Discussionweek12

1. What is the research question that the authors are interested in estimating? (2-3 sentences in your own words)

The authors are interested in estimating the productivity of mental health care in improving mental health outcomes among adults in Puerto Rico. Specifically, they want to determine if the provision of mental health care has a causal effect on improving patients’ mental health status.

2. What is the OLS regression specification/functional form/estimating equation to answer the research question above that a novice Econometrician would run (that you know we should not run as it could be biased)? (1-line mathematical equation, though you can explain the variables in words. Make sure your subscripts are fine. It might be easier to type out the equation in RPubs and insert the link, or in Word equation mode and then screenshot it inside, or just write by hand and screenshot it into Canvas).

\[ Outcome_i = \alpha_0 + \alpha_1 MH + \beta_1 Formal2_i + \gamma X_i + \epsilon \] MH: Mental health condition. OUTCOME: Improvement in mental health status (binary outcome). FORMAL2: Indicator variable for whether the patient received any formal mental health care. X: Control variables (e.g., demographic characteristics, baseline mental health status). ϵ: Error term.

3. Why would running the above naive OLS specification cause bias? Please explain (2-3 sentences. EG reverse causation, simultaneity bias, et cetra in words)

Running the above naive OLS would be biased due to potential selection bias. The choice to seek treatment may be correlated with unobserved factors, such as the severity of the illness or motivation to get better, which also affect the mental health outcome. Thus, the treatment variable (‘FORMAL2’) may be endogenous, leading to biased and inconsistent estimates.

4. What instrument (Z) can you use to get around and get true causal effects?

The study uses travel distance to the nearest mental health provider, and its interaction with car ownership, as instrumental variables. These instruments are correlated with the likelihood of receiving treatment (relevance condition) but are assumed not to directly affect mental health outcomes (exogeneity condition).

1. Please give the first-stage and second-stage regression equations, and explain them. Try to convince the reader this is the better study design and should work.

The first stage estimates how the instrumental variables (Distance and Insurance) affect the likelihood of receiving mental health care (FORMAL2):

\[ FORMAL2_{estimation} = \beta_0 + \beta_1 * Z_i + \beta_2 * X_i + \epsilon_i \]

(Z_i the instrument like travel distance and insurance, X_i other covariates)

The second stage estimates the impact of the fitted value of FORMAL2 (from the first stage) on the improvement in mental health status.

\[ OUTCOME = \gamma_1 + \alpha_1 MH + δ_1 * FORMAL2_{estimation} + δ_2 * X + ν_i \] IV allows the isolation of exogenous variation in treatment, thereby addressing the bias that arises from non-random assignment in observational data.

1. Why would the instrument be relevant (strongly correlated with the endogenous variable)? Give an intuitive explanation in words.

Travel distance is relevant because it directly affects access to mental health services, thereby influencing the likelihood of seeking treatment. Health insurance coverage also affects access by reducing out-of-pocket costs, thereby encouraging the utilization of services.

2. Why would the instrument be exogenous (not affect the response variable in the second stage through any other channel except through the fitted value of the endogenous variables from the first stage)?

Travel distance and insurance are assumed to be exogenous because they are not directly related to the mental health improvement outcome, except through their effect on the likelihood of receiving treatment. It is assumed that they do not directly affect the patient’s health outcome beyond their effect on treatment access.

2. Can you give an example of when exogenetiy could be potentially violated? Just a theoretical case/use your imagination. This is in a way to argue why your opponent’s instrument may not be good and thus cast doubt on their study’s conclusion.

Exogeneity could be potentially violated if, for example, individuals with severe mental health issues choose to live closer to mental health facilities, leading to a direct correlation between distance and health outcomes. Similarly, insurance type may be correlated with socioeconomic factors that independently influence mental health outcomes, introducing endogeneity.