Weekly Discussion
Paper: The Productivity of Mental Health Care: An Instrumental Variable Approach
Mingshan Lu, Department of Economics, The University of Calgary, Canada
2. What is the OLS regression specification/functional form/estimating equation to answer the research question above that a novice Econometrician would run?
Model 1:
\[ OUTCOME = a_{11} +\alpha_{11} H_0 + \beta_{11} FORMAL_2 + \gamma_{11}X+ \eta_{11} \]
OUTCOME - representing the improvement in mental health status
H_0 - representing the individual’s mental health condition at the initial survey
FORMAL_2 - representing whether the individual received any formal mental health care in the past year
X - A set of control variables including socioeconomic characteristics such as age, gender, income, and education level.
3. Why would run the above naive OLS specification cause bias? Please explain
There is reverse causality in the model. Because the treatment variables may be influenced by unobserved factors like the severity of illness or the individual’s motivation to seek care. These unobserved factors can confound the relationship between treatment and the outcome.
4. what instrument can you use to get around and get true causal effects?
IV: Distance
First-Stage:
\[ FORMAL2_{11} = \pi_0 + \pi_1 DISTANCE_{11} + v_{11} \]
FORMAL_2 is the endogenous treatment variable indicating whether the individual received formal mental health care in the past year.
Distance is the instrument, representing the physical distance between the individual’s residence and the nearest mental health care facility.
Second-Stage
\[ OUTCOME_i = a_{11} +\alpha_{11} H_0 +\sigma_{11}\hat{FORMAL2} + \gamma_{11}X +\eta_{11} \]
OUTCOME is the mental health outcome variable, measured as the change in mental health status.
hat_FORMAL2 is the predicted value from the first-stage regression, representing the exogenous variation in treatment due to distance.
4.1.1 Why would the instrument be relevant?
Distance will affect the decision to seek formal care.
Individuals who live closer to mental health care facilities are more likely to seek formal treatment due to lower transportation costs and easier access. Conversely, individuals who live further away from care facilities may face logistical and financial barriers that discourage them from seeking care.
4.1.2 Why would the instrument be exogenous?
The instrument is exogenous because the distance to the care facility is unlikely to directly influence the mental health outcome. The physical distance to a mental health care facility itself does not directly affect the individual’s mental health status. It merely affects their ability to access formal care.
4.2 Can you give an example of when exogeneity could be potentially violated?
As an example, people living in rural areas who are more likely to be far from care facilities also have less access to other resources like education, social support, or financial security, which may influence their mental health status independently of their treatment. In this case, the distance variable could be correlated with unobserved factors like socioeconomic status that directly affect mental health outcomes. For instance, rural areas might have higher rates of poverty and lower education levels, which could contribute to worse mental health outcomes, regardless of whether individuals receive formal care.