Two-stage Least-squares Estimation Research Articles

Csa2sls: A complete subset approach for many instruments using Stata

We developed a command, csa2sls, that implements the complete subset averaging two-stage least-squares (CSA2SLS) estimator in Lee and Shin (2021, Econometrics Journal 24: 290–314). The CSA2SLS estimator is an alternative to the two-stage least-squares estimator that remedies the bias issue caused by many correlated instruments. We conduct Monte Carlo simulations and confirm that the CSA2SLS estimator reduces both the mean squared error and the estimation bias substantially when instruments are correlated. We illustrate the usage of csa2sls in Stata with an empirical application.

Estimating causal effects with hidden confounding using instrumental variables and environments.

Recent works have proposed regression models which are invariant across data collection environments [24, 20, 11, 16, 8]. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent example, the Causal Dantzig (CD), is consistent under hidden confounding and represents an alternative to classical instrumental variable estimators such as Two Stage Least Squares (TSLS). In this work we derive the CD as a generalized method of moments (GMM) estimator. The GMM representation leads to several practical results, including 1) creation of the Generalized Causal Dantzig (GCD) estimator which can be applied to problems with continuous environments where the CD cannot be fit 2) a Hybrid (GCD-TSLS combination) estimator which has properties superior to GCD or TSLS alone 3) straightforward asymptotic results for all methods using GMM theory. We compare the CD, GCD, TSLS, and Hybrid estimators in simulations and an application to a Flow Cytometry data set. The newly proposed GCD and Hybrid estimators have superior performance to existing methods in many settings.

How does knowledge spur the productivity of private Egyptian firms? An instrumental variable approach

PurposeThis study aims to dissect firm knowledge into two main types: internal firm knowledge (knowledge workers) and external firm knowledge (relational knowledge with other firms). This study aims to investigate how each type affects the productivity of the firms. This study also examines how this effect differs among Egyptian firms in the agriculture, manufacturing and service sectors.Design/methodology/approachThe authors use firm-level data in Egypt on the sectoral level. The properties of instrumental variables regression using two-stage least-squares estimation are adopted to overcome endogeneity and omitted variable bias in the empirical estimations.FindingsThe study’s findings reveal that the effects of internal and external knowledge on the firm productivity are sector-specific; knowledge-workers and relational knowledge are two times more effective for agriculture than manufacturing and service firms; external knowledge plays a vital role in increasing productivity relative to internal knowledge for the manufacturing sector; finally, internal and external knowledge has the same effect on the service firms.Originality/valueThis research adds to the body knowledge-based theory of the firm by examining the effects of internal and external knowledge on the firms’ productivity. In particular, the paper differentiates this effect across three sectors: agriculture, manufacturing and services. This paper also suggests a novel empirical methodology to address endogeneity and omitted variable bias in this literature of firm knowledge and productivity.

Relationship between rice farming and polygenic scores potentially linked to agriculture in China.

Following domestication in the lower Yangtze River valley 9400 years ago, rice farming spread throughout China and changed lifestyle patterns among Neolithic populations. Here, we report evidence that the advent of rice domestication and cultivation may have shaped humans not only culturally but also genetically. Leveraging recent findings from molecular genetics, we construct a number of polygenic scores (PGSs) of behavioural traits and examine their associations with rice cultivation based on a sample of 4101 individuals recently collected from mainland China. A total of nine polygenic traits and genotypes are investigated in this study, including PGSs of height, body mass index, depression, time discounting, reproduction, educational attainment, risk preference, ADH1B rs1229984 and ALDH2 rs671. Two-stage least-squares estimates of the county-level percentage of cultivated land devoted to paddy rice on the PGS of age at first birth (b = −0.029, p = 0.021) and ALDH2 rs671 (b = 0.182, p < 0.001) are both statistically significant and robust to a wide range of potential confounds and alternative explanations. These findings imply that rice farming may influence human evolution in relatively recent human history.

The Effects of Corruption, Renewable Energy, Trade and CO2 Emissions

Corruption reflects a set of illegal activities that jeopardize the smooth functioning of economies, society, and climate and environmental issues. This article tests the relationships between economic growth, corruption, renewable energies, international trade, and carbon dioxide emissions using panel data for European countries, namely Portugal, Spain, Italy, Ireland, and Greece, from 1995–2015. As an econometric strategy, this research uses the panel fully modified least squares (FMOLS), panel dynamic least squares (DOLS), and panel two-stage least squares estimator (TSLS). Considering the variables utilized in the research and the panel unit root test, we observed that the variables are integrated I (1) in the first difference. The variables of corruption, economic growth, renewable energies, international trade, and carbon dioxide emissions are cointegrated in the long run, using the Pedroni and Kao residual cointegration test arguments. The methodology of Dumitrescu–Hurlin to test the causality between carbon dioxide emissions, corruption, economic growth, and renewable energy shows that there is unidirectional causality between carbon dioxide emissions and corruption and economic growth and corruption. The results suggest that the corruption index and economic growth have a statistically significant positive impact on carbon dioxide emissions. However, renewable energies and international trade reduce climate change and improve the environmental quality.

