 A COMPANION TO Theoretical Econometrics

# Detecting harmful collinearity

We can determine the number of collinear relations, their severity, and the vari­ables involved using the diagnostics in Section 3. This does not end the diagnostic process, because we must still determine if the collinearity present is actually harmful to our regression. Whether the collinearity matters depends on the mag­nitude of the regression parameters. The parameters matter in two regards. First, from equations (12.2) and (12.9), it is clear that a small value of the error variance, a2, can offset the effects of high correlation between the regressors or low regres­sor variability.

Second, the magnitudes of the pk matter. If the variance of bk is a, then 100(1 - a)% interval estimator for pk is bk ± fcch, where tc is a critical value from the f-distribution. Suppose we diagnose severe collinearity affecting (and inflat­ing) the variance of bk and compute fcdh = 3. Is collinearity harmful when pk = 1? What if pk = 1000? If you answered "yes" to the first question, but "no" to the second, you are saying, and rightly so, that the magnitude of the parameter pk also matters when determining if collinearity is harmful or not.  Belsley (1982) addresses these issues by developing tests for adequate "signal - to-noise," abbreviated s/n, in the regression model and data. For a single para­meter Belsley defines an s/n parameter,

If t is small, then the error variance a2 is not small enough, and/or pk is not large enough, to offset the effects of collinearity and/or lack of regressor variability. Belsley proposes to test the hypothesis that | t | > t*, where t* is an adequate magnitude. For details of this, and a more general multiparameter test, see Belsley (1982).

In the end, Belsley (1982, p. 225) proposes that investigators (i) examine collinearity using the diagnostics described in Section 3, and (ii) carry out the test for adequate s/n. The conclusions one can draw are summarized in Table 12.2.

The four possible outcomes are these: (I) negligible collinearity and adequate s/n; (II) collinearity present, but not harmful, since adequate s/n is present; (III) negligible collinearity, but inadequate s/n present, caused by lack of regressor variation; (IV) harmful collinearity, the joint occurrence of severe collinearity and inadequate s/n. In the next section we address what remedies are available in cases III and IV.

Table 12.2 Harmful collinearity decision matrix   Collinearity present? no yes

Добавить комментарий

## A COMPANION TO Theoretical Econometrics

### Normality tests

Let us now consider the fundamental problem of testing disturbance normality in the context of the linear regression model: Y = Xp + u, (23.12) where Y = (y1, ..., …

### Univariate Forecasts

Univariate forecasts are made solely using past observations on the series being forecast. Even if economic theory suggests additional variables that should be useful in forecasting a particular variable, univariate …

### Further Research on Cointegration

Although the discussion in the previous sections has been confined to the pos­sibility of cointegration arising from linear combinations of I(1) variables, the literature is currently proceeding in several interesting …

## Как с нами связаться:

Украина:
г.Александрия
тел./факс +38 05235  77193 Бухгалтерия
+38 050 512 11 94 — гл. инженер-менеджер (продажи всего оборудования)

+38 050 457 13 30 — Рашид - продажи новинок
e-mail: msd@msd.com.ua
Схема проезда к производственному офису:
Схема проезда к МСД

Партнеры МСД

## Контакты для заказов шлакоблочного оборудования:

+38 096 992 9559 Инна (вайбер, вацап, телеграм)
Эл. почта: inna@msd.com.ua

За услуги или товары возможен прием платежей Онпай: Платежи ОнПай