PE Test for Linear vs. Log-Linear Specifications
petest performs the MacKinnon-White-Davidson PE test for comparing
linear vs. log-linear specifications in linear regressions.
petest(formula1, formula2, data = list(), vcov. = NULL, ...)
formula1 |
either a symbolic description for the first model to be tested,
or a fitted object of class |
formula2 |
either a symbolic description for the second model to be tested,
or a fitted object of class |
data |
an optional data frame containing the variables in the
model. By default the variables are taken from the environment
which |
vcov. |
a function for estimating the covariance matrix of the regression
coefficients, e.g., |
... |
further arguments passed to |
The PE test compares two non-nest models where one has a linear
specification of type y ~ x1 + x2 and the other has a log-linear
specification of type log(y) ~ z1 + z2. Typically, the
regressors in the latter model are logs of the regressors in the
former, i.e., z1 is log(x1) etc.
The idea of the PE test is the following: If the linear specification is
correct then adding an auxiliary regressor with the difference of
the log-fitted values from both models should be non-significant.
Conversely, if the log-linear specification is correct then adding
an auxiliary regressor with the difference of fitted values in levels
should be non-significant. The PE test statistic is simply the marginal
test of the auxiliary variable(s) in the augmented model(s). In petest
this is performed by coeftest.
For further details, see the references.
An object of class "anova" which contains the coefficient estimate
of the auxiliary variables in the augmented regression plus corresponding
standard error, test statistic and p value.
W.H. Greene (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.
J. MacKinnon, H. White, R. Davidson (1983). Tests for Model Specification in the Presence of Alternative Hypotheses: Some Further Results. Journal of Econometrics, 21, 53-70.
M. Verbeek (2004). A Guide to Modern Econometrics, 2nd ed. Chichester, UK: John Wiley.
if(require("AER")) {
## Verbeek (2004), Section 3
data("HousePrices", package = "AER")
### Verbeek (2004), Table 3.3
hp_lin <- lm(price ~ . , data = HousePrices)
summary(hp_lin)
### Verbeek (2004), Table 3.2
hp_log <- update(hp_lin, log(price) ~ . - lotsize + log(lotsize))
summary(hp_log)
## PE test
petest(hp_lin, hp_log)
## Greene (2003), Example 9.8
data("USMacroG", package = "AER")
## Greene (2003), Table 9.2
usm_lin <- lm(m1 ~ tbill + gdp, data = USMacroG)
usm_log <- lm(log(m1) ~ log(tbill) + log(gdp), data = USMacroG)
petest(usm_lin, usm_log)
## matches results from Greene's errata
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