PcGive dialogs
 Models for crosssection data
 Dialogs for Crosssection Regression
 Models for discrete data
 Dialogs for Binary Discrete Choice Models
 Dialogs for Multinomial Discrete Choice Models
 Dialogs for Count Models
 Models for financial data
 Dialogs for GARCH Models
 Models for timeseries data
 Dialogs for Singleequation Dynamic Modelling
 Dialogs for Multipleequation Dynamic Modelling
 Dialogs for ARFIMA Models
 Models for panel data
 Dialogs for Static Panel Methods
 Dialogs for Dynamic Panel Methods
 Monte Carlo
 Other models
 Dialogs for Nonlinear Modelling
 Dialogs for Descriptive Statistics
Dialogs for Crosssection Regression
 Dialogs for model formulation and estimation:
 Formulate
 Estimate
 Progress
 Options
 Dialogs for model evaluation:
 Graphic Analysis
 Further Output
 Test
 Exclusion Restrictions
 Linear Restrictions
 General Restrictions
 Omitted Variables
 Store in Database
Formulate  Crosssection Regression
Use this dialog for single equation crosssection model formulation: to
formulate a new model, or reformulate an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Specials

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is only:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Removes the current status so that the default applies.
 Y: endogenous
Label the current model selection as endogenous variables.
The first Y variable will be the dependent variable.
Additional endogenous variables will be required for instrumental
variables estimation. Endogenous variables are preceded by Y in the model list.
 Z: regressor
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so a Z variable or unmarked variable
are treated in the same way.
 A: instrument
Label the current model selection as additional instruments.
This button is only relevant if you wish to do an Instrumental Variables estimation.
Additional instruments are marked by A in the model list.
 Select By
Crosssection modelling automatically drops all observations
with missing values. This can be refined by marking a
variable as Select By.
When a model variable is marked as S variable, only observations
for which that variable has nonzero values are included for estimation.
When predicting, the default is to use all valid observations
which were not used in estimation, but it is also possible to
only predict for observations which have a value 2 for the select by
variable.
 Recall a previous model

Use this to recall a previously estimated model.
 OK
Press OK to move to model estimation.
Estimate  Crosssection Regression
The estimation method is automatically selected for
the formulated model.
 estimation sample

Crosssection modelling defaults to using the full sample, while
automatically dropping all observations with missing values.
It is possible here to specify a subsample for estimation.
This can be further refined by adding a
select by variable in the model formulation stage.
 OK

Pressing OK starts the estimation.
Graphic Analysis  Crosssection Regression
The Graphic analysis command gives various options to graph actual and
fitted values, residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Actual and fitted values

Show the fitted and actual values of the dependent variable over time,
over the whole sample period, including the forecast period.
 Crossplot of actual and fitted

As above, but now a crossplot of actual and fitted values.
 Residuals (scaled)

Show the scaled residuals against time, over the whole sample
period, including the forecast period. The residuals are scaled by the
residual standard deviation.
 Residual density and histogram (kernel estimate)

Show the density estimate and histogram of the residuals.
The normal density with the same mean and variance is drawn for
reference.
To zoom a graph, adjust the area inside OxMetrics.
Test  Crosssection Regression
This dialog box gives access to a selection of diagnostic
testing procedures. Mark the tests you want to be executed, then press OK.
Many tests report a χ^{2} and an F form. In the
summary, only the Ftest is reported, which is expected to have better
smallsample properties.
 Normality

Shows the first four moments, together with a
test for normality.
 Heteroscedasticity test (squares)

Tests for the residuals being heteroscedastic owing to omitting squares
of the regressors. Redundant variables (like the square of the Constant)
are automatically eliminated. The test will be skipped if there are not
enough observations.
 Heteroscedasticity test (squares and cross products)

This is the White test for heteroscedasticity, which includes all squares
(as in the previous heteroscedasticity test) and all crossproducts of
variables. Redundant variables (like the square of the Constant) are
automatically eliminated. The test will be skipped if there are not
enough observations (which can happen easily in large models).
 Reset test (using squares)

The Reset test adds squares of the fitted y (only for OLS).
Dialogs for Singleequation Dynamic Modelling
 Dialogs for model formulation and estimation:
 Formulate
 Model Settings
 Estimate
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Recursive graphics
 Dynamic analysis
 Forecast
 Further Output
 Test
 Exclusion Restrictions
 Linear Restrictions
 General Restrictions
 Omitted Variables
 Store in Database
Formulate  Singleequation Dynamic Modelling
Use this dialog for single equation dynamic model formulation: to
formulate a new model, or reformulate an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model with the default
lag length.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Trend
The trend has value 1,2,3,... with value 1 occurring for the first
observation in the database. This may be different from the first
observation in the estimation sample, for example when using lags
(of course, this only affects the value of the constant term).
 Seasonal
Seasonal is only present if the database has a nonannual frequency s.
Selecting this variable will lead to s  1 seasonals being
added when a Constant is present in the model (s otherwise).
For example, for quarterly data, this adds:
Seasonal (1 in quarter 1, zero otherwise),
Seasonal_1 (1 in quarter 2, zero otherwise),
Seasonal_2 (1 in quarter 3, zero otherwise).
 CSeasonal
This behaves as Seasonal, except that the variable has zero
mean within a year. For quarterly data, for example, CSeasonal
has value 0.75 in the first quarter, and 0.25 in the remaining quarters.
 Lags

At the top you can choose how the lag length is set with which variables
are added to the model:
 None: no lags.
 Lag: just using the lag specified below.
 Lag 0 to: from lag 0 to the lag specified below.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Removes the current status so that the default applies.
 Y: endogenous
Label the current model selection as endogenous variables
(this is not possible for lagged variables).
The first Y variable will be the dependent variable.
Additional endogenous variables will be required for instrumental
variables estimation. Endogenous variables are preceded by Y in the model list.
 Z: regressor
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so a Z variable or unmarked variable
are treated in the same way.
 A: instrument/unrestricted
Label the current model selection as additional instruments
(Instrumental Variables estimation).
Additional instruments are marked by A in the model list.
Otherwise, when using Autometrics, the variable is entered as fixed:
it is always forced to enter the model, and not a candidate for removal.
 Recall a previous model

Use this to recall a previously estimated model.
 OK

Press OK to move to the Model Settings
or Estimation.
Model Settings  Singleequation Dynamic Modelling
This dialog is for choosing a model type.
 The Model Type

The Autometrics related options are:
 Automatic model selection

Mark this box to activate Autometrics.
 Target size

Select a target pvalue at which the reduction should be run. Use advanced
settings for a pvalue thst is not listed.
 Outlier detection

Select the outlier method: none, large residuals or dummy saturation (adding
an impulse dummy for each observation).
 Presearch lag reduction

By default, presearch lag reduction is switched on.
 Advanced Autometrics settings

Mark this box for an additional dialog with advanced options.
Autometrics Settings  Singleequation Dynamic Modelling
Autometrics Settings  Multipleequation Dynamic Modelling
Search settings
 Outlier detection

Select the outlier method: none, large residuals or dummy saturation (adding
an impulse dummy for each observation).
 Presearch lag reduction

By default, presearch lag reduction is switched on.
 Presearch variable reduction

This is switched off by default.
 Search effort

Changing the search effort may result in a different terminal model.
 Backtesting

The default is backtesting with respect to GUM 0 (in PcGets this was w.r.t
the current GUM).
 Tiebreaker

When there are multiple terminal candidate models, the tiebreaker decides
which one to choose as the final model.
 Print level

Controls theamount of Autometrics output.
 Target size

Select a target pvalue at which the reduction should be run.
Select User to specify a pvalue directly in the next field.
 User determined pvalue

Active if User is selected in the previous field.
 Diagnostic test pvalue

The default is to run the test at 1%, independently of the reduction pvalue.
 Standard errors

Gives the option to use robust standard errors (HACSE or HCSE) in the reduction.
 GIVE: first do reduced form

By default, the system reduction is used on the unrestricted reduced
form, after which the IV equation is reduced.
Block identification when there are too many parameters
 When k/T fraction exceeds

Determines the ratio of parameters to sample size at which the block reduction
kicks in.
 Block method

Allows experimentation with other block methods, which may take longer than the
default (except for "quick", which does the block search with diagnostic
testing switched off).
 Maximum block size (1: unlimited)

The block size is roughly 0.5T times the k/T fraction, so 0.4T by default.
This is subject to the maximum size specified here.
 Diagnostic test set

Allows customization of the test battery used by Autometrics.
Estimate  Singleequation Dynamic Modelling
Select an estimation method, sample period, and number of forecasts for
the formulated model.
For recursive estimation also select the number of initializations.
 Estimation sample

Enter the sample period you wish to use for the estimation (including
initialization and forecasts), e.g. 1960(1) to 1980(4). The maximum
sample is given one line up.
The default is the sample of the previous estimation (of course
only if possible). PcGive automatically excludes observations with
missing values.
 Less forecasts

Enter the number of observations you wish to withhold for
static forecasting.
 Estimation method depends on the model settings:

2SLS is only available the model has more than one endogenous variable,
and at least as many additional instruments as endogenous regressors.
For rth order Autoregressive Least Squares (RALS)
the estimation method is nonlinear estimation.
An additional checkbox allows for automatic maximization (the default),
or maximization through the maximization control dialog,
which provides more control over the iterative process.
 Recursive estimation:

Select this option to use recursive estimation.
Recursive estimation is available
with OLS and IV estimation.
 Initialization:

Enter the number of observations you wish to use for
initializing the recursive estimation.
 OK

Pressing OK starts the estimation, unless there still is something missing or
wrong in the dialog.
Progress
The Progress dialog is used to review the progress made to date
in the model reduction, when using the
generaltospecific modelling strategy.
To offer a default sequence, PcGive decides that model A could
be nested in model B if the following conditions hold:
 model A must have a lower loglikelihood (i.e.~higher RSS),
 model A must have fewer parameters,
 model A and B must have the same sample period and database.
PcGive does not check if the same variables are involved, because
transformations could hide this. As a consequence PcGive does not
always get the correct nesting sequence, and it is the user's
responsability to ensure nesting.
E.g. DCONS = α + βDINC is nested in:
CONS = a + b_{1} CONS_{1} + b_{2} INC +
b_{3} INC_{1}
through the restrictions
b_{1} = 1 and b_{3} =
b_{2}.
There are two options on the dialog to select a nesting sequence:
 Mark Specific to General

Marks more general models, finding a nesting sequence with strictly
increasing loglikelihood.
 Mark General to Specific

Marks all specific models that have a lower loglikelihood.
The default selection is found by first setting the most recent
model as specific, and then setting the general model that was found
as the general model.
Additional dialog items are:
 <

To move a model up in the modelling sequence.
 >

To move a model down in the modelling sequence.
 Del

Tp permanently delete a model from the modelling sequence.
 OK

Prints the progress report, consisting of:
1. number of observations, paramaters, and loglikelihood.
2. Information criteria: reported are the Schwarz Criterion (SC),
the HannanQuinn (HQ) Criterion, and the Akaike criterion (AIC).
3. F or Chisquared tests of each reduction.
Options (all)
Controls maximization settings, and what is automatically printed
after estimation (in addition to the normal estimation report).
Model options referes to settings which are changed infrequently,
and are persistent between runs of PcGive.
 Maximization Settings

Maximum number of iterations:
Note that it is possible
that the maximum number of iterations is reached before
convergence. The maximum number of
iterations also equals the maximum number of switches in cointegration.
Write results every:
By default no iteration progress
is displayed in the results window. It is possible to write intermediate
information to the Results window for a more permanent record.
A zero (the default) will write nothing, a 1 every iteration, a
2 every other iteration, etc.
Write in compact form:
Writes one line per printed
iteration (see Write results every).
Convergence tolerance:
Change the convergence tolerance
levels (the smaller, the longer the estimation will take to converge).
See under numerical optimization for an explanation
of convergence decisions.
Default:
Resets the default maximization settings.
 Additional output to be printed after estimation

A range of items can be selected for automatic printing
after each estimation. Note that these can always be obtained
from the Test menu as well.
Graphic Analysis (singleequation/nonlinear/multipleequation modelling)
The Graphic analysis command gives various options to graph actual and
fitted values, forecasts and residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Actual and fitted values

Show the fitted and actual values of the dependent variable over time,
over the whole sample period, including the forecast period.
 Crossplot of actual and fitted

As above, but now a crossplot of actual and fitted values.
 Residuals (scaled)

Show the scaled residuals against time, over the whole sample
period, including the forecast period. The residuals are scaled by the
residual standard deviation.
 Forecasts and outcomes

Show the static forecasts and actual values of the dependent variable over time,
over the forecast period only. This option is only available if observations
were withheld for forecasting when the estimation sample was selected.
 Residual density and histogram

Show the density estimate and histogram of the residuals.
The normal density with the same mean and variance is drawn for
reference. To omit any of these items see under Further graphs.
 Residual correlogram (ACF)

