On-the-job search and strategic bargaining

This paper studies wage bargaining in a simple economy in which both employed and unemployed workers search for better jobs. The axiomatic Nash bargaining solution and standard strategic bargaining solutions are inapplicable because the set of feasible payoffs is nonconvex. I instead develop a strategic model of wage bargaining between a single worker and firm that is applicable to such an environment. I show that if workers and firms are homogeneous, there are market equilibria with a continuous wage distribution in which identical firms bargain to different wages, each of which is a subgame perfect equilibrium of the bargaining game. If firms are heterogeneous, I characterize market equilibria in which more productive firms pay higher wages. I compare the quantitative predictions of this model with Burdett and Mortensen's [1998. Wage differentials, employer size and unemployment. International Economic Review 39, 257-273.] wage posting model and argue that the bargaining model is theoretically more appealing along important dimensions.     

Efficiency of two sided investments in an equilibrium unemployment framework

This paper investigates the efficiency of investments by firms and workers in a matching model with high- and low-productivity jobs. Search is sector specific and random within sectors. Search frictions and ex-post bargaining imply that wage inequality arises as a result of the difference in investment costs between the sectors. The efficiency properties of the equilibrium are analyzed under the particular division in bargaining proposed by Hosios (1990). The conclusion is that the equilibrium is inefficient, with a too low fraction of workers and a too high vacancy-unemployment ratio in the high-productivity sector. The opposite happens in the low-productivity sector.     

Commitment and choice of partner in a negotiation with a deadline

This paper analyses the effects of partially revocable endogenous commitments of a seller in a negotiation with a deadline. In particular, we examine when commitment is a source of strength, a source of inefficiency and when it does not affect the bargaining outcome at all. We show that when commitment possesses a minimum amount of irrevocability this crucially determines the bargaining outcome. In the bilateral bargaining case, commitment becomes a source of inefficiency since it causes a deadline effect. In the choice of partner framework, however, the deadline effect disappears and there is an immediate agreement and, moreover, commitment becomes a source of strength since it increases the seller's equilibrium payoff by triggering off competition between the buyers.     

Household bargaining over fertility: Theory and evidence from Malaysia

We develop and test a model of household bargaining over fertility when transfers between spouses are possible. The model makes precise how the fertility preferences of each spouse translate into fertility outcomes. We show this depends on whether or not spouses can commit to their future actions within marriage. If couples bargain with commitment, fertility outcomes take account of both spouses' fertility preferences and do not depend on the threat point in marital bargaining. If couples bargain without commitment, the influence of each spouse's fertility preference on fertility outcomes depends on the relevant threat point in marital bargaining, and the distribution of bargaining power. We test the models using household data from the Malaysia Family Life Survey. This data set contains information on each spouse's desired fertility level, as well as fertility outcomes. We exploit differences in threat points in marital bargaining across ethnic groups to help identify the underlying bargaining model. The evidence suggests couples bargain without commitment.     

Sorting by search intensity

In this paper, I characterize matching in an on-the-job search model with endogenous search intensity, heterogeneous workers and firms, and match surplus is shared between workers and firms through bargaining. I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient matched and unmatched search, the worker skill conditional distribution of firm productivity over matches is stochastically increasing (decreasing) in worker skill if the production function is supermodular (submodular). I also show that this strong notion of sorting does not obtain everywhere for the firm productivity conditional match distribution.     

The trade-offs from pattern bargaining with uncertain production costs

Pattern bargaining is a negotiating strategy that is often employed by industry-wide unions in oligopolistic industries to set wages. The conventional wisdom is that pattern bargaining “takes labor out of competition” and therefore softens bargaining between the union and firms, resulting in higher industry wide wages. However, this does not explain why firms agree to pattern bargaining. We introduce a model in which the agents face uncertainty about the relative product-market positions of the firms and compare the trade-offs involved in adopting different bargaining mechanisms. We show that with sufficient heterogeneity in non-labor costs, there are situations in which both the union and the firms prefer pattern bargaining. We also show that in such situations, the adoption of pattern bargaining harms consumers. This provides an explanation as to how pattern bargaining can arise in equilibrium and why there is often strong political opposition to it.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

WHO SEARCHES?*

We consider a directed search model with buyers and sellers and determine whether buyers look for sellers or vice versa. The buyers and sellers can choose to search or wait; what they do in equilibrium depends on the relative size of the two populations and the price formation mechanism. We study bargaining and auctions and find that when one population is much larger than the other the former searches and the latter waits. Under auction with roughly equal populations some buyers and sellers search and some wait. Our results challenge the practice of postulating who searches and who waits.     

The role of labor markets for euro area monetary policy

In this paper, we explore the role of labor markets for monetary policy in the euro area in a New Keynesian model in which labor markets are characterized by search and matching frictions. We first investigate to which extent a more flexible labor market would alter the business cycle behavior and the transmission of monetary policy. We find that while a lower degree of wage rigidity makes monetary policy more effective, i.e. a monetary policy shock transmits faster onto inflation, the importance of other labor market rigidities for the transmission of shocks is rather limited. Second, having estimated the model by Bayesian techniques we analyze to which extent labor market shocks, such as disturbances in the vacancy posting process, shocks to the separation rate and variations in bargaining power are important determinants of business cycle fluctuations. Our results point primarily towards disturbances in the bargaining process as a significant contributor to inflation and output fluctuations. In sum, the paper supports current central bank practice which appears to put considerable effort into monitoring euro area wage dynamics and which appears to treat some of the other labor market information as less important for monetary policy.     

