panel ar(1) model:
方程是:
y(i,t)= rho * y(i,t-1) +ai + e(i,t)
对rho作bias和t test
问题: 因为t比较小,ols算出来的rho应该是inconstant,这个inconstancy is measured by bias, 但是为什么rho越大,比如0.8-0.9-0.95, bias反而越小呢?当rho增大的时候,这个estimator不应该偏离的更厉害吗(当rho增大了,the size of the test也增大了,这个和预期一致)?为什么反而bias减少了呢?
n= 50 t=30 rho=.3
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
bias | 10 .0784436 .0439183 -.0147862 .1343976
b | 10 .8 .421637 0 1
n= 50 t=30 rho=.8
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
bias | 10 .0786781 .0186809 .0494827 .1011455
b | 10 1 0 1 1
n= 50 t=30 rho=.9
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
bias | 10 .0529194 .006639 .0409468 .0615557
b | 10 1 0 1 1
n= 50 t=30 rho=.95
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
bias | 10 .0341334 .0063702 .0233213 .0437388
b | 10 1 0 1 1