Capturing recession effect using year dummies

[Konstantina Boutsioukou]

Hi everyone,

I seek to examine whether selection into highly selective university programmes in Greece changed following the recession of 2008, and if so, whether the socio-economic gradient of entry to elite university departments became steeper or flatter. I utilise two linear probability models (LPM) with year effects that have the specification forms below. My data is repeated cross-sectional.

Elitei=β0+β1*Yeari + β2*ParOccupi + β3 *(ParEdui × Yeari) +β4 Xi+ εi
Elitei=β0+β1*Yeari + β2*ParEdui + β3 *(ParOccupi × Yeari) +β4 Xi+ εi
where the dependent variable Elite_i is a dummy variable that takes the value 1 if student i is admitted to an elite university department and 0 if he is admitted to a non-elite university programme. The independent variables in the model are Year_i, representing the years between 2004 and 2016, ParEdu_i, a categorical variable representing different parental education levels and ParOccup_i, a categorical variable representing different parental occupational groups. ParEdu_i×Year_i is the interaction term between parental education and years and ParOccup_i×Year_i isthe interaction term between parental occupation and years. By examining the interaction between years and parental education and occupation, I aim to capture the recession’s impact on access to elite university departments. Finally, xistands for some controls, namely, student’s gender and nationality. I estimate paternal and maternal effects separately.

I received the following comment:

The estimation strategy is really a dynamic/event-study difference-in-differences and should be referred to as such. It would also be helpful to re-estimate everything with 2007 as the base year and comment on issues such as pre-trends and related DiD issues. If there are diverging pre-trends it might also be useful to consider recent sensitivity analysis such as Rambachan/Roth (2023, A more credible approach to parallel trends. Review of Economic Studies forthcoming). To address this I was thinking to take 2007 as the base year as it is the last year before the crisis. Also, to include both education and the interaction of education and year in the equation. Any further recommendations about addressing these issues would be more than welcome.

An example of my dataset follows below:

[CODE]
* Example generated by -dataex-. To install: ssc install dataex
clear
input double(elite yeard1) float(occup_f occup_m edu_f edu_m)
1 18 1 1 1 2
0 10 2 1 1 1
0 10 1 1 1 1
0 22 1 2 1 2
0 13 1 1 1 1
0 15 1 1 1 1
0 14 2 2 1 2
0 21 1 2 1 2
0 17 2 1 1 1
1 14 1 1 1 1
0 20 1 4 1 1
0 21 4 2 1 2
0 19 4 4 1 2
0 22 4 4 1 4
0 11 1 4 1 2
0 10 1 2 1 1
0 22 2 4 1 2
0 12 3 3 1 2
0 11 1 1 1 1
0 15 1 1 1 1
0 20 4 2 1 1
0 22 2 2 1 4
1 21 1 1 1 1
1 21 1 2 1 3
0 10 1 1 1 1
0 16 1 1 1 2
0 19 2 2 1 2
0 16 1 2 1 2
0 11 1 3 1 1
0 13 1 2 1 1
0 19 1 1 1 1
0 20 4 3 1 4
0 16 1 3 1 1
1 22 2 1 1 1
1 14 2 2 1 2
0 20 4 4 1 4
0 11 2 2 1 2
1 12 1 2 1 2
0 12 1 1 1 1
0 15 1 2 1 2
0 15 1 2 1 2
0 19 1 4 1 1
0 20 2 1 1 1
0 16 1 3 1 4
0 10 1 1 1 1
0 10 1 1 1 1
1 15 1 1 1 2
0 16 1 2 1 2
0 15 1 2 1 2
0 14 2 3 1 2
1 13 1 2 1 2
0 20 1 1 1 1
1 10 1 2 1 3
0 18 1 2 1 2
0 14 1 2 1 1
0 18 1 2 1 2
0 13 4 4 1 2
0 15 1 2 1 2
0 15 1 4 1 2
0 20 4 1 1 1
0 16 1 1 1 1
0 10 1 2 1 2
0 17 1 1 1 1
0 16 1 1 1 2
0 13 2 2 1 1
0 20 1 2 1 2
0 16 2 1 1 2
0 19 1 2 1 2
0 17 4 1 1 1
0 16 1 1 1 1
0 11 2 2 1 1
0 10 1 2 1 3
0 19 4 2 1 1
0 17 2 2 1 1
0 13 1 2 1 2
0 12 1 2 1 2
0 17 1 1 1 1
0 16 1 4 1 2
0 10 1 1 1 1
0 11 1 1 1 1
0 18 1 2 1 2
0 20 1 1 1 1
0 10 2 1 1 1
0 10 2 2 1 2
0 18 1 1 1 2
0 15 3 4 1 2
0 16 2 2 1 2
0 12 1 3 1 4
1 20 1 1 1 1
0 13 1 1 1 1
0 16 1 1 1 1
0 19 1 1 1 2
0 21 1 1 1 2
0 14 1 3 1 4
0 20 2 2 1 2
0 19 3 2 1 2
0 12 2 4 1 1
1 13 1 1 1 1
0 16 3 3 1 4
0 10 1 4 1 2
end


Thank you very much in advance for any input.

Best,
Konstantina

[George Ford]

No sense in running two models. Both can be assessed in a single equation (and probably should be; else ov bias).

You need some data prior to 2008 if you are looking for a change in slope over time caused by the recession, probably several years worth to see if that trend was already taking place.

Use reghdfe (or similar approach) to absorb the year fixed effect.

[Konstantina Boutsioukou]

Dear George, thank you very much for your help. Just as a clarification, since my data is repeated cross-sectional can i use the reghdfe? I also have years prior the crisis of 2008, in particular i have data from 2004-2016, so that's why i was thinking of taking 2007 as the base year, to explore pre and post trends.

[George Ford]

reghdfe is fine. you could also use areg. you're just eliminating the excess coefficients. But you may want to see them. The coefficients of interest are the year interactions.

All the pre 2008 data is the "base". It looks to me like the recession started in 2009.

This is not a clean diff-in-diff situation (the test is for a difference in a "treatment" before, during, and after a recession, though it appears Greece was in a recession through 2016; I suppose we can take parent education/occupation are exogenous to the student.). I'm not sure how you are treating education or occupation, as they are dichotomous. Might make more sense to think of a few classes: college educated versus not and professional occupations versus not.

I think what you're after is the pattern in the coefficients over time. You'd want them to be the same prior to 2009 (interaction terms are 0), and then changing in a regular pattern after 2009 (parent education is becoming more-or-less important).

[Konstantina Boutsioukou]

Thank you very much, George, I will try to incorporate your comments in my analysis!