arXiv subjects

Katsumi Shimotsu

Publications and source records attributed to Katsumi Shimotsu.

9 recordsLinked to original sources

arXiv2026

Sequential Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity

Unobserved heterogeneity is empirically central in dynamic discrete choice models but computationally costly to incorporate: estimation requires repeatedly solving fixed-point equations for every latent type. We develop EM-NPL($q$), a unified framework combining the sequential pseudo-likelihood (NPL) and finite-mixture Expectation-Maximization (EM) algorithms, truncating the inner solver to $q$ iterations, and accommodating the Bellman, policy valuation, Euler, and Efficient Pseudo-Likelihood (EPL) equations, with step-by-step implementation guidance. For linear-in-parameters models estimated via the policy valuation or EPL equations, we establish truncation invariance: for any $q\geq 1$, EM-NPL($q$) is numerically identical to the fully converged EM-NPL estimator, so q affects computation but not statistical properties. We establish consistency, asymptotic normality, and local convergence. Truncation reduces runtime by up to 26\% for PV\_GMRES in single-agent simulations and 58\% for EPL in dynamic games. In a cola-demand application, ignoring unobserved heterogeneity understates own-price elasticities and soda-tax compensating variation by up to 85\% and 90\%.

econ.EM↗

arXiv2025

Semiparametric Identification of the Discount Factor and Payoff Function in Dynamic Discrete Choice Models

This paper investigates how the discount factor and payoff functions can be identified in stationary infinite-horizon dynamic discrete choice models. In single-agent models, we show that common nonparametric assumptions on per-period payoffs -- such as homogeneity of degree one, monotonicity, concavity, zero cross-differences, and complementarity -- provide identifying restrictions on the discount factor. These restrictions take the form of polynomial equalities and inequalities with degrees bounded by the cardinality of the state space. These restrictions also identify payoff functions under standard normalization at one action. In dynamic game models, we show that firm-specific discount factors can be identified using assumptions such as irrelevance of other firms' lagged actions, exchangeability, and the independence of adjustment costs from other firms' actions. Our results demonstrate that widely used nonparametric assumptions in economic analysis can provide substantial identifying power in dynamic structural models.

econ.EM↗

arXiv2024

Inference in Predictive Quantile Regressions

This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation consistent (HAC) t-statistic in terms of functionals of Ornstein-Uhlenbeck processes. We then propose a switching-fully modified (FM) predictive test for quantile predictability. The proposed test employs an FM style correction with a Bonferroni bound for the local-to-unity parameter when the predictor has a near unit root. It switches to a standard predictive quantile regression test with a slightly conservative critical value when the largest root of the predictor lies in the stationary range. Simulations indicate that the test has a reliable size in small samples and good power. We employ this new methodology to test the ability of three commonly employed, highly persistent and endogenous lagged valuation regressors - the dividend price ratio, earnings price ratio, and book-to-market ratio - to predict the median, shoulders, and tails of the stock return distribution.

econ.EM↗

arXiv2021

Identification of Regression Models with a Misclassified and Endogenous Binary Regressor

We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

econ.EM↗

arXiv2019

Testing the Order of Multivariate Normal Mixture Models

Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture models is a long-standing challenge even in the most important case of testing homogeneity. This paper develops likelihood-based tests of the null hypothesis of $M_0$ components against the alternative hypothesis of $M_0 + 1$ components for a general $M_0 \geq 1$. For heteroscedastic normal mixtures, we propose an EM test and derive the asymptotic distribution of the EM test statistic. For homoscedastic normal mixtures, we derive the asymptotic distribution of the likelihood ratio test statistic. We also derive the asymptotic distribution of the likelihood ratio test statistic and EM test statistic under local alternatives and show the validity of parametric bootstrap. The simulations show that the proposed test has good finite sample size and power properties.

math.ST↗

arXiv2018

Asymptotic Properties of the Maximum Likelihood Estimator in Regime Switching Econometric Models

Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the asymptotic distribution of the MLE has been unknown for models in which some elements of the transition probability matrix have the value of zero, as is commonly assumed in empirical applications with models with more than two regimes. This also includes models in which the regime-specific density depends on both the current and the lagged regimes such as the seminal model of Hamilton (1989) and switching ARCH model of Hamilton and Susmel (1994). This paper shows the asymptotic normality of the MLE and consistency of the asymptotic covariance matrix estimate of these models.

math.ST↗

arXiv2018

Testing the Number of Regimes in Markov Regime Switching Models

Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of $M_0$ regimes against the alternative hypothesis of $M_0 + 1$ regimes for any $M_0 \geq 1$ both under the null hypothesis and under local alternatives. We show that the contiguous alternatives converge to the null hypothesis at a rate of $n^{-1/8}$ in regime switching models with normal density. The asymptotic validity of the parametric bootstrap is also established.

econ.EM↗

arXiv2005

Exact local Whittle estimation of fractional integration

An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0,{1/4}) limit distribution for all values of d if the optimization covers an interval of width less than {9/2} and the initial value of the process is known.

math.ST↗

arXiv2004

Local Whittle estimation in nonstationary and unit root cases

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2} 1 and when the process has a polynomial trend of order α>{1/2}, the estimator is shown to be inconsistent and to converge in probability to unity.

math.ST↗