Unexpected Inflation, Real Wages, and Employment Determination in Union Contracts

David Card

The American Economic Review, Vol. 80, No. 4. (Sep., 1990), pp. 669-688.

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http://www.jstor.org Mon Jul 2 13:58:03 2007 Unexpected Inflation, Real Wages, and Employment Determination in Union Contracts

This paper examines the effect of nominal contracting provisions on employment determination in union contracts. In most contracts the nominal wage" rate is wholly or partially predetermined. Real wage rates therefore contain unanticipated components that reflect unexpected price changes and the degree of indexation. The empirical analysis, based on a large sample of indexed and nonindexed contracis, suggests that unexpected real wage changes are associated with systematic employment responses in the opposite direction. I conclude that nominal contracting provisions play a potentially important role in the cyclical properties and persistence of employment movements in the union sector. (JEL 130,820)

What role do nominal wage contracts play and empirical performance of nominal con- in the determination of employment and tracting models. One the one hand, there the characteristics of the business cycle? An are as yet no convincing theoretical expla- influential series of papers by Stanley Fis- nations for the existence of nominally fixed cher (1977), Edmund S. Phelps and John B. contracts. Many of the models developed Taylor (1977), and John B. Taylor (1980) over the past decade predict constant real argued that fixed wage contracts create a wages or constant real earnings.' On the link between employment and aggregate de- other hand, the evidence in support of nom- mand. More recent models of macro fluc- inal contracting models is also weak. The tuations stress other channels for the trans- simplest of these models asserts that aggre- mission and persistence of aggregate shocks. gate demand shocks lead to real wage Real business cycle models (for example, changes that induce movements along a Finn E. Kydland and Edward C. Prescott, downward-sloping demand schedule. Al- 1982) assume that supply and demand in though unanticipated price increases are the labor market are equilibrated at Wal- apparently correlated with real economic rasian levels and ignore the institutional activity (see the review by Jo Anna Gray structure of wage determination. Recent and David Spencer, forthcoming), the ab- models in the Keynesian tradition, on the sence of a clear negative correlation be- other hand, have shifted attention from tween aggregate employment and real wages nominal wage rigidities to real wage rigidi- (Patrick T. Geary and John Kennan, 1982) ties (for example, Olivier J. Blanchard and poses a serious challenge to models of nom- Lawrence H. Summers, 1986) or nominal inal wage rigidity. price rigidities (for example, N. Gregosy This paper presents new evidence on the Mankiw, 1985; Olivier J. Blanchard and consequences of nominal contracting provi- Nobuhiro Kiyotaki, 1987). sions for employment determination in the This shift in interest reflects dissatisfac- unionized sector of Canadian manufactur- tion with both the theoretical underpinnings ing. The analysis, based on data for 1300

*Department of Economics, Princton University, 'see the survey of implicit contracting models by Princeton, NJ 08540. I am grateful to Robert Hall, Sherwin Rosen (1985). A concise summary of the im- Robert King, and two referees for their comments on plications of these models from a macroeconomic per- earlier drafts. Thomas Lemieux and Sara Turner pro- spective is presented by Stanley Fischer (1987, pp. vided expert assistance in data preparation. 42-50). 670 THE AMERICAN ECONOMIC REVIElY SEPTE,bIBER 1990 indexed and non-indexed contracts written the staggering of expiration dates also make between 1966 and 1982, suggests that nomi- it possible to control for aggregate-level dis- nal contracting provisions play an important turbances that affect all contracts at a point role in the link between aggregate demand in time. Second, the analysis pays special and employment. As predicted by the sim- attention to the issue of endogenous wage ple models of Fischer (1977) and Jo Anna determination.' Even in a simple Fischer- Gray (1976), I find that real wage changes Gray contracting framework this is a poten- induced by aggregate price surprises lead to tially serious problem, insofar as the bar- systematic employment responses in the op- gaining parties have information on future posite direction. Unexpected real wage employment demand that is unavailable to changes also affect subsequent wage deter- an outside data analyst. If predictable com- mination: the empirical results suggest that ponents of future employment demand af- roughly one-third of such changes carry over fect wages, they create a simultaneity bias in to the following contract. Unanticipated ordinary least-squares estimates of the elas- price increases therefore generate short-run ticity of employment with respect to real- employment responses and persistent wage ized wage rates. changes among firms in the union sector. To solve this problem I use the unex- Two features of the empirical analysis pected component of real wages as an in- distinguish these results from eariier at- strumental variable for the level of wages. tempts to measure the effects of nominal By assumption, unexpected changes in real wage rigidities. First, the analysis is based wages are correlated with wages but uncor- on individual contract data rather than ag- related with information known at the nego- gregate or industry-level data.2 Since union tiation date of the contract. Unexpected contracts differ in their negotiation dates wage changes therefore form a valid instru- and degrees of indexation, it is possible to mental variable for a structural analysis of calculate contract-specific measures of unemployment demand. This procedure also expected price increases and unexpected provides a direct test of the role of nominal real wage changes, and to estimate the sep- wage rigidities in generating employment arate effects of price surprises and real wage responses to nominal shocks. The instru- surprises. Variation in contract lengths and mental variables estimate of the elasticity of labor demand is nonzero if and only if employment is correlated with unexpected real wage changes. The empirical results confirm the value of 'MUC~ of the earlier literature on nominal contract- this approach. In ordinary least-squares re- ing models focuses on their implications for aggregate gressions, changes in employment are only price and wage dynamics: see Taylor (1980) and Orley weakly related to changes in contract wages. Ashenfelter and David Card (1982). A recent study by When unexpected real wage changes are Shaghil Ahmed (1987) correlates the degree of wage flexibility in an industry, measured by the elasticity of used as an instrumental variable, however, indexation among indexed labor contracts, with the employment is found to be systematically slope of the industry-specific Phillips curve. Ahmed's negatively related to wages. This finding measure of wage flexibility is based on a sample of only continues to hold when unexpected price 98 contracts in 20 industries. and fails to take into changes are added directly to the employ- account any of the characteristics of the nonindexed contracts in an industry. Furthermore, his measure of ment demand equation. It is also robust to flexibility only pertains to workers in large union con- the addition of unrestricted dummy vari- tracts and ignores variation across industries in the extent of unionization or the share of large firms. Thus, I do not interpret his findings as strong evidence for or against the hypothesis that nominal contract rigidities are important. The approach taken by Mark Bils (1989) '~ohnKennan (1988) presents an illuminating analy- is perhaps most similar to that in this paper. He sis of the difficulties that arise in the interpretation of compares the variability of industry employment growth aggregate employment and wage data when the data in months with a significant number of contract negoti- are generated by a simple model of demand and sup- ations to the variability in other months. ply. VOL.80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTRACTS 671 ables representing each year of the sample. of the contract and whether or not it con- I conclude that nominal wage contracts play tains a cost-of-living escalation clause.' an important role in determining the cycli- Assume that n(t) is determined by an cal properties and persistence of employ- employment demand schedule of the form ment in the union sector.

