A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

This chapter addresses two different but related approaches, both widely used within the literature on the econometrics of program evaluation: the Local average treatment effect (LATE) and the Regression-discontinuity-design (RDD). Considered as nearly quasi-experimental methods, these approaches have recently been the subject of a vigorous interest as tools for detecting treatment effects within special statistical settings. The first part of the chapter covers the theory behind LATE, thus illustrating how such approach can be embedded within the setting of a randomized experiment with imperfect compliance. The discussion then goes on to present the Wald estimator of LATE, and to extend LATE to the case of multiple instruments and multiple treatments. The second part of the chapter illustrates the RDD econometric theoretical background; in particular, it discusses separately sharp RDD and fuzzy RDD, and suggests a protocol for the empirical implementation of such approaches. The chapter ends with some illustrative empirical implementation of both LATE and RDD performed using Stata on both real and simulative examples.

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post-regularization and post-selection inference that are uniformly valid (honest) across a wide-range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment condition framework, which arises from structural equation models in econometrics. Here too the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, modern machine learning methods can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxilliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsity-based estimation of regression functions for function-valued outcomes.

Political scientists frequently use instrumental variables (IV) estimation to estimate the causal effect of an endogenous treatment variable. However, when the treatment effect is heterogeneous, this estimation strategy only recovers the local average treatment effect (LATE). The LATE is an average treatment effect (ATE) for a subset of the population: units that receive treatment if and only if they are induced by an exogenous IV. However, researchers may instead be interested in the ATE for the entire population of interest. In this article, we develop a simple reweighting method for estimating the ATE, shedding light on the identification challenge posed in moving from the LATE to the ATE. We apply our method to two published experiments in political science in which we demonstrate that the LATE has the potential to substantively differ from the ATE.

Relaxing conditions for local average treatment effect in fuzzy regression discontinuity

The local average treatment effect (LATE) may differ from the average treatment effect (ATE) when those influenced by the instrument are not representative of the overall population. Heterogeneity in treatment effects may imply that parameter estimates from 2SLS are uninformative regarding the average treatment effect, motivating a search for instruments that affect a larger share of the population. In this paper, I present and estimate a model of home production with heterogeneous costs and benefits to fertility. The results indicate that a sex-preference instrument in Taiwan produces IV estimates closer to the estimated ATE than in the United States, where sex preference is weaker.

We examine the heterogeneous and dynamic impact of China's New Rural Pension Scheme on intergenerational wealth dependence using a nationally representative longitudinal household survey covering the period 2011-13.We adopt an instrumental quantile regressiondiscontinuity design to address the endogeneity of partial compliance of the pension scheme and the observed individual heterogeneity.Overall, we find that the pension scheme smooths wealth dependence between generations in the short term, but strengthens the persistence of assets among the wealthiest households in the medium term.The mechanisms underlying these distributional effects are intergenerational transfers, time reallocation, and filial adjustments of the wealth portfolio.Complementary policy interventions, particularly for the poor across generations, would be needed to neutralize the distributional impact of the pension in terms of intergenerational wealth persistence.

This thesis examines the impact of parental job loss and parental job insecurity on several academic outcomes of their offspring. Recent evidence has shown that parental job loss negatively influences the school performance of their offspring. Chapter 2 uses an original dataset I collected myself (described in Chapter 1) to study the effect of parental job loss on children’s school performance during the Great Recession in Spain. Conditioning on student fixed effects and observed covariates, the Great Recession generates variation in job loss that could be considered analogous to that provided by randomisation. The results show that after father’s job loss, students experience a negative and significant decrease on average grades of about 13 to 19% of a standard deviation. This effect remains unaltered once the impact of mother’s job loss on grades is accounted for. Interestingly, maternal job loss has no significant effect on the school performance of her offspring. Moreover, school performance prior to father’s job loss is not affected by future job losses, reinforcing the causal interpretation of the link between father’s job loss and children’s educational outcomes. Finally, the impact of paternal job loss is not homogeneous across students, but it is rather largely concentrated among children whose fathers suffer long unemployment spells after job loss and those students in already disadvantaged families in terms of the level of education of the father. Therefore, these results are pointing out a mechanism (paternal job loss) through which further inequalities might develop during and after a deep economic crisis. Chapter 3 uses exogenous variation in regional labour market policies in Spain to identify the impact of paternal job insecurity on the students’ probability of graduating from compulsory education on time. Using data from the Spanish Labour Force Survey, average marginal effects and local average treatment effects (LATE) are estimated. Results indicate that students whose fathers hold a permanent contract (as opposed to a temporary, fixed-term contract) the year they should graduate from compulsory education are, on average, 7 percentage points more likely to graduate on time. LATE estimates are considerably higher, suggesting that those students whose fathers obtained a permanent contract as a result of the availability of regional subsidies reaped bigger benefits from paternal job stability. These results hold when maternal job insecurity is also accounted for, and they are concentrated on male students. Importantly, these findings seem to indicate that the pervasive effects of temporary contracts found elsewhere in the literature go beyond the employees and affect negatively their children’s educational outcomes.

In causal randomized experiments or psychological trials, the two-stage least squares (2SLS) model with instrument variables (IVs) is a widely used approach to address the issue of treatment endogeneity. The IVs are used to estimate a part of the causal effect whose estimation is not affected by the violation of the linearity assumption in the causal model, and the causal effect of interest in the 2SLS model becomes the local average treatment effect (LATE). Because practical data usually violate the normality assumption, the LATE estimate from the traditional normal-distribution-based method may be inefficient or even biased. This study proposes a robust Bayesian estimation method using Student’s t distributions to model data with heavy tails or containing outliers and compares the performance of the proposed robust method to that of the traditional normal-distribution-based method. A Monte Carlo simulation study is conducted and shows that the proposed robust method outperforms the traditional method when data are contaminated. The robust method provides more accurate and efficient LATE estimates and better model fits and thus is recommended to be used in general in the 2SLS modeling with IVs.

