Zhipeng Liao

  Assistant Professor of Economics, UCLA

 


 

   Curriculum Vitae

 

   Research Statement

 

 

Field of Concentration:

Econometric Theory and Applied Econometrics

 

 

 

 

 

 

Research Interest:

Model Selection and Model Averaging, Inference of Semi/Nonparametric Models, Modelling and Inference of Nonstationary Time Series

 

Office:

8379 Bunche Hall, UCLA

 

Email:

zhipeng.liao[at]econ.ucla.edu

 

Phone:

(310) 794-5427

 

Fax:

(310) 825-9528

 

Mailing Address:

 

 

Department of Economics
8283 Bunche Hall
Mail Stop: 147703

Los Angeles, CA 90095


  Working Papers

 

1.      "Nonparametric Series Inference for Dependent Data with an Application to the Search and Matching Model", (with Jia Li).

 

    This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We show that sample averages of serially dependent random vectors with divergent dimensions can be approximated by Gaussian random vectors. This approximation theory is first proved for heterogenous martingale difference arrays and then extended to general mixingales through martingale approximation, readily accommodating a majority of applications in applied econometrics. We use these results to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. The validity of high-dimensional heteroskedasticity and autocorrelation consistent (HAC) estimators is established for making feasible inference. The proposed method is broadly useful for forecast evaluation, empirical microstructure, dynamic stochastic equilibrium models and inference problems based on intersection bounds. We demonstrate the empirical relevance of the proposed method by studying the Mortensen-Pissarides search and matching model for equilibrium unemployment, and shed new light on the unemployment volatility puzzle from an econometric perspective.

 

2.      "Contrarian Opinion and Its Predictability: Application to Exchange Rates", (with Hyo Sang Kim, Young Ju Kim and Aaron Tornell).

 

    Many asset prices tend to follow trends that often last several quarters. Although these trends can be identified in-sample, they are difficult to predict out-of-sample. Associated with these trends is the puzzling contrarian pattern observed in market position data: at the end of an uptrend the average speculator tends to be overly optimistic, while she is overly pessimistic at the end of a downtrend. In this paper, we rationalize contrarianism in asset markets. We use the foreign exchange market both in our theoretical model and in the empirical application. We show that if only a few speculators are informed, exchange rates may follow bubbly trends in response to news, and the contrarian pattern necessarily arises in such trending equilibria. Informed speculators have no incentives to arbitrage away the gap between the exchange rate and its fundamental value until a trend reversal becomes nigh. When informed speculators exit, trends continue because uninformed speculators trade more enthusiastically with hedgers, although trend reversals may approach shortly. Since the Commitment-of-Traders position data we use is an unknown mixture of informed and uniformed speculators’ positions, we estimate the latent entry and exit decisions of informed speculators using a hidden Markov-switching model, which then allow us to construct forecasts of trend reversals. Our model’s signals are related to major monetary shocks in Japan and the Eurozone, which shows that our forecasts are not mere statistical objects. We also propose a new forecast-accuracy test which weights directional-forecasts by subsequent exchange rate changes.

 

3.      "Estimation and Inference of Semiparametric Models Using Data from Several Sources", (with Moshe Buchinsky and Fanghua Li).

 

    There are many cases in empirical studies where data needed to analyze a particular phenomenon is not available in one data set. Typically, this hampers the possibility of meaningful empirical research. One way of addressing this problem is first imputing the variables missing from the main data set using other sources of data, and then employing the imputed sample to estimate the empirical model. Although data imputation is widely used in practice, its validity relies heavily on the forms of the models. In the nonlinear models, the estimators based on imputed data are usually inconsistent. This paper examines estimation and inference of a class of nonlinear semiparametric models where the regressors are in different data sets, but each data set contains a same set of instrumental variables. We propose a series minimum distance (SMD) estimation of the model and establish the asymptotic normality of the SMD estimators. Consistent estimators of the variances of the SMD estimators are also provided. These results are useful to get consistent estimators of the model parameters and perform hypothesis tests, and therefore to conduct meaningful empirical research where no complete data sets are available.

