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This paper aims to study the improved effect of the instrumental variable method to estimate parameters of linear regression model with the stochastic explanatory variables problem.

By Monte‐Carlo method, taking a linear regression model with intercept of 3, slope of 4 as an example, whose random error in standard normal distribution, to test whether parameter estimators are biased and how about the average relative error of estimator of slope when random explanatory variables are in different contemporaneously correlated with random error item. By the instrumental variables which are independent with random error item and in varying degrees related to random explanatory variable, the study tests the estimation accuracy of the slope using the instrumental variable method.

This paper tests that the ordinary least square parameter estimators are biased, and especially that the average relative error of estimator of slope is significantly large, more than 10 percent, when random explanatory variables are different and contemporaneously correlated with the random error item. For the instrumental variables that are independent from random error item and in varying degrees related to the random explanatory variable, the estimation accuracy of the slope is significantly improved and the relative error dropped to less than 4 percent, but the estimation accuracy of the intercept term showed no significant improvement by the instrumental variable method.

The method exposed in the paper shows how to improve estimation by an instrumental variable method.

The paper succeeds in showing how to improve estimation by the instrumental variable method of numerical simulation.

The different types of estimators of rational expectations models are surveyed. A key feature is that the model′s solution has to be taken into account when it is estimated. The two ways of doing this, the substitution and errors‐in‐variables methods, give rise to different estimators. In the former case, a generalised least‐squares or maximum‐likelihood type estimator generally gives consistent and efficient estimates. In the latter case, a generalised instrumental variable (GIV) type estimator is needed. Because the substitution method involves more complicated restrictions and because it resolves the solution indeterminacy in a more arbitary fashion, when there are forward‐looking expectations, the errors‐in‐variables solution with the GIV estimator is the recommended combination.

We estimate the parental investment response to the child endowment at birth, by analysing the effect of child birth weight on the hours worked by the mother two years after birth. Mother’s working hours soon after child birth are a measure of investments in their children as a decrease (increase) in hours raises (lowers) her time investment in the child. The child birth endowment is endogenously determined in part by unobserved traits of parents, such as investments during pregnancy. We adopt an instrumental variables estimation. Our instrumental variables are measures of the father’s health endowment at birth, which drive child birth weight through genetic transmission but does not affect directly the mother’s postnatal investments, conditional on maternal and paternal human capital and prenatal investments. We find an inverted U-shape relationship between mothers worked hours and birth weight, suggesting that both low and extremely high child birth weight are associated with child health issues for which mothers compensate by reducing their labour supply. The mother’s compensating response to child birth weight seems slightly attenuated for second and later born children. Our study contributes to the literature on the response of parental investments to child’s health at birth by proposing new and more credible instrumental variables for the child health endowment at birth and allowing for a heterogeneous response of the mother’s investment for first born and later born children.

Higher education researchers are often challenged by the difficulty of empirically validating causal links posited by theories or inferred from correlational observations. The instrumental variable (IV) estimation strategy is one approach that researchers can use to estimate the causal impact of various higher education–related interventions. In this chapter, we discuss how the body of quantitative research specifically devoted to higher education has made use of the IV estimation strategy: we describe how this estimation strategy was used to address causality concerns and provide examples of the types of IVs that were used in various subfields of higher education research. Our discussion is based on a systematic review of a corpus of econometric studies on higher education–related issues that spans the last 30 years. The chapter concludes with a critical discussion of the use of IVs in quantitative higher education research and a discussion of good practices when using an IV estimation strategy.

I propose a general framework for instrumental variables estimation of the average treatment effect in the correlated random coefficient model, focusing on the case where the treatment variable has some discreteness. The approach involves adding a particular function of the exogenous variables to a linear model containing interactions in observables, and then using instrumental variables for the endogenous explanatory variable. I show how the general approach applies to binary and Tobit treatment variables, including the case of multiple treatments.

This paper aims to investigate the effects of using poor-quality instruments to remedy endogeneity in logit-based demand models. Endogeneity problems in demand models occur when certain factors, unobserved by the researcher, affect both demand and the values of a marketing mix variable set by managers. For example, unobserved factors such as style, prestige or reputation might result in higher prices for a product and higher demand for that product. If not addressed properly, endogeneity can bias the elasticities of the endogenous variable and subsequent optimization of the marketing mix. In practice, instrumental variables (IV) estimation techniques are often used to remedy an endogeneity problem. It is well-known that, for linear regression models, the use of IV techniques with poor-quality instruments can produce very poor parameter estimates, in some circumstances even worse than those that result from ignoring the endogeneity problem altogether. The literature has not addressed the consequences of using poor-quality instruments to remedy endogeneity problems in non-linear models, such as logit-based demand models.

Using simulation methods, the authors investigate the effects of using poor-quality instruments to remedy endogeneity in logit-based demand models applied to finite-sample data sets. The results show that, even when the conditions for lack of parameter identification due to poor-quality instruments do not hold exactly, estimates of price elasticities can still be quite poor. That being the case, the authors investigate the relative performance of several non-linear IV estimation procedures utilizing readily available instruments in finite samples.

