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Hi,

A simple way of correcting for cross sectional dependance is to demean the data before running a regression, y(t)-ybar(t), where ybar(t) is the cross-sectional averages for each time period.

In the manual it states about the Dynamic OLS estimator that: "Kao and Chiang (2000) describe the pooled DOLS estimator in which we use ordinary least squares to estimate an augmented cointegrating regression equation: ... where yt and xt are the data purged of the individual deterministic trends".

Does this mean that the cross-sectional averages has been removed?

I tried to estimate two different specifications,
1) log(tfpr) log(at)
2) log(tfpr)-@meansby(log(tfpr), "@year") log(at)-@meansby(log(at), "@year") ,

and they gave the same result, which to me indicates that the answer to my question is yes.

Is this correct?

Thomas

Only if you specify the deterministics to be a constant only. If you have a trend in the deterministic specification, then the individual means and trends are removed. If there are no deterministics, then the raw data are employed.

Hi Glenn, and thanks for your reply.

Im a bit unsure about how to interpret it.

a) trend = constant
If i understand you correctly, if i include the option trend=constant, then yt (and xt) are purged of the individual trends, i.e. yt(t)=y(t)-ybar(t), where ybar(t) is the cross-sectional averages for each time period.

b) trend = linear
but what do you mean by "If you have a trend in the deterministic specification, then the individual means and trends are removed."? is that not what happens in a)?

to clarify, can you please specify more explicitly what yt(t) looks like in case a) and b) ?
Thomas

(ps, running the regressions
1) log(tfpr) log(at)
2) log(tfpr)-@meansby(log(tfpr), "@year") log(at)-@meansby(log(at), "@year") ,

with trend=linear yields identical results. also, trend=constant yields also identical results for 1 and 2. )

The cross-sectional averages for each period have not been removed. You are seeing an artifact of an error in your demeaning expression. The correct expressions are of the form Note the absence of the quotes around @year. Your expression creates an auto-series containing the string value "@year" for all observations, then computes the average over values of the string series that equal "@year", which is the entire sample. Once corrected, you will see differences in the two estimates.

More generally, as to the trend assumptions:

1. Trend = constant assumes that there is an individual specific intercept deterministic regressor for each cross-section
2. Trend = trend assumes that there is there is an individual specific intercept and trend regressor for each cross-section
3. Trend = quadratic assumes that there is an individual specific intercept, trend, and trend squared regressor for each cross-section

In all cases, we remove the deterministics by running cross-section specific regressions on the appropriate deterministics and obtaining residuals. For case 1 it's a constant so it's equivalent to demeaning, but for the remaining cases, it's a detrending regression.

Note that the demeaning of the data prior to running the regression changes the underlying specification that you are estimating in cases where the data are unbalanced, or where there are trend components in the deterministics. Mark and Sul do not discuss this latter issue in the working paper version of their paper (which suggests the demeaning to remove cross-sectional dependence).

Hi Glenn,

and thank you for this answer. It was very informative!
Thomas

... In all cases, we remove the deterministics by running cross-section specific regressions on the appropriate deterministics and obtaining residuals. For case 1 it's a constant so it's equivalent to demeaning ...

Hello Glenn,

Does the above applies to pmg/ardl regressions as well, in estimations where the only deterministic trend is a constant?

Many thanks.