Economic growth in the aftermath of floods in Indian states

Flood disaster is a recurrent phenomenon in India. The geo-climatic conditions are a major cause for higher flood damages in Indian states. This study employs the pooled mean group (PMG) approach to examine economic growth in the aftermath of floods in 14 non-special category states in India using flood disaster data over the period 1981–2011. The PMG estimates show that flood impacts in terms of area affected, the population affected, and economic losses due to floods decline real per capita GSDP growth in the long run after taking into account growth-enhancing factors. Moreover, instrumental variables (IV)-two-stage least-squares (2SLS) estimates also confirm that states experience lower real per capita GSDP growth due to higher flood impacts. The results, further, show that higher urbanization and enrollment of higher education increases real per capita GSDP growth in the long run. For robustness check, the study investigates the impact of floods on real per capita GSDP growth after taking into account government capital expenditure and per capita power consumption. The PMG and IV-2SLS estimates produce same results and confirm that flood impacts reduce real per capita GSDP growth, while government capital expenditure and per capita power consumption enhances real per capita GSDP growth. Overall, results confirm that flood management policies are essential to minimize the adverse impacts of floods on the growth of real per capita GSDP.

Note on approximate skewness and kurtosis of the two-stage least-square estimator

In the present paper we obtain the first four exact moments of the two-stage least-squares estimator of the scalar coefficient of the endogenous variable on the right of the structural equation to be estimated. We also derive approximations to the skewness and kurtosis coefficients of this estimator.

Two-sample instrumental-variables regression with potentially weak instruments

We develop a command, weaktsiv, for two-sample instrumentalvariables regression models with one endogenous regressor and potentially weak instruments. weaktsiv includes the classic two-sample two-stage least-squares estimator whose inference is valid only under the assumption of strong instruments. It also includes statistical tests and confidence sets with correct size and coverage probabilities even when the instruments are weak.

How Social Status Contributes to Sustainable Livelihoods? An Empirical Analysis in Ethiopia

This paper scrutinized the links between social status and income of rural households to provide insight into how social status is indicated and used as a strategy for improving livelihood income. It also provides a brief look into some selected key determinants of livelihood income. We applied a two-stage least-squares estimation to household-level data from rural areas in the Tigray regional state of Ethiopia. We also proposed the latent class analysis model to identify the number of classes for the variable “social status”. The results indicate that livelihood income is significantly affected by households’ social status, indicating that high status household heads tend to enhance their participation in different social networks with the intention of strengthening the social bonds that they have and improving their status in the community, which in turn has an economic payback. Apart from this, household heads’ access to off-farm work, size of owned land, exposure to multimedia, livestock ownership and spatial proximity to towns were the variables that have significant positive effects on livelihood income.

The Effects of Corporate Governance on Credit Ratings: The Role of Corporate Social Responsibility

ABSTRACTThis study examines the effects of corporate governance and corporate social responsibility (CSR) on credit ratings for firms in Taiwan. We examine this causal relationship using ordered logit regressions with two-stage least-squares estimates. We document that CSR performance demonstrates both moderation and partial mediation effects in the relationship between corporate governance and credit rating. Our results indicate that a firm should practice good corporate governance and engage in CSR activities to improve its credit rating. This study further shows that family firms with strong corporate governance and good CSR performance do not benefit from higher credit ratings. However, large firms with good corporate governance practices benefit from higher credit ratings.

Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE

Abstract Strong consistency and (weak) distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators of linear and threshold ARCH (p) models, with special attention paid to the ARCH (1) and threshold ARCH (1) cases. Conditions supporting these results include (relatively) mild moment existence criteria that enjoy empirical support. These conditions are not shared by competing estimators like OLS. Identification of the TSLS estimators depends on asymmetry, either in the model’s rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation can sizably outperform quasi maximum likelihood (QML) in small samples and even best recently proposed two-step estimators specifically designed to enhance the efficiency of QML.

Attendance demand in a developing football market: the case of the Peruvian first division

ABSTRACTResearch question: Most of the empirical research on football demand has focused on leagues in developed countries while those in developing countries have received comparatively limited attention. In the absence of more specific analyses of leagues in developing countries, an implicit assumption is that the demand for football across different economies is homogenous. However, such an assumption may lead to inappropriate policies. Therefore, decision-making and policies aimed at attendance and pricing in developing countries should be substantiated with empirical evidence reflecting their settings.Research methods: This paper models match level attendance demand and price in the first tier of the Peruvian football league from 2012 to 2016 inclusive. Using a sample of 1719 matches, two-stage least-squares estimation with instrumental variables is used.Results and findings: We find that attendance in the Peruvian football league is driven by market size, distance between teams and recent performance while local rivalry and price do not exert significant impacts. More importantly, attendance exhibits properties of an inferior good given its relationship with levels of poverty and associated correlation with income.Implications: The implications are that demand models for football in developing and developed economies generate different results as the impacts of some exogenous variables on attendance offer different outcomes. For example, the impact of price and income differ from prior expectations indicating that different approaches are necessary to managing football in developing countries including distinct policies on stadium accommodation.

