Labor Markets and the Macroeconomy: Theory, Evidence and Policy Implications

Jordi GALI (Director and Senior Researcher, Centre de Recerca en Economia Internacional / Professor, Department of Economics, Universitat Pompeu Fabra / Research Fellow, CEPR)

This paper was motivated by some changes experienced in labor markets in the United States. The first observation was that labor productivity used to be procyclical in the U.S., but that is no longer so. Second, the relative volatility of labor input has increased. Third, the volatility of real wages has increased relative to output and in absolute terms.

The goals of the paper are to document those observations and to assess the hypothesis that there is a single common source for those three observations. The hypothesis to be assessed is that there has been a decline in labor market frictions and that decline has implied the three simultaneous observations. Changes in the labor markets that were documented take place around the same time that the U.S. economy was experiencing a decline in its volatility. The hypothesis is that there is some connection between those changes in the labor markets and the so-called Great Moderation.

Suppose that firms have two margins of adjustment when it comes to labor input: they can either change employment (which we observe); or they can adjust the level of effort, which is unobservable. Labor market frictions are defined as large costs of adjusting employment. Supposing there are large labor market frictions, employment will change little and most of the adjustment will take place in terms of effort. In that case, output can still be volatile because effort may move around, but employment will not be volatile relative to output. In addition, labor productivity is likely to be procyclical. This is because employment will not change much but effort will be procyclical, thus making labor productivity also procyclical. In addition, the presence of those frictions makes room for wage rigidity. In response to technology shocks or supply shocks in general, the economy may be more volatile.

When labor market frictions decline, an exogenous increase in the relative volatility of employment and countercyclical productivity can be expected. With these changes would come more flexible wages, and increased wage volatility relative to output would be seen. Wages would absorb much more of the supply shock and thus supply shocks would have a smaller effect on output and employment. This would make more room for the Great Moderation.

In analyzing the data, the sample period was split into the 1948-1984 and post-1984 periods. Three alternative measures of labor productivity were used: non-farm labor, total hours and total employment. For all measures, there is a large decline in the correlation with output and the correlation with labor input. Before 1984, labor productivity was procyclical relative to output and largely acyclical relative to labor input. After 1984 it becomes largely acyclical relative to output and highly countercyclical relative to labor input.

Next, the volatility of labor input was measured. In absolute terms, the volatility declines as an effect of the Great Moderation. However, relative to output it increases no matter what measure is used. There must have been some structural shock that caused this.

Real wage volatility was also assessed using the measures of product wage and the consumption wage. The results were then split into absolute terms, terms relative to output, and terms relative to hours. There was an increase in the volatility of real wages no matter what measure or benchmark was used. These figures suggest that wages have become more flexible.

Product wage and labor productivity was then assessed. Simple real business cycle models implied a very strong correlation between labor productivity and real wages. The volatility of the variables was also similar. It is as if the U.S. economy was coming closer and closer to a standard real business cycle model.

Given this evidence, the paper aims to develop a relatively simple real model with labor market frictions that can account for the evidence. The representative household maximizes given utility functions for their preferences and constraints. The representative firm maximizes its profits through functions for their objectives and constraints. Frictions are introduced into the labor market through functions for cost per hire.

Once employed, the effort made by an individual worker is determined efficiently. It is also assumed that effort is perfectly observable. This means that the utility of that additional effort equals the marginal product of that additional effort. The marginal product of labor has two components: a direct component; and an induced component that results from the changes in effort that pre-existing workers in a firm will make, which is a result of their efforts being provided in an efficient manner, when the firm hires additional workers. That can be shown to be proportional to average labor productivity.

What needs to be determined is how much labor the firm will hire in each period. A function is given for this problem that states that the firm will keep hiring workers up to the point where the cost of hiring an additional worker is equal to the marginal product minus the wage plus the savings from hiring an additional worker today and thus having to hire fewer workers in the subsequent period. Basically, the savings in terms of hiring costs.

The bargaining set is a set of wages that are consistent with the surplus basically being positive for both the firm and the worker. The lower bound of that set is given by the reservation wage of the household and the upper bound is given by the highest wage that the firm is willing to accept in order to hire a new worker.

