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Working Paper Series Identification of Inflation—Unemployment B ennett T. McCallum Working P a p e rs S eries M acroeconom ic Issu es R esearch D epartm ent Federal R eserve Bank of C hicago S ep tem b er (W P-94-16) FEDERAL RESERVE BANK O F CHICAGO Identification of Inflation-Unemployment Tradeoffs in the 1970s Bennett T. McCallum Carnegie Mellon University Preliminary March 1994 This note constitutes an extended version of comments made at the CarnegieRochester Conference on Public Policy meeting of November, 1993. I am indebted to Bob King, Allan Meltzer, and Mark Watson for helpful discussions. In an ingenious and stimulating paper, which draws on important prior work of their own, * King and Watson (1994) have (along with more substantive contributions) analyses of provided a "revisionist" Phillips-curve inflation-unemployment properly devoted tradeoff exists; to phenomena— i.e., tradeoff. the whether, historical A substantial once-prominent that is, of of issues involving amount question the permanent account of of account, King and Watson distinguish with Keynesian and monetarist economists, cycle (RBC) position for 2 the attention whether a is long-run maintenance of a higher inflation rate would permanently induce less unemployment. historical econometric In discussing the two positions, associated and then add a third real business the sake of comparison. The difference between econometric results obtained and promoted by Keynesians and monetarists is ascribed to different assumptions dynamic structural relationship. Keynesians and exogeneity that monetarists led to used to provide identification of the In particular, King and Watson suggest that made crucially different choices different of variables in estimated regression relationships. assumptions dependent and about explanatory 3 The purpose of the present note is to argue that, from a historical perspective, the King-Watson account is seriously inaccurate. Both Keynesian and monetarist economists relied upon the same identification assumptions and estimated Phillips variables. Then proponents entered relations when the with the Lucas, Sargent, fray, they same and dependent other introduced identification of expectational values an and explanatory rational-expectations issue that was critical pertaining for the to long-run tradeoff issue, but did not introduce new identification arguments regarding short-run dynamics. In sum, the King-Watson reinterpretation of history is, 4 like many revisionist analyses, basically unwarranted. paragraphs will seek to establish these points. 1 The following In order to describe the issues with any clarity, have at hand a schematic macroeconomic model. it will be useful to Consider, then, the following system in which yt, Pt» and mt denote the logarithms of aggregate output, the price level, and the money stock, respectively: (1) Apt = ao + a,yt + a2yt-i + a3Apt + ut |a21<a1>0, 0<a3^l (2) yt = 0o + Pi (nit ~ Pt) + 02Yt-i + vt- 01*0. 1021^i• Here equation (1) represents the dynamic Phillips relation between inflation and unemployment, for we assume (throughout this note) that the unemployment rate is negatively correlated with yt, to a very high degree."* A lagged value of yt is included to reflect the possibility of some adjustment-cost dynamic aspects anticipated to the relationship inflation rate. while Finally, Apt reflects the disturbance ut random components of suppliers’ behavior. an expected or reflects omitted Equation (2) is, by contrast, an aggregate demand relation in which the quantity demanded in period t depends upon again prevailing levels represented of by real yt-i- money The components of buyers’ behavior. balances, disturbance with term dynamic effects vt reflects random The disturbances ut and vt are white noise but may be mutually correlated contemporaneously. Assuming that |a2/a1|<1.0, Apt and yt requires, of course, researchers sought to (NRH),^ by estimating test the absence of a long-run tradeoff between thata3 equals unity. this hypothesis, the parameters of the the Consequently, natural structural rate and well-known example was Gordon (1970); somewhat well-known were the studies of Solow (1968, 1969). hypothesis equation determining whether or not a3 was significantly different from 1.0. earlier various (1) and An early but less In all of these studies a distributed lag of past values of Apt was used to proxy for Apt; let us write the implied expectational