Analyzing the Impact of Police Presence on Crime Rates

INSTRUCTIONS TO CANDIDATES:
The short release coursework will be available from 10:00 on Thursday 25 July – 10:00 on Wednesday 31 July (UK time). Work should be submitted on KEATS.

The coursework has two questions. You must answer both questions.

The file that you upload on KEATS should contain two parts:

Short written answers to the questions
The STATA output in pdf format

You can merge two pdf files using Acrobat Professional or an online pdf merger.
The word limit is 2,000 words, excluding the STATA output, tables, references, and the cover sheet.

You must complete the coursework coversheet. This is very important to ensure that your work can be identified. In addition, you should name the file with your candidate number as follows: Candidatenumber.pdf.
To avoid collusion, each student is given a unique version of the datasets. This means that you should answer the questions with the datasets that have been provided to you. If your answers or the STATA output file are based on the datasets given to another student, you will lose marks and face an allegation of collusion. Because the datasets are different, you should not expect to replicate the results in the papers exactly.

Question 1 (50 marks)

This question is based on a paper by Draca, Machin and Witt (2011) which studies the causal effect of police presence on crime using evidence from the July 2005 terror attacks in London. Police activity in central London increased in the six weeks following the terror attacks.
The dataset crime.dta contains data on crime rates and the level of police deployed for 28 London boroughs for the period from January 2004 to December 2005. The variable treat in the dataset is equal to 1 for five London boroughs that were either affected by the terror attacks or considered to be potential terrorist targets (Westminster, Camden, Islington, Kensington and Chelsea and Tower Hamlets) and 0 for other boroughs. To look at the effect during the six-week period of increased police presence, the dataset contains the variable policy6, which is equal to 1 in the period July 7, 2005 to August 18, 2005 and is equal to 0 in the equivalent period the year before (July 8, 2004 to August 19, 2004). To look at the effect over a longer period, the dataset contains the variable post, which is equal to 1 for the whole period after July 7, 2005 and 0 otherwise.

Complete the table below with the average levels of police deployment (police in the dataset) and crime rate (crime in the dataset) for treated and control boroughs in the six-week period after the attacks (post-period) and the equivalent six-week period the year before (use the variable policy6 in the dataset).

Police deployment (hours worked per
1,000 population) Crime rate (crimes per 1,000
population)
Pre-period Post-period Difference
(post-pre) Pre-period Post-period Difference
(post-pre)
Treatment
Control

What are the difference-in-differences (DD) estimates of the effect of the terror attacks on police deployment and crime? Use a simple regression to calculate the standard errors of the DD estimates. Explain what type of standard errors you are using and why. Are the estimates statistically significant? Comment on the results. (10 marks)

You are interested in the causal effect of police on crime and estimate the following model by OLS:
𝑐𝑏𝑡 = 𝛼𝑂𝐿𝑆 + 𝛽𝑂𝐿𝑆𝑃𝑂𝑆𝑇𝑡 + 𝛿𝑂𝐿𝑆𝑝𝑏𝑡 + 𝜀𝑏𝑡
⬚ ⬚ ⬚

The dependent variable 𝑐𝑏𝑡 is the log of the crime rate and the regressor 𝑝𝑏𝑡 is the log of the level of police deployment. The variable 𝑃𝑂𝑆𝑇𝑡 (post in the dataset) is equal to 1 for the whole period after July 7, 2005 and 0 otherwise.
Comment on the results. What are the potential sources of bias in this regression? (8 marks)

Estimate the following model for the effect of the terror attacks on police deployment:

∆52𝑝𝑏𝑡 = 𝛼1 + 𝛽1𝑃𝑂𝑆𝑇𝑡 + 𝛿1(𝑇𝑏 × 𝑃𝑂𝑆𝑇⬚) + ∆52𝜀1𝑏𝑡

The dependent variable ∆52𝑝𝑏𝑡 is the change in the log level of police deployment. The change is measured relative to the same week one year before, to account for seasonality in crime. The treatment variable is 𝑇𝑏 (treat in the dataset). The variable
𝑃𝑂𝑆𝑇𝑡 is as defined in part b).
Comment on the results. (6 marks)

Estimate the following model for the effect of the terror attacks on crime:

∆52𝑐𝑏𝑡 = 𝛼2 + 𝛽2𝑃𝑂𝑆𝑇𝑡 + 𝛿2(𝑇𝑏 × 𝑃𝑂𝑆𝑇⬚) + ∆52𝜀2𝑏𝑡

The dependent variable ∆52𝑐𝑏𝑡 is the change in the log of the crime rate. The other variables are as defined in part c).
Comment on the results. (6 marks)

Instead of using OLS, you decide to estimate an instrumental variables (IV) model for
the causal impact of police on crime using 𝑇𝑏 × 𝑃𝑂𝑆𝑇⬚ as an instrument for the change
in the log level of police deployment ∆52𝑝𝑏𝑡:
∆52𝑐𝑏𝑡 = 𝛼𝐼𝑉 + 𝛽𝐼𝑉 𝑃𝑂𝑆𝑇𝑡 + 𝛿𝐼𝑉∆52𝑝𝑏𝑡 + ∆52𝜀𝑏𝑡
⬚ ⬚ ⬚

Estimate the model and comment on the results. What is the relation between the coefficient 𝛿𝐼𝑉 and the coefficients 𝛿1 and 𝛿2 in the parts c)
and d)? Explain. (8 marks)
Under what assumptions is 𝑇𝑏 × 𝑃𝑂𝑆𝑇⬚ a valid instrument for the change in the log level of police deployment? Do those identification assumptions seem plausible? Explain in detail, with reference to the findings in the paper. (12 marks)

References:

Mirko Draca, Stephen Machin and Robert Witt (2011), “Panic on the Streets of London: Police, Crime and the July 2015 Terror Attacks”, American Economic Review, Vol. 110, No. 5., pp. 2157-2181.