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Applied Micro-econometrics

ECON5006

Practice problems on IVs

Part 1: Definitions and Basic Concepts

1.   A good instrument in IV implementation has the following properties:

I.      It affects program participation directly.

II.      It does not affect the outcome variable directly but only through program participation.

III.      It affects other control variables (e.g., sex, age, mother’s education, etc.) directly.

a.   I and II

b.   II and III

c.   I and III

d.   III only

Solution: a. A good instrument: i) should predict the variation in the endogenous variable; ii) can only affect the outcome of interest through its effects on the         endogenous variable; iii) cannot affect other control variables (otherwise it would violate the exclusion restriction).

2.   Which method provides a local average treatment effect (LATE) under certain conditions?

I.      RCT

II.      IV

III.      OLS and RCT

a.   I and II

b.   II and III

c.   II only

d.   III only

Solution: a. Both RCT and IV strategies estimate causal impacts on a specific       population, which is the population that changes its behaviour (e.g., participates or does not participate in the program) because of the random assignment or the        instrument.

3.   In your own words, please explain how does the instrumental variables technique help address the issue of endogeneity in a variable/treatment of interest?

Solution: the instrumental variables technique helps address the issue of endogeneity in a variable/treatment of interest by predicting the variation in the endogenous          variable that is free” from selection bias or endogeneity.

4.   In your own words, please define each of the four potential subpopulations in empirical analysis:

I.      Compliers

II.      Always-takers

III.     Never-takers

IV.      Defiers

V.      Which of these populations is essential for policy analysis? Why?

Solution:

• Compliers: the population that is subject to change its behaviour as a result of the instrument, policy, or random assignment.

• Always-takers: the population that, no matter what, will always try to participate in the program.

• Never-takers: the population that, no matter what, will never participate in the program.

• Defiers: the population that will always behave in the opposite way to that predicted by the instrument, policy, or random assignment.

Compliers are essential for policy analysis because this is the population that responds to the policy incentives (or the instrument).

5.   Please define the concept of attenuation bias” and how the instrumental variables technique helps address this particular empirical threat.

Solution: attenuation bias is a type of bias induced by measurement error in the         treatment variable. Instrumental variables help address this particular empirical threat by predicting the variation in the endogenous variable that is “free” from                    measurement error.

Part 2: Study using an IV model (*)

There is no dispute that severely abused or neglected children should be protected, and a        foster family home has been judged the best alternative whenever possible. But child              protection agencies trade off two competing goods: family preservation and child protection. Thus, an important policy question is: how aggressive should child protective services be?     More aggressive child protection may reduce child abuse or neglect, but removal from           parents may be traumatic to children as well. A better understanding of the causal effects of  foster care on short and long-term outcomes for children at risk of placement would be useful to inform child-welfare policy.

Policy makers want to know the effects of foster care (FC) on juvenile delinquency (JD). To do so, they estimate two equations, 1b and 2b:

  

As in the study by Aizer and Doyle Jr. (2015) discussed in class, policy makers use              information on “the tendency of Foster Care placement” of individual investigators who      examine cases of child abuse or neglect. Table 1 below shows the characteristics of cases     (i.e., who reported the case, the age, sex, and race of the child, and the type of allegation) by whether an investigator has a “high” vs. “low” tendency of Foster Care placement:

 

Table 3 below shows results for the first stage, reduced form, and instrumental variables estimates:

 

Questions:

1)  Explain why estimating Equation 1b may provide a biased estimate of β1?

Solution: because Equation 1b does not account for the strong negative selection that exists among children being placed in Foster Care or in committing crimes (for          instance, children that come from more disadvantaged/ dysfunctional families are not only more likely to be placed in Foster Care as a child, but they may also have higher odds to commit a crime in the future, compared to other children coming from           “better” environments).

2)  Does adding control variables X in Equation 2b help reduce the bias of coefficient β1? If yes, by how much? Use estimates in Table 3 to support your answer.

Solution: Yes, to some extent. However, because of the strong negative selection that exists in Foster Care and in juvenile delinquency, controlling for observable                characteristics is insufficient to account for unobserved bias into FC/JD.

Estimates shown in Table 3 do not allow to identify this bias. To do so, you would need to compare the association between FC and JD in a model with and without  covariates (which is not shown in Table 3).

3)  To measure the effects of FC on JD, policy makers estimate a two-stage model using “the propensity” of an investigator of child abuse cases to place a child in Foster Care as instrument Z. Please write the first and second stage equations of this framework.

Solution:

First stage: FCi = β0 + β 1Zi + β2Xi + εi

 

Second stage: Yi = α0 + α1 FC_hati + α2Xi +μi                                                                                               Where FC is a dummy variable that takes the value of 1 if child i is placed in Foster  Care and 0 otherwise; α is the intercept; Z is the instrument that captures “the             propensity” of an investigator of child abuse cases to place a child in Foster Care; the variable X controls for individual characteristics (those shown in Table 1). ε is the

error term. The coefficient of interest in the first stage is β1 that represents the causal effect of being assigned to an investigator with a high propensity to place children in Foster Care on the probability of being placed in FC.

The second stage regresses the outcome of interest, Juvenile Delinquency, on      “FC_hati”, which is the predicted (or instrumented) probability of being placed in Foster Care obtained from estimating the first stage. The variable X controls for  individual characteristics (those shown in Table 1) and μ is the error term. The     coefficient of interest in the second stage is α 1 that represents the causal effect of being placed in Foster Care on the likelihood of being a juvenile delinquent.

4)  What are the assumptions that the instrument Z needs to satisfy for it to be a valid     instrument? Is the instrument valid based on the evidence shown? What does Table 1 say about the Independence assumption of Z?

Solution: For the instrument Z to be a valid instrument, the following assumptions need to hold:

•   There needs to be a meaningful first stage. That is, the instrument Z needs to have predictive power on the endogenous variable.

•   The instrument needs to be independent (or conditionally independent, after  accounting for some observable characteristics as predicted by the CIA). The instrument cannot be correlated with the error term.

•   The instrument can ONLY affect the outcome of interest through its effect on the endogenous variable. This is a crucial assumption!

•   The relationship between the instrument and the endogenous variable needs to be monotonic (that the instrument affects the endogenous variable in the same direction for everyone).

Summary statistics shown in Table 1 suggest that the characteristics of cases assigned to investigators with different types of “tendencies” for FC placement are similar,       which implies that the instrument Z is independent. [Another way of thinking about   the independence assumption of the instrument is that: If high FC-placement rate        investigators had cases that were more serious of abuse/neglect, it would suggest that particular cases were assigned to particular investigators and there would not be         random variation to exploit.]

5)  What is the IV estimate?

Solution: The IV (or LATE) estimate shown in Table 3 suggests that placing children in FC increases the likelihood of becoming a juvenile delinquent by 14.2 to 18.3         percentage points.

6)  Based on the results in Table 3, what is the policy recommendation? Is this LATE representative of all children placed in the Foster Care system?

Solution: The results suggest that foster care placement increases the likelihood of juvenile delinquency.

The LATE is not representative of what would happen to all children that go to FC. The LATE only represents the effect obtained from “marginal cases”, that is, cases where the investigators’ tendencies for FC placement can be the defining force to   decide whether or not to place a child in FC.