# Price prediction errors and real activity: a reassessment.

PRICE PREDICTION ERRORS AND REAL ACTIVITY: A REASSESSMENT

I. INTRODUCTION

Macro models employing rational expectations and natural rate assumptions have proven to be powerful and tractable analytical tools. In these models output and employment fluctuations are typically demand-driven, with aggregate demand disturbances transmitted to the real sector through price prediction errors. The waning popularity of natural-rate models is due in part to the widely held belief that, although theoretically appealing, the models are of questionable empirical relevance. This view appears to be based on a small number of studies which fail to find evidence of a robust empirical relationship between price level surprises and aggregate real activity. Indeed, the available evidence has led some influential macroeconomists to conclude that the channels through which aggregate demand influences the economy have yet to be identified. [1] This has had the two-fold effect of (i) stimulating research on channels other than price through which aggregate demand may affect the economy and (ii) discouraging research on channels that do act through the price level. While the first of these effects may be desirable, the second is of concern. This paper is motivated by our conviction that potentially valuable research has been discouraged on the basis of thin and seriously suspect evidence.

The sections that follow reassess the role of price prediction errors in determining aggregate real activity. We provide evidence that the inability of other researchers to verify a positive correlation between demand-driven price prediction errors and real activity is due to misspecified models and, in some cases, inappropriate estimation procedures. We demonstrate that in a more correctly specified and estimated model, the relationship between price surprises and real activity is positive and strongly significant. Thus we conclude that previous researchers were incorrect in discarding the major natural-rate paradigms as empirically irrelevant. These models do appear to identify an important channel, namely price surprises, through which aggregate demand influences the real sector.

II. ISSUES AND EARLY EVIDENCE

Price prediction errors play a central role in the most prominent natural-rate macro-models. These models typically fall into one of two general classes: equilibrium models and contracting models. In both classes of models unanticipated movements in the price level are the channel through which aggregate demand disturbances influence the real sector. The exact nature of transmission process, however, differs across the two sets of theories. Equilibrium models of the sort pioneered by Lucas [1973] depend on the assumption of incomplete information to produce non-neutrality of aggregate demand disturbances. In the best-known examples of this kind of model, confusion between relative and aggregate price movements causes firms to react to unanticipated price level movements as though they were, at least in part, relative price movements. Thus positive price level shocks cause all firms to increase output and generate positive deviations of aggregate output from its natural rate.

Contracting models, as developed in the work of Fischer [1977] and Gray [1976], depend on contractually set wages to produce non-neutrality. In these models nominal wages are incompletely responsive to unexpected changes in the price level during the term of the contract under which they are set. Consequently, an unanticipated rise in the price level causes a fall in the real wage of all workers whose contracts are not in the process of renegotiation at that moment. With employment determined by the firm during the contract interval, the result is a rise in aggregate employment and output.

Our present concern is with testing the common implications of equilibrium and contracting models. Possibilities for distinguishing between the two classes of models are explored in separate work. [2] The most controversial of the shared implications is the predicted positive correlation between price surprises resulting from aggregate demand disturbances and deviations of output and employment from their natural rates. This implication is commonly referred to as the natural-rate hypothesis. Tests of the hypothesis have taken two directions. In one, the empirical relationship tested is the structural relationship between price prediction errors and real activity. In the other, the link between unanticipated movements in aggregate demand (often measured by money surprises) and real activity is directly tested.

The most frequently cited evidence on the effect of price level surprises on real variables is the work of Sargent [1976] and Fair [1979]. Their empirical work is formulated in terms of the U.S. unemployment rate, which is presumed to be negatively related to the level of U.S. aggregate real activity. Thus the theories under consideration here are construed to imply a negative relationship between price level surprises and deviations of unemployment from its natural rate. While Sargent does find a negative (but weak) relationship, Fair's work seems to show that this finding can be reversed by choosing a slightly different sample period. In fact, using a sample period which includes the mid-1970s he produces a very significant positive relationship between price surprises and unemployment. Mishkin [1982] also reports evidence of a positive (though insignificant) correlation. Thus these earlier studies provide no decisive support for the theoretically predicted relationship between price prediction errors and real activity.

By contrast, there exists an extensive literature (Barro [1977] was the first of numerous papers) that broadly supports a role for money surprises, as well as other measures of unanticipated aggregate demand movements, in explaining real economic activity. These studies generally find a negative and highly significant relationship between unanticipated movements in the money supply and the unemployment rate, and a significant positive relationship between money surprises and output. The existing evidence on price surprises and money surprises appears to have generated a consensus among economists: the data fail to support an important role for price prediction errors in explaining observed macroeconomic fluctuations. Accordingly, the theoretical natural-rate macro-models introduced in the 1970s are empirically irrelevant. There is, on the other hand, considerable evidence that aggregate demand disturbances are a significant determinant of real activity. It follows that the channels through which aggregate demand influences real activity have yet to be isolated.

These conclusions are suspect for several reasons. First, the theoretical models discussed above imply that the correlation between price prediction errors and unemployment deviations is necessarily negative only in an economy in which aggregate real (supply-side) disturbances are absent. [3] There is ample evidence that this condition is not met for the post-war U.S. economy. Thus the failure of previous researchers to substantiate a negative correlation is not grounds for rejecting the theoretical models we are concerned with. Second, the existing econometric studies of the effects of price prediction errors incorporate highly simplified views of the determination of the natural rate of real activity; the natural rate is typically represented by a simple function of time and lagged values of the level of real activity. [4] Recent work by Lilien [1982a; 1982b] suggests that changes in natural rates may account for half of the overall movement in unemployment rates through time. [5] These results point to a need for a more careful examination of the role of natural rates in studies that attempt to assess the role of price prediction errors in the economy. Finally, the estimation procedures employed in earlier studies of the relationship between price surprises and real activity can be criticized for various reasons that are addressed at the end of section IV.

III. SPECIFICATION AND ESTIMATION ISSUES

In this section and the next we formulate and estimate a set of empirical models that provide new insights into the role of price prediction errors in determining real activity. The analysis is distinguished from its precursors in its treatment of supply-side disturbances and the natural rate of real activity, as well as in econometric methodology. The specification of the empirical models involves a number of choices involving empirical representation of the theory, nonstationarity, measurement of natural rates, modelling of expectations, treatment of adjustment costs, and estimation technique. We address each of these in turn.

Theoretical Considerations

Our specification of the empirical model includes among the explanatory variables a measure of energy price surprises and a more sophisticated proxy for the natural rate of real activity than was employed in earlier studies. Energy price surprises are included in an effort to incorporate at least one important source of real disturbances into the analysis. [6] This allows us to explore the problems that may arise when such variables are omitted, as they are in most existing work on this subject. The improved natural rate proxy is motivated by Lilien's work. It represents an attempt to capture changes in frictional unemployment due to changes in the variance of industry-specific (as opposed to aggregate) disturbances.

Both the equilibrium and contracting models described above imply that deviations of aggregate real activity from its natural rate should be positively related to errors in predicting the price level and negatively related to errors in predicting the economy-wide average of energy prices. [7] Thus, in the absence of adjustment costs (which are treated later in this section), these theories suggest a model of the following general form:

X(t) [equal to] X*(t) + [X.sub.c(t)], (1) where

[Mathematical Expression Omitted]

Here X(t) measures aggregate real activity at time t, [X.sub.*] (t) its natural rate, and [X.sub.c] (t) its "cyclical" component. Three different proxies for real activity are used: the unemployment rate, the log value of private output, and the log value of private employment.

The explanatory variables PS(t) and QS(t) represent errors in predicting the price of output and the real price of energy. We assume that the error term e(t) is zero mean, but otherwise place no additional restrictions on its properties at this point. At this level of generality PS(t) and QS(t) may be regarded as vectors of price prediction errors, with different elements of the vectors representing forecast errors over different forecast horizons. For the equilibrium model each vector will contain only one element, a one-step-ahead forecast error. For the contracting model, the vector may contain as many as [Tau] elements where [Tau] is the length of the longest contract in the economy. In this case the individual elements will be price forecast errors over horizons ranging from one through [Tau] periods in length. In fact, however, we find that when annual data are used, price prediction errors over horizons of two years or greater are never important in our empirical models. Thus a single representation which includes only one-step-ahead forecast errors can be used for the two models when annual data are employed. Accordingly, PS(t) and QS(t) are defined as follows throughout the remainder of the paper:

PS(t) [equal to] P(t) - [E.sub.t-1] P(t), (2)

QS(t) [equal to] Q(t) - [E.sub.t-1] Q(t).

Here P(t) and Q(t) denote the logarithms of the price level and the real price of energy at time t. [E.sub.t-1] P(t) represents the expectation of P(t) conditioned on information available at time t-1, and similarly for [E.sub.t-1] Q(t).

The hypotheses to be tested involve the signs of the price surprise coefficients, [alpha] and [beta]. The signs predicted by our theoretical models depend on the proxy for real activity that is employed. In the case of the unemployment rate, which is presumed to be negatively related to the level of real activity, we expect a negative [alpha] and a positive [beta] the case of output and employment we expect the opposite signs.

Nonstationarity

An issue that must be resolved prior to estimation is the method of "trend removal" to be used when the measures of aggregate real activity are nonstationary. While it is possible to argue that the unemployment rate is a stationary series (see Nelson and Plosser [1982] ), it is clear that the levels of output and employment are nonstationary; they do not exhibit mean-reverting behavior. The traditional approaches to dealing with this problem are to either remove a linear time trend from the original series, producing a detrended series to use in its place, or, equivalently, to include time as a regressor in the model.

