimate of potential output is virtually identi cal to the old CEA estimates in their benchmark year 1955 as well as in 1969-70. Chart IV shows the ratio of the estimated potential GNP to the old CEA measure of potential output. Except for the early and mid1950s and 1969-70, the old CEA estimates show the economy with greater potential than the estimates here. The chart indicates that the old CEA measure grows more rapidly in the late 1950s and early 1960s, but that this is compensated for by a lower estimate of potential output growth in the late 1960s.37 Chart 3“The exponential of the estimate of the logarithm of potential output is a biased estimate of potential output. An exact correction for this bias is derived in Dan Bradu and Yair Mundlak, “Estimation in Lognormal Linear Models,” Amer ican Statistical Association Journal (March 1970), pp. 198211. The bias correction factor was computed for the esti mates of potential output presented here. In no case was the correction more than .1 billion dollars. :!,1The equations necessary to construct quarterly potential output employing the same methodology are presented in Appendix III. 37Black and Russell, “An Alternative Estimate of Potential GNP,” p. 74, also found that the Council overstated the trend growth in the late fifties. The fairly constant percent age from 1963-65 in Chart IV is also in agreement with Black and Russell’s claim that the Council estimate of growth was about right in this period. Page 17 JUNE FEDERAL RESERVE BANK OF ST. LOUIS 1977 E stim a te s o f P o te n tia l G N P P ercentages indicate c o m pounded annual rates of chan ge in our estim ates of Potential G N P . Latest d a ta plotted: 1976 Source: C oun cil of Economic Ad vise rs IV also indicates that, according to our estimates, a four percent trend rate of growth is slightly too high for the period 1969-71 and about right for 1971-73. Page 18 After 1973, the ratio plummets as the old trendbased estimates of potential output are unaffected by energy developments. C h art IV R a tio o f E stim a te d P o te n tia l G N P to " O l d C E A ” P o te n tia l G N P FEDERAL RESERVE BANK OF ST. LOUIS As indicated in Chart II, the new CEA measures of potential output are about 99 percent of the old measures until 1967. Thus, the new CEA series shows potential output to be smaller than the estimates here from 1952-59 and from 1968-73. The new official CEA estimates do not account for energy price de velopments so they are higher than the production function estimates for 1974-75. However, when the additional productivity shift discussed by the CEA is taken into account, their new estimate of potential output for 1974 and 1975 is not much different from those presented in Chart III. JUNE Table V An A ggre gate For comparison purposes, a potential output series was estimated as before using the production function in Table V. The comparison is essentially the same as that discussed above without the shift term T2. The ratio of the estimated potential output, with and without the slowdown in productivity growth, to new CEA potential output is shown in Chart V. The new 38The principal source cited by Clark, “A New Estimate of Potential GNP,” for the productivity slowdown is the study by J. R. Norsworthy and L. J. Fulco, “Productivity and Costs in the Private Economy, 1973,” Monthly Labor Re view (June 1974), pp. 3-9. The reason given by Norsworthy and Fulco is a slowdown in the shift of labor from the agri culture sector. The slowdown in the shift appears to' be contradicted by more recent evidence. See Robert Reinhold, “Decrease in Farm Population Accelerates: Figures Show a 14 percent Decline from 1970-75,” New York Times, April 15, 1977, p. A14. P ro d u c tio n Function w ith E n e r g y a n d A S h ift in the T re n d R ate o f G r o w t h A ft e r 1 9 6 6 (A nnu al Data 1 9 4 9 -7 5 ) In Y = 1.5 6 1 6 + (9 .9 3 ) + .7405 In I + (1 1 .5 5 ) .0202 t (9 .0 3 ) .2595 In K (4 .4 1 ) .10 8 3 In P (-4 .2 1 ) .00 4 7 T2 (-2 .1 8 ) 0; 1 94 9 — 6 6 1 , 2 ........ 9; 1967, 1968, . . . . 1975 R2 = S.E. A primary difference, besides excluding energy con siderations, between the new CEA potential output series and that presented in Chart III is a produc tivity slowdown in 1967. The new CEA series includes such a slowdown and it is estimated that the trend rate of growth falls 25 percent after 1966. The timing of this shift appears to be arbitrary and its size ap pears to be quite large given the reasons cited.38 Nonetheless, such a shift is statistically significant when a variable intended to capture such an effect is added to the equation in Table I. Moreover, the size of the reduction in the trend rate of growth agrees with the estimates of the CEA. The estimated equation is presented in Table V. It may be noted that the equation implies a significant output elas ticity of energy of 9.8 percent and an output elasticity of manhours of 66.8 percent. Given the size of the standard errors of the coefficients, it does not appear that the inclusion of the productivity shift parameter, T2, significantly affects the results indicated in Tables I and II. The only major differences between the equation in Table V and the equation in Table I are the differences in the trend rate and the slight im provement in the standard error. 