Endogenous Explanatory Variables Research Articles

Extending the Scope of Instrumental Variable Methods

Abstract Since Philip Wright’s (1928) proposal of the linear instrumental variables (IV) estimator the scope of application of IV models has greatly expanded. There are now nonlinear IV models in use with both additive and nonadditive latent variables, employing both semiparametric and nonparametric specifications. A notable feature of Wright’s linear IV estimator is that it is applicable to incomplete models that leave the genesis of endogenous explanatory variables unspecified. On the other hand, inversion of the linear model enables the value of unobservable heterogeneity to be expressed as a function of observable variables. Only recently has the application of incomplete IV models been extended to cases in which this inversion produces a non-singleton set of values of unobservable variables. This situation arises in many models such as those featuring discrete choice, counts, or censored outcomes, or when there are multiple sources of heterogeneity as in random coefficient models, or when economic considerations result in inequality restrictions on values taken by observed and unobserved variables. This paper provides an introduction to the methods set out for analyzing such generalized instrumental variable (GIV) models in Chesher and Rosen (2017). An illustrative example is provided in which an outcome is determined by a random coefficients linear model with an endogenous explanatory variable and instrumental variable exclusion and independence restrictions.

Did Australia's brief period of carbon pricing impact corporate environmental, financial or social performance?

This study utilizes transaction cost and legitimacy theories to examine whether a carbon tax affects listed companies' environmental, financial and social performance within the context of Australia's National Greenhouse Energy Reporting (NGER) Act. We use a base sample of 346 listed company-year observations for 2012–2017 and employ the System Generalized Method of Moments (GMM) to deal with bias arising from endogenous explanatory variables in our analysis. We find that the short period of implementation of a carbon tax in Australia was not successful in improving the carbon emissions of the high polluters subject to the tax in our sample. High polluters subject to the tax experienced a positive impact on financial performance and social performance. However, many entities beyond listed companies were subject to the tax, and the period of the tax saw a reduction in total emissions. We conjecture that industry assistance and free carbon credits granted to companies explain these results.

Estimating multinomial logit models with endogenous variables: Control function versus two adapted approaches

It is shown that the control function (CF) method’s estimates of the modal constants in a multinomial logit model (MNL) with endogenous explanatory variables are biased. This has not previously been reported in the literature, and has consequences in demand analysis, transportation policy design and project evaluation. Two adaptations of existing approaches are proposed as alternatives to CF for deriving estimators of parameters in MNL models with endogenous explanatory variables that evidence good consistency properties. The first approach is based on moment conditions while the second one combines parameters obtained in two consecutive estimation stages. Both approaches employ instrumental variables. These two adapted approaches are implemented using simulated data from a transport mode choice problem. The results are compared with those obtained using the classic control-function method, typically used by practitioners for estimating transport demand models with endogenous variables and making quantitative evaluations of transport policies and projects. All three approaches generate similar estimates for the parameters of the explanatory variables, but the two proposed adaptations produce considerably more accurate estimates of the modal constants. This greater accuracy has potentially significant consequences for multinomial logit models’ predictive ability and estimates of marginal effects, elasticities and the social benefits of projects based on consumer surplus calculations.

Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables

We consider multivariate Markov switching first-order autoregression models with endogenous explanatory variables, propose a joint estimation algorithm of type EM, written at vector–matrix level, to account for endogeneity, and derive matrix formulas for the ML estimators of model parameters. Then we prove the consistency of such estimators, provide matrix expressions for their asymptotic covariances, and present some tests for endogeneity. Further, a simulation study is proposed to illustrate the theoretical results and provide evidence on the usefulness of the considered model.

IV methods for Tobit models

This paper studies models of processes generating censored outcomes with endogenous explanatory variables and instrumental variable restrictions. Tobit-type left censoring at zero is the primary focus in the exposition. Extension to stochastic censoring is sketched. The models do not specify the process determining endogenous explanatory variables and they do not embody restrictions justifying control function approaches. Consequently, they can be partially or point identifying. Identified sets are characterized and it is shown how inference can be performed on scalar functions of partially identified parameters when exogenous variables have rich support. In an application using data on UK household tobacco expenditures inference is conducted on the coefficient of an endogenous total expenditure variable with and without a Gaussian distributional restriction on the unobservable and compared with the results obtained using a point identifying complete triangular model.