Show the ACF of the residuals, using the
lag length supplied in the text entry field.
 Length of correlogram and spectrum

The lag length must be < T.
 Partial autocorrelation function (PACF)

Show the PACF of the residuals, using the
lag length supplied in the text entry field.
Further graphs
 Forecasts Chow tests

Shows the forecast Chow tests.
 Residuals (unscaled)

Show the residuals against time, over the whole sample
period, including the forecast period.
 Residual spectrum

Show the Spectral density of the residuals,
using the lag length as the truncation point.
 Residual QQ plot against N(0,1)

Plots the ordered residuals against in a QQ plot
against the normal distribution.
 Crossplots matrix of residuals

Show the crossplots of the residuals, by default over the whole sample
period, including the forecast period. This option is only available
for multivariate models.
 Residual density
 Residual histogram

Show the density estimate of the residuals
with the normal density for reference.
If residual histogram is also checked, the histogram will be
drawn on top of the density.
 Residual distribution (normal quantiles)

Show the distribution of the residuals in a QQ plot
against the normal distribution. This is based on the smoothed
density estimate.
Options
 Order by equation

Choose an ordering for multipleequation models.
Cointegration graphics (multipleequation dynamic modelling)
 Cointegration relations

β_{0}'
(y_{t};z_{r})
or
β_{0}'
r_{1t}.
 Actual and fitted

The graphs of the cointegrating relations are split into two components: the
actuals y_{t} and the fitted values
y_{t}  β_{0}'
(y_{t};z_{r}).
All lines are graphed in deviation from mean.
 Components of relations

Graphs all the components of in deviations from their means.
 Use (Y:Z) or (Y_1:Z) with lagged DY and U removed

Chooses between
y_{t};z_{r}
and
r_{1t}.
To zoom a graph, adjust the area inside OxMetrics.
Recursive Graphics: Singleequation Dynamic Modelling
The Recursive graphics command graphs the recursive output
as generated by a recursive estimation.
 Coefficients
 Mark all the variables in the model you wish to include in the betacoefficient
and/or tvalue graphs in this list box.
 Beta coefficient ±2*S.E.
 Graph the beta coefficient ±2*SE of all variables selected in the variables list box.
 Beta tvalue

 Graph the tvalues of all variables selected in the variables list box.
 Residual Sums of squares
 Graph the Residual Sums of Squares.
 1step Residuals ±2*S.E.
 Graph the 1step residuals with with error bands of two residual
standard errors around zero.
 Standardized innovations
 Graph the Standardized innovations.
 1step Chow tests
 Graph the 1step Chow tests scaled by their critical values.
 Breakpoint Chow tests
 Graph the N decreasing Chow tests scaled by their critical values.
 Forecast Chow tests
 Graph the N increasing Chow tests scaled by their critical values.
 Chow test pvalue
 The critical value by which the all the Chow tests need to be scaled.
Default is 1%, enter 0 for unscaled chow tests.
 Write results instead of graphing
 Write the information to the Results window.
To zoom a graph, adjust the area inside OxMetrics.
Dynamic Analysis (singleequation/nonlinear modelling)
The formulation and econometrics of dynamic analysis are described
in Volume I.
 Static long run solution
 Determines whether the solved form is computed.
 Lag structure analysis
 This option gives a table of lag coefficients for every variable,
Ftests on the significance of each lag and each variable, as well as
the PcGive unit root test.
 Roots of lag polynomials
 Prints the roots of the lag polynomials
 Test for common factor
 The common factor test (COMFAC test) evaluates
errorautocorrelation claims by checking if the model's lag polynomials have
factors in common.
Lag weights
 Graph normalized weights

Plot the normalized lag weights.
 Graph cumulative normalized weights

Plot cumulative normalized lag weights, either instead of the normalized lag
weights, or in addition to them.
 Write lag weights

Write the information to the Results window.
Forecast (singleequation/nonlinear/multipleequation modelling)
Shows the dynamic forecasts or static (onestep)
forecasts optionally with standard error bars, bands or fans
(± 2 forecast standard errors).
Dynamic forecasting is not possible for systems with identities (use the model
in that case, so that the identities are known to PcGive).
If there are unmodelled variables in the model, forecasting is only
possible while data is available.
 Equation

Mark all the equations you wish to do the graphing for in this
list box. In singleequation modelling there is only one equation,
so only one variable listed in the box.
 Number of forecasts

By default, this displays the maximum number of dynamic forecasts.
If there are unmodelled variables in the model, forecasting is only
possible while data is available.
 The forecast types

 Dynamic forecasts
Select this to graph the dynamic forecasts (the sequence of 1,2,3,... Hstep forecasts).
 hstep forecasts
Enter the required number for h in the edit field.
Up to h forecasts, the graphs will be identical to the dynamic forecasts.
 Forecast standard errors

 Do not compute;
 Error variance only;
 With parameter uncertainty
(i.e., taking both parameter and error variance uncertainty into account).
Options
 Type of error bars:

 Use error bars
 Use error bands
 Use error fans
 Critical value to use for errors bars

The default is ±2SE corresponding to 95% bands. Use 1.6 for 90% bands.
 Number of preforecast observations to graph

By default 1 + the data frequency observations are included from
the preforecasting sample.
 Write results instead of graphing
 Write the information to the Results window.
Transformations
 Derived

Allows the specification for additional (derived) equations to forecast.
The derived equations are specified in algebra code.
For example, when a variable (CONS say) is in logs, you could add log(CONS).
When more than one variable is derived, they must involve assignment, and be
terminated by a semicolon, for example:
x = exp(CONS); y = x + 2;
Forecast error standard errors will be computed numerically.
Linear derived expressions can also be created using
identities.
Further Output
 Information criteria

if checked: report information criteria
 Heteroscedasticconsistent standard errors (HCSE)

When selected the HCSEs will be computed: HCSE, HACSE
(heteroscedasticity and autocorrelation consistent standard errors),
JHCSE (jackknife HCSE, but only for single equation OLS).
 R^2 relative to difference and seasonals

if checked: report R^2 relative to difference and seasonals
 Correlation matrix of regressors

Print out the regressor correlation matrix, means and standard deviations.
 Covariance matrix of estimated parameters

Print out the covariance matrix of the estimated parameters for each model,
and the covariance matrix of constrained parameters following general
restrictions.
 Reduced form estimates

These can only be printed after instrumental variables or simultaneous
equations models.
 Static (1step) forecasts

These can only be printed if observations were withheld at the formulation
stage. Forecasts can also be made from the test menu.
 Print large residuals

Check this box t list all observations that have an (absolute) residual
exceeding if the specified value times the equation standard error (in other
words, standardized residual in excess of the specified value).
Write model results
 Equation format

write the results in equation format.
 LaTeX format

This resulting output can be pasted to a LaTeX document.
 Nonlinear model format

This resulting output can be useed as a starting point for nonlinear
modelling.
 Significant digits for parameters

 Significant digits for std.errors

These control the format of the output.
 Batch code to map CVAR to I(0) model

This option is available after estimating a cointegrated VAR.
It prints the batch code to map it to a model with the
cointegrating vectors as identities. This batch code can then
be run from OxMetrics.
Test (singleequation/nonlinear/multipleequation modelling)
This dialog box gives access to a selection of diagnostic
testing procedures. Mark the tests you want to be executed, then press OK.
Many tests report a Chi^2 and an F form. In the
summary, only the Ftest is reported, which is expected to have better
smallsample properties.
In multipleequation models, there is a choice to compute
vector tests, singleequation tests, or both.
 Residual correlogram and Portmanteau statistic with length

Prints the residual correlogram (both ACF and PACF),
as well as the Portmanteau statistic.
You can change the lag length.
 Error autocorrelation from lag .. to ..

Offers the choice of testing for autocorrelation, with the option to
change the default starting and ending lag.
Information on the auxiliary regression is printed in addition
to the Chi^2 and Fform of the test statistic.
 Normality

Shows the first four moments, together with a
test for normality.
 Heteroscedasticity (squares)

Tests for the residuals being heteroscedastic owing to omitting squares
of the regressors. Redundant variables (like the square of the Constant)
are automatically eliminated. The test will be skipped if there are not
enough observations.
 Heteroscedasticity (squares and cross products)

This is the White test for heteroscedasticity, which includes all squares
(as in the previous heteroscedasticity test) and all crossproducts of
variables. Redundant variables (like the square of the Constant) are
automatically eliminated. The test will be skipped if there are not
enough observations (which can happen easily in large models).
 ARCH with order (no vector form)

Tests for Autoregressive Conditional Heteroscedasticity, for a user
defined order. Information on the auxiliary regression is printed in addition
to the Fform of the test statistic.
 Reset up to power (only for singleequation OLS)

The Reset test adds squares of the fitted y.
 Instability tests (only for singleequation OLS)

Tests for variance, joint, and coefficient instability.
 Encompassing tests (only for singleequation OLS/IVE)

Computes encompassing tests
for single equation models estimated by OLS or IVE. Model 2 is the current
model, and model 1 the previously estimated model (for the current database).
These models must have the same dependent variable, and not be nested.
Test Exclusion Restrictions
Allows you to select explanatory variables and test whether
they are jointly significant.
A more general form is the test for linear restrictions.
 Selection

Mark all the variables you wish to include in the test in this
list box.
PcGive tests whether the selected variables can be deleted from the model.
Test Linear Restrictions
Tests for linear restrictions
are specified in the form of a matrix R, and a vector r.
These are entered as one matrix [R : r]' in the dialog.
(This is a more general than testing for
exclusion restrictions, but not
as general as the general restrictions test.)
For example, if the model is CONS on Constant, CONS_1, INC, INC_1,
and we wish to test that the coefficients on INC and INC_1 add up to
one, and that on CONS_1 equals zero. Then the R:r matrix can be written as
0 0
1 0
0 1
0 1
0 1
The first four rows are the columns of R, specifying two
restrictions. The last row is r, which specifies what the
restrictions should add up to.
The dimensions of the matrix must be specified in the rows and
columns fields.
 Matrix

This window is a matrix editor in which you can specify the values,
very similar to an OxMetrics database.
 Rows

The number of rows in the matrix.
 Columns

The number of columns in the matrix.
 Load

Enables you to load an existing matrix file into
the editor.
Any existing matrix in the editor will be lost.
 Save

Enables you to save the contents of the editor in an matrix file,
so that it can be used again.
General Restrictions
This is the most general form for testing restrictions:
restrictions are given in the form of expressions involving the coefficients.
The mathematics is explained in tests for general restrictions.
Restrictions have to be entered when testing for parameter restrictions and
for imposing parameter constraints for estimation. The syntax is similar to
that of algebra, but simpler.
Restrictions code may consist of the following components:
(1) Comment
(2) Constants
(3) Arithmetic operators
These are all identical to algebra. In addition there are:
(4) Parameter references
Parameters are referenced by an ampersand followed by the parameter number.
Counting starts at 0, so, for example, &2 is the third
parameter of the model. What this parameter is depends on your model.
Ensure that when you enter restrictions through the
batch language, you use the right order for
the coefficients. In case of IV estimation PcGive will reorder your model
so that the endogenous variables come first.
Restrictions for testing are entered in the format: f(c)=0.
The following restrictions test the significance of the
longrun parameters in an unconstrained model:
(&1 + &2) / (1  &0) = 0;
&3 / (1  &0) = 0;
Omitted Variables
This implements the omitted variables test,
which tests if some variables should be added to the model.
For example, if the estimated model is
y = Xβ + u,
then the omitted variables test, tests for γ= 0 in
y = Xβ + Zγ +v,
The Lagrange Multiplier Ftest is reported, and the null hypothesis is rejected when its value is significant.
This test is not available for autoregressive least squares or nonlinear models.
Any variable can be selected, as long as it matches the present sample.
 Database

Select variables to test as omitted from the model in this
list box. Variables
already in the model and variables which would reduce the sample size
are not allowed and are automatically deleted.
 Lag length

Specify the maximum lag length to use (not for crosssection regression).
Store in database
Allows you to save any of the listed items in
the OxMetrics database. Note that forecasts must
be generated using Test/Forecast before they can be stored.
OxMetrics will prompt for a variable name.
Dialogs for Nonlinear Modelling
 Dialogs for model formulation and estimation:
 Formulate
 Model Settings
 Estimate
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Recursive graphics
 Further Output
 Test
 Exclusion Restrictions
 Linear Restrictions
 General Restrictions
 Store in Database
Formulate  Nonlinear Modelling
[A] Nonlinear least squares
A nonlinear model is formulated in Algebra code.
The following extensions are used:
 parameter references
Parameters are referenced by an ampersand followed by the parameter number.
 the numbering does not have to be consecutive, so your model can use,
 for example &1, &3 and &4.
The following two variables must be defined for NLS to work:
 actual defines the actual values of the dependent variable (the y variable, e.g. CONS).
 fitted defines the fitted values (the yhat variable).
This is the formula for the explained component.
Consider, for example, the following specification of the fitted part:
fitted = &0*lag(CONS,1) + &1*INC + &3*INFLAT + &4;
Starting values are entered in the format: ¶meter=value;.
For example:
&0 = 0; &1 = 1; &3 = 1; &4 = 1;
Together, these formulate the whole nonlinear model, as in the following example:
actual = CONS;
fitted = &0 + &1*lag(CONS,1) + &2*INC  &1*&2*lag(INC,1);
&0 = 0; &1 = 1; &2 = 1;
[B] Maximum likelihood
Maximum likelihood models are defined using the three variables:
 actual
 fitted
 loglik
Both actual and fitted only define the variables being used in the graphic
analysis and the residual based tests. The loglik variable defines the
function to be maximized. Parameters and starting values are as for NLS.
More information is available under nonlinear models.
After estimating a linear model, and before starting nonlinear
estimation, you can use Test/Further Output
to write the linear model in the form of nonlinear model code.
This could be a good starting point for formulating a nonlinear model.
The dialog fields are:
 Model