1977 = a = (S.E. = .97 D.W. = .00 8 9 p 6 6 .8 % js = 6 .6 3 % ) Values in indicated. parentheses (S.E. = are 2 3 .4 % 6 .6 3 % ) t-stastitics, = y = (S.E. = except where 1.54 .41 9 .8 % 2 .3 2 % ) otherwise CEA estimates are lower than our estimates of poten tial output before 1959 and in 1968-73. Like the old CEA estimates, the new CEA estimates indicate a higher rate of growth of potential output until the mid-1960s and a lower rate of growth of potential from 1965-69. The new CEA rate of growth of poten tial output from 1969-73 is in agreement with the energy based estimate. Finally, like the old CEA estimates, the new CEA estimates show a higher rate of growth of potential output in 1974-75. THE IMPLICATIONS OF NEW ESTIMATES OF POTENTIAL OUTPUT Regardless of the historical pattern of the alterna tive estimates of potential output, the new CEA esti mates and those presented here have similar implica tions for the recent and near term performance of the economy. Table V I shows the potential output meas ures for 1973-76 from the old series, the new series, and those estimated using the equation in Table I and shown in Chart III.39 Both of the new estimates show that the economy was much closer to potential output in 1973 than the old CEA series, indicates. More importantly, both new series show a substantially slower growth of potential output in recent years, compared to the old series and, thus, a substantially smaller gap between actual and potential output in 1976. Our estimate of potential output also supports the CEA’s recent suggestion that energy price develop39The conclusions from Table VI would be unaffected by using the production function in Table V since the potential meas ures for 1973-76 are essentially the same on either basis. Page 19 JUNE FEDERAL RESERVE BANK OF ST. LOUIS 1977 C h a rt V R a t io of E s tim a t e d P o t e n t ia l G N P * to " N e w C E A ” P o t e n t ia l G N P P e rc e n t 1 0 3 1-------- P e rc e n t 11 0 3 — R a tio for P ro d u c tiv ity Shift ________ To 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 *T h e s o lid lin e is b a s e d u p o n a i e stim a te o f p o te n tia l o u tp u t f ro m T a b le V . The d a s h e d lin e is b a s e d u p o n o u r e st im a t e of p o te n tia l o u tp u t from T a b le I. S o u r c e : C o u r :il o f E c o n o m ic A d v i s e r s L a te st d a t a p lo tte d : 1 9 7 6 ments reduced potential output by an additional $30 billion by 1976.40 W hen this effect is subtracted from the new CEA estimate for 1976, the result is within one percent of our estimate of potential output.41 Our estimate of potential output suggests that in 1975, the economy failed to produce about 7 percent 40The $30 billion reduction is a “conservative” estimate. Clark, “A New Measure of Potential Output,” shows a 4.2 percent reduction in productivity in the private business- sector which implies potential output measures for 1975 and 1976 of $1,273.7 billion and $1,318.9 billion, respectively. These estimates are even closer to our estimates derived from the Table I equation and given in Table VI. 41A regression of the relative price of energy on the time trend variables used by Clark, “A New Measure of Potential Output,” shows why the estimates agree so well in recent years. The coefficients, with t statistics in parentheses, for the quarterly time variables are: .0034 (2 0 .7 ) for a time trend for 1948 through 1975; .0036 (5 .6 ) for a time trend beginning in the first quarter of 1967; and .4823 (2 3 .0 ) for a shift variable which takes values of .25, .5, .75 from the first through the third quarter of 1974, and one after that. The adjusted R2 of this equation is .92 and the standard error is 3.5 percent. The first trend reflects the historical decline of 1.33 percent in the relative price of energy from 1948 to the end of the 1960s. The shift term beginning in 1974 shows a rise of 48 percent in the relative price, 35.4 percent of which occurred from the fourth quarter of 1973 to the fourth quarter of 1974. Such a shift in the relative price of energy shows how Clark’s shift of potential private sector output down by 4.2 percent can be associated with the energy price. The coefficient of Clark’s shift variable (.4823) in the energy price regression times the energy rice coefficient in Table I (.1363) yields a permanent ecline in potential output of 6.6 percent, about 50 percent larger than Clark’s 4.2 percent. Digitized for Page FRASER 20 of its potential output due to the recession. In contrast the old and new CEA estimates suggest that the gap was about 13 percent and 10 percent, respectively. More importantly, the gap fell to 4.5 percent of poten tial output in 1976 while the CEA estimates indicate it only fell to 11 or 7 percent of potential output. On the basis of the old CEA series, the worst loss of potential output, prior to the 1973-75 recession, oc curred in 1958 when the gap was about 6.5 percent of potential. Thus, both CEA estimates imply the econ omy performed very poorly relative to potential out put in 1976. In contrast, a 4.5 percent shortfall of actual from potential output is about the same as the performance indicated by our historical series for 1960-61 or 1971. The gain in output to be achieved by moving to a fully-employed economy is substantially smaller than Table VI T h re e M e a s u r e s o f P o te n tia l O u tp u t (Billions of 1972 Dollars) O ld CEA 1973 1974 1975 1 97 6 $ 1 2 6 5 .4 1315.9 136 8.6 1421.2 New