INTERMEDIATE MACROECONOMIC THEORY Writing Project

American Economic Association Some International Evidence on Output-Inflation Tradeoffs Author(syf 5 R E H U W ( / X F D V - U . Source: The American Economic Review, Vol. 63, No. 3 (Jun., 1973yf S S 4 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1914364 Accessed: 08-02-2017 17:06 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms Some International Evidence on Output-Inflation Tradeofs By ROBERT E. LUCAS, JR.* This paper reports the results of an empirical study of real output-inflation tradeoffs, based on annual time-series from eighteen countries over the years 1951-67. These data are examined from the point of view of the hypothesis that average real output levels are invariant under changes in the time pattern of the rate of inflation, or that there exists a "natural rate" of real output. That is, we are con- cerned with the questions (iyf G R H V W K e natural rate theory lead to expressions of the output-inflation relationship which perform satisfactorily in an econometric sense for all, or most, of the countries in the sample, (iiyf Z K D W W H V W D E O H U H V W U L F W L R Q s does the theory impose on this relation- ship, and (iiiyf D U H W K H V H U H V W U L F W L R Q V F R Q - sistent with recent experience? Since the term "'natural rate theory" refers to varied aggregation of models and verbal developments,' it may be helpful to sketch the key elements of the particular version used in this paper. The first essential presumption is that nominal out- put is determined on the aggregate demand side of the economy, with the division into real output and the price level largely dependent on the behavior of suppliers of labor and goods. The second is that the partial "rigidities" which dominate short- run supply behavior result from suppliers' lack of information on some of the prices relevant to their decisions. The third presumption is that inferences on these relevant, unobserved prices are made optimally (or "rationally"yf L Q O L J K W R I W K e stochastic character of the economy. As I have argued elsewhere (1972yf , theories developed along these lines will not place testable restrictions on the co- efficients of estimated Phillips curves or other single equation expressions of the tradeoff. They will not, for example, imply that money wage changes are linked to price level changes with a unit coefficient, or that {"long-run"' (in the usual distrib- uted lag senseyf 3 K L O O L S V F X U Y H V P X V W E e vertical. They will (as we shall see belowyf link supply parameters to parameters governing the stochastic nature of demand shifts. The fact that the implications of the natural rate theory come in this form sug- gests an attempt to test it using a sample, such as the one employed in this study, in which a wide variety of aggregate demand behavior is exhibited. In the following section, a simple ag- gregative model will be constructed using the elements sketched above. Results based on this model are reported in Sec- tion II, followed by a discussion and con- clusions. 1. An Economic Model The general structure of the model de- veloped in this section may be described very simply. First, the aggregate price- quantity observations are viewed as inter- section points of an aggregate demand and an aggregate supply schedule. The former is drawn up under the assumption of a cleared money market and represents the output-price level relationship implicit in * Graduate School of Industrial Administration, Car- negie-Mellon University. 1 The most useful, general statements are those of . Milton Friedman (1968yf D Q G ( G P X Q G 3 K H O S V 6 S H F L I L c illustrative examples are provided by Donald Gordon and Allan Hynes and Lucas (April 1972yf . 