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The object is to specify and analyze equilibrium in a labor market with frictions when there is a significant public sector. In the vast majority of equilibrium studies on labor markets, a public sector has been ruled out by assumption. This seems a strange oversight as about 17% of workers in the US are public sector workers, whereas in western Europe, approximately 22% of workers work in the public sector. The goal in this study is to provide answers to such questions as: what happens to private sector wages if the public sector is increased? If the Government increases the number of public sector jobs, does this crowd out private sector jobs? When will private sector wages be greater (less) than the public sector wage? Reasonably complete answers to these questions (and others) are provided within the context of the model developed.

There is now a large literature on equilibria in labor markets where frictions are suitably taken into account (see, for example, Mortensen and Pissarides, 1999 for a still useful review). These contributions have added many new insights. All these studies, however, have ignored the possible influence of public sector employment. This seems a strange oversight as about 17% of workers in the US are public sector workers, whereas in western Europe, approximately 22% of workers work in the public sector. Further, there is significant movement of workers between the private and public sector. For example, 13% of public sector workers in the US moved to the private sector in year 2000, whereas 3% of private sector workers moved to the public sector (see Borjas, 2002). The object of this study is to analyze equilibria in a labor market where there is a significant public sector. I want to address such questions as: what happens to private sector wages if the public sector wages change? If the Government increases the number of public sector jobs, does this crowd out private sector jobs? When will private sector wages be greater (less) than the public sector wage? As will be shown later, reasonably complete answers to these questions, and others, are provided within the context of the model developed. The basic labor market model used in the study is not standard. Essentially, I construct a model where private sector firms post wages in a manner similar to that considered by Burdett and Mortensen (1998). Unlike Burdett and Mortensen, however, I assume that the number of participating private sector firms is driven by a zero profit condition.1 This construction allows me to investigate how the size of the public sector determines the number of participating private sector employers. In the first part of the study I consider labor market equilibria among private sector firms that take as given the decisions made in the public sector. It is assumed that the public sector can be described by a doubleton (x, Og) where Og is the number of public sector outlets, and x, the wage paid at public sector jobs. Within the context of the model developed for fixed (x, Og) (in a certain range) there exists a unique market equilibrium and this can be fully characterized. In the rest of this study I investigate what happens when there are changes in government policy, as well as enquiring about what public sector wage should be offered. There are, of course, many different objectives that a government can have when deciding the number of public jobs and the wages to be paid to public sector workers. In this study, I consider the special case where a government attempts to minimize its costs after it has chosen to employ a given number of public sector workers in a steady-state. For example, suppose a local government wishes to have a given number of employed fire fighters. What wage should it offer and how many vacancies should it post? The model used here has been kept as simple as possible to reveal the basic logic of the argument. This implies several important issues are ruled out. First, the public sector considered in this study can be thought of as a large firm with many outlets. The private sector consists of many small firms each having a single outlet. This seems a reasonable first step but it, of course, leaves several questions unaddressed. For example, some have argued that public sector jobs offer greater job security, and therefore the public sector jobs can offer smaller wages than private sector employers. Second, I assume throughout that all public sector workers obtain the same wage. It is difficult to ascertain the objective of a government controlling the wages in the public sector, and some objectives may imply it offers a distribution of wages. If, however, the government wants to minimize the costs of hiring workers, it is straightforward to show that it will only offer one wage. Further, legal restriction may force them to offer a single wage to homogeneous workers. Finally, to keep the analysis as simple as possible it is assumed that the arrival rate of job offers is the same for unemployed workers and employed workers. It has been established beyond reasonable doubt that this is not the case in many countries. Nevertheless, imposing this restriction much simplifies the exposition. Although there is a significant empirical literature on the size of the public sector and the movements of public sector workers (see Borjas, 2002 for an interesting example), there is little theoretical work on this topic. Indeed, I was unable to find any apart from standard textbook expositions. The work presented here can be thought of as a tentative first step to rectifying this hole in the literature.

The framework developed and analyzed above has led to a number of insights that have important empirical implications. Market entry and exit by private sector firms played a central role in establishing many of these results For example, in both the HPW Region and MPW Region, public sector vacancies crowd out private sector vacancies on a one-to-one basis. A public jobs program to stimulate the economy when the labor market is in the HPW or MPW Region would fail. Further, given a government wants to minimize the costs of employing a given number of public sector employees, market exit of private sector firms plays a crucial role in determining the public sector wage that achieves this goal. Indeed, if the number of private sector outlets is held fixed, the public sector wage that minimizes the costs of employing a given number of government workers would always be at the reservation wage, z. In the LPW Region an increase in the public sector wage increases the equilibrium level of unemployment. As illustrated in the example presented in Table 2, this increase can be significant — from 7% unemployed at x = z to 13% at x = x2. At x > x2, changes in the public sector wage have no influence on unemployment. It should be noted that the average wage paid to private sector workers is non-monotonically related to the public sector wage. In the LPW Region, an increase in the public sector wage increases the average paid to workers in the private sector. An increase in the public sector wage in the MPW Region leads to (a) an increase in the average wage paid to workers in the private sector who are employed at firms offering a wage greater than x, (b) has little effect on the wages paid to private sector workers employed at firms offering a wage less than x, and (c) more private sector firms offer a wage less than x. This implies the average wage paid to private sector workers drifts down as the public sector wage increases in the MPW Region.7 Indeed, at the public sector wage x = x1, (at the border between the HPW Region and the MPW Region), the average wage paid to private sector workers is essentially the same as when the public sector wage is x = z. As stated before, in the HPW Region the average private wage paid to employed workers in private sector is independent of the public sector wage. To obtain the results presented above, several simplifications have been made. Two appear significant. First, it has been assumed that the arrival rate of job offers is the same for unemployed and employed workers. This appears not to be satisfied in the real world. The restriction was imposed as it simplifies the analysis and this reveals the logic of the analysis. To allow for different arrival rate of offers, complicates (and enriches the model) but is clearly a doable task. Indeed, as a detailed policy analysis using the framework developed seems a task well worth doing. Second, many have argued that public sector jobs are “safer” than private sector jobs. One way of interpreting this claim is to assume the job destruction rate at public sector firms, δg, is smaller than the job destruction rate at private sector jobs, δp. Again, this significantly complicates the analysis as a wage offer at a private sector job is worthless to a worker than the same wage offer made by a public sector outlet. Nevertheless, it seems well worth attempting such a task. Above it has been established that changes in the public sector wage significantly influence the private sector labor market. Until now many labor policy discussions have focussed on the influence of changes in what are perceived to be the two major policy instruments — unemployment insurance payments paid to unemployed worker, and the mandated minimum wage. It appears reasonable to conjecture that public sector wages play an equally important role as these much discussed policy instruments.