Endogenous Regressors Research Articles

EXPRESS: Addressing Endogeneity Using a Two-stage Copula Generated Regressor Approach

The ubiquitous presence of endogenous regressors presents a significant challenge when drawing causal inference using observational data. The classical econometric method used to handle regressor endogeneity requires IVs that must satisfy the stringent condition of exclusion restriction, rendering it unfeasible in many settings. Herein, we propose a new IV-free method that uses copulas to address the endogeneity problem. Existing copula correction methods require nonnormal endogenous regressors: normally or nearly normally distributed endogenous regressors cause model non-identification or significant finite-sample bias. Furthermore, existing copula control function methods presume the independence of exogenous regressors and the copula control function. While maintaining the Gaussian copula regressor-error dependence structure, our generalized two-stage copula endogeneity correction (2sCOPE) method simultaneously relaxes the two key identification requirements. Under the Gaussian copula dependence structure, we prove that 2sCOPE yields consistent causal-effect estimates with correlated endogenous and exogenous regressors as well as normally distributed endogenous regressors. In addition to relaxing the identification requirements, 2sCOPE has superior finite-sample performance and addresses the significant finite-sample bias problem due to insufficient regressor nonnormality. Moreover, 2sCOPE employs generated regressors derived from existing regressors to control for endogeneity, and can thus considerably increase the ease and broaden the applicability of IV-free methods for handling regressor endogeneity. We further demonstrate 2sCOPE’s performance using simulation studies and illustrate its use in an empirical application.

Identifying the reciprocal causation between hit-and-run behavior and crash injury severity

Objective Hit-and-run behavior is believed to exacerbate the injury severity of traffic crashes due to the delayed emergency response for the victims. However, several previous studies indicated the opposite finding that hit-and-run crashes were associated with less severe injuries. The relevant studies mainly identified the statistical associations between hit-and-run behavior and injury severity without revealing causation between them. To this end, the study aims to explore the reciprocal causation between the two variables. Method The two-stage probit model with endogenous regressors is employed to identify the reciprocal causation between hit-and-run behavior and crash injury severity for single- and two-vehicle crashes, respectively, with the use of crash data extracted from the Crash Report Sampling System and Fatality Analysis Reporting System (2016-2019). Results The results indicate that 1) for both single- and two-vehicle crashes, the fleeing behavior can significantly increase the injury severity of the victims in the crashes while the severe injury of the victims has a negative impact on the propensity of such behavior, 2) the propensity of hit-and-run behavior is influenced by various instrumental variables such as driver age, gender, alcohol involvement, weekday, area type, and light condition, and 3) crash injury severity is significantly related to the victim age, gender, and vehicle damage. Conclusions There is a reciprocal causation between hit-and-run behavior and injury severity in traffic crashes. The analytical results can provide a reasonable explanation for the counterintuitive finding on hit-an-run crashes and help mitigate the injury severity.

A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors

A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors

Frisch–Waugh–Lovell theorem-type results for the k-Class and 2SGMM estimators

The Frisch–Waugh–Lovell (FWL) theorem shows that for the least squares estimator, parameter estimates from full and partial models are identically same. I show that in linear regression models with a mix of exogenous and endogenous regressors, FWL theorem-type results hold for the k-class estimators (including LIML) and the two-step optimal GMM estimator.

Comparison of GMM and MD estimators for a panel regression model with endogenous regressors and an AR(1) disturbance

ABSTRACT In this paper, we investigate the asymptotic properties of nonlinear GMM and linear MD estimators for a panel regression model with endogenous regressors and an AR(1) disturbance. We demonstrate that the linear MD estimator has a smaller asymptotic variance than the nonlinear GMM estimator when a non-optimal weighting matrix is used. However, when the optimal weighting matrix is used, both the nonlinear GMM and linear MD estimators have the same asymptotic distribution. The simulation results indicate that the linear two-step MD estimator is a practical choice due to its performance and simplicity.

Semiparametric distribution regression with instruments and monotonicity

This paper proposes IV-based estimators for the semiparametric distribution regression model in the presence of an endogenous regressor, which are based on an extension of IV probit estimators and the idea of control functions. We discuss the causal interpretation of the estimators and two methods (monotone rearrangement and isotonic regression) to ensure a monotonically increasing distribution function. Asymptotic properties and simulation evidence are provided. An application to income equations with German SOEP data reveals statistically significant and heterogeneous differences to the inconsistent non-IV-based estimator.

