I am running a regression on a Cross section time series data set (cross sectional dominant) that has the following characteristics:

  • 1,200 cross sections (6 countries * 200 products). Each country - product combination is one cross section
  • 30 consecutive months of data in each cross section
  • Total of 36,000 observations
  • Some independent variables vary by country, others by product, but most are the same data in each country - product combination
  • the products are not particularly correlated with each other, but the product time series move similarly across countries
  • normalized the dependent variable

I first built the model in OLS (proc reg in SAS), but then included an intercept based on the average of the dependent variable in each country - product cross-section. While I only get one coefficient for this variable, effectively I'm running a fixed effects regression (please correct me if wrong).

As a next step I wanted to see if the t-values of my independent variables hold up under robust standard errors (I have about 50 variables in the model without multi collinearity). I thus ran proc surveyreg. The robust t-values dropped 50% on average. On one variable of interest the t-value dropped from a classical t-value of 14 to a robust t-value of 1.5. This variable varied by product, but not across countries. For another variable of interest the t-value dropped from 2 to 1, this variable had the same data in each cross section. The way I specified the clusters is across the products, so each cluster has 180 observations (30 months * 6 countries).

Believe this means there is evidence of heteroskedasticity. Would appreciate if you could help with path forward here:

  • Since my t-values are still above 1 with robust standard errors, can I still make inferences based on the results of my model?
  • Is the problem that my cross-sections are too different from each other and I am not accounting for these differences enough?
  • Will switching to mixed effects solve the problem - proc mixed?

Help much appreciated. Thanks, Michael

  • $\begingroup$ Interesting analysis. What IS the DV -- unit sales? -- and how did you normalize it? With a natural log transformation? This sounds like a marketing mix model, is it? It's surprising that, with 50 variables, multicollinearity is not a problem. I don't see how obtaining "robust t-values" helps you. I have greater concerns with using OLS PTS related to autocorrelation, cointegrated trends and multi-level effects not being captured -- most of which are simply assumed away with these models. I don't like the sound of the "intercept" you included, why was this done? $\endgroup$ – Mike Hunter Nov 5 '15 at 21:26
  • $\begingroup$ See follow up post please $\endgroup$ – MichaelG Nov 10 '15 at 20:33

Enclosed, answers to your q's DJohnson:

  1. Yes volume (number of units) is the dependent variable. We did not want to aggregate the products because each product has a different value (i.e. price)

  2. Yes we are trying to understand the impact of distribution, sales, marketing

  3. Half of the 50 variables are dummy type variables explaining one-off events. A lot of the variables vary at the product level.

  4. The DW statistic is close to two. We also included a lagged dependent variable

  5. What are some tests you would run to ensure we can draw accurate inferences from the model?

  6. The intercept was included in order to reset the mean in each of the cross sections, accounting for the structural differences.

Thank you, Michael

  • $\begingroup$ I don't understand how you can have a single DW since each cross-section should have its own metric. Since it's a marketing mix model, why not treat it like one? You can use pooled OLS or a mixed effects functional form. Lee Cooper's book Market Share Analysis (free on his UCLA website) is the single best intro I'm aware of for this approach, forget the "market share" part, it's just a great overview. He has recommendations for several possible functional forms for fitting the response as well as elasticities. Mixed effects models are another way to go. Play around. $\endgroup$ – Mike Hunter Nov 11 '15 at 0:06

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