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Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools
TL;DR: In this article, the authors developed estimation methods that use the amount of selection on the observables in a model as a guide to the amount that should be selected on the unobservables in order to identify the effect of the endogenous variable.
Abstract: We develop estimation methods that use the amount of selection on the observables in a model as a guide to the amount of selection on the unobservables. We show that if the observed variables are a random subset of a large number of factors that influence the endogenous variable and the outcome of interest, then the relationship between the index of observables that determines the endogenous variable and the index that determines the outcome will be the same as the relationship between the indices of unobservables that determine the two variables. In some circumstances this fact may be used to identify the effect of the endogenous variable. We also propose an informal way to assess selectivity bias based on measuring the ratio of selection on unobservables to selection on observables that would be required if one is to attribute the entire effect of the endogenous variable to selection bias. We use our methods to estimate the effect of attending a Catholic high school on a variety of outcomes. Our main conclusion is that Catholic high schools substantially increase the probability of graduating from high school and, more tentatively, college attendance. We do not find much evidence for an effect on test scores.
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TL;DR: This article developed an extension of the theory that connects bias explicitly to coefficient stability and showed that it is necessary to take into account coefficient and R-squared movements, and showed two validation exercises and discuss application to the economics literature.
Abstract: A common approach to evaluating robustness to omitted variable bias is to observe coefficient movements after inclusion of controls. This is informative only if selection on observables is informative about selection on unobservables. Although this link is known in theory in existing literature, very few empirical articles approach this formally. I develop an extension of the theory that connects bias explicitly to coefficient stability. I show that it is necessary to take into account coefficient and R-squared movements. I develop a formal bounding argument. I show two validation exercises and discuss application to the economics literature. Supplementary materials for this article are available online.
2,115 citations
Cites background or methods from "Selection on Observed and Unobserve..."
...In two articles following on their original article (Altonji, Elder, and Taber 2005b; Altonji et al. 2008) Altonji and coauthors suggested two methods for adjusting for idiosyncratic variance, an approach parallel to my use of Rmax....
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...…is fully identified by the observed controls corresponds to the extreme assumption that the relationship between treatment and unobservables can be fully recovered from the relationship between treatment and observables (Murphy and Topel 1990; Altonji, Elder, and Taber 2005a; Altonji et al. 2011)....
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...The derivation of closed-form estimators in the linear case represents an extension of the case of nonlinear estimation in Altonji, Elder, and Taber (2005a) and Altonji, Elder, and Taber (2002)....
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...The article follows most closely a series of articles that explore bias in treatment effect under proportional selection (Murphy and Topel 1990; Altonji, Elder, and Taber 2005a; Altonji et al. 2011)....
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...The calculation used is that from Altonji, Elder, and Taber (2005)....
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TL;DR: In this paper, the authors formalize the concepts of self-productivity and complementarity of human capital investments and use them to explain the evidence on skill formation, and provide a theoretical framework for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies, and for formulating policy.
Abstract: This paper presents economic models of child development that capture the essence of recent findings
from the empirical literature on skill formation. The goal of this essay is to provide a theoretical framework
for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical
studies, and for formulating policy. Central to our analysis is the concept that childhood has more than one
stage. We formalize the concepts of self-productivity and complementarity of human capital investments
and use them to explain the evidence on skill formation. Together, they explain why skill begets skill
through a multiplier process. Skill formation is a life cycle process. It starts in the womb and goes on
throughout life. Families play a role in this process that is far more important than the role of schools.
There are multiple skills and multiple abilities that are important for adult success. Abilities are both
inherited and created, and the traditional debate about nature versus nurture is scientiÞcally obsolete.
Human capital investment exhibits both self-productivity and complementarity. Skill attainment at one
stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity). Early
investment facilitates the productivity of later investment (complementarity). Early investments are not
productive if they are not followed up by later investments (another aspect of complementarity). This
complementarity explains why there is no equity-efficiency trade-off for early investment. The returns to
investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very
costly as a consequence of both self-productivity and complementarity.
1,585 citations
Cites background from "Selection on Observed and Unobserve..."
...With common investment goods, we can solve out for S 1 and S N 1 in terms of I1 to simplify (5) and (6) to reach S 2 = {(γ1 + γ2) (I1) + (1− γ1 − γ2) (I2)} 1 α (10)...
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...Technologies (5) and (6) can rationalize this pattern....
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...= © γ1 ¡ S 1 ¢α + γ2 ¡ S 1 ¢α + (1− γ1 − γ2) ¡ I 2 ¢αa 1 α where 1 ≥ γ1 ≥ 0 1 ≥ γ2 ≥ 0 1 ≥ 1− γ1 − γ2 ≥ 0 , (5)...
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...For parameterization (5), this is obtained by imposing γ1+ γ2 = 1....
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TL;DR: This article examined the long-term impacts of Africa's slave trade and found that individuals whose ancestors were heavily raided during the slave trade are less trusting today, which may persist to this day.
