I am currently trying to estimate some panel data models in R using PLM package. This includes the estimation of basic pooled, fixed effects and random effects models. Therefore I make use of this code:

# read in data
mydata<- read.csv2("Panel.csv")
attach(mydata)

# define dependant variable
standarddeviation <- cbind(sd)
# define independant variable
x <- cbind(ratio1, ratio2, ratio3, ratio4, mean)

# Set data as panel data
pdata <- plm.data(mydata, index=c("id","t"))

# Pooled OLS estimator
pooling <- plm(standarddeviation ~ x, data=pdata, model= "pooling")
summary(pooling)

# Between estimator
between <- plm(standarddeviation ~ x, data=pdata, model= "between")
summary(between)

# First differences estimator
firstdiff <- plm(standarddeviation ~ x, data=pdata, model= "fd")
summary(firstdiff)

# Fixed effects or within estimator
fixed <- plm(standarddeviation ~ x data=pdata, model= "within")
summary(fixed)

# Random effects estimator
random <- plm(standarddeviation ~ x, data=pdata, model= "random")
summary(random)

Now here's the problem: I can without any problem estimate all models except for the random effects model. After entering the "random"-formula, R produces the following error:

"Error in solve.default(crossprod(X.m)) : 
  system is computationally singular: reciprocal condition number = 9.57127e-023"

First guesses:

• Linear combinations in x? A first guess would be that there are exact linear dependencies of the exogenous variables in x. The data is balance sheet data and I would like to explain the standard deviation (y) of a specific balance sheet position by other balance sheet positions (or the ratio of the position and the balance sheet sum). Of course, the variables in x are related to each other. For example some of the ratios are calculated by dividing by the mean which is also a separate independant variable. And the dependant variable, which is the standard deviation, is also calculated by using this mean. But again: There should be no EXACT correlation. But: If I exclude some of my exogenous variables, the problem disappears, but I have to include them actually.
• Unbalanced panel / NAs? The data is unbalanced and there are NAs. Fixed effects output says: n=16, T=18-40, N=455. Probably the unbalanced data or the NAs are the reason for the error?

Traceback-Code:

random <- plm(standarddeviaution ~ x, data=pdata, model= "random") Error in solve.default(crossprod(X.m)) : system is computationally singular: reciprocal condition number = 9.57127e-023 traceback() 8: solve.default(crossprod(X.m)) 7: solve(crossprod(X.m)) 6: diag(solve(crossprod(X.m)) %*% crossprod(X.sum)) 5: swar(object, data, effect) 4: ercomp.formula(formula, data, effect, method = random.method) 3: ercomp(formula, data, effect, method = random.method) 2: plm.fit(formula, data, model, effect, random.method, inst.method) 1: plm(standarddeviation ~ x, data = pdata, model = "random")

Is there anybody who can give me a hint what this error does actually mean and especially: how to solve the problem? How do I have to correct the code in order to get results? Thanks a lot!