Analysing the spatial concentrations of crime across London

[William Riley]

Hello,

I am using Stata version 15.1. My goal is to identify the neighbourhood effects of crime in London. To do this I am estimating how much of crime can be explained the characteristics of the area, the weighted characteristics of the surrounding areas and also the weighted crime levels of the surrounding areas. I am using a contiguity weights matrix and my unit of analysis are Lower Super Output Areas (LSOAs). I have monthly data on crime from police.uk and am using 2011 census data for my characteristics (these include levels of social housing, unemployment, proportions of different ethnicities).

In order to try to estimate causal impacts my ID strategy I am using an exogenous informational shock which occurred in January 2011 which I believe will have an impact on neighbourhood effects. Therefore by analysing the change in neighbourhood effects between December 2010 and December 2011 I hope to identify the effect of this policy on neighbourhood effects thus identifying their existence. One of the biggest problems I am having with this is that I only have characteristic data for March 2011 - so I am having to assume these characteristics remain constant over time.

So my question is twofold. I put my data into a panel with two periods (December 2010 and December 2011). Then have performed a pooled OLS as shown below:

Crime_i,t=α + βX_i + φWX_i + ρWcrime_i,t + γWcrime_i,t*2011 + u_i

Where X represents the characteristics and W is the contiguity weights matrix. With the aim to capture the additional neighbourhood effect with the γ coefficient. I am concerned that this model will be inconsistent because it simply pools together all of the characteristics and so includes them twice. So my question here is: is this model correctly specified and if so how do I interpret the coefficients on the characteristics X.

I realise that there are problems with consistency when using a spatially weighted dependent variable, therefore I planned to use a Maximum Likelihood estimate to accommodate for this. However I am unsure how to apply this to this particular model where the dependent variable changes over time but the other explanatory variables are unit fixed effects.

Any help with this would be really appreciated. I hope my question wasn't too long!

Thanks in advance.

William Riley

[Sebastian Kripfganz]

You would essentially need to assume that the time-invariant characteristics are uncorrelated with the unobserved unit-specific heterogeneity, i.e. a random-effects model rather than a fixed-effects model. The bigger problem might be the endogeneity of the spatial lag of the dependent variable because the available estimation commands for spatial models do not allow for interaction effects of the type Wcrime_i,t*2011.

[William Riley]

Thanks Sebastian.

I have now used the random effects model and, provided my assumptions hold, this seems to provide a better estimate for my model. I assume I would not then need an interaction term with a random effects model as the coefficient for Wcrime would show the effect over time of the neighbourhood effect. I am wondering how I could incorporate this RE model into a model which is more consistent when measuring the effects of the spatially lagged dependent variable. Like a maximum likelihood model.

Some guidance for this would be useful, thanks.