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Wage Indexation and Compensating Wage Differentials Author(s): Wallace E. Hendricks and Lawrence M. Kahn Source: The Review of Economics and Statistics, Vol. 68, No. 3 (Aug., 1986), pp. 484-492 Published by: The MIT Press Stable URL: http://www.jstor.org/stable/1926026 . Accessed: 28/06/2014 10:42 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to The Review of Economics and Statistics. http://www.jstor.org This content downloaded from 91.213.220.103 on Sat, 28 Jun 2014 10:42:34 AM All use subject to JSTOR Terms and Conditions

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Page 1: Wage Indexation and Compensating Wage Differentials

Wage Indexation and Compensating Wage DifferentialsAuthor(s): Wallace E. Hendricks and Lawrence M. KahnSource: The Review of Economics and Statistics, Vol. 68, No. 3 (Aug., 1986), pp. 484-492Published by: The MIT PressStable URL: http://www.jstor.org/stable/1926026 .

Accessed: 28/06/2014 10:42

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

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Page 2: Wage Indexation and Compensating Wage Differentials

WAGE INDEXATION AND COMPENSATING WAGE DIFFERENTIALS

Wallace E. Hendricks and Lawrence M. Kahn*

A stract- The theory of wage indexation implies that if workers are more risk averse than firms, then workers will pay a price in order to obtain wage indexation. This prediction is tested on a sample of 3,115 U.S. manufacturing collective bargaining negotiations from 1967 to 1982. The dependent variable is the expected real wage level taking into account expected cost of living payments (Colas). Using instrumental variables or fixed effects techniques to account for the endogeneity of indexation, ve find a 2% to 22% real wage premium paid to get a Cola. However, the 2% figure is most consistent with existing esti- mates of worker risk aversion and union-nonunion wage dif- ferentials.

M X ACROECONOMIC models of the impact of wage indexation have typically com-

pared the behavior of a hypothetical economy with and without wage indexation. These compari- sons assume that the behavioral parameters of the economy would remain unchanged upon govern- ment imposition or proscription of wage indexa- tion. However, as pointed out by Azariadis (1978), such an assumption is likely to be unwarranted since other aspects of employment contracts (ex- plicit or implicit) would change.

Microeconomic models of the determinants of the demand for indexation (Shavell, 1976; Azariadis, 1978; Card, forthcoming; Ehrenberg, Danziger and San, 1983) provide some predictions about these changes. Specifically, Shavell's (1976) model predicts that if workers are more risk averse than firms (as is likely), workers will pay to obtain indexation. In effect, the firm insures workers in return for a lower overall level of wages. This prediction is analogous to the theory of com- pensating wage differentials. In that theory, workers will accept a lower wage to improve, say, work place safety (Smith, 1979). If Shavell's model is valid then a government policy outlawing or restricting the use of wage indexation would lead to wage increases, although the workers as well as the firms that gave up indexation would be made

worse off. These increases in the overall wage level might have macroeconomic effects unintended by those who designed the indexation policy.

In this paper we estimate the compensating wage differential union workers pay to obtain a cost of living allowance (Cola) clause in their contracts and compute the implied worker risk aversion parameter associated with this com- pensating differential. To our knowledge, this is the first attempt to perform such an analysis. In estimating these differentials, account is taken of the potential econometric problems induced by unobserved variables such as labor quality or un- ion relative bargaining power. The empirical liter- ature on compensating wage differentials has often obtained inconclusive results in part due to the problem of unobserved labor quality (Brown, 1980). For example, not controlling for quality, a positive correlation between wages and job safety might be observed, even if a worker of a given quality has a choice between high wage-unsafe jobs and low wage-safe jobs. In the case of wage indexation, strong unions have higher wage levels and are more likely to negotiate Colas than weak unions. However, a union of given bargaining power will, according to the theory of wage in- dexation, pay a price to obtain a Cola.

Two alternative methods, in addition to ordinary least squares (OLS), are used to estimate this price: traditional instrumental variables analysis as applied in simultaneous equations models and fixed effects models that exploit the panel nature of our data base. OLS analysis of our data indi- cates a positive relationship (controlling for ob- served variables) between Colas and wage levels. This result seemingly contradicts compensating differentials analysis. However, each technique that corrects for omitted variables yields an estimate of the price of a Cola that is in the expected direc- tion: these estimates are a 7%-22% wage reduc- tion (instrumental variables) and a 2% wage re- duction (fixed effects) to obtain a Cola. However, the 2% estimate is most consistent with what we know about worker risk aversion and union wage differentials.

