Interpretation ARDL/Asymmetric error correction model, with interaction terms

[Tor Jakobsen]

Sorry for the long post. It is difficult to make it shorter, because then I will loose crucial points.

I am writing a master thesis on the gasoline market in Norway. My master thesis is supposed to be a replica Verlinda (2008) ”Do rockets rise faster and feathers fall slower in an atmosphere of local market power”. Verlinda use the same econometric model as Borenstein, Cameron and Gilbert (1997) ”Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes”, but introduce heterogeneity among gasoline stations regarding the ”rockets and feathers” effect ie. the asymmetry effect.

I am very confused regarding the interpretation from my regression. I will be very very thankful for any hints or tips.

First I have estimated a static long term model by OLS. Then I have predicted the residuals. I have put the residuals into a dynamic model, in according to the rockets and feathers litterature.

The results from the dynamic OLS model are given below. Here I have used zero lags for simplification, and thereby included only the difference of COST from period zero. I have four market characteristics besides constant terms:
1) Population per square meter
2) Median income
3) Population
4) Number of competitors within 10 minutes (maximum is set to four competitors)

Each of these market characteristics are continous variables, counting from zero to one. In the dynamic model I use interaction terms for each of these characteristics, for example:
Product price * Population
Product price positive * Population
Residual * Population
Residual positive * Population

My final goal is to estimate the isolated effects on asymmetry, ie. rockets and feathers; when one of the population characteristics increases, for example when population increases.

Now, the big question is how I interpret the coefficients from the dynamic regression. What follows is mye suggestion on how to interpret. The isolated effects on pricediff0 when corrected from the above market characteristics are the constant terms (productpricediff0, productpricediff0pos, resmin1, resmin1pos). Eg. the extra effect from population are given by the respective terms (productpricediff0population, productpricediff0pospopulation, resmin1population, resmin1pospopulation). If this is a correct reasoning, the isolated effect on pricediff0 from population is:
productpricediff0 + productpricediff0[population]
productpricediff0pos + productpricediff0pos[population]
resmin1 + resmin1[population]
resmin1pos + resmin1pos[population]

productpricediff0 + productpricediff0[population], can be interpreted as the isolated effect on pricediff0 when population REDUCES from one to zero (eg. reduces from minimum to maximum). Is this interpretation correct?

Many of the Stata listers are probably not familiar with the CRF’s (cumulative response functions). But for those Stata listers who are, in the next step, I calcultate the isolated effect on asymmetry from REDUCING one of the market characteristics from one to zero (ie. reducing from maximum value to minimum value). I first add together the constant and the respective market characteristic, for example:
productpricediff0 + productpricediff0[population]
productpricediff0pos + productpricediff0pos[population]
resmin1 + resmin1[population]
resmin1pos + resmin1pos[population],

and then I apply the CRF’s on these variables. Is this interpretation correct?

[Sebastian Kripfganz]

Some comments on the starting point of your analysis: Estimating a "static long term model" is not a good idea at all. You are neglecting all the dynamics. In the best case, this is a very inefficient way of estimating the long-run relationship because your error term will be serially correlated. However, it is likely that your estimates will suffer from omitted variables biases and, in the worst case, you may get spurious regression results if your variables are non-stationary. The predicted residuals from this regression are then of no use for the further analysis.

With the ARDL approach, an error-correction model can be estimated in a single step (after having obtained the optimal lag order) with consistent estimates for the long-run and short-run coefficients. Please see the discussion in the following Statalist topic:
ARDL in Stata

[Tor Jakobsen]

Thank you Kripfganz, for a constructive answer.