relation as (3) Apt = w, Apt-i + w 2 Apt - 2 + --- 2 The weights w 1#w2,... were assumed by Gordon and Solow to sum to 1.0. (1) could be operationally implemented by including a distributed Thus lag of 7 Apt-j values and taking the sum of their coefficients as an estimate of a3. Sargent (1971) and Lucas (1972) expectations are formed rationally then recognized, it however, is entirely possible that if that the weights in a rational forecasting relation of the form (3) might sum to less than 1.0, in which case the sum of the Apt.j coefficients in an estimated version of (1) would not provide a consistent estimate of a3. Suppose, for example, that the actual univariate process for Apt is (4) Apt = SiApt-i + <52Apt-2 + £t, with et white noise and with + S2 equal to 0.6. Then the Solow-Gordon procedure would yield an estimate of a3 of about 0.6 even if the true value is 1.0 (provided that expectations are in fact rational). That something much like this is what was in fact going on has been suggested by Sargent (1976b), McCallum (1987), Alogoskoufis and Smith (1991), and others. All of the foregoing is well known and is not, dispute with King and Watson. I believe, a source of Where disagreement begins to arise is with regard to the difference between the Keynesian procedure of Gordon and Solow and that utilized by monetarist analysts. According to King and Watson, Keynesian studies estimated supplier behavior as shown in formulation i.e., with exogenous Apt to Monetarists, the Apt dependent and variable, therefore by contrast, did not because uncorrelated they with assumed the take yt to be exogenous yt to disturbance in the (1), be ut. (1) and so estimated it in the form (1') yt = a0 + a^t-i + a2Apt + Aa3Ap£ + u', where a^ = -a2/a1, a2 = l/ccu a3 = 0. a3 = -a3/a1, and with the NRH expressed as a2 + It is this claim that is, I contend, historically incorrect. In discussing this contention it is necessary to distinguish between the 3 original "monetarist" economists— including Friedman, Brunner, Meltzer, and others to be mentioned shortly— and rational-expectations analysts such as Lucas, Sargent, and Barro. Considering first the monetarists, there is a slight difficulty in collecting evidence relating to their procedures because Friedman, Brunner, and Meltzer engaged in time series econometric analysis g very rarely. there were But evidence significant and is available, directly if one searches a bit, relevant studies conducted because by other influential members of the monetarist camp including Anderson and Carlson (1970, 1972), Laidler (1972), and Parkin (1973). Furthermore, a collection of six empirical studies of the inflation process was conducted under the sponsorship of Brunner and Meltzer, with scope and procedures determined in collaborative sessions. the Five of these studies were published in Volume 8 of Carnegie-Rochester Conference Series in Public Policy (Brunner and Meltzer, 1978). An examination of the nine monetarist studies just listed reveals that all of them conform to the same basic framework as described above for the Gordon (1970) and Solow (1968, 1969) studies. In particular, all nine of these monetarist studies utilize Apt as the dependent variable in a relation basically of form (1), not (1'). Furthermore the issue of identification was not raised in any explicit manner that would reveal differences relative to Keynesian analyses. The only significant specificational differences stem from the inclusion of some additional variables, pertaining to taxes or other institutional details, and alternative measures of "excess demand" variables utilized in place of yt or the unemployment rate. Why then, one might ask, did the monetarist studies tend to find estimates of a3 much closer to 1.0 than the 0.5 - 0.6 values estimated by Gordon and Solow? Clearly, the answer may be different for the various studies and in some cases may depend upon the particular variables utilized. 4 But it is also true that the monetarist studies were conducted somewhat later than those of Gordon and Solow, which is of relevance because estimated autoregressive (AR) models of Apt were by then yielding parameter estimates that implied larger values for Ewj. This tendency is documented in Table 1, where Zwj values are reported for AR(5) models estimated over sample periods beginning with 1954.1 and ending with the fourth quarter of each year from 1966 through 1980. 