We start out briefly explaining the search model. We then discuss how the search model can be applied to analyze issues such as the possible discrimination of second-generation immigrants at the time of labor market entry.
3.1 The equilibrium search model (ESM)
Job search theory extends neoclassical theory by incorporating the notion that workers only have partial information about employment opportunities. Given this fact, employers have monopsony power in the sense that a higher wage relative to those offered by competing employers will attract more workers giving employers an incentive to differentiate wage policy, which implies wage dispersion. In the search model, differences in firm behavior are possible because of the presence of search friction, and this can explain the persistence of differences even over time, in contrast to the wage equation approach (Mortensen ()).
The first attempt to use an ESM to interpret wage differentials was made by Bowlus (). In her paper, Bowlus focused on the effect of gender differences in friction patterns on wage differentials. We are similarly interested in applying the search model to try to identify if and how labor market dynamics and friction explain ethnic native–immigrant entry wage and early career differences in Denmark.4 We follow Bowlus et al. () and base our analysis on the Burdett-Mortensen ESM (Burdett and Mortensen ()).
The Burdett-Mortensen general ESM characterizes the labor market as having two states (employment and unemployment) with on- and off-the-job searches and a job destruction process. Workers receive a wage offer while unemployed at rate λ
> 0 and employed at rate λ
> 0. Jobs are destroyed at rate σ. It is assumed that there are a continua of F firms and L workers in the labor market analyzed. We assume that workers base their decision to accept or decline employment solely on the basis of wage and that the decision is independent of whether they are ethnic natives or second-generation immigrants. Workers take the wage offer distribution of the firms as given and solve the standard search utility maximization problem by adopting a state-dependent reservation wage strategy. Following Mortensen and Neumann (), a worker’s reservation wage r while unemployed is
showing that the optimal reservation wage depends on market opportunities as summarized in the wage-offer distribution G(w), the transition rates and supply-side factors. Lastly, h is the highest wage paid to the workers and b is unemployment benefit.5
Employers maximize profit by setting wages for the workers, taking reservation wages and wage offer distributions as given. The wages are chosen given the wage posting of the other firms and the search strategies of the workers. Profit maximization requires that employers of the same type earn the same profit in equilibrium. Our approach is to incorporate possible differential firm behavior by estimating structural parameters separately for second-generation immigrants and ethnic Danes rather than by relaxing the profit maximization condition. We allow firms to be heterogenous in productivity by assuming that there are Q types of firms with productivity P
< … < P
, i.e. discrete heterogeneity.6 Each firm faces the following profit function:
where prices have been normalized to one, the firm productivity is P and the wage for the worker is w.
In equilibrium, each employer maximizes profit given the search strategies of the workers and the wages offered by the other employers. At the same time, each worker searches sequentially from the wage offer distribution using an expected wealth maximizing stopping strategy. The market wage offer distribution G(w) is thus determined endogenously as an equilibrium outcome in this model (for details, see Bunzel et al. ()). The explicit functional form of the cumulative density function (CDF) under discrete firm heterogeneity results in
is the productivity, α
is the fraction of firms with productivity P
or less, r
is the lowest wage offered by a firm of type j, and h
is the highest wage paid by these firms. To estimate the model, we use the methodology developed by Bowlus et al. ().
Overall, the ESMs are good for exploring wage variation, which is difficult to correlate with observables. However, it is less well suited for understanding the effect of variables that correlate with wages. Thus, it is important to compare groups that are similar in terms of wage-enhancing characteristics. Since the sample we examine only contains young individuals, and we estimate the model separately for males and females as well as for ethnic natives, Western, and non-Western second-generation immigrants, and we divide the sample into three educational levels (high school, vocational school and primary school), we believe that the subsamples are homogenous.7 For the ethnic natives, we furthermore estimate separate models for a matched sample with characteristics matching second-generation immigrants.
