[R] Testing for weak exogeneity in a SUR ECM

[Kathrinchen]

Dear all,

I have set up a Labour Demand Error Correction Model for some German federal
states.

As I expect the labour markets to be correlated I used a Seemingly Unrelated
Regression using systemfit in R.

My Model  is:

d(emp)_it = c + alpha*ln(emp)_i,t-1 + beta_1*ln(gdp)_i,t-1 + +
beta_2*ln(wage)_i,t-1 + + beta_1*ln(i)_i,t-1 + gamma_1*d(gdp)_it +
gamma_2*d(wage)_it

with emp_it being the employment in state i at time t, i stands for the real
interest rate, ln() is the logarithmed data, while d() stands for the
difference operator.

I would like to test now for weak exogeneity and I am not quite sure what
kind of regression to run.  If I run: 
d(gdp)_it = c + alpha*ln(emp)_i,t-1 + beta_1*ln(gdp)_i,t-1 + +
beta_2*ln(wage)_i,t-1 + + beta_1*ln(i)_i,t-1 + gamma_1*d(emp)_it +
gamma_2*d(wage)_it

with Systemfit, alpha is statistically significant, so I have to reject the
hypothesis of weak exogeneity...Literature is in my opinion not so clear on
what to test!

I use data from an application, they conclude that endogeneity is not a
problem: they regress the possible endogenous variables "on the presumed
equilibrium relation, a constant and one autoregressive lag" - here I am not
sure, what they mean.

I would very much appreciate your help!

Thanks a lot!





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