Estimating the Impact of Medical Care Usage on Work Absenteeism by a Trivariate Probit Model with Two Binary Endogenous Explanatory Variables

Estimating the Impact of Medical Care Usage on Work Absenteeism by a Trivariate Probit Model with Two Binary Endogenous Explanatory Variables

The role of information communication technologies on carbon emissions in OECD countries: new evidence from method of moments quantile approach.

This paper aims to investigate the effects of information and communication technologies (ICT) on carbon emissions (CO2) in the OECD area. For this purpose, a comprehensive panel data set is utilized covering the 1994-2018 period for 38 countries and a novel method of moments panel quantile regression model which allows to account for fixed effects and endogenous explanatory variables. Results suggest that the ICT, represented by the percentage of individuals using the Internet in the total population, contributes positively to CO2 emissions up to 0.40th quantile and has no effect after this level. The results imply that countries with relatively low per capita emissions are susceptible to the rebound effects, in which better energy efficiency results in increased demand for energy and ICT-related items, hence increasing carbon emissions. At this juncture, one policy idea would be to include a carbon tax into the per-unit purchase price of smartphones, tablets, smart gadgets, and any other relevant ICT items. Additionally, this legislation can assist decrease conspicuous consumption, which can be viewed as a trigger for the demand for ICT products. Additionally, these countries should encourage enterprises to invest in and employ energy-efficient technologies through tax incentives or subsidies.

Official development assistance and carbon emissions of recipient countries: A dynamic panel threshold analysis for low- and lower-middle-income countries

Better use of official development assistance (ODA) to mitigate carbon emissions in developing countries requires a better understanding of the effects of ODA on carbon emissions. The dynamic panel threshold regression model is employed to explore the effects of ODA and carbon emissions in 59 low-income and lower-middle-income countries. Urbanization is employed as a threshold variable. The proposed model can better reflect endogenous explanatory variables, which indicate the inertial characteristics and dynamic changes of carbon emissions. The first-order lag coefficients of carbon emissions in the proposed model have a significant positive effect, indicating that the growth of carbon emissions in these countries has a strong path dependence. Moreover, when the urbanization of recipient countries is below the threshold value, a 1% increase in ODA leads to a 0.2259% increase in carbon emissions. When urbanization exceeds the threshold value, a 1% increase in ODA leads to a 0.2281% increase in carbon emission. In addition, the conditional convergence level of carbon emission growth in low-urbanization areas is much greater than that in high-urbanization areas. With the development in urbanization, if no effective measures are developed and implemented, there is a risk that carbon emissions of recipient countries might develop from “low-emission balanced growth” to “high-emission balanced growth.”

Assessing the Impact of Neighborhood Conditions on Neurodevelopmental Disorders during Childhood.

Nearly three out of ten neurodevelopmental disabilities in the United States have been linked to environmental conditions, prompting emerging lines of research examining the role of the neighborhood on children’s developmental outcomes. Utilizing data from a natural experiment in Denver, this study quantifies the impact of exposure to varied neighborhood contexts on the diagnosis of neurodevelopmental disorders over the course of childhood. Our analysis is based upon retrospective child, caregiver, household and neighborhood data derived from the Denver Child Study for a sample of approximately 590 Latino and African American children and youth whose families were quasi-randomly assigned to subsidized housing operated by the Denver (CO) Housing Authority during part of their childhood. We employed binary response models with endogenous explanatory variables, estimated using instrumental variables (IV) probit and average marginal effects to identify predictors of a neurodevelopmental disorder diagnosis during childhood. We found that multiple dimensions of neighborhood context—especially neighborhood socioeconomic status, older housing stock, residential instability and prevalence of neurological hazards in the ambient air—strongly and robustly predicted the diagnosis of a neurodevelopmental disorder during childhood.

On the instrument functional form with a binary endogenous explanatory variable

I demonstrate that, in a linear regression model with a binary endogenous explanatory variable, a two-step IV estimation procedure could avoid the weak identification issue caused by a first-stage linear projection onto the linear instruments.

