arXiv subjects

Zhentao Shi

Publications and source records attributed to Zhentao Shi.

At least 19 recordsLinked to original sources

arXiv2026

Social Interactions Models with Latent Structures

This paper studies estimation and inference of heterogeneous social interactions featuring group fixed effects and slope heterogeneity under latent structure. Theoretically, in a binary choice model with social interactions we characterize the asymptotic bias of the slope coefficient due to the presence of high dimensional incidental parameters. Computationally, we invoke parametric bootstrap method to debias and establish asymptotic validity. Furthermore, tailored algorithms are employed to explore the latent structures and determine the number of clusters. Monte Carlo simulations confirm strong finite sample performance of our methods. In an application to students' risky behaviors, the algorithm detects two latent clusters and finds that peer effects are significant within one of the clusters, demonstrating the practical applicability in uncovering heterogeneous social interactions.

stat.ME↗

arXiv2026

Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions

In panel predictive regressions with persistent covariates, coexistence of the Nickell bias and the Stambaugh bias imposes challenges for estimation and hypothesis testing. This paper introduces an innovative estimator, the Double IVX (DIVX), inspired by the IVX technique in time series. DIVX effectively removes this composite Nickell-Stambaugh bias and reinstates standard inferential procedures based on the t-statistic. This new procedure achieves unified inference across a wide range of modes of persistence in panel predictive regressions when the cross-sectional dimension and the time dimension are comparably large. Such desirable properties were unattainable by existing methods, including the popular within-group estimator. Extensive Monte Carlo simulations demonstrate the robustness of DIVX under a variety of settings. We apply DIVX to panel data of financial markets in developed economies to examine the predictability of stock returns.

econ.EM↗

arXiv2026

A Relaxation Approach to Synthetic Control

The synthetic control method (SCM) is widely used for constructing the counterfactual of a treated unit based on data from control units in a donor pool. Allowing the donor pool contains more control units than time periods, we propose a novel machine learning algorithm, named SCM-relaxation, for counterfactual prediction. Our relaxation approach minimizes an information-theoretic measure of the weights subject to a set of relaxed linear inequality constraints in addition to the simplex constraint. When the donor pool exhibits a group structure, SCM-relaxation approximates the equal weights within each group to diversify the prediction risk. Asymptotically, the proposed estimator achieves oracle performance in terms of out-of-sample prediction accuracy. We demonstrate our method by Monte Carlo simulations and by an empirical application that assesses the economic impact of Brexit on the United Kingdom's real GDP.

econ.EM↗

arXiv2026

Bagging the Network

We develop a unified estimation and inference framework for dyadic network formation with individual fixed effects, covering both transferable-utility (TU) and nontransferable-utility (NTU) links under general link functions. Under NTU, bilateral consent makes the fixed effects non-additive and the log-likelihood non-concave in the high-dimensional fixed effects, so differencing and profile-likelihood methods fail. We combine a joint method-of-moments initial estimator, a Le Cam one-step refinement, and a split-network jackknife bagging step that removes the incidental parameter bias without inflating variance. The resulting homophily estimator is asymptotically normal, unbiased, and attains the Cramér--Rao lower bound without requiring the log-likelihood to be concave in the fixed effects; we extend the theory to average partial effects and establish robustness to link-function misspecification. Simulations under both TU and NTU designs confirm these predictions. Applied to Thai village networks (TU), kinship and wealth differences both increase linking; in the Nyakatoke risk-sharing network (NTU), wealth differences have no significant effect, mirroring the two regimes' distinct logics.

econ.EM↗

arXiv2026

LASSO Inference for High Dimensional Predictive Regressions

LASSO inflicts shrinkage bias on estimated coefficients, which undermines asymptotic normality and invalidates standard inferential procedures based on the t-statistic. Given cross sectional data, the desparsified LASSO has emerged as a well-known remedy for correcting the shrinkage bias. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors modeled as local unit roots. To restore standard inference, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso simultaneously eliminates both shrinkage bias and Stambaugh bias and does not require prior knowledge about the identities of nonstationary and stationary regressors. We establish the asymptotic properties of XDlasso for hypothesis testing, and our theoretical findings are supported by Monte Carlo simulations. Applying our method to real-world applications from the FRED-MD database, we investigate two important empirical questions: (i) the predictability of the U.S. stock returns based on the earnings-price ratio, and (ii) the predictability of the U.S. inflation using the unemployment.

