When the first stage is linear, like the case of 2sls, the test of weak IV is straight forward, method like Stock and Yogo (2005) test are available in standard package command, like ivreg2 in Stata. But when I specify something nonlinear in the first stage (like a ordered probit model), the situation become complicated. Can I find some counterpart test for the nonlinear case, or I can specify a "linear" specification as the baseline (which I believe is problematic). Any suggestion is warmly welcome and literatures are desired, thanks in advance.
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Non-linear 1st stage may not necessarily be a good idea. See: http://stats.stackexchange.com/questions/125830/consistency-of-2sls-with-binary-endogenous-variable – landroni Apr 02 '16 at 08:56