9 As can readily be seen, the ZWj values obtained fell well below 1.0 through the end of the 1960s, but then began to climb to the vicinity of 0.85 - 0.90. to its true value, The latter values would yield estimates of a3 close according to the Sargent-Lucas hypothesis, whereas the lower values would not. Even more telling, perhaps, than our examination of the nine monetarist studies mentioned above is the evidence provided by a comprehensive review of empirical work through 1974 in Laidler and Parkin’s "Inflation: (1975). A Survey" Considerable attention is devoted to relevant methodological econometric issues— including the Sargent-Lucas point— but there and is no mention of alternative identification assumptions utilized by Keynesians and monetarists. Now let us turn to studies conducted by the second group of critics of the Keynesian position, the rational-expectations analysts. The studies mentioned most prominently by King and Watson are Sargent (1976a) and Barro and Rush (1980). In both of these, basically of the form (l7), rather the Phillips equations estimated are than (1) — i.e., rather than Apt as the dependent variable. are expressed with yt As an empirical matter, this switch of the dependent and regressor variables will yield quite different estimates of particular, of the short-run (i.e., single period) In the estimated value of a2 will be much smaller than an estimate the same magnitude but based on tradeoff magnitude. (1) and calculated as 5 l/o^. And the Table 1 Coefficient Sums, AR(5) Model for Apt Sample Period: 1954.1 - indicated date Note: Final Date, Sum of Coefficients 4th Qtr. of in Estimated AR(5) 1966 0.3872 1967 0.2861 1968 0.5641 1969 0.6947 1970 0.7040 1971 0.7807 1972 0.7399 1973 0.8792 1974 1.0162 1975 0.8975 1976 0.8516 1977 0.8575 1978 0.8781 1979 0.8891 1980 0.9212 pt is log of GNP deflator, SA. Constant term included in AR model 6 switch may also tradeoff. results, lead But in in practice in principle the following other least squares simultaneous consistency. sense. of the long-run imply any difference viewed as in jointly then neither (1) nor (l7) is appropriate for estimation: equations an instrumental procedure is variable needed to (IV) obtain or some estimator Of course different results might again be forthcoming from (1) equation sample estimates If yt and Apt are and (l7) even with IV estimation. the different the switch does not dependent endogenous variables, ordinary to is mispecified size is large or enough But such an outcome would indicate that the for instruments asymptotic are illegitimate, distribution if theory the to be relevant. It is not the case, furthermore, that all rational-expectations analysts used formulation (l7). My own studies (McCallum 1975, 1976) relied on formulation (1) even though they were expressly designed to take account of the Sargent-Lucas point about the effect on the estimate of a3, and thus the long-run tradeoff, Interestingly, of the possibility that Zwj is less than 1.0. taking account of that point raised my estimated value of a3 from about 0.4 to 0.8 in the case of the United States and from about 0.4 or 0.7 to 0.75 or 0.9 for the United Kingdom (depending on the wage index used).^ Returning distinguish to the two aspects. issue of identification, The first of these it will be useful to is the Sargent-Lucas point, mentioned above, which concerns the proxy for expected inflation whereas the second aspect concerns the basic identification of supplier behavior as distinct from that of demanders, an issue that would remain even if inflation expectations were directly observed. With regard to the latter aspect, it is my impression that treating yt as exogenous in (1) was not the method of identification used in the Keynesian studies (or, given the argument above, 7 the monetarist studies). determined with Apt, To the extent the problem that yt was recognized as jointly was viewed as one simultaneous-equation bias, not as a loss of identification. of potential The manner in which identification was ostensibly obtained relied upon variable exclusion restrictions; even if yt and Apt are jointly dependent in (1), that equation’s basic identification will be not be lost if (1) excludes at least one predetermined variable that is important elsewhere in the system. model In the (1) - (3), mt is excluded from (1) and is treated as a predetermined variable. That last assumption is actually dubious, to put it mildly, but it was made by all parties to the dispute in the 1970s, including the rational expectations analysts. Indeed, there was not much concern