TSLS and LIML Estimators in Panels with Unobserved Shocks

The properties of the two stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators in panel data models where the observables are affected by common shocks, modelled through unobservable factors, are studied for the case where the time series dimension is fixed. We show that the key assumption in determining the consistency of the panel TSLS and LIML estimators, as the cross section dimension tends to infinity, is the lack of correlation between the factor loadings in the errors and in the exogenous variables—including the instruments—conditional on the common shocks. If this condition fails, both estimators have degenerate distributions. When the panel TSLS and LIML estimators are consistent, they have covariance-matrix mixed-normal distributions asymptotically. Tests on the coefficients can be constructed in the usual way and have standard distributions under the null hypothesis.

Financial Inclusion under Internet Plus and Household Entrepreneurial Decisions

By using the data of China Family Panel Studies 2014, this paper investigates the effect of financial inclusion under Internet Plus on household entrepreneurial decisions from two perspectives of width and depth based on discrete variables selection model and two-stage least-squares estimation method. It arrives at the following conclusions:through the fusion of the information flow and the financing flow, the fusion of Internet Plus and financial inclusion reduces the risks in household business financing and increases its participation in formal financial market, thereby promoting ordinary household entrepreneurial probability; especially in urban families, high income families and families at higher education level, it plays a significantly promotion role in their entrepreneurial decisions; besides, the fusion of Internet Plus and financial inclusion also makes families be more active in opportunity-based entrepreneurial activities. This paper validates the availability of the effects of financial inclusion under Internet Plus on formal financial financing preference and risk preference channels in household entrepreneurial decisions, which is of great significance to the improvement of financial supportive environment in present work of popular entrepreneurship and innovation.

Reconsidering Moments-Based Estimators for ARCH Processes

Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation to sizably outperform quasi maximum likelihood estimation in (relatively) small samples. This outperformance is most pronounced when returns are heavily skewed.

Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance

Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation to sizably outperform quasi maximum likelihood estimation in (relatively) small samples. This outperformance is most pronounced when returns are heavily skewed.

2SLS vs 2SRI: Appropriate Methods for Rare Outcomes and/or Rare Exposures.

Using Monte-Carlo simulations, we compare the two-stage least-squares estimator with two-stage residual inclusion estimators, with varying forms of residuals, to estimate the local average treatment effect parameter for a binary outcome and endogenous binary treatment model in the presence of binary covariates and a binary instrumental variable. We vary the rarity of both the outcome and the treatment and find different estimators to produce the least bias in different settings. We develop guidance for applied researchers and illustrate the utility of this guidance with estimating the effects of long-term care insurance on a variety of binary health care use outcomes among the near-elderly using the Health and Retirement Study. Copyright © 2017 John Wiley & Sons, Ltd.

Dose–response modeling in mental health using stein‐like estimators with instrumental variables

A mental health trial is analyzed using a dose–response model, in which the number of sessions attended by the patients is deemed indicative of the dose of psychotherapeutic treatment. Here, the parameter of interest is the difference in causal treatment effects between the subpopulations that take part in different numbers of therapy sessions. For this data set, interactions between random treatment allocation and prognostic baseline variables provide the requisite instrumental variables. While the corresponding two‐stage least squares (TSLS) estimator tends to have smaller bias than the ordinary least squares (OLS) estimator; the TSLS suffers from larger variance. It is therefore appealing to combine the desirable properties of the OLS and TSLS estimators. Such a trade‐off is achieved through an affine combination of these two estimators, using mean squared error as a criterion. This produces the semi‐parametric Stein‐like (SPSL) estimator as introduced by Judge and Mittelhammer (2004). The SPSL estimator is used in conjunction with multiple imputation with chained equations, to provide an estimator that can exploit all available information. Simulated data are also generated to illustrate the superiority of the SPSL estimator over its OLS and TSLS counterparts. A package entitled SteinIV implementing these methods has been made available through the R platform. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

The unconditional distributions of the OLS, TSLS and LIML estimators in a simple structural equations model

ABSTRACTThe exact distributions of the standard estimators of the structural coefficients in a linear structural equations model conditional on the exogenous variables have been shown to have some unexpected and quirky features. Since the argument for conditioning on exogenous (ancillary) variables has been weakened over the past 20 years by the discovery of an “ancillarity paradox,” it is natural to wonder whether such finite sample properties are in fact due to conditioning on the exogenous variables. This article studies the exact distributions of the ordinary least squares (OLS), two-stage least squares (TSLS), and limited information maximum likelihood (LIML) estimators of the structural coefficients in a linear structural equation without conditioning on the exogenous variables.

Endogeneity in Semiparametric Threshold Regression

In this paper, we investigate semiparametric threshold regression models with endogenous threshold variables based on a nonparametric control function approach. Using a series approximation we propose a two-step estimation method for the threshold parameter. For the regression coefficients, we consider least-squares estimation in the case of exogenous regressors and two-stage least-squares estimation in the case of endogenous regressors. We show that our estimators are consistent and derive their asymptotic distribution for weakly dependent data. Furthermore, we propose a test for the endogeneity of the threshold variable, which is valid regardless of whether the threshold effect is zero or not. Finally, we assess the performance of our methods using a Monte Carlo simulation.