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

• Author: Gray, Jo Anna

1. Introduction

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

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

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

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

2. Theoretical Considerations and Empirical Strategy

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

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

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

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

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

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

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

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

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

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

   Equation (1) is a direct implication of the theoretical model discussed earlier in the section. This is a highly simplified framework in which unanticipated movements in aggregate demand are the only aggregate source of uncertainty in...