Package 'prais' reference manual

Title:	Prais-Winsten Estimator for AR(1) Serial Correlation
Description:	The Prais-Winsten estimator (Prais & Winsten, 1954) takes into account AR(1) serial correlation of the errors in a linear regression model. The procedure recursively estimates the coefficients and the error autocorrelation of the specified model until sufficient convergence of the AR(1) coefficient is attained.
Authors:	Franz X. Mohr [aut, cre]
Maintainer:	Franz X. Mohr <[email protected]>
License:	GPL-2
Version:	1.1.3
Built:	2024-11-25 19:32:01 UTC
Source:	CRAN

Barium

Description

Monthly microeconomic data from the U.S. chemical industry from February 1978 to December 1988 as used in Krupp and Pollard (1996) and subsequently re-used by Wooldridge (2000) as a textbook dataset. Raw data was obtained from http://fmwww.bc.edu/ec-p/data/wooldridge/barium.dta.

Usage

data("barium")
data("barium")

Format

A data frame with 131 rows and 31 variables:

chnimp: Chinese imports, bar. chl.
bchlimp: Total imports, bar. chl.
befile6: Dummy varialbe, which is 1 for all six months before filing.
affile6: Dummy varialbe, which is 1 for all six months after filing.
afdec6: Dummy varialbe, which is 1 for all six months after decision
befile12: Dummy varialbe, which is 1 for all twelve months before filing.
affile12: Dummy varialbe, which is 1 for all twelve months after filing.
afdec12: Dummy varialbe, which is 1 for all twelve months after decision.
chempi: Chemical production index.
gas: Gasoline production.
rtwex: Exchange rate index.
spr: Dummy varialbe, which is 1 for spring months.
sum: Dummy varialbe, which is 1 for summer months.
fall: Dummy varialbe, which is 1 for fall months.
lchnimp: Log of chnimp.
lgas: Log of gas.
lrtwex: Log of rtwex.
lchempi: Log of chempi.
t: Time trend.
feb: Dummy varialbe for February.
mar: Dummy varialbe for March.
apr: Dummy varialbe for April.
may: Dummy varialbe for May.
jun: Dummy varialbe for June.
jul: Dummy varialbe for July.
aug: Dummy varialbe for August.
sep: Dummy varialbe for September.
oct: Dummy varialbe for October.
nov: Dummy varialbe for November.
dec: Dummy varialbe for December.
percchn: Percent of imports from China.

References

Krupp, C.M., & Pollard, P.S., (1996). Market responses to antidumpting laws: Some evidence from the U.S. chemical industry. Canadian Journal of Economics 29(1), 199–227. doi:10.2307/136159

Wooldridge, J., (2000). Instructional Stata datasets for econometrics. [barium]. Boston College Department of Economics.

Prais-Winsten Estimator for AR(1) Serial Correlation

Description

The Prais-Winsten estimator takes into account AR(1) serial correlation of the errors in a linear regression model. The procedure recursively estimates the coefficients and the error autocorrelation of the specified model until sufficient convergence of the AR(1) coefficient is reached. All estimates are obtained by OLS.

Usage

prais_winsten(
  formula,
  data,
  index,
  max_iter = 50L,
  tol = 1e-06,
  twostep = FALSE,
  panelwise = FALSE,
  rhoweight = c("none", "T", "T1"),
  ...
)

## S3 method for class 'prais'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
prais_winsten(
  formula,
  data,
  index,
  max_iter = 50L,
  tol = 1e-06,
  twostep = FALSE,
  panelwise = FALSE,
  rhoweight = c("none", "T", "T1"),
  ...
)

