arXiv subjects

Jiti Gao

Publications and source records attributed to Jiti Gao.

At least 19 recordsLinked to original sources

arXiv2026

Identification, Estimation and Inference Based on Structural Error Projection

This paper proposes to project and expand the conditional mean function of the structural error given the regressors in an endogenous regression under consideration. As the projection process is semiparametric, we define this procedure as a semiparametric projection (SP) method to address endogeneity in regression models by internally constructed instrumental variables. The SP method is applicable to many classes of regression models associated with endogeneity, such as linear, nonlinear, and non- and semi-parametric models, and provides a simple and computationally tractable alternative to conventional instrumental variable approaches available from the existing literature. This paper establishes identification conditions and derives the asymptotic properties of the resulting estimators. It then proposes a simple LASSO selection method to examine the finite-sample performance of both the proposed method and the established theory by simulated and real data examples.

econ.EM↗

arXiv2026

Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation

We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world settings such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10-70x speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

cs.LG↗

arXiv2026

Inference for High-Dimensional Local Projection

This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility.

econ.EM↗

arXiv2025

Panel Data Estimation and Inference: Homogeneity versus Heterogeneity

In this paper, we define an underlying data generating process that allows for different magnitudes of cross-sectional dependence, along with time series autocorrelation. This is achieved via high-dimensional moving average processes of infinite order (HDMA($\infty$)). Our setup and investigation integrates and enhances homogenous and heterogeneous panel data estimation and testing in a unified way. To study HDMA($\infty$), we extend the Beveridge-Nelson decomposition to a high-dimensional time series setting, and derive a complete toolkit set. We exam homogeneity versus heterogeneity using Gaussian approximation, a prevalent technique for establishing uniform inference. For post-testing inference, we derive central limit theorems through Edgeworth expansions for both homogenous and heterogeneous settings. Additionally, we showcase the practical relevance of the established asymptotic theory by (1). connecting our results with the literature on grouping structure analysis, (2). examining a nonstationary panel data generating process, and (3). revisiting the common correlated effects (CCE) estimators. Finally, we verify our theoretical findings via extensive numerical studies using both simulated and real datasets.

econ.EM↗

arXiv2025

Robust Estimation and Inference for High-Dimensional Panel Data Models

This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, (2) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator, (3) we also allow for the number of regressors to grow faster than the sample size. Methodologically and technically, we develop two Nagaev--types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator. We demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive effects. Moreover, we conduct extensive numerical studies using simulated and real data examples.

econ.EM↗

arXiv2025

Semiparametric Single-Index Estimation for Average Treatment Effects

We propose a semiparametric method to estimate the average treatment effect under the assumption of unconfoundedness given observational data. Our estimation method alleviates misspecification issues of the propensity score function by estimating the single-index link function involved through Hermite polynomials. Our approach is computationally tractable and allows for moderately large dimension covariates. We provide the large sample properties of the estimator and show its validity. Also, the average treatment effect estimator achieves the parametric rate and asymptotic normality. Our extensive Monte Carlo study shows that the proposed estimator is valid in finite samples. Applying our method to maternal smoking and infant health, we find that conventional estimates of smoking's impact on birth weight may be biased due to propensity score misspecification, and our analysis of job training programs reveals earnings effects that are more precisely estimated than in prior work. These applications demonstrate how addressing model misspecification can substantively affect our understanding of key policy-relevant treatment effects.

econ.EM↗

arXiv2024

Quantile Random-Coefficient Regression with Interactive Fixed Effects: Heterogeneous Group-Level Policy Evaluation

We propose a quantile random-coefficient regression with interactive fixed effects to study the effects of group-level policies that are heterogeneous across individuals. Our approach is the first to use a latent factor structure to handle the unobservable heterogeneities in the random coefficient. The asymptotic properties and an inferential method for the policy estimators are established. The model is applied to evaluate the effect of the minimum wage policy on earnings between 1967 and 1980 in the United States. Our results suggest that the minimum wage policy has significant and persistent positive effects on black workers and female workers up to the median. Our results also indicate that the policy helps reduce income disparity up to the median between two groups: black, female workers versus white, male workers. However, the policy is shown to have little effect on narrowing the income gap between low- and high-income workers within the subpopulations.

