# Justification for my Random Effects estimation

I need to defend my use of the Random Effects (RE) estimator in my economics project. I've been told in cross validated that the proper place for the question is here.

The causal effect of the exchange rate on shopping in the neighbouring country, is estimated using the following equation:

$$\begin{eqnarray} \ln⁡(\text{Traffic})_{i,t} &=& \beta_0+ \beta_1 \ln⁡(\text{Exchange rate})_t + \beta_2 \ln⁡(\text{Distance})_i \\&& + \beta_3 \ln⁡(\text{Exchange rate})\cdot\ln⁡(\text{Distance})_{i,t}+ \text{Month}_t \\&& + \beta_4(\text{Consumer confidence})_t + \epsilon_{i,t} \end{eqnarray}$$

-$$i$$= 16 roads, $$t$$= day (2010-14)

-Exchange rate: foreign currency per unit of domestic currency

-Distance: distance between road and border

-Month: month dummies

-Consumer confidence: consumer confidence indices

Here are the reasons I can think of so far to argue for the validity of my specification:

1. Fixed effects is not viable. I do not have the full population/large sample of roads. D-I-D is not possible either, as there is no control group. RE is an alternative.

2. RE’s allows me to exploit the spatial dimension i.e. distance, which is really important for causality. Distance would be wiped out by alternative specifications that include road dummies.

3. All roads are the same classification of major road, there are not large differences between roads e.g. different speed limits are not altering the volume of traffic flow.

4. I can’t think of any unobservable in the residual that is correlated with the explanatory variables. The only one is maybe that larger shopping areas attract more cross border shoppers, and so some roads are affected more than others by the exchange rate. But in my case I know that people go the nearest shopping area, not the biggest.

5. All shoppers/roads receive the same shock/exchange rate. And shoppers are affected by national factors e.g. those contained in consumer confidence. So there’s no reason to have controls for each road.

Random effects scares me, so any advice is greatly appreciated! Thank you.

• I can see a research paper in the making... – london Dec 13 '18 at 21:51