stat.ME↗

arXiv2026

Benign Overfitting in Economic Forecasting via Noise Regularization

This paper studies linear overparameterized models in economic forecasting and highlights that including noise variables (regressors with no predictive power) regularizes the estimator. We consider a setting where both the outcome variable and the high-dimensional predictors are driven by a small number of latent factors, and show that the linear forecast model is dense rather than sparse. It turns out that a ridgeless regression augmented with noise predictors attains the same asymptotic forecast accuracy as an oracle with known true factors, without estimating the factors or assuming them to be strong. The gain comes from shrinkage of the eigenvalues of the design matrix, which reduces the out-of-sample variance. In contrast, perfect variable selection that removes noise variables can worsen forecasts when the number of retained predictors is comparable to the sample size. Empirically, we apply this approach to forecasting U.S. inflation, international GDP growth, and the U.S. equity risk premium, finding that noise regularization improves and stabilizes predictive performance.

econ.EM↗

arXiv2026

Zero Variance Portfolio

When the number of assets is larger than the sample size, the minimum variance portfolio interpolates the training data, delivering pathological zero in-sample variance. We show that if the weights of the zero variance portfolio are learned by a novel ``Ridgelet'' estimator, in a new test data this portfolio enjoys out-of-sample generalizability. It exhibits the double descent phenomenon and can achieve optimal risk in the overparametrized regime when the number of assets dominates the sample size. In contrast, a ``Ridgeless'' estimator which invokes the pseudoinverse fails in-sample interpolation and diverges away from out-of-sample optimality. Extensive simulations and empirical studies demonstrate that the Ridgelet method performs competitively in high-dimensional portfolio optimization.

stat.ME↗

arXiv2026

Nickell Bias in Panel Local Projection: Financial Crises Are Worse Than You Think

Panel local projection (LP) with fixed-effects (FE) is widely adopted for evaluating the economic consequences of financial crises across countries. This paper highlights a fundamental methodological issue: the presence of the Nickell bias in the panel FE estimator due to inherent dynamic structures of predictive specifications, even if the regressors have no lagged dependent variables. The Nickell bias invalidates the standard inferential procedure based on the $t$-statistic. We propose a split-panel jackknife (SPJ) estimator as a simple, easy-to-implement, and yet effective solution to eliminate the bias and restore valid statistical inference. We revisit four influential empirical studies on the impact of financial crises, and find that the FE method underestimates the economic losses of financial crises relative to the SPJ estimates. Replication files are available at https://metricshilab.github.io/panel-lp-replication/, with links to R and Stata packages.

econ.EM↗

arXiv2025

L2-relaxation for Economic Prediction

We leverage an ensemble of many regressors, the number of which can exceed the sample size, for economic prediction. An underlying latent factor structure implies a dense regression model with highly correlated covariates. We propose the L2-relaxation method for estimating the regression coefficients and extrapolating the out-of-sample (OOS) outcomes. This framework can be applied to policy evaluation using the panel data approach (PDA), where we further establish inference for the average treatment effect. In addition, we extend the traditional single unit setting in PDA to allow for many treated units with a short post-treatment period. Monte Carlo simulations demonstrate that our approach exhibits excellent finite sample performance for both OOS prediction and policy evaluation. We illustrate our method with two empirical examples: (i) predicting China's producer price index growth rate and evaluating the effect of real estate regulations, and (ii) estimating the impact of Brexit on the stock returns of British and European companies.

econ.EM↗

arXiv2025

A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data

This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating counterfactual outcomes, we caution researchers against assuming a common nonstationary trend factor across units for macroeconomic outcomes, as doing so may result in misleading causal estimation-a pitfall we refer to as the spurious synthetic control problem. To address this issue, we propose a synthetic business cycle framework that explicitly separates trend and cyclical components. By leveraging the treated unit's historical data to forecast its trend and using control units only for cyclical fluctuations, our divide-and-conquer strategy eliminates spurious correlations and improves the robustness of counterfactual prediction in macroeconomic applications. As empirical illustrations, we examine the cases of German reunification and the handover of Hong Kong, demonstrating the advantages of the proposed approach.

econ.EM↗

arXiv2025

Empirical likelihood approach for high-dimensional moment restrictions with dependent data

Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a unified framework, with high-dimensional parameters identified by moment conditions. As the number of parameters and moment conditions may surpass the sample size, we propose adding a double penalty to the empirical likelihood criterion to induce sparsity and facilitate dimension reduction. Notably, we utilize a marginal empirical likelihood approach despite temporal dependence in the data. Under regularity conditions, we provide asymptotic guarantees for our method, making it an attractive option for estimating large-scale multivariate time series models. We demonstrate the versatility of our procedure through extensive Monte Carlo simulations and three empirical applications, including analyses of US sectoral inflation rates, fiscal multipliers, and volatility spillover in China's banking sector.

econ.EM↗

arXiv2024

The boosted HP filter is more general than you might think

The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper extends boosting's trend determination capability to higher order integrated processes and time series with roots that are local to unity. The theory is established by understanding the asymptotic effect of boosting on a simple exponential function. Given a universe of time series in FRED databases that exhibit various dynamic patterns, boosting timely captures downturns at crises and recoveries that follow.

econ.EM↗

arXiv2024

On LASSO for High Dimensional Predictive Regression

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds for these components, suggesting that LASSO's rates of convergence are different from those typically observed in cross-sectional cases. When applied to a mixture of stationary, nonstationary, and cointegrated predictors, LASSO maintains its asymptotic guarantee if predictors are scale-standardized. Leveraging machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate, as evidenced by its application to the FRED-MD database.

econ.EM↗

arXiv2022

L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis

This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequality constraints. The magnitude of relaxation, controlled by a tuning parameter, balances the bias and variance. When the variance-covariance (VC) matrix of the individual forecast errors or financial assets exhibits latent group structures -- a block equicorrelation matrix plus a VC for idiosyncratic noises, the solution to L2-relaxation delivers roughly equal within-group weights. Optimality of the new method is established under the asymptotic framework when the number of the cross-sectional units $N$ potentially grows much faster than the time dimension $T$. Excellent finite sample performance of our method is demonstrated in Monte Carlo simulations. Its wide applicability is highlighted in three real data examples concerning empirical applications of microeconomics, macroeconomics, and finance.

econ.EM↗

arXiv2022

Culling the herd of moments with penalized empirical likelihood

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This paper investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approximation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.

econ.EM↗

arXiv2021

Forward-Selected Panel Data Approach for Program Evaluation

Policy evaluation is central to economic data analysis, but economists mostly work with observational data in view of limited opportunities to carry out controlled experiments. In the potential outcome framework, the panel data approach (Hsiao, Ching and Wan, 2012) constructs the counterfactual by exploiting the correlation between cross-sectional units in panel data. The choice of cross-sectional control units, a key step in its implementation, is nevertheless unresolved in data-rich environment when many possible controls are at the researcher's disposal. We propose the forward selection method to choose control units, and establish validity of the post-selection inference. Our asymptotic framework allows the number of possible controls to grow much faster than the time dimension. The easy-to-implement algorithms and their theoretical guarantee extend the panel data approach to big data settings.

econ.EM↗

arXiv2021

On LASSO for Predictive Regression

Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with zero regression coefficients. This new finding motivates a novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to restore variable selection consistency. Accommodating the system of heterogeneous regressors, TAlasso achieves the well-known oracle property. In contrast, conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously. We apply these LASSO methods to evaluate the short- and long-horizon predictability of S\&P 500 excess returns.

econ.EM↗

arXiv2020

Boosting: Why You Can Use the HP Filter

The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. Like all nonparametric methods, the HP filter depends critically on a tuning parameter that controls the degree of smoothing. Yet in contrast to modern nonparametric methods and applied work with these procedures, empirical practice with the HP filter almost universally relies on standard settings for the tuning parameter that have been suggested largely by experimentation with macroeconomic data and heuristic reasoning. As recent research (Phillips and Jin, 2015) has shown, standard settings may not be adequate in removing trends, particularly stochastic trends, in economic data. This paper proposes an easy-to-implement practical procedure of iterating the HP smoother that is intended to make the filter a smarter smoothing device for trend estimation and trend elimination. We call this iterated HP technique the boosted HP filter in view of its connection to $L_{2}$-boosting in machine learning. The paper develops limit theory to show that the boosted HP (bHP) filter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks. A stopping criterion is used to automate the iterative HP algorithm, making it a data-determined method that is ready for modern data-rich environments in economic research. The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach. These examples show that the bHP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility.

econ.EM↗