Bargaining structure and nominal wage flexibility

In a model with wage setting by monopoly unions and monetary policy conducted by a central bank, the duration of nominal wage contracts is shown to be u-shaped in the degree of centralization, with intermediate bargaining systems yielding contracts of shorter duration and thus, more flexible nominal wages than both decentralized and centralized systems. The theoretical predictions of the model are tested on OECD data, and there is empirical support for the main results on contract length.     

Optimal tax progressivity in unionised labour markets: What are the driving forces?

In labour markets with collective wage bargaining higher progressivity of the labour income tax creates a trade-off. On the one hand, wages are lowered and unemployment decreases, on the other hand, the individual labour supply decision is distorted at the hours-of-work margin. The optimal level of tax progressivity within this trade-off is determined using a numerical general equilibrium model with imperfect competition on the goods market, collective wage bargaining and a labour-supply module calibrated to empirically plausible elasticity values. The model is calibrated to macroeconomic and institutional parameters of both the OECD average and a number of individual OECD countries. In most cases the optimal degree of tax progressivity is below the actual level. A decomposition approach shows that the optimal level is increased by high unemployment and by the general tax level.     

Trade and unions: Does size matter?

Our empirical analysis builds upon the hypothesis that unions are detrimental to a firm's efficiency. Using a rich survey of German manufacturers, we investigate firm-level determinants on the probability of collective wage bargaining with particular focus on the impact of a firm's engagement in foreign markets. An interesting and very robust finding is that exporters are less likely to engage in union wage bargaining. This finding is in line with a pessimistic perception of unions. The negative effect of collective bargaining can be offset by efficiency gains for larger exporters, who can benefit from operation cost saving effects. Size does matter as larger firms export and may find bargaining with a single entity representing the workforce more convenient than bargaining with each worker individually. We are using firm level information on IT investment as instrument for the export dummy and successfully test for the validity of this instrument.     

On the asymptotic uniqueness of bargaining equilibria

This note reexamines the connection between the asymmetric Nash bargaining solution and the equilibria of strategic bargaining games. A first example shows non-convergence to the asymmetric Nash bargaining solution. A second example demonstrates the possibility of multiple limits.     

Wage bargaining and turnover costs with heterogenous labor and perfect history screening

We study effects of mobility costs in a model of (Nash) wage bargaining between workers and firms, with instantaneous matching, heterogeneous workers, identical firms and free firm entry, and where firms can screen workers perfectly according to their previous work history but not their actual productivity. We derive the employment level and the minimum worker quality standard, in the market solution, and in the efficient solution established by a social planner. When workers have positive bargaining power, there is always some inefficient unemployment among desired workers in the market solution. The lowest hiring standard chosen by firms is higher than the planner's standard when firing costs are high relative to hiring costs, but may be lower in the opposite case. We show that any higher established hiring standard corresponds to a market equilibrium. The model explains a tendency for a high initial unemployment rate to remain high, particularly for low-skilled workers.     

Profit sharing and strike activity in Cournot oligopoly

Within an incomplete-information framework, we develop a model of wage determination in a unionized Cournot oligopoly. The assumption of incomplete information allows the possibility of strikes or lockouts, which waste industry potential resources, at equilibrium. Facing such deadweight loss, the government or the social planner may decide to adopt a policy, such as a profit-sharing scheme. Under two different bargaining structures (firm level vs. industry level), we investigate the effects of adopting profit sharing on the wage outcome and the strike activity. If the base-wage bargaining takes place at the industry level, then the introduction of a profit-sharing scheme increases the strike activity. But if the base-wage bargaining takes place at the firm level and the number of firms in the industry is greater than two, then the introduction of a profit-sharing scheme reduces the strike activity.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Trade unions vs. statistical discrimination: Theory and application to post-apartheid South Africa

A simple model of statistical discrimination is analyzed, which captures some stylized facts of the South African labor market. It shows that this type of discrimination disappears when the wage rates are determined by efficient bargaining between a representative firm and a union, with endogenous membership. This may explain why the wage gap between Black and White workers in post-apartheid South Africa is smaller among unionized workers than among non-unionized ones.     

ON THE NEUTRALITY OF COALITION FORMATION IN A PURE BARGAINING PROBLEM*

We consider the sequential bargaining game à la Stahl–Binmore–Rubinstein with random proposers, juxtaposing an ex ante coalition formation stage to their bargaining game. On the basis of the expected outcomes in the negotiation over how to split a dollar, players can form coalitions in a sequential manner, within each of which they can redistribute their payoffs. It turns out that the grand coalition does form, and that each player receives his discounted expected payoff, which is obtained by playing as a single player in the negotiation, although there could be many equilibria in the bargaining stage.     

The Rise and Fall of Centralized Wage Bargaining

During the three decades spanning the early 1950s to the early 1980s, the wage‐setting process in most Northern European countries was dominated by centralized bargaining (i.e., peak‐level labor and employer associations set wages nationwide). In the early 1980s, centralized wage bargaining began to collapse. In this paper, we assess a novel explanation for both the initial establishment of a centralized wage‐setting process, and its subsequent collapse. According to our theory, centralized wage bargaining was set up as a response to the spillovers created by the unemployment benefit program. Its collapse was the result of the increase in the productivity gap across workers, brought about by equipment‐specific technological progress and equipment–skill complementarity.