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,
Joachim
Prof. Dr. Joachim Wagner
University of Lueneburg
Institute of Economics
Campus 4.210
D-21332 Lueneburg
Germany
Phone: +49-4131-78-2330
Fax: +49-4131-78-2026
homepage: www.uni-lueneburg.de/fb2/vwl/wifo
You can access working paper versions of some of my papers on the Social
Science Research Network (SSRN) at the following URL: http://ssrn.com/author=139529