I. Employment and Wages in a Simple Contract Model where ~(t)is a vector of observable variables shifting the demand for labor, @ rep- A. Interpreting the Correlation of resents the elasticity of labor demand (@< Employment and Wages 0), and ~(t)is an unobservable component of employment variation. The specification This section outlines a simple model of of ~(t)and the corresponding interpreta- long-term contracting in which nominal tion of p are discussed in the next section. wages are predetermined and employment Note that supply considerations are explic- is set unilaterally by the firm after aggregate itly ignored: there are assumed to be enough prices and firm-specific demand shocks are available workers to fill the firm's demand observed. Even in this simple model the irrespective of the forecast error in real interpretation of the partial correlation of wages. This assumption is a plausible one in employment and real wages is clouded by the context of the available data, which per- the fact that the contracting parties may tain to unionized manufacturing establish- have better information on future demand ments. shocks than is available to an outside data This simple model is completed by a spec- analyst. To develop this point more for- ification of the determinants of w*(t). As- mally, suppose that wages are negotiated in sume that the expected real wage rate in some base period (period 0) for a contract period t is determined at the negotiation of duration T. Let n(t) and w(t) denote the date by variables known at that time, say logarithms of employment and real wages in x(O), and by the parties' expectations of z(t) period t of the contract, respectively, and and ~(t),z*(t) and s*(t), respectively: assume that hours per worker are fixed. The notion of "nominal cohtracting" is captured by the assumption that the bargaining parties do not set w(t) directly: rather, they The realized real wage rate in the tth pe- establish a series of nominal wage increases riod of the contract is therefore from the start of the contract, possibly in conjunction with an indexation f~rmula.~ Let w*(t) represent the parties' expectation of w(t), conditional on their information in The presence of simultaneity bias in ordi- the negotiating period, and let u(t) repre- nary least squares (OLS) estimates of the sent the forecast error w(t)- w*(t). The employment demand equation (1) depends distribution of u(t) depends on the length on two factors. If ~*(t)= 0, then the parties have no informational advantage and there is no simultaneity problem. Alternatively, if c = 0, negotiated wages are unaffected by expected employment demand and again 4~henature of typical indexation formulas in North there is no simultaneity problem. If the par- American labor contracts is described in my 1983 paper. The only case in which the real wage is set directly ties are better able to forecast employment by the parties is the case of a contract in which norni- nal wages are indexed to the consumer price level with a formula that increases the wage by one percent for each percentage point increase in prices. Such forrnu- las are rare, particularly in the manufacturing sector of co his point is made by Wallace E. Hendricks and the United States and Canada. Lawrence M. Kahn (1987). 672 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990 demand than an outside observer, however, consumer price increases directly in the em- and if higher forecasted demand leads to an ployment equation and to use variation increase in negotiated wage rates, then real across contracts in the degree of indexation wage rates will be positively correlated with to separately identify the effects of unex- the error in the employment equation, lead- pected wage changes and unexpected price ing to a positively biased estimate of the changes. A complementary approach is to wage elasticity P. include dummy variables representing the Irrespective of the parties' wage setting year in which employment is measured. behavior, the elasticity P may be consis- These year etfects absorb any aggregate de- tently estimated by considering the correla- mand shocks (or supply-side shocks) that tion between unanticipated wage rates and affect all contracts in any given year. employment outcomes. The forecast error A second difficulty may arise if unex- u(t) forms a natural instrumental variable pected changes in real wages during the for w(t): by definition, it is correlated with term of a contract are immediately offset in wages but uncorrelated with information subsequent negotiations. If this is the case available to the parties at the time of their then unexpected changes in real wages are neg~tiations.~Additional instruments may inherently short-lived, and the presence of also be available if there are determinants adjustment costs will substantially dampen of negotiated wages that can be legitimately the employment responses to such change^.^ excluded from the employment demand In the empirical analysis reported below I equation (the variables denoted as x(0) in investigate the effect of real wage surprises equation (2) above). on subsequent wage negotiations, and find There are two important caveats to this that real wage rates in the subsequent con- procedure. The first is the possibility that tract move in the same direction as unex- forecast errors in real wages are directly pected wage changes occurring during the correlated with unobservable determinants previous contract. Thus, unexpected changes of labor demand. Suppose for example that in real wages generate persistent effects on employment demand shocks are positively the cost of contractual labor, and should be correlated with unexpected price increa~es.~ expected to generate significant employ- Then unexpected real wage increases are ment effects if the wage elasticity /3 is negatively correlated with employment de- nonzero. mand shocks, leading to a negative bias in the instrumental variables estimate of the B. Specijication of the Employment wage elasticity P. A simple way to control Demand Function for this possibility is to include unexpected This section discusses the specification of the employment demand function (1) introduced above. An important limitation of the 6~tis interesting to compare this procedure to the contract-based data set used in the empiri- one suggested by Bennett T. McCallum (1976) for the cal analysis is the absence of firm-specific estimation of a structural equation that contains the price or output data. Selling prices, inter- expected value of a future endogenous variable. Mc- Callum's procedure replaces the expected future value mediate input prices, and output indexes by its actual value and uses the predicted value (from a are only available at the three-digit industry linear forecasting equation) as an instrumental vari- level. Nevertheless, these industry-level data able. His procedure therefore eliminates simultaneity may be used as proxies for the underlying bias induced by a correlation between the dependent firm-specific variables. To derive an inter- variable and the unexpected component of the explanatory variable. In the present context, the si- pretation of the resulting specification, sup- multaneity bias arises from a correlation between the pose that output is produced from three dependent variable and the expected value of the explanatory variable. Hence, the proposed instrument is the unexpected component of the explanatory variable. h his may arise if employers have imperfect infor- 8~nexpectedlylow real wage rates could induce an mation on their relative demand shocks. increase in overtime hours, however. VOL. 80 NO. 4 CARD: EMPLOYMENTDBTERMIINATION IN UNION CONTRACTS 673 factors: labor, capital, and intermediate in- nativeIy, equation (4) can be interpreted as puts (raw materials and energy). Ignoring an approximation to the output share equa- firm-specific constants, assume that the log- tion arising from a simple differentiated arithm of employment at a given firm in a product oligopoly model. In either case, the particular industry in period t,n(t) is re- error component +(t) represents a mixture lated to the logarithm of firm-specific out- of firm-specific relative demand shocks and put, y(t), the logarithm of firm-specific firm-specific productivity shocks. wages, w(t), the logarithm of firm-specific The combination of equations (3) and (4) nonlabor input prices, v(t), the user cost of leads to an expression for firm-specific em- capital in period t, r(t) (assumed to be con- ployment in terms of firm-specific wages, stant across firms and industries), and an industry-level output and intermediate in- error term q(t): put prices, the aggregate cost of capital, and industry wages:

This equation can be derived from an underlying Cobb-Douglas production function, or alternatively it can be interpreted as a loglinear approximation to an arbitrary employment demand equation. The restriction that the elasticities of employment demand Under the assumption that increases in with respect to the three factor prices sum marginal cost at a particular firm lead to to zero is a consequence of the homogeneity decreases in its relative share of industry of the cost function. This restriction implies output, the coefficients y, and y2 are nega- that the equation is invariant to the deflator tive. Thus, the elasticity of employment with used to index wages and other factor prices. respect to firm-specific wages, holding con- The magnitude of the coefficient u reflects stant industry output, is larger in absolute the degree of returns to scale: constant re- value than the elasticity holding constant turns to scale implies. a = 1. firm-spec$c output. Under the assumption Let J(t) represent the logarithm of indus- of price-taking behavior the elasticity hold- try output in period t, and let F(t) and i;(t) ing constant industry output is the uncondi- represent weighted averages of wages and tional elasticity of employment with respect intermediate input prices in the industry. to wages, allowing for the effect of changes Ignoring constants, assume that the logarithm of the firm's relative share of industry output is given by written as

This equation can be derived by assuming where q(t)is the selling price for the output of the firm that firms with identical Cobb-Douglas pro- and B(t) represents a total factor productivity shock. duction functions act as price takers with Define industry output as a geometric weighted aver- respect to firm-specific selling price^.^ Alter- age of the outputs of the individual firms in the industry. Then aggregate output follows a similar equation, and equation (4) can be derived directly, with