Testing underidentification in linear models, with applications to dynamic panel and asset pricing models

This paper develops the links between overidentification tests, underidentification tests, score tests and the Cragg and Donald (1993, 1997) and Kleibergen and Paap (2006) rank tests in linear instrumental variable (IV) models. For the structural linear model y=Xβ+u, with the endogenous explanatory variables partitioned as X=x1X2, this general framework shows that standard underidentification tests are tests for overidentification in an auxiliary linear model, x1=X2δ+ɛ, estimated by IV estimation methods using the same instruments as for the original model. This simple structure makes it possible to establish valid robust underidentification tests for linear IV models where these have not been proposed or used before, like clustered dynamic panel data models estimated by GMM. The framework also applies to tests for the rank of general parameter matrices. Invariant rank tests are based on the LIML or continuously updated GMM estimators of both structural and first-stage parameters. This insight leads to the proposal of new two-step invariant asymptotically efficient GMM estimators, and a new iterated GMM estimator that, if it converges, converges to the continuously updated GMM estimator.

A dynamic microeconomic analysis of the impact of physical activity on cognition among older people

This microeconomic study explores the dynamic relationship between physical activity and cognition, using longitudinal data from 6 waves of the Survey of Health, Ageing and Retirement in Europe (SHARE) between 2004 and 2017. Physical activity has drawn significant attention as a potentially successful action for protecting brain health and cognition in the aging population, but the empirical evidence in observational studies is inconclusive to date. We add to the literature by estimating the effect of physical activity on cognition, tackling many sources of bias, which have previously not been addressed consistently. The challenge in estimating the effect of physical activity on cognition is the dynamics of cognition and the endogeneity of physical activity caused by unobserved heterogeneity, reverse causality and measurement error. To address this endogeneity and at the same time control for lagged cognition, we propose a system – generalized method of moments (GMM) estimator, using lagged levels and differences of the endogenous explanatory variables as instruments, while transforming out the fixed effects. We find that being moderately & vigorously physically active at least once a week increases memory status by 0.282 and 0.552 standard deviations for men and women respectively. We find different effects for varying physical activity intensity.

Impact of the institutional quality on NAFTA's international trade: a system GMM approach

PurposeThis paper aims to analyze the impacts of institutional quality on trade flows of NAFTA with a panel data set of 105 countries spanning the period 2006–2017.Design/methodology/approachWe applied the system generalized method of moment (GMM) estimator to investigate the impacts.FindingsThe results show that institutional quality is a positive and significant determinant of international trade flows of the NAFTA bloc and its trading partners. Our results also indicate that the impact of institutional quality depends on the level of economic development of NAFTA's trading partners. Specifically, the trade elasticity of institutional quality is the highest for NAFTA’s trade with middle-income countries and the lowest for NAFTA's trade with low-income countries. In the long run, the trade elasticity of institutional quality increased significantly, with the highest increase in the case of NAFTA's trade with medium-income countries and the lowest increase in the case of NAFTA's trade with low-income countries.Originality/valueThis study contributes to the existing literature in three different ways. First, we examine the differential impact of institutions on NAFTA's trade according to the level of economic development of NAFTA's trading partners. Second, we compare the differential trade elasticity of institutional quality in the long run. Finally, we support our findings through an improved research methodology by using the system GMM estimation. This method allows us to overcome the potential sample bias, omitted variable problems and endogeneity of explanatory variables.

Does board gender diversity influence firm profitability? A control function approach

We investigate the relation between board gender diversity and firm profitability using the control function (CF) approach recently suggested by Wooldridge (2015). The CF method takes account of the problem of endogenous explanatory variables that have potential to bias the results. Using a sample of firms that made up the S&P 500 over the period 2004–2015, we find that the presence of women on corporate boards (measured either by the percentage of female directors on corporate boards or the Blau index of heterogeneity) has a positive and significant (at the 1% level) effect on firm profitability (measured by the return on assets). We compare our results to more traditional approaches (such as pooled OLS or the fixed-effects model). Through this study, we shed light on the effect of women on corporate boards on firm performance, as it is still a controversial issue (Post and Byron, 2015).

