Lecture 5

In the context of heterogeneous treatment effects and instrumental variables, what is the most precise interpretation of what an IV estimator captures when neither the Average Treatment Effect (ATE) nor the Average Treatment Effect on the Treated (ATET) is accurately estimated?

Consider a scenario where $Z_i$ represents an instrument and $D_i$ represents treatment status. If $D_{1i}$ denotes individual $i$'s potential treatment status when $Z_i = 1$ and $D_{0i}$ denotes individual $i$'s potential treatment status when $Z_i = 0$, how is observed treatment status $D_i$ mathematically expressed in terms of $D_{0i}$, $D_{1i}$, and $Z_i$?

Assume an instrumental variable (IV) setup with heterogeneous treatment effects. If the instrument is only weakly correlated with treatment status, what inferential challenge is most likely to arise, potentially undermining the validity of causal claims?

In the context of Local Average Treatment Effect (LATE) estimation, which assumption is LEAST necessary for the LATE to be a valid causal effect for the subpopulation of compliers?

Consider a scenario where an instrument $Z$ is used to estimate the effect of treatment $D$ on outcome $Y$, but there is suspicion that $Z$ directly affects $Y$ for some individuals, violating the exclusion restriction. Which identification strategy could be employed to assess the sensitivity of the IV estimates to this violation, without requiring an additional instrument?

Suppose researchers use a draft lottery as an instrument ($Z$) to estimate the effect of military service ($D$) on subsequent earnings ($Y$). Assume that participating in Reserve Officers' Training Corps (ROTC) provides an alternative pathway to military service, irrespective of the lottery outcome. How does this affect the interpretation of the LATE?

In an instrumental variables context, what econometric specification can be employed to explicitly test for and, if present, address potential heterogeneity in the effect of the instrument on the treatment (i.e., heterogeneous first-stage effects)?

In the context of Local Average Treatment Effect (LATE), if a treatment has a uniformly positive effect across an entire population, under what specific condition would the reduced form be zero?

Given that different instrumental variables (IVs) can yield different LATEs, which primarily reflects variations in the complier groups, what is the MOST significant challenge this poses for causal inference?

Instrumental variable (IV) estimations are characterized by a trade-off between internal and what other form of validity; considering the nature of LATE?

What is a central argument made by scholars such as Angrist, Imbens, and Rubin regarding the practical utility of LATE estimates in econometric studies?

Heckman, Deaton, and others express skepticism about the usefulness of LATE. What is their primary critique concerning the application of instrumental variables in economic research?

Why is understanding the characteristics of the compliant sub-populations crucial for extrapolating causal effects derived from instrumental variables to broader populations?

Acemoglu and Angrist (2000) suggest that quarter-of-birth instruments and state compulsory laws affect similar groups for similar reasons. What implication does this have for the validity and interpretation of IV estimates?

If two or more instruments yield similar IV estimates, despite their compliant sub-populations being substantially different, what hypothesis might researchers be inclined to adopt regarding the nature of the treatment effect?

In the study by Angrist, Lavy, and Schlosser (2006) on the effects of family size on children’s education, what kind of inferences are they able to draw?

Consider a scenario where an intervention has heterogeneous effects across a population. Some individuals benefit significantly, while others experience negligible or even negative consequences. Under what conditions would the LATE provide a policy-relevant estimate of the treatment effect?

Under the aegis of the Local Average Treatment Effect (LATE) theorem, which constellation of conditions must be rigorously satisfied to ensure the instrument reliably estimates the average causal effect exclusively for the complier subpopulation?

In experimental designs marred by imperfect compliance, which of the following scenarios most accurately exemplifies the manifestation of 'resisters' and 'always-takers' within a cohort randomized to a novel therapeutic intervention?

Within the framework of instrumental variable analysis applied to draft lottery scenarios, how are 'compliers' most precisely characterized in relation to their behavioral response to the lottery outcome and subsequent military service?

Consider a scenario where a draft lottery is employed as an instrument to estimate the causal effect of military service on long-term earnings. If the lottery outcome predominantly influences military service decisions among individuals from lower socioeconomic strata, while having negligible impact on those from privileged backgrounds due to deferment options, what population parameter is most accurately identified by the LATE estimator in this specific context?

What critical role does the monotonicity assumption play within the theoretical underpinnings of the Local Average Treatment Effect (LATE) theorem, and how does its violation fundamentally compromise the interpretability of instrumental variable estimates?

In the absence of monotonicity within the LATE framework, how does the decomposition of the reduced form effect on the outcome variable, $E[Y_i | Z_i = 1] - E[Y_i | Z_i = 0]$, reveal the potential for compromised causal inference, particularly concerning the roles of compliers and defiers?

The LATE theorem explicitly estimates the average causal effect 'for the group affected by the instrument.' In the context of a randomized controlled trial employing encouragement design with imperfect compliance, which specific population's causal effect is being precisely quantified?

Within the stipulated conditions for valid LATE estimation, the requirement that the instrument 'affects the outcome through a single known channel' is paramount. In scenarios where a draft lottery influences both military service and educational attainment due to deferment policies, how is the validity of the single channel condition potentially jeopardized?

The 'first stage' requirement in LATE theorem mandates a statistically significant association between the instrument and the treatment. In an experimental context where a novel educational voucher program (instrument) intended to promote private school enrollment (treatment) exhibits minimal impact on actual enrollment rates due to logistical barriers and parental inertia, what implication does this weak first stage have for LATE estimation?