9~pecifically,the Cobb-Douglas assumption implies that the output supply equation of the ith firm can be 674 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990 in wages on the output supply decision of ployment determination and serve only to the firm. Under these same assumptions the transfer income between employers and-em- predicted elasticity of employment with re- pl~~ees.'~ spect to industry wages is positive, reflecting In light of the differing implications of the fact that as industry wages increase efficient contracting models and models with (holding constant the firm's wage) the firm's unilateral employment determination, it is share of industry output will increase. important to adopt an empirical framework that encompasses either possibility. In prin- C. Allowing for the Presence of ciple this can be accomplished by including Efficient Contracting a measure of the appropriate shadow wage of labor in the em~lovmentdemand func- The specification of equation (5) assumes tion. A convenient1as;umption is that the that employment levels are determined by shadow wage in an efficient contract is a the firm taking the realized real wage rate weighted average of the observed contract as given. Except under very special circum- wage and some measured alternative wage.13 stances, however, unilateral employment This leads to a specification of employment determination by the firm fails to provide an demand that includes both the contract wage efficient allocation of employment between and the measured alternative wage. ~ven contractual and extra-contractual opportu- though this procedure cannot provide a nities.1° For this reason, the empirical rele- definitive test against the efficient contract- vance of simple nominal contracting models ing hypothesis,li it can provide useful evi- has been sharply criticized (see Robert J. dence for or against the unilateral em- Barro, 1977, and Robert E. Hall, 1980, for ployment determination model, when the example). The efficient determination of alternative is a testable version of the effi- contractual employment is formally ad- cient contracting hypothesis. dressed in the implicit contracting literature and also the more recent efficient contract- 11. Data Description and Measurement ing literature." The point of both litera- Framework tures is that a jointly optimal contract (i.e., one that maximizes profit subject to a utility The empirical analysis in this paper is constraint for workers) determines employ- based on a sample of 1293 contracts negoti- ment on the basis of a shadow wage that ated by 280 firm and union bargaining pairs can differ from the contractual wage. A in the Canadian manufacturing sector.15 The contracting model with homogeneous work- available information for each contract in- ers and unrestricted transfers between em- ployed and unemployed workers implies that the appropriate shadow wage is the marginal productivity of workers in their best alterna- 12see John M. Abowd (1989) for an attempt to test tive job. Brown and Ashenfelter (1986) refer this hypothesis using stock market data on negotiating to this as the "strong form" efficient con- firms. tracting hypothesis. Strong form efficiency 13~hishypothesis can be motivated formally by assuming that employees' preferences are represented by implies that contractual wages (and contrac- a Cobb-Douglas utility function defined over employ- tual wage rigidities) are irrelevant for em- ment and the difference between the contractual wage and the alternative wage: see Brown and Ashenfelter (1986, p. S54). 14see Thomas E. MaCurdy and John H. Pencavel (1986), especially p. $13. 'Osee Robert E. Hall and David Lilien (1979). 15~hedata set only includes contracts with 500 or h he implicit contracts literature is reviewed by more workers. The sample is drawn from a public use Sherwin Rosen (1985). See Ian M. McDonald and tape distributed by Labour Canada. A complete de- Robert M. Solow (1981) for a theoretical treatment of scription of the sample and its derivation is presented efficient contracting and James N. Brown and Orley in the Data Appendix. Louis N. Christofides and An- Ashenfelter (1986) for a concise summary of the empir- drew J. Oswald (1987) have also analyzed employment ical implications of simple efficient contracting models. and wage data drawn from this source. VOL. 80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTRACTS 675

Real Employ- Number Percent with Wage ment Average of Average Escalation Indexa Indexb Forecast ErrorC Year Contracts Duration Clause 1971= 100 1971= 100 Prices Real Wages (1) (2) (3) (4) (5) (6) (7) 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 Overall Source: See Data Appendix. aEstimated wage index for level of real wages at the end of expiring contracts. b~stimatedemployment index for level of employment at the end of expiring contracts. 'Average percentage difference between price level (or real wage) at the end of contract and expected price level (or real wage) as forecast at the signing date of contract. See text.

cludes its starting (or effective) date, its though durations vary somewhat by year, ending (or expiration) date, and the base with relatively shorter contracts in the mid- wage rate in each month of the contract.16 1970s. The fraction of contracts with escala- The number of employees covered by the tion clauses shows a steadily increasing trend agreement is only available at renegotiation until the mid-1970s and then varies errati- dates. I associate this level of employment cally, with an overall average of 33 percent. with the expiring agreement. Thus, each An indication of the trends in employ- sample point consists of an end-of-contract ment and wages in the sample is provided employment observation and a series of by the indexes in columns (4) and (5) of the wages, including the beginning-of-contract table." Real wage rates among expiring and end-of-contract wage rates. contracts show significant growth until 1977 Some summary characteristics of the sam- and then remain relatively constant. Aver- ple are presented in Table 1. The expiration age employment shows no secular trend but dates of the contracts span a 16-year period reflects cyclical downturns in 1971, 1975, between 1968 and 1983, with relatively few and 1983. contracts in the first 2 years. The average The empirical strategy of this paper is to duration of the contracts is 26 months, al- fit regressions based on equation (5)to end-

I6~hebase wage rate is typically the wage paid to he wage and employment indexes represent esti- the lowest-skill group covered by the collective bargain- mated year effects from regression equations for con- ing agreement. An important assumption for the analy- tract-to-contract percentage changes in end-of-contract sis in this paper is that variation over time in intracon- wages and employment. These indexes therefore contract wage differentials is small enough to be safely trol for the composition of the set of expiring contracts ignored. in each year. 676 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990 of-contract observations on employment and the marginal elasticity of indexation evalu- wages for each contract. Assuming that the ated at the expected level of prices at the employment demand function is homoge- end of the contract. neous of degree zero in factor prices, the Given an estimate of the elasticity of in- analysis is invariant to the choice of defla- dexation, 2, and an estimate of the parties' tors for wages and intermediate input prices. expected price level at the end of the con- Given the nature of wage indexation clauses, tract, @(T), it is possible to decompose the however, it is particularly convenient to work real wage rate at the end of a contract into with real wages deflated by the consumer an estimate of its expected component, price index. In the remainder of the paper, $(T), and an estimate of its unexpected wages and industry prices are therefore ex- component: pressed as real variables, deflated by the consumer price index. The real wage rate at the end of each contract is measured directly. This rate dif- where fers from its expectation as of the negotiation date of the contract by a component that depends on the indexation provisions of the contract and the deviation between Using the definition of $(T), the estimated actual and expected prices at the end of the unexpected component of real wages can be contract. Following the notation above, let written as w*(T) represent the expected value of the logarithm of the real wage at the end of the contract. In a nonindexed contract, the logarithm of the actual real wage rate at the end of the contract, w(T), is related to w*(T) by This estimate differs from the true value u(T) by two terms: one that depends on the difference between the actual and measured where p(T) represents the logarithm of the elasticity of indexation (and is therefore consumer price index at the end of the identically zero in a nonindexed contract), contract, and p*(T) represents the parties' and another that depends on the difference expectation of p(T), formed T months ago between measured price expectations and at the negotiation date of the contract. the parties' true expectations. Provided that In an indexed contract, unexpected the measurement errors in the indexation changes in prices generate unexpected elasticity and the expected price level are changes in real wage rates only to the extent orthogonal to unmeasured components of that indexation is incomplete. For example, employment demand, however, these errors if an escalation clause increases nominal do not preclude the use of G(T) as an wages by e percent for each one percent instrumental variable for the level of wages increase in the consumer price index, then at the end of the contract. w(T) and w*(T) are related by In this paper I use a naive forecasting model to form estimates of the expected price level at the end of the contract, based on the average rate of inflation over the 12 months prior to the negotiation date.18 This

Although most escalation clauses in North American labor contracts do not specify a he forecasting equation predicts the one-year fixed elasticity of indexation, this equation is ahead inflation rate at the negotiation date t as 0.0144 approximately correct when e is defined as +0.7858 DP(t - 121, where DP(t - 12) is the actual VOL. 80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTRACTS 677 model was selected by comparing the non- escalated contracts. The average estimated contingent wage increases in the first year elasticity of indexation among indexed con- of 24-36 month nonindexed contracts to tracts is 0.50, implying that the forecast alternative forecasts of the 12-month infla- errors in real wages among these contracts tion rate formed at the negotiation date of are about one-half as large as the corre- the contract. I have also experimented with sponding forecast errors in prices.19 more sophisticated forecasting equations The average forecast errors in end-of- and found few differences in the results. contract real wages are also negatively cor- Since the forecasts are only used to form related with the employment index in col- instrumental variables, the choice of an in- umn (5): the correlation coefficient over 16 efficient forecasting model should not bias annual observations is -0.54, and the re- the empirical results. gression coefficient of the employment in- The other ingredient in the calculation of dex on unanticipated real wage changes is unexpected real wage changes is the elastic- -0.70, with a standard error of 0.27. This ity of indexation e. Precise information on provides some evidence that contractual the actual indexation formulas in the sam- employment outcomes are negatively re- ple is not readily available. I therefore use lated to unexpected changes in real wages. the ratio of total escalated increases over By comparison, the employment index is the life of the contract to the total increase positively correlated with the index of real in consumer prices over the life of the con- wage levels in column (4). tract as a rough estimate of e. This measure Contract-specific correlations between is reasonably Bccurate for contracts with no employment and wages are reported in restrictions on the escalation formula. For Table 2. All the data in this table are mea- contracts with restricted escalation formulas sured as changes from the expiration date that delay the start of indexation or specify of the previous contract, using the sample a maximum escalated wage increase, this of negotiations described in Table 1. Also measure introduces some noise into the cal- presented in the table are the correlations culation of li(T). of employment and wages with two mea- Column 6 of Table 1 reports the average sures of outside wages: the average real forecasting errors in the end-of-contract wage rate in the same (two-digit) industry, price level. The average annual forecast er- measured in the expiration month of the ror is 1.2 percent, butit varies considerably contract, and the average real wage for un- by year, ranging from 7.0 percent for coi- skilled nonproduction laborers in the same tracts expiring in 1974 and 1975, to -4.5 province, measured in the expiration year of percent for contracts expiring in 1971. As the contract.20 Finally, the last two rows of the formulas in equations (6) and (7) imply, Table 2 present the correlations of employ- forecasting errors in end-of-contract real ment and wages with contract-specific mea- wage rates are negatively correlated with sures of unexpected price changes and un- the forecast errors in prices. The average expected real wage changes. forecast errors in real wages in column 7 of the table are close to mirror images of the associated price forecasting errors. Relative 19~heforecast error in end-of-contract real wages is to the forecasting errors in prices, however, -(I- e)p, where p is the forecast error in end-of-con- the forecast errors in real wages are damp- tract prices, and e is the elasticity of indexation. The ened by the indexation provisions of the average forecast error in real wages is therefore -(1- i?)@ + covariance(e, p), where i? is the average elasticity of indexation and fi is the average forecast error in prices. he provincial wage is measured from data collected annually by Labour Canada in its area wage percentage change in prices over the preceding 12 survey. Data in this survey is collected by city. I have months. The two-and three-year-ahead inflation rate used the wage rate for the largest city in each province forecasts generated by this equation are 0.021 +0.693 as a measure of the province-specific wage. See the DP(t - 121, and 0.026+0.6135 DP(t - 121, respectively. Data Appendix. THE AMERICAN ECONOMIC REVIEW SEPTEMBER I990

