I would like to do a simple joint Wald test on my fixed-effects regression coefficients but I want to set the restriction to something other than zero. More specifically I would like to test: H0: ai=0 and b=1 for every i or basically, whether the extracted intercepts from fixed effects model (ai) (I know there is no intercept in fixed-effects model but you can still extract them through fixef() command and they should be close to zero if fixed-effects model is the correct model) is equal to zero for each i and my coefficients (bi) are equal to 1.
Here is what I have:
library(plm)
form <- R_excess ~ I(beta_MKT_RF*MKT_RF) + I(beta_HML*HML) + I(beta_SMB*SMB)
reg1 <- plm(form, data=nlspd, model="within")
summary(reg1, vcov =function(x) vcovSCC(x, type="HC3", maxlag=12))
And here is the output as you can see my coefficients are all close to 1:
Call:
plm(formula = form, data = nlspd, model = "within")
Balanced Panel: n = 10, T = 624, N = 6240
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-7.8706e-02 -9.0319e-03 3.8278e-05 8.9624e-03 1.1349e-01
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
I(beta_MKT_RF * MKT_RF) 1.0023818 0.0072942 137.422 < 2.2e-16 ***
I(beta_HML * HML) 0.9985867 0.0527123 18.944 < 2.2e-16 ***
I(beta_SMB * SMB) 0.9731437 0.0355880 27.345 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 18.067
Residual Sum of Squares: 1.5037
R-Squared: 0.91677
Adj. R-Squared: 0.91661
F-statistic: 7808.71 on 3 and 623 DF, p-value: < 2.22e-16
I can also get the fixed-effect intercepts ai by using:
summary(fixef(reg1), vcov =function(x) vcovSCC(x, type="HC3", maxlag=12))
Estimate Std. Error t-value Pr(>|t|)
1 0.00127680 0.00062245 2.0512 0.040285 *
2 0.00136923 0.00062251 2.1995 0.027877 *
3 0.00104805 0.00062246 1.6837 0.092283 .
4 0.00132979 0.00062259 2.1359 0.032727 *
5 -0.00061048 0.00062252 -0.9807 0.326795
6 0.00085262 0.00062247 1.3697 0.170816
7 -0.00104724 0.00062250 -1.6823 0.092557 .
8 -0.00089731 0.00062275 -1.4409 0.149672
9 -0.00174805 0.00062292 -2.8062 0.005028 **
10 -0.00271173 0.00062343 -4.3497 1.385e-05 ***
Now I want to do the joint wald test on these coefficients to test whether for every i: H0: ai =0 and b=1.
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