In an influential paper, Nelson and Plosser [1982] report rather strong evidence that real output and employment are appropriately modelled, not as trend stationary processes, but as difference stationary processes. Furthermore, Nelson and Klang [1981; 1984] show that assuming trend stationarity when in fact a series is difference stationary can have unfortunate econometric consequences. We therefore tested these alternative representations for output and employment using the tests employed by Nelson and Plosser in the context of our output and employment models. The results (available on request) confirmed Nelson and Plosser's findings, and accordingly we estimate our empirical models of output and employment in first-difference form. This choice has important implications for the specification of the natural rate of real activity. We turn to this subject next.

Unobservable Variables

None of the explanatory variables that enter equation (1) is observable. This complicates estimation and statistical inference in two ways. First, it is necessary to obtain proxies for the natural rate, output price surprises and energy price surprises in order to estimate the model at all. Second, to obtain efficient estimates and conduct valid tests, it is necessary to estimate the equations generating the natural rate and price surprises proxies jointly with equation (1). Joint estimation allows us to appropriately impose the cross equation restrictions that arise when estimated proxies are included among the regressors. This subjection deals only with the task of selecting suitable proxies. Estimation issues are treated in the following subsection.

A Natural Rate Measure. As discussed above, it is fairly common to model the natural rate as a simple function of time and lagged measures of real activity. This paper employs a more sophisticated measure of the natural rate which takes explicit account of the role of sector-specific shocks in determining the level of aggregate real activity. Following Lilien [1982a] we assume that a rise in the size of sector-specific disturbances increases "frictional" unemployment and thereby reduces the natural rate of aggregate real activity. Our proxy for the size of sector-specific shocks is constructed in a two-stage process, with the first stage producing a measure directly analogous to Lilien's. This measure, denoted SIGMA, is an index of the dispersion of employment changes across industries at a point in time. It is obtained by taking the employment changes that occur between time t-1 and t in each of twenty-nine industry classifications, normalizing these changes on the change in aggregate employment, summing their weighted squared values, and taking the square root of the result.(8) The details of calculating this measure are described in equation (3).

[Mathematical Expressions Omitted]

where [Mathematical Expressions Omitted] and [Mathematical Expression Omitted] = ratio of employment in industry i at time t to total employment in the twenty-nine industry classifications at t. Here [emp.sub.i] denotes the log value of the level of employment in industry i and EMP denotes the log value of the level of aggregate employment. The term [Zeta.sub.i](t) represents the difference between the percentage change in employment in industry i and the percentage change in the level of aggregate employment that occurs between periods t-1 and t.

This proxy for the size of industry-specific disturbances has been criticized on the grounds that one may reasonably expect aggregate disturbances to affect industries differentially (see Abraham and Katz [1986]). If this is the case, SIGMA will reflect the influence not only of industry-specific disturbances, but also the influence of some aggregate disturbances. In our model, this raises the possibility that the effects of SIGMA may be confounded with the effects of the price surprise terms. To eliminate this problem we purge SIGMA of the effects of these terms; we regress SIGMA on a constant term and the output and energy price surprises that enter the model. The residual from this regression, denoted SIG, is our proxy for the size of industry specific disturbances.(9)

The way in which SIG enters our empirical model depends on whether it is unemployment, output, or employment that the model is explaining. In all cases SIG enters the model as a determinant of the natural rate, [X.sup.*(t)]. In the case of the unemployment rate, which we model as a stationary process, [X.sup.*(t)] is given by

(4) [X.sup.*(t) = [mu] + [gamma] SIG(t) + u(t),

where u(t) is a zero mean error term. Substituting this expression into equation (1) produces the following model of the unemployment rate:

(5) X(t) = [mu] + [gamma] SIG(t) + aPS(t) + [Beta] QS(t) + v(t),

where v(t) = e(t) + u(t).

In the cases of output and employment, we assume that the nonstationarity of the series is due to the fact that their natural rate components reflect the effects of nonstationary factors such as capital accumulation, technological change and population growth as well as stationary factors such as SIG. Since the results reported above indicate that output and employment are difference stationary series, we model their natural rate components as the sum of two process. One is an unobserved difference stationary process, denoted [X.sup.*(t)], that captures the resource and technology factors just mentioned. The other is a stationary process involving SIG. Thus for output and employment [X.sup.*] (t) is given by

(6) [Mathematical Expressions Omitted]

where [X.sup.*] (t) [equalto] [mu] + [X.sup.*] (t-1) + u(t). Equation (6) can be rewritten as

(7) [DX.sup.*] (t) [equalto] [mu] + [gamma] DSIG(t) + u(t),

where D(.) is the first-difference operator and u(t) is a zero mean error term. First-differencing equation (1) and substituting equation (7) into the resulting expression produces the following representation of output and employment:

(8) DX(t) = [mu] + [gamma] DSIG(t) + aDPS(t) + [Beta] DQS(t) + v(t),

where v(t) = De(t) + u(t).

We place no a priori restrictions on the properties of the error terms, denoted v(t), that enter equations (5) and (8), with the exception that they be zero mean stationary processes. Accordingly, our empirical methodology, described below, takes account of the possibility that v(t) is serially correlated.

Output and Energy Price Surprises. Obtaining a proxy for ex ante forecasts of the real price of energy, which is assumed to be exogenous, is complicated by our assumption that the generating process experienced a structural change between 1973 and 1974. For both the period 1948-1973 and the period 1974-1986 we assume the generating process is known to be second-order autoregressive, or AR(2). Thus, with the exception of 1974, forecasts for each sub-period are obtained as the fitted values from a regression of Q(t), the logarithm of the real price of energy at t, on a constant, Q(t-1), and Q(t-2).

In dealing with the changes that occured between 1973 and 1974, it seems reasonable to assume that by the end of 1974 economic agents recognized that the process generating energy prices had changed. Thus we incorporate a brief delay in recognition into the forecasting procedure by assuming that the forecast for 1974 is based on the pre-1974 AR(2) model. After 1974, forecasts are based on the post-1974 AR(2) model. (What we have described here is equation (13) below.) The proxy for energy price surprises is then formed by subtracting the forecast of the price of energy from the actual price of energy.(10)

Obtaining a proxy for output price surprises is complicated by the fact that the price level is endogenous. Price level forecasts are generated by taking the fitted values of a reduced form equation for the GNP deflator(11) in which the explanatory variables include lagged endogenous and lagged exogenous variables. Specifically, the logarithm of the GNP deflator is regressed on a constant, lagged values of the real activity measure and SIGMA, and lagged values of the logarithms of the money stock (M), the real price of energy, and the GNP deflator itself (P). (See equation (12) of the next subsection for more detail.) The fitted values from this equation are then subtracted from the actual value of the logarithm of the GNP deflator to obtain a proxy for output price surprises.

Examples of the output and energy price surprise series, as well as the SIGMA and SIG series, are reported in the data appendix at the end of the paper. The output price surprises and energy price surprises pass the usual rationality tests; they are zero mean, serially independent, and orthogonal to past information.

Adjustment Costs

As empirical models, equations (5) and (8) suffer from an important shortcoming in that they omit all consideration of adjustment costs. If firms find it costly to adjust input levels there will be lags in the response of real activity to price surprises. We follow numerous other researchers (including Sargent and Fair) in attempting to capture the effects of such costs parsimoniously by including a lagged value of the dependent variable among the explanatory variables.(12) Thus the model of the unemployment rate that is estimated in section IV below is given by:

[Mathematical Expression Omitted]

Similarly, the model of output and employment is of the form

[Mathematical Expression Omitted]

Estimation

In order to obtain efficient estimates and to assure correct inferences (i.e. to obtain consistent variance estimates) we estimate the equations for each of the measures of aggregate economic activity jointly with the equations which determine the proxy variables.(13) For example, for the model of unemployment given by equation (9) above we estimated the following system using nonlinear three-stage least squares.(14)

[Mathematical Expression Omitted]

Exactly the same system is estimated for output and employment except that equation (11) takes the first difference form given in equation (10).

The fitted value from equation (12) is out one-step-ahead forecast of the price level. In equation (13) DUM(t) is a dummy variable which is zero for the period 1948-1973 and is one for the period 1974-1986. The forecast of the real price of energy is the fitted value from equation (13) after substituting DUM(t-i-1) for DUM(t-i), i=0,1,2, to reflect the recognition lag discussed above. SIG(t) in equation (11) is formed by subtracting the fitted value from equation (14) from actual SIGMA (t). The final term in each equation is an error term. In equation (11), the equation of primary interest, the error term, v(t), is assumed to follow an AR(1) process when unemployment is used as the measure of real activity. When output or employment is used, v(t) is assumed to be serially independent.(15)

Jointly estimating equations (11) through (14) not only efficiently incorporates the restrictions implicit in the models for expected output and energy prices, but also the restrictions implicit in the "correction" of SIGMA for aggregate influences. Thus our estimation procedure does not suffer from the "generated regresson" problem discussed by Pagan [1984; 1986] and (under the maintained hypothesis) the statistical inference procedures used here will be appropriate.

Finally, in addition to the fully-specified models of real activity given by equation (9) for the unemployment rate and equation (10) for output and employment, several variations on these models are estimated and reported in the next section. Some of these specifications omit either energy price shocks or the proxy for industry-specific disturbances (SIG) or both from the list of variables used to explain aggregate real activity. They are intended as an aid in assessing the contribution of these factors to our results and in comparing our results to the findings of other researchers. In each case any variable that is omitted from the model is also omitted (along with any lagged values) from the rest of the equations comprising the jointly estimated system and from the list of instruments used in estimating the model (see footnote 14).

