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Difference-in-differences analysis

Difference-in-differences analysis
In this video, we will talk a bit more about one of the papers we saw earlier, Professors Rafael Di Tella and Ernesto Schargrodsky’s 2004 paper “Do Police Reduce Crime?”. The main focus here is to elaborate more on the empirical strategy used by the authors to estimate the causal relationship between police presence and crime. In July 1994, the main Jewish center in Buenos Aires was destroyed by a terrorist attack. After the attack, the Argentine government immediately ramped up protection for other Jewish and Muslim institutions around the country, providing a 24-hour police protection for more than 270 Jewish and Muslim synagogues, mosques, schools, and cemeteries.
Authors of this paper used this sudden, unanticipated increase in police presence to estimate the effect of police presence on crime. In order to find the effect of additional police presence on crime, we may just compare the crime rates near those Jewish and Muslim institutions before and after the attack. Because the level of police presence was at the usual level before the attack, but was sharply increased after the attack. Then we may take this difference in crime rates before and after the attack as the causal effect of the additional police presence on crime. But there is a problem with this simple before-after analysis. A lot of things may have changed in Argentina after the attack.
This terrorist attack should have made many Argentinean people feel angry, upset, depressed, and more patriotic, and the mood and behavior of many potential victims in criminals in Argentina would have change to. The attack may also have reduced the number of tourists, changing the economic and labor market conditions in Argentina after the attack. Because all these changes could have influenced crime rates in Argentina after the attack, the overall change in crime rates near those Jewish and Muslim institutions may have been driven by not only additional police presence but also by all these other changes. But if we want to focus on the effect of additional police presence on crime, how can we separate this effect from all these other changes?
One possible strategy is to extend this simple before and after analysis by exploiting the fact that only the Jewish and Muslim institutions were subject to this increased police presence. Let’s think about one neighborhood in Buenos Aires that has one of these institutions and another neighborhood that has none. After the terrorist attack, there will be an increased police presence in the first neighborhood but no change in police presence in the second neighborhood.
Then, the change in crime rates in the first neighborhood before and after the attack should be driven by additional police presence and all these other changes, but the change in crime rates in the second neighborhood should be driven by all these other changes but not by additional police presence. So, when we compare the difference in crime rates in the first neighborhood before and after the attack, relative to the difference in crime rates in the second neighborhood before and after the attack, we can recover the causal effect of additional police presence on crime. This technique is called “difference-in-differences”, and is widely used by economists to evaluate the effect of a policy intervention.
When we want to investigate the causal effect of the increased police presence on crime rates, it is usually more preferable to compare the changes in crime rates and police presence within the same unit of observation over time than to compare the differences in crime rate and police presence across different units of observation.
However, this within-unit comparison may still confound the causal relationship of interest with underlying crime trends.
Difference-in-differences analysis can mitigate this concern by removing the underlying crime trend that equally affects the “treated” units (those that experienced a sharp increase in police presence) and untreated units (those that did not).
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Economics of Crime

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