This is an explanation of the following sentence in our article: “To avoid bias and inconsistency that might be caused by instruments proliferation, we collapse the instruments matrix.” We are using longer lags of the dependent variable as additional instruments. Intuitively, there is a trade-off, on one hand, using longer lags gives more information and improves efficiency, but on the other hand sample gets smaller (as it is the case in standard 2SLS models). GMM is a way around this trade-off between lag length and sample length. However, implementation of System-GMM is not exempt from weaknesses. With the instruments count being quadratic in the time dimension, the variance matrix of the moments can be very large. Estimating its elements may be problematic in particular in a finite sample lacking the adequate amount of information. This finite sample bias can weaken Hansen J-test and overstate its p-value and therefore generate suspicious high pass rate of instruments validity. The problem is known as instruments proliferation (Roodman 2009). To avoid bias and inconsistency due to instruments proliferation, we limit the number of instruments used and collapse the instrument matrix which prevents the model from being over-fitted.
7- Explain your sentences in lines 242-244. What did you do specifically?