## S3 method for class 'prais'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

`formula`	an object of class `"formula"` (or one that can be coerced to that class): a symbolic description of the model to be fitted.
`data`	a data frame containing the variables in the model. If panel data is used, it must also contain the ID and time variables.
`index`	a character vector specifying the ID and time variables. If only one variable is provided, it is assumed to be the time variable and the data will be reordered accordingly.
`max_iter`	integer specifying the maximum number of allowed iterations. Default is 50.
`tol`	numeric specifying the maximum absolute difference between the estimator of $rho$ in the current and the previous iteration that has to be attained to reach convergence. Default is 1e-6.
`twostep`	logical. If `TRUE`, the estimation will stop after the first iteration.
`panelwise`	logical. If `TRUE`, $\rho$ will be calculated for each panel separately. Default is `FALSE`. Only used for panel data. See 'Details'.
`rhoweight`	character specifying how $\rho$ should be calculated if `panelwise = TRUE`. See 'Details'.
`...`	arguments passed to `lm`.
`x`	an object of class "prais", usually, a result of a call to `prais_winsten`.
`digits`	the number of significant digits to use when printing.

Details

If $\rho$ takes a value above 1 during the estimation process, the Prais-Winsten transformation cannot be applied to the first observations, because $(1 - \rho^2)^{(1 / 2)}$ is not real. These observations are dropped during the respective iteration and the estimator effectively becomes the Cochrane-Orcutt estimator.

If panelwise = TRUE, twostep = FALSE and rhoweight = "none", each individual estimate of $rho$ is re-estimated until convergence is achieved for all coefficients.

If panelwise = TRUE, the calculation of $\rho$ can be further specified in argument rhoweight. If rhoweight = "none", $\rho$ is assumed to be panel-specific. If rhoweight = "T", $\rho$ is calculated as a weighted mean of panel-specific estimates, where the number of available observations per panel, i.e. $T_i$ , is used as weight. If rhoweight = "T1", $\rho$ is calculated as a weighted mean of panel-specific estimates, where the number of available observations per panel minus one, i.e. $T_i - 1$ , is used as weight.

Value

A list of class "prais" containing the following components:

`coefficients`	a named vector of coefficients.
`rho`	the values of the AR(1) coefficient $\rho$ from all iterations.
`residuals`	the residuals, that is the response minus the fitted values.
`fitted.values`	the fitted mean values.
`rank`	the numeric rank of the fitted linear model.
`df.residual`	the residual degrees of freedom.
`call`	the matched call.
`terms`	the terms object used.
`model`	the original model frame, i.e., before the Prais-Winsten transformation.
`index`	a character specifying the ID and time variables.

References

Beck, N. L. and Katz, J. N. (1995): What to do (and not to do) with time-series cross-section data. American Political Science Review 89, 634-647.

Prais, S. J. and Winsten, C. B. (1954): Trend Estimators and Serial Correlation. Cowles Commission Discussion Paper, 383 (Chicago).

Wooldridge, J. M. (2013): Introductory Econometrics. A Modern Approach. 5th ed. Mason, OH: South-Western Cengage Learning Cengage.

Examples

# Generate an artificial sample
set.seed(1234567)
n <- 100
x <- sample(20:40, n, replace = TRUE)
rho <- .5

# AR(1) errors
u <- rnorm(n, 0, 5)
for (i in 2:n) {
  u[i] <- u[i] + rho * u[i - 1]
}
pw_sample <- data.frame("x" = x, "y" = 10 + 1.5 * x + u, "time" = 1:n)

# Estimate
pw <- prais_winsten(y ~ x, data = pw_sample, index = "time")
summary(pw)

# Generate an artificial sample
set.seed(1234567)
n <- 100
x <- sample(20:40, n, replace = TRUE)
rho <- .5

# AR(1) errors
u <- rnorm(n, 0, 5)
for (i in 2:n) {
  u[i] <- u[i] + rho * u[i - 1]
}
pw_sample <- data.frame("x" = x, "y" = 10 + 1.5 * x + u, "time" = 1:n)

# Estimate
pw <- prais_winsten(y ~ x, data = pw_sample, index = "time")
summary(pw)

Summarising the Prais-Winsten Estimator

Description

Summary method for class "prais".

Usage

## S3 method for class 'prais'
summary(object, ...)

## S3 method for class 'summary.prais'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)
## S3 method for class 'prais'
summary(object, ...)