Edit field for formulating the nonlinear model as outlined above.
 OK

Moves to the estimation dialog.
 Load

Loads a file with a nonlinear model (as an algebra file: .ALG) from disk.
 Save As

Saves the contents of the edit window to disk as an algebra file (.ALG).
 Recall

Recalls the most recently estimated nonlinear model.
 Database dropdown box

Allows changing database, if multiple databases have been loaded into OxMetrics.
The selected database is used for the nonlinear estimation.
 Database

At the bottom of the dialog is a list of all the variables in the database.
Double clicking on a variable will paste it to the editor.
Estimate  Nonlinear Modelling
Determines the estimation sample for nonlinear models.
 Estimation sample

Enter the sample period you wish to use for the estimation (including
initialization and forecasts), e.g. 1960(1) to 1980(4). The maximum
sample is given one line up.
The default is the sample of the previous estimation (of course
only if possible). PcGive automatically excludes observations with
missing values.
 Less forecasts

Enter the number of observations you wish to withhold for
static forecasting.
 Estimation method

and nonlinear models the choices is
the estimation method is nonlinear estimation.
An additional checkbox allows for automatic maximization (the default),
or maximization through the maximization control dialog,
which provides more control over the iterative process.
 Recursive estimation:

Select this option to use recursive estimation.
Recursive estimation is available
with OLS and IV estimation.
 Initialization:

Enter the number of observations you wish to use for
initializing the recursive estimation.
 OK

Pressing OK starts the estimation, unless there still is something missing or
wrong in the dialog.
This dialog controls the estimation of nonlinear models by
numerical optimization.
 Optimization status

Initially, the first line says: No convergence (yet)
Subsequently, the first line shows the current convergence status:
 No convergence
 Aborted: no convergence
 Function evaluation failed: no convergence
 Failed to improve in line search: weak convergence
 Failed to improve in line search: no convergence
 Strong convergence
 Maximum number of iterations reached: no convergence
Only after convergence will it be possible to press OK, which results
in writing the estimation results. Note that grid plotting, and
resetting parameter values, will result in loss of the previous convergence status.
 Parameters

Make a selection and doubleclick:
you can then edit the parameter value.
 Optimization method

Lists the choice of optimization method (which could only be one).
 Estimate

Start or continue the Numerical Optimization from
the current parameter values.
 Reset

Reset the parameters to the values they had when this dialog started.
 Grid

Sparks off the grid dialog enabling grid searches
over a single parameter.
 OK

If the optimization process has converged, you will be able to press this
button (then PcGive will write the estimation results), otherwise it is
deactivated.
 Cancel

Cancels the iterative model estimation, no model results will be available.
 Options

Allows setting the estimation options,
in particular the maximum number of iterations, the amount of intermediate
output, and the convergence tolerance.
See under numerical optimization for an explanation
of convergence decisions.
There are two types of grids:
 Max: maximize over remaining parameters;
 Fixed: keep all remaining parameters fixed.
When the grid is over one parameter, the
max grid does a complete loglikelihood maximization over the remaining
parameters, with the first fixed at the grid values.
The fixed grid only involves likelihood evaluations, keeping the other
parameters fixed at its current value, while computing the first over the
grid coordinates.
Therefore, the max grid method can be much slower, especially for a
bivariate grid. For example, a 20 by 20 grid would require 400 likelihood
maximizations (i.e.,~400 FIML estimates).
As long as you press Next Grid, this dialog keeps on asking for
the next graph. When you press OK, the grids are drawn.
So you can have many grids onscreen.
These can include mixes of different parameters or the same parameter
on different scales and/or locations.
 3D grid

Check this to do a threedimensional grid. A second column of
grid parameters will appear to select the other parameter.
 Parameter

Select the parameter over which you wish to do the grid search.
 Grid center

The value on which the grid should be centred, the default is the current
parameter value.
 Number of steps

The number of steps over which the grid should be computed, with a default of 20.
 Step length

The step length default is 0.1 which, together with the other defaults, gives:
20 * 0.1 equal to 2, which spans the range [1,1]. For example,
when the grid id centred at 0, the grid points are 1, 0.9,.., 0.9, 1.
 Write grid values

This will write the function values to the results window.
 Maximize over remaining parameters

Check this box to do the full maximization.
Recursive graphics: Nonlinear Modelling
The Recursive graphics command graphs the output
as generated by a recursive estimation.
 Residual Sums of squares
 Graph the Residual Sums of Squares.
 1step Residuals ±2*S.E.
 Graph the 1step residuals with with error bands of two residual
standard errors around zero.
 Loglikelihood/T (full sample)
 Graph the loglikelihood.
 1step Chow tests
 Graph the 1step Chow tests scaled by their critical values.
 Breakpoint Chow tests
 Graph the N decreasing Chow tests scaled by their critical values.
 Forecast Chow tests
 Graph the N increasing Chow tests scaled by their critical values.
 Chow test pvalue
 The critical value by which the all the Chow tests need to be scaled.
Default is 1%, enter 0 for unscaled chow tests.
 Write results instead of graphing
 Write the information to the Results window.
To zoom a graph, adjust the area inside OxMetrics.
Dialogs for Multipleequation Dynamic Modelling
 Dialogs for model formulation and estimation:
 Formulate
 Model Settings
 Equations (for simultaneous equations)
 Cointegrated VAR Settings (for cointegrated VAR)
 Restrictions for Cointegration (for cointegrated VAR with general restrictions)
 Restrictions for CFIML (for CFIML)
 Estimate
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Recursive graphics
 Dynamic analysis
 Forecast
 Simulation and Impulse Responses
 Further Output
 Test
 Exclusion Restrictions
 Linear Restrictions
 General Restrictions
 Omitted Variables
 Store in Database
Use this dialog for Dynamic System Formulation: to
formulate a vector autoregression (perhaps for cointegration analysis) or
unrestricted reduced form of a simultaneous equations model, or
reformulate an existing system.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model with the default
lag length.
Variables that are not lagged (and not special variables)
will by default become the endogenous (Y) variables.
To select a different dependent variable, see below.
 Specials

 Constant
A constant will be added automatically in a new model but can be deleted.
 Trend
The trend has value 1,2,3,... with value 1 occurring for the first
observation in the database. This may be different from the first
observation in the estimation sample, for example when using lags
(of course, this only affects the value of the constant term).
 Seasonal
Seasonal is only present if the database has a nonannual frequency s.
Selecting this variable will lead to s  1 seasonals being
added when a Constant is present in the model (s otherwise).
For example, for quarterly data, this adds:
Seasonal (1 in quarter 1, zero otherwise),
Seasonal_1 (1 in quarter 2, zero otherwise),
Seasonal_2 (1 in quarter 3, zero otherwise).
 CSeasonal
This behaves as Seasonal, except that the variable has zero
mean within a year. For quarterly data, for example, CSeasonal
has value 0.75 in the first quarter, and 0.25 in the remaining quarters.
 Lags

At the top you can choose how the lag length is set with which variables
are added to the model:
 None: no lags.
 Lag: just using the lag specified below.
 Lag 0 to: from lag 0 to the lag specified below.
 Selection

This list box shows the current model.
By default, the unlagged variables are added as endogenous variables.
If you have marked variables in the model, you can delete them, or assign a
different status to them. Variables marked with an Y are the endogenous variables.
Those with an I are identity endogenous, those with a U are unrestricted,
(i.e. partialled out prior to estimation), unmarked variables or Z variables
are 'exogenous' (unmodelled).
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Removes the current status so that the default applies.
 Y: endogenous
Label the current model selection as endogenous variables
(this is not possible for lagged variables).
Endogenous variables are preceded by Y in the model list.
 Z: regressor
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so a Z variable or unmarked variable
are treated in the same way.
 I: Identity
Label the current system selection as identity endogenous variables.
Identities are preceded by I in the model list.
 U: Unrestricted
Label the current system selection as unrestricted.
Such variables are preceded by U in the system list.
 Recall a previous model

Use this to recall a previously estimated model.
 OK

Press OK to move to the Model Settings
or Estimation.
Model Settings  Multipleequation Dynamic Modelling
This dialog is for choosing a model type for Dynamic System analysis.
 Model type

Cointegrated VAR settings: Multipleequation Dynamic Modelling
This dialog specifies the restrictions for the cointegrated VAR.
The rank of the longrun matrix can be set to the desired value,
and further restrictions on alpha or beta can be imposed.
 Cointegrating rank

Specify the rank of the longrun matrix.
 Additional longrun restrictions

If required, choose a method for imposing additional restrictions.
 Recursive estimation

Reestimation of the short run during recursive estimation mimicks
the cointegration procedure as it would be applied to a shorter
sample. However, partialling out the short run estimated at the full
sample leads to faster recursive estimation.
Restrictions for Cointegration  Multipleequation Dynamic Modelling
General restrictions on α and β'
may be expressed directly as a function of the unrestricted elements
of α, β'.
It allows general (nonlinear) within and cross equation restrictions
on the cointegration vectors β,
as well as on the feedback coefficients α,
and including imposing links between these. An important aim is to
uniquely identify the parameters of
the longrun relationships.
Using rank two and three variables, the elements are referenced as,
for alpha:
&0 &1
&2 &3
&4 &5
and for beta:
&6 &7 &8
&9 &10 &11
Three examples of general restrictions are:
 ex. 1: &0 = 0; &1 = 0;
 ex. 2: &7 = &6; &10 = &9;
 ex. 3: &6 = 1; &7 = 1; &8 = 1;
Identification of the cointegrating space is checked prior
to estimation; afterwards, the degrees of freedom for the test
statistic are properly computed if any restrictions are imposed.
Note that:
 normalization restrictions on each beta vector have to be
imposed explicitly.
 A specification can impose restrictions, yet not identify
all cointegrating vectors.
The standard errors of α are
printed; if the specification is identifying, those
of β are also printed.
A chisquared test of the overidentifying restrictions is reported.
It is important to realise that not all impositions of fixed parameter
values, or of relations between parameters, entail testable
restrictions. The simplest example is when there is only one
cointegrating vector: normalizing the first element does not
impose a restriction, although it does fix the scale of the vector.
More generally, deriving the degrees of freedom involved in the
chisquared test is not straightforward, especially when
α restrictions are involved, see
Boswijk, H. P., and Doornik, J. A. (2004).
"Identifying, estimating and testing restricted cointegrated
systems: An overview" Statistica Neerlandica, 58, 440465.
The following situations may occur:
 some cointegrating vectors are identified, but others are not;
 although restrictions have been imposed, these are just rotations, not affecting the likelihood;
 restrictions have been imposed, but no identification achieved.
Assume that the identifying restrictions are imposed
on β. In the unrestricted
case of rank p, there are np parameters in
α and nppp in
β. Restrictions on
β are only binding if they cannot
be `absorbed' by the αs, and vice
versa. This is easily seen for rank n: restricting
β'= I_n results in
α = P_o, whereas imposing
α = I_n gives
β' = P_o.
Nevertheless, setting α = 0
imposes n^{2} restrictions (which, of course, violate cointegration).
Fixing a row of β' constrains only
np parameters, as the first p may be absorbed.
Finally, some forms of constraint on α
and β can induce a failure of
identification of the other under the null, in which case the
tests need not have chisquareddistributions (see, for example,
Toda, H.Y. and Phillips, P.C.B. (1993),
"Vector Autoregressions and Causality", Econometrica, 61, 13671393).
The dialog fields are:
 Restrictions

Edit field for formulating the restrictions as outlined above.
 OK

Moves to the estimation dialog.
 Load

Loads a file with a nonlinear model (as an algebra file: .ALG) from disk.
 Save As

Saves the contents of the edit window to disk as an algebra file (.ALG).
 Recall

Recalls the most recently estimated nonlinear model.
 Parameters

At the bottom of the dialog is a list of all the parameters in the model.
Restrictions for CFIML  Multipleequation Dynamic Modelling
Parameter constraints for CFIML are written in the format: θ^{*}=g(θ);. First consider an example which restricts parameter 0 as a
function of three other parameters, creating a model which is nonlinear in
the parameters:
&0 = (&1  &2) * &3;
&4 = 0;
The dialog fields are:
 Restrictions