 

4.      "On Cross-Validated Lasso", (with Denis Chetverikov and Victor Chernozhukov).

 

The Least Absolute Shrinkage and Selection Operator (LASSO) is a popular method for estimating regression models in large datasets, where the number of covariates is comparable or even larger than the sample size of available data. The LASSO estimator has become important in recent years since large datasets are now prevalent in many disciplines, including economics, and OLS-type techniques are either non-efficient or non-applicable when the number of covariates is comparable or larger than the sample size of available data. Implementing the LASSO estimator requires selecting the regularization parameter and in practice, it is often recommended to use cross-validation for these purposes. However, theoretical properties of the cross-validated estimators are not known in many cases. In this paper, we study LASSO estimators of high-dimensional linear regression models where the tuning parameter of the LASSO penalty is selected by a cross-validation procedure. For models with Gaussian noise, we show that the cross-validated LASSO estimator achieves the optimal convergence rate up to a logarithm term. When the noise is not Gaussian, the cross-validated LASSO estimator is shown to have a convergence rate not slower than the square root of the optimal rate, up to a logarithm term. These results provide theoretical justification for the commonly used LASSO estimators whose regularization parameters are determined through cross-validation.

 

5.      "A Nondegenerate Vuong Test and A Post Selection Confidence Interval for Semi/Nonparametric Models", (with Xiaoxia Shi). [Supplemental Appendix]

 

Model selection in the semi/nonparametric models is important, since in practice there may be different functional forms for the economic model. Indeed, even for the nonparametric models, there may still be modelling issues such as which variables should be included. Model comparison is particularly useful when, for the same phenomenon, different economic theories may imply different functional forms. In this paper, we develop an easy-to-implement test to select from two semi/nonparametric models according to their distances to their population quasi-log likelihood. The test determines the statistical significance of the quasi-log likelihood difference and, when the difference is significantly different from zero, draws the directional conclusion that one model is better than the other. Our test is different from the naïve extension of the standard parametric model comparison test in the literature. The latter (naïve) test favors large model in finite samples due to over-fitting and usually requires one to perform pre-testing or sample splitting when the relationship of the candidate models (e.g., models are nested or non-nested) is unknown. Both features may lead the naïve test to produce highly misleading results in practice. In contrast, our model selection test is a one-step procedure which accounts for the over-fitting of the large models and is valid regardless of the model relationships. Moreover, we provide uniformly valid post model selection inference procedures which are useful for conducting inference on parameters of the selected model.

 

6.      "On Uniform Asymptotic Risk of Averaging GMM Estimators", (with Xu Cheng and Ruoyao Shi), revised for Quantitative Economics.

 

When there are possibly misspecified moment conditions, moment selection may improve the accuracy of GMM estimation by selecting valid moment conditions in estimation, which reduces variances of the GMM estimators. In practice, there are non-zero probabilities that invalid moment conditions may be selected for any moment selection procedure. Therefore, moment selection may also introduce a (pre-testing) bias to the subsequent GMM estimator and reduce its accuracy. In this paper, we study the finite-sample bias and variance trade-off in the moment selection problem. We propose an averaging GMM estimator which combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite-sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. This uniform dominance is established in non-Gaussian semiparametric nonlinear models.

 

7.      "Speculators’ Positions and Exchange Rate Forecasts: Beating the Random Walk Models", (with Aaron Tornell and Young Ju Kim).

 

Speculators’ positions in the futures markets contain useful information to forecast exchange rates over horizons of up to a year. We extract such information by fitting a micro-founded regime switching model to the speculators’ net positions. Using the model, we forecast whether speculators will be increasing or decreasing their positions. We then use this predicted state to form both directional and point exchange rate forecasts. When our model detects that speculators in a given currency-say the Yen-start to increase their net Yen positions, they tend to remain in such an accumulation state for several months, and during this period the Yen tends to appreciate. Analogously, when speculators in the Yen shift to a decumulation state, the Yen tends to exhibit a persistent depreciation. Over forecasting horizons from 6 to 12 months, our directional forecasts have a 58 percent average success ratio and most of our point forecasts are more accurate than those implied by the random walk models. Forecasting evaluation tests show that our empirical findings are significant.