econ.EM↗

arXiv2024

Estimation and Inference for Three-Dimensional Panel Data Models

Hierarchical panel data models have recently garnered significant attention. This study contributes to the relevant literature by introducing a novel three-dimensional (3D) hierarchical panel data model, which integrates panel regression with three sets of latent factor structures: one set of global factors and two sets of local factors. Instead of aggregating latent factors from various nodes, as seen in the literature of distributed principal component analysis (PCA), we propose an estimation approach capable of recovering the parameters of interest and disentangling latent factors at different levels and across different dimensions. We establish an asymptotic theory and provide a bootstrap procedure to obtain inference for the parameters of interest while accommodating various types of cross-sectional dependence and time series autocorrelation. Finally, we demonstrate the applicability of our framework by examining productivity convergence in manufacturing industries worldwide.

econ.EM↗

arXiv2024

Localized Neural Network Modelling of Time Series: A Case Study on US Monetary Policy

In this paper, we investigate a semiparametric regression model under the context of treatment effects via a localized neural network (LNN) approach. Due to a vast number of parameters involved, we reduce the number of effective parameters by (i) exploring the use of identification restrictions; and (ii) adopting a variable selection method based on the group-LASSO technique. Subsequently, we derive the corresponding estimation theory and propose a dependent wild bootstrap procedure to construct valid inferences accounting for the dependence of data. Finally, we validate our theoretical findings through extensive numerical studies. In an empirical study, we revisit the impacts of a tightening monetary policy action on a variety of economic variables, including short-/long-term interest rate, inflation, unemployment rate, industrial price and equity return via the newly proposed framework using a monthly dataset of the US.

econ.EM↗

arXiv2024

Estimation and Inference for a Class of Generalized Hierarchical Models

In this paper, we consider estimation and inference for the unknown parameters and function involved in a class of generalized hierarchical models. Such models are of great interest in the literature of neural networks (such as Bauer and Kohler, 2019). We propose a rectified linear unit (ReLU) based deep neural network (DNN) approach, and contribute to the design of DNN by i) providing more transparency for practical implementation, ii) defining different types of sparsity, iii) showing the differentiability, iv) pointing out the set of effective parameters, and v) offering a new variant of rectified linear activation function (ReLU), etc. Asymptotic properties are established accordingly, and a feasible procedure for the purpose of inference is also proposed. We conduct extensive numerical studies to examine the finite-sample performance of the estimation methods, and we also evaluate the empirical relevance and applicability of the proposed models and estimation methods to real data.

econ.EM↗

arXiv2023

Smoothing the Nonsmoothness

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is established and an illustration of its application is then provided.

econ.EM↗

arXiv2023

Higher-order Expansions and Inference for Panel Data Models

In this paper, we propose a simple inferential method for a wide class of panel data models with a focus on such cases that have both serial correlation and cross-sectional dependence. In order to establish an asymptotic theory to support the inferential method, we develop some new and useful higher-order expansions, such as Berry-Esseen bound and Edgeworth Expansion, under a set of simple and general conditions. We further demonstrate the usefulness of these theoretical results by explicitly investigating a panel data model with interactive effects which nests many traditional panel data models as special cases. Finally, we show the superiority of our approach over several natural competitors using extensive numerical studies.

econ.EM↗

arXiv2023

Time-Varying Vector Error-Correction Models: Estimation and Inference

This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this framework can be used to estimate shifts in the predictability of non-stationary variables, test whether economic theories hold periodically, etc. We first develop a time-varying Granger Representation Theorem, which facilitates the establishment of asymptotic properties for the model, and then propose estimation and inferential methods and theory for both short-run and long-run coefficients. We also propose an information criterion to estimate the lag length, a singular-value ratio test to determine the cointegration rank, and a hypothesis test to examine the parameter stability. To validate the theoretical findings, we conduct extensive simulations. Finally, we demonstrate the empirical relevance by applying the framework to investigate the rational expectations hypothesis of the U.S. term structure.