Edit field for formulating the restrictions as outlined above.
 OK

Moves to the estimation dialog.
 Load

Loads a file with a nonlinear model (as an algebra file: .ALG) from disk.
 Save As

Saves the contents of the edit window to disk as an algebra file (.ALG).
 Recall

Recalls the most recently estimated nonlinear model.
 Parameters

At the bottom of the dialog is a list of all the parameters in the model.
Use this dialog to formulate
the simultaneous equations for a dynamic system.
 Select from

Shows the current unrestricted reduced form (URF) from which the variables
for each equation can be selected.
Mark all the variables you wish to add to the current equation,
using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the variables are added to the equation.
 Equations

At the top of the lefthand side is a dropdown box allowing you
to select an equation. You can also change to the next (or previous)
equation using the spin buttons.
The list box shows the specification of the current equation.
 <<

Adds the currently selected URF variable to the equation.
 >>

Deletes the currently selected variables from the equation.
 Clear>>

Deletes all variables from the current equation.
 <<Default All

Resets all equations to their default, the unrestricted
reduced form.
 OK

Press OK to move to the Estimation.
The Estimate command provides dynamic model estimation.
Select an estimation method, sample period, and number of forecasts for
the formulated model.
For recursive methods also select the number of initializations.
 Estimation sample

Enter the sample period you wish to use for the estimation (including
initialization and forecasts), e.g. 1960(1) to 1980(4). The maximum
sample is given one line up.
The default is the sample of the previous estimation (of course
only if possible). PcGive automatically excludes observations with
missing values.
 Less forecasts

Enter the number of observations you wish to withhold for
static forecasting.
 Estimation method

The estimation method depends on thge model type. For
an unrestricted system it is only OLS, for a cointegrated VAR
it is reduced rank regression, while for simultaneous equations models
it is one of:
Only the first option is available for constrained
simultaneous equations estimation.
An additional checkbox allows for automatic maximization (the default) when
numerical optimization is required.
Switch automatic maximization off to access
the maximization control dialog,
which provides more control over the iterative process.
 Recursive estimation, initialization:

Select this option and enter the number of observations you wish to use for
initializing the recursive estimation.
 OK

Pressing OK starts the estimation, unless there still is something missing or
wrong in the dialog.
The Recursive graphics command graphs the output
as generated by a recursive estimation.
 Equations
 Mark all the equations in the model you wish to include in the output.
 Residual Sums of squares
 Graph the Residual Sums of Squares.
 1step Residuals ±2*S.E.
 Graph the 1step residuals with with error bands of two residual
standard errors around zero.
 Loglikelihood (nonlinear modelling)
 Graph the loglikelihood.
 Loglikelihood/T (full sample) (multipleequation modelling)
 Graph the loglikelihood.
 1step Chow tests
 Graph the 1step Chow tests scaled by their critical values.
 Breakpoint Chow tests
 Graph the N decreasing Chow tests scaled by their critical values.
 Forecast Chow tests
 Graph the N increasing Chow tests scaled by their critical values.
 Chow test pvalue
 The critical value by which the all the Chow tests need to be scaled.
Default is 1%, enter 0 for unscaled chow tests.
 Write results instead of graphing
 Write the information to the Results window.
For cointegrated VARs the entries are:
 Eigenvalues
 Recursively estimated eigenvalues from cointegration tests
 Beta coefficients
 The coefficients in the cointegrating vectors.
 Loglikelihood/T (full sample) (multipleequation modelling)
 Graph the loglikelihood.
 Test for restrictions
 The recursive tests for restrictions on the cointegration space.
 Test pvalue (%) =
 The critical value for the tests.
 Write results instead of graphing
 Write the information to the Results window.
To zoom a graph, adjust the area inside OxMetrics.
The formulation and econometrics of dynamic analysis are described
in Volume II.
 Static long run

Determines whether the solved form is computed.
 Roots of companion matrix

Prints the roots of the companion matrix.
 Plot roots of companion matrix

Plots the roots of the companion matrix.
 I(1) cointegration analysis

Performs the I(1) cointegration tests.
 I(2) cointegration analysis

Performs the I(2) cointegration tests.
Simulation and Impulse Responses  Multipleequation Dynamic Modelling
Use this dialog to perform dynamic simulation and
impulse response analysis.
Dynamic simulation is performed in the same way as dynamic forecasting,
but starts at a point within the estimation sample, rather than
immediately afterwards.
Note that dynamic simulation is not a valid technique for model
evaluation, as discussed in Y. Chong and D.F. Hendry (1986),
"Econometric Evaluation of Linear MacroEconomic Models",
Review of Economic Studies, 53, 671690.
Impulse response analysis ignores nonmodelled variables and sets
the history to zero, apart from the initial values.
These can be taken as unity for each endogenous variable in turn,
the equation standard error, orthogonal (based on the Choleski
decomposition of the residual covariance matrix), or set by the user.
By default this leads to n*n graphs.
Using unit or standard error initial values will only have
the initial value of the ith endogenous variable nonzero in
the ith set of graphs.
Orthogonal initial values will have initial values up to the ith
endogenous variable nonzero in the ith set of graphs.
Dialogs for Descriptive Statistics
Various types of data descriptions are offered:
Means, standard deviations, correlations
Normality tests and descriptive statistics
Unit root tests
The first step is to select variables for descriptive statistics:
 Database

Mark all the variables you wish to include in the descriptive statistics,
in this list box, using the spacebar or the mouse.
 Lag length

Specify the default lag length to use.
 Change Database

Allows changing database, if multiple databases have been loaded into OxMetrics.
 Means, standard deviations and correlations

Writes the means, standard deviations and correlations of all selected variables.
 Normality tests and descriptive statistics

Writes the normality test, together with some summary
statistics of all selected variables.
 Unit root tests

Writes the unit root tests.
Compute unit root tests
Tick this option to do unit root tests.
Report summary table only
This will produce a table of ADF tests, dropping one lag at a time.
Also reported are the tvalue and significance of the highest lag, and the pvalue of the Ftest on the lags dropped up to that point.
Lag length for differences
Enter the lag length you wish to use in the augmented DickeyFuller test
(0 gives the DickeyFuller test only).
Constant
Tick this if you wish to include a constant term in the test.
Trend (and constant)
Tick this if you wish to include a trend and constant term in the test.
Add seasonals and constant
Tick this if you wish to include seasonals in the test (a constant term is also added).
 Select sample

Allows selecting a subsample. The default is the full sample.
Dialogs for ARFIMA Models
 Dialogs for model formulation and estimation:
 Estimate
 Formulate
 Model Settings
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Forecast
 Test
 Exclusion Restrictions
 Linear Restrictions
 Store in database
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, in this list box, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model with the default
lag length.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Trend
The trend has value 1,2,3,... with value 1 occurring for the first
observation in the database. This may be different from the first
observation in the estimation sample, for example when using lags
(of course, this only affects the value of the constant term).
 Seasonal
Seasonal is only present if the database has a nonannual frequency s.
Selecting this variable will lead to s  1 seasonals being
added when a Constant is present in the model (s otherwise).
For example, for quarterly data, this adds:
Seasonal (1 in quarter 1, zero otherwise),
Seasonal_1 (1 in quarter 2, zero otherwise),
Seasonal_2 (1 in quarter 3, zero otherwise).
 CSeasonal
This behaves as Seasonal, except that the variable has zero
mean within a year. For quarterly data, for example, CSeasonal
has value 0.75 in the first quarter, and 0.25 in the remaining quarters.
 Lags

At the top you can choose how the lag length is set with which variables
are added to the model:
 None: no lags.
 Lag: just using the lag specified below.
 Lag 0 to: from lag 0 to the lag specified below.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Removes the current status so that the default applies (X).
 Y: endogenous
Label the current model selection as endogenous variables
(this is not possible for lagged variables).
Endogenous variables are preceded by Y in the model list.
 X: variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so an X variable or unmarked variable
are treated in the same way. X variables enter the mean of Y
before the AR and fractional lag polynomials are applied.
 Z: variable
Marks the selected model variables as a Z regressor.
Z variables enter the mean of Y after the AR and fractional lag
polynomials are applied. Forecasting with Z variables is
currently not available.
 W: weight
Optionally, a variable can be marked for weighted maximum likelihood
estimation.
 Recall a previous model

Use this to recall a previously estimated model.
This dialog is for choosing an ARFIMA specification.
 AR order, MA order

Specify the orders p and q for the
ARMA(p,q) process.
 Fix AR lags, Fix MA lags

These edit field allow for ARMA parameters to be fixed at zero.
For example, when both p and q are set to 4,
and both fields are set to
1;2;3
then only the fourth AR and MA coefficients are estimated.
 Fractional parameter d

By default d is estimated, but it is possible to fix
d at zero or another userspecified value.
 Treatment of mean

The default usage is to add a Constant as regressor, and set
the treatment of the mean to None. It is also possible to
estimate the model in deviations from the sample mean, or to fix the
mean to a userspecfied value.
Select an estimation method and sample period for
the formulated model.
 Estimation sample

Enter the sample period you wish to use for the estimation (including
initialization and forecasts), e.g. 1960(1) to 1980(4). The maximum
sample is given one line up.
The default is the sample of the previous estimation (of course
only if possible). PcGive automatically excludes observations with
missing values.
 Less forecasts

Enter the number of observations you wish to withhold from the sample.
 Estimation method

 Maximum Likelihood
 Nonlinear Least Squares
 Modified Profile Likelihood
 Starting values only
 NLS with stationarity imposed
PcGive provides three estimation methods,
Exact Maximum Likelihood (EML), Modified Profile Likelihood (MPL) and nonlinear least squares (NLS).
By definition, EML and MPL impose 1 < d < 0.5. MPL is preferred over EML if the model includes
regressor variables and the sample is not very large. NLS allows for d > 0.5 and can be used
to estimate models for nonstationary processes directly, without a priori differencing. NLS estimation
is usually fast.
Starting values only reports the GPH estimates of d,
from the (frequency domain) log periodogram regression,
the AR starting values from solving the YuleWalker equations,
and the MA parameters derived from TunnicliffeWilson's method.
NLS with stationarity imposed enforces that the oots are inside
the unit circle.
The Graphic analysis command gives various options to graph actual and
fitted values, forecasts and residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Actual and fitted values

Show the fitted and actual values of the dependent variable over time,
over the whole sample period, including the forecast period.
 Crossplot of actual and fitted

As above, but now a crossplot of actual and fitted values.
 Residuals (scaled)

Show the scaled residuals against time, over the whole sample
period, including the forecast period. The residuals are scaled by the
residual standard deviation.
 Residual density and histogram

Show the density estimate and histogram of the residuals.
The normal density with the same mean and variance is drawn for
reference. To omit any of these items see under Further graphs.
 Residual correlogram (ACF)

Show the ACF of the residuals, using the
lag length supplied in the text entry field.
 Length of correlogram and spectrum

The lag length must be < T.
Further graphs
 Partial autocorrelation function (PACF)

Show the PACF of the residuals, using the
lag length supplied in the text entry field.
 Residuals (unscaled)

Show the residuals against time, over the whole sample
period, including the forecast period.
 Residual spectrum

Show the Spectral density of the residuals,
using the lag length as the truncation point.
To zoom a graph adjust the area inside OxMetrics.
Shows the dynamic forecasts
forecasts optionally with standard error bars, bands or fans
(± 2 forecast standard errors).
 Number of forecasts

By default, this displays the maximum number of dynamic forecasts.
If there are unmodelled variables in the model, forecasting is only
possible while data is available.
 Naive forecasts only

`Naive' forecasts are derived from the autoregressive representation of the
process, truncated at T+h.
Naive forecasts are faster to compute.
Undo data transformations
 Base level for reintegration

Specify the level from which to reintegrate the series.
This is the last observation of the levels (loglevels if
growth rates are used) in the estimation sample.
For second differences, specify two values separated by a comma
(the last two observations in the estimation sample).
 Undo logarithm

Click this box to takes exponents of the forecasts.
Options
 Type of error bars:

 Use error bars
 Use error bands
 Use error fans
 Critical value to use for errors bars

The default is ± 2SE corresponding to 95% bands. Use 1.6 for 90% bands.
 Number of preforecast observations

By default 1 + the data frequency observations are included from
the preforecasting sample.
 Write results
 Write the information to the Results window.
This dialog box gives access to a selection of diagnostic
testing procedures. Mark the tests you want to be executed, then press OK.
Many tests report a Chi^2 and an F form. In the
summary, only the Ftest is reported, which is expected to have better
smallsample properties.
 Residual correlogram and Portmanteau statistic with length

Prints the residual correlogram (both ACF and PACF),
as well as the Portmanteau statistic.
You can change the lag length.
 Normality

Shows the first four moments, together with a
test for normality.
 ARCH with order (no vector form)

