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on Econometrics |
| By: | Sloczynski, Tymon (Brandeis University); Uysal, Derya (LMU Munich); Wooldridge, Jeffrey M. (Michigan State University) |
| Abstract: | In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie (2003)'s kappa theorem. Our framework presumes a binary endogenous explanatory variable ("treatment") and a binary instrumental variable, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which we show is weight normalized, is likely to dominate the others in many contexts. A notable exception is in settings with one-sided noncompliance, where certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. We use a simulation study and three empirical applications to illustrate our findings. In applications to causal effects of college education using the college proximity instrument (Card, 1995) and causal effects of childbearing using the sibling sex composition instrument (Angrist and Evans, 1998), the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both. Overall, our results suggest that (i) the relative performance of different kappa weighting estimators varies with features of the data-generating process; and that (ii) the normalized version of Tan (2006)'s estimator may be an attractive alternative in many contexts. Applied researchers with access to a binary instrumental variable should also consider covariate balancing or doubly robust estimators of the LATE. |
| Keywords: | instrumental variables, local average treatment effects, one-sided noncompliance, weighting |
| JEL: | C21 C26 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15241&r= |
| By: | Christis Katsouris |
| Abstract: | We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate slower than the sample size n. Then, extending the framework proposed by Phillips and Magdalinos (2007), we consider the limit theory for the near-stationary and the near-explosive cases when the model is estimated with a conditional quantile specification function and model parameters are quantile-dependent. Additionally, a Bahadur-type representation and limiting distributions based on the M-estimators of the model parameters are derived. Specifically, we show that the serial correlation coefficient converges in distribution to a ratio of two independent random variables. Monte Carlo simulations illustrate the finite-sample performance of the estimation procedure under investigation. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.02073&r= |
| By: | Ali Mehrabani (Southern Illinois University); Aman Ullah (Department of Economics, University of California Riverside) |
| Abstract: | Mukhtar M. Ali has made many innovative and influential contributions in different areas of economics, finance, econometrics, and statistics. His contributions include developing econometric models to examine the determinants of the demand for casino gaming, investigating the approximate and exact distribution and moments of various econometric estimators and test statistics, and studying the statistical properties of time series based statistics under stationary and non-stationary processes (for example, see Ali and Thalheimer (1983, 2008), Ali (1977, 1979, 1984, 1989), Ali and Sharma (1993, 1996), Tsui and Ali (1992, 2002), Ali and Giaccotto (1982a, 1982b, 1984), Ali and Tiao (1971), and Ali and Silver (1985, 1989), among others). All of these have made significant impact on the profession and have been instrumental in advancing further research in statistics and econometrics. In this paper, we study the approximate rst two moments of two weighted average estimators of the slope parameters in linear panel data models. The weighted average estimators shrink a generalized least squares estimator towards a restricted generalized least squares estimator, where the restrictions represent possible parameter specifications. The averaging weight is inversely proportional to a weighted quadratic loss function. The approximate bias and second moment matrix of the weighted average estimators using the large-sample approximations are provided. We give the conditions under which the weighted average estimators dominate the generalized least squares estimator on the basis of their mean squared errors. |
| Keywords: | Asymptotic approximations; xed-e ects; panel data; random-e ects; Stein-like shrinkage estimator. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202209&r= |
| By: | Qihui Chen |
| Abstract: | This paper develops a simple sieve estimation for conditional quantile factor models. We establish large-$N$-asymptotic properties of the estimators without requiring large $T$. We also provide a weighted bootstrap for estimating the distributions of the estimators. The methods allow us not only to estimate conditional factor structures of distributions of asset returns utilizing characteristics, but also to conduct robust inference in conditional factor models, which enables us to analyze the cross section of asset returns with heavy tails. We apply the methods to analyze the cross section of individual US stock returns. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.00801&r= |
| By: | Xavier D'Haultfoeuille; Christophe Gaillac; Arnaud Maurel |
| Abstract: | We consider the identification of and inference on a partially linear model, when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics. Using recent tools from optimal transport theory, we derive a constructive characterization of the sharp identified set. We then build on this result and develop a novel inference method that exploits the specific geometric properties of the identified set. Our method exhibits good performances in finite samples, while remaining very tractable. Finally, we apply our methodology to study intergenerational income mobility over the period 1850-1930 in the United States. Our method allows to relax the exclusion restrictions used in earlier work while delivering confidence regions that are informative. |
| JEL: | C14 C21 J62 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29953&r= |
| By: | Federico Bugni; Ivan Canay; Azeem Shaikh; Max Tabord-Meehan |
| Abstract: | This paper considers the problem of inference in cluster randomized experiments when cluster sizes are non-ignorable. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the cluster; by non-ignorable cluster sizes we mean that "large" clusters and "small" clusters may be heterogeneous, and, in particular, the effects of the treatment may vary across clusters of differing sizes. In order to permit this sort of flexibility, we consider a sampling framework in which cluster sizes themselves are random. In this way, our analysis departs from earlier analyses of cluster randomized experiments in which cluster sizes are treated as non-random. We distinguish between two different parameters of interest: the equally-weighted cluster-level average treatment effect, and the size-weighted cluster-level average treatment effect. For each parameter, we provide methods for inference in an asymptotic framework where the number of clusters tends to infinity and treatment is assigned using simple random sampling. We additionally permit the experimenter to sample only a subset of the units within each cluster rather than the entire cluster and demonstrate the implications of such sampling for some commonly used estimators. A small simulation study shows the practical relevance of our theoretical results. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.08356&r= |