Abstract: In a recent study, Nunn (2008) examines the long-term impacts of Africa’s slave trade. He finds that the slave trade, which occurred over a period of more than 400 years, had a significant negative effect on long-term economic development. Although the article arguably identifies a negative causal relationship between the slave trade and income today, the analysis is unable to establish the exact causal mechanisms underlying this reduced-form relationship. In this article, we examine one of the channels through which the slave trade may affect economic development today. Combining contemporary individual-level survey data with historical data on slave shipments by ethnic group, we ask whether the slave trade caused a culture of mistrust to develop within Africa. Initially, slaves were captured primarily through state organized raids and warfare, but as the trade progressed, the environment of ubiquitous insecurity caused individuals to turn on others—including friends and family members—and to kidnap, trick, and sell each other into slavery (Sigismund Wilhelm Koelle 1854; P. E. H. Hair 1965; Charles Piot 1996). We hypothesize that in this environment, a culture of mistrust may have evolved, which may persist to this day. We show that current differences in trust levels within Africa can be traced back to the transatlantic and Indian Ocean slave trades. Combining contemporary individual-level survey data with historical data on slave shipments by ethnic group, we find that individuals whose ancestors were heavily raided during the slave trade are less trusting today. Evidence from a variety of identification strategies suggests that the relationship is causal. Examining causal mechanisms, we show that most of the impact of the slave trade is through factors that are internal to the individual, such as cultural norms, beliefs, and values. (JEL J15, N57, Z13)
1,325 citations
TL;DR: The authors used the different mortality rates of European colonialists to estimate the effect of institutions on economic performance and found that in places where mortality rates were high, colonizers did not settle, but set up extractive institutions that exist to the present day.
Abstract: This article uses the different mortality rates of European colonialists to estimate the effect of institutions on economic performance. Europeans adopted very different colonization policies in different colonies. In places where mortality rates were high they did not settle, but set up extractive institutions that exist to the present day. By exploring the different mortality rates faced by soldiers, bishops and sailors in the colonies in the 17th, 18th and 19th Centuries, we were able to estimate the long-term effect of colonial institutions on per capita income.
941 citations
TL;DR: This paper studied the 1991-2002 Sierra Leone civil war using nationally representative household data on conflict experiences, postwar economic outcomes, local politics and collective action, and found that individuals whose households directly experienced more intense war violence are robustly more likely to attend community meetings, more likely join local political and community groups, and more likely vote.
910 citations
Cites background from "Selection on Observed and Unobserve..."
...14 In an analogous set-up, Altonji et al. (2005) estimate a ratio of 3.55, and they interpret that (much smaller) ratio as evidence that unobservables are unlikely to explain away their entire effect of Catholic school attendance on outcomes. percentage point increase in social group membership and…...
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...Following Altonji et al. (2005), we formalize this intuition and derive the ratio of the “influence” of omitted variables relative to the observed control variables that would be needed to fully explain away our victimization result....
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References
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TL;DR: In this paper, the authors investigated conditions sufficient for identification of average treatment effects using instrumental variables and showed that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect.
Abstract: We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.
3,154 citations
TL;DR: In this article, a nonparametric maximum likelihood estimator for the distribution of unobservables and a computational strategy for implementing it is developed. But the estimator does not account for population variation in observed and unobserved variables unless it is assumed that individuals are homogeneous.
Abstract: Conventional analyses of single spell duration models control for unobservables using a random effect estimator with the distribution of unobservables selected by ad hoc criteria. Both theoretical and empirical examples indicate that estimates of structural parameters obtained from conventional procedures are very sensitive to the choice of mixing distribution. Conventional procedures overparameterize duration models. We develop a consistent nonparametric maximum likelihood estimator for the distribution of unobservables and a computational strategy for implementing it. For a sample of unemployed workers our estimator produces estimates in concordance with standard search theory while conventional estimators do not. ECONOMIC THEORIES of search unemployment (Lippman and McCall [34]; Flinn and Heckman [14]), job turnover (Jovanovic [25]), mortality (Harris [17]), labor supply (Heckman and Willis [23]) and marital instability (Becker [3]) produce structural distributions for durations of occupancy of states. These theories generate qualitative predictions about the effects of changes in parameters on these structural distributions, and occasionally predict their functional forms.2 In order to test economic theories about durations and recover structural parameters, it is necessary to account for population variation in observed and unobserved variables unless it is assumed a priori that individuals are homogeneous.3 In every microeconomic study in which the hypothesis of heterogeneity is subject to test, it is not rejected. Temporally persistent unobserved components are an empirically important fact of life in microeconomic data (Heckman [19]). Since the appearance of papers by Silcock [39] and Blumen, Kogan, and McCarthy [5], social scientists have been aware that failure to adequately control for population heterogeneity can produce severe bias in structural estimates of duration models. Serious empirical analysts attempt to control for these unob
2,940 citations
TL;DR: In this article, the authors investigated conditions sufficient for identification of average treatment effects using instrumental variables and showed that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect.
Abstract: We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.(This abstract was borrowed from another version of this item.)
2,940 citations
Book•
01 Jan 1984
TL;DR: The Linear Model and Instrumental Variables Estimators as mentioned in this paper have been used to estimate Asymptotic Covariance Matrices, and Central Limit Theory has been applied to this problem.
Abstract: The Linear Model and Instrumental Variables Estimators. Consistency. Laws of Large Numbers. Asymptotic Normality. Central Limit Theory. Estimating Asymptotic Covariance Matrices. Functional Central Limit Theory and Applications. Directions for Further Study. Solution Set. References. Index.
1,746 citations
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TL;DR: In this article, the authors developed asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero.
Abstract: This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).
1,739 citations