IV. ESTIMATION RESULTS

We estimated the model of aggregate economic activity developed in section III for three measures of economic activity: the civilian (sixteen years and over) unemployment rate (UN), the log value of real gross private domestic product (Y), and the log value of full-time equivalent employment in all domestic industries (EMP).(16) The results for annual data over the period 1948-1986 are reported in Tables I through III.(17) In each table we first report the outcome of estimating a fully specified model which includes energy price surprises and our proxy for the variance of industry-specific disturbances, SIG. Results reported in the next three rows illustrate the consequences of omitting first energy price shocks only, then SIG only, and finally both energy price shocks and SIG from the fully specified equation.

Our empirical findings uniformly support the model developed in this paper. Consider, for example, the results for the unemployment rate which are reported in Table I. The coefficient on output price surprises (PS) is negative and highly significant in all specifications except the one in which both energy price shocks and SIG are omitted. The improved measure of the natural rate of unemployment also performs well; the coefficient on SIG is of the correct sign (positive) and highly significant in both specifications in which it appears.(18) And finally, energy price shocks (QS) are positively and significantly correlated with the rate of unemployment in the fully specified model and is of the correct sign (although insignificant) in the specification that omits SIG.

[TABULAR DATA OMITTED]

Comparing the various specifications reported in the first four rows of Table I allows us to assess the contributions of energy price shocks and SIG, individually and jointly, to the finding that output price surprises significantly impact unemployment. It is readily apparent that the deletion of either energy price surprises or SIG reduces the size and significance of the price surprise coefficient. The effect is dramatic, however, when both are deleted; the coefficient estimate is less than a quarter of its value in the fully specified model, and it is not statistically significant. We conclude that not only are SIG and energy price shocks important in their own right in explaining unemployment variation, but their omission may lead to severe under-assessment of the importance of output price surprises in determining real activity.

The results reported in Tables II and III for output and employment are similar to those for the unemployment rate. The coefficient on output price surprises is of the "correct" sign (positive in these cases) and highly significant in all specifications. The coefficient on SIG is negative and highly significant. Energy price surprises are negatively correlated with output and employment in all specifications in which they appear, but significantly so only in the fully specified equations. The effects of

[TABULAR DATA OMITTED] omitting energy price shocks and SIG, individually and jointly, from the fully specified equation are qualitatively similar to those reported for the unemployment rate. Note, however, that price surprises remain significant even in the specification that omits both energy price shocks and SIG.

In addition to the model variations reported in the first four rows of Tables I through III, we also estimated equations which include the expected value of the price level (EP) along with price level surprises. Thus we tested the restriction, implicit in most natural rate models, that price level changes which are anticipated have no effect on aggregate real economic activity. The results of this exercise for the "fully specified" equations are reported in the final rows of Tables I through III. They reveal no systematic or statistically significant relationship between anticipated price and economic activity.(19)

The empirical results reported in this section provide considerable support for the proposition that price level surprises have a significant impact on aggregate real economic activity.(20) The distinctive features of our model - the inclusion of energy price shocks and an improved natural rate measure - are important (and in the case of the unemployment rate, critical) to this result. Thus, contrary to widely held belief, the data do not reject theoretical natural-rate models in which price surprises play an important role in transmitting aggregate demand disturbances to the real sector.

The fact that output price surprises remain positively and (except for unemployment) significant correlated with real activity even when energy price shocks and SIG are omitted from the empirical models is provocative. It raises the question of why previous researchers, particularly Fair and Mishkin, obtained the results they did. In this regard we note that the differences between our work and the work carried out by Sargent, Fair, and Mishkin go beyond our treatment of supply-side shocks and natural rates. Where both Fair and Mishkin are concerned, the differences lead us to conclude that their empirical findings do not provide very useful information on the nature of aggregate supply as captured by the relationship between output price surprises and the unemployment rate.

Fair's principle purpose was not to test the importance of price prediction errors in explaining unemployment fluctuations but rather to examine the empirical usefulness of Sargent's complete macro model. In forming a proxy for price level expectations, Fair calculates iteratively the rational expectations that follow from the restrictions implied by Sargent's complete general equilibrium model. Accordingly, his results should be interpreted as calling into question Sargent's entire model without identifying any particular component of the model (e.g., the unemployment equation) as the source of the problem. Fair's results could be as easily explained by a misspecified aggregate demand equation as by a misspecified aggregate supply equation. Thus, it may be the case that many have been too hasty in interpreting Fair's results as evidence against the role of price prediction errors hypothesized by conventional natural rate macro models - a claim Fair himself does not make.

In comparing Mishkin's work to our own another critical difference becomes immediately apparent. Mishkin, although acknowledging the assumption to be tenuous, maintains that the price level is exogenous. By contrast we (as well as Sargent and Fair) account for the endogeneity of the price level through the use of instrumental variables. Since the price level is unambiguously endogenous in the models we are concerned with, we regard Mishkin's findings on the relationship between price surprises and unemployment as suspect.

Our results support Sargent's [1976] conclusion that price level prediction errors lower unemployment. Our findings are particularly convincing since they are obtained over a sample period that subsumes those of Fair and Mishkin as well as Sargent. The major difference between our findings and Sargent's is the higher significance levels generally associated with the output price surprise coefficients in our study. This difference is partly explained by the inclusion of energy price shocks and SIG in our regressions. Two additional differences are also worthy of note: We jointly estimated the price forecast equations along with each equation explaining real activity; Sargent does not and thus his estimation procedure suffers from the generated regressor problem mentioned earlier. And, finally, we employ annual data in our study, whereas Sargent (as well as Fair and Mishkin) employ quarterly data.(21)

VI. CONCLUSIONS

In this paper we reexamine the role of price prediction errors in determining the level of real aggregate activity. Our approach to the issue is distinguished by accounting for aggregate supply-side disturbances and by a more careful treatment of natural rates. To incorporate the influence of aggregate supply shocks we include errors in predicting the real price of energy as an additional variable in the empirical models. In modelling natural rates, we construct a proxy for the variance of industry-specific (or relative) disturbances which is included in our models. We estimated the empirical models with U.S. data over the period 1948-1986 and draw the following conclusions:

Contrary to some previous studies, we find that the data are

consistent with the hypothesis that demand-driven price level surprises

are positively and significantly correlated with aggregate

real economic activity.

We also find that energy price surprises are negatively and significantly

correlated with aggregate real economic activity.

Our improved natural rate measure is strongly supported by the

data. This confirms previous results obtained by Lilien.

Estimates of equations which omit both energy price surprises

and our natural rate proxy exhibit a marked reduction in the

magnitude and statistical significance of the coefficient on output

price surprises. Thus the strength of our first conclusion depends

on a "correctly" specified equation.

Once we have accounted for price surprises, expected output prices

are of no additional help in explaining real macroeconomic fluctuations.

In summary, we find no support for the view that natural-rate equilibruim and contracting models are empirically irrelevant. Quite the contrary, our findings provide considerable support for the view that these models identify an important channel, namely price surprises, through which aggregate demand influences aggregate real activity.

DATA APPENDIX

The variables employed in our empirical analysis are as follows:

- unemployment is the civilian (16 years and over) unemployment

rate,

- output is real private gross domestic product,

- employment is full-time equivalent employment in all private domestic

industries,

- money supply is new M1,

- price of output is the GNP deflator,

- treasury bill rate is the three-month Treasury bill rate,

- price of energy is the producer price index for fuels and related

products and power,

- surplus is the nominal natural employment federal government

surplus.

Data have been taken directly from the Citibase data bank except as follows:

SIGMA = proxy for variation in sectoral employment; computed as in Lilien [1982a, 787], and described in equation (3) of the text. The twenty-nine industries used in calculating SIGMA come from the usual twenty-nine industry decomposition of aggregate employment. The industry employment data were obtained from the Citibase data bank. Minor smoothing was done to adjust for the effects of significant work stoppages. This series is not adjusted for the effects of output and energy price surprises. It is reported in Table A.

Table : TABLE A Variables Appearing in the Fully Specified Unemployment Model 1948-1986

Note: The constructed explanatory variables reported here are those associated with the fully specified unemployment model reported in row 1 of Table I. Because they are estimated as part of a system of equations, the values of PS, SIG and QS will vary somewhat from model to model and across the three real activity measures employed. SIGMA, on the other hand, will not.

money supply =new M1 (from Citibase) for 1959-1986, and old M1 (from Citibase) multiplied by .985 for 1948-1958. The splicing factor, .985, represents the average of the ratios of new M1 to old M1 for 1959 and 1960.

surplus = real natural employment surplus (from Gordon [1987]) multiplied by the GNP deflator (from Citibase).

( 1.) For example, Barro [1981, 71] states that "Given the relatively minor role played by price surprises....it appears that monetary influences on output involve channels that have yet to be isolated."

( 2.) In Gray, Kandil, and Spencer [1990] we explore differences in the cyclical behavior of the contract and non-contract sectors of the U.S. economy in an effort to identify the role played by contractual wage rigidities in the macroeconomy.

( 3.) This point has become more generally recognized in the wake of the oil price shocks of the 1970s. Fethke [1983], for example, points out that with an optimally indexed wage rate and both real and nominal aggregate demand disturbances, innovations in output will be negatively correlated with innovations in the price level.

