The relevant lines in the code file xtcsd.ado, to view which type
viewsource xtcsd.ado
are 163-165, which read
di in gr "Pesaran's test of cross sectional independence = "/*
*/in ye %9.3f `pesaran' in gr ", Pr = " %6.4f /*
*/ in ye 2*(1-norm(abs(`pesaran')))
The last line of code is the one that produces the p-value, and it behaves as expected under version control, with the value of the statistic that you get
. version 9: di 2*(1-norm(abs(-2.673)))
.00751763
So, there is no ostensible reason why your computed statistic should result in an abnormal p-value. I suggest you set trace on and check what is going on, or show us the output.
By the way, you should check what version of the xtcsd package you have. You can check using
. which xtcsd
*! version 1.1.1 R.E. De Hoyos and V. Sarafidis 16may2006
I'm just thinking out loud here,
Suppose you have industry-county-year level data, your outcome is $Y_{ict}$, and you are interested in the effect of some variable $x_{ict}$.
In your strategy you would correctly think you can use:
(1) industry-county (panel) fixed effects to control for time invariant confounding factors across these panels as well as the average difference in time varying covariates across industry-county pairs
(2) year fixed effects to control for shocks that are common to all industries and counties in a given year
However what if there are shocks that are common across some counties in regions indexed by $r$, yet are both time varying and different across regions?
That is, perhaps the true data generating process is
$Y_{ict}=\underbrace{\theta_{ic}}_\text{panel fixed effect}+\underbrace{\theta_t}_\text{year fixed effect}+\underbrace{\theta_{rt}}_\text{regional shocks}+\underbrace{\beta}_\text{parameter of interest} X_{ict}+\underbrace{\epsilon_{ict}}_\text{idiosyncratic shock}$
But you estimate a model
$Y_{ict}=\theta_{ic}+\theta_t+\beta X_{ict}+\epsilon_{ict}$
which does not attempt to proxy for this regional shock, then,to to the degree that $Cov(\theta_{rt},X_{ict})\neq 0$, I believe your estimate $\hat{\beta}$ would in part reflect the variation in $\theta_{rt}$ that covaries with $X_{ict}$.
That is,
$plim \; \hat{\beta} =\underbrace{ \beta}_\text{true parameter} + \underbrace{\frac{Cov(X_{ict},\theta_{rt})}{Var(X_{ict}}}_\text{bias}$
to solve this I believe it is possible that you could
(1) Cluster your standard errors at the geographical level where you think there may be correlated disturbances
and
2) Find an instrument $Z_{ict}$ for $X_{ict}$ that is strongly correlated with $X_{ict}$ (relevant) that has an effect on the outcome only through its effect on $X_{ict}$ and not through $\theta_{rt}$ influencing $Z_{ict}$ or through $Z_{ict}$ influencing $Y_{ict}$ directly (excludibility).
Best Answer
Time effects is an easy and efficient way to reduce cross-sectional dependence as your results show. Now, if the addition of time effects into your model, can be explained theoretically, then you could add them and thus use the model with time fixed effects included.