Does contractual wage rigidity play a role in determining real activity?

I. Introduction

Interest in nominal wage ridigity as a source of macroeconomic fluctuations has waxed and waned over the past half-century. The most recent wave of interest was triggered by the rational expectations revolution of the 1970s, which inspired an improved sticky-wage paradigm. The paradigm posits the existence of short-term contractual arrangements that, in their simplest form, fix wage schedules in nominal terms for a predetermined period (the life of the contract) and leave employment at the discretion of the firm. The most influential examples of the paradigm incorporate rational expectations and satisfy the natural-rate hypothesis [9; 14], thus meeting the new minimum standards for demand-driven theories of the business cycle.

Nominal wage contracting models have been vigorously criticized for both a lack of theoretical rigor and an absence of empirical support. Despite their critics, however, the models have remained a popular analytical tool and, after almost a decade of inattention, economists are showing a renewed interest in empirical tests of nominal contracting models.(1) The studies produced to date are small in number and offer conflicting conclusions. They are, perhaps, as important for the objections they provoke as for the answers they provide.(2) While the work reported in this paper also has its limitations, we believe the perspective we offer is sufficiently fresh, and our results sufficiently interesting, to make the paper an important contribution to the empirical contracting literature.

The approach we pursue is distinctive in that it uses to its advantage the observation that contractual wage arrangements are not equally pervasive across the various sectors of the U.S. economy. Indeed, if the ratio of union membership to sector employment is used as an index of the importance of contractual wage arrangements,(3) the private U.S. economy can be readily divided into contract an non-contract sectors of roughly equal size. The contract sector includes manufacturing, mining utilities, construction, transportation, and communications, with unionization ratios ranging from .44 to .92. The non-contract sector includes wholesale trade, retail trade, finance, insurance, real estate, agriculture, forestry, and fisheries, with ratios from .01 to .14.

As demonstrated in Duca [18] and Gray, Kandil and Spencer [16], output in both the contract and non-contract sectors of an economy will rise in response to a positive aggregate demand shock and the price level movement it causes. But the impact on the contract sector will be unambiguously larger than the impact on the non-contract sector. These predictions are testable and, indeed, we find in our first set of empirical exercises that they are supported by the data. We recognize, however, that there are other possible explanations for our empirical findings than the contracting explanation. In the final section of the paper we offer some additional empirical evidence and a preliminary assessment of the relative merits of these alternatives.

II. Theoretical Considerations and Empirical Strategy

Our empirical work tests the implications of the simple two-sector contracting model developed in Duca [8] and Gray, Kandil and Spencer [16].(4) In discussing the model, we refer to the sector in which nominal wages are contractually fixed as the contract sector and to the sector in which wages move freely to clear labor markets as the non-contract sector. Two predictions provide the focus for our work. First, wage rigidity in the contracting sector is responsible for a non-neutral response to aggregate demand shocks in both sectors. Second, the response of the contract sector to aggregate demand shocks necessarily exceeds the response of the non-contract sector.

The intuition underlying these predictions is straightforward. A positive disturbance to aggregate demand raises demand for the output of both sectors. In the absence of wage rigidities and imperfect information this would result in equiproportionate changes in the prices of both outputs and no change in quantities or relative prices. However, the presence of a contractually fixed nominal wage in the contract sector leads to a very different result.

An unanticipated increase in aggregate demand does raise the prices of both outputs. In the contract sector the price rise lowers the real product wage faced by firms, causing it to fall below its market clearing value. The fall in the real wage, in turn, causes output and employment in the contract sector to rise above their natural (full equilibrium) levels, producing an excess supply of the sector's output at pre-existing relative prices. To restore equilibrium, the price of contract sector output must fall relative to the price of non-contract sector output. Equivalently, the relative price of non-contract output must rise.