( 4.) Exceptions include Barro [1977; 1978] who incorporates additional variables to capture the effects of military conscription and the minimum wage on the unemployment rate.

( 5.) Nelson and Plosser [1982] also find evidence of significant variation in natural rates over time.

( 6.) The potential importance of this particular supply side disturbance in explaining output, prices, and shifts in the "Phillips curve," particularly during the 1970s, has been recognized by a number of authors. These include Gordon [1975; 1982], Hamilton [1983] and Nordhaus [1980].

( 7.) Incorporating supply-side disturbances such as energy price shocks into the simpler versions of the contracting and equilibrium theories is not particularly difficult (see Mohammadi [1988]). In both classes of models the anticipated as well as the unanticipated component of energy price changes appear along with output price surprises as determinants of the level of aggregate real activity. The anticipated component of the real price of energy appears because it can affect the natural rate of real activity. The unanticipated component appears because it is a source of output price surprises that are negatively rather than positively correlated with output; its omission would cause the estimated coefficient on price surprises to be biased toward zero. Consistent with these theoretical considerations, we have estimated models of real activity that include anticipated energy price changes as well as energy price shocks. Since the anticipated component has been consistently insignificant in these exercises, it is not included in the empirical models reported in this paper.

( 8.) Here we follow Lilien [1982b] in using a twenty-nine industry decomposition of employement in forming the proxy for the variance of industry-specific disturbances. This is in contrast to the eleven industry decomposition he uses in his earlier work. See the data appendix for a description of the industry data used.

( 9.) See Lilien [1982b] for an alternative approach to purging SIGMA of the influence of aggregate disturbances.

(10.) Since we are modelling expectations, the occurrence of a structural break in the generating process for Q(t) requires us to address the issue of how economic agents learn the new generating process. In the absence of a formal model of learning we employed several alternative ad hoc specifications for energy price expectations to check the robustness of our results. These include a specification which models the generating process as a stable AR(2) over the entire sample period without accounting for any structural change and another which admits a structural break, basing expectations on an AR(2) model through 1974 and a random walk after 1974. In each of the cases we examined, our central results are essentially unchanged.

(11.) We chose the broadest available measure of output price for our empirical exercises since our objective is to capture unanticipated price movements due to aggregate demand disturbances. Movements in narrower price measures are more likely to be contaminated by relative disturbances.

(12.) Given the number of explanatory variables in many of our equations, we do not have the degrees of freedom necessary to estimate all of the equations with unrestricted distributed lags. Consequently we chose to adopt the more restrictive approach of including a lagged dependent variable in our models of real activity. This choice presumes that the distributed lag response of real activity to each of its determinants declines (approximately) at the same geometric rate over time.

(13.) The important econometric issues which arise from the presence of estimated proxies, or generated regressors, in empirical models are thoroughly discussed by Pagan [1984; 1986].

(14.) In estimating the system given by equations (11) through (14) we assumed that the price level is the only endogenous variable appearing on the right-hand-side of the unemployment equation. SIG and the price of energy are assumed to be exogenous. These choices were based on the results of Engle's [1982] Lagrange-multiplier version of the test developed by Spencer and Berk [1981]. We were unable to reject the hypothesis that SIG and energy price surprises are exogenous at any reasonable level of significance. The set of instruments used in estimating equation (11) contains a constant and a linear time trend; three lags each of the dependent variable, SIGMA, the GNP deflator, and the three-month Treasury bill rate; the current as well as the first three lagged values of the money supply, the nominal natural employment federal government surplus, and the real price of energy. In specification which do not include SIG, the lagged values of SIGMA are dropped from the instrument list. Similarly, in specifications which do not include energy price shocks, the current and lagged values of the real price of energy are dropped from the instrument list. In order to examine the sensitivity of our results to instrument choice, we estimated our models under several alternative sets of instrumental variables. Each of these alternatives yielded results which are quite similar to those reported here.

(15.) Using the Lagrange multiplier test that follows from Theorem 2 in Engle [1982] (appropriate for simultaneous equations), we found evidence of AR(1) errors in some of our enemployment specifications. No evidence of higher order AR processes was found. We thus chose to estimate all our enemployment models under the assumption that the errors follow an AR(1) process. If the finding of serial correlation is a reflection of potential specification error, then the reliability of the empirical results for unemployment models may be subject to question. However, the consistency of these results with those found for output and employment models (in which we find no evidence of serial correlation) leads us to conclude that the results are reliable.

(16.) These measures of output and employment are used because they correspond more closely to their theoretical counterparts than more inclusive measures. We have also estimated models for several more inclusive output and employment measures (e.g., real gross national product, real gross domestic

product, and total employment) and obtain results which are quite similar to those reported here.

(17.) We have experimented with quarterly data as well. While our results are qualitatively similar to those reported here, they are not nearly so strong. We are in the process of exploring the possiblity that the weakness of the quarterly results is a consequence of inappropriate temporal disaggregation. For example, in a contracting model that incorporates adjustment costs, we expect employment to exhibit a greater response to thoseaggregate price level shocks that are perceived to be permanent than to those that are perceived to be transitory. Our empirical results, however, are obtained without decomposing price surprises into perceived permanent and temporary components. Since it is likely that observed quarterly data will contain a larger transitory component than annual data, we would expect weaker results using the quarterly data.

(18.) Our results concerning SIG provide an interesting counterpoint to those of Loungani (1986), who finds that after correction for oil price changes, Lilien's sectoral shift variable (SIGMA) is not significant. There are a number of possible reasons for the difference between our results and Loungani's: We "correct" for the influence of oil price shocks on SIGMA in a different way than Loungani does. While Loungani regresses his individual industry employment series on energy prices before constructing his SIGMA measure, we regress the equivalent of Lilien's SIGMA on energy price shocks (as well as price level shocks) after it is constructed from the original employment series. (We have also tried purging SIGMA of the squared values of these shocks and found, like others, that it makes little difference.) While both methods are intuitively appealing, we can't be sure they produce the same result. A second difference is that Loungani uses quarterly data whereas we use annual data. And another is that the real activity model in which Loungani imbeds his SIGMA measure is quite a bit different from the one in which we imbed ours.

(19.) It is interesting to note that the result is the same when EP is added to each of the other (misspecified) equations reported in Tables I-III.

(20.) In models of the type under investigation here, numerous decisions must be made in order to obtain empirical results. It is thus important to have some idea as to the robustness of our principal results to reasonable alternative decisions. In the course of the study of which this paper is a part we have estimated models associated with many alternative specification and estimation decisions. We have employed alternative instruments (see footnote 14), alternative forecasting models for Q(t) (see footnote 10), alternative forecasting models for P(t) (i.e., different information sets), alternative methods of detrending, alternative assuptions regarding SIGMA (t), and alternative assuptions regarding the distribution of the errors as well as using both two-step and joint estimation procedures. In this wide range of empirical models, each of which is consistent with the theory, the conclusions regarding the role of output price prediction errors and SIG(t) (or SIGMA (t) are quite robust. Each of these virtually always exhibits the expected sign and is almost always stongly significant. On the other hand, energy prices surprises are occasionally insignificant (although rarely in fully specified models).

(21.) See footnote 17.

REFERENCES

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JO ANNA GRAY and DAVID E. SPENCER(*)

(*) Washington State University and Brigham Young University. We are grateful to the National Science Foundation (grant SES-8608885) for research support; to the participants of the October 1985 NBER Economic Fluctuations Research Meeting, particularly Steve Cecchetti, Robert Gordon, Robert Hall, Frederic Mishkin, Knut Mork, and William Nordhaus, for their comments on an earlier version of this paper; to Steve Davis, Stan Fishcer, Bob Flood, Robert Shiller, Jeff Wrase, and Doug Young for their helpful suggestions; to John Anderson, Jonghwa Cho, Chan Chee Pang and Mark Thoma for computational assistance in the early stages of this project; and to Magda Kandil for her excellent research assistance in the later stages of the project. Finally, we thank Richard Sweeney, Danny Quah, Jeffrey Woolridge, and an anonymous referee for their help on the final draft of the paper. All data employed in this paper can be obtained from readily available public sources; see our data appendix.

I. INTRODUCTION

Macro models employing rational expectations and natural rate assumptions have proven to be powerful and tractable analytical tools. In these models output and employment fluctuations are typically demand-driven, with aggregate demand disturbances transmitted to the real sector through price prediction errors. The waning popularity of natural-rate models is due in part to the widely held belief that, although theoretically appealing, the models are of questionable empirical relevance. This view appears to be based on a small number of studies which fail to find evidence of a robust empirical relationship between price level surprises and aggregate real activity. Indeed, the available evidence has led some influential macroeconomists to conclude that the channels through which aggregate demand influences the economy have yet to be identified. [1] This has had the two-fold effect of (i) stimulating research on channels other than price through which aggregate demand may affect the economy and (ii) discouraging research on channels that do act through the price level. While the first of these effects may be desirable, the second is of concern. This paper is motivated by our conviction that potentially valuable research has been discouraged on the basis of thin and seriously suspect evidence.

The sections that follow reassess the role of price prediction errors in determining aggregate real activity. We provide evidence that the inability of other researchers to verify a positive correlation between demand-driven price prediction errors and real activity is due to misspecified models and, in some cases, inappropriate estimation procedures. We demonstrate that in a more correctly specified and estimated model, the relationship between price surprises and real activity is positive and strongly significant. Thus we conclude that previous researchers were incorrect in discarding the major natural-rate paradigms as empirically irrelevant. These models do appear to identify an important channel, namely price surprises, through which aggregate demand influences the real sector.

