Fan Zhuo 
Ph.D. Candidate in Economics
Boston University  

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Likelihood Ratio Based Tests for Markov Regime Switching (joint with Zhongjun Qu)

Markov regime switching models are widely considered in economics and finance. Although there have been persistent interests (see e.g., Hansen, 1992, Garcia, 1998, and Cho and White, 2007), the asymptotic distributions of likelihood ratio based tests have remained unknown. This paper considers such tests and establishes their asymptotic distributions in the context of nonlinear models allowing for multiple switching parameters. The analysis simultaneously addresses three difficulties: (i) some nuisance parameters are unidentified under the null hypothesis, (ii) the null hypothesis yields a local optimum, and (iii) conditional regime probabilities follow stochastic processes that can only be represented recursively. Addressing these issues permits substantial power gains in empirically relevant situations. Besides obtaining the tests’ asymptotic distributions, this paper also obtains four sets of results that can be of independent interest: (1) a characterization of conditional regime probabilities and their high order derivatives with respect to the model’s parameters, (2) a high order approximation to the log likelihood ratio permitting multiple switching parameters, (3) a refinement to the asymptotic distribution, and (4) a unified algorithm for simulating the critical values. For models that are linear under the null hypothesis, the elements needed for the algorithm can all be computed analytically. The above results also shed light on why some bootstrap procedures can be inconsistent and why standard information criteria, such as the Bayesian information criterion (BIC), can be sensitive to the hypothesis and the model’s structure. When applied to the US quarterly real GDP growth rates, the methods suggest fairly strong evidence favoring the regime switching specification, which holds consistently over a range of sample periods.

Testing for Regime Switching in State Space Models

This paper develops a modified likelihood ratio (MLR) test for detecting regime switching in state space models. I apply the filtering algorithm introduced in Gordon and Smith (1988) to construct the modified likelihood function under the alternative hypothesis of two regimes and extend the analysis in Qu and Zhuo (2015) to establish the asymptotic distribution of the MLR statistic under the null. I also illustrate the test with an application to U.S. unemployment rates. This paper is the first to develop a test that is based on the likelihood principle for detecting regime switching in state space models.

Estimating a Search and Matching Model with Sticky Price and Staggered Wage Negotiation

This paper estimates a search and matching model of the aggregate labor market with sticky price and staggered wage negotiation. It starts with a partial equilibrium search and matching model and expands into a general equilibrium model with sticky prices and staggered wages. I study the quantitative implications of the model and in particular the roles of sticky price and staggered wage negotiation. The results show that (1) the price stickiness and staggered wages are quantitatively important for the search and matching model of the aggregate labor market; (2) a relatively high outside alternative of the workers is needed to match the data; and (3) the workers have relatively lower bargaining power than the firms, which contrasts with the assumption in the calibration literature that workers and firms share equally the surplus generated from their employment relationship.

Economic Shocks and Savings Behavior by the Rural Poor (Master thesis), Economics Bulletin

Using data from 587 marginalized cooperative member households in rural Mexico, this paper examines how household formal financial savings fluctuates with economic shocks and other relevant variables. Regression results show that negative shocks, income, wealth, formal credit, distance from a bank branch, percent of non-working members in a household, and education have a significant influence on formal financial savings. Results from quantile regression show that the impact of negative shocks on formal savings is only statistically significant in households with a high propensity to save. These precautionary savings households not only save more, but are inclined to withdraw savings to alleviate potentially adverse personal income trends associated with the shocks.

Works in Progress:

Falling Behind or Catching Up - Structural Break Story of Africa's Convergence (joint with Aparna Dutta)



The MIT Press: Solutions Manual to Accompany Economic Dynamics in Discrete Time (joint with Yue Jiang and Jianjun Miao)