326 This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms VOL. 63 NO. 3 LUCAS: OUTPUT-INFLATION TRADEOFF 327 the standard IS-LM diagram. It is viewed as being shifted by the usual set of demand-shift variables: monetary and fiscal policies and variation in export de- mands. The supply schedule is drawn un- der the assumption of a cleared labor market; its slope therefore reflects labor and product market "rigidities." The structure of this model, which is essentially that suggested in Lucas and Leonard Rapping (1969yf Z L O O E H J U H D W O y simplified by an additional special assump- tion: that the aggregate demand curve is unit elastic.2 In this case, the level of nominal output can be treated as an "exogenous"' variable with respect to the goods market, and the entire burden of ac- counting for the breakdown of nominal income into real output and price is placed on the aggregate supply side. In the next subsection, A, a supply model designed to serve this purpose is developed. In subsec- tion B, solutions to the full (demand and supplyyf P R G H O D U H R E W D L Q H G . A. Aggregate Supply All formulations of the natural rate theory postulate rational agents, whose decisions depend on relative prices only, placed in an economic setting in which they cannot distinguish relative from gen- eral price movements. Obviously, there is no limit to the number of models one can construct where agents are placed in this situation of imperfect information; the trick is to find tractable schemes with this feature. One such model is developed below. We imagine suppliers as located in a large number of scattered, competitive markets. Demand for goods in each period is distributed unevenly over markets, leading to relative as well as general price movements. As a consequence, the situa- tion as perceived by individual suppliers will be quite different from the aggregate situation as seen by an outside observer. Accordingly, we shall attempt to keep these two points of view separate, turning first to the situation faced by individual sup- pliers. Quantity supplied in each market will be viewed as the product of a normal (or secularyf F R P S R Q H Q W F R P P R Q W R D O O P D U N H W s and a cyclical component which varies from market to market. Letting z index markets, and using ynt and yet to denote the logs of these components, supply in market z is: ( 1 yf \ W = \f = Ynt + yet(Zyf The secular component, reflecting capital accumulation and population change, fol- lows the trend line: (2yf \ W D " t The cyclical component varies with per- ceived, relative prices and with its own lagged value: (3yf \ H W ] \f y [Pt(zyf ( 3 W , W = \fyf ] + NyC_t-1(zyf where Pt(zyf L V W K H D F W X D O S U L F H L Q ] D W W D Q d E(PtI It(zyf \f is the mean current, general price level, conditioned on information available in z at t, It(zyf 6 L Q F H \ H W L V a deviation from trend, f I < 1. 2 An explicit derivation of the price-output relation- ship from the IS-LM framework is given by Frederic Raines. Of course, this framework does not imply an elasticity of unity, though it is consistent with it. Since the unit elasticity hypothesis is primarily a matter of convenience in the present study, I shall comment below on the probable consequences of relaxing it. 3 A supply function for labor which varies with the ratio of actual to expected prices is developed and veri- fied empirically by Lucas and Rapping (1969yf 7 K e effect of lagged on actual employment is also shown. In our 1972 paper, in response to Albert Rees's criti- cism, we found that this persistence in employment cannot be fully explained by price expectations behav- ior. Both these effects-an expectations and a persis- tence effect-will be transmitted by firms to the goods market. In addition, they are probably augmented by speculative behavior on the part of firms (as analyzed for example, by Paul Taubman and Maurice Wilkinsonyf . For a general equilibrium model in which suppliers behave essentially as given by (3yf V H H P \ S D S H U V . This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms 328 THE AMERICAN ECONOMIC REVIEW JUNE 1973 The information available to suppliers in z at t comes from two sources. First, traders enter period t with knowledge of the past course of demand shifts, of normal supply ynt, and of past deviations ye,t-i, yc,t-2 . While this information does not permit exact inference of the log of the current general price level, Pt, it does de- termine a "prior" distribution on Pt, com- mon to traders in all markets. We assume that this distribution is known to be nor- mal, with mean Pt (depending in a known way on the above historyyf D Q G D F R Q V W D Q t variance a2. Second, we suppose that the actual price deviates from the (geometricyf H F R Q R P \ - wide average by an amount which is dis- tributed independently of Pt. Specifically, let the