II. ISSUES AND EARLY EVIDENCE

Price prediction errors play a central role in the most prominent natural-rate macro-models. These models typically fall into one of two general classes: equilibrium models and contracting models. In both classes of models unanticipated movements in the price level are the channel through which aggregate demand disturbances influence the real sector. The exact nature of transmission process, however, differs across the two sets of theories. Equilibrium models of the sort pioneered by Lucas [1973] depend on the assumption of incomplete information to produce non-neutrality of aggregate demand disturbances. In the best-known examples of this kind of model, confusion between relative and aggregate price movements causes firms to react to unanticipated price level movements as though they were, at least in part, relative price movements. Thus positive price level shocks cause all firms to increase output and generate positive deviations of aggregate output from its natural rate.

Contracting models, as developed in the work of Fischer [1977] and Gray [1976], depend on contractually set wages to produce non-neutrality. In these models nominal wages are incompletely responsive to unexpected changes in the price level during the term of the contract under which they are set. Consequently, an unanticipated rise in the price level causes a fall in the real wage of all workers whose contracts are not in the process of renegotiation at that moment. With employment determined by the firm during the contract interval, the result is a rise in aggregate employment and output.

Our present concern is with testing the common implications of equilibrium and contracting models. Possibilities for distinguishing between the two classes of models are explored in separate work. [2] The most controversial of the shared implications is the predicted positive correlation between price surprises resulting from aggregate demand disturbances and deviations of output and employment from their natural rates. This implication is commonly referred to as the natural-rate hypothesis. Tests of the hypothesis have taken two directions. In one, the empirical relationship tested is the structural relationship between price prediction errors and real activity. In the other, the link between unanticipated movements in aggregate demand (often measured by money surprises) and real activity is directly tested.

The most frequently cited evidence on the effect of price level surprises on real variables is the work of Sargent [1976] and Fair [1979]. Their empirical work is formulated in terms of the U.S. unemployment rate, which is presumed to be negatively related to the level of U.S. aggregate real activity. Thus the theories under consideration here are construed to imply a negative relationship between price level surprises and deviations of unemployment from its natural rate. While Sargent does find a negative (but weak) relationship, Fair's work seems to show that this finding can be reversed by choosing a slightly different sample period. In fact, using a sample period which includes the mid-1970s he produces a very significant positive relationship between price surprises and unemployment. Mishkin [1982] also reports evidence of a positive (though insignificant) correlation. Thus these earlier studies provide no decisive support for the theoretically predicted relationship between price prediction errors and real activity.

By contrast, there exists an extensive literature (Barro [1977] was the first of numerous papers) that broadly supports a role for money surprises, as well as other measures of unanticipated aggregate demand movements, in explaining real economic activity. These studies generally find a negative and highly significant relationship between unanticipated movements in the money supply and the unemployment rate, and a significant positive relationship between money surprises and output. The existing evidence on price surprises and money surprises appears to have generated a consensus among economists: the data fail to support an important role for price prediction errors in explaining observed macroeconomic fluctuations. Accordingly, the theoretical natural-rate macro-models introduced in the 1970s are empirically irrelevant. There is, on the other hand, considerable evidence that aggregate demand disturbances are a significant determinant of real activity. It follows that the channels through which aggregate demand influences real activity have yet to be isolated.

These conclusions are suspect for several reasons. First, the theoretical models discussed above imply that the correlation between price prediction errors and unemployment deviations is necessarily negative only in an economy in which aggregate real (supply-side) disturbances are absent. [3] There is ample evidence that this condition is not met for the post-war U.S. economy. Thus the failure of previous researchers to substantiate a negative correlation is not grounds for rejecting the theoretical models we are concerned with. Second, the existing econometric studies of the effects of price prediction errors incorporate highly simplified views of the determination of the natural rate of real activity; the natural rate is typically represented by a simple function of time and lagged values of the level of real activity. [4] Recent work by Lilien [1982a; 1982b] suggests that changes in natural rates may account for half of the overall movement in unemployment rates through time. [5] These results point to a need for a more careful examination of the role of natural rates in studies that attempt to assess the role of price prediction errors in the economy. Finally, the estimation procedures employed in earlier studies of the relationship between price surprises and real activity can be criticized for various reasons that are addressed at the end of section IV.

III. SPECIFICATION AND ESTIMATION ISSUES

In this section and the next we formulate and estimate a set of empirical models that provide new insights into the role of price prediction errors in determining real activity. The analysis is distinguished from its precursors in its treatment of supply-side disturbances and the natural rate of real activity, as well as in econometric methodology. The specification of the empirical models involves a number of choices involving empirical representation of the theory, nonstationarity, measurement of natural rates, modelling of expectations, treatment of adjustment costs, and estimation technique. We address each of these in turn.

Theoretical Considerations

Our specification of the empirical model includes among the explanatory variables a measure of energy price surprises and a more sophisticated proxy for the natural rate of real activity than was employed in earlier studies. Energy price surprises are included in an effort to incorporate at least one important source of real disturbances into the analysis. [6] This allows us to explore the problems that may arise when such variables are omitted, as they are in most existing work on this subject. The improved natural rate proxy is motivated by Lilien's work. It represents an attempt to capture changes in frictional unemployment due to changes in the variance of industry-specific (as opposed to aggregate) disturbances.

Both the equilibrium and contracting models described above imply that deviations of aggregate real activity from its natural rate should be positively related to errors in predicting the price level and negatively related to errors in predicting the economy-wide average of energy prices. [7] Thus, in the absence of adjustment costs (which are treated later in this section), these theories suggest a model of the following general form:

X(t) [equal to] X*(t) + [X.sub.c(t)], (1) where

[Mathematical Expression Omitted]

Here X(t) measures aggregate real activity at time t, [X.sub.*] (t) its natural rate, and [X.sub.c] (t) its "cyclical" component. Three different proxies for real activity are used: the unemployment rate, the log value of private output, and the log value of private employment.

The explanatory variables PS(t) and QS(t) represent errors in predicting the price of output and the real price of energy. We assume that the error term e(t) is zero mean, but otherwise place no additional restrictions on its properties at this point. At this level of generality PS(t) and QS(t) may be regarded as vectors of price prediction errors, with different elements of the vectors representing forecast errors over different forecast horizons. For the equilibrium model each vector will contain only one element, a one-step-ahead forecast error. For the contracting model, the vector may contain as many as [Tau] elements where [Tau] is the length of the longest contract in the economy. In this case the individual elements will be price forecast errors over horizons ranging from one through [Tau] periods in length. In fact, however, we find that when annual data are used, price prediction errors over horizons of two years or greater are never important in our empirical models. Thus a single representation which includes only one-step-ahead forecast errors can be used for the two models when annual data are employed. Accordingly, PS(t) and QS(t) are defined as follows throughout the remainder of the paper:

PS(t) [equal to] P(t) - [E.sub.t-1] P(t), (2)

QS(t) [equal to] Q(t) - [E.sub.t-1] Q(t).

Here P(t) and Q(t) denote the logarithms of the price level and the real price of energy at time t. [E.sub.t-1] P(t) represents the expectation of P(t) conditioned on information available at time t-1, and similarly for [E.sub.t-1] Q(t).

The hypotheses to be tested involve the signs of the price surprise coefficients, [alpha] and [beta]. The signs predicted by our theoretical models depend on the proxy for real activity that is employed. In the case of the unemployment rate, which is presumed to be negatively related to the level of real activity, we expect a negative [alpha] and a positive [beta] the case of output and employment we expect the opposite signs.

Nonstationarity

An issue that must be resolved prior to estimation is the method of "trend removal" to be used when the measures of aggregate real activity are nonstationary. While it is possible to argue that the unemployment rate is a stationary series (see Nelson and Plosser [1982] ), it is clear that the levels of output and employment are nonstationary; they do not exhibit mean-reverting behavior. The traditional approaches to dealing with this problem are to either remove a linear time trend from the original series, producing a detrended series to use in its place, or, equivalently, to include time as a regressor in the model.

In an influential paper, Nelson and Plosser [1982] report rather strong evidence that real output and employment are appropriately modelled, not as trend stationary processes, but as difference stationary processes. Furthermore, Nelson and Klang [1981; 1984] show that assuming trend stationarity when in fact a series is difference stationary can have unfortunate econometric consequences. We therefore tested these alternative representations for output and employment using the tests employed by Nelson and Plosser in the context of our output and employment models. The results (available on request) confirmed Nelson and Plosser's findings, and accordingly we estimate our empirical models of output and employment in first-difference form. This choice has important implications for the specification of the natural rate of real activity. We turn to this subject next.

Unobservable Variables

None of the explanatory variables that enter equation (1) is observable. This complicates estimation and statistical inference in two ways. First, it is necessary to obtain proxies for the natural rate, output price surprises and energy price surprises in order to estimate the model at all. Second, to obtain efficient estimates and conduct valid tests, it is necessary to estimate the equations generating the natural rate and price surprises proxies jointly with equation (1). Joint estimation allows us to appropriately impose the cross equation restrictions that arise when estimated proxies are included among the regressors. This subjection deals only with the task of selecting suitable proxies. Estimation issues are treated in the following subsection.

