Struggling for simultaneous equation models
Recently, I have been reading the paper Refinancing risk and cash holdings by Jarrad Harford.
This is a simple example of his model:
y_1=a_0+a_1*y_2+a_2*Z_1+v;
y_2=b_0+b_1*y_1+b_2*Z_2+u;
Z_1, Z_2 are two different sets of control variables from previous literature.
Estimation procedure:
First, he separately estimates two OLS regressions for y_1 and y_2
Second, he simultaneously estimates the two structural equations by including the predicted values from the first-stage regressions as explanatory variables.
Below are my questions:
1. Does simultaneously estimation in the second stage refer to SUR (seemingly unrelated regression)? or is it just another two separate OLS regression on predicted values from the first stage?
2. He said this method can apply to the situation when two variables are endogenous and jointly determined. Is there any other assumption to his statement? like Z_1 and Z_2 must be exogenous.
3. I am really confused by his quotation, ''The 2SLS methodology accounts for any correlation between the residuals of the y_1 and y_2 models that is caused by unobserved influences on y_2 and y_1. ''
Can someone help me? I'd really appreciate it.
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