After estimation, we compare estimates across subsamples. If all the parameters are similar across two subsamples (i.e. natives and immigrants), then it is reasonable to assume that all workers in the two subsamples are in the same market, behave similarly and are treated equally. On the other hand, if some of the parameters are different across two subsamples, then we technically assume that a separate market exists for each of the two subgroups, and the homogenous search model applies to each market, and the degree of search friction will influence the degree of wage dispersion. For example, Nielsen et al. () found significant differences in the job-finding rate and the duration of the first employment spell between ethnic natives and second-generation immigrants, differences that were partially explained by parental capital and neighborhood effects. These differences in job arrival and separation across ethnic natives and second-generation immigrants could reflect potential differences in firm behavior, and, thus, cannot be handled in traditional human capital wage regressions. Although hazard based transition reduced-form models also are able to estimate job and unemployment durations, they cannot simultaneously estimate the wage offer distribution. Thus, the added value of the ESM approach is the joint modelling of the wage distribution and the unemployment and job durations, including in particular that the job arrival rate is conditional on wages, however, at the cost of assuming separate markets and thus ruling out any spillovers and externalities between competing groups.
3.2 The ESM and network contributions
Recent research has shown that an individual’s network contributes significantly to the job search process. In particular, individuals’ successes or failures in the labor market are, to a large extent, influenced by the characteristics of the social networks in the local neighborhood. For example, Calvo-Armengol and Jackson () show that individuals living close to a large number of employed neighbors are more likely to have jobs than are individuals living in areas with fewer employed neighbors. Furthermore, Arrow and Borzekowski () show by way of simulations that differences in the number of ties workers have with firms can lead to substantial inequality and explain roughly 15% of the unexplained gap in wages and a substantial part of the disparity between black and white incomes in the US.
Pinkster () uses the ‘social isolation’ hypothesis according to which individuals living in disadvantaged neighborhoods are cut off from good job opportunities primarily because most of their contacts (their neighbors) are also out of work and, thereby, unable to provide them with important information about jobs openings and employers. High employment among one’s neighbors, on the other hand, can increase the chances of getting tips about openings, valuable information about employers and even recommendations. Furthermore, neighbors could directly assist with writing job applications or share their experiences with certain employers.
We believe that different search patterns among our groups might be a problem. This explanation has neither been captured in earlier wage regressions, employment regressions nor in duration models and this would not be captured in the ESM we use. If it is believed that second-generation immigrants behave differently in terms of the number of jobs applied for, how they write their applications or how they prepare for the job interview, this difference will in the search model transform into differences in the arrival rates of offers and give biased results. The solution is either to extend the existing search model or use matching to ensure homogeneity. We follow the second approach.
Because of the difficulty in obtaining a direct measure of contacts, a key challenge in the literature is how to construct a measure of an individual’s network. For our paper, this problem is even more complicated as we want to use the network variables in a matching analysis and, therefore, need to use variables that are comparable across ethnicity. We follow the previous literature and assume networks are geographic areas (see e.g. Topa ()). The data includes information on the postal code area in which the individual is residing. Based on this information, we construct a variable which we call ‘postal code employment rate’ defined as the percentage of individuals employed in the postal code area for each of 1,019 postal code areas. We thus follow Andersson et al. () and use small homogenous areas in terms of population characteristics, economic status and living conditions, for making the assumption of conditional independence of contacts more plausible. We expect that the ‘postal code employment rate’ captures the relevant network effect for finding jobs. We furthermore control for differences in labor market abilities through ten variables to proxy parental capital: four dummy variables for the education level of each of the parents and two dummy variables indicating whether the father and mother, respectively, are employed.8
The goal of matching is to make the two groups, second-generation immigrants and ethnic Danes, comparable in every way except for immigrant status. To do this we ensure, as Behrenz et al. () do that both groups have grown up under similar socioeconomic circumstances. Thus, we use matching to construct comparison samples of ethnic Danes according to their parents’ socioeconomic background, employment status and education. Furthermore, own age and gender are also used to match on to properly compare entry into the labor market. For example, whether an individual enters the labor market before or after 18 years of age will have a large impact on the wage rate and, therefore, might also have an effect on the likelihood of finding employment.
We find the ‘statistical ethnic Danish twins’ of second-generation immigrants among the ethnic Dane population, with the same background who face similar labor markets, by using propensity score matching (Rosenbaum and Rubin (). Since the pool of ethnic Danes consists of the whole population, it is possible to use nearest neighbor without replacement as the matching method and get a good match. After matching, we test whether the two groups are balanced with respect to the covariates using equality of means in the treated and non-treated groups, which is similar to the standardized difference test used by, for example, Smith and Todd ().