Received for publication February 25, 1985. Revision accepted for publication December 13, 1985.

* University of Illinois at Urbana-Champaign. The authors thank seminar participants at the University of

Chicago and SUNY-Binghampton, Daniel Hamermesh, and anonymous referees for helpful comments and suggestions.

[ 484 ] Copyright (Q 1986

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Page 3: Wage Indexation and Compensating Wage Differentials

WAGE INDEXATION 485

I. The Demand for Indexation and Compensating Wage Differentials

Recent models of the demand for wage indexa- tion in the context of collective bargaining agree- ments view labor and management as maximizing a weighted function of their joint utilities (Card, forthcoming; Ehrenberg, Danziger and San, 1983):

L = E(U(y) + hV(1l)) (1)

where U(-) and V( -) are, respectively, the worker and employer utility functions, y is worker real income, HI is real profits, and h is a positive constant reflecting employer rela- tive bargaining power.

Labor and management choose a payment schedule (including its height and elasticity with respect to the consumer price index (CPI)) to maximize (1). Shavell (1976) has shown that in Pareto-optimal contracts (of which maximizing L is an example), bargaining power would influence only the height of the payment schedule but not the degree of wage indexation (E). Under Pareto- optimal contracts, the parties would choose a de- gree of indexation to optimally pool risks; any bargaining considerations could be handled through appropriate side payments.

Factors influencing U( -) or V(-) will in- fluence the degree of wage indexation and create a trade-off between wage levels and indexation. For example, if employer risk aversion is held constant (and employers are not risk neutral), an increase in employee risk aversion will move E toward one and lower the expected wage level. This is the compensating differentials argument.

Relative risk aversion of employees is not the only factor that will influence the choice of the optimal degree of indexation. One very important element is the relative risk associated with individ- ual negotiations from the firm's viewpoint. If this risk is high, or alternatively if the cost of negotia- tions are high, the firm's value for contracts of longer duration will increase. Since the gain asso- ciated with indexation is greater with longer con- tract duration (Gray, 1978), these considerations can indirectly influence E. For example, suppose than an increase in union bargaining power in- creases both the risk associated with a given negotiation and the expected costs of that negotia-

tion. Then the union strike threat will generate longer optimal contracts and move E toward one. Thus, we might observe a positive association between union bargaining power and indexation not predicted in Shavell's model, which ignored negotiation costs and considered only inflation risks.

This discussion suggests that a number of fac- tors associated with characteristics of workers and firms can influence the degree of indexation as well as wage levels. This creates a problem in studying the trade-off between wage levels and indexation as it does in other compensating dif- ferentials studies. Unless the set of variables which influence wages is perfectly specified, the coeffi- cient on a wage indexation variable will pick up both the market tradeoff and the influence of omitted variables to the extent that indexation is related to these variables. The next section deals with these problems.

II. Empirical Procedures for Estimating the Price of Wage Indexation

Suppose that an appropriate estimating equa- tion for testing the compensating differentials argument is

ln WE = BP + aIlE-11 + ,2 (2)

where

WE = the expected real wage level of the con- tract,

P = a vector of wage determinants (includ- ing human capital, bargaining power, etc.),

E = optimal degree of wage indexation in the contract,

a, B are positive coefficients, and 2 is an error term.

In practice, equation (2) cannot be estimated be- cause wage determinants are not completely observable and E may be very difficult to measure.' Instead, we replace P with a vector of variables X which are observable and E - 1f with a dummy variable (COLA) indicating presence or absence

1 Some of the problems of measuring e involve the difficulty of separating out the parties' intentions from the realized payments under a Cola. See Card (1983), Ehrenberg, Danziger and San (1983) and Hendricks and Kahn (1985). Below, we discuss problems of observing the expected wage level.

