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st: sqreg - interpretation of results

From   joachim Wagner <>
Subject   st: sqreg - interpretation of results
Date   Wed, 27 Oct 2004 12:36:49 +0200

Dear List:

May I ask for some advice on a topic related to Stata's sqreg - simultaneous quantile regression procedure? (Version 8.2)

I estimated an empirical model using plant level data. The endogenous variable is value added per employees (i.e. productivity), the exogenous variables include a dummy variable for the presence or not of a works council. The point estimate and statistical significance of the coefficient for this dummy are the topic of my research. When I use OLS the coefficient estimate is positive (16.124) and significant with a prob-value of 0.013. There are reasons to suspect that plants are heterogeneous, and that not all heterogeneity is controlled for by the variables included in the model. Using fixed or random effects is not possible for data reasons. Therefore, I tried sqreg to see whether the impact of a works council varies over the distribution of productivity. It turns out that it does: The coefficient is insignificant at any conventional level for q10, q25, q50 and q75, but the prob-value is 0.29 for q90 (and the point estimate is higher than the OLS estimate).

Question 1: Assuming that my empirical model makes sense, does this indicate that a positive impact of the works council is only present at the top of the conditional productivity distribution?

Question 2: How can I find out more about these "top firms" - e.g., wether they are larger than those at the bottom?

To elaborate on these two questions please let me add some more thoughts: I read a paper by Barreto and Hughes published in the Economic Record early in 2004. They use quantile regressions to look at determinants of growth of countries, and they compare their results to OLS. They start with OLS, then look at the residuals from OLS. They identify under performers / over achievers as follows: Countries with a higher (lower) observed than predicted growth rate - conditional on the variables included in their empirical model - are over achievers (under performers). They then list the top 10 and bottom 10 countries according to this procedure. And then they argue: Using quantile regression "we measure the marginal effects of changes in the independent variables for over achieving countries like Botswana and contrast them with the marginal effects of changes in the independent variables for under performing countries like Surinam." Than they add a footnote: "Note that quantile regression uses all of the data in the estimation procedure, in no way are subsets of observations considered. Here, we motivate the discussion with reference to specific countries even though quantile regression relates to hypothetical, representative countries. We do this strictly for ease of exposition."

Question 3: Is it correct to classify units (countries, plants, etc.) as under performing and over achieving in this way, and to argue that quantile regression looks at these bottom / top group when q10 and q90 are estimated?

I would be very grateful for any comments from quantile regression experts, and for hints to papers that deal with this kind of questions.

Thanks in advance,


Prof. Dr. Joachim Wagner
University of Lueneburg
Institute of Economics
Campus 4.210
D-21332 Lueneburg
Phone: +49-4131-78-2330
Fax: +49-4131-78-2026

You can access working paper versions of some of my papers on the Social Science Research Network (SSRN) at the following URL:

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