Tests for Autoregressive Conditional Heteroscedasticity, for a user
defined order. Information on the auxiliary regression is printed in addition
to the Fform of the test statistic.
Dialogs for GARCH Models
 Dialogs for model formulation and estimation:
 Estimate
 Formulate
 Model Settings
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Forecast
 Recursive graphics
 Test
 Exclusion Restrictions
 Linear Restrictions
 Store in Database
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model with the default
lag length.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Trend
The trend has value 1,2,3,... with value 1 occurring for the first
observation in the database. This may be different from the first
observation in the estimation sample, for example when using lags
(of course, this only affects the value of the constant term).
 Seasonal
Seasonal is only present if the database has a nonannual frequency s.
Selecting this variable will lead to s  1 seasonals being
added when a Constant is present in the model (s otherwise).
For example, for quarterly data, this adds:
Seasonal (1 in quarter 1, zero otherwise),
Seasonal_1 (1 in quarter 2, zero otherwise),
Seasonal_2 (1 in quarter 3, zero otherwise).
 CSeasonal
This behaves as Seasonal, except that the variable has zero
mean within a year. For quarterly data, for example, CSeasonal
has value 0.75 in the first quarter, and 0.25 in the remaining quarters.
 Lags

At the top you can choose how the lag length is set with which variables
are added to the model:
 None: no lags.
 Lag: just using the lag specified below.
 Lag 0 to: from lag 0 to the lag specified below.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
You can also double click on a model variable to delete it.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Clears the status of all selected model variables.
Cleared variables behave as Z variables.
 Y: endogenous
Label the current model selection as endogenous variables
(this is not possible for lagged variables).
The first Y variable will be the dependent variable.
Additional endogenous variables will be required for instrumental
variables estimation. Endogenous variables are preceded by Y in the model list.
 Z: variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so a Z variable or unmarked variable
are treated in the same way.
 H: X in h_t
Label the current model selection as regressors for the variance
equation h_{t}.
 Recall a previous model

Use this to recall a previously estimated model.
This dialog is for choosing a GARCH or EGARCH specification.
 GARCH(p,q)

Specify the orders p and q for the
GARCH(p,q) process. Set p to zero for
an ARCH(q) process.
Set a check in the EGARCH box to estimate an EGARCH model.
Optionally, a nonnormal error distribution can be estimated.
This is a standardized Studentt distribution for GARCH, and a
generalized error distribution (GED) for EGARCH. The Studentt
approaches the standard normal as the degrees of freedom go to infinity.
The GED(nu) coincides with the normal when nu=2.
 GARCH variations

Optionally, a threshold or asymmetry effect can be added to the
GARCH model.
Both GARCH and EGARCH can be estimated with the conditional
variance (or its square root or logarithm) entering as a regressor
in the mean.
 GARCH parameter restrictions

An important aspect of GARCH modelling is the choice of parameter space.
In PcGive the options are:
 Unrestricted estimation
All parameters are unrestricted, except for the intercept
in the variance equation, which is forced to be nonnegative.
 Impose conditional variance >= 0
This imposes the Nelson & Cao conditions to keep the conditional variance
positive.
 Impose stationarity and alpha+beta >= 0
This imposes coefficients of the ARMA representation of the conditional
variance to be positive, and bounds sum of the alpha and beta coefficients
to be less than or equal to one (IGARCH boundary).
 Impose alpha,beta >= 0
This imposes all coefficients to be nonnegative.
 Startup of GARCH variance recursion

There are two options for the startup of the variance recursion:
using the sample mean of the variance, or estimate the missing variance
terms as extra parameters. The former is the default.
 Preferred covariance estimator

 Second derivatives
This uses minus the inverse of the numerical second derivative of the
loglikelihood function.
 Information matrix
The information matrix is computed analytically, but only
for standard GARCH models. This is the default.
 Outer product of gradients
In addition, the robust standard errors are printed by default
when the information matrix J is available.
These are of the form inv(JG inv(J),
where G is the outer product of the gradients.
 Search for global maximum after initial estimation

Especially when q>1, it is possible that the likelihood has
multiple optima. This final set of advanced options allows
for a search from random starting values. Because each of these
involves maximization of the likelihood, this option can be time consuming.
Select an estimation method, and sample period for
the formulated model. Optionally select recursive estimation.
 Estimation method

ML is the only available estimation methods.
 Estimation sample

Enter the sample period you wish to use for the estimation (including
initialization and forecasts), e.g. 1960 1 to 1980 4. The maximum
sample is given one line up.
The default is the sample of the previous estimation (of course
only if possible). PcGive automatically excludes observations with
missing values.
 Recursive estimation, initialization:

Select this option and enter the number of observations you wish to use for
initializing the recursive estimation. Recursive estimation is available
for all GARCH and EGARCH type models, and estimates the model for
all sample sizes down to the size specified for initialization.
 Less forecasts

Enter the number of observations you wish to withhold from the estimation sample.
 Options

Allows setting the estimation options.
 OK

Pressing OK starts the estimation, unless there still is something missing or
wrong in the dialog.
Controls maximization settings, and what is automatically printed
after estimation (in addition to the normal estimation report).
Model options referes to settings which are changed infrequently,
and are persistent between runs of PcGive.
 Maximization Settings

Maximum number of iterations:
Note that it is possible
that the maximum number of iterations is reached before
convergence. The maximum number of
iterations also equals the maximum number of switches in cointegration.
Write results every:
By default no iteration progress
is displayed in the results window. It is possible to write intermediate
information to the Results window for a more permanent record.
A zero (the default) will write nothing, a 1 every iteration, a
2 every other iteration, etc.
Write in compact form:
Writes one line per printed
iteration (see Write results every).
Convergence tolerance:
Change the convergence tolerance
levels (the smaller, the longer the estimation will take to converge).
See under numerical optimization for an explanation
of convergence decisions.
Default:
Resets the default maximization settings.
The Graphic analysis command gives various options to graph actual and
fitted values, forecasts and residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Actual and fitted values

Show the fitted and actual values of the dependent variable over time,
over the whole sample period, including the forecast period.
 Crossplot of actual and fitted

As above, but now a crossplot of actual and fitted values.
 Residuals (scaled)

Show the scaled residuals against time, over the whole sample
period, including the forecast period. The residuals are scaled by the
residual standard deviation.
 Conditional standard deviation

Show the square root of the estimated conditional variance:
sqrt(h_{t}).
Further graphs
 Residual density and histogram

Show the density estimate and histogram of the residuals.
The normal density with the same mean and variance is drawn for
reference. To omit any of these items see under Further graphs.
 Residual correlogram (ACF)

Show the ACF of the residuals, using the
lag length supplied in the text entry field.
 Length of correlogram and spectrum

The lag length must be < T.
 Partial autocorrelation function (PACF)

Show the PACF of the residuals, using the
lag length supplied in the text entry field.
 Partial autocorrelation function (PACF)

Show the PACF of the residuals, using the
lag length supplied in the text entry field.
 Residuals (unscaled)

Show the residuals against time, over the whole sample
period, including the forecast period.
 Residual spectrum

Show the Spectral density of the residuals,
using the lag length as the truncation point.
 Residual correlogram of squares (scaled)

Shows the ACF of the squared scaled residuals
u_{t}^{2}/h_{t},
using thelag length supplied in the text entry field.
To zoom a graph adjust the area inside OxMetrics.
The Recursive graphics command graphs the recursive output
as generated by a recursive estimation.
 Coefficients
 Mark all the variables in the model you wish to include in the betacoefficient
and/or tvalue graphs in this list box.
 Coefficients ±2*S.E.
 Graph the estimated coefficients ±2*SE of all variables selected in the variables list box.
 tvalue
 Graph the tvalues of all variables selected in the variables list box.
 alpha(1)+beta(1)
 Graph α(1)+β(1).
 Loglikelihood (nonlinear modelling)
 Graph the loglikelihood.
 Write results instead of graphing
 Write the information to the Results window.
To zoom a graph adjust the area inside OxMetrics.
Shows the dynamic forecasts
forecasts optionally with standard error bars, bands or fans
(± 2 forecast standard errors).
 Number of forecasts

By default, this displays the maximum number of dynamic forecasts.
If there are unmodelled variables in the model, forecasting is only
possible while data is available.
 Conditional variance graph

Allows for the conditional variance to be graphed separately.
Options
 Type of error bars:

 Use error bars
 Use error bands
 Use error fans
 Critical value to use for errors bars

The default is ±2SE corresponding to 95% bands. Use 1.6 for 90% bands.
 Number of preforecast observations

By default 1 + the data frequency observations are included from
the preforecasting sample.
 Write results
 Write the information to the Results window.
This dialog box gives access to a selection of diagnostic
testing procedures. Mark the tests you want to be executed, then press OK.
Many tests report a Chi^2 and an F form. In the
summary, only the Ftest is reported, which is expected to have better
smallsample properties.
 Residual correlogram and Portmanteau statistic with length

Prints the residual correlogram (both ACF and PACF),
as well as the Portmanteau statistic.
You can change the lag length.
 Normality

Shows the first four moments, together with a
test for normality.
 ARCH with order (no vector form)

Tests for Autoregressive Conditional Heteroscedasticity, for a user
defined order. Information on the auxiliary regression is printed in addition
to the Fform of the test statistic.
Dialogs for Discrete Choice and Count Models
 Dialogs for model formulation and estimation:
 Formulate  Binary Discrete Choice
 Formulate  Multinomial Discrete Choice
 Formulate  Count Data
 Model Settings  Discrete Choice
 Model Settings  Count Data
 Estimate
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Norm Observation
 Outliers
 Predictions
 Test
 Further Output
 Exclusion Restrictions
 Linear Restrictions
 Store in Database
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
You can also double click on a model variable to delete it.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Clears the status of all selected model variables.
Cleared variables behave as X variables.
 Y: endogenous
Label the current model selection as endogenous variables.
Normally, there is one dependent variable which holds
the binary response 0 or 1 (although 1 and 2 are also allowed).
If two Y variables are marked, the data are assumed to be grouped.
 X: variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so an X variable or unmarked variable
are treated in the same way.
 S: Select By
By default, all valid observations are used for estimation.
Select by can be used to estimate over a subsample.
When a model variable is marked as S variable, only observations
which have a nonzero value are included for estimation.
When predicting, the default is to use all valid observations
which were not used in estimation, but it is also possible to
only predict for observations which have a value 2 for the select by
variable.
 Recall a previous model

Use this to recall a previously estimated model.
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
You can also double click on a model variable to delete it.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Clears the status of all selected model variables.
Cleared variables behave as X variables.
 Y: endogenous
Label the current model selection as endogenous variables.
Normally, there is one dependent variable which holds
the multinomial response 0,1,...,S1 (although 1,2,...,S are also allowed).
If S Y variables are marked, the data are assumed to be grouped
or to just hold 0/1 indicators.
 X: variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so an X variable or unmarked variable
are treated in the same way.
 Z: variable
Marks the selected model variables as an alternativedependent regressor.
Because Z variables are dependent on the alternative, they must be
entered in groups of size S at a time (where S is the number
of alternatives). A model with only alternativedependent regressors
is sometimes called a conditional logit model.
 W: variable
Optionally, a variable can be marked for weighted maximum likelihood
estimation.
 S: Select By
By default, all valid observations are used for estimation.
Select by can be used to estimate over a subsample.
When a model variable is marked as S variable, only observations
which have a nonzero value are included for estimation.
When predicting, the default is to use all valid observations
which were not used in estimation, but it is also possible to
only predict for observations which have a value 2 for the select by
variable.
 Recall a previous model

Use this to recall a previously estimated model.
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
 Special

The listbox below the database variables shows the socalled special
variables, which are predefined. Here it is:
 Constant
A constant will be added automatically in a new model but can be deleted.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
You can also double click on a model variable to delete it.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Clears the status of all selected model variables.
Cleared variables behave as X variables.
 Y:endogenous
Label the current model selection as the endogenous variable.
Only one endogenous variable, holding the counts, is allowed.
 X:variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so an X variable or unmarked variable
are treated in the same way.
 S: Select By
By default, all valid observations are used for estimation.
Select by can be used to estimate over a subsample.
When a model variable is marked as S variable, only observations
which have a nonzero value are included for estimation.
 Recall a previous model

Use this to recall a previously estimated model.
Model Settings
This dialog is for choosing a discrete choice model.
 The Model Type

 Logit
 Probit
Only binary probit can be estimated.
Model Settings  Count Data
This dialog is for choosing a count data model.
 The Model Type

 Poisson
 Negative binomial
 Truncated above at (0 is untruncated)

Optionally, a truncated Poisson or negative binomial model can be estimated.
 Negative binomial type

A type I (k=1) or type II (k=0) negative binomial model can be estimated, or
k set directly.
Estimate
Select an estimation method for the formulated model.
 Estimation method

 Newton's method
 BFGS method
Because the multinomial logit and binary probit likelihoods
are concave, Newton's method, which uses analytical second derivatives,
is the preferred estimation method.
Count data models are always estimated by BFGS.
 Estimation sample