The rise in the relative price of non-contract output will, in general, lead to an increase in production in the non-contract sector. The increase is due to the fact that the price received by a non-contract firm rises relative to the price that its workers pay for the basket of goods they consume (a mix of contract and non-contract output). Under these circumstances, the firm will attempt to hire more workers, bidding up the nominal wage. Equilibrium will be reached at a nominal wage that provides increased purchasing power to workers. And, unless the supply of labor is completely inelastic with respect to the real wage, employment and output in the non-contract sector will be higher.

We see, then, that although nominal wage rigidity is confined to the contract sector, its effects are felt in both sectors; a positive aggregate demand disturbance will (unless non-contract labor is completely inelastic) cause output in both sectors to rise. The additional implication that the response of the contract sector must exceed the response of the non-contract sector follows from the fact that the relative price of non-contract output must rise to induce the increase in non-contract production. For this to occur it must be true that non-contract production rises proportionately more than non-contract production.

Finally, the relative price and quantity effects produced by aggregate demand shocks are transitory. Wage contracts are finite in duration, seldom exceeding three years in the United States. As contract wages are renegotiated each sector will adjust back toward its original equilibrium. If no further shocks occur the economy will eventually return to the levels of production and relative prices that existed prior to the aggregate demand shock. The only permanent change will be in the level of nominal prices, which will mirror the permanence of the shift in aggregate demand. The model is, then, a natural-rate model; unanticipated movements in aggregate demand cause temporary deviations of output from a natural or full-employment rate, but fully anticipated movements in aggregate demand have no real effects.

The simple two-sector natural-rate model discussed above suggests aggregate and sectoral supply functions of the following general form: Model I (1) Y(t) = Y*(t) + [Y.sub.c] (t), where [Y.sub.c](t) = [Alpha] PS (t) + e(t).

Here Y(t) represents the level of real activity at time t, Y*(t) is its natural rate, and [Y.sub.c](t) its "cyclical" component. Our study employs two different measures of real activity, an output measure and an employment measure. The explanatory variable PS(t) is the error made in forecasting the price level ad e(t) is a zero mean disturbance.

At this level of generality, PS(t) may be regarded as a vector of price prediction errors. The elements of the vector reflect certain institutional features of the U.S. economy: contract negotiation dates are staggered rather than synchronized, and contracts vary in duration, most ranging from one to three years in length. In this situation, the price surprise vector may contain as many as T elements where T is the length of the longest contract in the economy. The individual elements will be price forecast errors made over horizons ranging from one through T periods. In fact, however, we find that with annual data(5) price prediction errors over horizons of two years or greater are generally unimportant in our empirical models. Accordingly, PS(t) is defined as follows throughout the remainder of the paper: PS(t) = P(t) - [E.sub.t - l] P(t), where P(t) denotes the logarithm of the price level at time t and [E.sub.t -l] P(t) the expectation of P(t) conditioned on information available at time t - 1.

The hypotheses to be tested involve the price surprise coefficient, [Alpha], which appears in equation (1). The contracting model predicts a strictly positive [Alpha] when measures of aggregate real activity or real activity in the contract sector are employed, and a non-negative [Alpha] for the non-contract sector. In addition, the contracting model implies that the value of [Alpha] for the contract sector of the economy will be larger than the value for the non-contract sector.

Equation (1) is a direct implication of the theoretical model discussed earlier in the section. This is a highly simplified framework in which unanticipated movements in aggregate demand are the only aggregate source of uncertainty in the economy; supply-side disturbances are omitted from the models. This omission is potentially troublesome where our empirical model is concerned since it can cause the estimate of the price surprise coefficient, [Alpha] to be biased toward negative values. The problem arises because shifts in the aggregate supply curve, given a fixed aggregate demand curve, produce a negative correlation between the price level and our measures of real activity. If the sources of the shifts are omitted from our empirical model, as they are in equation (1), this negative correlation is captured in [Alpha].

