OrthoPanels: Orthogonalized Panel Model

Description

This package includes the function opm(), which implements the orthogonal reparameterization approach recommended by Lancaster (2002) to estimate dynamic panel models with fixed effects (and optionally: panel specific intercepts). The OLS estimator for such models is biased with a fixed (small) N (Nickell 1981). Equivalently, a maximum likelihood estimation leads to an incidental parameters problem (Neyman and Scott 1948; Lancaster 2000). The approach by Lancaster (2002) uses an orthogonal reparameterization of the fixed effects to produce a likelihood-based estimator of the remaining parameters that is exact and consistent as N approaches infinity for T greater than or equal to 2.

Details

Orthopanels can accomodate unbalanced panel data, in that some respondents may drop out early (attrition) and some respondents may enter the panel late (refreshment). It is assumed that once respondents enter the panel, they will have observations up until they dropout and then NAs in subsequent waves. The estimation is conducted under the assumption that the data is missing at random

References

Lancaster, T. (2000) The incidental parameter problem since 1948. Journal of Econometrics, 95, 391–413.

Lancaster, T. (2002) Orthogonal parameters and panel data. Review of Economic Studies, 69, 647–666.

Neyman, J. and Scott, E. L. (1948) Consistent estimation from partially consistent observations. Econometrica, 16, 1–32.

Nickell, S. (1981) Biases in dynamic models with fixed effects. Econometrica, 49, 1417–1426.

Responses from the 2010 British Election Study

Description

A survey of 1845 respondents using 3 waves of panel survey data from the 2010 British Election Study. The variables are as follows:

Format

A data frame with 5535 rows and 11 variables

Details

• n case number

• t time wave

• Econ Assessment of change in the national economic situation over the past 12 months (1-5, 1=‘got a lot worse’, 5=‘got a lot better’)

• Clegg Evaluation of Liberal Party leader Nick Clegg (0-10, 0=‘strongly dislike’ and 10=‘strongly like’)

• Brown Evaluation of Labour Party leader Gordon Brown

• Cameron Evaluation of Conservative Party leader David Cameron

• Approve Approval of the government, as expressed by feeling about the ruling Labour Party (0-10, 0=‘strongly dislike’, 10=‘strongly like’)

• NHS Assesment of the current government's handling of the National Health Service (1-5, 1=‘very badly’, 5=‘very well’)

• Terror Assesment of the current government's handling of terrorism (1-5, 1=‘very badly’, 5=‘very well’)

• PID Personal identification with the Labour Party (0/1, 0=‘no’, 1=‘yes’)

• Tax Preference for policy on taxes and health and social spending (0-10, 0=‘cut taxes a lot and spend much less’, 10=‘increase taxes a lot and spend much more’)

Deviance Information Criterion (DIC)

Description

Computes the Deviance Information Criterion (DIC), which is a generalization of the Akaike Information Criterion. Models with smaller DIC are considered to fit better than models with larger DIC.

Usage

DIC(object, ...)

Arguments

Details

DIC is defined as DIC = 2*\bar{D} - D_\theta where: \bar{D} = -2 mean(log-likelihood at parameter samples) D_\theta = -2 * log(likelihood at expected value of parameters)

DIC is calculated as: 2 * (-2 * mean(log-likelihood at each element of parameter samples)) - (-2 * log(likelihood at mean parameter sample value))

Value

a numeric value with the corresponding DIC

Note

Note the speed of computation of the DIC in proportional to the number of sampled values of the parameters in the opm object.

UK Company Data Panel

Description

The dynamics of labour demand of firm id in the United Kingdom in year year as a function of real product wages, gross capital stock and industry output. This is done using the data used by Arellano and Bond (1991).

Format

A data frame with 813 rows and 16 variables

Details

A survey of 1845 respondents using 3 waves of panel survey data from the 2010 British Election Study. The variables are as follows:

• id case number

• year time wave

• n log of employment in firm id at time year

• w natural log of the real product wage

• k natural log of gross capital stock

• ys natural log of industry output

• l_w lag of w

• l_k lag of k

• l2_k two-step lag of k

• l_ys lag of ys

• l2_ys two-step lag of ys

• yr1980..yr1984 time dummies

References

Arrelano M., and Bond S. (1991) Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. Review of Economic Studies, 58(2), 277–297.

Caterpillar Plots of opm Model Parameters

Description

Creates side-by-side plots of equal-tailed credible intervals of opm model parameters. The intervals are displayed as horizontal lines, with 90% interval using a thicker line width and 95% interval a thinner one. The posterior median is indicated with a dot.

Usage

caterplot(
  x,
  parm,
  main = paste("Caterpillar plot of", xname),
  xlab = "Range of parameter samples",
  labels = colnames(ranges)
)

Arguments

Value

A matrix of 2.5%, 5%, 50%, 95%, and 97.5% quantiles for each of the desired parameters, with parameters arranged in columns.

Examples

## Not run: 
caterplot(o, main = NULL, labels = expression(alpha, beta, sigma^2))

## End(Not run)

Caterpillar Plots of long run effects based on opm Model Parameters

Description

Creates side-by-side plots of equal-tailed credible intervals of opm the long run effects parameters. The intervals are displayed as horizontal lines, with 90% interval using a thicker line width and 95% interval a thinner one. The posterior median is indicated with a dot.