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486 THE REVIEW OF ECONOMICS AND STATISTICS

of wage escalation:

lnWE=C'X+dCOLA+I3, (3)

where d < 0 and I3 is an error term. From our earlier discussion, OLS estimation of

(3) should yield biased estimation of (- a), for at least two reasons. First, X is likely to be an imperfect proxy for P, i.e.,

P = f'X + 14. (4)

If indexation and I'4 are partially correlated given X, then OLS applied to (3) will be biased. For example, if union bargaining power raises the likelihood of indexation and moves E toward one, this will cause a positive bias. Second, the dummy variable COLA is an imperfect proxy for the proximity of E to 1. In this case, a measurement error arises, and it too is likely to be correlated with P given X. That is, if two bargaining units both have a Cola, the stronger union is likely to have E closer to one. While a random measure- ment error would bias the coefficient estimate of (- a) downward in absolute value, the effects of the systematic measurement error are more com- plicated. Suppose that

COLA = j - 1E - 11 + I5 (5)

where j > 0 and the term (-IE - 1I) reflects the fact that for the typical bargaining unit, E < 1. Error term ,i5 reflects the mismeasurement of

IE - 11 by COLA. For unindexed agreements, COLA = E = 0, and [5 = 1 - j. For indexed con- tracts, /15 = 1 + IE - 11 -j. For E(151E) to be

zero, j must be greater than one. Thus for unin- dexed contracts, /15 is negative and for agreements with Colas, I5 ? 0. However, among contracts with Colas, i5 is smaller the closer E is to one. Thus the relationship of [5 to P is theoretically ambiguous.2

Rewriting (2) using observable variables:

ln WE = Bf'X - aCOLA + aj + [2

+ Bpu4 + a? 5 (6)

While it is probable that stronger unions are more likely to get Colas (controlling for X), it is not clear that stronger unions have higher values of I5. Thus the partial correlation of IL5 and ln WE

given X and COLA has an ambiguous sign; there- fore so does the measurement error bias. In fact, by chance the measurement error bias might be zero or it could even be negative and cancel out the omitted variable bias discussed above. Because such an event is very unlikely, we must presume that OLS estimation of (6) yields a biased estimate of a.

In principle, a standard instrumental variables analysis of (6) can eliminate both types of asymp- totic bias. Because COLA is a qualitative depen- dent variable, a nonlinear approach is suggested; in this case, the instrumental variables estimator of (6) will not be the same as the two stage least squares (2SLS) estimator (Heckman, 1976).

The first stage of the instrumental variable pro- cedure is to estimate a reduced form equation for the probability of observing indexation:

P(COLA = 1) = F(C'Z) (7)

where F(-) is the standard normal c.d.f. and Z is a vector of variables affecting wage indexation. In addition to the wage determination proxies X, Z includes employer and union risk aversion, infla- tion uncertainty and the relationship of the firm's value added to the CPI. The instrumental vari- ables estimator for equation (6) is then

b= (W'Y)<'W'x (8)

where W = (X COLA), Y = (X COLA), x is the

vector of observations on ln WE, COLA is the vector of predicted P(COLA = 1) from (7) and X is the matrix of wage determining variables. Estimator b, is consistent and asymptotically nor- mal (Heckman (1976)), and its asymptotic vari- ance-covariance matrix can be computed with the usual instrumental variables formula (V =

a2(W'Y)-<W'W(W'Y)-', with a = standard er-

ror of the regression). In effect, COLA is an esti- mate of the parties' "sentiment" for indexation.

This type of simultaneous equation analysis has been criticized by Freeman and Medoff (1981a) in the context of analyzing union impact on relative wages. In particular, they argue that simultaneous equation estimates of union impact tend to be sensitive to identification restrictions. In addition, the identifying variables need to be truly exoge-

2 Ehrenberg, Danziger and San (1983) point out that where there are costs of indexing, we may observe no Cola even if e* 0, because the benefits of a Cola don't outweigh the costs. However, since these authors find that the benefits are a positive function of E, COLA will also be a positive function of E. Further, when COLA = 0, 5 = 1 - 1i -j in this case, and among unindexed contracts, 5 gets more negative as P and e rise. This result reinforces the ambiguity in the relationship between P and 5.