A solution to the problem would be to include measures of significant aggregate supply disturbances in our empirical models. This solution is not practical since many potential important sources of aggregate supply shifts are difficult to identify and measure empirically. We have, however, pursued the following alternative. We have incorporated an important (and measurable) source of aggregate supply shifts, the real price of energy, into our empirical model. The results of the experiment confirm our expectation that the bias produced by omitting this variable from our model is in the expected direction. The estimated value of [Alpha] is higher when energy price shocks are included in the model than when they are excluded.(6) This being the case, we can be reasonably confident that the bias present in our results does not invalidate the conclusions we draw since we find a positive and significant relationship between price surprises and output. The inclusion of supply-side disturbances in the price surprise model reported in this paper would only increase the estimated value of [Alpha] and strengthen our conclusions.

Another solution to the problem is to avoid it entirely by replacing the price surprises in equation (1) with aggregate demand shocks, producing a model of the form: Model II (2) Y(t) = Y* (t) + [Y.sub.c] (t), where [Y.sub.c] (t) = [Alpha] NS(t) + e(t). Here NS(t) represents the one-step-ahead error made in forecasting N(t), the level of aggregate demand at time t. That is, NS(t) is equal to N(t) - [E.sub.t-l] N(t). As before the hypotheses to be tested involve the coefficient on the aggregate demand shock, [Alpha], and are identical to those discussed above for the case of price surprises.

The omission of supply-side disturbances from equation (2) does not result in biased estimates of [Alpha] provided the empirical measure of aggregate demand that is employed is uncorrelated with aggregate supply disturbances. The most popular empirical proxies for aggregate demand are the nominal money stock and nominal GNP. While these measures are often assumed to be exogenous, there is no compelling reason to believe a priori that they are completely free of the affects of aggregate supply disturbances. In contrast to the case of price surprises, however, there is no presumption as to the direction of bias that may be present in our estimates of [Alpha] due to the omission of supply-side disturbances. We have explored the problem empirically by estimating an augmented version of equation (2) that incorporates energy price shocks. We find that the exclusion of energy prices from the model makes much less difference than in the case of our price surprise model. In addition, there is no systematic pattern to the effect on [Alpha]; [Alpha] sometimes rises and sometimes falls when energy price shocks are introduced into the model. In all cases the estimate of [Alpha] remains positive and impressively significant.(7)

III. Estimation and Results

Estimation of empirical models based on equations (1) and (2) involves a number of decisions, one of which is how to deal with the nonstationarity of our output and employment series. The traditional response to the presence of non-stationarity in economic time series is to assume a linear time trend. However, in an influential paper, Nelson and Plosser [23] report strong evidence that aggregate real activity is more appropriately modelled as a difference stationary process than as a trend stationary process. We have repeated the tests employed by Nelson and Plosser in the context of our output and employment models and confirm their findings. Accordingly, we estimate our models in first-difference form. This choice has important implications for the specification of the natural rate of real activity, the problem to which we turn next.

It is fairly common to model natural rates as simple functions of time and lagged measures of real activity. We employ a more sophisticated natural rate model which can be viewed as the sum of a measured and an unmeasured component: (3) [Mathematical Expression Omitted] where [Mathematical Expression Omitted]

The term [Mathematical Expression Omitted] (t) represents the unmeasured component of the natural rate of real activity. It captures the effects of factors such as population growth, capital accumulation, and technological change. It is presumed to be the source of the nonstationarity in our real activity series and, accordingly, is modelled as a difference stationary process with drift. The terms [Mu] and u(t) in equation (3) are a constant and a covariance stationary disturbance.

The measured component of the natural rate is a linear function of the stationary variable SIG(t). This specification is motivated by David Lilien's [19; 20] finding that sector specific shocks play an important role in explaining the natural rate of unemployment. Following the procedure used in Gray and Spencer [17], SIG is computed in two steps. First, using the usual 29 industry decomposition, we calculate Lilien's SIGMA, the standard deviation of employment changes across industries. The second step is intended to overcome the possibility that Lilien's measure reflects the differential industry effects of aggregate disturbances and not just the influence of sectoral disturbances. To eliminate this problem, we regress SIGMA on a constant and any aggregate surprise terms (PS or NS) that enter a particular model. The residual from this regression, denoted SIG, is then used as our proxy for the variance of industry-specific disturbances in that specification.

