Periodic Reporting for period 2 - MARNET (Bipartite Network Models for Marriage and Labour Markets)
Berichtszeitraum: 2023-03-01 bis 2024-08-31
Research proposal MARNET aims at improving our empirical knowledge of markets structured as bipartite networks. A bipartite network involves two different categories of agents (employers and employees, husbands and wives) that can only connect across categories. I wish to provide better statistical models of network formation and of the effects of the network structure on outcomes. Graph-theoretic methods have known important developments in the Machine Learning literature.
I have two main applications.
The first one is related to the matching of household partners (say husband and wife) in the marriage market. We need to understand why two individuals marry instead of remaining single. In particular, it is important to disentangle what stems from different comparative advantages of the husband and the wife, from what stems from cultural norms. People marry with certain expectations in mind, and they divorce if unforeseen events break the expectations.
The second application is related to the matching of workers and employers in the labour market. The aim of the research is to understand how much of this matching stems from the match productivity and wages, and how much stems from non-wage factors (job amenities for example).
I have two main applications.
The first one is related to the matching of household partners (say husband and wife) in the marriage market. We need to understand why two individuals marry instead of remaining single. In particular, it is important to disentangle what stems from different comparative advantages of the husband and the wife, from what stems from cultural norms. People marry with certain expectations in mind, and they divorce if unforeseen events break the expectations.
The second application is related to the matching of workers and employers in the labour market. The aim of the research is to understand how much of this matching stems from the match productivity and wages, and how much stems from non-wage factors (job amenities for example).
Project Mar1 (Marriage markets in East and West Germany after the reunification) is closed to giving rise to a first draft ready for submission to a journal. This paper is coauthored with Marion Goussé (CREST-ENSAI) and Nicolas Jacquemet (Paris School of Economics and University Paris 1 Panthéon–Sorbonne). Recent work by Lippman et al. (2020) examines the effect of German reunification in 1989 on gender and family norms, and show that female labor supply varies with husband-wife relative wage more in the West than in the East. In this paper, we try to understand what factors explain this fact. We first construct a cultural identity index from the attitude questionnaire in the GSOEP, with significant overlapping across East and West. We then build a search-matching/Nash bargaining model of marriage formation and divorce, and intrahousehold resource allocation, assuming same preferences in East and West, conditional on heterogeneous wages, education and cultural identity. We estimate 4 independent models in four 7-year periods (1992-1998, 1999-2005, 2006-2012, 2013-2019) using the GSOEP. We then use the estimated model to measure how much of the observed differences between East and West (time uses and marriage sorting) are due to differences and changes in education, wages and cultural identity. Cultural identity explains half of differences in time uses and marriage sorting on observables between East and West. Identity also interacts with education and wages (another 50% reduction).
Project Net1 (The Anatomy of Sorting – Evidence from Danish Data) was completed during the first 18 months of MARNET. It gave rise to a paper co-authored with Rasmuz Lentz (University of Wisconsin-Madison) and Suphanit Piyapromdee (University College London). This paper was published in Econometrica (Nov. 2023). In this paper, we formulate and estimate a flexible model of job mobility and wages with two-sided heterogeneity. The analysis extends the finite mixture approach of Bonhomme, Lamadon, Manresa (2019) and Abowd, McKinney, Schmutte (2019) to develop a new Classification Expectation-Maximization algorithm that ensures worker and firm latent type identification using wage and mobility variations in the data. Workers receive job offers in worker type segmented labor markets. Offers are accepted with a probability that depends on the difference between the value of the current job and that of the new job. In combination with flexibly estimated layoff and job finding rates, the analysis quantifies the four different sources of sorting: preferences (job values), segmentation, layoffs, and job finding. We find evidence of a strong pecuniary motive in job preferences. While, the correlation between preferences and current job wages is positive, the net present value of the future earnings stream given the current job correlates much more strongly with preferences for it. While layoffs are less important than the other channels, we find all channels to contribute substantially to sorting. In early career, job arrival processes are the key determinant of both types of sorting, whereas the role of job preferences becomes increasingly important as cohorts age. Over the life cycle, job preferences intensify, type sorting increases and pecuniary considerations wane.
Project Net2 (A hidden Markov model of wages and employment mobility with worker and firm heterogeneity) builds on Project Net1 and is a collaboration with Rasmus Lentz (Professor at UWM) and Long Hong (Arizona State, a former student of Rasmus’s). In Net1, the types of all agents were unobserved, but supposed to remain fixed over time. Here, we want to allow them to vary stochastically over time. If the unobserved types follow a Markov chain, we speak of a Hidden Markov Model. We have developed an estimation algorithm for an extension of the Net1 model when worker types follow such a Markov chain and firm types are fixed. We also have preliminary results on simulated data. We will soon move to the estimation on actual data (Italian and Danish).
