Question

Some policy-makers have raised concerns that having early starting times for schools hurts child learning outcomes and long-term development due to sleep deprivation. For the 2012-2013 school year, Los Angeles Unified School Districts decides to change the high school start time from 7:15am to 8:30am in 21 of its high schools, but leaves the 7:15am start time in the other 44 high schools. a) You want to construct a differences-in-differences estimate of the effect of this policy on child test scores at the end of the 2012-13 school year. What data do you need to collect to do this? b) You estimate the regression equation T estscore = 70 + 7 ∗ treatment + 2 ∗ post + 7 ∗ post ∗ treatment Where the p-value for βˆtreatment is .03, for βˆpost is .23, and for βˆpost∗treatment is .007. (i) Are the test scores initially higher or lower in areas that changed their start times? Why? (ii) Based on this regression output, what do you conclude about the effect of the change in school start times? (iii) What assumption are you making for the differences-in-differences estimate to give a valid estimate of the effect of the law? How could you test that in this context?

Answer 1

(a) The data required to do a difference in difference estimate are:

• The two groups that are the treatment groups and the control groups. A response variable can be selected specifically for the group. This variable will denote the effect of treatment on the study.
• A variable that measures the learning outcomes of school children for the two groups such as marks scored in a class test. This will be our response variable.
• An additional variable to measure the sleep deprivation can help model the situation. This will be the independent variable in the study.

(b) (i) The test scores are initially lower in areas that changed their start times. This is because in the estimated regression equation the value of the coefficient is positive for the variable measuring the treatment effect. Thus for the units who received the treatment the test score was higher.

(ii) Since the p-value for the βˆtreatment is 0.03 and βˆpost∗treatment is .007 we see that it is not significant at 0.05 level. Thus it can be said that there is no significant effect of the change in school start times.

(iii) We make assumptions similar to the assumptions of an OLS model in a difference-in-differences analysis. These assumptions are:

• The regression model is linear in the error terms.
• The regression model is linear in the coefficients.
• The error terms are independent and normally distributed with mean 0.
• All the independent variables are uncorrelated.
• There is no heteroscedasticity.
• And the Parallel trend assumption which states that in the absence of treatment, the difference between the 'treatment' and 'control' group is constant over time.