Considering the condition that the instrument 'affects the causal channel of interest only in one direction' within the LATE framework, evaluate a hypothetical scenario where a job training program (instrument) intended to improve employment rates (causal channel) inadvertently discourages some highly skilled individuals from seeking employment due to perceived program inadequacy, while encouraging less skilled individuals. How does this bidirectional influence challenge the assumptions of LATE?

Consider a scenario where an instrumental variable (IV) is employed to estimate the causal impact of education on income. Years of schooling completed is endogenous due to potential omitted variable bias (ability bias, motivation etc.). A researcher proposes using proximity to a historically black college or university (HBCU) as an instrument, arguing that access to HBCUs is exogenous to individual ability, but influences educational attainment. The researcher finds a statistically significant first stage and proceeds to estimate the effect using 2SLS. Given the nuanced challenges inherent in IV estimation, what potential threat to the validity of the IV estimates should the researcher MOST rigorously address to ensure the causal interpretation of the results?

In a study examining the effect of class size on student test scores, a researcher uses school enrollment as an instrument for class size. The assumption is that larger school enrollments lead to larger class sizes, but do not directly affect individual student test scores. Suppose, however, that schools with larger enrollments also tend to have more resources (e.g., better facilities, more experienced teachers) that directly improve student performance, independent of class size. How does this scenario impact the validity of the instrumental variable (IV) estimation, and what specific consequence arises from this situation?

A researcher seeks to estimate the causal effect of job training programs on individual earnings. However, individuals who enroll in job training programs may be more motivated or skilled than those who do not, leading to selection bias. To address this, the researcher proposes using the proximity to job training centers as an instrument, arguing that it affects participation in job training but is otherwise unrelated to individual earnings potential. Assume the first stage is strong. Which of the following statements MOST accurately describes the Local Average Treatment Effect (LATE) that the IV estimator will identify in this context, given the assumptions of independence, exclusion restriction, monotonicity, and a valid first stage?

In an instrumental variables (IV) framework designed to correct for measurement error in an explanatory variable, $X$, which is measured with classical error as $X = \hat{X} + \nu$ (where $\hat{X}$ is the true value and $\nu$ is the measurement error), what is the MOST critical condition that the chosen instrument, $Z$, must satisfy to ensure consistent estimation of the parameter of interest?

Consider the following model where $X$ is suspected to be endogenous: $y = \alpha + \beta X + u$. To address this, an instrumental variable $Z$ is used. Suppose we know that $Cov(X, u) \neq 0$ and we have a valid instrument $Z$ such that $Cov(Z, u) = 0$ and $Cov(Z, X) \neq 0$. However, it is discovered that the measurement of $X$ is subject to classical measurement error, such that the observed value is $X_{obs} = X + \nu$, where $\nu$ is a random error independent of $X$ and $u$. What is the MOST accurate characterization of the effect of this measurement error on the consistency of the 2SLS estimator for $\beta$?

In the context of Instrumental Variables (IV) estimation, which of the following scenarios would MOST severely undermine the validity of the Local Average Treatment Effect (LATE) interpretation?

Consider an instrumental variable (IV) model where the instrument, Z, is thought to influence the treatment, D, which in turn affects the outcome, Y. If it is discovered that $E[Y|Z=1] - E[Y|Z=0] = 0$, which of the following inferences is MOST accurate, assuming all IV assumptions hold except where explicitly noted?

In a Local Average Treatment Effect (LATE) framework, imagine a scenario where the instrument is randomly assigned encouragement to attend a job training program (D), and the outcome is subsequent employment (Y). If the encouragement has no impact on employment rates (i.e., the reduced form effect is zero), which type of participant poses the greatest threat to the identifiability of a non-zero LATE?

Assume you are employing an instrumental variables (IV) strategy to estimate the causal impact of college attendance (D) on future earnings (Y), using proximity to a college as an instrument (Z). If individuals who live closer to a college also tend to have higher levels of parental education and greater access to resources, how can one MOST rigorously address concerns regarding the independence assumption $E[Y_{0i}, Z_i] = 0$?

In the context of the LATE theorem, consider a randomized experiment where a voucher is provided to encourage individuals to seek job training. Suppose the voucher increases participation in job training but does not perfectly predict it. Under what specific circumstance would the LATE be equivalent to the average treatment effect (ATE) of job training on the entire population?

In an instrumental variable framework, what is the MOST rigorous method to assess the exclusion restriction's validity when estimating the causal effect of a new drug ($D$) on patient recovery ($Y$), using a physician's preference for prescribing the drug as an instrument ($Z$)?

Within the context of instrumental variables (IV) estimation, suppose you are estimating the effect of education ($D$) on income ($Y$), using proximity to a 4-year college ($Z$) as an instrument. If it is suspected that individuals residing closer to colleges are systematically different along unobservable dimensions that also affect income (e.g., inherent motivation, access to better networks), which strategy would be MOST effective in mitigating bias while still leveraging the instrumental variable?

Suppose a researcher uses a randomized lottery for access to a specialized tutoring program as an instrument to estimate the effect of program participation on student test scores. However, a significant portion of the lottery winners do not actually participate in the tutoring program. How does this imperfect compliance affect the interpretation of the IV estimate?

Consider a scenario where a researcher aims to estimate the impact of attending a prestigious university ($D$) on future earnings ($Y$), using admission based on an exceptionally high standardized test score ($Z$) as an instrument. However, it is plausible that individuals with high test scores also possess inherent abilities and connections (e.g., innate intelligence, well-connected families) that would independently influence their earnings regardless of university attendance. Which advanced econometric technique MOST directly addresses this violation of the exclusion restriction while still leveraging the information from the instrument?