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WAGE INDEXATION 487

nous and free of measurement error if this tech- nique is to eliminate the two kinds of bias previ- ously discussed. They advocate use of "fixed effects" models estimated on longitudinal data as a way of adjusting for omitted variables while avoiding the pitfalls of simultaneous equations analysis. In our context, fixed effects methods can be used as follows to obtain an alternative esti- mate of the price of wage indexation. Consider observations on consecutive collective bargaining contracts t for a given union-management rela- tionship i. Suppose that the unobservable variable P is related to X as follows:

P= BXj, + 1 4j. (9)

According to (9), the unobserved determinants of P do not change over time. Suppose further that the measurement error IL5 in COLA (as a proxy for JE - 1() doesn't change much over time. A first difference equation corresponding to (6) is (sup- pressing i subscripts):

In Wt - ln Wt, = Bf'(X,t -Xt

-a(COLA, - COLA,t1) + (aj - aj)

+ ( I' 2, t -I 2, t - I

+B( 4,t- 4 t/ - )

+a( I ,t IL 5,Y t -- I Bf'(X, -Xt1) -a(COLA, - COLA,t1) + ( IL 2. t - tL 2 t - I ) (10)

Under these assumptions, equation (10) can be estimated to give approximately unbiased esti- mates of a, since COLA, and I'2, are uncorre- lated.

While the fixed effects approach avoids the identification problems associated with instrumen- tal variables, it is not without difficulties. First, the unobserved aspects of P as well as the measure- ment error in COLA must not change over time. These are likely to be strong assumptions. Second, equation (10) takes the change in Cola status as exogenous. If Colas are added or deleted from contracts in light of dynamic considerations, un- observed determinants of expected wage change (the dependent variable) may be partially corre- lated with the determinants of Cola change, pro- ducing a biased fixed effects estimate. Third, the fixed effects model is particularly sensitive to er-

rors in classifying the Cola status of contracts, since the estimate of a in (10) depends heavily on contracts where (COLAt - COLAt_ 1) * 0?

In the context of our problem there is no a priori method of choosing between these alterna- tive estimators since both have potential problems. Therefore, we use both methods (as well as OLS) and compare the results.

III. Data and Results

We have collected wage level data, Cola provi- sions and other information for a sample of 2,638 manufacturing contracts negotiated between 1967 and 1982.4 These Cola provisions include timing, formula, floors, ceilings, etc., as well as any changes in provisions. Four-digit industry information al- lows us to attach a variety of industry and per- sonal characteristics data to each contract, while inclusion of starting and ending dates allows the use of associated time-series variables from other sources. Industry characteristics include market structure variables, such as concentration ratio and degree of unionization as well as occupa- tional, demographic, and regional variables associ- ated with workers in the industry. An additional industry characteristic is time series data on wholesale prices for the industry. Unemployment data are taken from BLS sources. Price expecta- tions data are taken from the Livingston Surveys of economists' inflation forecasts. Finally, the BLS has provided additional information about each contract (e.g., number of workers covered, union, location, bargaining structure, etc.).5

Although the contracts provide wage level infor- mation, our analysis focuses on the expected wage level. Our proxy for ln WE is the log of the real wage level (for janitors and laborers) expected at the end of the contract being negotiated, corrected for contract length. This expected wage level is constructed as follows. Let W0 be the real wage level as of the end of the previous agreement (using the base 1967 CPI as a deflator). Let W1 be

3For further discussion of these criticisms of fixed effects models in the context of estimating the union relative wage effect, see Lewis (1983).

4 We are indebted to the following research assistants, who aided in collecting and assembling these data: Debashish Bhattacherjee, Andrew Bruns, Daniel Burgard, Cynthia (iramm, Steven Merkin, Christopher Pawlowicz, Ronald Seeber, and Roger Wolters.

