Abstract: We develop a theory of sales based on product market search by heterogeneous consumers. By a theory of sales we mean a theory that explains how it can be optimal for sellers to follow a repeated pattern of posting a high price for several periods and then posting a low price for one period. More formally, we demonstrate the existence of periodic nonstationary equilibria with self-generating cycles in a simple model of sequential search. We consider a market in which consumers search for a good price for a single unit of a semi-durable good - we use shoes as an example. We assume two consumer types, fashionistas and sensible shoppers. Fashionistas receive a higher utility from consuming the good (wearing their shoes) and shop more frequently than sensible shoppers. We exhibit equilibria where sellers post high prices for several periods and then "hold a sale" by posting a low price for a single period. The mechanism that lies behind our model is straightforward. Demand from sensible shoppers accumulates during the high-price periods (in which sensible shoppers refrain from buying). At some point, it becomes sensible to hold a sale to exploit the pent-up demand. Once that demand is satisfied, sellers revert to the high-price regime.

Abstract: In other work (see here), we find a distinct cyclical pattern to the relative performance of large and small businesses in terms of net job creation. Large employers destroy proportionally more jobs during and right after recessions, and create proportionally more jobs late in expansions, relative to small employers. Differential size growth between small and large firms is strongly positively correlated with the unemployment rate. This pattern is observed both in a 1978-2005 census of U.S. employers, the Business Dynamics Statistics, and among listed companies, in Compustat. In this paper, we show that this cyclical pattern of relative performance is also reflected in stock returns. Specifically, we show that the difference in returns between benchmark portfolios of small cap stocks and portfolios of large cap stocks is also positively correlated with the unemployment rate. We propose an explanation of both facts based on dynamic competition between employers of different sizes and different productivities. The model is a stochastic dynamic version of the job search and wage posting model of Burdett and Mortensen (1998).

Abstract: We present new empirical evidence that large firms or establishments are more sensitive than small ones to business cycle conditions. Larger employers shrink faster, or expand more slowly, during and after a typical recession, and create more of their new jobs late in the following expansion, both in gross and net terms. The differential growth rate of employment between large and small firms is strongly negatively correlated with the unemployment rate, and varies by about 5% over the business cycle. Omitting cyclical indicators may lead to conclude that, on average, these cyclical effects wash out and size does not predict subsequent growth (Gibrat's law). We employ a variety of measures of relative employment growth and size classifications. We revisit two statistical fallacies, the Regression and Reclassification biases, that can affect our results, and we show empirically that they are quantitatively modest given our focus on relative cyclical behavior. We exploit a variety of (partly novel) U.S. datasets, both repeated cross-sections and job flows with employer longitudinal information, starting in the late 1970s and now spanning four business cycles. The pattern that we uncover is robust to different treatments of entry and exit of firms and establishments, and occurs within, not across, sectors and states. We find the same pattern in several other countries, including in longitudinal censuses of employers from Denmark, France and Brazil. Finally, we sketch a simple firm-ladder model of turnover that can shed light on these facts.

Abstract: We study a stochastic economy where both employed and unemployed workers search randomly for labor contracts posted by ex ante heterogeneous firms, while aggregate productivity is subject to shocks. A firm can commit to a (Markov) contract, which specifies a wage contingent on all payoff-relevant states, but must pay equally all of its workers, who have limited commitment and are free to quit at any time. Our exercise provides the first dynamic stochastic general equilibrium analysis of a popular class of search wage-posting models, drawing in part from the literature on recursive contracts under moral hazard. An equilibrium of the contract-posting game is Rank-Preserving [RP] if larger firms offer a larger value to their workers in all states of the world. We find two sufficient (but not necessary) conditions for every equilibrium to be RP: either firms only differ in their initial size, or they also differ in their fixed idiosyncratic productivity but more productive firms are also initially weakly larger. In the latter case, turnover is always efficient, as workers always move from less to more productive firms. In both cases, the ranking of firm sizes never changes on the RP equilibrium path, a property that has two useful implications. First, the stochastic dynamics of firm size provide an intuitive and robust explanation for the empirical finding that large employers in the US are more cyclically sensitive (Moscarini and Postel-Vinay, 2009). Second, RP equilibrium computation is fairly tractable, and we construct and simulate calibrated examples.

Abstract: Job-to-job turnover provides a way for employers to escape statutory redundancy pay. While the primary effect of statutory redundancy pay is to induce firms to keep employees in unprofitable matches, such unprofitable employees may willfully quit their job on receiving an outside offer, thus sparing their incumbent employer the firing costs. Furthermore, employers can induce their unprofitable workers to accept outside job offers that they would otherwise reject by offering endogenous severance packages, which are less costly than the full statutory redundancy pay. We formalize these mechanisms within an extension of the standard Diamond-Mortensen-Pissarides (DMP) matching model with endogenous job destruction that allows for employed job search and negotiation over severance packages. We then analyze the impact of statutory severance pay on various labor market indicators. We find that, while essentially preserving most standard quantitative predictions of the DMP model without employed job search, our model explains why higher firing costs will intensify job-to-job turnover at the expense of transitions out of unemployment. We also find that, as firing costs are increased beyond a certain point, it becomes profitable for firms to induce workers to quit into unemployment by offering suitable compensation, thus making further increases in statutory severance pay marginally ineffective.

Abstract: We present a tractable equilibrium job search model of individual worker careers allowing for human capital accumulation, employer heterogeneity and individual-level shocks. We estimate our structural model on a panel of Danish matched employer-employee data and use it to analyze the determinants of wage dispersion and individual wage dynamics. Our main motivation for doing this is to quantify the respective roles of human capital accumulation coming along with work experience and the forces of labor market competition activated by workers' job search behavior in shaping individual labor earnings dynamics over the life cycle. We shall pay particular attention to the definition of differences between the returns to work experience as opposed to the returns to tenure at a particular firm.

Abstract: Individual labor earnings observed in worker panel data have complex, highly persistent dynamics. We investigate the capacity of a structural job search model with i.i.d. productivity shocks to replicate salient properties of these dynamics, such as the covariance structure of earnings, the evolution of individual earnings mean and variance with the duration of uninterrupted employment, or the distribution of year-to-year earnings changes. Specifically, we show within an otherwise standard job search model how the combined assumptions of on-the-job search and wage renegotiation by mutual consent act as a quantitatively plausible ``internal propagation mechanism'' of i.i.d. productivity shocks into persistent wage shocks. The model suggests that wage dynamics should be thought of as the outcome of a specific acceptance/rejection scheme of i.i.d. productivity shocks. This offers an alternative to the conventional linear ARMA-type approach to modelling earnings dynamics. Structural estimation of our model on a 12-year panel of highly educated British workers shows that our simple framework produces a dynamic earnings structure which is remarkably consistent with the data.