Question

In an important 1992 paper, Card and Krueger used difference-in-differences to examine the effects of a New Jersey wage law on employment. They got data on fast-food employment in New Jersey and Pennsylvania, which did not increase its minimum wage.

a) What is the treatment here? What are the treatment and control groups?

b) Card and Krueger focused on restaurants near the border between NJ and PA. Why?

c) Suppose that there are only two time periods. Pennsylvania had employment of 23.33 before and 21.17 after, and New Jersey had 20.44 before and 21.03 after. What is the ‘difference-in-differences’ number showing the effect of the minimum wage law on employment?

d) Now suppose you have data for more than two time periods. Write the regression equation.

e) Your teacher (and your conscience) say you should check trends in the outcome variable for treatment and control groups before the treatment happens. Why?

Answer 1

a.The treatment here is minimum wage law. The control group (cg) here is the Pennsylvania restaurant and the treatment group (tg) is the New Jersey (NJ) restaurant.

b.The restaurants along the border are well comparable as the experiences are supposed to be similar in those places, as NJ is a small state and it's economy is interlinked to the neighbourhood states.

c.DID estimation of effect of minimum wage law on employment is 3.03

d.yigt=λt+ag+xgtβ+zigtγ+ vgt+uigt where i=1,...,Mgt

e)Trends in the outcome variable for both tg and cg must be noted for comparing the trends for the variable for both groups after the treatment.

Step-by-step explanation

Difference-indifference (DID) is a statistical technique which is used to estimate the effect of a treatment (like implementation of new policy, new law, new programs) by comparing changes in outcome over a specific time period for a population who were getting affected by the treatment (intervention/treatment group) due to enrollment for that program and the population who are not getting affected. If the result of the outcome variable is better for the tg rather than the cg, then the treatment is considered to be a successful one.

a.DID is used by Card and Krueger to examine how New Jersey (NJ) wage law affects employment. It is given that the data on those fast-food restaurants in

NJ and Pennsylvania have been obtained, which did not increase their minimum wage.

After the minimum wage law was applied, the minimum wage remained constant in Pennsylvania but it increased in NJ.

So, the treatment here is minimum wage law. The control group (cg) here is those restaurants which haven't applied this law, that is, the Pennsylvania restaurant and the treatment group (tg) is those restaurants who have applied this law, that is, the NJ restaurant.

b. NJ is a small state and it's economy is closely linked with the neighbourhood states. Since cg should have similar characteristics with the tg, the restaurants along the border seem to be well comparable before and after minimum wage law application as the experiences and characteristics of these places are supposed to be similar.

c. Before the minimum wage law was imposed,

employment in Pennsylvania was 23.33 and in New Jersey was 20.44

After the minimum wage law, employment in Pennsylvania was 21.03 and 21.17 in NJ.

DID estimation of causal effect is calculated as

(eN1-eP1)-(eN0-eP0)

Where 0 is the before treatment and 1 is after treatment. N is New Jersey. P is Pennsylvania.

So, putting the values, we have,  

(21.17-21.03)-(20.44-23.33)=3.03

DID estimation of effect of minimum wage law on employment is 3.03

d. When there are many groups and time periods, the following regression equation can be used for DID estimation:

yigt=λt+ag+xgtβ+zigtγ+ vgt+uigt where i=1,...,Mgt

Here i,g,t stands for individuals, groups, and time, respectively. The λt,ag are time effects and group effects, xgt,zigt, vgt are the group or time covariates, individual's covariates, unobserved effects of groups or time, respectively. The variable uigt shows individual specific errors. We need to estimate the β for understanding DID estimation of the causal effect.

e. Before the treatment, trends in the outcome variable for both tg and cg must be noted. Again, after the treatment, the trends for both groups for the outcome variable should be checked. This is necessary for the comparison. We want to know how wage law is affecting employment. So, without knowing the trends before the treatment, it is not possible to understand the effect of treatment on the groups. The effect of treatment will be reflected in the difference between the outcome variable of the tg before and after the application of treatment. It will also help in DID estimation.