The Econometrics Journal Current Issue

17 Sep 2019

Reconsideration of a simple approach to quantile regression for panel data

Besstremyannaya G, Golovan S.

Summary
This note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate $\sqrt{nT}$, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator.
17 Sep 2019

Fragility of identification in panel binary response models

Forchini G, Jiang B.

Summary
The present paper considers a linear binary response model for panel data with random effects that differ across individuals but are constant over time, and it investigates the roles of the various assumptions that are used to establish conditions for identification. The paper also shows that even for this simple model, it is always possible—including in the logistic case—to find a distribution of the random effects given the exogenous variables, such that the slopes' parameters are arbitrarily different, but the joint distributions of the binary response variables are arbitrarily close.
01 Aug 2019

Estimating latent group structure in time-varying coefficient panel data models

Chen J.

Summary
This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.
11 Jul 2019

BLP-2LASSO for aggregate discrete choice models with rich covariates

Gillen B, Montero S, Moon H, et al.

Summary
We introduce the BLP-2LASSO model, which augments the classic BLP (Berry, Levinsohn, and Pakes, 1995) random-coefficients logit model to allow for data-driven selection among a high-dimensional set of control variables using the 'double-LASSO' procedure proposed by Belloni, Chernozhukov, and Hansen (2013). Economists often study consumers’ aggregate behaviour across markets choosing from a menu of differentiated products. In this analysis, local demographic characteristics can serve as controls for market-specific preference heterogeneity. Given rich demographic data, implementing these models requires specifying which variables to include in the analysis, an ad hoc process typically guided primarily by a researcher’s intuition. We propose a data-driven approach to estimate these models, applying penalized estimation algorithms from the recent literature in high-dimensional econometrics. Our application explores the effect of campaign spending on vote shares in data from Mexican elections.
06 Jun 2019

Quantile-based smooth transition value at risk estimation

Hubner S, Čížek P.

Summary
Value at risk models are concerned with the estimation of conditional quantiles of a time series. Formally, these quantities are a function of conditional volatility and the respective quantile of the innovation distribution. The former is often subject to asymmetric dynamic behaviour, e.g., with respect to past shocks. In this paper, we propose a model in which conditional quantiles follow a generalised autoregressive process governed by two parameter regimes with their weights determined by a smooth transition function. We develop a two-step estimation procedure based on a sieve estimator, approximating conditional volatility by using composite quantile regression, which is then used in the generalised autoregressive conditional quantile estimation. We show that the estimator is consistent and asymptotically normal, and we complement the results with a simulation study. In our empirical application, we consider daily returns of the German equity index (DAX) and the USD/GBP exchange rate. Although only the latter follows a two-regime model, we find that our model performs well in terms of out-of-sample prediction in both cases.
22 May 2019

A guided nonparametric goodness-of-fit test with application to income distributions

Wen K, Wu X.

Summary
We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of the hypothesized density. Our test requires no such devices and possesses enhanced powers against alternative densities because the guided density estimator is free of the typical nonparametric bias under the null hypothesis and attains bias reduction when the underlying density is in a broad nonparametric neighborhood of the hypothesized density. Here, we establish the statistical properties of our test and use Monte Carlo simulations to demonstrate its finite sample performance. We use this test to examine the goodness-of-fit of normal mixtures to the distributions of log income of U.S. states. Although normality is rejected decisively, our results suggest that normal mixtures with two or three components suffice for all but one state.