econ.EM↗

arXiv2023

Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models

Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized functions incorporate local integrable functions, the so-called regular generalized functions, while the so-called singular generalized functions (e.g. Dirac delta function) can be obtained as the limits of a sequence of sufficient smooth functions, so-called regular sequence in generalized function context. This makes it possible to use these singular generalized functions through approximation. Nevertheless, a significant contribution of this paper is to establish the convergence rate of regular sequence to nonsmooth loss that answers a call from the relevant literature. For parameter estimation where objective function may be nonsmooth, this paper first shows as a general paradigm that how generalized function approach can be used to tackle the nonsmooth loss functions in Section two using a very simple model. This approach is of general interest and applicability. We further use the approach in robust M-estimation for additive single-index cointegrating time series models; the asymptotic theory is established for the proposed estimators. We evaluate the finite-sample performance of the proposed estimation method and theory by both simulated data and an empirical analysis of predictive regression of stock returns.

econ.EM↗

arXiv2022

Time-Varying Multivariate Causal Processes

In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model which is the foundation to initiate the theoretical development. Afterwards, we consider the QMLE estimation approach, and provide both point-wise and simultaneous inferences on the coefficient functions. In addition, we demonstrate the theoretical findings through both simulated and real data examples. In particular, we show the empirical relevance of our study using an application to evaluate the conditional correlations between the stock markets of China and U.S. We find that the interdependence between the two stock markets is increasing over time.

econ.EM↗

arXiv2021

Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects

In this paper, we investigate binary response models for heterogeneous panel data with interactive fixed effects by allowing both the cross-sectional dimension and the temporal dimension to diverge. From a practical point of view, the proposed framework can be applied to predict the probability of corporate failure, conduct credit rating analysis, etc. Theoretically and methodologically, we establish a link between a maximum likelihood estimation and a least squares approach, provide a simple information criterion to detect the number of factors, and achieve the asymptotic distributions accordingly. In addition, we conduct intensive simulations to examine the theoretical findings. In the empirical study, we focus on the sign prediction of stock returns, and then use the results of sign forecast to conduct portfolio analysis.

econ.EM↗

arXiv2021

Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice

This paper proposes a class of parametric multiple-index time series models that involve linear combinations of time trends, stationary variables and unit root processes as regressors. The inclusion of the three different types of time series, along with the use of a multiple-index structure for these variables to circumvent the curse of dimensionality, is due to both theoretical and practical considerations. The M-type estimators (including OLS, LAD, Huber's estimator, quantile and expectile estimators, etc.) for the index vectors are proposed, and their asymptotic properties are established, with the aid of the generalized function approach to accommodate a wide class of loss functions that may not be necessarily differentiable at every point. The proposed multiple-index model is then applied to study the stock return predictability, which reveals strong nonlinear predictability under various loss measures. Monte Carlo simulations are also included to evaluate the finite-sample performance of the proposed estimators.

econ.EM↗

arXiv2021

Productivity Convergence in Manufacturing: A Hierarchical Panel Data Approach

Despite its paramount importance in the empirical growth literature, productivity convergence analysis has three problems that have yet to be resolved: (1) little attempt has been made to explore the hierarchical structure of industry-level datasets; (2) industry-level technology heterogeneity has largely been ignored; and (3) cross-sectional dependence has rarely been allowed for. This paper aims to address these three problems within a hierarchical panel data framework. We propose an estimation procedure and then derive the corresponding asymptotic theory. Finally, we apply the framework to a dataset of 23 manufacturing industries from a wide range of countries over the period 1963-2018. Our results show that both the manufacturing industry as a whole and individual manufacturing industries at the ISIC two-digit level exhibit strong conditional convergence in labour productivity, but not unconditional convergence. In addition, our results show that both global and industry-specific shocks are important in explaining the convergence behaviours of the manufacturing industries.

econ.EM↗