5 For further description of the data, see Hendricks and Kahn (1983 and 1985).

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488 THE REVIEW OF ECONOMICS AND STATISTICS

the real wage level expected at the end of the current contract duration. For unindexed agree- ments, WI is computed by adding deferred wage increases to the nominal base wage and deflating by the CPI expected to prevail at the end of the contract. The expected CPI level is computed by applying the Livingston sample's average 12- month inflation forecast as of the signing of the current contract to the entire contract duration.6 For indexed agreements, WI is computed by ad- ding the deferred wage increases to the Cola pay- ments that the particular indexation formula would yield at the expected inflation rate. These expected Cola payments take into account all of the aspects of the Cola, including caps, timing of reviews, triggers, corridors, etc. Thus, for each indexed agreement, we obtain the best guess as to the expected yield of its Cola. As was the case for contracts without Colas, the expected final wage is deflated by the expected CPI as of the end of the contract. The variable ln WI is not used as depen- dent variable because longer contracts allow more time for productivity increases in real wages. In- stead, the expected real wage is defined as follows:

In WE-ln WO + (ln WI - ln WO)(12/DUR), (11)

where DUR = contract duration in months. In effect, In WE uses the contract provisions and forecasts a real wage by scaling the expected total real wage increase to twelve months.

The vector X of explanatory variables includes measures of union, bargaining unit, industry, and worker characteristics. These variables are:

SIZE = number of workers covered by the contract (as of 1975)

SOUTH = dummy variable referring to loca- tion of the bargaining unit in the South

MULTI = dummy variable referring to mul- tiemployer bargaining units

UNION = fraction of the 3-digit industry's workers covered by collective bargaining

CR8 = eight firm concentration ratio for the 4-digit SIC (1972)

CONSOL = fraction of union workers in the 3-digit industry organized by the largest union

CRAFT = fraction of the 3-digit industry's union workers who are craftsmen (1973-75)

OPER = fraction of the 3-digit industry's union workers who are operators (1973-75)

SMSA = fraction of the 3-digit industry's union workers who live in the 34 largest SMSAs (1973-75)

MAR = fraction of the 3-digit industry's union workers who are married, spouse present (1973-75)

MALE = fraction of the 3-digit industry's union workers who are male (1973-75)

WHITE = fraction of the 3-digit industry's union workers who are white (1973-75)

ED = average grades of school com- pleted by the 3-digit industry's union workers (1973-75)

EXP = average of (age - ED - 5) for the 3-digit industry's union workers (1973-75)

CHILD = average number of children for the 3-digit industry's union workers (1973-75)

UMALE = male unemployment rate as of the signing of the agreement

TIME = time trend variable.

These variables have been used in many previ- ous studies of union wage levels and, for brevity, are not discussed here in any detail.7

In the first stage of the instrumental variables analysis the vector Z includes all variables in X and the following additional variables:

COEFF, SIGMA = respectively, the coefficient on ln(CPI) and the standard error of the regression from a regression of ln(industry wholesale price index) on ln(CPI) using monthly data from 1971-1977;

VARINFL = variance of twelve-month Living- ston forecasts of consumer price inflation,

6 Since the Livingston forecasts are given every six months, we used linear interpolation for months between these fore- casts.

7 See, for example, Freeman and Medoff (1981b), Bloch and Kuskin (1978) or Feuille, Hendricks and Kahn (1981).

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Page 7: Wage Indexation and Compensating Wage Differentials

WAGE INDEXATION 489

as of the time of the signing of the agree- ment.

The variables COEFF and SIGMA are included in the analysis to attempt to proxy the relationship between industry prices and inflation. COEFF is a measure of the responsiveness of the industry's price to the CPI; a higher value for this variable may indicate that inflation increases (or at least does not decrease) the firm's net worth. In this case a higher degree of indexation should occur (Ehrenberg, Danziger and San, 1983; Shavell, 1976). SIGMA is a proxy for the unanticipated volatility of the industry's price and therefore is an inverse measure of the informational content of a CPI-based formula. VARINFL is intended to cap- ture uncertainty about future prices and is ex- pected to increase the incidence of Cola clauses.8 In addition to these variables, many of the vari- ables in X such as CONSOL, MULTI, MAR, CHILD, SMSA, ED or CR8 may affect indexa- tion through the costs of indexing, risk aversion or the informational content of the CPI, as well as bargaining power.9

IV. Empirical Results

A. Compensating Differentials

Table 1 contains the results for the basic OLS and instrumental variables estimates, while tables 2 and 3 contain the fixed effects results. The first column of table 1 gives a positive significant OLS estimate of the effect of having a Cola on wages: this estimate is 0.0886, implying a 9.3% wage advantage associated with Colas, ceteris paribus (e-0886 = 1.093). This estimate is likely to be bi- ased. In contrast, the instrumental variables esti- mate implies that to obtain a Cola, workers must take a 22% (e250 .78) pay cut, a large estimate that is significantly different from zero.'?