percentage deviation of the price in z from the average Pt be denoted by z (so that markets are indexed by their price deviations from averageyf Z K H U H ] L V Q R U - mally distributed, independent of Pt, with mean zero and variance r2. Then the ob- served price in z, Pt(zyf L Q O R J V \f is the sum of independent, normal variates (4yf 3 W ] \f = Pt + z The information It(zyf U H O H Y D Q W I R U H V W L P D - tion of the unobserved (by suppliers in z at tyf 3 W F R Q V L V W V W K H Q R I W K H R E V H U Y H d price Pt(zyf D Q G W K H K L V W R U \ V X P P D U L ] H d in P.t To utilize this information, suppliers use (4yf W R F D O F X O D W H W K H G L V W U L E X W L R Q R I 3 W , conditional on Pt(zyf D Q G 3 W 7 K L V G L V W U L E X - tion is (by straightforward calculationyf normal with mean: E(Pt I(zyf \f = E(Pt Pt(zyf L 3 W \f (~ ~ ~~~ yf \fPt (zyf 3 t where 0 = i2/(u2+i2yf D Q G Y D U L D Q F H 2 R D . Combining (1yf \f, and (5yf \ L H O G V W K e supply function for market z: (6yf \ W = \f = Ynt + O@Y[Pt(zyf 3 7 W ] + XYc,t-1(zyf Averaging over markets (integrating with respect to the distribution of zyf J L Y H V W K e aggregate supply function: (7yf \ < Q W * \ 3 W 3 W \f + xLyt-1 - yn,t-1I The slope of the aggregate supply func- tion (7yf W K X V Y D U L H V Z L W K W K H I U D F W L R Q R f total individual price variance, a2+r2, which is due to relative price variation,, In cases where r2 is relatively small, so that individual price changes are virtually cer- tain to reflect general price changes, the supply curve is nearly vertical. At the other extreme when general prices are stable (a2 is relatively smallyf W K H V O R S H R f the supply curve approaches the limiting value of y.4 B. Completion and Solution of the Model A central assumption in the develop- ment above is that supply behavior is based on the correct distribution of the unobserved current price level, Pt. To proceed, then, it is necessary to determine what this correct distribution is, a step which requires the completion of the model by inclusion of an aggregate de- mand side. As suggested earlier, this will be done by postulating a demand function for goods of the form: (8yf \ W 3 W [ t where xt is an exogenous shift variable- equal to the observable log of nominal GNP. Further, let Axt } be a sequence of independent, normal variates with mean 6 and variane2 r ande var'lance ax 0 4This predicted relationship between a supply elas- ticity and the variance of a component of the price series is analogous to the link between the income elasticity of consumption demand and the variances of permanent and transitory income components which Friedman (1957yf R E V H U Y H V $ V Z L O O E H V H H Q L Q 6 H F W L R Q , , L W Z R U N s in empirical testing in much the same way as well. This particular characterization of the "shocks" to the economy is not central to the theory, but to discuss This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms VOL. 63 NO. 3 LUCAS: OUTPUT-INFLATION TRADEOFF 329 The relevant history of the economy then consists (at mostyf R I \ Q W Z K L F K I L [ H s calendar timeyf W K H G H P D Q G V K L I W V [ W , xt1,... , and past actual real outputs Yt-1, Yt-2. * Since the model is linear in logs, it is reasonable to conjecture a price solution of the form: 6 (9yf 3 W U 2 U O ; W U ; W B O U ; W B * +l1 Yt_1+?12Yty2+ +tOynt Then 7Pt will be the expectation of Pt, based on all information except Xt (the current demand levelyf R U : Pt = 750 + 7rl(Xt-1 + 5yf ; W l (10yf U ; W " O \ W l + n72yt.-2 + + tOynt To solve for the unknown parameters 7ri, Ij and 4o we first eliminate yt between (7yf D Q G \f, or equate quantity demanded and supplied. Then inserting the right sides of (9yf D Q G \f in place of Pt and Pt, one obtains an identity in Xt }, {yt , and ynt, which is then used to obtain the parameter values. The resulting solutions for price and output are:' Pt= - + X- , 1+GY 1 +OY + - Xt-1 - (1 - Xyf < t 1 + O-Y +X0 + -Axt I8 1- + O + 1 + 8 AX + Xyt-1 + (1 - Xyf \ Q t In terms of APt and yet, and letting 7r= y/(1+G'yyf W K H V R O X W L R Q V D U H : (11yf < H W L U E U $ [ W ; \ H W B 1 (12yf $ 3 W G U \fAXt + 7rAXt-i Let us review these solutions for internal consistency. Evidently, Pt is normally dis- tributed about Pt. The conditional vari- ance of Pt will have