TABLE2-MEANS AND CORRELATIONOF EMPLOYMENTAND WAGECHANGES BETWEENCONSECUTIVECONTRACT^

Real Contract Employment Wage Standard (End of (End of Mean Deviation Contract) Contract) 1. Employment -0.017 0.201 1.00 -0.07 (End of Contract) 2. Real Contract Wage 0.052 0.075 -0.07 1.00 (End of Contract) 3. Industry Wage 0.045 0.056 -0.04 0.59 (Expiration Month) 4. Provincial Wage 0.044 0.060 -0.07 0.51 (Expiration Year) 5. Unanticipated Change in -0.004 0.060 -0.12 0.45 Real Wages Over Contractb 6. Unanticipated Change in 0.006 0.069 0.13 -0.44 Consumer Prices Over ContractC asample size is 1293. A11 variables are measured as changes in logarithms between expiration dates of consecutive contracts. b~ercentagedifference between real wage at end of contract and expected real wage forecast at signing date of contract. 'Percentage difference between Consumer Price Index at end of contract and expected price index forecast at signing date of contract.

These simple correlations reveal three 111. The Effect of Previous Wage Rates on features of the contract-level data. First, Subsequent Wage Determination changes in employment are only weakly negatively correlated with changes in end- As a preliminary step in the analysis of of-contract real wage rates. Second, the cor- employment demand, this section presents a relations between employment and outside brief summary of estimated wage equations wages are of similar magnitude to the corre- for the sample of collective bargaining con- lations between employment and contract tracts described above. The purpose of this wages. Third, changes in employment are analysis is to identify any "spillover" effect more strongly negatively correlated with from real wage rates at the end of one changes in the unexpected component of contract to wage rates in the next contract. real wages. Thus, the OLS estimate of the A finding of significant spillovers implies elasticity of employment with respect to that unexpected changes in real wages have contract wages is much smaller in absolute persistent effects on the cost of contractual value than the corresponding instrumental labor. A finding of insignificant spillovers, variables estimate formed using unexpected on the other hand, implies that these unex- changes in real wages as an instrumental pected changes are relatively short-lived. variable. The OLS estimate is -0.19, with a The degree of persistence in unexpected standard error of 0.08, while the instrumen- wage changes is important for assessing the tal variables estimate is -0.70, with a stan- magnitude of the effect that these changes dard error of 0.18. As will be seen below, will exert on employment determination. this pattern continues to hold when other The analysis is based on two alternative covariates are added to the employment measures of negotiated wages: the real wage determination equation. at the start of the contract and the expected VOL. 80 NO. 4 CARD: EMPLOYMENT DETEM dINATION IN UNION CONTRACTS 679 average real wage over the term of the ponents of Ax,,- ,. First-differencing also entire contract. In the presence of adjust- introduces a moving average error compo- ment costs the wage at the start of the next nent into consecutive wage observations contract is particularly relevant for employ- from the same bargaining pair. The esti- ment setting behavior in the last few months mated standard errors and test statistics of an existing agreement. The expected av- throughout this paper therefore allow for a erage real wage over the next contract gives first-order moving average error component a longer-term measure of the costs of con- among the observations from each bargain- tractual employment. ing pair, as well as for arbitrary conditional A convenient statistical framework for heteroskedasticity. analyzing the determinants of wages is a Estimation results for the first-differ- simple components-of-variance model of the enced wage equation (9) are reported in form Table 3. Columns 1-4 of the table report estimates using the real wage at the start of the contract as the measure of wage outcomes, while columns 5-8 report estimates where wi, represents the measure of wages using the first-difference of the expected (either the real wage at the start of the average real wage rate over the life of the contract or the expected average real wage contract as the dependent variable.22 The over the life of the contract) for the jth components of x,, include the regional un- contract of the ith firm, 8, represents a employment rate and the real wage rate in permanent firm-specific component of wage aggregate manufacturing (measured in the variation, xi, represents a vector of deter- effective month of the contract), a province- minants of wages (measured at the negotia- specific real wage rate for unskilled workers tion date), w(T),,-I represents the real wage (measured in the effective year of the con- at the end of the previous contract, and tij tract), and a set of unrestricted year effects represents a contract-specific component of for the effective date of the contract. The variance. The parameters b and A can be year effects capture a number of omitted estimated by taking contract-to-contract factors, including a period of wage-price first-differences: controls between 1975 and 1978. Their addition provides a significant improvement in the fit of the wage equations, although they hardly affect the estimated coefficient of previous wages. I have also estimated wage Ordinary least-squares estimates of this equations that include industry-specific out- first-differenced wage equation may be input and price variables. These are only appropriate, however, if there is any corre- weakly related to negotiated wages, how- lation between the real wage at the end of ever, and their inclusion has virtually the (j- 1)st contract and the error compo- no effect on the reported coefficients in nent tl,-t,,- in the first-differenced wage Table 3. eq~ation.~'This problem is readily over- Colunms 1 and 5 of Table 3 report OLS come by using instrumental variables for the estimates of equation (9) for the two alter- lagged change in ending real wage rates. Suitable instruments include the first-difference in the unexpected component of 22~heexpected average real wage in each month of ending real wages and any exogenous com- the contract is estimated by formulas analogous to equations (6) and (71, using estimates of the expected price level in that month and estimates of the elasticity of indexation as described above. The expected aver- 21~hisproblem is similar to one of estimating the age real wage is an unweighted average of expected effect of a lagged dependent variable in a panel data monthly rates sampled at six-month intervals through- model: see Douglas Holtz-Aitken, Whitney Newey, and out the contract period, starting in the first month of Harvey S. Rosen (1988). the contract. 680 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990

