I have a linear regression with one dependent variable and ten INdependent variables. I want to estimate this relationship using GMM, but I need at least ten instruments.
Can I use the same dependent variables as instruments for the regression? If not, how would I go about choosing instruments in such a case?
EDIT: my research studies reported generalized trust levels in 77 nations and has covariates such as lnGDP2013 lnPopulationSize2014 dummy variables for history of legal institutions from: Germany, Scandinavia, Britain, France, Germany, a dummy variable for whether or not a nation was involved in the transatlantic slave trade and a dummy variable for whether or not a nation was colonized by Europe in the last 300 years.
I have transformed the dependent variable from a percentage TRUST = Percentage of people who answered that 'most people can be trusted' when surveyed to ln(TRUST/1-TRUST) which gives residuals whose estimated kernel density is roughly normal.
In addition I have a few other covariates such as probability of two individuals chosen from a nation being of the same ethnic group.
EDIT2: I've parsed the model down so I am using GMM to explain the impact of whether or not a nation send or received slaves during the transatlantic slave trade on reported generalized trust levels using Africa as an instrument for whether or not a nation sent or received slaves. I can argue that being an African nation in and of itself should not having a dampening impact on trust but would be correlated with the likelihood that a nation was involved in the transatlantic slave trade.