Incentivizing biofortification- defeating malnutrition and nutrient deficiency; a novel approach to food-nutritional security in Nigeria was investigated. Purposive sampling technique selected 201 respondents used for the study. Data collection was made using research instrument and data were analyzed using frequency, percentage, charts, local average treatment effect (LATE), food security index and probit model. Research findings indicated that 52.2% practiced agronomic biofortification, 25.4% practiced conventional biofortification and the least 22.4% engaged in transgenic biofortification. Enhanced protein composition and bioavailability 93.5%, enhanced oil composition and nutrient 84.6%, enhanced vitamin nutrient 88.6% and enhanced mineral components and micro elements 95.5% were major rationale for biofortification engagement. The LATE (WALD) and LATE (IV) results produced 0.8721 and 0.9109 estimates, indicating that practice of biofortification increased nutritional index by 87.2% and 91.1%. A total of 92 respondents were food secured and met the nutrient calorie requirements, while 109 were food in-secured. Food nutritional index showed that vegetables and legumes occupied the peak with values of 30.8 and 24.7. Technological innovation (P<0.01), land size (P<0.05), modified varieties (P<0.01), pests and diseases (P<0.01), soil-types (P<0.05), and climate issues (P<-0.01) exhibited both favorable and unfavorable influence on food crop biofortification. The study recommended awareness creation, agro-seminars/symposiums, capacity development and research and innovation and government involvements as necessary procedures for improving food crops biofortification in the State.

This paper provides a review of methodological advancements in the evaluation of heterogeneous treatment effect models based on instrumental variable (IV) methods. We focus on models that achieve identification by assuming monotonicity of the treatment in the IV and analyze local average and quantile treatment effects for the subpopulation of compliers. We start with a comprehensive discussion of the binary treatment and binary IV case as for instance relevant in randomized experiments with imperfect compliance. We then review extensions to identification and estimation with covariates, multi-valued and multiple treatments and instruments, outcome attrition and measurement error, and the identification of direct and indirect treatment effects, among others. We also discuss testable implications and possible relaxations of the IV assumptions, approaches to extrapolate from local to global treatment effects, and the relationship to other IV approaches.

Summary Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges of causal estimation with a binary outcome and show that, surprisingly, it can be more difficult than in the case with a continuous outcome. We propose novel modelling and estimation procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness and efficiency. Our approach is illustrated via simulation studies and a real data analysis.

In this paper, we consider a switching regression model with count data outcomes, where the possible outcome differs across two alternate states and individuals endogenously select one of the states. We assume lognormal latent heterogeneity. Building on the switching regression model, we derive estimators of various treatment effects: the average treatment effect, the average treatment effect on the treated, the local average treatment effect, and the marginal treatment effect. We illustrate an application that examines the effects of public insurance on the number of doctor visits using the data employed by previous studies.

This paper aims to assess the impact of the use of credit in rice farming on productivity and income in Benin. It applies the potential outcomes framework to data collected from 342 rice farmers in Benin to estiamte the Local Average Treatment Effect (LATE). Findings show that the use of credit in rice farming has positive and significant impact on farmers' rice yield, rice output, rice income, per capita rice income, annual household income and per capita annual household income. Therefore, facilitating access of rice farmers to agricultural credit is a good strategy for supporting rice sector development, and therefore contributing to food security and poverty alleviation in Benin. Moreover, the impacts were higher for female farmers than male farmers. Therefore, it is important to control for heterogeneity in impact assessment studies in order to appreciate the real effect of interventions on different social categories in the target population.

This paper finds evidence of positive neighborhood effects on adult labor market outcomes using the Moving to Opportunity (MTO) housing mobility experiment. Our results stand in such sharp contrast to the current literature because our analysis focuses on outcomes of the subpopulation induced by the program to move to a higher quality neighborhood, while previous analyses have focused on outcomes of either the entire population or the subpopulation induced by the program to move to any neighborhood. We propose and implement a new strategy for identifying heterogeneous transition-specific effects that exploits the identification of the idiosyncratic component of an ordered choice model. We estimate Local Average Treatment Effects (LATEs) of the change in quality most commonly induced by MTO vouchers, between the first and second deciles of the national distribution of neighborhood quality. Although MTO vouchers induced much larger changes in neighborhood quality than standard Section 8 vouchers, these LATEs only pertain to a subpopulation representing under 10 percent of program participants.

Recent theoretical contributions to the problem of job mobility decisions during the transition from a centrally planned economy to a market economy suggest that individuals self-select into specific forms of job mobility behaviour on the basis of their unobservable characteristics. In this case, standard results from both simple treatment-control comparisons of average income and from OLS regressions of reduced-form earnings equations do generally not identify any causal effect of job mobility on income. This paper addresses the endogeneity problem related to job mobility in a quasi-experimental framework and estimates the returns to (early) job mobility in the Eastern German transition process for the period 1990-96. Identification is based on instrumental variables estimation. Two instruments are suggested that account for some of the variation in the job mobility behaviour throughout transition. They allow further for a natural distinction between forced and voluntary movers on the basis of the local average treatment effect (LATE) interpretation of IV estimates. Estimation results contrast strongly with results from both simple treatment-control comparisons and simple OLS estimation. They suggest negative returns to forced job mobility as opposed to positive returns to voluntary job mobility early in transition, thus stressing the existence of heterogeneous returns to job mobility.