the constant (as assumedyf Y D U L D Q F H * \ \f2o-,. Thus those features of the behavior of prices which were assumed "known" by suppliers in subsection A are, in fact, true in this economy. To review, equations (11yf D Q G \f are the equilibrium values of the inflation rate and real output (as a percentage deviation from trendyf 7 K H \ J L Y H W K H L Q W H U V H F W L R n points of an aggregate demand schedule, shifted by changes in xt, and an aggregate supply schedule shifted by variables (lagged pricesyf Z K L F K G H W H U P L Q H H [ S H F W D - tions. In order to avoid the introduction of an additional, spurious "expectations pa- rameter," one cannot solve for this inter- section on a period-by-period basis; 4c- cordingly, we have adopted a method which yields equilibrium "paths" of prices and output. Otherwise, the interpretation of (11yf D Q G \f is entirely conventional. Not surprisingly, the solution values of inflation and the cyclical component of real output are indicated by (11yf D Q G \f to be distributed lags of current and past changes in nominal output. A change in the nominal expansion rate, Axt, has an im- mediate effect on real output, and lagged effects which decay geometrically. The rational expectations formation at all, some explicit stochastic description is clearly required. Independence is used here partly for simplicity, partly because it is empirically roughly accurate for most countries in the sample. The effect of autocorrelation in the shocks would, as can be easily traced out, be to add higher order lag terms to the solutions found below. 6 This solution method is adapted from Lucas (1972yf , which is in turn based on the ideas of John Muth. 7 If a demand function of the form Yt=-Pt+xt had been used, these solutions would assume the same form, with different expressions for the coefficients. If t $1, however, xt is an unobserved shock, unequal in general to observed nominal income. In this case, the model still predicts the time-series structure (moments and lagged momentsyf R I W K H V H U L H V < H W D Q G $ 3 W D Q G L V W K X V L Q S U L Q F L - ple, testable. I have found empirical experimenting along these lines suggestive, but the series used are simply too short to yield results of any reliability. This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms 330 THE AMERICAN ECONOMIC REVIEW JUNE 1973 immediate effect on prices is one minus the real output effect, with the remainder of the impact coming in the succeeding pe- riod. We note in particular that this lag pattern may well produce periods of simul- taneous inflation and below average real output. Though these periods arise be- cause of supply shifts, the shifts result from lagged perception of demand changes, and not from autonomous changes in the cost structure of suppliers. In addition to these features, the model does indeed assert the existence of a nat- ural rate of output: the average rate of de- mand expansion, 5, appears in (11yf Z L W K a coefficient equal in magnitude to the co- efficient of the current rate, and with the opposite sign. Thus changes in the average rate of nominal income growth will have no effect on average real output. On the other hand, unanticipated demand shifts do have output effects, with magnitude given by the parameter ir. Since this effect de- pends on "fooling" suppliers (in the sense of subsection Ayf R Q H H [ S H F W V W K D W U Z L O O E e larger the smaller the variance of the demand shifts. We next develop this im- plication explicitly. From the definition of ir in terms of 0 and y, and the definition of 6 in terms of q2 and r2 we have r27 a2 + r2(1 + yyf Combining with the expression for u2 ob- tained above, this gives (13yf U - *, (1 - yf D U \ \f For fixed r2 and y, then, ir takes the value y/(1 +yyf D W D [ D Q G W H Q G V P R Q R W R Q L F D O O y to zero as o2 tends to infinity. The prediction that the average devia- tion of output from trend, E(y,,yf L V L Q - variant under demand policies is not, of course, subject to test: the deviations from a fitted trend line must average to zero. Accordingly, we must base tests of the natural rate hypothesis (in this contextyf on (13yf D U H O D W L R Q V K L S E H W Z H H Q D Q R E - servable variance and a slope parameter. II. Test Results Testing the hypothesis advanced above