#### Working papers

##### Kao, C., Kim, M. S., and Zhang, Z. (2019), “Mahalanobis Metric Based Clustering for Fixed Effects Model,” Accepted by Sankhya, Series B. (Job Market Paper)

##### Abstract

This paper improves the estimation procedure in the linear panel data model with time-varying group fixed effects in Bonhomme and Manresa (2015). We introduce a Mahalanobis distance-based K-means algorithm (KMM) which takes serial correlation and heteroscedasticity into a count. It will significantly improve the accuracy of estimation in the case of ellipse-shaped data. The Euclidean distance failed in such a situation. Also, we find that the estimator of the common parameter may not converge to the true value during the iteration procedure in Bonhomme and Manresa (2015) since the true value is not the best choice concerning clustering. We compute the infeasible optimal option of beta given the specific structure. Lastly, we provide our empirical method to amplify the group signal and hence improve the estimation of group membership and then the estimator of the common parameter.

##### Kao, C. and Zhang, Z. (2019), “Is the recursive preference asset pricing model more flexible? A piece of evidence,” Manuscript.

##### Abstract

This paper investigates why there exists considerable variation in estimates of the coefficient of relative risk aversion (CRRA) and the elasticity of intertemporal substitution (EIS) in the consumption-based asset pricing model with Epstein and Zin (1989) preferences. Using the estimation method developed by Chen et al. (2013), we show the Epstein and Zin (1989) structure collapses to the time-separable structure. This result is consistent with the argument in Kocherlakota (1990) saying that the recursive preference-based utility function does not have more explanatory power than the time-separable one. We also show the choice of parameters might lead to ”ill-behaved” conditional moment, which might cause either GMM method to get ”stuck”, or the estimates do not move much from the starting points. Lastly, our result is robust to the choice of instruments for computing the conditional moment function in the GMM method.

##### Zhang, Z. (2019), “Nonlinear models with latent grouping and grouped fixed effect,” Manuscript.

##### Abstract

We extend the linear panel data model with grouped fixed effect and unknown group membership in Bonhomme and Manresa (2015) to nonlinear. Unlike Bonhomme et al. (2017, Working Paper), we assume the unobservable heterogeneities are from the mixture of a certain number of group-specific distributions. Our method provides information on higher moments than k-means which only offer the first moment. We also give the researcher an option to relax the restrictions on the group-specific distribution and leave it to be estimated nonparametrically, and provide a guide on selecting bandwidth. We show that the coefficient of interest covariate in the grouping object or ”moment” in Bonhomme et al. (2017, Working Paper) is a ”nuisance” concerning grouping. This implies, in the grouping step, we can choose some particular value for the latent common parameter just for grouping purpose. Lastly, we study the distribution of unobservable heterogeneities given different values of common parameter and T through Monte Carlo simulation.