The estimates in table 1 assume that the wage functions for indexed and unindexed contracts have the same coefficients except for a shift term.

TABLE 1.-OLS AND INSTRUMENTAL VARIABLE ESTIMATES OF THE PRICE OF WAGE INDEXATION

(DEPENDENT VARIABLE IS In WE)

Explanatory Variables OLS Instrumental Variables

CONSTANT - 1.6159C - 1.4564c (0.1671) (0.1708)

SIZE (%103) 0.007b 0.0010C (0.0003) (0.0004)

UNION 0.0007c 0.0017c (0.0002) (0.0003)

CR8 0.0003a 0.0015c (0.0002) (0.0002)

CONSOL 0.0002 0.0017c (0.0002) (0.0003)

CRAFT - 0.5495c -0.0388 (0.0464) (0.0881)

OPER - 0.2799c 0.1072 (0.0450) (0.0726)

SMSA -0.0027 0.3289c (0.0310) (0.0570)

MAR 0.7367c 0.1059 (0.0973) (0.1348)

MA LE 0.3438c 0.6918c (0.0377) (0.0636)

WHITE - 0.6789c - 0.2624c (0.0716) (0.0944)

ED 0.1290c 0.0293 (0.0128) (0.0194)

EXP 0.0084 0.0522c (0.0102) (0.0121)

EXP2 0.00001 - 0.0012c (0.0002) (0.0003)

CHILD -0.0440 0.0002 (0.0296) (0.0306)

SOUTH - 0.0475c - 0.0983C (0.0079) (0.0109)

MULTI 0.0289b 0.0003 (0.0119) (0.0127)

TIME 0.0125c 0.0140c (0.0012) (0.0012)

UMA LE -0.0179c -0.0186c (0.0032) (0.0033)

COLA 0.0886C - 0.2501c (0.0071) (0.0499)

Sample size 3115 3115 R 2 0.4919 -

a Coefficient is significantly different from zero at the 10% level (2-tailed test).

b Coefficient is significantly different from zero at the 5% level (2-tailed test).

' Coeflicient is significantly different from zero at the 1% level (2-tailed test).

We have also performed estimates where these coefficients are allowed to vary. In particular, sup- pose that for indexed contracts,

ln WE = BX +? 12 (12)

and for unindexed contracts,

ln WE = B{,X?+I13, (13)

where B, and BU are coefficient vectors, and j,12

x As was the case for expected inflation, we used interpola- tion to compute this variable (see footnote 6).

9 See Hendricks and Kahn (1983 and 1985) for further dis- cussion of these variables.

'() The reduced form probit results for P(COLA = 1) are available upon request. They are similar to those in Hendricks and Kahn (1983 and 1985).

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490 THE REVIEW OF ECONOMICS AND STATISTICS

and I' are error terms. Because of the impact of omitted variables on Colas and the measurement error discussed above, OLS estimation of (12) and (13) is likely to lead to biased results. Using Heckman (1974) and Lee's (1978) two stage tech- nique to correct for this selectivity bias, we find that contracts with Colas have 7.5% lower average expected wages than unindexed agreements, other things equal. On the other hand, OLS estimation of (12) and (13) implied a 7.2% expected wage advantage to indexed contracts.

Tables 2 and 3 contain the fixed effects results. The results in table 2 include all consecutive pairs of negotiations, even if COLA - COLA11 = 0. The results in table 3 are based on a sample where COLA, - COLA__ is -1 or +1 but never zero. The tables include only two other explanatory variables because all of the other variables in X were time-invariant.'1 In each case, the price of

obtaining a Cola is a cut in expected wage levels of about 2%, and in each case this estimate is significantly different from zero. While the fixed effects estimates of 2% are considerably smaller than the simultaneous equation estimates of 7%--22%, both sets of estimates bear out the com- pensating differentials theory, unlike the positive OLS COLA coefficient in table 1.12

The compensating differentials discussed so far estimate the average effect of a Cola. However, theory suggests that the expected wage level should be negatively affected by Cola generosity. This concept can be tested by noting that