Expected Average Real Wage at Start of Contract Real Wage During Contract OLS IVa OLS IVa (1) (2) (3) (4) (5) (6) (7) (8) 1. Year Effects Yes Yes Yes Yes Yes Yes Yes Yes 2. Regional Unemployment Rate -0.50 -0.45 -0.46 -0.46 -0.38 -0.44 -0.45 -0.47 (0.12) (0.12) (0.12) (0.12) (0.12) (0.13) (0.13) (0.13) 3. Real Wage in 0.04 0.11 0.11 0.10 0.40 0.30 0.31 0.26 Manufacturing (0.10) (0.11) (0.11) (0.12) (0.11) (0.12) (0.12) (0.12) 5. Real Wage in Region 0.02 0.04 0.04 0.03 0.04 0.02 0.02 0.01 (0.05) (0.04) (0.04) (0.05) (0.05) (0.05) (0.05) (0.05) 5. Real Wage at End of 0.48 0.36 0.35 - 0.25 0.41 0.35 - Previous Contract (0.03) (0.05) (0.07) (0.03) (0.06) (0.07) 6. Expected Real Wage at - - - 0.46 - - - 0.36 End of Previous Contract (0.08) (0.09) 7. Unexpected Real Wage at - - - 0.41 - - - 0.43 End of Previous Contract (0.06) (0.07) 8. Change in Prices During - - -0.01 - - - -0.05 - Previous Contract (0.03) (0.03) 9. Standard Error 0.039 0.039 0.039 0.038 0.038 0.039 0.038 0.038 10. Overidentification - 0.261 0.273 0.489 - 0.037 0.016 0.006 ~est~ Note: Standard errors in parentheses. Sample size is 1293. All regressions include a (first-differenced) linear trend. The mean and standard deviation of the dependent variable in columns (1)-(4) are 0.050 and 0.066. The mean and standard deviation of the dependent variable in columns (5148) are 0.043 and 0.061. Standard errors are corrected for first-order moving average error component and heteroskedasticity. columns (Z), (31, (61, and (71, instrumental variables for real wage at the end of the previous contract include 18-year effects, the real wage in manufacturing at the start of the previous contract and the unanticipated change in real wages over the previous contract. In columns (4) and (8) instrumental variables for expected real wage at the end of the previous contract include 18-year effects, the real wage in manufacturing at the start of the previous contract, and the change in consumer prices during the previous contract. b~robabilityvalue of test for orthogonality of residuals and instruments. The statistic is distributed as chi-squared with 19 degrees of freedom in columns (2), (3), (61, and (7), and with 18 degrees of freedom in columns (4) and (8). native dependent variables, while columns 2 In columns 3 and 7 the change in prices and 6 report instrumental variables (IV) es- over the preceding contract is introduced timates. These specifications suggest that directly into the wage determination equa- negotiated wages are significantly positively tion. This addition permits a test of the related to the level of wages at the end of hypothesis that aggregate price movements the preceding contract. The OLS estimates affect future wage determination only to the of the spillover coefficient A (in row 6) differ extent that they affect the level of real wages somewhat between the two alternative mea- at the end of the preceding contract. The sures of the dependent variable, although estimated coefficients in row 8 of the table the IV estimates are closer together. The provide no evidence against this hypothesis. last row of the table reports overidentifica- Finally, the specifications in columns 4 and tion test statistics for the instrumental vari- 8 relax the assumption that the expected ables estimators. There is no evidence and unexpected components of the end- against the exclusion restrictions implicit in of-contract wage W(T),~-have the same the IV procedure for the specification in effect on subsequent wages.23 Perhaps sur- column 2. The test statistic for the specification in column 6, on the other hand, presents mild evidence against these restric- 23These equations are estimated using the change in tions. prices over the previous contract, the manufacturing VOL. 80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTRACTS 681 prisingly, there is no evidence against the assumed to be constant across industries. restricted specification: the t-statistics for Although this is unlikely to be true, the the hypothesis of equal coefficients for the relatively small number of contracts in each expected and unexpected components are industry makes it difficult to estimate pa- 1.32 in column 4 and 1.22 in column 8. rameters other than the average demand These results suggest that unexpected elasticity across industries. Heteroskedastic- changes in wages have persistent effects on ity introduced by variation in P is taken into the costs of contractual labor. An unantici- account in the calculation of the standard pated 10 percent decrease in real wages errors. leads to an approximately 3 percent lower Again, a convenient method for eliminat- real wage throughout the following con- ing the pair-specific effects is to take first- tract. Thus even in the presence of substan- differences between consecutive contracts, tial adjustment costs, employment should be yielding expected to respond to unanticipated changes in real wages, provided that the unilateral employment determination model is correct. In many previous studies, employment outcomes have been found to follow a partial IV. The Determinants of Contractual adjustment equation of the form n,, = (1- Employment p)n: + pn,,-,, where n,*j represents the optimal level of employment in the absence This section turns to estimates of the of adjustment costs, as given by an equation employment demand function (5). As in the such as (5). Partial adjustment is readily previous section, the framework for the accommodated within the framework of analysis is a components-of-variance model equation (11) by the addition of a lagged for the logarithm of end-of-contract em- dependent variable. In the present context, ployment in the jth contract of the ith firm however, consecutive employment outcomes (nij): are 20-36 months apart. Thus, the extent of partial adjustment is likely to be much smaller than that observed in quarterly or annual data. This issue is addressed more In this equation, Gi represents a permanent thoroughly below. firm-specific effect, zij represents a vector Estimation results for the first-differenced of determinants of employment, measured employment equation are presented in Ta- at the end of the contract, wij(T) represents bles 4 and 5. Following the discussion in the real wage rate at the end of the con- Section I, Part B, the determinants of em- tract, and E~~ is a contract-specific distur- ployment include the three-digit industry bance. Assuming that industry output and input price index (deflated by the consumer prices are used as proxies for firm-specific price index), industry-level real output, and output and price data, the wage elasticity P the end-of-contract real wage rate. Specifi- in equation (10) is related to the underlying cations that add outside wage rates and a parameters of the employment demand lagged dependent variable are presented in schedule (3) and the relative output equa- Table 5. The odd-numbered columns of tion (4) by P = -(PI + ayl). Note that P is Table 4 present estimated equations that include a linear time trend, while the even- numbered columns report estimates that include a set of unrestricted dummy variables for the different expiration years in the sam- wage at the effective date of the previous contract, and ple. I have not made any attempt to mea- year effects for the effective date of the previous contract as instrumental variables for the expected and sure the user cost of capital. On the as- unexpected components of real wages at the end of the sumption that capital costs are constant previous contract. across manufacturing industries, variation in 687 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990

TABLE4-ESTIMATED EMPLOYMENTDETERMINATION EQUATIONS

OLS 1va IV" (1) (2) (3) (4) (5) (6) (7) (8) 1. Year Effects Yes Yes Yes Yes 2. Real Industry Input Price 0.16 0.16 0.16 0.15 (0.08) (0.08) (0.08) (0.08) 3. Real Industry Output 0.29 0.28 0.28 0.28 (0.09) (0.09) (0.09) (0.09) 4. Real Industry Output 0.10 0.11 0.11 0.10 (Previous Year) (0.07) (0.07) (0.07) (0.07) 5. Real Wage at End of - 0.02 -0.45 -0.51 -0.40 Contract (0.10) (0.35) (0.29) (0.42) 6. Unexpected Inflation - - - 0.10 During Contract (0.20) 7. Standard Error 0.194 0.195 0.196 0.195 8. Test for Exclusion of 0.003 0.006 0.004 0.004 Year Effects (p-Value) 9. Overidentification - - 0.97 0.96 Test

Note: Standard errors in parentheses. Sample size is 1293. All regressions include a (first-differenced) linear trend. The mean and standard deviation of the dependent variable are -0.017 and 0.201. Standard errors are corrected for first-order moving average error component and heteroskedasticity. "Instrumental variable for real wage at end of contract is the unanticipated change in real wages during the contract. bInstrumental variables for real wage at end of the contract include 18 year effects, the real wage in manufacturing at the start of the contract, and the unanticipated change in real wages during the contract. robab ability value of test for orthogonality of residuals and instruments. The test statistic is distributed as chi-squared with 19 degrees of freedom in all cases.

the user cost of capital is absorbed by the ment is positively related to intermediate trends and/or time effects in the empirical input prices and current and last year's level specification. The unrestricted year effects of output. The elasticity of employment with also capture any aggregate-level shocks respect to output (i.e., the sum of the coef- (such as aggregate demand shocks or pro- ficients of current and last years' output) is ductivity shocks) that are shared by all con- substantially less than unity, implying in- tracts in a given year. creasing returns to scale in the framework In an effort to capture partial adjustment of equation (5). The addition of the year effects, and also to control for the fact that effects results in a relatively small improve- industry output is measured annually, the ment in the fit of the employment equa- employment equations in Tables 4 and 5 tions: the probablity value of an exclusion include industry output in both the expira- tests for the year effects is reported in row 8 tion year of the agreement and the previous of the table. When the year effects are year. I have experimented with specifica- included, however, the estimated wage elas- tions that also include wage rates and input ticity of employment demand falls to essen- prices in the year prior to the expiration tially zero. date, but the effects of these variables are The estimated wage elasticity is substan- always poorly determined and small in mag- tially larger (in absolute value) when the nitude. end-of-contract wage rate is instrumented The first two columns of Table 4 present by the unanticipated change in real wages OLS estimates of the employment equation over the term of the contract. The results of with and without dummy variables for the this exercise are reported in columns 3 and expiration date of the contract. Employ- 4 of Table 4. Without year effects, the esti- VOL. 80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTR4CTS 683