Substituting equation (3) into equations (1) and (2) and taking first-differences and accounting for the possibility of significant adjustment costs through the inclusion of a lagged dependent variable produces. Model 1: DY(t) = [Mu] + [Lambda] DY (t - 1) + [Gamma] DSIG(t) + [Alpha] DPS(t) + v(t). Model II: DY(t) = [Mu] + [Lambda] DY (t - 1) + [Gamma] DSIG(t) + [Alpha] DNS(t) + v(t). The error term v(t) is equal to u(t) + De(t) for both models and D is the first difference operator.

Since the surprise terms entering both models are unobservable, empirical proxies must be constructed before estimation can take place. Thus, our empirical models include equations describing the processes generating the price level and the level of aggregate demand. The predicted values generated by these regressions become our proxies for the expectations that enter our models through PS (t) and NS(t). Price level forecasts are generated by taking the fitted values of a reduced form equation for the GNP deflator in which the explanatory variables include lagged variables. For Model I, the explanatory variables include a constant, one lagged value of SIGMA, and two lags each of the logarithms of GNP, the GNP deflator, and the money stock. The fitted values from their equation are subtracted from the actual values of the logarithm of the GNP deflator to obtain our price level surprises. The procedure used to form our proxy for aggregate demand surprises (also endogenous) is exactly analogous.

Finally, in order to obtain estimates and to assure correct inferences (i.e. to obtain consistent variance estimates), we estimate each model of output and employment determination jointly with the equations that determine our proxy variables. In the case of Model I, for example, the equation determining the expected value of the price level and the equation determining SIG are jointly estimated with the equation explaining real activity. In order to account for the endogeneity of the price level, nominal GNP, and SIG, instrumental variables are used.(8)

Tables I and II contain the results of estimating the two models of real activity developed above using annual data for the period 1948-1986. Each model is estimated for total private U.S. output and total hours worked in private U.S. industries, as well as for several disaggregated output and hours series representing relevant decompositions of the private U.S. economy. Table I reports estimates of Model I and Table II reports of Model II.

We begin, in the first three rows of Table I, by reporting the outcome of estimating Model I for total private U.S. output, contract sector output, and non-contract sector output under the sector definitions given in Section I above. The results are conclusive; we cannot reject this model of output determination. The response of output to price level surprises is positive and highly significant for all three output measures. In addition, the price surprise coefficient for the contract sector of the U.S. economy is more than three times the size of the price surprise coefficient for the non-contract sector. This difference is (easily) significant at the one percent level.(9) We note that our proxy for sector-specific disturbances, SIG, also enters with the expected sign (negative) and is very significant.(10)

As the findings recorded in the bottom half of Table I confirm, the results obtained when employment is used as our measure of real activity are equally impressive. We again conclude that the data fail to reject the implications of the contracting model. (The results reported in Table I and II for manufacturing, for wholesale and retail trade, and for the other non-contract industries are discussed later in the section.)

In Table II we report the results of estimating Model II for our output and employment measures. Here again, we find strong evidence that the restrictions implied by the contracting model are satisfied. The responses of both output and employment to unanticipated movements in nominal GNP (our proxy for aggregate demand shocks) are positive and highly significant for the private U.S. economy as a whole, for the contract sector of the economy, and for the non-contract sector of the economy. In addition, the size of this response for the contract sector is more than three times the size of the response for the non-contract sector--a difference that is, once again, highly significant.