A Natural Rate Measure. As discussed above, it is fairly common to model the natural rate as a simple function of time and lagged measures of real activity. This paper employs a more sophisticated measure of the natural rate which takes explicit account of the role of sector-specific shocks in determining the level of aggregate real activity. Following Lilien [1982a] we assume that a rise in the size of sector-specific disturbances increases "frictional" unemployment and thereby reduces the natural rate of aggregate real activity. Our proxy for the size of sector-specific shocks is constructed in a two-stage process, with the first stage producing a measure directly analogous to Lilien's. This measure, denoted SIGMA, is an index of the dispersion of employment changes across industries at a point in time. It is obtained by taking the employment changes that occur between time t-1 and t in each of twenty-nine industry classifications, normalizing these changes on the change in aggregate employment, summing their weighted squared values, and taking the square root of the result.(8) The details of calculating this measure are described in equation (3).

[Mathematical Expressions Omitted]

where [Mathematical Expressions Omitted] and [Mathematical Expression Omitted] = ratio of employment in industry i at time t to total employment in the twenty-nine industry classifications at t. Here [emp.sub.i] denotes the log value of the level of employment in industry i and EMP denotes the log value of the level of aggregate employment. The term [Zeta.sub.i](t) represents the difference between the percentage change in employment in industry i and the percentage change in the level of aggregate employment that occurs between periods t-1 and t.

This proxy for the size of industry-specific disturbances has been criticized on the grounds that one may reasonably expect aggregate disturbances to affect industries differentially (see Abraham and Katz [1986]). If this is the case, SIGMA will reflect the influence not only of industry-specific disturbances, but also the influence of some aggregate disturbances. In our model, this raises the possibility that the effects of SIGMA may be confounded with the effects of the price surprise terms. To eliminate this problem we purge SIGMA of the effects of these terms; we regress SIGMA on a constant term and the output and energy price surprises that enter the model. The residual from this regression, denoted SIG, is our proxy for the size of industry specific disturbances.(9)

The way in which SIG enters our empirical model depends on whether it is unemployment, output, or employment that the model is explaining. In all cases SIG enters the model as a determinant of the natural rate, [X.sup.*(t)]. In the case of the unemployment rate, which we model as a stationary process, [X.sup.*(t)] is given by

(4) [X.sup.*(t) = [mu] + [gamma] SIG(t) + u(t),

where u(t) is a zero mean error term. Substituting this expression into equation (1) produces the following model of the unemployment rate:

(5) X(t) = [mu] + [gamma] SIG(t) + aPS(t) + [Beta] QS(t) + v(t),

where v(t) = e(t) + u(t).

In the cases of output and employment, we assume that the nonstationarity of the series is due to the fact that their natural rate components reflect the effects of nonstationary factors such as capital accumulation, technological change and population growth as well as stationary factors such as SIG. Since the results reported above indicate that output and employment are difference stationary series, we model their natural rate components as the sum of two process. One is an unobserved difference stationary process, denoted [X.sup.*(t)], that captures the resource and technology factors just mentioned. The other is a stationary process involving SIG. Thus for output and employment [X.sup.*] (t) is given by

(6) [Mathematical Expressions Omitted]

where [X.sup.*] (t) [equalto] [mu] + [X.sup.*] (t-1) + u(t). Equation (6) can be rewritten as

(7) [DX.sup.*] (t) [equalto] [mu] + [gamma] DSIG(t) + u(t),

where D(.) is the first-difference operator and u(t) is a zero mean error term. First-differencing equation (1) and substituting equation (7) into the resulting expression produces the following representation of output and employment:

(8) DX(t) = [mu] + [gamma] DSIG(t) + aDPS(t) + [Beta] DQS(t) + v(t),

where v(t) = De(t) + u(t).

We place no a priori restrictions on the properties of the error terms, denoted v(t), that enter equations (5) and (8), with the exception that they be zero mean stationary processes. Accordingly, our empirical methodology, described below, takes account of the possibility that v(t) is serially correlated.

Output and Energy Price Surprises. Obtaining a proxy for ex ante forecasts of the real price of energy, which is assumed to be exogenous, is complicated by our assumption that the generating process experienced a structural change between 1973 and 1974. For both the period 1948-1973 and the period 1974-1986 we assume the generating process is known to be second-order autoregressive, or AR(2). Thus, with the exception of 1974, forecasts for each sub-period are obtained as the fitted values from a regression of Q(t), the logarithm of the real price of energy at t, on a constant, Q(t-1), and Q(t-2).

In dealing with the changes that occured between 1973 and 1974, it seems reasonable to assume that by the end of 1974 economic agents recognized that the process generating energy prices had changed. Thus we incorporate a brief delay in recognition into the forecasting procedure by assuming that the forecast for 1974 is based on the pre-1974 AR(2) model. After 1974, forecasts are based on the post-1974 AR(2) model. (What we have described here is equation (13) below.) The proxy for energy price surprises is then formed by subtracting the forecast of the price of energy from the actual price of energy.(10)

Obtaining a proxy for output price surprises is complicated by the fact that the price level is endogenous. Price level forecasts are generated by taking the fitted values of a reduced form equation for the GNP deflator(11) in which the explanatory variables include lagged endogenous and lagged exogenous variables. Specifically, the logarithm of the GNP deflator is regressed on a constant, lagged values of the real activity measure and SIGMA, and lagged values of the logarithms of the money stock (M), the real price of energy, and the GNP deflator itself (P). (See equation (12) of the next subsection for more detail.) The fitted values from this equation are then subtracted from the actual value of the logarithm of the GNP deflator to obtain a proxy for output price surprises.

Examples of the output and energy price surprise series, as well as the SIGMA and SIG series, are reported in the data appendix at the end of the paper. The output price surprises and energy price surprises pass the usual rationality tests; they are zero mean, serially independent, and orthogonal to past information.

Adjustment Costs

As empirical models, equations (5) and (8) suffer from an important shortcoming in that they omit all consideration of adjustment costs. If firms find it costly to adjust input levels there will be lags in the response of real activity to price surprises. We follow numerous other researchers (including Sargent and Fair) in attempting to capture the effects of such costs parsimoniously by including a lagged value of the dependent variable among the explanatory variables.(12) Thus the model of the unemployment rate that is estimated in section IV below is given by:

[Mathematical Expression Omitted]

Similarly, the model of output and employment is of the form

[Mathematical Expression Omitted]

Estimation

In order to obtain efficient estimates and to assure correct inferences (i.e. to obtain consistent variance estimates) we estimate the equations for each of the measures of aggregate economic activity jointly with the equations which determine the proxy variables.(13) For example, for the model of unemployment given by equation (9) above we estimated the following system using nonlinear three-stage least squares.(14)

[Mathematical Expression Omitted]

Exactly the same system is estimated for output and employment except that equation (11) takes the first difference form given in equation (10).

The fitted value from equation (12) is out one-step-ahead forecast of the price level. In equation (13) DUM(t) is a dummy variable which is zero for the period 1948-1973 and is one for the period 1974-1986. The forecast of the real price of energy is the fitted value from equation (13) after substituting DUM(t-i-1) for DUM(t-i), i=0,1,2, to reflect the recognition lag discussed above. SIG(t) in equation (11) is formed by subtracting the fitted value from equation (14) from actual SIGMA (t). The final term in each equation is an error term. In equation (11), the equation of primary interest, the error term, v(t), is assumed to follow an AR(1) process when unemployment is used as the measure of real activity. When output or employment is used, v(t) is assumed to be serially independent.(15)

Jointly estimating equations (11) through (14) not only efficiently incorporates the restrictions implicit in the models for expected output and energy prices, but also the restrictions implicit in the "correction" of SIGMA for aggregate influences. Thus our estimation procedure does not suffer from the "generated regresson" problem discussed by Pagan [1984; 1986] and (under the maintained hypothesis) the statistical inference procedures used here will be appropriate.

Finally, in addition to the fully-specified models of real activity given by equation (9) for the unemployment rate and equation (10) for output and employment, several variations on these models are estimated and reported in the next section. Some of these specifications omit either energy price shocks or the proxy for industry-specific disturbances (SIG) or both from the list of variables used to explain aggregate real activity. They are intended as an aid in assessing the contribution of these factors to our results and in comparing our results to the findings of other researchers. In each case any variable that is omitted from the model is also omitted (along with any lagged values) from the rest of the equations comprising the jointly estimated system and from the list of instruments used in estimating the model (see footnote 14).

IV. ESTIMATION RESULTS

We estimated the model of aggregate economic activity developed in section III for three measures of economic activity: the civilian (sixteen years and over) unemployment rate (UN), the log value of real gross private domestic product (Y), and the log value of full-time equivalent employment in all domestic industries (EMP).(16) The results for annual data over the period 1948-1986 are reported in Tables I through III.(17) In each table we first report the outcome of estimating a fully specified model which includes energy price surprises and our proxy for the variance of industry-specific disturbances, SIG. Results reported in the next three rows illustrate the consequences of omitting first energy price shocks only, then SIG only, and finally both energy price shocks and SIG from the fully specified equation.

Our empirical findings uniformly support the model developed in this paper. Consider, for example, the results for the unemployment rate which are reported in Table I. The coefficient on output price surprises (PS) is negative and highly significant in all specifications except the one in which both energy price shocks and SIG are omitted. The improved measure of the natural rate of unemployment also performs well; the coefficient on SIG is of the correct sign (positive) and highly significant in both specifications in which it appears.(18) And finally, energy price shocks (QS) are positively and significantly correlated with the rate of unemployment in the fully specified model and is of the correct sign (although insignificant) in the specification that omits SIG.