Crosssection modelling automatically drops all observations
with missing values. This can be refined by specifying a
select by variable in the model formulation stage.
 Options

Allows setting the estimation options.
 OK

Pressing OK starts the estimation, unless there still is something missing or
wrong in the dialog.
Controls maximization settings, and what is automatically printed
after estimation (in addition to the normal estimation report).
Model options referes to settings which are changed infrequently,
and are persistent between runs of PcGive.
 Maximization Settings

Maximum number of iterations:
Note that it is possible
that the maximum number of iterations is reached before
convergence. The maximum number of
iterations also equals the maximum number of switches in cointegration.
Write results every:
By default no iteration progress
is displayed in the results window. It is possible to write intermediate
information to the Results window for a more permanent record.
A zero (the default) will write nothing, a 1 every iteration, a
2 every other iteration, etc.
Write in compact form:
Writes one line per printed
iteration (see Write results every).
Convergence tolerance:
Change the convergence tolerance
levels (the smaller, the longer the estimation will take to converge).
See under numerical optimization for an explanation
of convergence decisions.
Default:
Resets the default maximization settings.
Graphic Analysis
The Graphic analysis command gives various options to graph actual and
fitted values, forecasts and residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Histograms of probabilities for each state

Plots the histograms of probabilities for each state
separately (S histograms).
 Histograms of probabilities of observed state

Plots the histograms of probabilities of observed state,
for each state separately (S histograms), and all states together.
 Number of bars

Sets the number of bars for the above histograms.
 Cumulative correct predictions for each state

Plots the cumulative correct predictions,
for each state separately (S graphs), and all states together.
 Cumulative response for each state (sorted by probability)

Plots the cumulative response for each state
(S graphs), sorted by probability (with the highest probabilities
first).
Predictions
Writes the predictions for the observations that were excluded
from estimation or for observations which have a value 2
for the select by variable.
Allows for the printing of
 Summary statistics for explanatory variables

 Table of actual and predicted

 Derivatives of probabilities at regressor means

 Derivatives of probabilities at sample frequencies

Writes the observations which have small estimated probabilities
for the observed state.
Norm observation
Writes or graphs the probabilites observations for a `norm' observation
with specified values for the explanatory variables.
Dialogs for Static and Dynamic Panel Models
 Dialogs for model formulation and estimation:
 (static and dynamic panel methods)
 Model Settings (static panel methods)
 Model Settings (dynamic panel methods)
 Estimate Model (static panel methods)
 Estimate Model (dynamic panel methods)
 Options
 Progress
 Dialogs for model evaluation:
 Graphic Analysis
 Dynamic Analysis
 Further Output
 Exclusion Restrictions
 Linear Restrictions
 Store in Database
 Test
Use this dialog for to formulate a new model, or reformulate
an existing model.
 Database

Mark all the variables you wish to include in the new model or add to the
existing model, using the spacebar or the mouse.
After you have pressed << (or doubleclicked if you are using a mouse),
the database variables are added to the model with the default
lag length.
The variable at the top of the list will by default become the endogenous
(Y) variable.
To select a different dependent variable, see below.
A Constant and other dummy variables can be entered at the next
stage.
A year variable must always be added to the model.
 Model

This MultipleSelection List box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and clear its status;
 mark the new variable, and press the Y:Endogenous button.
If you have marked variables in the model, you can delete them, or assign a status to them.
 Lags

At the top you can choose how the lag length is set with which variables
are added to the model:
 None: no lags.
 Lag: just using the lag specified below.
 Lag 0 to: from lag 0 to the lag specified below.
 Selection

This list box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:
 mark the current dependent variable and rightclick to clear its status;
 mark the new variable, and rightclick to change to Y: endogenous.
If you have marked variables in the model, you can delete them, or
assign a status to them.
 <<

Adds the currently selected database or special variables to the model.
 >>

Deletes the currently selected variables from the model.
You can also double click on a model variable to delete it.
 Clear>>

Deletes the whole model, so that you can start from scratch.
 Status

The status dropdown box lists all the available variable types for the
current model class.
Variables are added to the model using the selected status.
To change the status of variables that have been selected into the model,
highlight the variable(s), choose a new status and set using the Set button.
The status can also be changed by rightclicking on highlighted variables,
and using the context menu.
 Use default status
The default status is used for variables that are added to the model.
 Clear status
Clears the status of all selected model variables.
Cleared variables behave as Z variables.
 Y: endogenous
Label the current model selection as endogenous variable
(there can only be one endogenous variable, which cannot be a lagged variable).
If endogenous regressors are present for instrumental
variables estimation, these should be marked X, but not appear as instrument.
 X: variable
Marks the selected model variables as a normal regressor. This is the
default for an unmarked variable, so an X variable or unmarked variable
are treated in the same way.
A nonendogenous regressors for instrumental variables estimation
can be marked both as X, and appear as instrument (I or L).
 I: Instrument
Label the current model selection as instruments.
These instruments will be transformed along with the regressors
(e.g. if the model is in first differences, I instruments
will also be used in first differences).
 L: Level instrument
Label the current model selection as instruments.
These instruments will not be transformed
(e.g. if the model is in first differences, Level instruments
will be used in levels).
 R: Year
Label the current variable as the year variable.
Such a variable must always be defined, and there can only be one
year variable.
 N: Index
An optional variable can be defined which holds the individual
indices. If added, that variable will be used to determine
the panel structure.
 G: Group
If group or group interaction dummies are to be used, a group
variable must be defined which assigns individuals to groups.
 Recall a previous model

Use this to recall a previously estimated model.
Model Settings  Static Panel Methods
This dialog is for further static panel model specification.
 Dummies

The following dummy variables can be added to the model:
 Constant
 Time
 Group
 Time and Group
 Individual
Group and time/group interaction dummies can only be used if a Group
variables has been added to the model.
 Specification tests

Check this box to include Wald tests for the significance
of dummy variables and other regressors.
 AR tests up to order

Unlike other PcGive packages, for panel data the order of the
AR test must be specified in advanced. By default it is set to two.
Set to zero to avoid the computation of the test.
 Use robust standard errors

By default standard errors which are robust to heteroscedasticity
are reported, and all tests based on the robust variance.
This can be switched off, but not that twostep dynamic panel standard
errors are particularly unreliable.
 Concentrate dummies (not exact with instruments)

When this option is checked, the dependent variable, and
all regressors and instruments are used after partialling the
dummy variables out. This can help to reduce the dimensionality
of the parameter space.
 Transform dummies (OLS on differences)

This option is only relevant when estimating with OLS on differences.
When selected, the first differences of the dummy variables
is used in the model.
Model Settings  Dynamic Panel Methods
This dialog is for further dynamic panel model specification.
 Dummies

The following dummy variables can be added to the model:
 Constant
 Time
 Group
 Time and Group
 Individual
Group and time/group interaction dummies can only be used if a Group
variables has been added to the model.
 Transformations
Select the transformations to applied prior to model estimation:

 None
 Differences
 Othogonal Deviations
 Within group
estimation replaces the dependent variable and regressors by deviations
from time means (i.e.,subtracting the means of each time series).
 Between group
estimation replaces the dependent variable and regressors by the means
of each individual (leaving N observations).
 Specification tests

Check this box to include Wald tests for the significance
of dummy variables and other regressors.
 AR tests up to order

Unlike other PcGive packages, for panel data the order of the
AR test must be specified in advanced. By default it is set to two.
Set to zero to avoid the computation of the test.
 Use robust standard errors

By default standard errors which are robust to heteroscedasticity
are reported, and all tests based on the robust variance.
This can be switched off, but not that twostep dynamic panel standard
errors are particularly unreliable.
 Concentrate dummies (not exact with instruments)

When this option is checked, the dependent variable, and
all regressors and instruments are used after partialling the
dummy variables out. This can help to reduce the dimensionality
of the parameter space.
 Transform dummies (OLS on differences)

This option is only relevant when estimating with OLS on differences.
When selected, the first differences of the dummy variables
is used in the model.
 Print contents of GMM instruments

This option can help understanding the format of the GMMtype
instruments that was used in the estimation.
Estimate  Static Panel Methods
Select an estimation method for the formulated model.
 Estimation method

 OLS (pooled regression)
 OLS on differences
 LSDV (fixed effects)
 Within groups estimation
 Between groups estimation
 GLS (using within/between)
 GLS (using OLS residuals)
 Maximum likelihood estimation
 Estimation sample

Panel modelling automatically drops all observations
with missing values.
The Graphic analysis command gives various options to graph actual and
fitted values, forecasts and residuals, etc.
The list box on the right lists the selected equations for
which the graphs are drawn.
 Actual and fitted values

Show the fitted and actual values of the dependent variable over time,
over the whole sample period, including the forecast period.
 Crossplot of actual and fitted

As above, but now a crossplot of actual and fitted values.
 Residuals (scaled)

Show the scaled residuals against time, over the whole sample
period, including the forecast period. The residuals are scaled by the
residual standard deviation.
 Residual density and histogram

Show the density estimate and histogram of the residuals.
The normal density with the same mean and variance is drawn for
reference. To omit any of these items see under Further graphs.
 Residual correlogram (ACF)

Show the ACF of the residuals, using the
lag length supplied in the text entry field.
 Length of correlogram and spectrum

The lag length must be < T.
Further graphs
 Partial autocorrelation function (PACF)

Show the PACF of the residuals, using the
lag length supplied in the text entry field.
 Residuals (unscaled)

Show the residuals against time, over the whole sample
period, including the forecast period.
 Residual spectrum

Show the Spectral density of the residuals,
using the lag length as the truncation point.
To zoom a graph adjust the area inside OxMetrics.
 Covariance matrix of estimated parameters

Print out the covariance matrix of the estimated parameters for each model,
and the covariance matrix of constrained parameters following general
restrictions.
Write model results
 Equation format

write the results in equation format.
 LaTeX format

This resulting output can be pasted to a LaTeX document.
 Significant digits for parameters

 Significant digits for std.errors

These control the format of the output.
When creating lags, PcGive appends the lag length as extra characters in a name, preceded by an underscore. E.g. CONS_1 is CONS one period lagged.
Lagging a variable leads to the loss of observations, but seasonals can be lagged up to the frequency without loss. PcGive handles variables in models through lag polynomials.
Sample periods are automatically adjusted when lags are created.
PcGive stores the lag information, and uses it to recognize lagged variables for Dynamic Analysis. Lags created this way are not physically created, and do not consume any memory.
However, when you compute a lag using the calculator, a new variable will be
created in the database, which will NOT be treated as a lagged version of that variable,
but as any other variable.
A dynamic equation is specified as an autoregressivedistributed lag model:
B_{0}(L) y_{t} = c +
B_{1}(L) x_{1,t} +
B_{2}(L) x_{2,t} + ... +
B_{k}(L) x_{k,t} +
e_{t}, t = 1,...,T.
(1)
In (1), the lag polynomials are defined by:
B_{i} (L) = Σ^{ni}_{j=mi}
b_{i,j} L^{j} with 0 ≤ mi ≤ ni, i = 1,...,k.
`Solving' (1) yields:
y_{t} = Σ^{k}_{i=1}
H_{i} (L) x_{it}, where
H_{i} (L)=B_{i} (L) / B_{0}(L).
Zero is a legitimate order for a lag polynomial. Thus, static or dynamic
models are equally easily specified.
A model in PcGive is formulated by:
 Which variables are involved;
 The orders of the lag polynomials;
 The status of variables (only when it is not legitimate to treat all
regressors as valid conditioning variables, and you wish
to use Instrumental Variables).
The following information is needed to estimate an equation:
 The model formulation;
 The sample period;
 Optionally, the number of static forecasts to be withheld for testing parameter constancy;
 The method of estimation;
 Optionally, the number of observations to be used to initialize the recursive estimation (when available).
The available singleequation estimators are (see Volume I):
Singleequation estimation output is discussed
in Volume I.
Models may be revised interactively after formulation and after estimation.
Afterwards, the estimated model can be analyzed.
PcGive facilitates a generaltospecific modelling strategy.
Ordinary Least Squares is the standard textbook method. OLS is valid if
the data model is congruent.
Congruency
The requirements for congruency are:
 Homoscedastic innovation errors;
 Weakly exogenous regressors;
 Constant parameters;
 Theory consistency;
 Data admissibility;
 Encompassing rival models.
PcGive provides tests of most of the aspects of model congruency.
A structural representation is parsimonious with parameters but has
regressors which are correlated with the error term.
IV requires that the reduced form is a congruent data model.
The Instrumental variables are the reduced form regressors.
Instrumental Variables include two stage least squares (2SLS) as a special case.
PcGive needs to know the status of the variables in the model:
1. At least one endogenous variable on the righthand side;
2. At least as many instruments as endogenous rhs variables.
PcGive computes:
1. The estimate of all the reduced form equations;
2. The estimate of the structural form equation;
3. Tests of the overidentifying restrictions.
Autoregressive least squares requires that the restricted dynamic model
is data congruent, where the restrictions correspond to COMFAC constraints
selected (since an autoregressive error is a more parsimonious representation).
Various orders of autoregression can be selected, and
a grid is estimable for single orders.
Multiple optima to the likelihood function commonly occur in the
COMFAC class, thus case 5. is recommended. Direct fitting of 4.
may not find the optimum.
.
RALS numerical optimization
The loglikelihood function f(θ) for RALS
is a sum of squares of nonlinear terms.
Let the regression and the autoregressive error parameters be
β and ρ.
Then f(β, ρ)
is nonlinear but is linear in β
given ρ and conversely.
The GaussNewton method exploits this fact. It is a reliable choice,
but need not find global optima. Like NewtonRaphson, GaussNewton uses
analytical first and second derivatives.
Hendry (1976) reviews alternative methods.
The autoregressive error can be written as
u_{t} = Σ^{r}_{i=s}
ρ_{i} u_{ti}
+ ε_{t} with
ε_{t} ~ IN(0, σ^{2}).
Numerical optimization is used to maximize the likelihood log
L(θ) as an unconstrained nonlinear
function of θ.
PcGive maximization algorithms are based on a Newton scheme:
θ_{k+1} =
θ_{k} +
s_{k}Q_{k}^{1}
q_{k},
with
 θ parameter value at iteration k
 s step length, normally unity
 Q symmetric positivedefnite matrix (at iteration k)
 q first derivative of the loglikelihood (at iteration k) (the score vector)

