The Logic of Causal Order (J.A. Davis, 1985)

“Which variables shall I include in this run? Shall I run X against Y or Y against X? Should I control for this? And if I control for this, must I also control for that?

à Substantive empirical matters: the more you know about social stratification, presidential voting, job satisfaction, or whatever, the easier it will be to plan your run.

Logical rules:

Rules about causal order in a set of variables: assumptions about which is the “cause” and which is the “effect” when you look at the relationship between two variables.

Three ideas:

1. the idea of indirect effects;

2. the idea of causally spurious effects; and

3. the idea of signed effects.

Two variables

Variable X is a cause of Variable Y when

-         change in X (sooner or later) produces change in Y

-         or (because some Xs don’t change) Ys tend to line up with the fixed values of
X.

Examples:

Employment is a cause of earnings: People who get (lose) jobs increase (decrease) their earnings.

Martial status is a cause of sociability patterns: when people get married they cut their frequency of visits to bars and taverns.

Race is a cause of party: Blacks are more likely to become Democrats than are whites.

Education is a cause of occupational prestige: People who hold college degrees are more likely to get high-status jobs. 

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

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.

See Also

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)}

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