Time series, cross section, and quasi-experiment analysis simple example

Three ways to use the data to predict changes in labor effort in response to benefit guarantee change

Approach #1Time series analysis:
compare Arkansas in 1996 vs. Arkansas in 1998
Use just two data points (same place, different times)
Benefit guarantee went down by $1,000 (5K to 4K) and labor went up 200 hours (across that time period within Arkansas.

Time series analysis prediction:
$1,000 benefit guarantee cut ==> 200 hour increase in labor

Problem with this? Lots of other things changed over time, maybe the increase is due to something else besides the benefit guarantee that changed over that time period.

Approach #2Cross section analysis:
compare Louisiana in 1998 vs. Arkansas in 1998
Use just two data points (two places, same time)
Benefit guarantee is $1000 less in Arkansas than in Lousisiana (5K vs. 4K) and labor is 100 hours greater in Arkansas than in LA that year

Cross-section prediction:
$1,000 benefit guarantee cut ==> 100 hour increase in labor

Problem with this? Lots of other differences between Louisiana and Arkansas besides the benefit differnce, maybe the increase is due to something else different between the two states.

Approach #3Quasi-experiment analysis also known as "difference-in-difference" analysis

Use all four data points across time AND space.

Use Louisiana as "control group" for study because benefit guarantee stayed the same there.

Use Arkansas as "treatment group" for study because benefit guarantee changed there.

Compare CHANGE over time in labor in Arkansas vs. CHANGE over time in Louisiana labor

change over time in Arkansas (treatment group)
= 200 more hours of work = 1,200 - 1,000

change in Louisiana (control group)
= 50 more hours of work = 1,100 - 1,050

Now take difference between 200 and 50 = 150 hours predicted effect of $1,000 increase in benefits

Quasi-experiment prediction is
$1,000 benefit guarantee cut ==> 150 hour increase in labor

This approach isn't perfect, but it's better than the other two, because it "controls" for some of the differences between the states (i.e., those that stayed the same over time.)

Example above is very simple. In practice might use more time periods, more variables, more states, etc.