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AW: st: Chi-squared test for independence of observed and expected frequencies

From   "Marc Michelsen" <>
To   <>
Subject   AW: st: Chi-squared test for independence of observed and expected frequencies
Date   Fri, 16 Jul 2010 10:22:40 +0200

Stas, Maarten,

many thanks for your comments.

The complete reference is: Dittmar, A., and A. Thakor. "Why do firms issue
equity?" Journal of Finance 62 (2007), 1-54.

You are totally right, the authors use this analysis only as an add-on /
robustness test. The main body of the paper are multivariate analyses.
Nevertheless, it would be quite helpful to determine the relative importance
of the two explanatory variables (dimensions), i.e. prior stock return
(divided into quartiles) and credit rating outlook (positive, negative,
stable). Do you have any idea how the authors have tested the significance
of each of the frequencies?

I will have a look at your three proposed alternatives and see how fancy
they are.


-----Ursprüngliche Nachricht-----
[] Im Auftrag von Stas Kolenikov
Gesendet: Donnerstag, 15. Juli 2010 23:52
Betreff: Re: st: Chi-squared test for independence of observed and expected

On Thu, Jul 15, 2010 at 10:33 AM, Marc Michelsen
<> wrote:
> I am trying to copy the approach of Dittmar/Thakor (2007) "Why do firms
> issue equity?" p. 27: The authors divide their sample of debt and equity
> issuers into quartiles based on two explanatory variables, i.e. building a
> matrix. Specifically, they examine the observed number of firms that fall
> into one of the four categories and compare them to the expected
> frequencies. After that, they apply a chi-squared test for independence to
> determine if there are more or fewer firms than expected in each category.
> Untabulated results show that each of these frequencies is significant.

I agree with Maarten: that's a strange approach. Not that it is
totally inappropriate... but it smells like 1960s when computations
were essentially restricted to how much handwriting you can fit onto
two sheets of paper. Propagating strange approaches does not do a good
service to whatever discipline you are in (finance?).

If those are continuous variables, you can use two-sample
Kolmogorov-Smirnov tests to compare the distributions. I am pretty
sure that bivariate versions of K-S tests exist, but they are not
implemented in Stata. If the explanatory variables are categorical,
you can compare the samples using -tabulate variable debt_vs_equity-
as they are.

If you want a fancier analysis, you can run -qreg- (or rather -sqreg-)
over a set of quantiles, with debt/equity as the explanatory
variables, to gauge whether the distributions of the continuous
variables are the same for two types of firms.

Stas Kolenikov, also found at
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