Linearity in Instrumental Variables Estimation: Problems and Solutions

The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all margins. This paper investigates the problems caused by the linearity restriction in IV estimation, and discusses possible remedies. We first examine the biases due to nonlinearity in the commonly used tests for non-zero treatment effects, selection bias, and instrument validity. Next, we consider three applications where theory suggests a nonlinear relationship, yet previous research has used linear IV estimators. We find that relaxing the linearity restriction in the IV estimation changes the qualitative conclusions about the relevant economic theory and the effectiveness of different policies.linear model, variable treatment intensity, nonlinearity, instrumental variables

Household Choices and Child Development

The growth in labor market participation among women with young children has raised concerns about the potential negative impact of the mother's absence from home on child outcomes. Recent data show that mother's time spent with children has declined in the last decade, while the indicators of children’s cognitive and noncognitive outcomes have worsened. The objective of our research is to estimate a model of the cognitive development process of children nested within an otherwise standard model of household life cycle behavior. The model generates endogenous dynamic interrelationships between the child quality and employment processes in the household, which are found to be consistent with patterns observed in the data. The estimated model is used to explore the effects of schooling subsidies and employment restrictions on household welfare and child development.Time Allocation; Child Development; Household Labor Supply

How much should we trust linear instrumental variables estimators? An application to family size and children's education

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. These results motivate a re-examination of recent evidence suggesting no causal effect of family size on children's education. Following common practice, a linear IV estimator has been used, assuming constant marginal effects of additional children across family sizes. We find that the conclusion of no effect of family size is an artifact of the linear specification, which masks substantial marginal family size effects

Instrumental variables estimation with partially missing instruments

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the instrument is non-randomly missing, standard IV estimators require strong, auxiliary assumptions to be consistent. In many (quasi)natural experiments, the auxiliary assumptions are unlikely to hold. We therefore introduce alternative IV estimators that are robust to non-randomly missing instruments without auxiliary assumptions. A Monte-Carlo study illustrates our results

Linearity in instrumental variables estimation: Problems and solutions

The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all margins. This paper investigates the problems caused by the linearity restriction in IV estimation, and discusses possible remedies. We first examine the biases due to nonlinearity in the commonly used tests for non-zero treatment effects, selection bias, and instrument validity. Next, we consider three applications where theory suggests a nonlinear relationship, yet previous research has used linear IV estimators. We find that relaxing the linearity restriction in the IV estimation changes the qualitative conclusions about the relevant economic theory and the effectiveness of different policies

What Linear Estimators Miss: Re-Examining the Effects of Family Income on Child Outcomes

This paper uses a rich Norwegian dataset to re-examine the causal relationship between family income and child outcomes. Motivated by theoretical predictions and OLS results that suggest a nonlinear relationship, we depart from previous studies in allowing the marginal effects on children’s outcomes of an increase in family income to vary across the income distribution. Our nonlinear IV and fixed-effect estimates show an increasing, concave relationship between family income and children's educational attainment and IQ. The linear estimates, however, suggest small, if any, effect of family income, because they assign little weight to the large marginal effects at the lower part of the income distribution.instrumental variables estimation, fixed effects estimation, nonlinearities, child development, family income, linear models

Policymakers must be mindful that transfers to households to support young children will also be used to finance parents’ leisure and consumption

There is a growing consensus among academics and policymakers that interventions in early childhood to improve cognitive skills help to boost those made later during adolescence. In new research, Daniela Del Boca, Christopher Flinn, and Matthew Wiswall find evidence to support these interventions, but they argue that policymakers need to understand that households do not act solely to maximize their child’s development. They write that while government transfers of money and goods to households to support young children will be used to support them, they may also be used by parents to finance their own purchases of consumption goods and leisure

Household choices and child development

The growth in labor market participation among women with young children has raised concerns about the potential negative impact of the mother's absence from home on child outcomes. Recent data show that mother's time spent with children has declined in the last decade, while the indicators of children's cognitive and noncognitive outcomes have worsened. The objective of our research is to estimate a model of the cognitive development process of children nested within an otherwise standard model of household life cycle behavior. The model generates endogenous dynamic interrelationships between the child quality and employment processes in the household, which are found to be consistent with patterns observed in the data. The estimated model is used to explore the effects of schooling subsidies and employment restrictions on household welfare and child development

Transfers to Households with Children and Child Development

In this paper we utilize a model of household investments in the development of children to explore the impact of various transfer policies on the distribution of child outcomes. We develop a cost criterion that can be used to compare the cost effectiveness of unrestricted, restricted, and conditional cash transfer systems, and find that an optimally chosen conditional cash transfer program is the most cost efficient way to attain any given gain in average child quality. We explore several design elements for the conditional cash transfer system and discuss the role of production function uncertainty and measurement error