- - OLS IVa IV (1) (2) (3) (4) (5) (6) (7) 1. Year Effects Yes Yes Yes Yes Yes No Yes 2. Real Industry Input Price 0.16 0.16 0.14 0.16 0.14 0.13 0.10 (0.08) (0.08) (0.08) (0.08) (0.08) (0.07) (0.09) 3. Real Industry Output 0.29 0.29 0.27 0.28 0.27 0.20 0.25 (0.09) (0.09) (0.09) (0.09) (0.09) (0.07) (0.09) 4. Real Industry Output (Previous Year) 0.10 0.10 0.11 0.11 0.11 0.15 0.13 (0.07) (0.07) (0.07) (0.07) (0.07) (0.07) (0.08) 5. Real Wage at End of Contract -0.03 -0.02 -0.56 -0.51 -0.56 -0.52 -0.58 (0.10) (0.10) (0.32) (0.31) (0.33) (0.22) (0.32) 6. Real Wage in Industry 0.06 - 0.23 - 0.23 0.26 0.38 (0.22) (0.26) (0.26) (0.22) (0.25) 7. Real Wage in Region - -0.03 - 0.04 0.06 - - (0.15) (0.16) (0.21) 8. Lagged Dependent Variable ------0.13 -0.08 (Instrumented) (0.14) (0.15) 9. Standard Error 0.194 0.194 0.196 0.196 0.196 0.193 0.194 10. Overidentification - - 0.972 0.967 0.972 0.451 0.666 Test

Note: See note to Table 4. Standard errors in parentheses. aInstrumental variables for the real wage at the end of the contract include 18-year effects, the real wage in manufacturing at the start of the contract, and the unanticipated change in real wages during the contract. b~stimatedon subsample of 1107 observations. Mean and standard deviation of the dependent variable are -0.015 and 0.0200, respectively. Instruments include the instrument set above plus the lagged value of industry output. 'Probability value of test for orthogonality of residuals and instruments. The test statistic is distributed as chi-squared with 19 degrees of freedom in columns (3)-(51, and 16 degrees of freedom in columns (6)-(7).

mated elasticity rises from -0.15 to -0.28, these are below conventional significance although the estimated standard error rises levels. I have also estimated employment proportionately. With year effects, the equations that use only the additional in- change in the point estimate is even more struments (i.e., excluding the unexpected remarkable: from -0.02 to -0.45. Due to change in real wages) toidentify the effect the imprecision of the IV estimators, how- of wages on employment. As the overidenti- ever, tests of the difference between the fication statistics suggest, these estimates are OLS and IV estimates are insignificant in very similar to those in Table 4. either case. Even with the additional instrumental The specifications in columns 5 and 6 variables the estimated elasticity of employ- attempt to reduce this imprecision by ex- ment demand in column 6 is only signifi- panding the list of instrumental variables cantly different from zero at the 10 percent for the end-of-contract real wage rate to level. Nevertheless, a test of the difference include the level of real wages in manufac- between the estimated demand elasticities turing at the start of the contract and year in columns 1 and 5 is significant at the 1 effects for the signing date of the contract. percent level, and a test-of the difference The additional instrumental variables lead between the estimated elasticities in to a slight increase in the magnitude of the columns 2 and 6 is significant at the 10 estimated wage elasticities and provide some percent level. These results suggest that increase in the precision of the estimates. OLS estimates of the elasticity of employ- Overidentification test statistics for the in- ment demand are positively biased. ternal consistency of the instruments are The final two columns of Table 4 Dresent reported in row 9 of the table. In all cases employment equations that include the un- 684 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1990 expected change in consumer prices during contract wage is instrumented, however, the the term of the contract as an additional point estimate of the effect of the industry- explanatory variable. These specifications specific wage rises substantially, while the provide a simple check on whether unex- estimated effect of the regional wage mea- pected price increases affect employment sure remains close to zero. A similar pat- through the contractual wage, or whether tern emerges in column 5 when both out- there is a direct correlation between unex- side wage measures are included. Given the pected inflation and employment demand.24 imprecision of the estimated elasticities it is Neither specification provides any evidence difficult to draw strong conclusions from of a direct role for unexpected price these results. Nevertheless, the estimates changes. Nevertheless, the standard errors lend much stronger support to the view that of the wage and price terms in column 8 are outside wages belong in the employment sufficiently large that one cannot rule out a equation as a proxy for the level of competi- direct effect of inflationary surprises on em- tors' costs than to the view that outside ployment demand.25 Taken together with wages belong in the employment equation the other estimates in the table, however, I as a proxy for the shadow value of employ- interpret the results in columns 7 and 8 as ees' time.26 If the former view is taken supporting the conclusion that price sur- literally, the point estimates in column 3 prises affect employment determination suggest that the output-constant elasticity of solely through their effect on realized wages. employment demand with respect to wages The effect of outside wage rates on con- is -0.33, while the elasticity of output sup- tractual employment is addressed in Table ply with respect to an increase in wages is 5. The theoretical analysis in Section I iden- -0.70.~~This estimate of the output-con- tifies two alternative routes for this effect. stant demand elasticity is in the midpoint of On one hand, increases in average wages in the range of estimates usually reported in the industry may have a positive effect on the static employment demand literature employment, reflecting the competitive ad- (see Daniel S. Hamermesh, 1986, pp. vantage implied by higher costs elsewhere 451-54). in the industry. On the other hand, in- The question of whether the estimated creases in wage rates representing the alter- employment equations are robust to the in- native value of workers' time may have a clusion of lagged employment is explored in negative effect if employment is influenced the last two columns of Table 5. Since the by efficient contracting considerations. In an employment models are estimated in first- effort to distinguish between these hypothe- differences, and the covariance of consecu- ses, I have included the industry average tive changes in employment is biased down- wage in columns 1 and 3 of the table, and a ward by any measurement error, the lagged province-specific wage for unskilled laborers value of industry output is added to the list in columns 2 and 4 of the table. Both wage of instrumental variables, and lagged em- measures are included in column 5. ployment and real wages are treated as The OLS estimates in columns 1 and 2 of jointly endogenous. The results show no evi- Table 5 show no evidence of a role for either outside wage measure. When the 26 My 1986 paper and Stephen J. Nickell and Sushi1 Wadhwani (1987) report employment specifications that show a positive effect of outside wages, while Brown 24~tis worth pointing out, however, that aggregate and Ashenfelter (1986) report positive effects in more demand shocks (or any other variables that affect all than one-half of their specifications. contracts at a point in time) are absorbed by the year 27~ecallfrom equation (5) that the elasticity of effects included in columns 4 and 6. employment with respect to wages is -(PI +ayl), 25~tthe suggestion of a referee, I estimated an while the elasticity of employment with respect to employment equation that includes unexpected price industry average wages is oy,. An estimate of a from increases (and year effects) and excludes wages. In this column (3) of Table 5 is 0.39 (the sum of the coeffi- specification the estimated elasticity of employment cients of current and last year's output). Using the with respect to unanticipated price increases is 0.23, other estimated coefficients from this equation leads to with a standard error of 0.14. the estimates of p, and y, reported in the text. VOL. 80 NO. 4 CARD: EMPLOYMENT DETERMINATION IN UNION CONTRACTS 685 dence of a role for lagged employment. As nonindexed contracts, indicates that these mentioned earlier, this probably reflects the unexpected real wage changes are associ- 20-36 month interval between consecutive ated with systematic employment responses observations in the data set. Over two or in the opposite direction. This suggests that three years the effects of partial adjustment nominal contracts play a role in the link are likely to be much smaller than over an between aggregate demand shocks and real interval of a quarter or year.28 economic activity, at least in the part of the The estimates in Tables 4 and 5 suggest economy covered by explicit nominal con- two main conclusions. First, employment tracts. outcomes are negatively related to contrac- Three other findings emerge from the tual wage rates. Although the simple corre- empirical analysis. First, the contract-level lation between end-of-contract wage rates correlation between employment and wages and employment is small and statistically apparently reflects both demand and wage- insignificant, this is apparently a conse- setting behavior. Similar simultaneity prob- quence of simultaneity bias. When unantici- lems may arise in other studies of pated real wage changes and/or other ex- firm-specific employment and wage data. ogenous variables are used as instrumental Second, unanticipated changes in prices are variables for the end-of-contract wage, the found to generate changes in real wages estimated wage elasticity is consistently neg- that spill over from existing labor contracts ative and stable in magnitude across alter- to subsequent agreements. Inflation sur- native specifications. Second, there is no prises therefore have persistent effects on evidence that employment is related to out- real wages in the union sector, in addition side wages in a manner consistent with sim- to their short-run effects on employment. ple efficient contracting models. Even Finally, the empirical results suggest that though employment is uncorrelated with re- employment outcomes in union contracts gion-specific wage measures, it is weakly are determined on a conventional down- positively correlated with industry average ward-sloping demand schedule, taking the wages. This positive correlation is consistent prevailing contract wage as given. There is with the hypothesis that higher average in- no indication that employment is related to dustry wages lead to improvements in the outside wages in a manner consistent with a firm's competitive position and increases in simple model of efficient contracting. employment. DATA APPENDIX V. Conclusions I. Contract Sample