[TABULAR DATA OMITTED]

Comparing the various specifications reported in the first four rows of Table I allows us to assess the contributions of energy price shocks and SIG, individually and jointly, to the finding that output price surprises significantly impact unemployment. It is readily apparent that the deletion of either energy price surprises or SIG reduces the size and significance of the price surprise coefficient. The effect is dramatic, however, when both are deleted; the coefficient estimate is less than a quarter of its value in the fully specified model, and it is not statistically significant. We conclude that not only are SIG and energy price shocks important in their own right in explaining unemployment variation, but their omission may lead to severe under-assessment of the importance of output price surprises in determining real activity.

The results reported in Tables II and III for output and employment are similar to those for the unemployment rate. The coefficient on output price surprises is of the "correct" sign (positive in these cases) and highly significant in all specifications. The coefficient on SIG is negative and highly significant. Energy price surprises are negatively correlated with output and employment in all specifications in which they appear, but significantly so only in the fully specified equations. The effects of

[TABULAR DATA OMITTED] omitting energy price shocks and SIG, individually and jointly, from the fully specified equation are qualitatively similar to those reported for the unemployment rate. Note, however, that price surprises remain significant even in the specification that omits both energy price shocks and SIG.

In addition to the model variations reported in the first four rows of Tables I through III, we also estimated equations which include the expected value of the price level (EP) along with price level surprises. Thus we tested the restriction, implicit in most natural rate models, that price level changes which are anticipated have no effect on aggregate real economic activity. The results of this exercise for the "fully specified" equations are reported in the final rows of Tables I through III. They reveal no systematic or statistically significant relationship between anticipated price and economic activity.(19)

The empirical results reported in this section provide considerable support for the proposition that price level surprises have a significant impact on aggregate real economic activity.(20) The distinctive features of our model - the inclusion of energy price shocks and an improved natural rate measure - are important (and in the case of the unemployment rate, critical) to this result. Thus, contrary to widely held belief, the data do not reject theoretical natural-rate models in which price surprises play an important role in transmitting aggregate demand disturbances to the real sector.

The fact that output price surprises remain positively and (except for unemployment) significant correlated with real activity even when energy price shocks and SIG are omitted from the empirical models is provocative. It raises the question of why previous researchers, particularly Fair and Mishkin, obtained the results they did. In this regard we note that the differences between our work and the work carried out by Sargent, Fair, and Mishkin go beyond our treatment of supply-side shocks and natural rates. Where both Fair and Mishkin are concerned, the differences lead us to conclude that their empirical findings do not provide very useful information on the nature of aggregate supply as captured by the relationship between output price surprises and the unemployment rate.

Fair's principle purpose was not to test the importance of price prediction errors in explaining unemployment fluctuations but rather to examine the empirical usefulness of Sargent's complete macro model. In forming a proxy for price level expectations, Fair calculates iteratively the rational expectations that follow from the restrictions implied by Sargent's complete general equilibrium model. Accordingly, his results should be interpreted as calling into question Sargent's entire model without identifying any particular component of the model (e.g., the unemployment equation) as the source of the problem. Fair's results could be as easily explained by a misspecified aggregate demand equation as by a misspecified aggregate supply equation. Thus, it may be the case that many have been too hasty in interpreting Fair's results as evidence against the role of price prediction errors hypothesized by conventional natural rate macro models - a claim Fair himself does not make.

In comparing Mishkin's work to our own another critical difference becomes immediately apparent. Mishkin, although acknowledging the assumption to be tenuous, maintains that the price level is exogenous. By contrast we (as well as Sargent and Fair) account for the endogeneity of the price level through the use of instrumental variables. Since the price level is unambiguously endogenous in the models we are concerned with, we regard Mishkin's findings on the relationship between price surprises and unemployment as suspect.

Our results support Sargent's [1976] conclusion that price level prediction errors lower unemployment. Our findings are particularly convincing since they are obtained over a sample period that subsumes those of Fair and Mishkin as well as Sargent. The major difference between our findings and Sargent's is the higher significance levels generally associated with the output price surprise coefficients in our study. This difference is partly explained by the inclusion of energy price shocks and SIG in our regressions. Two additional differences are also worthy of note: We jointly estimated the price forecast equations along with each equation explaining real activity; Sargent does not and thus his estimation procedure suffers from the generated regressor problem mentioned earlier. And, finally, we employ annual data in our study, whereas Sargent (as well as Fair and Mishkin) employ quarterly data.(21)

VI. CONCLUSIONS

In this paper we reexamine the role of price prediction errors in determining the level of real aggregate activity. Our approach to the issue is distinguished by accounting for aggregate supply-side disturbances and by a more careful treatment of natural rates. To incorporate the influence of aggregate supply shocks we include errors in predicting the real price of energy as an additional variable in the empirical models. In modelling natural rates, we construct a proxy for the variance of industry-specific (or relative) disturbances which is included in our models. We estimated the empirical models with U.S. data over the period 1948-1986 and draw the following conclusions:

Contrary to some previous studies, we find that the data are

consistent with the hypothesis that demand-driven price level surprises

are positively and significantly correlated with aggregate

real economic activity.

We also find that energy price surprises are negatively and significantly

correlated with aggregate real economic activity.

Our improved natural rate measure is strongly supported by the

data. This confirms previous results obtained by Lilien.

Estimates of equations which omit both energy price surprises

and our natural rate proxy exhibit a marked reduction in the

magnitude and statistical significance of the coefficient on output

price surprises. Thus the strength of our first conclusion depends

on a "correctly" specified equation.

Once we have accounted for price surprises, expected output prices

are of no additional help in explaining real macroeconomic fluctuations.

In summary, we find no support for the view that natural-rate equilibruim and contracting models are empirically irrelevant. Quite the contrary, our findings provide considerable support for the view that these models identify an important channel, namely price surprises, through which aggregate demand influences aggregate real activity.

DATA APPENDIX

The variables employed in our empirical analysis are as follows:

- unemployment is the civilian (16 years and over) unemployment

rate,

- output is real private gross domestic product,

- employment is full-time equivalent employment in all private domestic

industries,

- money supply is new M1,

- price of output is the GNP deflator,

- treasury bill rate is the three-month Treasury bill rate,

- price of energy is the producer price index for fuels and related

products and power,

- surplus is the nominal natural employment federal government

surplus.

Data have been taken directly from the Citibase data bank except as follows:

SIGMA = proxy for variation in sectoral employment; computed as in Lilien [1982a, 787], and described in equation (3) of the text. The twenty-nine industries used in calculating SIGMA come from the usual twenty-nine industry decomposition of aggregate employment. The industry employment data were obtained from the Citibase data bank. Minor smoothing was done to adjust for the effects of significant work stoppages. This series is not adjusted for the effects of output and energy price surprises. It is reported in Table A.

Table : TABLE A Variables Appearing in the Fully Specified Unemployment Model 1948-1986

Year UN SIGMA SIG PS QS 1948 3.75000 1949 6.05000 0.0501865 1950 5.20833 0.0339199 0.021649 0.022474 0.05940 1951 3.28333 0.0666129 0.063285 0.031403 0.02664 1952 3.02500 0.0381846 0.000617 -0.008772 0.02253 1953 2.92500 0.0410256 0.010219 0.000418 0.05053 1054 5.59167 0.0513749 0.015708 -0.007987 -0.00850 1955 4.36667 0.0190972 0.002370 0.015139 0.01331 1956 4.12500 0.0241472 -0.007312 -0.000729 0.04222 1957 4.30000 0.0278449 -0.003540 -0.000840 0.03792 1958 6.84167 0.0520462 0.012625 -0.014428 -0.05297 1959 5.45000 0.0248224 0.010345 0.018664 0.03275 1960 5.54167 0.0223044 -0.010627 -0.003420 0.02118 1961 6.69167 0.0290651 -0.009817 -0.010793 0.01203 1962 5.56667 0.0237363 0.003838 0.009802 -0.02200 1963 5.64167 0.0178781 -0.016340 -0.005676 0.00488 1964 5.15833 0.0194604 -0.011249 -0.003212 -0.03042 1965 4.50833 0.0241332 -0.002156 0.004235 0.01899 1966 3.79167 0.0353741 0.008843 0.002435 -0.01383 1967 3.84167 0.0266747 -0.009857 -0.009013 -0.00885 1968 3.55833 0.0211423 0.003197 0.009992 -0.06720 1969 3.49167 0.0212034 -0.003214 0.005175 -0.00794 1970 4.98333 0.0373705 0.007532 -0.000990 -0.00438 1971 5.95000 0.0343248 0.004290 -0.000915 0.00222 1972 5.60000 0.0200597 -0.014581 -0.009275 -0.06226 1973 4.85833 0.0222467 -0.001121 0.008982 0.04787 1974 5.64167 0.0301777 -0.000414 0.011670 0.28841 1975 8.47500 0.0607027 0.018446 -0.016344 -0.02279 1976 7.70000 0.0182731 -0.016905 -0.009585 -0.05539 1977 7.05000 0.0200290 -0.003482 0.008147 0.03343 1978 6.06667 0.0206034 0.001656 0.009099 -0.06124 1979 5.85000 0.236076 0.008852 0.023717 0.14902 1980 7.17500 0.0347484 0.002642 0.003897 0.15857 1981 7.61667 0.0258648 0.000674 0.003260 -0.02985 1982 9.70000 0.0414343 0.003826 -0.012371 0.05426 1983 9.60000 0.0341023 0.004280 0.001291 0.04453 1984 7.50833 0.0273371 0.004855 0.011108 0.07147 1985 7.20000 0.0320781 -0.008492 -0.012378 0.02037 1986 7.01667 0.0299710 -0.005706 -0.020300 -0.27448

Note: The constructed explanatory variables reported here are those associated with the fully specified unemployment model reported in row 1 of Table I. Because they are estimated as part of a system of equations, the values of PS, SIG and QS will vary somewhat from model to model and across the three real activity measures employed. SIGMA, on the other hand, will not.

money supply =new M1 (from Citibase) for 1959-1986, and old M1 (from Citibase) multiplied by .985 for 1948-1958. The splicing factor, .985, represents the average of the ratios of new M1 to old M1 for 1959 and 1960.

surplus = real natural employment surplus (from Gordon [1987]) multiplied by the GNP deflator (from Citibase).