 


  Published and Forthcoming Papers

 

8.      "Nonparametric Two-Step Sieve M Estimation and Inferences", (with Jinyong Hahn and Geert Ridder), Econometric Theory, forthcoming, 2018. [Supplemental Appendix]

 

    In this paper, we study two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance of the sieve M estimate may not have closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimate. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation.

 

9.      "On Standard Inference for GMM with Local Identification Failure of Known Forms", (with Ji Hyung Lee), Econometric Theory, Vol.34, 2018, pp. 790--814. [Supplemental Appendix]

 

   Given the validity of the moment conditions, their identification strength, measured by the information they contain about the unknown parameters, plays the key role of determining the properties of the GMM estimator. The GMM estimator may be inconsistent or converge to the true value slowly as the sample size increases if the identification strength is weak. One interesting example arises in testing the existence of common conditionally heteroskedastic factors among financial assets through the GMM specification test. In such case, the Jacobian of the moment conditions may be zero which leads to a slow rate of convergence of the GMM estimator and a non-standard asymptotic distribution of the J-test statistic. In this paper, we show that the zero Jacobian may provide non-trivial local identification for unknown parameters. By exploiting such information in estimation, we provide GMM estimator and specification tests with standard properties. The standard properties are attractive because the resulting GMM estimation and inference are more accurate in finite samples.

 

10.  "Nonparametric Instrumental Variables and Regular Estimation", (with Jinyong Hahn), Econometric Theory, Vol.34(3), 2018, pp. 574--597.

 

This paper investigates whether there can exist regular estimators in models characterized by nonparametric instrumental variable (NPIV). We show by a number of examples that regular estimation is impossible in general for nonlinear functionals.

 

11.  "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities", (with Xu Cheng and Frank Schorfheide), Review of Economic Studies, Vol.83(4), 2016, pp. 1511--1543. [Supplemental Appendix]

 

    In this paper, we study panel data models with latent factors where the number of factors and their loadings may change due to structural breaks in the economy. We provide a LASSO estimation that consistently determines the numbers of pre- and post-break factors, and the stability of factor loadings. A novel feature of the LASSO estimator is its robustness to unknown break date, whereas existing procedures either over-estimate the number of factors by neglecting the breaks or require known break dates. We apply the new LASSO estimation to the recent (2007--2009) recession to investigate the stability of factor loadings and the emergence of new factors. Using the U.S. data, our procedure detects an increase in the number of factors at the onset of the recession and a substantial change in the factor loadings. The series in the categories of interest rate levels, interest rate spreads, and employment and unemployment experience big changes in their factor loadings. The new factor mainly effects the financial sector (e.g., the series in the categories of interest rate levels, interest rate spreads, money and credit, stock prices and wealth, and exchange rate), but also generate spillovers to the real economy, which is consistent with the narratives of the recession.

 

12.  "Sieve Semiparametric Two-Step GMM Under Weak Dependence", (with Xiaohong Chen), Journal of Econometrics, Vol.189(1), 2015, 163--186.

 

    Many recently introduced empirical methodologies adopt semiparametric two-step estimation approaches, where certain functions are estimated nonparametrically in the first step, and some Euclidean parameters are estimated parametrically in the second step using the nonparametric estimates from the first stage as inputs. In this paper, we consider semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present both consistent and robust long-run variance estimators, Wald tests and Hansen’s (1982) over-identification tests for the second-step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric.

 

13.  "Select the Valid and Relevant Moments: An Information-based LASSO for GMM with Many Moments", (with Xu Cheng), Journal of Econometrics, Vol.186 (2), 2015, 443--464. [Supplemental Appendix]

 

This paper studies the selection of valid and relevant moments for the GMM estimation. For applications with many candidate moments, our asymptotic analysis accommodates a diverging number of moments as the sample size increases. We refine the LASSO penalty in Liao (2013) such that the new penalty signals both moment validity and relevance for consistent moment selection. The proposed procedure achieves three objectives in a one-step GMM LASSO estimation: (i) the valid and relevant moments are distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a stepwise manner; (iii) the parameters of interest are automatically estimated with all selected moments as opposed to a post-selection estimation. We develop asymptotic results for the high-dimensional GMM LASSO estimator, allowing for non-smooth sample moments and weakly dependent observations.

