Question

1. Questions about Difference in Differences Consider the following hypothetical scenario. Washington (state) passes a law subsi- dizing child care for working mothers in 2005. Suppose we are interested in examining the impact of this law on the labor supply of women, and we gather data on the hours of work, Hit for a sample of women across the United States, from 2000-2010. Assume also that Oregon has an economy that is similar to that of Washington, but Oregon did not change its child care policies between 2000-2010. . (4 points) (a) Describe the "difference in differences" regression that you would run (and the sample you would use) to estimate the impact of Washington's child care subsidy on female labor supply. Explain the role of every term that you include in the regression . (3 points) (b) Describe at lcast one cconomctric problem that the diffcrcnce in difference method solves here. That is, why is this approach better than some other more naive specifications. Full points awarded for clearly explained, con crete scenarios. (3 points) (e) Suppose we observe the following average hours worked among women in each state and time period: Table 1: Average Hours Worked by Women: Washington Oregon 2000-2004 2005-2010 23 21 27 Based on this data, what would be our basic difference in differences estimate of the impact of the child care subsidy on hours worked for women? (provide a number and show work)

Answer 1

Answer:

a). Before answering ,we need to understand as ot what difference in difference method is .

Difference in differences is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group, compared to the average change over time for the control group.

In the current problem the treatment group is the working women from Washinton and we are interested in observing their working hours. The control group in this case willl be the working women from Oregon and we shall measure the working hours of working women from orgeon which will be out control group.

Thus

Treatment group -Sample of working hours of women from Washington

Control group -Sample of working hours of women from Oregon.

Now since Difference in differences (DiD) regression is a tool to estimate treatment effects comparing the pre- and post-treatment differences in the outcome of a treatment and a control group, In general, the outcome Yi (working hours.) will be given by

The outcome Y is modeled by the following equation (Outcome) where the coefficients given by the greek letters α, β, γ, δ, are all unknown parameters and εί Is a random, unobserved "error" term which contains all determinants of Y, which our model omits. By inspecting the equation you should be able to see that the coefficients have the following interpretation a-constant term β treatment group specific effect (to account for average permanent differences between treatment and control) y time trend common to control and treatment groups 6true effect of treatment

b). An ecomnometric problem that can be solved here is that we can know if there has been a change in the working patterns of working women with children ? This is solved by DID regression since it involves stratification of unquantifiable data into quantifiable data points and considers them into the equation.

c). The difference in difference(DID) estimator is given by subtracting the average gain in the second (control) group from the average gain in the first(treatment) group.

The average gain in treatment group =21-23 =-2

The average gain in control group =22-27 =-5

Thus the DID estimsator =

The average gain in treatment group -The average gain in control group =-2-(-5)=3

Thus the DID estimator =3