This paper presents new evidence on the The contract sample is derived from the December role of nominal wage contracts in the union 1985 version of Labour Canada's Wage Tape. This sector. An important feature of these con- tape contains information on collective bargaining tracts, emphasized by the simple macro agreements covering more than 500 employees in models of Fischer (1977) and Taylor (1980), Canada. Starting from the 2868 manufacturing contracts on the tape, I merged together contract is the predetermined nature of nominal chronologies between the same firm and union cover- wages. Real wage rates at the end of a ing different establishments, and eliminated contracts contract therefore contain unanticipated from bargaining pairs with fewer than four contracts. components that reflect unexpected changes These procedures yield a sample of 2258 contracts negotiated by 299 firm and union pairs. Further infor- in consumer prices and the degree of index- mation on the merging process and the characteristics ation in the contract. The empirical analy- of the resulting sample are presented in the Data sis, based on a large sample of indexed and Appendix to my 1988 paper and in Tables 1 and 2 of that paper. The employment data for this sample were then

28 checked in two stages. First, the number of workers In principle, the coefficient of the lagged depen- covered in each contract was compared to the number dent variable will differ, depending on the duration of covered in the preceding and subsequent agreements. the previous contract. In view of the imprecision of the Second, in cases where the number of workers changed estimated partial adjustment coefficients in Table 5, dramatically between contracts, the contract sum- however, I have not attempted to address this issue. maries in the appropriate issue of the Collective Bar- 686 THE AMERlCAiV ECONOMIC REVi'EW SEPTEMBER 1990 gaining Review were consulted. In 238 contracts, the ous editions. For contracts that cover two or more employment counts recorded on the wage tape were provinces, I used a weighted average of Montreal, found to be in disagreement with the counts reported Toronto, and Vancouver rates with weights of 0.35, in the Collective Bargaining Review. In these cases, 0.55, and 0.10, respectively. counts from the published contract summaries were (d) Unemployment rates, seasonally adjusted. For used. In cases for which the set of establishments contracts in Quebec, Ontario, and British Columbia, I covered by the contract changed over time, contracts used the province-specific unemployment rates for all with inconsistent coverage were deleted from the sam- workers. For contracts in other provinces, I used the ple. Of the 2258 contracts in the subsample of merged national average unemployment rate. The series used contracts, valid coverage data are available for 1813 were as follows: Quebec-Cansim D768478; Ontario- contracts (80.3 percent). Checking of the employment Cansim D768648; British Columbia-Cansim D769233; data was performed by Thomas Lemieux. I am ex- all others-Cansim D767611. Data for January 1966 tremely grateful for his assistance with these data. through November 1983 were obtained from the 1983 In this paper, employment at the end of a contract Cansim University Base. Data for December 1983 were is measured by the number of workers covered by the taken from the Bank of Canada Review, November subsequent agreement. Furthermore, the estimation 1986. procedures require information on employment and (e) Industry selling prices, input prices, and out- wage outcomes in the previous agreement and on vari- put. Three-digit industry level annual data for 1961-71 ous industry and aggregate data that are only available were taken from Statistics Canada, Real Domestic between 1966 and 1983. The sample of contracts used Product by Industry 1961 -71. These data are classified in this paper therefore consists of the subset of con- by 1960 standard industrial codes (SICS). Data on a tracts in the initial 2258 contract merged subsample 1971 SIC basis for 1971-83 were taken from the 1978 that satisfy the following criteria: and 1984 issues of Statistics Canada, Gross Domestic (a) Information on at least one previous contract Product by Industry. The 1960 and 1971 SIC codes were is available in the sample. then matched, and the price and output indexes spliced (b) Information on at least one subsequent con- using the 1971 observations from the two sources. Of tract is available in the sample. 65 three-digit industries represented in the contract (c) The expiration dates of the current and previ- sample, there were a total of 31 for which three-digit- ous contract are after January 1966 and before Decem- level data were not available on a consistent basis. For ber 1983. these industries, two-digit-level data were used. The (d) Valid employment data are available for both publications report the value of gross output and im- the current and preceding contract (i.e., valid counts of plicit price indexes for gross output and intermediate workers covered are available for both the current and inputs. These data were used to construct the value of subsequent contracts). real gross output (the measure of "output" used in this paper). Implicit price indexes for gross output and 11. Aggregate and Industry-Level Data intermediate inputs were deflated by the annual average consumer price index to obtain real selling prices The following aggregate and industry-level data were and input prices used in the paper. merged to the contract sample. (f) Industry average hourly earnings. Monthly (a) Consumer price index, all items, 1981 = 100. two-digit industry-level average hourly earnings data January 1961 to November 1985: Cansim D484000, for the period January 1961 to March 1983 were taken from the 1985 Cansim University Base Tape. Decem- from the 1983 Cansim University Base. Earnings data ber 1985 to June 1986: from the Bank of Canada are unavailable for two industries: knitting mills and Review, November 1986. miscellaneous manufacturing. For the former, I used (b) Average hourly earnings in manufacturing. earnings in clothing industries. For the latter, I used January 1961 to March 1983: Cansim D1518, from the average earnings in all manufacturing. Wage rates for 1983 Cansim University Base Tape. April 1983 to De- April through December 1983 were constructed by cember 1983: Cansim L5607, from the Bank of Canada index-linking wage rates from the new establishment Review, various issues. Data from April 1983 and later survey to the rates in the old survey using their values are multiplied by 1.04035 to correct for the revision in in March 1983. Earnings data from the new survey for the establishment survey. March-December 1983 were taken from the 1985 Can- (c) Average hourly earnings of nonproduction sim University Base. production laborers, by province. Annual data on hourly earnings for selected occupations are available for major cities. I matched data for the following cities to their respective provinces: Halifax, St. John, Mon- treal, Toronto, Winnipeg, Regina, Edmonton, Vancou- REFERENCES ver. The wage rates used are listed as rates for "male general laborers" between 1966 and 1977, for "general Abowd, John M., "The Effect of Wage Bar- laborers in service occupations" between 1978 and gains on the Stock Market Value of the 1981, and for "nonproduction laborers" between 1982 and 1985. 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Model of Monopoly," Quarterly Journal of 163-90. Economics, May 1985, 100, 529-39. Rosen, Sherwin, "Implicit Contracts: A Sur- McCallum, Bennett T., "Rational Expecta- vey," Journal of Economic Literature, tions and the Natural Rate Hypothesis: September 1985, 23, 1144-76. Some Consistent Estimates," Economet- Bank of Canada Review, various issues, Ot- rica, January 1976, 44, 43-52. tawa: Bank of Canada. McDonald, Ian M. and Solow, Robert M., "Wage Canada Department of Labour, Wage Rates, Bargaining and Employment," American Salaries and Hours of Labour, various is- Economic Review, December 1981, 71, sues, Ottawa: Information Canada. 896-908. Labour Canada, Collective Bargaining Review, Nickell, Stephen J. and Wadhwani, Sushil, various issues, Ottawa: Labour Canada. "Financial Factors, Efficiency Wages and Statistics Canada, Information Division, Employment: Investigations Using U.K. Canada Year Book, various issues, Ot- Micro-Data," London School of Eco- tawa: Statistics Canada. nomics Center for Labour Economics Statistics Canada, Industry Product Division, Working Paper No. 993, November 1987. Gross Domestic Product by Industry, Ot- Phelps, Edmund S. and Taylor, John B., "Sta- tawa: Statistics Canada, September 1984. bilization Powers of Monetary Policy Un- , Real Domestic Product by Industry der Rational Expectations," Journal of 1961-1971, Ottawa, Statistics Canada, Political Economy, February 1977, 85, July 1977. http://www.jstor.org

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You have printed the following article: Unexpected Inflation, Real Wages, and Employment Determination in Union Contracts David Card The American Economic Review, Vol. 80, No. 4. (Sep., 1990), pp. 669-688. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28199009%2980%3A4%3C669%3AUIRWAE%3E2.0.CO%3B2-V