involves two steps. First, within each country (11yf D Q G \f should perform reasonably well. In particular, under the presumption that demand fluctuations are the major source of variation in APt and yct, the fits should be "good." The esti- mated values of 7r and X should be between zero and one. Finally, since (11yf D Q G \f involve five slope parameters but only two theoretical ones, the estimated ir and X values obtained from fitting (11yf V K R X O d work reasonably well in explaining varia- tions in APt. The main object of this study, however, is not to "explain" output and price level movements within a given country, but rather to see whether the terms of the output-inflation "tradeoff'' vary across countries in the way predicted by the nat- ural rate theory. For this purpose, we shall utilize the theoretical relationship (13yf and the estimated values of r and a'2. Under the assumption that r2 and y are relatively stable across countries, the esti- mated r values should decline as the sam- ple variance of Axt increases. Descriptive statistics for the eighteen countries in the sample are given in Table 1., As is evident, there is no association 8 The raw data on real and nominal GNP are from Yearbook of National Accounts Statistics, where series from many countries are collected and put on a uniform basis. The choice of countries is by no means random: the eighteen used are all the countries from which con- tinuous series are available. The sample could thus be broadened considerably by use of sources from indi- vidual countries. To obtain the variables used in the tests, the logs of real and nominal output, Yt and xt, are logs of the series in the source. The log of the price level, Pt, is the difference xt-yt; yt is the residual from the trend line yt= a+bt, fit by least squares from the sample This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms VOL. 63 NO. 3 LUCAS: OUTPUT-INFLATION TRADEOFF 331 TABLE 1-DESCRIPTIVE STATISTICS, 1952-67 Mean Mean Variance. Variance Variance Cyt Apt Yet Axt Argentina .026 .220 .00096 .01998 .01555 Austria .048 .038 .00104 .00113 .00124 Belgium .034 .021 .00075 .00033 .00072 Canada .043 .024 .00109 .00018 .00139 Denmark .039 .041 .00082 .00038 .00084 West Germany .056 .026 .00147 .00026 .00073 Guatemala .046 .004 .00111 .00079 .00096 Honduras .044 .012 .00042 .00084 .00109 Ireland .025 .038 .00139 .00060 .00111 Italy .053 .032 .00022 .00044 .00040 Netherlands .047 .036 .00055 .00043 .00101 Norway .038 .034 .00092 .00033 .00098 Paraguay .054 .157 .00488 .03192 .03450 Puerto Rico .058 .024 .00205 .00021 .00077 Sweden .039 .036 .00030 .00043 .00041 United Kingdom .028 .034 .00022 .00037 .00014 United States .036 .019 .00105 .00007 .00064 Venezuela .060 .016 .00175 .00068 .00127 between average real growth rates and average rates of inflation: this fact seems to be consistent with both the conventional and natural rate views of the tradeoff. Since our interest is in comparing real out- put and price behavior under different time patterns of nominal income, these statistics are somewhat disappointing. Essentially two types of nominal income behavior are observed: the highly volatile and expansive policies of Argentina and Paraguay, and the relatively smooth and moderately ex- pansive policies of the remaining sixteen countries. But if the sample provides only two "points," they are indeed widely separated: the estimated variance of de- mand in the high inflation countries is on the order of 10 times that in the stable price countries. The first three columns of Table 2 sum- marize the performance of equation (11yf in accounting for movements in yet. The estimated values for ir all lie between zero and one; with the exceptions of Argentina and Puerto Rico, so do the estimated X values. The R's indicate that for many, or perhaps most countries, important out- put-determining variables have been omit- ted from the model. The R s for the infla- tion rate equation, (12yf D U H J L Y H Q L n column (4yf R I 7 D E O H , Q J H Q H U D O W K H V e tend to be lower than for equation (11yf , and not surprisingly the estimated co- efficients from (12yf Z K L F K D U H Q R W V K R Z Q \f tend to behave erratically. Column (5yf R f Table 2 gives the fraction of the variance of AP' explained by (12yf Z K H Q W K H F R - efficient estimates from (11yf D U H L P S R V H G . (A "-" indicates a negative value.yf 9 With respect to its performance as an intracountry model of income and price determination, then, the system (11yf \f passes the formal tests of significance. On the other hand, the goodness-of-fit statis- period. The moments given in Table 1 are maximum likelihood estimates based on these series. The estimates reported in Table 2 are by ordinary least squares. 