I have employed 2-step GMM, however, I am getting Lag1 and Lag2 giving different direction of serial correlation. While Lag1 is positively influencing the Dependent variable whereas Lag2 is negatively influencing the Dependent Variable? Is it unusual to get such a result? What would be the possible interpretation?
This is not unusual finding.
LAG refers to the period that it takes for the process to return to its original long-rum equilibrium after a shock to the system. LAG 1 and LAG 2 just means that after one period, the system returned to its old mean and LAG 2 means that it took 2 period to return to the old mean.
SIGNS in positive and negative also should not be surprise. Some shock to the system may have positive and other may have negative effect. This is quite normal.
You can test as well for deeper lags and see how the results will behave. What really should govern your decision is the scientific theory, if different signs of lag lengths can be explained by the theory or not, also make sure to check the validity of the used instruments based on the GMM post estimation tests.
Sherif Maher Hassan Thank you Sir for offering your answer. Would be able to enlighten me a bit about GMM Post Estimation Tests?
I meant the sargan or hansen tests of exogeneity along with the AR1 and AR2 tests of autocorrelation. These should give you an idea if the used instruments are fine in terms of removing the autocorrelation problem within the differenced equation and the validity of the instruments.
Sherif Maher Hassan I performed all the tests you have mentioned. Hansen/Sargan Test seems to be fine. AR1 is present but there in no presence of AR2 which is considered acceptable.
AR2 is the most important as it detects the second-order serial correlation. why it is not reported, maybe limited sample size or using more instruments than what you should be using. Cannot judge
Sherif Maher Hassan What I meant to say was that I did both AR1 and AR2 tests and tests show absence of 'Second Order Correlation'. The value of AR2 for Model1 (without period dummies) = 0.326 and Model 2 (with period dummies)= 0.822
I agree with Paul. The signage of the dependent variable and other variables should be supported by theory and multicollineraity test or correlation matrix results. Ensure that the correlation results do not report results of >0.80, otherwise there is high correlation amongst the variables on the right hand side of the model. Further, diagnostic tests should assure reliable and efficient results e.g AR1 can either be significant (due to differencing of variable) or positive. That is fine. AR2 should not be significant for the instruments used to be held valid. if significant the instruments used are not valid! The Sargan Over-identifying test results should not be significant while Wald test results should be significant. Check your Diagnostic Tests results and support the same with correct interpretations. Additionally, support the signage of variables with correct economic theory.
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