maotian 发表于 2015-12-21 00:37 
yliu1大侠，按照您的提示，我下载了weakiv，然后在ivtobit回归之后，使用了weakiv的命令。结果如下：
我有 ...
weakiv calculates Lagrange multiplier (LM) or minimum distance (MD) versions of weak-instrument-robust tests of the coefficient on the endogenous variable beta in an instrumental variables (IV) estimation. In an exactly-identified model where the number of instruments equals the number of endogenous regressors, it reports the Anderson-Rubin (AR) test statistic. When the IV model contains more instruments than endogenous regressors (the model is overidentified), weakiv also conducts the conditional likelihood ratio (CLR) test, the Lagrange multiplier K test, the J overidentification test, and a combination of the K and overidentification tests (K-J).
The default behavior of weakiv is to report LM versions of these tests for linear models, and MD versions for the IV probit and IV tobit models. The MD versions of these tests can be requested by the md option; for linear models, these are equivalent to Wald-type tests. The LM versions of these tests are not available for IV probit/tobit models. In the current implementation of weakiv, the CLR test is available for the 1-endog-regressor case only. For reference, weakiv also reports a Wald test using the relevant traditional IV parameter and VCE estimators; this Wald test is identical to what would be obtained by standard estimation using ivregress, ivreg2, ivreg2h, xtivreg, xtivreg2, xtabond2, ivprobit or ivtobit.
The AR test is a joint test of the structural parameter (beta=b0, where beta is the coefficient on the endogenous regressor) and the exogeneity of the instruments (E(Zu)=0, where Z are the instruments and u is the disturbance in the structural equation). The AR statistic can be decomposed into the K statistic (which tests only H0:beta=b0, assuming the exogeneity conditions E(Zu)=0 are satisfied) and the J statistic (which tests only H0:E(Zu)=0, assuming that beta=b0 is true). This J statistic is evaluated at the null hypothesis, as opposed to the Hansen J statistic from GMM estimation, which is evaluated at the parameter estimate.
The CLR test is a related approach to testing H0:beta=b0. It has good power properties, and in particular is the most powerful test for the linear model under homoskedasticity (within a class of invariant similar tests). An important advantage of the CLR test over the K test is that the K test can lose power in some regions of the parameter space when the objective function has a local extremum or inflection point; the CLR test does not suffer from this problem. The CLR test is a function of a rank statistic rk. For the case of more than one endogenous regressor, there are several such rank tests available; weakiv employs the SVD-based test of Kleibergen and Paap (2006) (see e.g. ranktest, which has the computational advantage of a closed-form solution. The rank statistic rk can also be interpreted as a test of underidentification of the model (see Kleibergen 2005); under the null hypothesis that the model is underidentified, rk has a chi-squared distribution.
The CLR test statistic has a non-standard distribution. For the case of i.i.d. linear models with a single weakly-identified endogenous regressor, weakiv uses the fast and accurate algorithm implemented by Mikusheva and Poi
(2006). The default behavior of weakiv for non-i.i.d. and nonlinear models with a single weakly-identified endogenous regressor is to use the same algorithm to obtain p-values for the CLR test; although this is not the correct
p-value function for these cases, the simulations by Finlay and Magnusson (2009) suggest it provides a good approximation. For all models with multiple endogenous regressors, weakiv obtains the p-value by simulation; the seed
for the random number generator is temporarily set to the value 12345 so that the resulting p-values are replicable. The default number of simulations is 10,000; this can be altered using the clrsims(#) option. This option can
also be used to override the default behavior of the i.i.d.-linear-model algorithm with single-endogenous regressor models. A larger number of simulations will give a more accurate p-value but can slow execution, especially in
grid searches. The simulation method can be turned off completely by specifying clrsims(0).
The K-J test combines the K and J statistics to jointly test the structural parameter and the exogeneity of the instruments. It is more efficient than the AR test and allows different weights or test levels to be put on the
parameter and overidentification hypotheses. Unlike the K test, the K-J test does not suffer from the problem of spurious power losses. To perform the K-J test, the researcher specifies the significance levels alpha_K and
alpha_J for the K and J statistics. Because the K and J tests are independent, the null of the K-J test is rejected if either p_K<alpha_K or p_J<alpha_J, where p_K and p_J are the K and J p-values, respectively. The overall
size of the K-J test is given by (1-(1-alpha_K)*(1-alpha_J)).
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