52 research outputs found

    Misspecified Markov Switching Model

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    I characterize the local power of an optimal test for a Markov Switching model under generalized alternatives. The result shows that the test still has power for the model with endogenous stochastic parameters unless they are orthogonal to the score functions.

    The Lasso for High-Dimensional Regression with a Possible Change-Point

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    We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the 1\ell_1 estimation loss for regression coefficients. Since the Lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a nearly n1n^{-1} factor even when the number of regressors can be much larger than the sample size (nn). We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data

    Testing for threshold effects in regression models

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    In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online.

    Factor-Driven Two-Regime Regression

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    We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies

    2014-2 Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks

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    We consider a general framework to study the evolution of wage and earnings residuals that incorporates features highlighted by two influential but distinct literatures in economics: (i) unobserved skills with changing non-linear pricing functions and (ii) idiosyncratic shocks that follow a rich stochastic process. Specifically, we consider residuals for individual i in period t of the form: Wi,t = ut(Øi) + ei,t, where Øi represents an unobserved permanent ability or skill, ut(.) a pricing function for unobserved skills, and ei,t idiosyncratic shocks with both permanent and transitory components. We first provide nonparametric identification conditions for the distribution of unobserved skills, all ut(.) skill pricing functions, and (nearly) all distributions for both permanent and MA(q) transitory shocks. We then discuss identification and estimation using a moment-based approach, restricting ut(.) to be polynomial functions. Using data on log earnings for men ages 30-59 in the PSID, we estimate the evolution of unobserved skill pricing functions and the distributions of unobserved skills, transitory, and permanent shocks from 1970 to 2008. We highlight five main findings: (i) The returns to unobserved skill rose over the 1970s and early 1980s, fell over the late 1980s and early 1990s, and then remained quite stable through the end of our sample period. Since the mid-1990s, we observe some evidence of polarization: the returns to unobserved skill declined at the bottom of the distribution while they remained relatively constant over the top half. (ii) The variance of unobserved skill changed very little across most cohorts in our sample (those born between 1925 and 1955). (iii) The variance of transitory shocks jumped up considerably in the early 1980s but shows little long-run trend otherwise over the more than thirty year period we study. (iv) The variance of permanent shocks declined very slightly over the 1970s, then rose systematically through the end of our sample by 15 to 20 log points. The increase in this variance over the 1980s and 1990s was strongest for workers with low unobserved ability. (v) In most years, the distribution of ut(Ø) is positively skewed, while the distributions of permanent and (especially) transitory shocks are negatively skewed

    2017-26 Wage Dynamics and Returns to Unobserved Skill

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    Economists disagree about the factors driving the substantial increase in residual wage inequality in the U.S. over the past few decades. We identify and estimate a general model of log wage residuals that incorporates: (i) changing returns to unobserved skills, (ii) a changing distribution of unobserved skills, and (iii) changing volatility in wages due to factors unrelated to skills. Using data from the Panel Study of Income Dynamics, we estimate that the returns to unobserved skills have declined by as much as 50% since the mid-1980s despite a sizable increase in residual inequality. Instead, the variance of skills rose over this period due to increasing variability in life cycle skill growth. Finally, we develop an assignment model of the labor market and show that both demand and supply factors contributed to the downward trend in the returns to skills over time, with demand factors dominating for non-college-educated men

    csa2sls: A complete subset approach for many instruments using Stata

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    We develop a Stata command csa2sls\texttt{csa2sls} that implements the complete subset averaging two-stage least squares (CSA2SLS) estimator in Lee and Shin (2021). The CSA2SLS estimator is an alternative to the two-stage least squares estimator that remedies the bias issue caused by many correlated instruments. We conduct Monte Carlo simulations and confirm that the CSA2SLS estimator reduces both the mean squared error and the estimation bias substantially when instruments are correlated. We illustrate the usage of csa2sls\texttt{csa2sls} in Stata by an empirical application.Comment: 10 pages, 1 figure, under review by the Stata Journa
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