Δθ_{k} =
θ_{k} 
θ_{k1}
is the change in the parameters
PcGive and PcGive use the quasiNewton method developed by Broyden,
Fletcher, Goldfarb, Shanno (BFGS) to update K = Q^{1} directly,
estimating the first derivatives numerically.
Owing to numerical problems, it is possible (especially close to
the maximum) that the calculated θ does
not yield a higher likelihood. Then an s in [0,1] yielding a higher function
value is determined by a line search. Theoretically, since the direction is
upward, such an s should exist; however, numerically it might be impossible to find one.
 The convergence decision is based on two tests:
 1. based on likelihood elasticities (dlogLik/dlogθ)
(scale invariant):
 q_{k,j}
θ_{k,j}  ≤ eps
 for all j when θ_{k,j}
not zero, 
 q_{k,j}  ≤ eps
 for all j when θ_{k,j} = 0.

 2. based on the onestepahead relative change in the parameter values
(assuming step length 1) (scale variant, but relative change is infinite
if any θ = 0)
 θ_{k+1,j} 
θ_{k,j}  ≤ 10 * eps *
 θ_{k,j} 
 for all j when θ_{k,j}
not zero,

 θ_{k+1,j} 
θ_{k,j}  ≤ 10 * eps
 for all j when θ_{k,j} = 0.

The status of the iterative process is given by the following messages:
 No convergence!
 Aborted: no convergence!
 Function evaluation failed: no convergence!
 Maximum number of iterations reached: no convergence!
 Failed to improve in line search: no convergence!
s has become too small.
Test 1 was passed, using eps2.
 Failed to improve in line search: weak convergence.
s has become too small.
Test 1 was passed, using eps2.
 Strong convergence
Both tests were passed, using eps1.
The chosen default values are:
eps1 = 1E4, eps2 = 5E3.
You can:
 Set the initial values of the parameters to zero or the previous values;
 Set the maximum number of iterations;
 Write iteration output;
 Change the convergence tolerances eps1 and eps2;
 Care must be exercised with this: the defaults are `finetuned':
some selections merely show the vital role of sensible choices!
 Choose the maximization algorithm;
 Plot a grid of the loglikelihood.
The `fineness', number of points and centre can be userselected.
Up to 16 grids can be plotted simultaneously.
A grid may reveal potential multiple optima.
Options 1., 5. and 6 are mainly for teaching optimization.
NOTE: estimation can only continue after convergence.
PcGive has two modes of operation: generaltospecific and unordered.
 Generaltospecific

1. Begin with the dynamic model formulation;
2. Check its data coherence and cointegration;
3. Transform to a set of variables with low intercorrelations but interpretable parameters;
4. Delete unwanted regressors to obtain a parsimonious model;
5. Check the validity of the model by thorough testing.
PcGive monitors the progress of the sequential reduction from the general to the specific and will provide the associated Ftests, Schwarz and σ values.
 Unordered Search

Nothing commends unordered searches:
1. No control is offered over the significance level of testing;
2. A `later' reject outcome invalidates all earlier ones;
3. Until a model adequately characterizes the data, standard tests are invalid
Dynamic analysis
After estimation, unrestricted general models like (1) in
the Dynamic Model Formulation are analysed:
B_{0}(L) y_{t} = c +
B_{1}(L) x_{1,t} +
B_{2}(L) x_{2,t} + ... +
B_{k}(L) x_{k,t} +
e_{t}, t = 1,...,T.
(1)
where
B_{i} (L) =
b_{i,0} + b_{i,1} L +
b_{i,2} L^{2} + ... +
b_{i,n} L^{n}.
 Static longrun solution

If the roots of B(L) lie outside the unit circle we can
rewrite (1) as (forgetting about c and e):
y_{t} = Σ^{k}_{i=1}
H_{i} (L) x_{i,t}, where
H_{i} (L)=B_{i} (L) / B_{0}(L).
(2)
If E[x] has remained at a constant level x for long enough,
y will reach its longrun solution:
E[y] = Σ^{k}_{i=1}
H_{i} (1) E[x_{i}], where
H_{i} (1)=B_{i} (1) / B_{0}(1).
(3)
(reported with asymptotic standard errors).
PcGive allows you to retain observations to compute forecast statistics.
For OLS/RLS/RALS these are comprehensive 1step ahead forecasts.
For IV/RIV, since there are endogenous regressor variables, the
only interesting issue is that of parameter constancy, and the only output is the forecast Chi˛ test.
Dynamic forecasts can be made from single equation models as well as from
simultaneous equations system. PcGive will compute analytical standard errors
of dynamic forecasts, and can take parameter uncertainty into account.
The correlation matrix of selected variables is a symmetric
matrix, with the diagonal equal to one. Each cell records
the simple correlations between the two relevant variables.
The mean:
m = T^{1} Σ^{T}_{i=1}
x_{i},
and standard deviation:
s = (T1)^{1} Σ^{T}_{i=1}
(x_{i}  m)^{2}
of the variables are also given.
NOTE that the standard deviation here is based on 1/(T1).
Histograms are a way of looking at the sample distributions of statistics.
Then, on the basis of the original data, density functions may be
interpolated to give a clearer picture of the implied distributional
shape: similarly, cumulative distribution functions may be constructed
(and compared onscreen to a Cumulative Normal Density).
Nonparametric density estimation
Given observations:
(x_{1} ... x_{T})
from some unknown probability density function f(X),
about which little may be known a priori. To estimate that density without
imposing too many assumptions about its properties, a nonparametric
approach is used in PcGive based on a kernel estimator.
The kernel K used is the Normal or Gaussian kernel.
Research suggests that the density estimate is little affected by the
choice of kernel, but is largely governed by the choice of window width, h.
Owing to the importance of the window width h in estimating the density,
the nonparametric density estimation menu offers control over the choice
of window width, h = CσT^{P}.
By default, P = 0.2 and C = 1.06 in PcGive.
For normal densities this choice will minimize the Integrated Mean Square Error.
For more information see:
Silverman B.W. (1986). Density Estimation for Statistics and Data Analysis,
London: Chapman and Hall.
Correlogram (ACF, PACF)
The correlogram or autocorrelation function (ACF) of a variable, or of the residuals
of an estimated model, plots the series of correlation coefficients
{ r_{j} } between x_{t} and
x_{tj}.
The length s of the ACF is chosen by the user,
leading to a figure which shows (r_{1}, r_{2}, ..., r_{s})
plotted against (1,2,..., s).
A related statistic is the Portmanteau (also called BoxPierce or Qstatistic):
T Σ^{s}_{j=1}
r_{j}^{2}.
The partial autocorrelation coefficients correct the autocorrelation
for the effects of previous lags. So the first
partial autocorrelation coefficient equals the first normal
autocorrelation coefficient.
A stationary series can be decomposed in cyclical components with different frequencies
and amplitudes. The spectral density gives a graphical representation of this.
It is symmetric around 0, and only graphed for [0,π]
(the horizontal axis in the PcGive graphs is scaled by π,
and given as [0,1]).
The spectral density consists of a weighted sum of the autocorrelations,
using the Parzen window as the weighting function. The truncation parameter m
can be set (the larger m, the less smooth the spectrum becomes, but the lower the bias).
A whitenoise series has a flat spectrum.
Diagnostic testing
 Test types

Many tests report a Chi^2 and an F form. In the
summary, only the Ftest is reported, which is expected to have better
smallsample properties.
Ftests are usually reported as
F(num,denom) = Value [Probability] /*/**
For example
F(1, 155) = 5.0088 [0.0266] *
where the test statistic has an F distribution with 1 degree of freedom
in the numerator, and 155 in the denominator. The observed value is 5.0088,
and the probability of getting a value of 5.0088 or larger under this
distribution is .0266.
This is less than 5% but more than 1%, hence the star.
Significant outcomes at a 1% level are shown by two stars: **.
Chi^2 tests are also reported with probabilities, as e.g.:
Normality Chi^2(2)= 2.1867 [0.3351]
The 5% Chi^2 critical values with 2 degrees of freedom is 5.99,
so here normality is not rejected (alternatively,
Prob(Chi^2 ³
2.1867) = 0.3351, which is more than 5%).
 Auxiliary regression tests

Many diagnostic tests are done through an auxiliary regression.
In this case two forms of the test are reported:
1. TR^2 which has a Chi^2(r) distribution for r restrictions;
2. (Tkr)R^2/r(1R^2), which has an F(r,Tkr) distribution.
The Fform may be better behaved in small samples.
 Autoregressive Conditional Heteroscedasticity (ARCH)

Checks whether the residuals have an ARCH structure:
E[ u_{t}^{2}  u_{t1}
, ..., u_{tr} ] =
Σ^{r}_{i=s}
α_{i} u_{ti}^{2},
with [0 ≤ s ≤ r ≤ 12] and e ~ IID(0, τ^{2}).
An Fstatistic and the αs are reported.
The null hypothesis is no ARCH, which would be rejected if the test
statistic is too high. This test is done by regressing the squared
residuals on a constant and lagged squared residuals (now some
observations are lost at the beginning of the sample).
 Normality

The Normality test checks whether the variable at hand (either a
database variable or the residuals), here called u,
are normally distributed as:
u_{t} ~ IN(0,1) with
E[u_{t}^{3}] = 0, and
E[u_{t}^{4}] = 3σ^{2}.
A Chi^2 test is reported (with 2 degrees of freedom), and the output includes
all moments up to the fourth. The null hypothesis is normality, which will be
rejected at the 5% level, if a test statistic of more than 5.99 is observed.
Full report includes:
mean:
m = T^{1} Σ^{T}_{i=1}
x_{i};
moments:
m_{j} = T^{1} Σ^{T}_{i=1}
(x_{i}  m)^{j};
(reported as m_{2}^{1/2});
skewness:
m_{3} / m_{2}^{3/2};
excess kurtosis:
m_{4} / m_{2}^{2}  3.
The reported test statistic has a smallsample correction.
Also reported is the asymptotic form of the test (skewness^{2} *T/6 +
excess_kurtosis^{2} *T/24), which requires large samples for the
asymptotic Chi^{2}(2) distribution to hold.
NOTE that the standard deviation here is based on 1/T.
If we write the model as
y = Xβ + u,
where y is (T x 1), β is
(k x 1) and X is (T x k),
then linear restrictions can be expressed in vector form as:
Rβ = r, where R is a
(p x k) matrix, and r a (p x 1) vector.
E.g. the two restrictions: α
= 1 and β
= γ
in
CONS = b + α CONS_{1}
+ β INC
+ γ INC_{1}
can be expressed as:
 0 1 0 0 
R =  , r' = [0 1].
 0 0 1 1 
PcGive allows you to test general linear restrictions by specifying R and r, in the form of a (p x k+1) matrix [R : r]. Simple linear restrictions of the form α
=... = δ
= 0 can be done by selecting the relevant variables.
The nullhypothesis Ho: Rβ = r is rejected if we observe a significant test statistic.
Two tests of linear restrictions are routinely reported in PcGive:
1. Ho: b = 0, where the teststatistic is the tratio of b.
2. Ho: α
= ... = δ
= 0 (all coefficients apart from the constant are zero).
Shown as the Fstatistic which follows R^^{2} (and can be derived from it).
Given the estimated coefficients θ,
and their variancecovariance matrix V[θ],
we can test for (non) linear restrictions of the form:
f(θ) = 0;
The null hypothesis Ho: f(θ) = 0
will be tested against Ha: f(θ)
≠
0 through a Wald test:
w = f(θ) ' (JV[θ]
J')^{1} f(θ)
where J is the Jacobian of the transformation:
J = ∂
f(θ)/∂q'.
The statistic w evaluated at θ
has a Chi^2(r) distribution, where r is the number of restrictions
(i.e. equations in f(θ)).
The null hypothesis is rejected if we observe a significant test statistic.
E.g. the two restrictions implied by the longrun solution of:
CONS = b + α CONS_{1}
+ β INC
+ γ INC_{1}
+ δ INFLAT
are expressed as
(β
+ γ) / (1  α) = 0;
δ / (1  α) = 0;
which has to be fed into PcGive as (coefficient numbering starts at 0!):
(&1 + &2) / (1  &0) = 0;
&3 / (1  &0) = 0;
The COMFAC test evaluates errorautocorrelation claims by checking
if the model's lag polynomials have factors in common.
If so, the model's lags can be simplified with an autoregressive error;
if not, the model cannot be reexpressed with an autoregressive error.
Chi^2 tests of each possible common factor and of sequences are shown.
The COMFAC test option is only feasible for unrestricted dynamic
models (which have a closed lag system), which
are not estimated by Autoregressive Least Squares.
The algorithm was developed and written by Denis Sargan and Juri Sylvestrowicz.
We have recently discovered that the COMFAC test outcome may change
if ordering of the variables in the model is changed (but only if there
are at least several lag polynomials of the same length).
This is due to testing different formulations of the restrictions
in the Wald test (i.e. computing determinants of different submatrices).
This tests if some variables should be added to the model, which can be any variables in the database matching the present sample.
If the estimated model is
y = Xβ + u,
then the omitted variables test, tests for γ
= 0 in
y = Xβ + Zγ
+v,
The Lagrange Multiplier Ftest is reported, and the null hypothesis is rejected when its value is significant.
This test is not available for Autoregressive Least Squares or nonlinear models.
Encompassing evaluates against rival models to see if they embody specific
information excluded from the model under test.
Encompassing tests are only available for single equation
models estimated by OLS or IV.
Four tests are calculated:
 1. The Cox nonnested hypotheses test (Cox, 1961)

