Consistent Evidence on Duration Dependence in Price Changes
with Fernando Alvarez and Robert Shimer
Conditionally accepted at American Economic Review
PDF, January 2025
We develop a linear GMM estimator of the discrete time mixed proportional hazard (MPH) model of duration with an arbitrary distribution of unobserved heterogeneity. We allow for competing risks, observable characteristics, and censoring. We prove our estimator is consistent and apply it to the duration of price spells. We find substantial unobserved heterogeneity with economically meaningful implications for the response of output to a monetary policy shock in a model with time-dependent pricing rules and for the degree of state dependence in a model of price plans.
Decomposing Duration Dependence in a Stopping Time Model
with Fernando Alvarez and Robert Shimer
Review of Economic Studies, Volume 91, Issue 6, November 2024
PDF, Online Appendix, September 2023
We develop an economic model of transitions in and out of employment. Heterogeneous workers switch employment status when the net benefit from working, a Brownian motion with drift, hits optimally-chosen barriers. This implies that the duration of jobless spells for each worker has an inverse Gaussian distribution. We allow for arbitrary heterogeneity across workers and prove that the distribution of inverse Gaussian distributions is partially identified from the duration of two completed spells for each worker. We estimate the model using Austrian social security data and find that dynamic selection is a critical source of duration dependence.
Heterogeneous Job Ladders
with Claudia Macaluso
Journal of Monetary Economics, in Press
PDF, September 2024
We investigate different wage growth rates over the life cycle for poor and rich workers, and how they relate to the frequency and quality of job-to-job transitions. Using the universe of labor market histories for Austrian workers born in 1960-62 to, we show that workers who are the bottom of the earnings distribution have higher employer-to-employer transition rates than richer workers throughout their life. Nevertheless, they work for worse- and worse-paying firms as they age and are more likely to undergo unemployment spells at all ages. We propose a structural framework with learning by doing and heterogeneity along five dimensions: initial level of human capital, learning ability, and job separation propensity on the worker side, and productivity level and quality of offered learning opportunities on the employer side. Our model replicates the wage gap and the difference in the frequency of labor market transitions we document in the data, and allows us to investigate several dimensions of heterogeneity in the quality of labor market transitions. We find that poor workers' lackluster wage growth stems from a combination of deteriorating human capital, employment in low-productivity jobs, and scarce on-the-job learning opportunities. We then evaluate a policy which matches low-wage workers to high-learning employers. We find that ameliorating the learning opportunities early in a worker's career has a non-negligible impact on lifetime earnings. The gains from matching with a better employer greatly increase with job stability, as lower separation rates limit human capital depreciation and improve the odds of matching with high-productivity employers in the future.
Comment on "An Anatomy of Monopsony: Search Frictions, Amenities and Bargaining in Concentrated Markets"
NBER Macroeconomics Annual 2023, Volume 38
PDF, May 2023
Assortative Matching and Wages: The Role of Selection
with Robert Shimer
R&R, Quarterly Journal of Economics
PDF, November 2024
We develop a random search model of the labor market with two-sided heterogeneity and match-specific productivity shocks. Our model has two robust predictions: i) the average log wage that a worker receives is increasing in the worker's and employer's productivity and ii) there is positively assortative matching between high wage workers and high wage firms. Wages and sorting are driven by the same selection force. All workers are equally likely to meet all firms, but low (high) productivity workers have a higher average surplus from meeting low (high) productivity firms. The high surplus meetings result in matches more frequently, generating positive assortative matching. Since only meetings that result in matches are observed in administrative wage data, such data contain only a selected subset of meetings, driving the result that average log wages are increasing and submodular. We show that our findings are consistent with recent results in the empirical wage literature.
Racial and Gender Differences in School-College-Career-Paths
with Alessia Leibert and Anusha Nath
PDF (available upon request), slides, June 2024
What determines the gender and racial gaps in initial wages of individuals just entering the labor market? Using Minnesota longitudinal data to examine the observed choices of individuals in high school, college, and the first job, we can quantify how much the differences in these observed choices contribute to the aggregate gender and racial gaps in initial wages. Knowing what choices are being made, and when, allows us to better understand the policy options for addressing these gaps.
High Wage Workers Work for High Wage Firms
with Robert Shimer
PDF, February 2020
We propose a new measure of the correlation between the types of matched workers and firms and show that this captures sorting in a variety of structural models. We also propose an estimator of the correlation and prove that the estimator is consistent when the number of workers and firms grows to infinity even if each worker only has a small number of jobs and each firm only employs a small number of workers. Model simulations also confirm that our estimator is accurate in small data sets. Using administrative data from Austria, we find that the correlation between worker and firm types lies between 0.4 and 0.6. In contrast, the Abowd, Kramarz, Margolis (1999) fixed effects estimator suggests no correlation in our data set. This reflects a combination of biases in the AKM correlation estimator and limitations of the AKM correlation as a measure of sorting.