Project Net5 (Merging top-down and bottom-up empirical methodologies) was calling for a better aligment between theoretical models of the labor market and empirical models. It was clearly embryonic. During these first 18 months, I developed this project in a more concrete way. Together with Thibaut Lamadon (University of Chicago, a former student of mine at UCL), Costas Meghir (Yale) and Jeremy Lise (then Minnesota, now Cornell) we are estimating a search-matching model of the labor market, where heterogeneous workers contact heterogeneous vacancies that differ in wages and amenities. This is in itself an outstanding development in the search-matching literature. Second, our way of bringing the model to the data is also innovative. We show that a version of the model we consider in Net1 contains a parametric version of the theoretical model as a particular case. This shows that the theoretical model is identified. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between firm and within firm dispersion.
Project Net1 (The Anatomy of Sorting – Evidence from Danish Data) was completed during the first 18 months of MARNET. It gave rise to a paper co-authored with Rasmuz Lentz (University of Wisconsin-Madison) and Suphanit Piyapromdee (University College London). This paper was published in Econometrica (Nov. 2023). In this paper, we formulate and estimate a flexible model of job mobility and wages with two-sided heterogeneity. The analysis extends the finite mixture approach of Bonhomme, Lamadon, Manresa (2019) and Abowd, McKinney, Schmutte (2019) to develop a new Classification Expectation-Maximization algorithm that ensures worker and firm latent type identification using wage and mobility variations in the data. Workers receive job offers in worker type segmented labor markets. Offers are accepted with a probability that depends on the difference between the value of the current job and that of the new job. In combination with flexibly estimated layoff and job finding rates, the analysis quantifies the four different sources of sorting: preferences (job values), segmentation, layoffs, and job finding. We find evidence of a strong pecuniary motive in job preferences. While, the correlation between preferences and current job wages is positive, the net present value of the future earnings stream given the current job correlates much more strongly with preferences for it. While layoffs are less important than the other channels, we find all channels to contribute substantially to sorting. In early career, job arrival processes are the key determinant of both types of sorting, whereas the role of job preferences becomes increasingly important as cohorts age. Over the life cycle, job preferences intensify, type sorting increases and pecuniary considerations wane.
Project Net2 (A hidden Markov model of wages and employment mobility with worker and firm heterogeneity) builds on Project Net1 and is a collaboration with Rasmus Lentz (Professor at UWM) and Long Hong (Arizona State, a former student of Rasmus’s). In Net1, the types of all agents were unobserved, but supposed to remain fixed over time. Here, we want to allow them to vary stochastically over time. If the unobserved types follow a Markov chain, we speak of a Hidden Markov Model. We have developed an estimation algorithm for an extension of the Net1 model when worker types follow such a Markov chain and firm types are fixed. We also have preliminary results on simulated data. We will soon move to the estimation on actual data (Italian and Danish).
Project Net5 (Merging top-down and bottom-up empirical methodologies) was calling for a better aligment between theoretical models of the labor market and empirical models. It was clearly embryonic. During these first 18 months, I developed this project in a more concrete way. Together with Thibaut Lamadon (University of Chicago, a former student of mine at UCL), Costas Meghir (Yale) and Jeremy Lise (then Minnesota, now Cornell) we are estimating a search-matching model of the labor market, where heterogeneous workers contact heterogeneous vacancies that differ in wages and amenities. This is in itself an outstanding development in the search-matching literature. Second, our way of bringing the model to the data is also innovative. We show that a version of the model we consider in Net1 contains a parametric version of the theoretical model as a particular case. This shows that the theoretical model is identified. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between firm and within firm dispersion.
Project Mar4 still needs a lot of work. The current literature on marriage is essentially static. The literature on household decision making has considered asset accumulation, but assumes marriage exogenous. It would be an important achievement to introduce the dimension of non stationarity embodied in asset accumulation.
As it happens, I also decided to absorb part of Project Net3 (Firm size dynamics) into Project Net2. In Net1 and the planned version of Net2, we have the following mechanism for sampling firms by workers. A workers of a given type first draws a firm type. Then, given the firm type, they draw a specific firm of that type uniformly at random. It is possible to extend this sampling mechanism by assuming that firms are drawn given type in a non uniform way. This type of model is known in the network literature as a Degree Corrected Stock Block Model (DC-SBM). Our model is not exactly a Stock Block Model but it is close to one. We still need to develop this part of the project further.
As it happens, I also decided to absorb part of Project Net3 (Firm size dynamics) into Project Net2. In Net1 and the planned version of Net2, we have the following mechanism for sampling firms by workers. A workers of a given type first draws a firm type. Then, given the firm type, they draw a specific firm of that type uniformly at random. It is possible to extend this sampling mechanism by assuming that firms are drawn given type in a non uniform way. This type of model is known in the network literature as a Degree Corrected Stock Block Model (DC-SBM). Our model is not exactly a Stock Block Model but it is close to one. We still need to develop this part of the project further.