EViews.com

We know that since time-invariant variables are collinear with fixed effects their coefficients cannot be estimated in FEM. However, when I include my time invariant variables (dummies representing state specific balance budget requirements, BBRs) with period fixed effects only I get estimates (see below----cross-section FE results in "near singular matrix" error message). I asked Professor Greene about this. He initially pointed out the impossibility of estimating the coefficients. However, after I sent him these results, he wrote:
"The time dummies are not time invariant, so they can coexist with your BBRs in the regression. I assume that is what EViews is computing, as if they were also including the individual dummies, there would be perfect collinearity, and you could not compute the coefficients of the model."

I'm not still sure whether the above estimated coefficients for BBRs are valid (what is Eviews computing?) and, if so, whether they can interpreted as capturing cross-state differences in BBRs. I would greatly appreciate it if somebody provides precise answers to these two questions.

Dependent Variable: PDEFSPI
Method: Panel Least Squares
Sample (adjusted): 1962 2008
Periods included: 47
Cross-sections included: 47
Total panel (balanced) observations: 2209
White cross-section standard errors & covariance (d.f. corrected)
WARNING: estimated coefficient covariance matrix is of reduced rank

Variable Coefficient Std. Error t-Statistic Prob.

C 1.747473 0.18274 9.56261 0
DEBTSPI(-1)0.053608 0.006981 7.678794 0
CYEXS -9.28E-08 2.09E-08 -4.439648 0
CYPI 1.66E-09 7.33E-09 0.225833 0.8214
SSLEXR -0.015457 0.002893 -5.343454 0
FIGRSPI 0.184401 0.029511 6.248451 0
BBR1 -0.252089 0.068381 -3.686536 0.0002
BBR2 0.170208 0.041812 4.070781 0
BBR3 -0.278214 0.050012 -5.562981 0
BBR4 0.237518 0.063448 3.743481 0.0002
BBR5 0.024095 0.049451 0.487258 0.6261
BBR6 -0.309481 0.077812 -3.977272 0.0001
BBR7 -0.274344 0.037716 -7.27401 0
BBR8 -0.192072 0.043681 -4.397194 0
BBR9 0.112029 0.055667 2.012466 0.0443[/b]
DEMGOV -0.087257 0.040194 -2.170892 0.03
REPGOV 0.017999 0.078129 0.230371 0.8178

Effects Specification

Period fixed (dummy variables)

Greene is right - period fixed effects are the same thing as period dummies, and you cannot have both.

If I'm interpreting the original question correctly it's about whether you can have time-invariant variables and period fixed effects, and the answer is yes. What you can't have are time-invariant variables and cross-section fixed effects, or cross-section invariant variables and period effects.

If I'm interpreting the original question correctly it's about whether you can have time-invariant variables and period fixed effects, and the answer is yes. What you can't have are time-invariant variables and cross-section fixed effects, or cross-section invariant variables and period effects.

Glenn,

You understood my question correctly! Am I right in interpreting the coefficients as capturing cross-sectional differences in BBRs? Thank you.

Greene is right - period fixed effects are the same thing as period dummies, and you cannot have both.

Thanks Gareth. I did not have both. It is just that because the variables are time invariant, I was not comfortable with the results from a specification that included time fixed effects.

I'm not certain how the BBRs are created, but if they are indeed cross-section specific variables (variables interacted with the corresponding cross-section dummy) then they should capture the variation in the marginal effects across cross-sections.