In addition to the findings already discussed, Tables I and II present the results of a second set of exercises that provide further information on the role of contractual wage rigidities in determining the cyclical behavior of real activity. These exercises are motivated by the following observations: First, the contract sector of the U.S. economy is dominated by manufacturing, which accounts for about two-thirds of total output and employment in this sector. Second, the non-contract sector of the U.S. economy can be divided into industries which are primarily involved in distributing the output of the manufacturing sector (wholesale and retail trade) and those which are not.

The complementarity between the output of the manufacturing sector and the outputs of the wholesale and retail trade sectors suggests that there may be systematic differences in behavior between the wholesale and retail trade and the remainder of the non-contract sector. In particular, we might expect the influence of aggregate demand disturbances on wholesale and retail trade to be stronger than on the remainder of the non-contract sector (the "other non-contract sector"). As the tables show, the data are consistent with this view. We conclude that the responsiveness of real activity to price level surprises is strongly associated with the presence (both direct and indirect) of explicit nominal wage contracts.

Finally, we note that the results and conclusions reported in this section are robust with respect to a number of reasonable changes in the specification of our empirical models. We have explored the consequences of (i) dropping SIG from our empirical models, (ii) fitting alternative forecasting models for the price level and nominal GNP, (iii) employing alternative methods of dealing with the nonstationarity of our output and employment series, (iv) using alternative sets of instruments, (v) employing alternative measures of real activity, and (vi) using a two-step rather than a joint estimation procedure. In this wide range of empirical models, our conclusions are uniformly supported. Price surprises and nominal GNP shocks are positively and significantly correlated with U.S. real activity, and the correlation is markedly stronger for the contract sector of the U.S. economy and for those industries with strong ties to the contract sector.

IV. Competing Explanations and Additional Evidence

While the consistency of the data with the predictions of contracting theory is impressive, one might argue that the results discussed above are, in principle, also consistent with the predictions of equilibrium business cycle theories of the sort pioneered by Lucas [21; 22]. Like the contracting model under consideration here, equilibrium models also predict the possibility of positive correlation between aggregate demand disturbances and real activity. The latter models do not, however, produce the much stronger restriction implied by contracting models; that the response of real activity to aggregate demand shocks will be strictly larger in the contracting sectors of an economy than in the noncontracting sectors.(11)

In the context of an equilibrium model, the larger response of contract sector output to aggregate demand and price shocks could be explained by a larger elasticity of labor supply with respect to the real wage in that sector, or by a larger elasticity of output with respect to labor employed. The findings summarized in Tables I and II above provide some evidence on the second of these elasticities. Consider, for example, the estimates reported in Table I. Dividing the response of contract sector output to a price surprise by the response of contract sector employment to a price surprise provides us with an estimate of the elasticity of output with respect to labor employed of approximately .8. Performing the same exercise for the non-contract sector yields an elasticity of about 1.0. This suggests that the elasticity of output with respect to labor is lower in the contract sector of the economy than in the non-contract sector, not higher. The estimates [Tabular Data I and II Omitted] reported in Table II produce the same conclusion. Thus, in the absence of evidence suggesting that workers in the contract sector have substantially more elastic labor supply schedules than workers in the non-contract sector, our results cast doubt on the explanatory ability of equilibrium models.

There are, of course, other competing explanations for the findings reported in section III of this paper. It can argued, for example, that recently developed real business cycle theories are compatible with the observed positive correlation between nominal GNP (our proxy for aggregate demand) and real activity reported in Table II. Real business cycle theories rely on shifts in tastes and technology to explain fluctuations in real activity. (See Prescott [24] for a discussion of this class of models.) They can explain a positive correlation between output and nominal GNP if nominal GNP is endogenous and responds positively to increases in output. Since nominal GNP is the product of the money supply and velocity, both of which are commonly regarded as (in part, at least) endogenous and positively related to changes in output, this condition may well be met.