CEA Production Function (Table 1) Actual G N P $1 228.2 1271.7 131 6.9 136 3.6 $ 1 2 4 9 .2 1257.8 1283.8 132 4.6 $1 235.0 1214.0 1 1 9 1 .7 12 6 4 .6 FEDERAL RESERVE BANK OF ST. LOUIS JUNE either the old or the new CEA measures indicate. Attempts to expand demand and production to such unattainable levels in the near term would conse quently accelerate inflation. The period of time over which output may grow at a given rate faster than the growth rate of potential output is correspond ingly smaller. The rate of growth of potential out put will constrain actual output growth much earlier than the old measure suggests. Also, at the output rate achieved at full employment, Federal tax re ceipts and budget surpluses will be smaller than the higher measures of potential indicate. Thus, a goal of a balanced budget at full employment will require more effort than either of the CEA estimates indicate. CONCLUSIONS Since 1962 estimates of potential output have be come popular and important sources of information for policy formulation. The early estimates, and until recently the official estimates, focused upon labor resources only. New estimates by the CEA have at tempted, to some extent, to account explicitly for the importance of capital resources and a production function. The CEA has also suggested that t:iergy developments are an important factor affecting the productivity of fully-employed resources. Using a production function which accounts ex plicitly for capital and energy resources, an alterna tive measure of potential output has been developed. The production function estimates support the argu 1977 ment that the new energy regime imposed in 1974 permanently reduced potential output by about four percent. The production function estimates show that failure to account for energy prior to 1973 is not critical, but that serious inconsistencies arise when the sample period is extended to include recent years. Until 1973 the historical series for potential output developed here tends to conform more to the old CEA series than the new series. After 1973, however, the new CEA estimates adjusted for the magnitude of their suggested decline in productivity are very close to our estimates. Thus, while our estimates cast some doubt on the historical accuracy of the new CEA estimates, they support the CEA’s suggestion that energy price developments after 1973 reduced poten tial output. The implications of the new CEA estimates and those presented here are of great significance for the full-employment and growth prospects of the econ omy. Attempts to achieve an unattainable potential output rate through stimulative policy will not only fail, but will add to inflationary pressures. Also, there is little prospect for an extended period of growth at rates higher than the rate of growth of potential out put (about 3.5 percent per year). The gap between potential and actual output will tend to close within two years, even with the moderate growth of actual output achieved in 1976. Finally, at full employment, existing tax and spending policies will result in a much larger budget deficit than higher measures of potential output indicate. APPENDIX I An Analysis of the Eckstein-Heien Model for Determining Potential Output1 In a recent study for the Joint Economic Committee, Eckstein and Heien (E -H ) have estimated an annual 1Albert J. Eckstein and Dale M. Heien, “Estimating Potential Output for the U.S. Economy in a Model Framework,” Achieving the Goals of the Employment Act of 1946 — Thir tieth Anniversary Review, U.S. Congress, Joint Economic Committee, 94th Cong., 2nd sess., December 3, 1976, pp. 1-25. model which they use to construct an alternative to the official C EA potential output series. Since their analy sis purports to introduce the im pact of energy price changes on potential output, and since the conclusions of their analysis are remarkably different from those re ported here, this appendix attempts to analyze the rea sons for the different conclusions. Page 21 FEDERAL RESERVE BANK OF ST. LOUIS The first difference involves the choice of data series. E-H choose to study the private nonfarm sector of the economy. This differs from the private business sector as defined in the text, in that the E-H measure excludes the farm sector of the economy, and includes the imputed output to owner-occupied housing and output originating in households and non-profit institutions. They also choose to use raw materials as the third factor of production in their estimated production function, in contrast to the energy input concept employed above. In practice this difference should not be too important, since 88 percent of the weight in their Laspeyres index of raw materials comes from the crude oil, refined petroleum products, natural gas and coal components of their index. The wholesale price index of energy used above measures just these components plus electrical power, so the cor relation of the two input measures should be very high. E-H estimate a three factor Cobb-Douglas production function on annual data from 1950-74. The estimated output elasticities in their function can be compared with those implied by the production function which is re ported above. All three estimated elasticities are essen tially identical in both studies. In addition, the estimated coefficient on the time variable is almost exactly the same in both