9 The loss of explanatory power when these coeffi- cients are imposed on (12yf F D Q E H D V V H V V H G I R U P D O O \ E y an approximate Chi-square test. By this measure, the loss is significant at the .05 level for Paraguay only. As Table 2 shows, however, this test is somewhat decep- tive: for several countries the least squares estimates of (12yf D U H V R S R R U W K D W W K H U H L V O L W W O H H [ S O D Q D W R U \ S R Z H U W o lose, and the test is "passed" vacuously. This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms 332 THE AMERICAN ECONOMIC REVIEW JUNE 1973 TABLE 2-SUMMARY STATISTICS BY COUNTRY, 1953-67 Country 7r R R R 2 R2 Argentina .011 -.126 .018 .929 .914 (.070yf \f Austria .319 .703 .507 .518 - (.179yf \f Belgium .502 .741 .875 .772 .661 (.100yf \f Canada .759 .736 .936 .418 - (.064yf \f Denmark .571 .679 .812 .498 .282 (.118yf \f West Germany .820 .784 .881 .130 - (.136yf \f Guatemala .674 .695 .356 .016 (.301yf \f Honduras .287 .414 .274 .521 .358 (.152yf \f Ireland .430 .858 .847 .499 .192 (.121yf \f Italy .622 .042 .746 .934 .914 (.134yf \f Netherlands .531 .571 .711 .627 .580 (.111yf \f Norway .530 .841 .893 .633 .427 (.088yf \f Paraguay .022 .742 .568 .941 .751 (.079yf \f Puerto Rico .689 1.029 .939 .419 (.121yf \f Sweden .287 .584 .525 .648 .405 (.166yf \f United Kingdom .665 .178 .394 .266 .115 (.290yf \f United States .910 .887 .945 .571 .464 (.086yf \f Venezuela .514 .937 .755 .425 (.183yf \f tics are generally considerably poorer than we have come to expect from annual time- series models. In contrast to these somewhat mixed re- sults, the behavior of the estimated 7r values across countries is in striking con- formity with the natural rate hypothesis. For the sixteen stable price countries, * ranges from .287 to .910; for the two volatile price countries, this estimate is smaller by a factor of 10! To illustrate this order-of-magnitude effect more sharply, let us examine the complete results for two countries: the United States and Argen- tina. For the United States, the fitted ver- sions of (11yf D Q G \f are: yct = - .049 + (.910yf $ [ W \fyc,t-l APt = - .028 + (.119yf $ [ W \f Axt_ - (.637yf $ \ F H W B 1 The comparable results for Argentina are: yct = - .006 + (.011yf $ [ W \fy,.,t_j APt = - .047 + (1.140yf $ [ W \f Axt- + (.102yf $ \ F W 1 In a stable price country like the United States, then, policies which increase nomi- This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms VOL. 63 NO. 3 LUCAS: OUTPUT-INFLATION TRADEOFF 333 nal income tend to have a large initial effect on real output, together with a small, positive initial effect on the rate of infla- tion. Thus the apparent short-term trade- off is favorable, as long as it remains un- used. In contrast, in a volatile price country like Argentina, nominal income changes are associated with equal, con- temporaneous price movements with no discernible effect on real output. These results are, of course, inconsistent with the existence of even moderately stable Phillips curves. On the other hand, they follow directly from the view that inflation stimulates real output if, and only if, it succeeds in "fooling" suppliers of labor and goods into thinking relative prices are moving in their favor. III. Concluding Remarks The basic idea underlying the tests re- ported above is extremely simple, yet I am afraid it may have become obscured by the rather special model in which it is em- bodied. In this section, I shall try to re- state this idea in a way which, though not quite accurate enough to form the basis for econometric work, conveys its essential feature more directly. The propositions to be compared empiri- cally refer to the effects of aggregate de- mand policies which tend to move infla- tion rates and output (relative to trendyf L n the same direction, or alternatively, un- employment and inflation in opposite directions. The conventional