( 1.) For example, Barro [1981, 71] states that "Given the relatively minor role played by price surprises....it appears that monetary influences on output involve channels that have yet to be isolated."

( 2.) In Gray, Kandil, and Spencer [1990] we explore differences in the cyclical behavior of the contract and non-contract sectors of the U.S. economy in an effort to identify the role played by contractual wage rigidities in the macroeconomy.

( 3.) This point has become more generally recognized in the wake of the oil price shocks of the 1970s. Fethke [1983], for example, points out that with an optimally indexed wage rate and both real and nominal aggregate demand disturbances, innovations in output will be negatively correlated with innovations in the price level.

( 4.) Exceptions include Barro [1977; 1978] who incorporates additional variables to capture the effects of military conscription and the minimum wage on the unemployment rate.

( 5.) Nelson and Plosser [1982] also find evidence of significant variation in natural rates over time.

( 6.) The potential importance of this particular supply side disturbance in explaining output, prices, and shifts in the "Phillips curve," particularly during the 1970s, has been recognized by a number of authors. These include Gordon [1975; 1982], Hamilton [1983] and Nordhaus [1980].

( 7.) Incorporating supply-side disturbances such as energy price shocks into the simpler versions of the contracting and equilibrium theories is not particularly difficult (see Mohammadi [1988]). In both classes of models the anticipated as well as the unanticipated component of energy price changes appear along with output price surprises as determinants of the level of aggregate real activity. The anticipated component of the real price of energy appears because it can affect the natural rate of real activity. The unanticipated component appears because it is a source of output price surprises that are negatively rather than positively correlated with output; its omission would cause the estimated coefficient on price surprises to be biased toward zero. Consistent with these theoretical considerations, we have estimated models of real activity that include anticipated energy price changes as well as energy price shocks. Since the anticipated component has been consistently insignificant in these exercises, it is not included in the empirical models reported in this paper.

( 8.) Here we follow Lilien [1982b] in using a twenty-nine industry decomposition of employement in forming the proxy for the variance of industry-specific disturbances. This is in contrast to the eleven industry decomposition he uses in his earlier work. See the data appendix for a description of the industry data used.

( 9.) See Lilien [1982b] for an alternative approach to purging SIGMA of the influence of aggregate disturbances.

(10.) Since we are modelling expectations, the occurrence of a structural break in the generating process for Q(t) requires us to address the issue of how economic agents learn the new generating process. In the absence of a formal model of learning we employed several alternative ad hoc specifications for energy price expectations to check the robustness of our results. These include a specification which models the generating process as a stable AR(2) over the entire sample period without accounting for any structural change and another which admits a structural break, basing expectations on an AR(2) model through 1974 and a random walk after 1974. In each of the cases we examined, our central results are essentially unchanged.

(11.) We chose the broadest available measure of output price for our empirical exercises since our objective is to capture unanticipated price movements due to aggregate demand disturbances. Movements in narrower price measures are more likely to be contaminated by relative disturbances.

(12.) Given the number of explanatory variables in many of our equations, we do not have the degrees of freedom necessary to estimate all of the equations with unrestricted distributed lags. Consequently we chose to adopt the more restrictive approach of including a lagged dependent variable in our models of real activity. This choice presumes that the distributed lag response of real activity to each of its determinants declines (approximately) at the same geometric rate over time.

(13.) The important econometric issues which arise from the presence of estimated proxies, or generated regressors, in empirical models are thoroughly discussed by Pagan [1984; 1986].

(14.) In estimating the system given by equations (11) through (14) we assumed that the price level is the only endogenous variable appearing on the right-hand-side of the unemployment equation. SIG and the price of energy are assumed to be exogenous. These choices were based on the results of Engle's [1982] Lagrange-multiplier version of the test developed by Spencer and Berk [1981]. We were unable to reject the hypothesis that SIG and energy price surprises are exogenous at any reasonable level of significance. The set of instruments used in estimating equation (11) contains a constant and a linear time trend; three lags each of the dependent variable, SIGMA, the GNP deflator, and the three-month Treasury bill rate; the current as well as the first three lagged values of the money supply, the nominal natural employment federal government surplus, and the real price of energy. In specification which do not include SIG, the lagged values of SIGMA are dropped from the instrument list. Similarly, in specifications which do not include energy price shocks, the current and lagged values of the real price of energy are dropped from the instrument list. In order to examine the sensitivity of our results to instrument choice, we estimated our models under several alternative sets of instrumental variables. Each of these alternatives yielded results which are quite similar to those reported here.

(15.) Using the Lagrange multiplier test that follows from Theorem 2 in Engle [1982] (appropriate for simultaneous equations), we found evidence of AR(1) errors in some of our enemployment specifications. No evidence of higher order AR processes was found. We thus chose to estimate all our enemployment models under the assumption that the errors follow an AR(1) process. If the finding of serial correlation is a reflection of potential specification error, then the reliability of the empirical results for unemployment models may be subject to question. However, the consistency of these results with those found for output and employment models (in which we find no evidence of serial correlation) leads us to conclude that the results are reliable.

(16.) These measures of output and employment are used because they correspond more closely to their theoretical counterparts than more inclusive measures. We have also estimated models for several more inclusive output and employment measures (e.g., real gross national product, real gross domestic

product, and total employment) and obtain results which are quite similar to those reported here.

(17.) We have experimented with quarterly data as well. While our results are qualitatively similar to those reported here, they are not nearly so strong. We are in the process of exploring the possiblity that the weakness of the quarterly results is a consequence of inappropriate temporal disaggregation. For example, in a contracting model that incorporates adjustment costs, we expect employment to exhibit a greater response to thoseaggregate price level shocks that are perceived to be permanent than to those that are perceived to be transitory. Our empirical results, however, are obtained without decomposing price surprises into perceived permanent and temporary components. Since it is likely that observed quarterly data will contain a larger transitory component than annual data, we would expect weaker results using the quarterly data.

(18.) Our results concerning SIG provide an interesting counterpoint to those of Loungani (1986), who finds that after correction for oil price changes, Lilien's sectoral shift variable (SIGMA) is not significant. There are a number of possible reasons for the difference between our results and Loungani's: We "correct" for the influence of oil price shocks on SIGMA in a different way than Loungani does. While Loungani regresses his individual industry employment series on energy prices before constructing his SIGMA measure, we regress the equivalent of Lilien's SIGMA on energy price shocks (as well as price level shocks) after it is constructed from the original employment series. (We have also tried purging SIGMA of the squared values of these shocks and found, like others, that it makes little difference.) While both methods are intuitively appealing, we can't be sure they produce the same result. A second difference is that Loungani uses quarterly data whereas we use annual data. And another is that the real activity model in which Loungani imbeds his SIGMA measure is quite a bit different from the one in which we imbed ours.

(19.) It is interesting to note that the result is the same when EP is added to each of the other (misspecified) equations reported in Tables I-III.

(20.) In models of the type under investigation here, numerous decisions must be made in order to obtain empirical results. It is thus important to have some idea as to the robustness of our principal results to reasonable alternative decisions. In the course of the study of which this paper is a part we have estimated models associated with many alternative specification and estimation decisions. We have employed alternative instruments (see footnote 14), alternative forecasting models for Q(t) (see footnote 10), alternative forecasting models for P(t) (i.e., different information sets), alternative methods of detrending, alternative assuptions regarding SIGMA (t), and alternative assuptions regarding the distribution of the errors as well as using both two-step and joint estimation procedures. In this wide range of empirical models, each of which is consistent with the theory, the conclusions regarding the role of output price prediction errors and SIG(t) (or SIGMA (t) are quite robust. Each of these virtually always exhibits the expected sign and is almost always stongly significant. On the other hand, energy prices surprises are occasionally insignificant (although rarely in fully specified models).

(21.) See footnote 17.

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JO ANNA GRAY and DAVID E. SPENCER(*)

(*) Washington State University and Brigham Young University. We are grateful to the National Science Foundation (grant SES-8608885) for research support; to the participants of the October 1985 NBER Economic Fluctuations Research Meeting, particularly Steve Cecchetti, Robert Gordon, Robert Hall, Frederic Mishkin, Knut Mork, and William Nordhaus, for their comments on an earlier version of this paper; to Steve Davis, Stan Fishcer, Bob Flood, Robert Shiller, Jeff Wrase, and Doug Young for their helpful suggestions; to John Anderson, Jonghwa Cho, Chan Chee Pang and Mark Thoma for computational assistance in the early stages of this project; and to Magda Kandil for her excellent research assistance in the later stages of the project. Finally, we thank Richard Sweeney, Danny Quah, Jeffrey Woolridge, and an anonymous referee for their help on the final draft of the paper. All data employed in this paper can be obtained from readily available public sources; see our data appendix.

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Publication: | Economic Inquiry |

Date: | Oct 1, 1990 |

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