The positive correlation between price surprises and real activity reported in Table I cannot, however, be so easily explained by real business cycle theories. An increase in output caused, for example, by improved productivity may be expected to cause the price level to fall and thus to produce a negative correlation between price and output innovations. This will be true even if money and/or velocity are endogenous and positively related to output movements. Intuitively, an outward shift of the aggregate supply curve along a conventional, negatively sloped demand curve must cause the price level to drop. Allowing the money stock and velocity to respond to output movements will not change this basic outcome, provided it does not result in an aggregate demand curve that is positively sloped and flatter than the aggregate supply curve--a condition that produces instability in most macroeconomic models.(12) We conclude that our empirical findings are inconsistent with real theories of the business cycle.

Another competing explanation for our findings turns on differences in the cyclical behavior of durable and non-durable goods. Because of the investment aspects of durable goods, cyclical movements in the production of these goods is much more pronounced than for non-durable goods. Furthermore, the share of durable goods in the contract sector of the U.S. economy is substantially higher than in the non-contract sector. It follows that the greater response of contract-sector output to aggregate demand shocks (and price surprises) could be due to the nature of the goods produced by that sector rather than to the presence of nominal wage contracts. A thorough evaluation of this argument is beyond the scope of this paper. We do, however, offer some preliminary evidence for the reader's consideration.

Table III reports the results of estimating our empirical models after dividing the manufacturing sector into those industries producing durable goods and those industries producing non-durable goods. The table contains estimates of Models I and II for both the durable and non-durable manufacturing sectors. For purposes of comparison, the estimates of the non-contract sector reported in Tables I and II also appear in Table III. The results indicate a larger response of durables than non-durables to price surprises and nominal GNP shocks. But, they also show that the response of the non-durable manufacturing sector to shocks is larger than the response of the non-contracting sector. This difference is uniformly statistically significant at the one percent level across models and real activity measures (see footnote 10). We concluded that the results presented in the preceding section cannot be entirely explained by the fact that contract sector output is more heavily concentrated in durable goods than non-contract sector output. [Tabular Data III Omitted]

Additional evidence is presented in Tables IV and V where we report the results of estimating comparable versions of our empirical models using both pre-war (1899-1929) and post-war (1948-1986) U.S. data. Given the data limitations of the pre-war period, some adjustments to the empirical methodology employed in earlier sections of the paper were necessary. The SIGMA constructed for this additional exercise is based on an 11-sector breakdown of GNP rather than the 29-sector breakdown described in section III. For a small number of our real activity measures, we find evidence of first-order autoregressive errors in our price surprise models (for the pre-war period). Accordingly, to maintain comparability across models and real activity measures, it is assumed in all cases that the errors follow an AR(1) process with autoregressive parameter RHO.

Due to the ongoing debate over the adequacy of the various available measures of pre-war GNP, we report results using both Romer's [25] and Balke and Gordon's [2] recent estimates of pre-war GNP. Our results for the post-war period are reported in the top half of each table and the results for the pre-war period in the bottom half. Comparing the two halves of each table reveals a pronounced pattern. The responses of output and employment to price surprises and to nominal GNP shocks is systematically (and in most cases dramatically) higher in the post-war period than in the pre-war period. Thus it appears that the aggregate supply curve of the post-war period is much flatter than the supply curve of the pre-war period. This difference may be plausibly explained by the presence of greater wage and price inflexibility in the post-war period due to the increased importance of contractual wage arrangements in that period.(13) Thus, our empirical findings support the contracting explanation for the observed differences in the cyclical behavior of U.S. real activity, both across sectors and across time.

The results reported in Tables IV and V may not, however, be so easily explained by differences over time in the shares of durable and non-durable goods in total output. Using data compiled by Nathan Balke and Robert Gordon (see Appendix B or [12]), we are able to calculate the average ratio of durable goods production(14) to total GNP for the periods 1919--1929 and 1951--1983. While these years represent only a subset of the two sample periods over which we have estimated our models, the results of this exercise are reassuring. The share of durable goods production averages 22 percent over the years 1951-1983 and 23 percent over the years 1919--1929. Clearly these figures do not support an explanation of our results that relies on durable goods production absorbing a substantially higher share of output in the post-war period than in the pre-war period.

