# Probit function, Difference in difference approach, Standard errors in R

I'm a novice R user.

I'm dealing with some CPS data to evaluate how labor force participation of single female with children changed in response to some policy implementation.

The below is my probit() function without any other specification:

probit_1 <- glm(lfp ~ anykids + post_arra + kids_x_arra, family=binomial(link = "probit"), data=Mcps_s)
summary(probit_1)


where anykids is a binary variable and equal to one if single women has any kid, zero otherwise. post_arra is another binary variable, equal to one if the time period is after the policy implementation, and zero if before the policy implementation.

Now then, I use the predict() to see how my treatment and control group's labor supply respond to policy implementation.

# this is for treatment group response

prediction1 <- predict(probit_1, newdata=data.frame("anykids" = 1,
"post_arra" = c(0,1),
"kids_x_arra" = c(0,1)),
se.fit=TRUE,
type = "response")


and

# this is for control group

prediction2 <- predict(probit_1, newdata=data.frame("anykids" = 0,
"post_arra" = c(0,1),
"kids_x_arra" = c(0,1)),
se.fit=TRUE,
type = "response")


This gives me predicted values with standard error.

So now here are two questions:

1. I want to difference the labor force participation rate of pre-ARRA from that of post-ARRA in each group, which gives me a first difference. But how can I find the standard error of it?

2. After difference, I want to difference the first differenced value of control group from that of treatment group, which gives me a difference-in-difference value. Again, I have little idea how to calculate standard error of it to make the estimate meaningful.

I attached a snapshot that supplement my explanation. I know how to calculate standard errors in column (I) and (II) as it comes with summary statistics. But SE for Column (III) and (IV) are my concerns. 