Soluzioni domande esercitazione linear probability model

The author use a LPM to estimate the change in probability of each

outcome. Does it make sense to use a LPM? Would you add

controls/covariates to the analysis? If yes, which ones?

SOL: Using LPM is correct given that the outcomes are binary. Analysis

could be performed using also logit or probit to see whether they are

robust. Important covariates could be: age, income, education, marital

status, country of birth, work status, health insurance.

3) Interpret columns 5 and 6 (2014 vs 2006) of tables 4 and 5 below.

What does unadjusted and adjusted mean?

SOL: Unadjusted models do not include any covariate, while adjusted

models include covariates. Table 4. “Between 2006 and 2014, there were

significant declines in emergency room visits among the total sample by

1.9 and 1.8 percentage points in the unadjusted and adjusted models,

respectively. During this period, the unadjusted models indicated

significant declines by 2 percent and 3 percent for white men and

women, respectively. These declines remained significant in the adjusted

models. The adjusted models showed a significant increase in emergency

room visits by 3 percent among black women.”

Table 5: “Based on models of unmet medical need (Table 5), the

percentage of respon- dents who reported unmet need increased

significantly by 2.1 and 2.5 percent- age points in adjusted models for

black men and women, respectively.”

4) Given that there is heteroskedasticity, the authors correct the S.E.

How?

SOL: They estimate the LPMs using robust S.E.

5) What empirical problems do you see in comparing 2006 with 2014?

Some changes to the policies occurred also during the period 2012

and 2014, therefore the authors compare also these two years.

What are the results in this case (check the final two columns of

each table)?

SOL: “While reductions in racial/ethnic and gender disparities in service

use and access are expected because of health care reform, the extent of

economic

changes during this period is unclear especially given the

turmoil in the years preceding the MHPAEA and ACA.” … “Findings

from the 2012-2014 subanalysis provide important information about the

short-term progress of health care reform on reducing racial/ethnic and

gender disparities in the initial years of implementation and after full

implementation of the ACA in 2014.”

Table 4. “The subanalysis from 2012 to 2014 revealed significant declines

in emergency room visits by 1.9 and 1.5 percentage points for white

women in unadjusted and adjusted models, respectively. In addition, after

full adjustment, emergency room visits fell by 2.3 percentage points for

Hispanic women.”

Table 5: “In the subanalysis of data from 2012 to 2014, the unadjusted

models showed significant declines among all respondents who reported

unmet need by 1.5 percent, including white women by 1.5 percent,

Hispanic men by 2.6 percent, Hispanic women by 2.9 percent, and black

men by 3.4 percent. How- ever, most of these differences disappeared in

the regression-adjusted models. Although the magnitudes of the adjusted

differences were smaller, changes among white men and Hispanic women

remained significant.”

6) The author performs a by-group analysis. Is this ideal? What could

have been a different alternative?

SOL: The authors could have pooled the data 2006 and 2014 and could

have created a dummy for the year (0 if 2006 and 1 if 2014). Suppose

that we are interested in seeing the differences in health care among

racial groups, then the empirical model can be:

Y =alpha+beta*year_dummy +gamma *Black +gamma *Hispanic +

it it 1 it 2 it

zeta *year_dummy * Black + zeta *year_dummy * Hispanic

1 it it 2 it it

+X ’delta+u

it it

Parameters zeta’s indicate the change in health care access or use of

Black or Hispanic with respect to Whites. This model and the subgroup

models are slightly different but this second alternative allows to

increase the sample size.

To really test whether there are differences both across race and gender,

the model should then include also all interactions with a gender dummy.