## S3 method for class 'summary.prais'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

`object`	an object of class `"prais"`, usually, a result of a call to `prais_winsten`.
`...`	further arguments passed to or from other methods.
`x`	an object of class `"summary.prais"`, usually, a result of a call to `summary.prais`.
`digits`	the number of significant digits to use when printing.
`signif.stars`	logical. If `TRUE`, 'significance stars' are printed for each coefficient.

Value

summary.prais returns a list of class "summary.prais", which contains the following components:

`call`	the matched call.
`residuals`	the residuals, that is the response minus the fitted values.
`coefficients`	a named vector of coefficients.
`rho`	the values of the AR(1) coefficient $\rho$ from all iterations.
`sigma`	the square root of the estimated variance of the random error.
`df`	degrees of freedom, a 3-vector (p, n-p, p)*, the first being the number of non-aliased coefficients, the last being the total number of coefficients.
`r.squared`	R^2, the 'fraction of variance explained by the model', $R^2 = 1 - \frac{\sum {(y_i - \hat{y}_i)^2}}{\sum {(y_i - \overline{y})^2}},$ where $\overline{y}$ is the mean of $y_i$ for $y_i = 1, ..., N$ if there is an intercept and zero otherwise.
`adj.r.squared`	the above R^2 statistic 'adjusted', penalising for higher p.
`fstatistic`	(for models including non-intercept terms) a 3-vector with the value of the F-statistic with its numerator and denominator degrees of freedom.
`cov.unscaled`	a $p \times p$ matrix of (unscaled) covariances of the coef[j], j=1, ..., p.
`dw`	a named 2-vector with the Durbin-Watson statistic of the original linear model and the Prais-Winsten estimator.
`index`	a character specifying the ID and time variables.

Semirobust Covariance Matrix Estimators

Description

Semirobust covariance matrix estimators for models of class "prais".

Usage

## S3 method for class 'prais'
vcovHC(x, type = c("const", "HC1", "HC0"), ...)
## S3 method for class 'prais'
vcovHC(x, type = c("const", "HC1", "HC0"), ...)

Arguments

`x`	an object of class `"prais"`, usually, the result of a call to `prais_winsten`.
`type`	a character string specifying the estimation type.
`...`	not used.

Details

vcovHC is a function for estimating a robust covariance matrix of parameters for the Prais-Winsten estimator. The weighting schemes specified by type are analogous to those in vcovHC in package sandwich with the caveat that only "const", "HC0" and "HC1" are available.

Value

An object of class "matrix" containing the estimate of the asymptotic covariance matrix of coefficients.

Extract Panel-Corrected Variance Covariance Matrix

Description

Panel-corrected covariance matrix estimators for models of class "prais".

Usage

## S3 method for class 'prais'
vcovPC(x, pairwise = FALSE, ...)
## S3 method for class 'prais'
vcovPC(x, pairwise = FALSE, ...)

Arguments

`x`	an object of class `"prais"`, usually, the result of a call to `prais_winsten`.
`pairwise`	logical. If `FALSE` (default), only those residuals from periods that are common to all panels are used to computed the covariances. If `TRUE` all observations that can be matched by period between two panels are used.
`...`	not used.

Details

vcovPC is a function for estimating a panel-corrected covariance matrix of parameters for the Prais-Winsten estimator.

Value

An object of class "matrix".

References

Beck, N. L. and Katz, J. N. (1995): What to do (and not to do) with time-series cross-section data. American Political Science Review 89, 634-647.

Package 'prais'

Help Index

Barium

Description

Usage

Format

References

Prais-Winsten Estimator for AR(1) Serial Correlation

Description

Usage

Arguments

Details

Value

References

Examples

Summarising the Prais-Winsten Estimator

Description

Usage

Arguments

Value

Semirobust Covariance Matrix Estimators

Description

Usage

Arguments

Details

Value

See Also

Extract Panel-Corrected Variance Covariance Matrix

Description

Usage

Arguments

Details

Value

References

See Also