WE = WB + COLADJ, (14)

where W' = expected real annualized base wage (in dollars per hour) and COLADJ = expected real annualized Cola adjustment. Assume further that

WE = a'X + gCOLADJ + I15 (15)

where g < 0 is the price of a more generous Cola. Collecting terms, we have

WB = a'X + (g - 1)COLADJ + P15 (16)

Equation (16) was estimated for indexed con- tracts using (1) OLS; (2) simultaneous equations (SIMULT) with the predicted value of COLADJ (with a selectivity variable in the COLADJ equa- tion for Cola status) and a selectivity variable for Cola status included; and (3) a fixed effects model with the sample restricted to consecutive Cola contracts.'3 The estimates of g were

2.6516 (OLS); -6.5644 (SIMULT) (.21814) (1.3716)

and -.1194 (Fixed effects), (.1463)

TABL.2. 2.-FIXED EFFECTS ESTIMATES OF THE PRICE OF A COLA

(DIEPENDENT VARIABLE IS (In W,' - In WL 1) WHERE

t REFERS TO A NEGOTIATION

Explanatory Variables Coefficients

UMALI, - UMAl E -.0136" (.0013)

TfIME1 TIMEt 1 .0168" (.0008)

COL.A, COLA --.0154a

(.0076) Sample Size 1556 R - .0893

('oefticient is significantlv diflerent froim zero at the 5Tri level (2-tailed

(o<efftiient is significantly dilterent fromn zero at the 1% level (2-tailed

TAm BLE 3. -FIxED EFFECTS ESTIMAIES, SAMPi,E RESTRICTED TO

CHANGES IN COLA STArUS (COLA TO No COLA OR VICE-VERSA)

Explanatory Variables Coefficients

UMAlE, UMA LE, -.0124b

(.0045) TI M E,- TIMEt I .01 34h

(.0038) NIO COLA, -' COLA, - .0218a

(.0117) Sanmple Size 104 R 2 .1075

Note: N( (CO1., C(1.A, is a dLninis variable for contracts that added a Cola. The reference categorv is contracts that dropped a (ola

(ieoecticent is significantlv ditkerent fro m zero at the 1O% level (2-tailed tct e )

h (i'(Cicficint is signiticantls diflerent from zero at the 19 level (2-tailed tcst ).

D1 ata limitations prevented us from obtaining time series information on the other elements of k.

12 In their study of the determinants of Canadian Cola clauses, Cousineau, Lacroix and Bilodeau (1983) found a posi- tive coefficient for real base wages in estimating the probability that a contract was indexed. The authors do not consider the compensating differentials theory and treat real wages as a proxy for asset income; real wage is an exogenous variable in their model. In our view, the omitted variable problem forces one to use techniques such as instrumental variables or fixed effects models. The result found by Cousineau et al. (1983) may well be due to omitted variables, as we believe our OLS results are.

13 A linear form of (16) was estimated instead of the more familiar semi-log form used earlier because of inherent simultaneity problems in the latter in this context. To see this,

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Page 9: Wage Indexation and Compensating Wage Differentials

WAGE INDEXATION 491

implying (at the mean) elasticities of base wages with respect to Cola generosity of +.0698 (OLS); -.3201 (SIMULT) and -.0261 (Fixed effects). These elasticities imply compensating differentials for Colas of average generosity of + 11.2% (OLS); - 32.4% (SIMULT); and - 2.6% (Fixed effects), relative to a Cola with no yield (i.e., an unindexed contract). These are similar to the results reported earlier. However, this analysis of WB and COL-ADJ should be treated cautiously because WB includes past COLA payments, which are likely to be correlated with expected future payments.

B. Implications for Relative Risk A version

The instrumental variables and fixed effects estimates imply, under certain assumptions, levels of worker relative risk aversion (RRA). Assume that workers have a utility function:

1 U(w) = R~W (17) 1 - R

where w is the real wage level and R > 0 is the degree of relative risk aversion (RRA). To solve for R, we need to know the variability of wages with and without a Cola and the premium workers must pay to get a Cola. At this premium, the "marginal bargaining unit" is just indifferent be- tween having and not having indexation. Since the typical agreement lasts for three years, we need some estimate of the variability of real wages with and without a Cola over a three year period. Cubing the Livingston one year inflation forecasts to get a proxy of three year inflation forecasts, the mean square error between this proxy and actual inflation over successive three year periods from 1967-70 through 1980-83 implies a standard de-

suppose

COLA DJ Wl = WB +COIA DJ = WB I +

COIA DJ WB fL15.