Phillips curve account of this observed co-movement says that the terms of the tradeoff arise from relatively stable structural features of the economy, and are thus independent of the nature of the aggregate demand policy pursued. The alternative explanation of the same observed tradeoff is that the positive association of price changes and output arises because suppliers misinter- pret general price movements for relative price changes. It follows from this view, first, that changes in average inflation rates will not increase average output, and secondly, that the higher the variance in average prices, the less "favorable" will be the observed tradeoff. The most natural cross-national com- parison of these propositions would seem to be a direct examination of the associa- tion of average inflation rates and average output, relative to "normal" or "full em- ployment." Unfortunately, there seems to be no satisfactory way to measure normal output. The deviation-from-fitted-trend method I have used defines normal output to be average output. The use of unem- ployment series suffers from the same diffi- culty, since one must somehow select the (obviously positiveyf U D W H W R E H G H Q R W H G I X O l employment. Thus although the issue revolves around the relation between means of inflation and output rates, it cannot be resolved by examination of sample averages. Fortu- nately, the existence of a stable tradeoff also implies a relationship between vari- ances of inflation and output rates, as illustrated in Figure 1. With a stable tradeoff, policies which lead to wide varia- tion in prices must also induce comparable variation in real output.' If these sample variances do not tend to move together (and, as Table 1 shows, they do notyf R Q e A Pt' Var(yctyf D 9 D U I $ 3 W \f 0 0 00 0 0 Stable Price Country 0 Volatile Price Country Yct FIGURE 1 This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms 334 THE AMERICAN ECONOMIC REVIEW JUNE 1973 can only conclude that the tradeoff tends to fade away the more frequently it is used, or abused. This simple argument leads to a formal test if the output-inflation association is entirely contemporaneous. In fact, how- ever, it involves lagged effects which make a direct comparison of variances, as just suggested, difficult in short time-series. Accordingly, it has been necessary to im- pose a specific, simple structure on the data. As we have seen, this structure ac- counts for output and inflation rate move- ments only moderately well, but well enough to capture the main phenomenon predicted by the natural rate theory: the higher the variance of demand, the more unfavorable are the terms of the Phillips tradeoff. REFERENCES M. Friedman, A Theory of the Consumption Function, Princeton 1957. , "The Role of Monetary Policy," Amer. Econ. Rev., Mar. 1968, 58, 1-17. D. F. Gordon and A. Hynes, "On the Theory of Price Dynamics," in E. S. Phelps et al., Micro-economics of Inflation and Employ- ment Theory, New York 1969. R. E. Lucas, Jr., "Expectations and the Neu- trality of Money," J. Econ. Theor., Apr. 1972, 4, 103-24. , "Econometric Testing of the Natural Rate Hypothesis," Conference on the Econ- ometrics of Price Determination, Washing- ton 1972, 50-59. and L. A. Rapping, "Real Wages, Employment and the Price Level," J. Polit. Econ., Sept./Oct. 1969, 77, 721-54. _ and , "Unemployment in the Great Depression: Is There a Full Expla- nation?", J. Polit. Econ., Jan./Feb. 1972, 80, 186-91. J. F. Muth, "Rational Expectations and the Theory of Price Movements," Economet- rica, July 1961, 29, 315-35. E. S. Phelps, introductory chapter in E. S. Phelps et al., Micro-economics of Inflation and Employment Theory, New York 1969. F. Raines, "Macroeconomic Demand and Sup- ply: an Integrative Approach," Washing- ton Univ. working paper, Apr. 1971. A. Rees, "On Equilibrium in Labor Markets," J. Polit. Econ., Mar./Apr. 1970, 78, 306-10. P. Taubman and M. Wilkinson, "User Cost, Capital Utilization and Investment Theory," Int. Econ. Rev., June 1970, 11, 209-15. United Nations, Department of Economic and Social Affairs, United Nations Statisti- cal Office, Yearbook of National Accounts Statistics, 66 and 68, New York 1958. This content downloaded from 131.162.129.148 on Wed, 08 Feb 2017 17:06:22 UTC All use subject to http://about.jstor.org/terms