3.10

# Difference-in-differences

In order to obtain a causal effect of police presence on crime, Di Tella and Schargrodsky exploited the sudden, unexpected increase in police presence near Jewish and Muslim institutions after the July 1994 Terrorist attack in Buenos Aires.

Table 1 shows the average number of car thefts (per month) in street blocks in Buenos Aires that received additional police protection because of the presence of a Jewish or Muslim institution. “Before” corresponds to the period before the terrorist attack (April, May, June and July of 1994). “After” corresponds to the period after the attack (August, September, October, November, and December of 1994).

##### [Table 1. Average Number of Car Thefts in Protected Blocks Before and After Terrorist Attack]
Before After Difference
Blocks Protected 0.090 0.035 -0.055

After the attack, the average number of car thefts per month in the “protected” blocks decreased by 0.055. But can we attribute all of the decrease in car thefts to the increased police presence on the block?

The number of car thefts on the protected blocks may have declined because of other reasons. For example, following the terrorist attack, Argentineans may have spent less time on outdoor activities, fewer tourists may have visited Buenos Aires, and thieves may have felt more guilt stealing in the aftermath of a national tragedy. Another possibility is that the number of car thefts was already falling in Buenos Aires for some other reason. In this case, the number of car thefts would have declined even in the absence of additional police protection, and the additional police presence on the protected blocks cannot be responsible for the total decline in the number of car thefts.

Consider Table 2 now, which shows the average number of car thefts in street blocks in Buenos Aires that did not have a Jewish or Muslim institution and thus did not receive additional police protection.

##### [Table 2. Average Number of Car Thefts in Unprotected Blocks Before and After Terrorist Attack]
Before After Difference
Blocks Unprotected 0.082 0.105 0.023

Table 2 shows that the number of car thefts per month on unprotected blocks in fact increased by 0.023 after the terrorist attack. This finding suggests that the average number of car thefts on protected blocks may have increased by 0.023 as well, had there been no additional police presence. Under this assumption (called the “common-trend assumption”), we can estimate the causal effect of additional police presence on car thefts as the difference between 1) the before-after difference in car thefts in protected blocks and 2) the before-after difference in car thefts in unprotected blocks.

##### [Table 3. Difference-in-differences, Number of Car Thefts in Buenos Aires]
Before After Difference(After-Before) Diff-in-diff
Block Protected 0.090 0.035 -0.055 -0.078
Block Unprotected 0.082 0.105 0.023

Table 3 presents the result of this difference-in-differences computation, which suggests that the additional police presence in protected blocks caused the monthly number of car thefts to decrease by 0.078. Note that this amounts to a 87 percent decrease in car thefts, compared to the baseline number of car thefts in protected blocks (0.090).

Question: Under the “common-trend assumption”, the difference-in-differences analysis gives us the causal effect of interest (in this case, the causal effect of additional police presence on car thefts). However, this assumption (that the crime trend in protected blocks would have followed the same trend as in unprotected blocks if the protected blocks did not receive additional police presence) cannot be tested with actual data—because the protected blocks did receive additional police presence in real life. What can we do to explore the empirical relevance of this assumption?

## References:

• Di Tella, Rafael, and Ernesto Schargrodsky. “Do Police Reduce Crime? Estimates Using the Allocation of Police Forces after a Terrorist Attack.” American Economic Review 94.1 (2004): 115-133.