help for ^bgtest^         (STB-55, updated by SSC distribution 11 August 2002)

Calculate the Breusch-Godfrey LM statistic after @regress@ or @newey@ -----------------------------------------------------------------

^bgtest^ [, lags(p) force]

^bgtest^ is for use after ^regress^ or ^newey^; see help @regress@ or @newey@.

^bgtest^ is for use with time-series data. You must ^tsset^ your data before using ^bgtest^; see help @tsset@.

Description -----------

^bgtest^ computes the Breusch (1978)-Godfrey (1978) Lagrange multiplier test for nonindependence in the error distribution. For a specified number of lags p, the test's null of independent errors has alternatives of either AR(p) or MA(p). The test statistic, a T R^2 measure, is distributed Chi-squared(p) under the null hypothesis. The test is asymptotically equivalent to the Box- Pierce portmanteau test, or Q statistic (@wntestq@), for p lags, but unlike the Q statistic, the Breusch-Godfrey test is valid in the presence of stochastic regressors such as lagged values of the dependent variable.

For p=1, the test is asymptotically equivalent to the Durbin-Watson 'h' statistic (@durbinh@), which may be considered a special case of the Breusch-Godfrey test statistic. See Greene (2000), Chapter 13.

This version, updated from that published in STB-55, follows the convention that lagged values of the estimated residual vector are set to zero, per Greene (2000), so that the auxiliary regression has the same number of degrees of freedom as the regression generating the residuals. The two computations are asymptotically equivalent and we know their distribution under the null only asymptotically. In small samples, this convention will prevent the loss of degrees of freedom experienced under the former version of the test.

The command displays the test statistic, degrees of freedom and P-value, and places values in the return array. @return list@ for details.

Options -------

The ^lags^ option specifies p, the number of lags to be included in the auxilia > ry regression. It must be less than 25% of the sample size.

The ^force^ option specifies that the test is to be allowed after @regress ..., robust@ and @newey@; by default it is not allowed. In these cases the test statistic is exactly the same as if standard OLS were performed using @regress@. This is true because the test is based on the residuals from the regression and they are the same for @regress@, @regress ..., robust@, and @newey@. There is no way the test can utilize any of the information used to make the standard errors robust after estimation with @newey@ or @regress ..., robust@. It is best to view the test as a test of the OLS disturbances whether estimation is by @regress@, @regress ..., robust@, or @newey@.

Examples --------

. ^use http://fmwww.bc.edu/ec-p/data/macro/wgmacro.dta^ . ^regress consumption L(1/4).income^ . ^bgtest, lags(4)^ . ^g Lincome = L.income^ . ^newey consumption Lincome, lag(4)^ . ^bgtest, lags(4) force^

References ----------

Breusch, T. "Testing for autocorrelation in dynamic linear models." Australian Economic Papers, 17, 1978, pp. 334-355. Godfrey, L. "Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables." Econometrica, 46, 1978, 1293-1302. Greene, W. Econmetric Analysis. 4th ed., 2000. New York: Prentice-Hall.

Authors -------

Christopher F Baum, Boston College, USA baum@@bc.edu

Vince Wiggins, Stata Corporation vwiggins@@stata.com

Acknowledgement --------------- We are grateful to Richard Sperling for suggesting that the zero-fill convention should be employed in this routine.

Also see --------

Manual: ^[R] regress^, ^[R] regression diagnostics^ On-line: help for @regdiag@, @regress@, @time@, @tsset@; @dwtest@; @newey@; @durbinh@ (if installed)