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Contact Information
William H. Sewell Social Science Building
Office 7428
1180 Observatory Drive
Madison, WI 53706-1393
Phone: 608-265-6594
Email: jfreyberger@ssc.wisc.edu
Field of Specialization: Econometrics
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Curriculum Vitae
Working papers
"Nonparametric panel data models with interactive fixed effects"
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This paper studies nonparametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed.
I focus on models where the unobservables have a factor structure and enter an unknown structural function nonadditively.
A key distinguishing feature of the setup is to allow for the various unobserved individual effects to impact outcomes differently in different time periods.
When individual effects represent unobserved ability, this means that the returns to ability may change over time. Moreover, the models allow for heterogeneous marginal effects of the covariates on the outcome.
The first set of results in the paper provides sufficient conditions for point identification when the outcomes are continuously distributed. These results lead to identification of marginal and average effects.
I provide further point identification conditions for discrete outcomes and a dynamic model with lagged dependent variables as regressors.
Using the identification conditions, I present a nonparametric sieve maximum likelihood estimator and study its large sample properties.
In addition, I analyze flexible semiparametric and parametric versions of the model and characterize the asymptotic distribution of these estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples.
Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.
"Asymptotic theory for differentiated products demand models with many markets"
CeMMAP working paper CWP19/12, resubmitted
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This paper develops asymptotic theory for estimated parameters in differentiated product demand systems with a fixed number of products, as the number of markets T increases, taking into account that the market shares are approximated by Monte Carlo integration.
It is shown that the estimated parameters are root-T consistent and asymptotically normal as long as the number of simulations R grows fast enough relative to T.
Monte Carlo integration induces both additional variance as well additional bias terms in the asymptotic expansion of the estimator. If R does not increase as fast as T, the leading bias term dominates the leading variance term and the asymptotic distribution might not be centered at 0.
This paper suggests methods to eliminate the leading bias term from the asymptotic expansion. Furthermore, an adjustment to the asymptotic variance is proposed that takes the leading variance term into account. Monte Carlo results show that these adjustments, which are easy to compute, should be used in applications to avoid severe undercoverage caused by the simulation error.
"Identification and shape restrictions in nonparametric instrumental variables estimation"
with Joel Horowitz, CeMMAP working paper CWP15/12, submitted
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This paper is concerned with inference about an unidentified linear functional, L(g), where the function g satisfies the relation Y = g(X) + U; E(U | W) = 0. In this relation, Y is the dependent variable, X is a possibly endogenous explanatory variable, W is an instrument for X, and U is an unobserved random variable.
The data are an independent random sample of (Y,X,W). In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, neither g nor L(g) is nonparametrically identified. Indeed, L(g) can have any value in (-∞,∞).
In applied research, this problem is typically overcome and point identification is achieved by assuming that g is a linear function of X. However, the assumption of linearity is arbitrary. It is untestable if W is binary, as is the case in many applications. This paper explores the use of shape restrictions, such as monotonicity or convexity, for achieving interval identification of L(g).
Economic theory often provides such shape restrictions. This paper shows that they restrict L(g) to an interval whose upper and lower bounds can be obtained by solving linear programming problems. Inference about the identified interval and the functional L(g) can be carried out by using by using the bootstrap.
An empirical application illustrates the usefulness of shape restrictions for carrying out nonparametric inference about L(g).
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