Usage

caterplot_longRun(
  x,
  parm = NULL,
  main = "Caterpillar plot of long run effects",
  xlab = "Range of parameter samples",
  probs = c(0.025, 0.05, 0.5, 0.95, 0.975),
  labels = colnames(ranges)
)

Arguments

Value

A matrix of 2.5%, 5%, 50%, 95%, and 97.5% quantiles for each of the desired parameters, with model parameters arranged in columns.

Examples

## Not run: 
caterplot_longRun(o, main = NULL)

## End(Not run)

Credible Intervals for Model Parameters

Description

Computes equal-tailed credible intervals for one or more parameters in a fitted opm model. The method used is the quantile interval of the posterior sample.

Usage

## S3 method for class 'opm'
confint(object, parm, level = 0.95, ...)

Arguments

Value

A matrix with columns giving lower and upper limits of the credible interval for each parameter. These will be labeled as (1 - level/2) and 1 - (1 - level)/2 in % (by default, "2.5%" and "97.5%").

See Also

confint

Histogram of an opm Object

Description

Method for hist applied to opm objects. Each parameter will be plotted in a separate figure.

Usage

## S3 method for class 'opm'
hist(
  x,
  parm,
  ask = dev.interactive(),
  plot = TRUE,
  main = NULL,
  xlab = NULL,
  ...
)

Arguments

Value

A list of objects of class "histogram", one for each requested model parameter. The elements are named after the parameter.

Long run effects based on the opm Model Parameters

Description

Computes long run effects and confidence intervals of opm Model Parameters

Usage

longRunEffects(opm_obj, parm = NULL, probs = c(0.025, 0.5, 0.975))

Arguments

Value

A matrix with quantiles on the rows, with number of rows specified as length of the probs vector for the specified quantiles, with covariates on the columns

Examples

## Not run: 
longRunEffects(opm_obj)
longRunEffects(opm_obj,probs=c(0.975, 0.16, 0.5, 0.84, 0.025))

## End(Not run)

Fitting orthogonal panel models

Description

opm is used to fit orthogonal panel models.

Usage

opm(x, ...)

## Default S3 method:
opm(x, y, n.samp, add.time.indicators = FALSE, ...)

## S3 method for class 'formula'
opm(x, data = environment(x), subset = NULL, index = 1:2, n.samp, ...)

Arguments

Details

The model can be either specified symbolically with the formula response ~ term1 + term2 ... or with the terms and response given as a pair of 3- and 2-dimensional arrays, x and y respectively. The arrays have to be in the format time x variable x case for terms and time x case for the response.

The lagged dependent variable does not need to be included in the formula or data, as it is included automatically.

Value

An object of class opm with the following elements:

samples

parameter samples used to estimate the model, as a list with following elements:

rho

a vector of n.samp samples of \rho.

v

a vector of n.samp samples of \frac{1}{\sigma^2}.

beta

an n.samp x variable matrix of samples of \beta.

call

the matched call

index

the index variables, when using the formula interface

time.indicators

TRUE if dummy time variables are used (see Notes), FALSE otherwise

terms

the terms object used

The function summary (i.e., summary.opm) can be used to obtain or print a summary of the results. The generic accessor functions coefficients, fitted.values, residuals, logLik, and df.residual can be used to extract various useful features of the value returned by opm.

Note

Dummy time variables exist as an additional column for each wave of data, excluding the first and second wave (i.e., at t=0 and t=1 using the terminology from Lancaster (2000)). The new variables are named tind.t, where t = 2, ..., and appear as such as elements of the estimated beta coefficient.

Examples

set.seed(123)
N <- 5
T <- 2
beta <- .5
rho <- .5
v <- 1

f <- runif(N, -2, 2)
K <- length(beta)
beta <- matrix(beta, K, 1)

## $x_i = 0.75 f + N(0, 1)$:
x <- array(.75*f, dim=c(N, K, (T+1))) + rnorm(N*K*(T+1))

## $y_{i,t} = \rho y_{i,t-1} + \beta x_{i,t} + f_i + N(0,1)$:
y <- matrix(0, N, T+1)
for (t in seq_len(T+1)) {
    yy <- if (t>1) y[,t-1] else 0
    y[,t] <- rho * yy + f  + x[,,t] %*% beta + rnorm(N, sd = sqrt(1/v))
}

d <- data.frame(i = rep(seq(N), T+1),
                t = rep(seq(T+1), each = N),
                as.data.frame(matrix(aperm(x, c(1, 3, 2)), N*(T+1), K,
                                     dimnames = list(NULL, paste0('x', seq(K))))),
                y = c(y))
opm(y~x1, d, n.samp = 10)

Returns the posterior density p(\rho|\Theta)

Description

Returns the posterior density p(\rho|\Theta)

Usage

p_rho(x, y, rho, log.p = FALSE)

Arguments

Plot Method for an opm Object

Description

Method for plot applied to opm objects. Each parameter will be plotted as a density plot in a separate figure.

Usage

## S3 method for class 'opm'
plot(x, parm, ask = dev.interactive(), main = NULL, xlab = NULL, ...)

Arguments

Value

A list of objects of class "density", one for each requested model parameter. The elements are named after the parameter.

Posterior Sample Quantiles

Description

Produces quantiles of the posterior samples corresponding to the given probabilities. In other words, it is equivalent to computing "quantile(x, ...)", where "x" is the original Monte Carlo sample of the parameter "parm", as produced by opm.

Usage

## S3 method for class 'opm'
quantile(x, parm, ...)

Arguments

Value

A matrix of quantiles for each of the desired parameters, with parameters arranged in columns. If arguments include "names = FALSE", the quantile labels won't be included (i.e., the rownames of the matrix will be NULL).

See Also

quantile