1. Difference-in-Difference Development Workshop

2. Typical problem in proving causal effects Using differences to estimate causal effects in experimental data (treatment+control groups) Wish: ‘treatment’ and ‘control’ group can be assumed to be similar in every way except receipt of treatment This may be very difficult to do

3. A Weaker Assumption is.. In absence of treatment, difference between ‘treatment’ and ‘control’ group is constant over time With this assumption can use observations on treatment and control group pre- and post-treatment to estimate causal effect Idea – Difference pre-treatment is ‘normal’ difference – Difference post-treatment is ‘normal’ difference + causal effect – Difference-in-difference is causal effect

4. Graphically… y Time Treatment Control Pre-Post- A B C

5. What is D-in-D estimate? Standard differences estimator is AB But ‘normal’ difference estimated as CB Hence D-in-D estimate is AC Note: assumes trends in outcome variables the same for treatment and control groups This is not testable Two periods (before and after) crucial

6. The Grand Experiment (Snow) Water supplied to households by competing private companies Sometimes different companies supplied households in same street In south London two main companies: – Lambeth Company (water supply from Thames Ditton, 22 miles upstream) – Southwark and Vauxhall Company (water supply from Thames)

7. In 1853/54 cholera outbreak Death Rates per 10000 people by water company – Lambeth10 – Southwark and Vauxhall150 Might be water but perhaps other factors Snow compared death rates in 1849 epidemic – Lambeth150 – Southwark and Vauxhall125 In 1852 Lambeth Company had changed supply from Hungerford Bridge

8. What would be good estimate of effect of clean water? 18491853/54Difference Lambeth15010-140 Vauxhall and Southwark 12515025 Difference-25140-165

9. Card and Krueger (1994) Basic microeconomic theory of the firm: factor demand curves slope downwards. Hence, if minimum wages are binding, we would expect employment to fall if minimum wage is raised. Natural experiment: New Jersey raising its minimum wage from $4.25 to $5.05 on 1 April 1992 while the minimum wage in neighbouring Pennsylvania remained unchanged. Data: wages and employment in 65 fast-food restaurants in Pennsylvania and 284 in New Jersey in Feb/March 1992 (i.e. before the rise in the NJ minimum wage) and in Nov/Dec 1992 (i.e. after the rise). Difference-in-difference design to investigate the impact of minimum wages on employment.

10. What data we have? 698 observations – Sheet: an identifier for each restaurant (each has two observations, pre- and post-) – NJ: dummy for whether a NJ restaurant – After: dummy for whether post- observation – Njafter: nj*after – Fte: full-time equivalent employment – Dfte: change in full-time equivalent employment

11. Tabulate command Tabulate in STATA: – tabulate var (or tab var) – just a simple table – tab var, g(newvar) – generating a new variable – tab var, su(othervar) – summarising some other variable

12. Let’s get our first DinD estimator tabulate nj after, su(fte) means BeforeAfterDiff PA 20.318.3-2.0 NJ17.317.5+0.2 Diff+3.0+0.8??

13. Going from means to statistics reg dfte nj

14. … and with robust standard errors CoeffSEP-value OLS2.3291.170.049 Robust OLS2.3291.470.114 reg dfte nj reg dfte nj, robust

15. An alternative specification … reg fte nj after njafter, robust

16. Alternative specifications… reg fte nj after njafter, cl(sheet) xtreg fte nj after njafter, fe i(sheet) Any key differences? Should there be any?

17. Suppose we’d like to observe many estimations STATA commands for results-sets Guy named Roger Newson – estimates store – outreg (works mostly with regressions) – parmest/parmby

18. Summary A very useful and widespread approach Validity does depend on assumption that trends would have been the same in absence of treatment Can use other periods to see if this assumption is plausible or not Uses 2 observations on same individual – most rudimentary form of panel data