The Effect of Military Expenditure on Economic Prosperity in Croatia

The objective of this study was to empirically evaluate the impact of military spending on the economic well-being of the Croatian economy. The objective of the study was as well to find out if military expenditure could bolster the economic growth. Croatia has been among the European nations with significant military expenditures over the past three decades. However, these expenses have substantially decreased due to successful peace initiatives and the country's accession to the European Union. Reflecting on Croatia's history, notably during the Croatian War of Independence, the government significantly augmented its military expenditures. The sample period of the study was for 40 years from 1981 to 2020. An applied econometrics methodology called the 2-Stage Least Squares with Instrumental Variables was utilised in the study. In the first stage, instrumental variables were used to instrument for the endogenous regressors. In the second stage, the predicted values obtained from the first stage were used as explanatory variables in the main regression equation. The study found that the effect of military expenditure on the economic prosperity of Croatia was positive and highly statistically significant. The study addressed an empirical gap in the literature by integrating distinctive characteristics into the model concerning the long-term relationship between Croatia's military expenditure and economic growth. These factors enhanced empirical accuracy and instilled confidence in the broader and diverse literature concerning military expenditure and economic growth. The implication of this study is that investing in the military provides an enabling environment for economic growth to increase.

Stock repurchases, ownership structure and board composition: evidence from Thailand

PurposeThis study aims to examine the influence of ownership structure and board composition on the probability and intensity of stock repurchases. The study’s sample comprises 3,744 firm-year observations, consisting of 53 repurchasing firms with 96 firm-year observations from 2008 to 2019.Design/methodology/approachProbit and fixed-effects regression models are used to obtain empirical results. Moreover, a probit model with a continuous endogenous regressor (IV-probit) and an instrumental variable method with two-stage least squares (IV-2SLS) estimation are used to address endogeneity.FindingsCorporations with high family or state ownership tend to inhibit stock repurchases to hoard excess free cash flow, supporting agency theory. Conversely, firms with high board independence tend to repurchase their stocks at least once to distribute free cash flows to shareholders, confirming agency theory. Nonetheless, corporations with more female directors on the board or CEO duality tend to conduct stock repurchases at least once but do not repurchase stocks with high values. Interestingly, more female directors on the board may send false signals about undervalued stocks.Originality/valueThis is the first study to reveal that firms with CEO duality repurchase their stocks at least once but avoid repurchasing shares with high values. It is also the first study to explore whether women on a board may cause false signaling about undervalued stocks. Furthermore, this study reveals that family and state ownership are potential determinants of stock repurchases in countries with high ownership concentration. This is the first study to address this issue in Thailand.

Demand and distribution in a dynamic spatial panel model for the United States: Evidence from state‐level data

AbstractWe estimate a modified demand‐and‐distribution system for the 48 contiguous US states and the District of Columbia (DC) employing dynamic spatial panel data for 1980–2019. We allow for endogenous regressors, test for the presence, significance, and magnitude of spatial spillovers, and estimate immediate and cumulative effects on our endogenous variables of interest. Without testing for spatial dependence and spillovers, we estimate that output growth and capacity utilization in the sample US states and DC rise in response to an increase in their own wage share. When we test for spatial dependence and spillovers as required by the state‐level nature of the data, and consider that the functional distribution of income and the level of economic activity are jointly determined, we estimate that a higher state wage share raises output growth in the own state and the neighboring states. Yet the effect of a change in the state wage share on capacity utilization in the own state and the neighboring states is not statistically significant. Meanwhile, a higher state output growth raises the wage share in the own state, but its impact on the wage share in the neighboring states is not statistically significant. A higher state capacity utilization raises the wage share in the own state, yet it reduces the wage share in the neighboring states.

Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments

Stochastic frontier models commonly assume positive skewness for the inefficiency term. However, when this assumption is violated, efficiency scores converge to unity. The potential endogeneity of model regressors introduces another empirical challenge, impeding the identification of causal relationships. This paper tackles these issues by employing an instrument-free estimation method that extends joint estimation through copulas to handle endogenous regressors and skewness issues. The method relies on the Gaussian copula function to capture dependence between endogenous regressors and composite errors with a simultaneous consideration of positively or negatively skewed inefficiency. Model parameters are estimated through maximum likelihood, and Monte Carlo simulations are employed to evaluate the performance of the proposed estimation procedures in finite samples. This research contributes to the stochastic frontier models and production economics literature by presenting a flexible and parsimonious method capable of addressing wrong skewness of inefficiency and endogenous regressors simultaneously. The applicability of the method is demonstrated through an empirical example.