over identification during the 1960s and 1970s because the usual way of formulating models— which did not rely on optimizing general presumptions equation to the model systems equations. equilibrium with lots analysis but instead applied theoretical “one equation at a time"— almost always of excluded predetermined variables led to for most Of course it is now realized that there are (at least) two very weak links in this identification scheme, both of which were brought to the profession’s attention principally by Sims (1980). variables cannot First, lagged endogenous legitimately be counted as predetermined unless there is some basis for a priori knowledge concerning the degree of serial correlation in the model’s disturbance terms.** Second, coherent general equilibrium theorizing tends to suggest that the relevant predetermined variables should be much the same for most of the model’s equations. Recognition of these points certainly makes 1970s-style identification highly dubious. But that does not imply that Keynesian and monetarists differed in their practice. is my contention that they did not, to any substantial extent. monetarists accepted the Lucas-Sargent 8 point about the It Of course the identification of expectational magnitudes much more promptly than did most Keynesians, that is another matter. but The fact that Sims (1980) attacked the credibility of identification via exclusion restrictions, and did not mention different identification schemes for Keynesians and monetarists, provides another piece of evidence in favor of the interpretation presented above. Thus my conclusion is that the King-Watson 12 revisionist account of identification restrictions utilized by tradeoff researchers during the 1970s is historically misleading. necessary disagreement That conclusion does not, of course, with substantive— as thought— aspects of their analysis. 9 opposed to imply any history-of- References Alogoskoufis, G.L., and R. Smith (1991) "The Phillips Curve, of Inflation, and the Lucas Critique: Evidence the Persistence From Exchange-Rate Regimes," American Economic Review 81 (December), 1254-1275. Anderson, L.C., and K.M. Carlson (1970) "A Monetarist Model for Economic Stabilization," Federal Reserve Bank of St. Louis Review (April), 7-25. _______________ Relation and of ____________ Monetary Unemployment," ed. by 0. in (1972) Variables "An to Econometric the Behavior Analysis of of Prices the and The Econometrics of Price Determination Conference, Eckstein. Washington: Board of Governors of the Federal Reserve System. Barro, R.J., and M. Rush (1980) "Unanticipated Money and Economic Activity," in Rational Expectations and Economic Policy. ed. by S. Fischer. Chicago: University of Chicago Press for NBER. Brunner, K. , and A. H. Meltzer, eds. (1978) Carnegie-Rochester Conference Series on Public Policy 8. Brunner, K. , A. Activity, Cukierman, and Inventories and A.H. Meltzer Business (1978) Cycles," "Money and Economic Journal of Monetary Economics 11 (May), 281-319. Duesenberry, J.S., G. Quarterly Fromm, Econometric L.R. Model Klein, and E. Kuh (1965) of the United States. The Brookings Amsterdam: North-Holland. Fisher, M., and J. Seater (1993) "Long-Run Neutrality and Superneutrality in an ARIMA Framework,: American Economic Review 83 (June), 402-415. Friedman, M. (1966) "Comments," in Guidelines. Informal Controls, and the Market Place, ed. by G.P. Shultz and R.Z. Aliber. Chicago: University of Chicago Press. 10 ____________ (1968) "The Role of Monetary Policy," American Economic Review 58 (March), 1-17. Gordon, R.J. (1970) "The Recent Acceleration of Inflation and Its Lessons for the Future," Brookings Papers on Economic Activity (No.1), 8-41. Griliches, 2. (1968) "The Brookings Model Volume: A Review Article," Review of Economics and Statistics 50 (May), 215-234. Hatanaka, M. (1975) "On the Global Identification of the Dynamic Simultaneous Equation Model Review 16 ( King, R.G., and with Stationary Disturbances," International Economic ) 545-554. M.W. Watson (1992) "Testing Long Run Neutrality," NBER Working Paper No. 4156. ___________ and ____________ (1994) "The Post-War U.S. Phillips Curve: A (1972) "The Influence of Money on Real Income and Inflation: A Revisionist Econometric History," Working Paper (March). Laidler, D. Simple Model with Some Empirical Tests for the United States 1953-72," Manchester School 41 (December), 125-144. Laidler, D., and M. Parkin (1975) "Inflation: A Survey," Economic Journal 85 (December), 741-809. Lucas, R.E., Jr. in (1972) "Econometric Testing of the Natural Rate Hypothesis," The Econometrics of Price Determination Conference. ed. by 0. Eckstein. Washington: Board of Governors of the Federal Reserve System. McCallum, B.T. (1975) "Rational Expectations and the Natural Rate Hypothesis: Some Evidence for the United Kingdom," Manchester School 43 (March), 56-67. ______________ (1976) "Rational Expectations and the Natural Rate Hypothesis: Some Consistent Estimates," Econometrica 44 (January), 43-52. 