How to explain the Difference-in-Difference for two groups two periods to undergraduate students?

I was asked to have a talk with some undergraduate students in an econometrics class regarding the standard Difference-in-Differences.

Even I understand what it is and I am quite familiar with it, but I do not know what is the outline that I should follow to explain it to them that benefits them most. Assuming that they know some models like OLS, GMM already.

If we compare two states (like two of the 50 states I mean) to see if some big policy change improves something, would that work? Where one state has the policy and one doesnt?

TX has the policy and Delaware doesnt. Tx just implemented the new policy at the beginning of 2020. And it’s a big rare change. Let’s say Tx gdp in 2020 was 1T and De was only 100B. Since the gdp of Tx was higher, it must be a good policy right? Ask them whats wrong with that logic. Then they see that it must be per capita.

Ok so now we are comparing this difference between per capita gdp’s. It’s a difference, and if it is positive (Tx minus DE), that’s good. But per capita, let’s say it turns out this difference is negative (Tx-De<0), so we conclude bad policy. Then say ok so that works?? No issue?? They say No doesnt work. Why not? Eventually they say the states have many other factors that could affect per capita gdp, not just this one policy. (Btw people in the popular media actually do that. This state has such n such and is doing good so..., as if it’s the only factor). Make sure they understand: That difference doesn’t work. The factors that affect it are anything that affects gdp differently BY STATE.

Check the clock assuming you should he about a quarter of the way through your time and hurry through the year example (next paragraph) if the time is more like halfway through.

Alright new plan. Tx just implemented the new policy at the beginning of 2020 and only grew 1% in 2020, but they grew 3% in 2019 when they didnt have the policy. The difference between the year without the policy and with the policy is -2%, so the policy is bad right? No, there could be other factors that affect gdp in 2019 vs 2020, not just the policy. That difference won’t work. The factors that affect it are anything that affects Tx differently BY YEAR.

What if we compare Tx change in gdp from 2019 to 2020, that difference, with DE change in gdp from 2019 to 2020. What if we compare those differences and see if they are different? That difference in the difference might work. Write some equation for that.

Now spend a long time while they try to figure out exactly what character of factors would affect that. (Things that vary by both state and year). How would you know if you had such factors? You couldnt.

What if had multiple years for each state? How would you know if the two states where good comparisons? (Look for parallel trajectories...