“Wrong” skewness and endogenous regressors in stochastic frontier models: an instrument-free copula approach with an application to estimate firm efficiency in Vietnam

Stochastic frontier models commonly assume positively skewed inefficiency. However, if the data speak against this assumption, sample-failure problems are often cited, but less attention is paid to economic reasons. We consider this phenomenon as a signal of distinctive population characteristics stemming from the inefficiency component, emphasizing its potential impact on evaluating market conditions. Specifically, we argue more generally that “wrong” skewness could indicate a lack of competition in the market. Moreover, endogeneity of model regressors presents another challenge, hindering the identification of causal relationships. To tackle these issues, this paper proposes an instrument-free estimation method based on Gaussian copulas to model the dependence between endogenous regressors and composite errors, while accommodating positively or negatively skewed inefficiency through simultaneous identification. Monte Carlo simulation experiments demonstrate the suitability of our estimator, comparing it with alternative methods. The contributions of this study are twofold. On the one hand, we contribute to the literature on stochastic frontier models by providing a comprehensive method for dealing with “wrong” skewness and endogenous regressors simultaneously. On the other hand, our contribution to an economic understanding of “wrong” skewness expands the comprehension of market behaviors and competition levels. Empirical findings on Vietnamese firm efficiency indicate that endogeneity hinders the detection of “wrong” skewness and suggests a lack of competitive market conditions. The latter underscores the importance of policy interventions to incentivize firms in non-competitive markets.

Weak identification with many instruments

Summary Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ‘technical’ instruments and more recently from the empirical strategy of ‘judge design’. This paper surveys and summarises ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak identification robust inference under heteroscedasticity. We establish new results for a jack-knifed version of the Lagrange Multiplier test statistic. Furthermore, we extend the weak identification robust tests to settings with both many exogenous regressors and many instruments. We propose a test that properly partials out many exogenous regressors while preserving the re-centring property of the jack-knife. The proposed tests have correct size and good power properties.

Outperforming the market: a comparison of Star and NonStar analysts’ investment strategies and recommendations

AbstractWe employ StarMine to investigate the impact of analyst recommendations on stock performance. We test whether star-ranked analysts generate abnormal returns and outperform non-stars in short and long portfolios. Utilizing buy-and-hold calendar-time portfolio methodology, we calculate portfolio alphas using various asset pricing models, including CPM, the Fama and French 3-factor model, and the Carhart 4-factor model. Results indicate that all analyst groups can generate abnormal returns exceeding the market average. Star-ranked analysts outperform non-stars in short portfolios by 0.5523% in monthly alpha, though no significant difference exists in long portfolio alphas. We also conduct regressor endogeneity tests and explore investor sentiment mechanisms by utilizing the GARCH model and frequency-domain causality analysis, with NASDAQ as a proxy for investor sentiment. These tests reveal that the momentum factor is exogenous, and investor sentiments have a statistically significant positive effect on stock return volatility, with changes occurring between 5 and 10 days. This research underscores the value of analyst insights for investors, validates StarMine’s ranking effectiveness, and suggests market participants can benefit from incorporating analyst recommendations into their investment decisions. Our study makes a significant contribution to the existing literature by introducing a novel approach to understanding investor sentiment mechanisms through a causality model.

Latent Group Structure in Linear Panel Data Models with Endogenous Regressors

Latent Group Structure in Linear Panel Data Models with Endogenous Regressors

Properties of Test Statistics for Nonparametric Cointegrating Regression Functions Based on Subsamples

Nonparametric cointegrating regression models have been extensively used in financial markets, stock prices, heavy traffic, climate datasets, and energy markets. Models with parametric regression functions can be more appealing in practice compared to nonparametric forms, but do result in potential functional misspecification. Thus, there exists a vast literature on developing a model specification test for parametric forms of regression functions. In this article, we develop two test statistics which are applicable for the endogenous regressors driven by long memory and semi-long memory input shocks in the regression model. The limit distributions of the test statistics under these two scenarios are complicated and cannot be effectively used in practice. To overcome this difficulty, we use the subsampling method and compute the test statistics on smaller blocks of the data to construct their empirical distributions. Throughout, Monte Carlo simulation studies are used to illustrate the properties of test statistics. We also provide an empirical example of relating gross domestic product to total output of carbon dioxide in two European countries. Supplementary materials for this article are available online.

A Spatial Econometric Analysis of Productivity Variations Across US Cities

Using a dynamic spatial panel model applied to 377 US Metropolitan Statistical Areas (MSAs), estimated over the period 2011-2021, significant differences are found between large MSAs regarding the relationship between labour productivity and economic mass, as measured by GDP. The methodology adopted illustrates the state of the art for spatial econometric modeling as it is often needed in practice, allowing for multiple endogenous regressors and dynamic effects. The estimation method applies synthetic instruments designed to limit negative effects of instrument overabundance.