11 ______________ (1987) "Inflationary Expectations," Dictionary of Economics, ed. by J. Eatwell, in The New Palgrave: A M. Milgate, and P. Newman. London: Macmillan Press. Meltzer, A. H. (1963) "The Demand for Money: The Evidence from the Time Series," Journal of Political Economy 71 (June), 219-246. Parkin, M. (1973) "The Short Run and Long Run Trade-Off Between Inflation and Unemployment in Australia," Australian Economic Papers 12 ( ), 127-144. Phelps, E.S. (1967) "Phillips Curve, Expectations of Inflation, and Optimal Unemployment Over Time," Economica 34 (August), 254-81. Sargent, T.J. (1971) "A Note on the Accelerationist Controversy," Journal of Money, Credit, and Banking 3 (August), 50-60. _____________ (1976a) "A Classical Macroeconometric Model for the United States," Journal of Political Economy 84 (April), 207-237. _____________ (1976b) "Testing for Neutrality and Rationality," in A Prescription for Monetary Policy: Proceedings from a Seminar Series. Minneapolis: Federal Reserve Bank of Minneapolis. Sims, C. A. (1980) "Macroeconomics and Reality," 'Econometrica 48 (January), 1-48. Solow, R.M. (1968) "Recent Controversies on the Theory of Inflation: An Eclectic View," in Inflation: Its Causes. Consequences, and Control, ed. by S.W. Rousseas. New York: New York University. ___________ (1969) Price Expectations and the Behavior of the Price Level. Manchester, U.K.: Manchester University Press. 12 F o o tn o te s ^Specifically, their "Testing Long Run Neutrality" (1992), one major message of which has also been delivered by Fisher and Seater (1993). 2 Actually, King and Watson sometimes monetarist-rational expectations group. refer to the latter In the argument below, as the I will treat monetarists and rational-expectationists separately. 3 The relevant discussion appears primarily in King and Watson’s sections 3.1, 3.2, 3.3, and 4.1, with 3.4 - 3.7 also of some importance. 4 This argument does not imply, of course, that the identification scheme used by King and Watson is uninteresting or implausible, but only that it was not used historically. It cannot, that is, explain why Keynesians and monetarists of the 1970s reached differing conclusions. ^This assumption, termed Okun’s Law, was extremely common in the research of the day. ^It is possible to distinguish between two related but distinct hypotheses. One, which policy I call behavior permanently low). output the NRH, that can postulates keep output that there permanently is no type of monetary high (and unemployment The second, termed the accelerationist hypothesis, is that (unemployment) can be kept permanently permanently accelerating rate of inflation. high (low) only by a The latter is due to Friedman (1966) (1968) and Phelps (1962); the former to Lucas (1972). 7 Solow assumed that Wj = Aw j .-i with 0<A<1 and relied upon a truncation of the infinite series for estimation, trying various values of A. This "adaptive expectations" case can be implemented instead, of course, by elimination of the unobservable Ap* and estimation of A. 13 g Exceptions include Meltzer (1964) and Friedman and Meiselman (1963), neither of which were concerned with the inflation-unemployment tradeoff. 9 In those estimates a fifth-order AR specification was used because for many of the samples the fifth lag term was the last to enter with a t statistic in excess of 1.0. *^The sample periods are 1952.1 - 1970.4 for the U.S. 1956.1 - 1971.4 for the U.K. (McCallum, 1976) and (McCallum, 1975). **This part of Sims's argument relies on the analytical results of Hatanaka (1975). 12Also relevant is the fact that identification is scarcely mentioned in the 700 page presentation by Duesenberry, Brookings model or in Griliches* Fromm, Klein, and Kuh (1968) critical review. 14 (1965) of the Working Paper Series A series ofresearch studieson regional economic issues relating to the Seventh Federal Reserve District,and on financial and economic topics. 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