pyblp.ProblemResults.run_lm_test

ProblemResults.run_lm_test()

Test the validity of model restrictions with the Lagrange multiplier test.

Following Newey and West (1987), the Lagrange multiplier or score statistic is

(1)\[\text{LM} = N\bar{g}(\hat{\theta})'W\bar{G}(\hat{\theta})V\bar{G}(\hat{\theta})'W\bar{g}(\hat{\theta})\]

where \(\bar{g}(\hat{\theta})\) is defined in (11), \(\bar{G}(\hat{\theta})\) is defined in (19), \(W\) is the optimal weighting matrix in (24), and \(V\) is the covariance matrix of parameters in (30).

If the restrictions in this model are valid, the Lagrange multiplier statistic is asymptotically \(\chi^2\) with degrees of freedom equal to the number of restrictions.

Warning

This test requires ProblemResults.W to be an optimal weighting matrix, so it should typically be run only after two-step GMM or after one-step GMM with a pre-specified optimal weighting matrix.

Returns

The Lagrange multiplier statistic.

Return type

float

Examples