Thus,

|CO[A DJA 1

In WB t: aX ,

g - + ,In t'

viation of about 10.9 percentage points,'4 In other work, we estimated that the average degree of indexation of janitors' and laborers' wages in in- dexed contracts was about 0.8.'5 To simplify the comparison of utilities with and without indexing, suppose that over the contract, there are only two possible values of unanticipated inflation: + 10.9% and - 10.9%, each equally likely. In this case, the standard deviation of forecast error will be 10.9%. Let Wu and Wc be, respectively, the expected real wage levels without and with a Cola, ceteris pari- bus. Then for the marginal contract:

E ( U I Cola)

2 ( 1 R - 109G - e))1)

2 ( - R w( + 109(1 og(,

= E(UINo Cola)

I I R RAO9Vu]1!

i2 1 -

+ 1 ( 1 [[(I - -- (18) 2 \l- R

Using our estimates for W,/ Wc, equation (18) can be solved for R. The fixed effects estimates from tables 2 and 3 imply R = 2.7-3.7 for union workers who are just indifferent having and not having a COLA. This range for the degree of RRA is remarkably close to Farber's (1978) estimates of 2.977 to 3.72 for the United Mineworkers, al- though higher than Carruth and Oswald's (1983) estimate of 0.8 for British coal miners. In contrast, the point estimate of about 7.5% from the selectiv- ity bias correction above implies an R well over 10, an implausible estimate. The instrumental variables estimate implies an even larger figure. We thus conclude that a point estimate of a 1.5%-2% wage cut as the price of a Cola is most consistent with existing evidence on union workers' risk aversion.

This equation would produce a spurious bias toward our compensating differentials hypothesis due to the appearance of WB in the denominator on the right hand side. In addition, while theory calls for a Cola elasticity, such a variable would produce a similar spurious bias.

14 That is, actual and expected inflation are compared for 1967-70,1968-71,...,1980-83, roughly the time period for our analysis.

15 See Hendricks and Kahn (1985). Janitors and laborers are relatively low paid, and Colas usually return equal cents per hour raises. Thus we found the degree of indexation for average workers to be lower than for janitors and laborers-on the average about 0.6.

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Page 10: Wage Indexation and Compensating Wage Differentials

492 THE REVIEW OF ECONOMICS AND STATISTICS

V. Conclusion

This paper has estimated the price workers must pay to obtain wage indexation. In the likely event that complete control for variables correlated with both wages and indexation is not possible, omitted variable estimation techniques are necessary to obtain consistent results. We use three alternative methods for handling this problem: OLS, instru- mental variables and fixed effects models. When OLS is used, an apparent positive "effect" of Colas on expected wage levels of 7%-9% is ob- served. However, accounting for omitted variables we find a significant, negative relationship be- tween wage indexation and expected real wage levels in collective bargaining agreements. These effects range from - 1.5% to -- 22%. However, the figures at the high end of this range seem incon- sistent with previous estimates of union worker risk aversion and union wage premiums. Suppose that the average measured union wage premium was 15% during the 1970s (Freeman and Medoff, 1981a). Approximately 60% of union workers were covered by Colas. A 20% Cola premium would imply a 30% union wage premium between union workers without Colas and nonunion workers (who virtually never have Colas), an implausibly high result. Thus, the estimates obtained from the fixed effect model of 1.5%-2% seem to be more plausi- ble. At a 2% compensating differential, the union-nonunion wage differential for workers without Colas becomes 16.4% (at an overall 15% union-nonunion differential).

We have found some evidence in favor of the theory of compensating wage differentials. In ad- dition, our results imply that a government policy against wage indexation would have the effect of raising average expected wage levels. Further, this paper gives further evidence of the risk aversion of American workers. Our most plausible parameter estimates imply a worker relative risk aversion of 2.7-3.7 for the subset of workers in the "marginal bargaining unit." Finally, the presence of a com- pensating differential for wage indexation implies that measured union-nonunion wage differentials may understate union relative wage effects.

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