| By: | Wüthrich, Kaspar; Zhu, Ying |
| Abstract: | Abstract We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can occur even when the coeffcients are sparse and the sample size is large and larger than the number of controls. Therefore, relying on the existing asymptotic inference theory can be problematic in empirical applications. We compare the Lasso-based inference methods to modern highdimensional OLS-based methods and provide practical guidance. |
| Keywords: | Economics, Applied Economics, Econometrics |
| Date: | 2021–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt1gp6g9gm&r= |
| By: | Clément de Chaisemartin |
| Abstract: | I consider estimation of the average treatment effect (ATE), in a population composed of $G$ groups, when one has unbiased and uncorrelated estimators of each group's conditional average treatment effect (CATE). These conditions are met in stratified randomized experiments. I assume that the outcome is homoscedastic, and that each CATE is bounded in absolute value by B standard deviations of the outcome, for some known B. I derive, across all linear combinations of the CATEs' estimators, the estimator of the ATE with the lowest worst-case mean-squared error. This minimax-linear estimator assigns a weight equal to group g's share in the population to the most precisely estimated CATEs, and a weight proportional to one over the estimator's variance to the least precisely estimated CATEs. I also derive the minimax-linear estimator when the CATEs' estimators are positively correlated, a condition that may be met by differences-in-differences estimators in staggered adoption designs. |
| JEL: | C21 C23 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29879&r= |
| By: | Myungkou Shin |
| Abstract: | Treatment effect estimation strategies in the event-study setup, namely a panel data with variation in treatment timing, often use the parallel trend assumption that assumes mean independence across different treatment timings. In this paper, I relax the parallel trend assumption by including a latent type variable and develop a conditional two-way fixed-effects model. With finite support assumption on the latent type variable, I show that an extremum classifier consistently estimates the type assignment. Firstly, I solve the endogeneity problem of the selection into treatment by conditioning on the latent type, through which the treatment timing is correlated with the outcome. Secondly, as the type assignment is explicitly estimated, further heterogeneity than the usual unit fixed-effects across units can be documented; treatment is allowed to affect units of different types differently and the variation in treatment effect is documented jointly with the variation in untreated outcome. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.02346&r= |
| By: | Philippe Casgrain; Martin Larsson; Johanna Ziegel |
| Abstract: | We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal building blocks for constructing nonnegative supermartingales under the null. This in turn yields anytime valid tests via Ville's inequality. Using regret bounds from Online Convex Optimization, we obtain rigorous guarantees on the asymptotic power of the tests for a wide range of alternative hypotheses. Our results allow for bounded and unbounded data distributions, assuming that a sub-$\psi$ tail bound is satisfied. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.05680&r= |
| By: | Li, Chenxing |
| Abstract: | This paper proposes a new Bayesian semiparametric model that combines a multivariate GARCH (MGARCH) component and an infinite hidden Markov model. The new model nonparametrically approximates both the shape of unknown returns distributions and their short-term evolution. It also captures the smooth trend of the second moment with the MGARCH component and the potential skewness, kurtosis, and volatility roughness with the Bayesian nonparametric component. The results show that this more-sophisticated econometric model not only has better out-of-sample density forecasts than benchmark models, but also provides positive economic gains for a CRRA investor at different risk-aversion levels when transaction costs are assumed. After considering the transaction costs, the proposed model dominates all benchmark models/portfolios when No Short-Selling or No Margin-Trading restriction is imposed. |
| Keywords: | Multivariate GARCH; IHMM; Bayesian nonparametric; Portfolio allocation; Transaction costs |
| JEL: | C11 C14 C32 C34 C53 C58 |
| Date: | 2022–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112792&r= |
| By: | Ji Hyung Lee; Yuya Sasaki; Alexis Akira Toda; Yulong Wang |
| Abstract: | Existing nonparametric density estimators typically require individual-level data. For administrative data, individual-level information is difficult to access, but tabulated summaries are often publicly available. In this light, we propose a novel method of maximum entropy density estimation from tabulated summary data. We establish the strong uniform consistency property for this nonparametric estimator. Applying the proposed method to the tabulated summary data of the U.S. tax returns, we estimate the national income distribution. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.05480&r= |
| By: | Alfred Galichon; Bernard Salani\'e |
| Abstract: | In this paper we propose two simple methods to estimate models of matching with transferable and separable utility introduced in Galichon and Salani\'e (2022). The first method is a minimum distance estimator that relies on the generalized entropy of matching. The second relies on a reformulation of the more special but popular Choo and Siow (2006) model; it uses generalized linear models (GLMs) with two-way fixed effects. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.00362&r= |
| By: | Zexuan Yin; Paolo Barucca |
| Abstract: | We propose Variational Heteroscedastic Volatility Model (VHVM) -- an end-to-end neural network architecture capable of modelling heteroscedastic behaviour in multivariate financial time series. VHVM leverages recent advances in several areas of deep learning, namely sequential modelling and representation learning, to model complex temporal dynamics between different asset returns. At its core, VHVM consists of a variational autoencoder to capture relationships between assets, and a recurrent neural network to model the time-evolution of these dependencies. The outputs of VHVM are time-varying conditional volatilities in the form of covariance matrices. We demonstrate the effectiveness of VHVM against existing methods such as Generalised AutoRegressive Conditional Heteroscedasticity (GARCH) and Stochastic Volatility (SV) models on a wide range of multivariate foreign currency (FX) datasets. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.05806&r= |