A standard assumption in the literature is to assume Nash bargaining, which yields a Nash wage which is a weighted average of the upper and lower bound. It turns out that a key result of this model is that the size of the bargaining set, the distance between the two wages, is proportional to the size of the labor market frictions. The implications of this are that if labor market frictions are large, it will be possible to keep the wage unchanged without hitting the upper or lower bounds of the bargaining set.

As a benchmark, the frictionless case is used. This is a case in which there are no hiring costs. In such a case, disequilibrium takes a very simple form. In logs, employment will be proportional to preference shocks, output will increase with the preference shocks and technology shocks, and the real wage will be proportional to labor productivity. Labor productivity will be inversely related to the preference shocks because the preference shock will increase employment. Labor productivity will increase with technology.

Given the simplicity of these equilibrium conditions, it is easy to derive closed-form expressions for all the statistics shown previously. Taking this frictionless model as a benchmark, the question is how do frictions affect the above statistics? To answer this question, the model is calibrated so that the frictionless case corresponds to the recent U.S. experience, after which labor market frictions are introduced. To what extent the labor market frictions can account for the differential behavior of U.S. labor market frictions in the pre-1984 period must then be ascertained.

In this simulation, the relative volatility of employment and the absolute volatility of output are compared against each other. It is observed that wages are less volatile than output, labor productivity is highly countercyclical relative to employment, and the covariance of labor productivity and output is close to zero. When labor market frictions with Nash bargaining are introduced, there is an increase in procyclicality of labor productivity. This is consistent with the evidence and occurs because labor market frictions create less of an incentive for the firm to adjust employment and more of an incentive to adjust effort in response to shocks. That generates increased procyclicality of labor productivity. In this model, counterfactually, the relative volatility of wages is higher and the volatility of employment is lower. This corresponds to the pre-1984 period. When wage rigidity is assumed, output becomes more volatile in response to supply shocks because wages do not respond to supply shocks and all the adjustment is absorbed by employment and effort.

Q. In regard to the costs of firms to hire and fire, cannot effort be used in the same way as hours are used in many other models?

Jordi GALI
In order to model hours-per-worker, if all the facts are looked at using labor productivity measured in terms of hours, they survive. The explanation cannot exclusively be the result of variations on that margin.

Q. It is probably true that friction in terms of hiring costs has declined, but it is also true that two things have happened over this period. One is that the labor market participation rate has gone up and a shift from manufacturing to services has occurred. If unemployment was introduced in the model, how would that evidence show up against the empirical evidence on unemployment volatility?

When the hiring costs were displayed, a productivity shock was entered into it. This is a somewhat unusual thing to do. Does this play any role in the study?

Jordi GALI
It is desirable to introduce very low participation into the model. The model has been rigged so that given wages, the household would want all of its members to be working. It is not clear how variable participation would affect the analysis, though it would complicate it.

The model makes predictions based on many variables, but the goal of the model is not to explain everything; it is a toy model that tries to make a theoretical point.

The productivity shock was entered for the sake of convenience. Introducing technology to the hiring cost function leads to homogeneity in the equilibrium condition that makes the equilibrium employment under flexible wages constant.

Q. How would these explanations stand up against other data? Is it true that there is evidence of a fall in labor market rigidities?

Have you tried to investigate if it is possible to explain these facts by changing the relative importance of various shocks?

Jordi GALI
Many of these observations hold for some, but not all countries. Labor productivity is procyclical in the euro area. This means that there is more labor hoarding.

A change in the composition of shocks could account for some of the changes. One implication of the model is that for a given degree of volatility of shocks, wages become more flexible when firms find it easier to hire and fire workers.

Q. Concerning the flexibility or friction of labor markets, a rapid increase in temporary workers was shown, similar to the phenomenon in Japan, where 30% of workers are currently temporary. Your focus on the frictionless labor market can help Japan in this regard.

Q. Please explain once again how to measure friction and effort.

Jordi GALI
Frictions in effort were not observed. Hiring costs were set to an arbitrary amount.

Q. Shouldn't friction be changed by changing the parameter of bargaining power in the Nash bargain?

Jordi GALI
In this model, a change in the bargaining power of firms relative to workers would not affect the dynamics between labor frictions and bargaining power. It would affect the level of unemployment, but not the dynamics.