 

14.  "Automated Estimation of Vector Error Correction Models", (with Peter C.B. Phillips), Econometric Theory, Vol.31(3), 2015, 581--646. [Supplemental Appendix]

 

    Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work, but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics.

 

15.  "Asymptotic Efficiency of Semiparametric Two-step GMM", (with Daniel Ackerberg, Xiaohong Chen, Jinyong Hahn), Review of Economic Studies, Vol.81(3), 2014, 919--943.

 

    In many moment-based econometric models, there are both unknown functions and finite dimensional parameters in the moment conditions. The one-step GMM estimation that estimates them simultaneously is theoretically feasible, but it may be difficult to implement in practice because there are too many parameters to estimate. Therefore, the two-step GMM estimation is more attractive. One estimates the unknown functions in the first step and estimates the finite dimensional parameters only in the second step. In this paper, we study the efficiency of the two-step GMM estimator. We characterize the semiparametric efficiency bound for a large class of semiparametric models and show that the two-step GMM estimator achieves this efficiency bound, where the nuisance functions could be estimated via any consistent nonparametric procedures in the first-step. This result shows that the widely used semiparametric two-step GMM estimator in empirical studies is not only computationally convenient, but also as efficient as the one-step GMM estimator.

 

16.  "Sieve M Inference of Irregular Parameters", (with Xiaohong Chen), Journal of Econometrics, Vol.182(1), 2014, 70--86.

 

    This paper presents sieve inferences on possibly irregular (i.e., slower than root-n estimable) functionals of semi-nonparametric models with i.i.d. data. We provide a simple consistent variance estimator of the plug-in sieve M estimator of a possibly irregular functional, and the asymptotic standard normality of the sieve t statistic. We show that, for hypothesis testing of irregular functionals, the sieve likelihood ratio statistic is asymptotically Chi-square distributed. These results complement Chen, Liao and Sun (2014) and are useful in inference on structural parameters that may have singular semiparametric efficiency bounds.  

 

17.  "Sieve Inference on Possibly Misspecified Semi-nonparametric Time Series Models", (with Xiaohong Chen and Yixiao Sun), Journal of Econometrics, Vol.178(3), 2014, 639--658.

 

    This paper establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference sequence, the asymptotic variance in the case of irregular functionals is the same as those for independent data. Using an orthonormal series long run variance estimator, we construct a “pre-asymptotic” Wald statistic and show that it is asymptotically F distributed. Simulations indicate that our “pre-asymptotic” Wald test with F critical values has more accurate size in finite samples than the conventional Wald test with chi-square critical values.

 

18.  "Adaptive GMM Shrinkage Estimation with Consistent Moment Selection", Econometric Theory, Vol.29, 2013, 1--48. [Early Version]

 

    The generalized method of moments (GMM) is a popular method to estimate economic models since restrictions implied by economic theories usually take the form of moment conditions. The validity of the moment conditions is very important because the GMM estimator based on invalid (misspecified) moment conditions may be inconsistent, i.e., the estimator is far from its true value even for a large dataset. In this paper, we provide a simple method which employs the LASSO method to select valid moment conditions. The key step is to construct a criterion that features a novel data-dependent penalty for each moment condition. The method selects a moment condition only if it can improve the model fit by more than this penalty. Compared to the conventional method that selects moment conditions one by one, this new method selects them simultaneously. Thus, it not only yields a much faster algorithm but also is particularly useful when there are many moment conditions to select.

 

19.  "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications", (with Peter C.B. Phillips) in A. Ullah, J. Racine and L. Su (eds.) Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics, Oxford University Press, 2013

 

20.  "Asymptotic Properties of Penalized M Estimators with Time Series Observations", (with Xiaohong Chen), in N.R. Swanson and X. Chen (eds.) Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis: Essays in Honor of Halbert L. White Jr, Springer, 2013