The final competing explanation we consider is an alternative story about price rigidity. Recent theoretical efforts have generated a class of sticky-price models in which output prices fail to respond to fluctuations in demand due to the combined presence of small costs of price adjustment and monopolistic competition in output markets. (See Blanchard and Kiyotaki [5] for an informative discussion of these models.) Despite the fact that price changes are assumed to involve only a relatively trivial resource cost, these models can produce large and costly fluctuations in output in response to fluctuations in aggregate demand. Since it may be plausibly argued that the contract sector of the U.S. economy is less competitive than the non-contract sector, this class of models would appear to supply an alternative "new Keynesian" explanation for the results presented in Tables I and II of this paper.

In evaluating this last argument, we once again appeal to the pre-war/post-war comparisons contained in Tables IV and V. If the degree of competition is the key to explaining differences in the response of output to aggregate demand shocks, then the greater responsiveness of output in the post-war period suggests that behavior has been less competitive in the later period. To the contrary, however, the available evidence suggests that, if anything, the post-war economy may be somewhat more competitive than the pre-war economy.(15) [Tabular Data IV and V Omitted]

We conclude that both the results reported in the preceding section and the comparisons reported in this section are consistent with natural-rate models. We have examined some competing explanations for our findings and further conclude that, given our present state of knowledge, there is no compelling reason to prefer any of these alternatives to the contracting explanation.

Data Appendix

I. Post-War Data

The Following Series Were Taken from the Citibase Databank All output series GNP deflator

Treasury bill rate ( month)

Real federal government expenditures Real price of energy: the producer price index for fuels and related products and power deflated by the GNP deflator Money stock: 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 1959 and 1960.

Hours Series

For 1948 through 1982, the data on hours worked were taken from Table 6.11 of The National Income and Product Accounts of the United States, 1929--82, Statistical Tables, U.S. Department of

Commerce, Washington D.C., 1986. For 198 through 1986, the data were taken from the Table 6.11 of the Survey of Current Business, U.S. Department of Commerce, Washington D.C., July 1987. In all cases, hours data are hours worked by full-time and part-time employees.

II. Pre-War Data

The Following Series Were Taken from Balke and Gordon [2] Gross national product (Balke/Gordon) GNP deflator

The Following Series Was Taken from Romer [25] Gross national product (Romer) The Following Series Were Taken from Long Term Economic Growth, 1860--1970, U.S. Department of Commerce, Washington, D.C., 197 All hours series Government spending Private domestic output

