I am trying to compute the coefficient and the respective p-value for the variation of the variable "Efficiency Ratio" (ER) between 2014 and 2011 (i.e., ∆=2014-2011). I have already computed individual regressions for 2011 and 2014 using the pooled OLS. I don't know the next step to compute the result of this variation (estimated coefficient and p-value). I am trying to conclude whether the sensitivity of the dependent variable concerning the ER variable has been less positively correlated.
Below, I present the individual regressions for 2011 and 2014, and part of my database. I would appreciate any insights on how to do this in R. Thank you.
pdata2011<-pdata.frame(paneldata2011, index = c("BANKS","YEARS"))
pooled2011<-plm(VCTC ~ ER + log(TA) + log(GDP), data = pdata2011, model = "pooling")
pdata2014<-pdata.frame(paneldata2014, index = c("BANKS","YEARS"))
pooled2014<-plm(VCTC ~ ER + log(TA) + log(GDP), data = pdata2014, model = "pooling")
BANKS YEARS VCTC ER TA GDP
1 2014 0.00000000 0.8559100 235193.8 534678.1
1 2011 0.16887878 1.5123620 301355.0 522645.5
2 2014 0.87297022 0.6225519 809343.3 1801480.1
2 2011 0.85148515 0.6321466 777083.1 1789140.7
3 2014 0.24422236 0.4315355 2573915.1 10438529.2
3 2011 0.24970615 0.4156023 1853465.0 7551500.4
4 2014 0.33174224 0.3927662 2457455.2 10438529.2
4 2011 0.28012834 0.4291702 1877624.1 7551500.4
5 2014 0.31638913 0.3525573 2697975.7 10438529.2
5 2011 0.32945877 0.3633482 1949372.7 7551500.4
6 2014 0.22575998 0.3450020 3320881.7 10438529.2
6 2011 0.21708543 0.3596391 2456488.5 7551500.4
...
34 2014 0.94692763 0.7477073 274119.0 17521746.5
34 2011 0.93822571 0.7259823 216827.0 15542581.1
35 2014 0.86932004 0.5752208 1687155.0 17521746.5
35 2011 0.85889245 0.6049802 1313867.0 15542581.1
You can do as @LynnL proposed, which is to include an interaction term. If there are significant differences (i.e not zero) between the effects of ER, this term will give you a small p-value.
Ideally provide the data next time, because we have no idea what are YEARS etc and whether the two data.frames can be combined. Below I suggest using a zscore to look at the difference between 2 coefficients:
library(plm)
Using the first 12 rows of your data, assuming this is the combined dataset:
df = structure(list(BANKS = c(1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 5L,
5L, 6L, 6L), YEARS = c(2014L, 2011L, 2014L, 2011L, 2014L, 2011L,
2014L, 2011L, 2014L, 2011L, 2014L, 2011L), VCTC = c(0, 0.16887878,
0.87297022, 0.85148515, 0.24422236, 0.24970615, 0.33174224, 0.28012834,
0.31638913, 0.32945877, 0.22575998, 0.21708543), ER = c(0.85591,
1.512362, 0.6225519, 0.6321466, 0.4315355, 0.4156023, 0.3927662,
0.4291702, 0.3525573, 0.3633482, 0.345002, 0.3596391), TA = c(235193.8,
301355, 809343.3, 777083.1, 2573915.1, 1853465, 2457455.2, 1877624.1,
2697975.7, 1949372.7, 3320881.7, 2456488.5), GDP = c(534678.1,
522645.5, 1801480.1, 1789140.7, 10438529.2, 7551500.4, 10438529.2,
7551500.4, 10438529.2, 7551500.4, 10438529.2, 7551500.4)), class = "data.frame", row.names = c(NA,
-12L))
You start from here, run the regression with the interaction term:
df$YEARS = factor(df$YEARS)
pooled2011<-plm(VCTC ~ ER + log(TA) + log(GDP),model = "pooling",data=pdata.frame(subset(df,YEARS==2011),index=c("BANKS","YEARS")))
pooled2014<-plm(VCTC ~ ER + log(TA) + log(GDP),model = "pooling",data=pdata.frame(subset(df,YEARS==2014),index=c("BANKS","YEARS")))
In the regression based on 6 data points each. Run that for your whole dataset.
b1 <- summary(pooled2011)$coefficients["ER",1]
se1 <- summary(pooled2011)$coefficients["ER",2]
b2 <- summary(pooled2014)$coefficients["ER",1]
se2 <- summary(pooled2014)$coefficients["ER",2]
The difference is simply the difference between the two regression coefficients (assuming all variables are on the same scale), and you can report the standard error :
compare.coeff <- function(b1,se1,b2,se2){
delta = b1-b2
se = sqrt(se1^2+se2^2)
Zscore = (delta)/se
p_value = 2*pnorm(-abs(Zscore))
c(delta=delta,se=se,Zscore=Zscore,p_value=p_value)
}
compare.coeff(b1,se1,b2,se2)
delta se Zscore p_value
-1.7461849 7.4390338 -0.2347328 0.8144162
You can also check out books or chapters like this, basically anything that describes the use of the interaction term. I also answered a similar question before, you can also check that.