Job Market Paper
This paper proposes a random coefficient panel model where the regressors can depend on the time-varying random coefficients in each period, a critical feature in many economic applications including production function estimation. The random coefficients are modeled as unknown functions of a fixed effect of arbitrary dimension and a random shock, thus incorporating rich forms of unobserved heterogeneity. A sufficiency argument is used to control for the fixed effect, which enables one to construct a feasible control function for the random shock and subsequently identify the moments of the random coefficients via a sequential argument. A three-step estimator is proposed and a new asymptotic normality result is proved. Simulation results show that the method can accurately estimate both the mean and the dispersion of the random coefficients. The estimation procedure is applied to panel data for Chinese manufacturing firms and three main findings emerge. First, larger capital, but smaller labor, elasticities than previous methods are obtained, which is consistent with the literature on factor income shares. Second, there is substantial variation in the output elasticities across firms and periods. Third, the dispersion of the random intercept among firms is larger than with traditional methods, caused by a negative correlation between the random intercept and output elasticities.
This paper proposes a simple yet robust method for semiparametric identification and estimation of panel multinomial choice models, where we allow infinite-dimensional fixed effects to enter consumer utilities in an additively nonseparable way, thus incorporating rich forms of unobserved heterogeneity. Such heterogeneity may take the form of, for example, brand loyalty or responsiveness to subtle flavor and packaging designs, which are hard to quantify but affect consumer choices in complex ways. Our identification strategy exploits the standard notion of multivariate monotonicity in its contrapositive form, which provides powerful leverage for converting observable events into identifying restrictions on unknown parameters. We provide consistent set (or point) estimators, together with a computational algorithm that adopts a machine learning algorithm and a novel minimization procedure on the spherical-coordinate space. We demonstrate the practical advantages of our method with simulations and an empirical example using the Nielsen data. The results show that our procedure produces estimates that conform well with economic intuition. For example, we find that special in-store displays boost sales not only through a direct promotion effect but also through the attenuation of consumers’ price sensitivity.
Logical Differencing in Network Formation Models under Non-Transferable Utilities, with Wayne Yuan Gao and Sheng Xu
R&R, Journal of Econometrics
This paper considers a semiparametric model of dyadic network formation under nontransferable utilities (NTU). NTU frequently arises in social interactions that require bilateral consent. The formation of informal risk-sharing networks among villagers in developing areas, which naturally requires mutual acceptance, is one particularly relevant example of considerable academic and policy interest. However, NTU inherently induces additive non-separability, which makes identification challenging. We show how to identify the parameters of interest without additive separability when networks form under NTU, using a novel method we call “logical differencing.” The key idea is to construct events involving the intersection of two mutually exclusive restrictions on the unobserved individual fixed effects based on multivariate monotonicity to cancel them out. We provide a consistent estimator and analyze its performance via simulation, and apply our method to the Nyakatoke risk-sharing networks.
Work in Progress
Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model, with Donald Andrews
Autoregressive models — stationary or nonstationary — are workhorse models in econometric time series. This paper considers nonparametric estimation and inference in autoregressive (AR) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit root behavior) in other periods, and smooth transitions between the two. We allow for all parameters of the model to be time-varying, not just the AR parameter. The estimation of the AR parameter at any time point is based on the local LS regression method, where the relevant initial condition is endogenous. We introduce a new method to eliminate the impact of the endogenous initial condition on the asymptotics, and obtain limit distributions after proper normalization for the AR parameter when it is unit root, local-to-unity, and stationary/stationary-like. Asymptotic properties for t-statistics are also established. These are used to construct confidence intervals for the AR parameter at any specified points in time. These confidence intervals have correct uniform asymptotic coverage probabilities regardless of the time-varying stationarity/nonstationary behavior of the observations.