The Following Series Were Taken from Friedman and Schwartz [10] Money stock Short-term interest rate SIGMA: constructed as in Lilien [19] using employment data on the eleven industries decomposition. Industry employment data were obtained from Historical Statistics of the United States, Colonial Times to 1970, U.S. Department of Commerce, Washington D.C. (1)Examples of studies that directly address the assumptions and implications of contracting models include Ahmed [1], Bils [4], Card [7], and Gray and Spencer [17]. In addition, recent work by Ball, Mankiw, and Romer [3] tests implications of the "new" Keynesian models that are shared by contracting models, and so provide evidence bearing on both classes of models. Finally, Blinder and Choi [6] report evidence of wage stickiness from a recen interview survey of wage-setters in small number of firms. (2)A more detailed suvey of the literature in our working paper [16] which is available upon request. (3)Union membership included retired and unemployed workers as well as members located in foreign countries. Consequently, the ratio of union membership to sector employment is an overstatement of the fraction of workers in each sector covered by explicit wage agreements. We have investigated alternative ways of assessing the importance of union wage contracts across sectors and arrive at the same designation of sectors as contract and non-contract. The critical underlying assumption in using any of these measures for the purpose at hand is the assumption that the prevalence of union contracts provides a reasonable index of the importance of implicit as well as explicit wage agreements across sectors. (4)The model we develop in our working paper [16] represents a slight generalization of Duca's [8] model since it does not assume identical structural parameters in the contract and non-contract sectors and includes sectoral shocks as well as aggregate shocks. (5)The disaggregated data we use are only available annually. (6)A complete description of this additional emperical exercise is contained in Gray, Kandil and Spencer [16]. For further discussion of the pitfalls of omitting supply-side disturbances from price surprise models, see Gray and Spencer [17]. (7)We have also explored augmented versions of both Model I and Model II that incorporate the anticipate component at the real price of energy as well as the unanticipated component. Again, our conclusions are unaffected. (8)For Model I the instrument list includes time, three lags each of the dependent variable, SIGMA, the GNP deflator, and the 3-month Treasury bill rate; and the current as well as the first three lagged values of the money supply (new M1) and federal government spending. The instrument for Model II are the same except that nominal GNP replaces the GNP deflator. (9)We tested the null hypothesis that the response of output to price surprises is the same in the contract and non-contract sectors using the following procedure. Unrestricted equations for both sectors are estimated jointly. The system is then reestimated under the restriction that the price surprise coefficients for the two sectors are equal. We then employ the test suggested by Gallant and Jorgenson [11] to determine if the restriction is rejected . In the case of Model I for output, the relevant chi-square statistic is 10.96 which greatly exceeds the one percent critical value (6.63) for a chi-square distribution with one degree of freedom. Thus, the restriction is strongly rejected in this case. The restriction is even more strongly rejected for the other casess subsequenly discussed in this section. (10)As with the price surprise coefficient, the coefficient on SIG is larger for the contract sector than for the non-contract sector. It can be argued that this result is consistent with the contract model. In our contracting mode, the response of output to relative demand shocks is larger for the contract sector of the economy than for the non-contract sector, just as in the case of aggregate demad shocks. Accordingly, an increase in the variance of industry specific disturbances will cause more frictional unemployment, and result in lower output, in the contract sector. (11)We investigate the relevant implications of equilibrium theory in a two-sector economy in our working paper [16]. Similar results are obtained by Lapp [18] in the context of a multi-sector Lucas-type equilibriumm model. (12)Velocity is, of course, endogenous along any aggregate demand curve produced by a conventional IS-LM model in which money demand is interest elastic. Endogencity of the money stock is a feature of some models and not others. Regardless, the assumption that the aggregate demand curve is downward sloping is typically preserved. We do note that the aggregate supply curve implied by real business cycle theories is vertical since these models typically fail to include any channel through which the price level might affect real outcomes. Thus, stability in these models requires only that the aggregate demand curve be negatively sloped. (13)One stylized fact that the has emerged from recent pre-war/post-war studies of U.S. macroeconomic performance is that wages and prices have been less flexible in the post-war period; see Taylor [28]. Contracting theory can explain this phenomenon, the flatter aggregate supply curve it has produced, and the simultaneous increase in output stability observed in the post-war period. See Gray and Kandil [15]. (14)Our measure of durable goods production is the sum of producer's durable equipment, nonresidential structures, consumer durables, and residential structures. These are the categories (and, indeed, the same data) used by Gordon and Veitch [13] in their historical study of fixed investment in the American business cycle. (15)These studies rely on structural factors such as market shares, concentration ratios, entry barriers, and regulatory environment. To our knowledge, there exist no comparison of pre-war/post war competitiveness based on pricing behavior. Using a variety of structural indicators, Shepherd [27] argues that the U.S. economy became more, not less, competitive between 1939 and 1980. Over the longer time span we are concerned with. Scherer [26, 68] documents a slight decline in concentration ratios for the manufacturing sector. He also offers the following conclusion [26, 70], taken from an earlier study of concentration ratios by Adelman: "Any tendency either way, if it exists, must be at the pace of a glacial drift."

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