equations. The differences in the conclu sions of the two studies, therefore, cannot be attributed to differences in the underlying production function, the central relationship in both analyses. E-H present a 12 equation model, while the analysis above explicitly involves only one equation. For the pur poses of constructing potential output, the elaboration in their 12 equations is somewhat misleading. They use the assumption that four percent unemployment is the ap propriate rate of labor force utilization at which to con struct potential output. With this assumption, their model can be characterized by three distinct blocks: 1 ) an employment block consisting of the labor force participa tion equations and the various identities defining em ployment, labor force and unemployment, 2 ) a wageprice block consisting of the equations for the wage rate in the private nonfarm economy and the price of output in the private nonfarm economy, and 3) an output block consisting of the production function, a derived demand equation for raw materials, and an equation for the aver age hours per worker. Under the assumed “full-employment” conditions, the employment block is completely independent of the rest of the model. The size of the male labor force is ex pressed solely as a function of exogenous variables, so it is also an exogenous variable for purposes of the model. The female labor force is a function of exogenous vari ables, other variables within the employment block of the model, and lagged variables from other blocks of the model. The various identities in this block relate vari ables defined within the block to exogenous variables. Therefore, it is possible to solve this subset of their equation system for the total private nonfarm employ ment as a function of only exogenous variables. Private nonfarm employment can affect variables in both the wage-price block and the output block. Digitized forPage FRASER 22 JUNE 1977 The wage-price block is affected by two exogenous variables, the price of raw materials and the full-employ ment unemployment rate. It is also affected by the em ployment block and the output block, since these parts of the model determine employment and output which affect unit labor costs. Unit labor costs are specified as an important influence in the determination of private nonfarm wages. The output block is affected by the exogenous capital stock and exogenous capacity utilization rate. It is af fected by the employment block through employment in the private nonfarm sector which enters into the aggregate production function. Furthermore, the only link between the wage-price block and the output block is through the relationship for the average number of hours per worker, which depends on the real wage rate. This relationship is not particularly strong, since the elasticity of the average number of hours per worker with respect to the real wage rate is only .2 , but it explains why E-H obtain a positive relationship between raw materials prices and potential output. In the E-H model, an increase in raw materials price directly affects the price of output in the nonfarm sector. A higher price level in turn causes higher wages, but the increase is less than proportional, so the real wage rate falls in response to the increase in raw materials prices. Real wages have a negative impact on the average num ber of hours per worker, so hours per worker rise in re sponse to the increase in raw materials prices. But total private sector employment in the model is exogenous at potential output as discussed above, so total manhours rise in response to the increase in raw materials prices. The net effect is an elasticity of real output with respect to raw materials prices in the E-H model of .02. The small magnitude of this elasticity illustrates the weakness of the interrelationship of the price-wage equations of the model with the output equation through the average hours equation. If E-H had assumed, as do the authors of other studies of potential output, a fixed number of hours per person at full employment, then the link between the wageprice block and output block in their model would be broken. Their potential output model would then consist only of two equations; the production function and the demand for raw materials equation, supplemented by exogenous assumptions on the magnitude of manhours supplied at potential output. Under these circumstances their analysis would imply that there is no effect of changes in raw materials prices on potential output. In practice, their analysis effectively implies such a conclu sion since the price elasticity reported above is so close to zero. The two equation model which is so closely approxi mated by the E-H model is exactly the two equation model which is implicit in the analysis presented above. The aggregate production function, with the relative price of energy as one of the right hand side variables, is derived by substituting the demand equation for energy under the assumption that the real price of energy FEDERAL RESERVE BANK OF ST. LOUIS JUNE inputs is exogenous. Recall that the estimates of the production function parameters are essentially the same for the two studies. Therefore, the difference in the re sults obtained must be attributable to differences in the explicit or implicit demand functions for energy inputs. The problem with the E-H model is that the demand functions for both labor and raw material inputs are misspecified. Such demand functions normally would be expected to be consistent with the first-order conditions for cost minimization and/or profit maximization. In the case of the Cobb-Douglas production function, this im plies that the input demand functions must be log-linear. Yet both the demand function for raw materials and the demand function for labor services in the E-H study are specified as linear functions. This probably accounts for the insignificance of the estimated coefficient of the relative price term in the raw material demand equation which E-H report in the text, but not in the equations of the model. 