Macroprudential policy and financing behaviour in emerging markets: bank-level evidence from Indonesian dual banking

The loan-to-funding ratio-based reserve-requirement (RR-LFR) is a macroprudential instrument used by Bank Indonesia (central bank) to maintain the stability of Indonesian financial system by considering the bank liquidity conditions. This paper examines the impact of RR-LFR on financing behaviour in a dual banking system (Islamic and conventional banks) using generalised method of moment estimation (GMM) technique to address the endogeneity of explanatory variables and reduce the possible biases from residual correlation. Using bank-level data for both Islamic and conventional banks covering the period 2001-2015, we analyse the reaction of bank financing behaviour toward RR-LFR policy. The findings indicate that RR-LFR is effective in curtailing financing behaviour of banking institutions. Further, we show that RR-LFR exerts more impacts on managing credit expansion of conventional banks than of Islamic banks. The study suggests that a specific macroprudential framework should be put in place to address systemic concerns for each type of banks. Hence, the supervisory authorities will be able to identify the channel of macroprudential transmission and to devise an optimum policy mix for their banking system.

Participation in contract farming and farm performance: Insights from cashew farmers in Ghana

AbstractThe global demand for cashew nuts continues to increase steadily. However, many African countries face difficulties in marketing and adding value to the product. Using recent survey data of 391 cashew farmers in Ghana, this paper contributes to the growing evidence on the significance of contract farming (CF) in improving the welfare of rural households in developing countries. Specifically, the paper analyzes the factors that influence cashew farmers’ decisions to participate in CF, and the impact of participation on farmers’ performance. We employ a recently developed switching regression model with endogenous explanatory variables and endogenous switching to control for selection bias caused by observable and unobservable factors. The empirical results show that participation in CF significantly increases labor productivity and price margins, as well as cashew yields, and net revenues. A disaggregated analysis of the sample into farm size categories reveals that small‐sized cashew farms tend to benefit more through CF, compared to medium‐ and large‐sized farms.

Firms’ performance and board size: A simultaneous approach in the European and American contexts

ABSTRACT The relation between performance and board size (BS) is analysed in the American and European contexts. It is found that return on assets (ROA) depends on BS defined as an endogenous explanatory variable. This potentially non-monotonous effect is modelled by introducing firm size and number of segments by board member as explanatory variables for ROA. BS net effect after accounting for the indirect effect resulting from these variables is negative. Differences in the results obtained for Tobin’s Q, strategic investors’ weight and equity to total assets, between America and Europe, suggest a more preventive management control in Europe.

Does a firm with higher Tobin’s q prefer foreign direct investment to foreign outsourcing?

In this study, we investigate whether firms’ choices of offshoring modes vary according to their characteristics that are reflected in the value of Tobin’s q. When a firm chooses its offshoring mode from foreign outsourcing (FO) and foreign direct investment (FDI), a model developed by Chen, Horstmann, and Markusen (2012, Canadian Journal of Economics) predicts that Tobin’s q is negatively associated with the share of FO in total offshoring activities. Using detailed Japanese firm-level data, we find that Tobin’s q is negatively and significantly correlated with the share of Japanese firms’ engagement in FO in the sum of FO and FDI. With regard to our empirical methodology, we employ fractional regression models, because our dependent variable (i.e., the share of FO) is bounded between zero and one. We also address the issue of endogeneity by using a simple two-step method to control endogenous explanatory variables in the fractional regression models. We show that the above finding is robust.

Synthetic Instrumental Variables

This paper presents a new method for synthesizing instrumental variables using only the dependent and endogenous explanatory variables of the regression model. We show that a valid instruments can be spanned using the dependent and endogenous variables. Then based on this rationale, we construct an estimator that uses moment conditions stemming from the validity of such synthetic instruments. We demonstrate the consistency of the newly-developed estimator using synthetic variables. A computational algorithm is developed using the moments conditions stemming from the consistency of the estimator. One can use this synthetic instrumental variables method as an alternative to traditional external instruments methods.

Quantiles via moments

We study the conditions under which it is possible to estimate regression quantiles by estimating conditional means. The advantage of this approach is that it allows the use of methods that are only valid in the estimation of conditional means, while still providing information on how the regressors affect the entire conditional distribution. The methods we propose are not meant to replace the well-established quantile regression estimator, but provide an additional tool that can allow the estimation of regression quantiles in settings where otherwise that would be difficult or even impossible. We consider two settings in which our approach can be particularly useful: panel data models with individual effects and models with endogenous explanatory variables. Besides presenting the estimator and establishing the regularity conditions needed for valid inference, we perform a small simulation experiment, present two simple illustrative applications, and discuss possible extensions.