Re: Critical t-values in large samples

Hi,

Thank you for the quick response.

What if my test statistics are measured using a consistent
variance-covariance matrix of errors? Would this ensure that the
values of my statistics already account for possible correlation?

Claudia



David Jones wrote:
ClaudiaC wrote:
Hi,

I'm running a linear regression on a number of variables using a
sample of 5000 observations.

I was told that since my sample is quite large I should adjust my
critical t-values when testing the significant of my coefficients
since standards errors tend to become very small with large sample
sizes so that most coefficients become significant using
conventional
critical t-values.

Is this right? Is this unanimous among econometricians or
statisticians?

How do you adjust the critical t-values?

Claudia

You should ask yourself, specificaly, are the standard errors being
calculated correct? Small standard errors are produced by the theory
for large samples, and so are correct so long as the assumptions made
in the theory are correct. Thus you need to think critically about the
assumptions being made. In fact the t-test depends also on assumptions
about the distribution of the residuals, which is a separate matter.
The standard errors being calculated depend substantialy on the two
assumptions: the residuals from the "true" model have equal variance;
the residuals from the "true" model are uncorrelated. Even a small
correlation in the residuals can build up to a large error in the
variances calculated for the estimated regression parameters.

Thus you should seek reasons for why there might be correlation in the
residuals ... this will dcepend a lot on the actual data-set you are
analysing, it background and how the data were collected. Then to
"adjust the critical t-values" either:
(i) extend the model to include the reasons why correlation might
occur, possibly using a mixed fixed/random effects model ... this
would actually change the value of the test-statistic as opposed to
"adjusting the critical t-values";
(ii) employ a resampling technique, but (importantly) one that
respects the reasons for the correlation ... the resampling would
effectively be a method to "adjust the critical t-values".

There is one special situation that has been dealt with extensively in
the literature: that of a time-series-like set of data, where there is
or may be serial correlation in the residuals.

David Jones

.

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