# petest: PE Test for Linear vs. Log-Linear Specifications In lmtest: Testing Linear Regression Models

 petest R Documentation

## PE Test for Linear vs. Log-Linear Specifications

### Description

`petest` performs the MacKinnon-White-Davidson PE test for comparing linear vs. log-linear specifications in linear regressions.

### Usage

``` petest(formula1, formula2, data = list(), vcov. = NULL, ...)
```

### Arguments

 `formula1` either a symbolic description for the first model to be tested, or a fitted object of class `"lm"`. `formula2` either a symbolic description for the second model to be tested, or a fitted object of class `"lm"`. `data` an optional data frame containing the variables in the model. By default the variables are taken from the environment which `petest` is called from. `vcov.` a function for estimating the covariance matrix of the regression coefficients, e.g., `vcovHC`. `...` further arguments passed to `coeftest`.

### Details

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.

### Value

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.

### References

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.

`jtest`, `coxtest`, `encomptest`

### Examples

```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
}
```

lmtest documentation built on March 22, 2022, 1:06 a.m.