Globalization and shadow economy: a panel analysis for Africa

PurposeThe study's objective is to examine the relevance of globalization in affecting the size of the shadow economy in selected African nations.Design/methodology/approachTo do this, the authors employ the KOF globalization index and implement both static and dynamic common correlated mean group estimators on a panel of 24 African nations from 1995–2017. This technique accommodates the issue of cross-sectional dependence, sample bias and endogenous regressors. Panel threshold analysis is also conducted to establish the nonlinearity between globalization and the shadow economy. To examine the causality between the variables, the study employs Dumitrescu and Hurlin's panel causality test.FindingsThe results show that globalization reduces the size of the shadow economy. The results of the nonlinear analysis suggest a U-shaped relationship. Overall globalization has a threshold impact of 48.837%, economic globalization has 45.615% and political globalization has 66.661% while social globalization has a threshold value of 35.744%. The results of the panel causality show that there is a bidirectional causality between the two variables.Practical implicationsThe results suggest that the government and other relevant authorities need to introduce capital controls and other policy measures to moderate the degree of social, political and cultural diffusion. Appropriate policies should be formulated to monitor the extent of African economic openness to other continents to maximize the gains from globalization.Originality/valueApart from being the first study in the African region that evaluates the relevance of globalization in controlling the shadow economy, it also analyzes the dynamics and threshold analysis between the two variables using advanced panel econometrics which makes the study unique. The study suggests that globalization tools are useful for affecting the size of the shadow economy in Africa. This study provides fresh empirical evidence on the impact of globalization on the shadow economy in the case of Africa.

Correcting Regressor-Endogeneity Bias via Instrument-Free Joint Estimation Using Semiparametric Odds Ratio Models

Endogenous regressors can lead to biased estimates for causal effects using methods assuming regressor–error independence. To correct for endogeneity bias, the authors propose a new method that accounts for the regressor–error dependence using flexible semiparametric odds ratio conditional models; the approach requires neither parametric distributional assumptions nor tuning parameters for modeling endogenous regressors’ distributions conditional on the error term and exogenous regressors. Inference is achieved via optimizing the profile likelihood concentrating on the parameters of interest. The proposed approach requires no use of instrumental variables (IVs), observed or latent, that must satisfy the stringent condition of exclusion restriction. Nonnormally distributed endogenous regressors are required for model identification with a normal error distribution. The approach's flexibility in capturing regressor–error dependence increases the capability of IV-free endogeneity correction and provides opportunities to improve the accuracy of causal effect estimation. Unlike existing IV-free methods, the proposed approach can handle discrete endogenous regressors with few levels, such as binary regressors or count regressors with small means, and is thus applicable to a plethora of applications involving such regressors. The authors demonstrate the versatility of the approach for binary, count, and continuous endogenous regressors using comprehensive simulation studies and empirical data.

Financing constraints, intellectual property rights protection and incremental innovation: Evidence from transition economy firms

Despite a growing literature, the relationship between financing constraints (FC), intellectual property rights (IPR) protection and firm innovation remains unclear within the transitional country context. Drawing on endogenous growth theory and extending the Gorodnichenko and Schnitzer (2013) framework, we hypothesize that in addition to firm-specific factors, country-level variables manifested within FC hamper incremental innovation, albeit in varying degrees due to industry heterogeneity. Secondly, as opposed to previous studies that solely focus on FC affecting firm innovation, we propose that due to resource constraints, firms in transition economies tend to follow an imitational innovation strategy, and therefore, from this perspective, IPR protection can be crucial for firm-level innovation within those economies. Using data from the World Bank Enterprise Survey (WBES) consisting of information for about 21,960 firms from 27 Eastern European and Central Asian transition countries and employing a two-step probit model with endogenous regressors, we find that adverse effects of FC and IPR on firms' innovation activities are driven from within as well as between industries. Focusing on the differential impacts of FC and IPR protection across industries, we direct potential causal pathways from easing FC and optimal IPR protection to encourage firms' innovation. Based on the findings, while very strict IPR protection is detrimental to firms' product and process innovation in industries with limited resource and skill capabilities, it is nevertheless helpful for research and development (R&D) activities in industries characterised by strong R&D and IP capacities. Our results offer useful insights for policymakers to support incremental innovation as well as boost invention. IPR protection policies require to be customised to the industries and firms, since invariably tight or lax IPR enforcement can be discouraging to both incremental and radical innovation, causing all industries suffering from the same treatment.

Estimation and testing of kink regression model with endogenous regressors

Estimation and testing of kink regression model with endogenous regressors