significance testing for the change in change

[GreenTree1]

Hello,

In SAS, Is there a way to test for significance for a change in change? This may sound confusing but I will try my best to explain

following is a sketch,

years            % diff in car sales               p value for the diff in sales

1998

2000 .           between 1998-2000            0.6

                      2% increase

2012             between 2000-2012            0.10

                     3% increase 

2014            between 2012-2014            0.002

                    6% increase

I  now want to know the significance of difference between the differences 1% (2%-3%) and  3% (3%-6%), Is there a better way to do this?

[StatDave · Accepted solution]

This is commonly called "difference in difference" (DID). See this note that discusses estimating the DID. 

[GreenTree1]

Thank you StatDave,

The note is very helpful. I read up on DID and it looks like it's based on comparing two groups (cases and controls) but what if I am looking at differences in one population such as an intervention that affects the entire population. In this case, a policy change that caused more people to buy a house

Another complexity is that the population is not the same during every period, so they may not serve as their own controls? Can I take

the groups before the policy change as controls and the ones after the change as cases assuming that they are exchangeable (I can do propensity score for that)?

period 1 ---------period2 ------ period3 ----(policy change)----period4

diff b/w house buyers for period1 and 2 =1% .     

diff b/w  house buyers for period 2-3 =2% .             

diff b/w housebuyers perriod 3-4= 5%

[GreenTree1]

Thanks for pointing to the right direction StatDave, I found some useful ways to do DID analysis in that document. looks like the two group assumption has to be there. I across some papers where the researchers split the same group into two.