Jean-Marc Robin

Estimation in Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems

Empirical demand systems that do not impose unreasonable restrictions on preferences are typically non-linear. We show, however, that all popular systems possess the property of conditional linearity. A computationally attractive iterated linear least squares estimator (ILLE) is proposed for large non-linear simultaneous equation systems which are conditionally linear in unknown parameters. The estimator is shown to be consistent and its asymptotic efficiency properties are derived. An application is given for a 22-commodity quadratic demand system using household-level data from a time series of repeated cross-sections.

Tests of Rank

This paper considers tests for the rank of a matrix for which a root-T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimators asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.

Frequency of purchase and the estimation of demand systems

In this paper we consider a joint model for frequency of purchase and consumer demand. We discuss sufficient identifying assumptions for the estimation of consumer demands from survey data for the general case of nonlinear (or linear) Engel curves. Moreover we show that in many cases the actual number of purchases is necessary in order to obtain consistent parameter estimates for the demand system. The empirical application relates to the estimation of a demand system for French foodstuffs.

The Demand for Food Products: An Analysis of Interpurchase Times and Purchased Quantities

In this paper we study household purchase behaviour of storable food products. An inventory model is developed in which the household chooses an optimal stock level of the product. Storage of the product is costly, there is a fixed cost per purchase occasion, and the market price is sometimes discounted because of price promotions. We show that the optimal purchase policy is an s, S policy. The model is used to derive predictions on the correlations between interpurchase times and purchased quantities on the one hand, and prices on the other. These predictions are empirically verified using consumer panel data.

Microeconometric search-matching models and matched employer-employee data

The recent advent of matched employer-employee data as part of the labor market scholar’s toolbox has allowed a great deal of progress in our understanding of individual labor earnings. A growing number of empirical analyzes of available matched employer-employee data sets now combine with the already voluminous literature on empirical wage equations based on individual or household survey data to draw an ever richer picture of wage dispersion, individual wage dynamics, and the productivity-wage relationship. In this chapter we tour the empirical wage equations literature along these three lines and make a case that viewing it through the lens of structural job search models can help clarify and unify some of its recurring findings. Among other things, we emphasize and quantify the role of matching frictions in explaining the share of “residual” wage dispersion that is left unexplained by the reduced-form approach. Secondly, we quantitatively assess the importance of labor market competition between employers relative to non-competitive wage formation mechanisms (namely, wage bargaining) as a theoretical underpinning of the wage-productivity relationship. Thirdly, we show how search frictions combined with a theoretically founded wage formation rule based on renegotiation by mutual consent can account for the widely documented dynamic persistence of individual wages. We conclude with a list of questions that are open to further research.

The macro-dynamics of sorting between workers and firms

We develop an equilibrium model of on-the-job search with ex ante heterogeneous workers and firms, aggregate uncertainty, and vacancy creation. The model produces rich dynamics in which the distributions of unemployed workers, vacancies, and worker-firm matches evolve stochastically over time. We prove that the surplus function, which fully characterizes the match value and the mobility decision of workers, does not depend on these distributions. This result means the model is tractable and can be estimated. We illustrate the quantitative implications of the model by fitting to US aggregate labor market data from 1951-2012. The model has rich implications for the cyclical dynamics of the distribution of skills of the unemployed, the distribution of types of vacancies posted, and sorting between heterogeneous workers and firms.

Estimating multivariate latent-structure models

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same non-orthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this simultaneous-diagonalization problem. Simple algorithms are available for computation. Asymptotic theory is derived for this joint approximate-diagonalization estimator.

Modeling Individual Earnings Trajectories Using Copulas: France, 1990-2002

Abstract We use copulas to construct a flexible dynamic model of individual earnings allowing for both observed and unobserved heterogeneity. We show that the dynamics of earnings ranks is best modeled using Placketts (1965) parametric copula. We use discrete mixtures to model unobserved heterogeneity. For estimation, we develop a sequential EM algorithm, which is shown to be root-N consistent and asymptotically normal. This algorithm is simple to implement and fast enough to converge for bootstrapping to be a recommendable procedure to estimate standard errors. We estimate this model using the 1990–2002 French Labour Force Survey data.

Dynamic stochastic dominance in bandit decision problems

The aim of this paper is to study the monotonicity properties with respect to the probability distribution of the state processes, of optimal decisions in bandit decision problems. Orderings of dynamic discrete projects are provided by extending the notion of stochastic dominance to stochastic processes.

Consumption Dynamics and Panel Data: A Survey

Since the permanent income hypothesis was posed by Friedman [1957] and by Modigliani and Brumberg [1954] stating that consumption is a function of the flow of income (“permanent income”) that, if sustained across one’s life time would just compensate expected earnings and wealth, the question of the sensitivity of consumption to current income has focussed the attention of three decades of econometricians. Yet, until the end of the seventies the analysts always came up against the problem that permanent income is unobservable. Then Hall [1978] showed that by incorporating rational expectations a household maximizing expected intertemporal utility subject to the budget constraint behaves such that the marginal utility of current consumption next year is expected to be proportional to the marginal utility this year (see also Sargent’s [1978] contribution). He also found empirical evidence (on macro data) which suggested that lagged real disposable income and other variables dated t — 1 or earlier had little explanatory power on present (aggregate) consumption so long as lagged consumption was a regressor.