Justification for my Random Effects estimation

Question

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.

Answer 1

Your first point is valid for not using fixed effects as you are interested in the entire border not just these 16 roads. Random effects can be advantageous when you have such a small sample compared to the population for your treatment group. Also note, if the unobserved effect has a large variance or T is very large then RE will be close to FE anyway. You can try both and do a Hausman test to see if the two models are different.

Your second point is not convincing. I don't see this as being a justification for using random effect. Don't lose site of what you are looking for, the effect of exchange rates on shopping across the border of your two countries. You don't care about the effect of roadway length on the roadway traffic, so why bother with the idea of holding on to it in your results. The one thing your distance variable can do is act as a sort of robustness check for you since that is one of the fixed effects you want to control for. Now I can understand your interaction term with distance as there is probably some sort of cost and benefit for people considering the exchange rate vs the distance they have to drive, but in FE models, your interaction will remain. Also note, that road dummies would be very similar to FE with your model specification.

I would probably likely try a First Difference approach as well since you are going to have serially correlated errors. You have controlled for some time-variant factors like seasonality with your months and some economic conditions with consumer confidence, but there could be other factors that change over time: road constructions, localized new regulation, new store openings on one side of the border, etc. These would create serial correlation in your error term.

As long as you have a good justification for each modeling approach, I would try them all and compare your results. Just use a straightforward pooled OLS model as your baseline, and then proceed from there. Don't just blindly try everything, but be thoughtful and understand the assumptions you make in each approach.