The study highlights the attractiveness of the control function approach (Petrin and Train, 2010) and readily available instruments, which together reduce the mean squared elasticity errors substantially for experimental conditions in which the theory-backed instruments are poor in quality. The authors find important effects for sample size, in particular for the number of brands, for which it is shown that endogeneity problems are exacerbated with increases in the number of brands, especially when poor-quality instruments are used. In addition, the number of stores is found to be important for likelihood ratio testing. The results of the simulation are shown to generalize to situations under Nash pricing in oligopolistic markets, to conditions in which cross-sectional preference heterogeneity exists and to nested logit and probit-based demand specifications as well. Based on the results of the simulation, the authors suggest a procedure for managing a potential endogeneity problem in logit-based demand models.

The literature on demand modeling has focused on deriving analytical results on the consequences of using poor-quality instruments to remedy endogeneity problems in linear models. Despite the widespread use of non-linear demand models such as logit, this study is the first to address the consequences of using poor-quality instruments in these models and to make practical recommendations on how to avoid poor outcomes.

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

Most spatial econometrics work focuses on spatial dependence in the regressand or disturbances. However, Lesage and Pace (2009) as well as Pace and LeSage2009 showed that the bias in β from applying OLS to a regressand generated from a spatial autoregressive process was exacerbated by spatial dependence in the regressor. Also, the marginal likelihood function or restricted maximum likelihood (REML) function includes a determinant term involving the regressors. Therefore, high dependence in the regressor may affect the likelihood through this term. In addition, Bowden and Turkington (1984) showed that regressor temporal autocorrelation had a non-monotonic effect on instrumental variable estimators.

We provide empirical evidence that many common economic variables used as regressors (e.g., income, race, and employment) exhibit high levels of spatial dependence. Based on this observation, we conduct a Monte Carlo study of maximum likelihood (ML), REML and two instrumental variable specifications for spatial autoregressive (SAR) and spatial Durbin models (SDM) in the presence of spatially correlated regressors.

Findings indicate that as spatial dependence in the regressor rises, REML outperforms ML and that performance of the instrumental variable methods suffer. The combination of correlated regressors and the SDM specification provides a challenging environment for instrumental variable techniques.

We also examine estimates of marginal effects and show that these behave better than estimates of the underlying model parameters used to construct marginal effects estimates. Suggestions for improving design of Monte Carlo experiments are provided.

This paper aims to analyse the influence of cooperation on the degree of novelty of technological innovations introduced by industrial firms in Argentina. This influence is analysed from three perspectives: cooperation by partner type [business partners or scientific and technological centres (S&T) partners]; cooperation by number of partner types, from no cooperation to cooperation with two partner types; and cooperation by goals pursued by firms.

The data come from one of the last national innovation surveys conducted in Argentina. The study controls for endogeneity, using instrumental variable procedures within the conditional mixed-process (CMP) framework.

The main result is the influence of cooperation with universities and S&T centres on the introduction of more novel innovations, which was found both in estimations with and without endogeneity correction. This influence was verified for more complex goals (R&D, technology transfer and industrial design and engineering) as well as for less complex ones (tests and trials, human resources training, quality management and certification). Business cooperation seems to impact only on a lower degree of novelty for more complex goals. The increase in the number of partners that the firm cooperates with, from no cooperation to joint cooperation with two partner types, influences more novel innovations.

Limitations and proposals for future research are discussed at the end of the study.

The results of this study contrast with the high propensity to cooperate with business partners shown by firms in Argentina and other Latin American countries. Therefore, this paper may help formulate more effective policies to promote cooperation conducive to firm innovation performance. Limitations and proposals for future research are discussed at the end of the study.

Although there is empirical evidence on this topic for developed countries, firm-level studies on cooperation and degree of novelty are scarce for Latin America. In addition, this paper analyses cooperation not only by type of partner but also by type of goal. This study attempted to control for endogeneity by using instrumental variables within the CMP framework.

Sub-Saharan Africa is a region that is highly vulnerable to the effects of climate change. Renewable energy consumption could play a major role in mitigating the effects of climate change by improving environmental quality in the region. The purpose of this paper is to examine the effect of renewable energy consumption on environmental quality in sub-Saharan African countries.

The empirical investigation is based on the estimation of an augmented Green Solow model through the defactored instrumental variables approach on a sample of 34 countries over the period 1996 to 2018.

The results of two-stage defactored instrumental variables estimator show that renewable energy consumption improves environmental quality. Indeed, renewable energies have a significant negative influence on CO₂ emissions. This result is robust when using the ecological footprint as an indicator of environmental quality.

In terms of implications, governments in Sub-Saharan Africa need to pursue policies to encourage investment in the renewable energy sector. This will promote renewable energy consumption, change the structure of the energy mix in favour of renewable energy, improve environmental quality and effectively combat climate change.

The originality of this research in relation to the existing literature lies at several levels. Firstly, the analysis is carried out using a unified framework combining the environmental Kuznets curve and the environmental convergence hypotheses. Secondly, this research uses a very recent econometric method. Finally, environmental quality is measured using two indicators.