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[Footnotes]

1 Implicit Contracts: A Survey Sherwin Rosen Journal of Economic Literature, Vol. 23, No. 3. (Sep., 1985), pp. 1144-1175. Stable URL: http://links.jstor.org/sici?sici=0022-0515%28198509%2923%3A3%3C1144%3AICAS%3E2.0.CO%3B2-9

2 Time Series Representations of Economic Variables and Alternative Models of the Labour Market Orley Ashenfelter; David Card The Review of Economic Studies, Vol. 49, No. 5, Special Issue on Unemployment. (1982), pp. 761-781. Stable URL: http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9

3 An Econometric Analysis of Fluctuations in Aggregate Labor Supply and Demand John Kennan Econometrica, Vol. 56, No. 2. (Mar., 1988), pp. 317-333. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198803%2956%3A2%3C317%3AAEAOFI%3E2.0.CO%3B2-P

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6 Rational Expectations and the Natural Rate Hypothesis: Some Consistent Estimates B. T. McCallum Econometrica, Vol. 44, No. 1. (Jan., 1976), pp. 43-52. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197601%2944%3A1%3C43%3AREATNR%3E2.0.CO%3B2-7

10 Efficient Wage Bargains Under Uncertain Supply and Demand Robert E. Hall; David M. Lilien The American Economic Review, Vol. 69, No. 5. (Dec., 1979), pp. 868-879. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28197912%2969%3A5%3C868%3AEWBUUS%3E2.0.CO%3B2-T

11 Implicit Contracts: A Survey Sherwin Rosen Journal of Economic Literature, Vol. 23, No. 3. (Sep., 1985), pp. 1144-1175. Stable URL: http://links.jstor.org/sici?sici=0022-0515%28198509%2923%3A3%3C1144%3AICAS%3E2.0.CO%3B2-9

11 Wage Bargaining and Employment Ian M. McDonald; Robert M. Solow The American Economic Review, Vol. 71, No. 5. (Dec., 1981), pp. 896-908. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28198112%2971%3A5%3C896%3AWBAE%3E2.0.CO%3B2-%23

11 Testing the Efficiency of Employment Contracts James N. Brown; Orley Ashenfelter The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S40-S87. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

12 The Effect of Wage Bargains on the Stock Market Value of the Firm John M. Abowd The American Economic Review, Vol. 79, No. 4. (Sep., 1989), pp. 774-800. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28198909%2979%3A4%3C774%3ATEOWBO%3E2.0.CO%3B2-M

NOTE: The reference numbering from the original has been maintained in this citation list. http://www.jstor.org

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13 Testing the Efficiency of Employment Contracts James N. Brown; Orley Ashenfelter The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S40-S87. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

14 Testing between Competing Models of Wage and Employment Determination in Unionized Markets Thomas E. MaCurdy; John H. Pencavel The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S3-S39. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS3%3ATBCMOW%3E2.0.CO%3B2-O

26 Testing the Efficiency of Employment Contracts James N. Brown; Orley Ashenfelter The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S40-S87. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

References

The Effect of Wage Bargains on the Stock Market Value of the Firm John M. Abowd The American Economic Review, Vol. 79, No. 4. (Sep., 1989), pp. 774-800. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28198909%2979%3A4%3C774%3ATEOWBO%3E2.0.CO%3B2-M

Time Series Representations of Economic Variables and Alternative Models of the Labour Market Orley Ashenfelter; David Card The Review of Economic Studies, Vol. 49, No. 5, Special Issue on Unemployment. (1982), pp. 761-781. Stable URL: http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9 NOTE: The reference numbering from the original has been maintained in this citation list. http://www.jstor.org

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Monopolistic Competition and the Effects of Aggregate Demand Olivier Jean Blanchard; Nobuhiro Kiyotaki The American Economic Review, Vol. 77, No. 4. (Sep., 1987), pp. 647-666. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28198709%2977%3A4%3C647%3AMCATEO%3E2.0.CO%3B2-X

Testing the Efficiency of Employment Contracts James N. Brown; Orley Ashenfelter The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S40-S87. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

Cost-of-Living Escalators in Major Union Contracts David Card Industrial and Labor Relations Review, Vol. 37, No. 1. (Oct., 1983), pp. 34-48. Stable URL: http://links.jstor.org/sici?sici=0019-7939%28198310%2937%3A1%3C34%3ACEIMUC%3E2.0.CO%3B2-Z

Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule Stanley Fischer The Journal of Political Economy, Vol. 85, No. 1. (Feb., 1977), pp. 191-205. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197702%2985%3A1%3C191%3ALCREAT%3E2.0.CO%3B2-M

The Employment-Real Wage Relationship: An International Study Patrick T. Geary; John Kennan The Journal of Political Economy, Vol. 90, No. 4. (Aug., 1982), pp. 854-871. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198208%2990%3A4%3C854%3ATEWRAI%3E2.0.CO%3B2-V

Employment Fluctuations and Wage Rigidity Robert E. Hall; Martin Neil Baily; Lawrence H. Summers; James Duesenberry; Franco Modigliani; William Nordhaus; James Tobin; Robert Gordon; Peter Kenen; Thomas Juster; Robin Marris Brookings Papers on Economic Activity, Vol. 1980, No. 1, Tenth Anniversary Issue. (1980), pp. 91-123+125-141. Stable URL: http://links.jstor.org/sici?sici=0007-2303%281980%291980%3A1%3C91%3AEFAWR%3E2.0.CO%3B2-5 NOTE: The reference numbering from the original has been maintained in this citation list. http://www.jstor.org

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Efficient Wage Bargains Under Uncertain Supply and Demand Robert E. Hall; David M. Lilien The American Economic Review, Vol. 69, No. 5. (Dec., 1979), pp. 868-879. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28197912%2969%3A5%3C868%3AEWBUUS%3E2.0.CO%3B2-T

Estimating Vector Autoregressions with Panel Data Douglas Holtz-Eakin; Whitney Newey; Harvey S. Rosen Econometrica, Vol. 56, No. 6. (Nov., 1988), pp. 1371-1395. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198811%2956%3A6%3C1371%3AEVAWPD%3E2.0.CO%3B2-V

An Econometric Analysis of Fluctuations in Aggregate Labor Supply and Demand John Kennan Econometrica, Vol. 56, No. 2. (Mar., 1988), pp. 317-333. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198803%2956%3A2%3C317%3AAEAOFI%3E2.0.CO%3B2-P

Time to Build and Aggregate Fluctuations Finn E. Kydland; Edward C. Prescott Econometrica, Vol. 50, No. 6. (Nov., 1982), pp. 1345-1370. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198211%2950%3A6%3C1345%3ATTBAAF%3E2.0.CO%3B2-E

Testing between Competing Models of Wage and Employment Determination in Unionized Markets Thomas E. MaCurdy; John H. Pencavel The Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference. (Jun., 1986), pp. S3-S39. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS3%3ATBCMOW%3E2.0.CO%3B2-O

Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly N. Gregory Mankiw The Quarterly Journal of Economics, Vol. 100, No. 2. (May, 1985), pp. 529-537. Stable URL: http://links.jstor.org/sici?sici=0033-5533%28198505%29100%3A2%3C529%3ASMCALB%3E2.0.CO%3B2-O

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Rational Expectations and the Natural Rate Hypothesis: Some Consistent Estimates B. T. McCallum Econometrica, Vol. 44, No. 1. (Jan., 1976), pp. 43-52. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197601%2944%3A1%3C43%3AREATNR%3E2.0.CO%3B2-7

Wage Bargaining and Employment Ian M. McDonald; Robert M. Solow The American Economic Review, Vol. 71, No. 5. (Dec., 1981), pp. 896-908. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28198112%2971%3A5%3C896%3AWBAE%3E2.0.CO%3B2-%23

Stabilizing Powers of Monetary Policy under Rational Expectations Edmund S. Phelps; John B. Taylor The Journal of Political Economy, Vol. 85, No. 1. (Feb., 1977), pp. 163-190. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197702%2985%3A1%3C163%3ASPOMPU%3E2.0.CO%3B2-I

Implicit Contracts: A Survey Sherwin Rosen Journal of Economic Literature, Vol. 23, No. 3. (Sep., 1985), pp. 1144-1175. Stable URL: http://links.jstor.org/sici?sici=0022-0515%28198509%2923%3A3%3C1144%3AICAS%3E2.0.CO%3B2-9

NOTE: The reference numbering from the original has been maintained in this citation list.