This tests whether the adjusted likelihoods of two rival models
are compatible. It is equivalent to checking variance encompassing.
This test is invalid for IV estimation, and omitted in that case.
 2. The Ericsson Instrumental Variables test (Ericsson, 1983)

This is an IV equivalent to the Cox test.
 3. The Sargan restricted/unrestricted reduced form test (Sargan, 1964)

This checks if the restricted reduced form of a structural model
encompasses the unrestricted reduced form including exogenous regressors from rival models.
 4. The joint model Ftest

checks if each model parsimoniously encompasses the linear nesting model.
Invariance
The Ftest is invariant to variables in common between the rival models.
The Cox and the Ericsson tests are not invariant: their values
change with the choice of overlapping variables.
Consult e.g. Ericsson (1983) or Hendry and Richard (1987) for details.
Status of variables
PcGive checks for valid choices of variables:
1. Endogenous variables are matched;
2. Instruments in Model 1 are treated as exogenous in Model 2 even if you
denote them as endogenous;
3. The models must be nonnested.
Output
The output is summarized in an encompassing table:
1. The type of test statistic;
2. The value of each outcome;
3. The degrees of freedom of each test;
4. The null that Model 1 is valid is on the left;
5. The null that Model 2 is valid is on the right.
If the leftside tests are insignificant, Model 1 encompasses Model 2.
If the leftside tests are significant, Model 1 fails to encompass Model 2.
Similarly for the rightside tests with models 1 and 2 interchanged.
Model 1 encompasses Model 2 implies Model 1 also parsimoniously
encompasses the linear nesting model. If not, Model 2 contains specific data information not captured by Model 1.
The algorithm incorporated in PcGive was written by Neil Ericsson.
Identities are exact (linear) relations between variables, as in the
components of GNP adding up to the total by definition. In PcGive,
identities are created by marking identity endogenous variables as such
during dynamic system formulation.
Identities are ignored during system estimation/analysis.
They come in at the model formulation level, where the identity
is specified just like other equations.
However, there is no need to specify the coefficients of the
identity equation, as PcGive automatically derives these by estimating
the equation (which must have an R^2 of at least 0.99).
Variables can be classified as unrestricted during dynamic system formulation.
Such variables will be partialled out, prior to estimation, and their
coefficients will be reconstructed afterwards. Although unrestricted
variables do not affect the basic estimation, there are important differences:
 Following estimation:

the R^2 measures and corresponding Ftest are relative to the unrestricted variables.
 In recursive estimation:

the coefficient of unrestricted variables are fixed at the full sample values.
 In cointegration analysis:

unrestricted variables are partialled out together with the shortrun
dynamics, whereas restricted variables (other then lags of the
endogenous variables) are restricted to lie in the cointegrating space.
 In simultaneous equations estimation:

unrestricted variables are partialled out prior to estimation.
FIML estimation of the smaller model could improve convergence
properties of the nonlinear estimation process.
The simultaneous equations modelling process in PcGive starts by focusing
on the System, often called the unrestricted reduced form (URF),
which can be written as:
(1) y_{t} = π_{0} +
π_{i} y_{ti} +
π_{j} z_{tj} +
v_{t}, v_{t} ~
IN(0,Ω)
i = 1,...,m, j = m+1,...,m+r.
where y_{t}, z_{t} are respectively
(n x 1) and (q x 1) vectors of observations at time t, t = 1,...,T,
on the endogenous and nonmodelled variables. A more compact way of
writing the system is:
(2) y_{t} = Πw_{t} +
v_{t}
where w contains z, lags of z and lags of y,
and Π is (n x k).
A vector autoregression (VAR) arises when there are no z's
(but there could be a constant, seasonals or trend). An example of a
2equation system is:
CONS = β_{0} +
β_{1} CONS_{1} +
β_{2} INC_{1} +
β_{3} CONS_{2} +
β_{4} INC_{2} +
β_{5} INFL,
INC = β_{6} +
β_{7} CONS_{1} +
β_{8} INC_{1} +
β_{9} CONS_{2} +
β_{10} INC_{2} +
β_{11} INFL.
This system would be a VAR when β_{5} =
β_{11} = 0.
Nonmodelled variables can be classified as
unrestricted. Variables defined by
identities are also allowed.
To obtain a structural dynamic model, premultiply the system (2)
by a nonsingular matrix B, which yields:
(3) By_{t} = BΠw_{t} +
Bv_{t}.
We shall write this as:
(4) By_{t} + Cw_{t} = u_{t},
t = 1,...,T; u_{t} ~ IN(0,σ),
or succinctly:
Ax_{t} = u_{t}
The restricted reduced form (RRF) corresponding to this model is
(note that the Π of (5) is a restricted
version of that in (3)):
(5) y_{t} = Πw_{t} +
v_{t}, with Π
= inv(B)C.
Identification of the model, through
within equation restrictions on A, is required for estimation.
Some equations of the model could be identities.
An example of a model with the previous system as unrestricted reduced form is:
CONS = β_{0} +
β_{1} CONS_{1} +
β_{2} INC +
β_{3} INFL,
INC = β_{4} +
β_{5} INC_{1}.
The philosophy behind PcGive is first to develop a congruent system.
If the system displays symptoms of misspecification, there is little
point in imposing further restrictions on it. From a congruent system
a model is derived.
A system in PcGive is formulated by:
 which variables y_{t}, z_{t} are involved;
 the orders of the lag polynomials;
 classification of the ys in endogenous variables and identity endogenous variables;
 any nonmodelled variable may be classified as unrestricted.
Such variables will be partialled out, prior to estimation, and
their coefficients will be reconstructed afterwards.
A model in PcGive is formulated by:
 which variables enter each equation, including identities;
 coefficients of identity equations need not be specified, as PcGive
automatically derives these by estimating the equation (requires an R^2 of at least 0.99);
 constraints, if the model is going to be estimated by CFIML or RCFIML.
When a model has been formulated, it can be
estimated and evaluated, a detailed
description of estimators and tests is in Volume II.
PcGive facilitates a generaltosimple modelling strategy.
Cointegration Analysis
The vector autoregression can be written in equilibriumcorrection form as:
Δy_{t}=( π_{1}+π_{2}I_{n})
y_{t1}π_{2}Δy_{t1}+Φq_{t}+v_{t},

or, writing P_{0}=π_{1}+π_{2}I, and δ_{1}=π:
Δy_{t}=P_{0}y_{t1}+δ_{1}Δy_{t1}+Φq_{t}+v_{t}.
  
Equation (eq:1.1) shows that the matrix P_{0}
determines how the level of the process y enters the system: for
example, when P_{0}=0, the dynamic evolution does not depend
on the levels of any of the variables. This indicates the importance of the
rank of P_{0} in the analysis. P_{0}=∑π_{i}I_{n} is the matrix of longrun responses. The statistical hypothesis of cointegration is:
Under this hypothesis, P_{0} can be written as the product of two
matrices:
where α and β have dimension n×p, and
vary freely. As suggested by Søren Johansen, such a restriction can
be analyzed by maximum likelihood methods.
So, although v_{t}~IN_{n}[0,Ω], and
hence is stationary, the n variables in y_{t} need not all be
stationary. The rank p of P_{0} determines how many linear
combinations of variables are I(0). If p=n, all variables in y_{t} are I(0), whereas p=0 implies that Δy_{t} is
I(0). For 0<p<n there are p cointegrating relations β'y_{t} which are I(0). At this stage, we
are not discussing I(2)ness, other than assuming it is not present.
The approach in PcGive to determining cointegration rank, and the associated
cointegrating vectors, is based on the Johansen procedure.
All model estimation methods in PcGive are derived from the
Estimator Generating Equation (EGE).
We require the reduced form to be a congruent data model,
for which the structural specification is a more parsimonious representation.
The structural model is:
BY' + CW' = U',
or using A = (B : C):
AX' = U',
with the restricted reduced form (RRF)
Y'= ΠW' + V'
(so Π = inv(B)C).
Writing Q' = (Π' : I),
we have that AQ = 0, and can write the restricted reduced form as:
X'= QW' + V'.
The structural model involves regressors which are correlated
with the error term. Instruments (reduced form regressors) are
used in place of structural form regressors to estimate the unknown
coefficients in A, denoted θ.
The general estimation formulation is based on the EGE.
The available estimation methods are
described in Volume II.
1SLS applies OLS to each equation, imposing a diagonal
errorr varance matrix.
This estimator is not consistent for a simultaneous system, but is
offered for systems that are large relative to the data available,
where its MSE properties may be the best that can be achieved.
PcGive allows you to retain observations to compute forecasts and forecast statistics. Both 1step ahead (static, expost) and hstep ahead (dynamic, exante) forecasts are available. The 1step forecasts are computed automatically after system and model estimation if observations are reserved. Three 1step test statistics are offered:
 Using Ω: This test ignores parameter
uncertainty and intercorrelations between forecast errors, thus taking
only innovation uncertainty into account.
 using V[e]: This test takes parameter uncertainty into account,
but ignores intercorrelations between forecast errors.
 using V[E] (only for the system): This statistic takes both
parameter uncertainty and intercorrelations between forecast errors into
account, making it a better calibrated test statistic.
Dynamic forecasts are available separately, up to the end of
the database sample period (observations are required for all exogenous variables, but not for endogenous variables and their lags). Dynamic forecasts can be with or without 95% error bars, but only the innovation uncertainty is allowed for in the computed error variances. Two types of forecasts are available for graphing:
 Dynamic forecasts
Select this to graph the dynamic forecasts (the sequence of
1, 2, 3,...,hstep forecasts).
 hstep forecasts
Up to h forecasts, the graphs will be identical to the dynamic forecasts.
Thereafter values of the endogenous variables which go more than h periods
back will use actual values.
The database sample can be extended with
ease if longerhorizon forecasts are desired.
Seceral formats are available to load and save matrices:
 in7, the OxMetrics format.
 xls, the Excel format.
 csv, the commaseparated spreadsheet format,
 mat, a text file with a matrix, preceded by the matrix dimensions.
An example of a matrix file is:
++
¦ 2 3 ¦ < dimensions, a 2 by 3 matrix
¦//comment¦ < a line of comment
¦ 1 0 0 ¦ < first row of the matrix
¦ 0 1 .5 ¦ < second row of the matrix
++
With a closed lag system is meant that there are no gaps in the lag polynomials.
So a closed system is e.g.:
CONS = b + α CONS_{1}
+ β INC
+ γ INC_{1}
however, without INC (i.e. β
= 0), it wouldn't be closed. You could then replace INC
lagged by INC1 = lag(INC, 1), and close the lag system
(because PcGive will not know that INC1 is a lagged variable;
PcGive only recognizes lags when they are created within
the model formulation dialog).
The data sample for analysis is automatically selected
to not include any missing values within the sample.
In crosssection regression, any observation with
missing values is automatically omitted from the analysis,
so insample observations with missing values are simply skipped.
This file last changed .