Risk Premia and Unemployment Fluctuations
with Jaroslav Borovička
We study the role of fluctuations in discount rates for the joint dynamics of expected returns in the stock market and employment dynamics. We construct a non-parametric bound on the predictability and time-variation in conditional volatility of the firm's profit flow that must be met to rationalize the observed business-cycle fluctuations in vacancy-filling rates. A stochastic discount factor consistent with conditional moments of the risk-free rate and expected returns on risky assets alleviates the need for an excessively volatile model of the expected profit flow.
Peer Effects in College Application
with Angela Crema and Anusha Nath
This paper examines the effect of peers on high school students' decision of whether and where to apply for colleges. We use a rich administrative data from a large school district in Minnesota to identify peers based on detailed information about courses taken by students and random classroom assignments. We identify the effect of peers by using an instrumental variables strategy where we instrument the choices made by a student’s direct peers by the decisions made by the peers of their peers. We find that peers have a significant positive effect on a student’s probability of applying. Moreover, the average quality of one’s peers’ applications increases own application quality sizably and significantly. The effect is virtually zero for the lowest performing students, but it gets larger as own GPA raises. Peer effects seem to be at work within ability groups: High-performing students are mostly affected by their high-performing peers, whereas low-performing students respond more to the decisions of their low-performing peers.
A Nonparametric Variance Decomposition Using Panel Data
with Fernando Alvarez and Robert Shimer
PDF, September 2014
We consider a population of individuals who draw a random variable from an individual-specific distribution that is fixed over time. We propose an unbiased within-between variance decomposition using a short panel of two observations for each individual. We illustrate the usefulness of our decomposition with two applications: decomposing heterogeneity versus structural duration dependence in unemployment, nonemployment, and employment durations; and calculating the importance of frictional wage dispersion for labor market outcomes.
Job Flows, Worker Flows and Labor Market Policies
PDF, February 2016
I study an equilibrium model of the labor market with firm- and worker-level shocks and evaluate the impact of labor market policies in this framework. Firms hire and shed workers in response to firm-specific productivity shocks. Workers and firms learn about the quality of their employment match and separate when they realize they are mismatched. Match quality and productivity shocks must interact in order to explain the hazard rates of separation in the cross section of firm growth rates and workers' tenures. The model is estimated using a large panel dataset of individual labor market histories in Austria. I find that accounting for worker flows generated by learning and direct job to job transitions, and job flows driven by firm-specific productivity shocks plays a crucial role for the evaluation of the impact of labor market policies on the unemployment rate, duration and average productivity.
The Accelerated Failure Time Model: Estimation and Testing using Price Change and Labor Market Data
with Fernando Alvarez and Robert Shimer
slides, April 2016
We use labor market data and data on price changes to examine the role of structural duration dependence and heterogeneity in shaping the aggregate hazard rates. In contrast to our companion paper "The Proportional Hazard Model: Estimation and Testing using Price Change and Labor Market Data," we examine this question through the lens of an accelerated failure time model, rather than a proportional hazard model. We focus on environments where we observe two observations per individual. We use a well-known lemma by Kotlarski (1967) to prove that the accelerated failure time model is non-parametrically identified. We also establish that the model is overidentified. In particular, we prove that the accelerated failure time model imposes restrictions on the characteristic function of the joint density of two spells. We examine this restriction and estimate the model using data on the timing of price changes and on the duration of employment and non-employment spells.
Aggregation Across Time and Space of the Labor Market Flows
I present new empirical evidence on the relationship between job flows, worker flows, and the time horizon at which these flows are measured. In particular, I show that worker flows grow linearly with the horizon at which they are measured while job flows grow approximately with the square root of the horizon. These patterns hold for all firm size categories separately, and the magnitude of the job and worker flows decreases with employer's size. To interpret these patterns, I explore a model of a representative firm which responds to productivity shocks by adjusting its employment subject to an integer constraint on employment. When the productivity process follows a Brownian motion, the model generates the observed relationship between the flows and the horizon at which they are measured. The integer constraint on employment explains why the flows rise with the employer size, even if these employers face the same productivity shocks. Finally, I discuss the implications of the presented facts for interpreting the differences in the characteristics of the labor markets in Europe and the U.S.