1977 The approach used in this study implicitly assumes that both the output elasticity and the price elasticity of the demand for energy are one, and that the functional form of this equation is log-linear. If this were not the case, then the output elasticities derived from the pro duction function parameter estimates should be biased. Three pieces of evidence suggest that this is not the case. First, the estimated output elasticity of labor services conform quite closely to the share of labor in total income as it should under the constant-returns-to-scale restric tion. Second, the estimated output elasticity of energy inputs conforms almost exactly with the estimates from cross-section time series data of several countries, includ ing the United States obtained by Griffin and Gregory. Third, as mentioned above, the estimated output elas ticity of energy (as well as of other resources) obtained in this study are almost identical to those obtained by E-H even though they used a measure of the quantity of raw materials input in estimating the production func tion directly. APPENDIX II Equation (2) constrains both the output and price elasticities of energy demand to unity. Consider the unconstrained hypothesis for the energy demand curve: In E = 80 + 8j In Y - S2ln (PE/PB) + e If this is substituted in the Cobb-Douglas production function: I n Y = a + a l n L + /3l nK + ' y l n E + u w here a + /3 + y - 1, the result is: [In Y - In K] = /3j + 0 2 [In L - In K] + In (Pe/P B) + 0 4 In K + 7€ + U 1 - 8 ,7 80 y w here /3. = (1 - S,y -y S2 1 - 8. y ft, = (- 1 - 8j y —1 + a + (3 + 5, y (----------------------— ) 1 - 8, y Therefore, if the output elasticity of energy demand, 8 i, were not unity, the specification which has been esti mated would have an omitted variable, In K, which would be correlated with at least one of the included regressors, (In L-ln K ), so all of the estimated regression coefficients (P’s) would be biased. If the price elasticity of energy demand, 62,^ is not unity, then the estimated regression coefficients (P’s) are not biased, but the output elasticities which we have derived from the regression coefficients are biased. Our estimates^ of the output elasticities for labor and energy are a* = ^2/(1 — $ 3) and y #= ^ / (1 — P3), respectively. The unbiased estimates of these output elasticities are y = y [- 1 + ( / - l)(l - 8„) -] and a = n ° [- 1 - 8, 2 Consequently, if 62 < 1, our estimate of the output elas ticity of energy is biased downward and our estimate of the output elasticity of labor is biased upward. The consistency of our estimates of the output elasticities with estimates from other sources and the consistency of the output elasticity with the labor share data, suggests that biases from these sources are not substantial. Even if the output elasticities were biased because the price elasticity of energy demand was less than unity, the biases would not affect our potential output computa tions, since these are Jaased on the unbiased estimated regression coefficients (P’s). Page 23 APPENDIX III A quarterly series for potential GNP can be constructed using the same method and data when some additional as sumptions are made concerning the data. The principal data problems involve quarterly estimates of the capital stock and potential employment or manhours. Quarterly data on the stock of capital are found by prorating the annual year-end changes in the net stock of fixed nonresidential equipment and structures over quar ters using quarterly rates of investment in nonresidential fixed investment as the weights. Clark’s annual data on the potential labor force are assumed to be for the second quarter of each year and a linear interpolation is used for other quarters. To find potential manhours, a quarterly estimate of hours per worker is obtained such as that contained in Table IV. The quarterly potential hours per worker is found by using Clark’s full-employ ment unemployment rate for the respective years in the equation (1 ) In H PW =.8120 - .0033 U - .0010 t (346.6) ( - 7 . 0 8 ) ( - 5 0 .7 5 ) R2= .97 D.W. = .31 S.E. = .0062 which is estimated for the period from the second quar ter of 1948 through 1975. The quarterly production function comparable to the annual estimate in Table I, (II/1948-IV/1975) is (2 ) In Y = 1.5974 + .7192 In L 4 - .2808 In K (14 .2 0 ) (20.85) (8 .1 4 ) - .1 1 6 4 In P + .0045 t (- 5 .6 4 ) (15.00) R2 = .98 D.W. = 1.90 S.E. = .008 p = .80 The estimated coefficients are essentially the same as for the equation in Table I. The estimated output elasticities and trend growth term are (standard errors in parentheses) a = 64.4% (3.08%), P = 25.2% (3.08% ), y = 10.4% (1.85% ), f = .4% (.03% ).