EViews Help: cointreg

cointreg

Estimate a cointegrating equation using Fully Modified OLS (FMOLS), Canonical Cointegrating Regression (CCR), or Dynamic OLS (DOLS) in single time series settings, and Panel FMOLS and DOLS in panel workfiles.

Syntax

cointreg(options) y x1 [x2 x3 ...] [@determ determ_spec] [@regdeterm regdeterm_spec]

List the coint keyword, followed by the dependent variable and a list of the cointegrating variables.

Cointegrating equation specifications that include a constant, linear, or quadratic trends, should use the “trend=” option to specify those terms. If any of those terms are in the stochastic regressors equations but not in the cointegrating equation, they should be specified using the “regtrend=” option.

Deterministic trend regressors that are not covered by the list above may be specified using the keywords @determ and @regdeterm. To specify deterministic trend regressors that enter into the regressor and cointegrating equations, you should add the keyword @determ followed by the list of trend regressors. To specify deterministic trends that enter in the regressor equations but not the cointegrating equation, you should include the keyword @regdeterm followed by the list of trend regressors.

Basic Options

method=arg (default=“fmols”)	Estimation method: Fully Modified OLS (“fmols”), Canonical Cointegrating Regression (“ccr”), Dynamic OLS (“dols”) Note that CCR estimation is not available in panel settings.
trend=arg (default=“const”)	Specification for the powers of trend to include in the cointegrating and regressor equations: None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Note that the specification implies all trends up to the specified order so that choosing a quadratic trend instructs EViews to include a constant and a linear trend term along with the quadratic.
regtrend=arg (default=“none”)	Additional trends to include in the regressor equations (but not the cointegrating equation): None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Only trend orders higher than those specified by “trend=” will be considered. Note that the specification implies all trends up to the specified order so that choosing a quadratic trend instructs EViews to include a constant and a linear trend term along with the quadratic.
regdiff	Estimate the regressor equation innovations directly using the difference specifications.
coef=arg	Specify the name of the coefficient vector; the default behavior is to use the “C” coefficient vector.
prompt	Force the dialog to appear from within a program.
p	Print results.

In addition to these options, there are specialized options for each estimation method.

Panel Options

panmethod=arg (default=“pooled”)	Panel estimation method: pooled (“pooled”), pooled weighted (“weighted”), grouped (“grouped”)
pancov=sandwich	Estimate the coefficient covariance using a sandwich method that allows for cross-section heterogeneity.

Options for FMOLS and CCR

To estimate FMOLS or CCR use the “method=fmols” or “method=ccr” options. The following options control the computation of the symmetric and one-sided long-run covariance matrices and the estimate of the coefficient covariance.

HAC Whitening Options

lag=arg (default=0)	Lag specification: integer (user-specified lag value), “a” (automatic selection).
infosel=arg (default=“aic”)	Information criterion for automatic selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn) (if “lag=a”).
maxlag=integer	Maximum lag-length for automatic selection (optional) (if “lag=a”). The default is an observation-based maximum.

HAC Kernel Options

kern=arg (default=“bart”)	Kernel shape: “none” (no kernel), “bart” (Bartlett, default), “bohman” (Bohman), “daniell” (Daniell), “parzen” (Parzen), “parzriesz” (Parzen-Riesz), “parzgeo” (Parzen-Geometric), “parzcauchy” (Parzen-Cauchy), “quadspec” (Quadratic Spectral), “trunc” (Truncated), “thamm” (Tukey-Hamming), “thann” (Tukey-Hanning), “tparz” (Tukey-Parzen).
bw=arg (default=“nwfixed”)	Bandwidth:: “fixednw” (Newey-West fixed), “andrews” (Andrews automatic), “neweywest” (Newey-West automatic), number (User-specified bandwidth).
nwlag=integer	Newey-West lag-selection parameter for use in nonparametric bandwidth selection (if “bw=neweywest”).
bwoffset=integer (default=0)	Apply integer offset to bandwidth chosen by automatic selection method (“bw=andrews” or “bw=neweywest”).
bwint	Use integer portion of bandwidth chosen by automatic selection method (“bw=andrews” or “bw=neweywest”).

Coefficient Covariance

nodf	Do not degree-of-freedom correct the coefficient covariance estimate.

Panel Options

hetfirst

Estimate the first-stage regression assuming heterogeneous coefficients. For FMOLS specifications estimated using pooled or pooled weighted methods

(“panmethod =pooled”, “panmethod=weighted”)

Options for DOLS

To estimate using DOLS use the “method=dols” option. The following options control the specification of the lags and leads and the estimate of the coefficient covariance.

lltype=arg (default=“fixed”)	Lag-lead method: fixed values (“fixed”), automatic selection - Akaike (“aic”), automatic - Schwarz (“sic”), automatic - Hannan-Quinn (“hqc”), None (“none”).
lag=arg	Lag specification: integer (required user-specified number of lags if “lltype=fixed”).
lead=arg	Lead specification: integer (required user-specified number of lags if “lltype=fixed”).
maxll=integer	Maximum lag and lead-length for automatic selection (optional user-specified integer if “lltype=” is used to specify automatic selection). The default is an observation-based maximum.
cov=arg	Coefficient covariance method: (default) long-run variance scaled OLS, unscaled OLS (“ols”), White (“white”), Newey-West (“hac”).
nodf	Do not degree-of-freedom correct the coefficient covariance estimate.

For the default covariance calculation or “cov=hac”, the following options control the computation of the long-run variance or robust covariance:

HAC Covariance Whitening Options (if default covariance or “cov=hac”)

covlag=arg (default=0)	Lag specification: integer (user-specified lag value), “a” (automatic selection).
covinfosel=arg (default=“aic”)	Information criterion for automatic selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn) (if “lag=a”).
covmaxlag=integer	Maximum lag-length for automatic selection (optional) (if “lag=a”). The default is an observation-based maximum.

HAC Covariance Kernel Options (if default covariance or “cov=hac”)

covkern=arg (default=“bart”)	Kernel shape: “none” (no kernel), “bart” (Bartlett, default), “bohman” (Bohman), “daniell” (Daniel), “parzen” (Parzen), “parzriesz” (Parzen-Riesz), “parzgeo” (Parzen-Geometric), “parzcauchy” (Parzen-Cauchy), “quadspec” (Quadratic Spectral), “trunc” (Truncated), “thamm” (Tukey-Hamming), “thann” (Tukey-Hanning), “tparz” (Tukey-Parzen).
covbw=arg (default=“nwfixed”)	Bandwidth: “fixednw” (Newey-West fixed), “andrews” (Andrews automatic), “neweywest” (Newey-West automatic), number (User-specified bandwidth).
covnwlag=integer	Newey-West lag-selection parameter for use in nonparametric bandwidth selection (if “covbw=neweywest”).
covbwoffset=integer (default=0)	Apply integer offset to bandwidth chosen by automatic selection method (“bw=andrews” or “bw=neweywest”).
covbwint	Use integer portion of bandwidth chosen by automatic selection method (“bw=andrews” or “bw=neweywest”).

Panel Options

Weighted coefficient or coefficient covariance estimation in panel DOLS requires individual estimates of the long-run variances of the residuals. You may compute these estimates using the standard default long-run variance options, or you may choose to estimate it using the ordinary variance.

For weighted estimation we have:

panwgtlag=arg (default=0)	Lag specification: integer (user-specified lag value), “a” (automatic selection).
panwgtinfosel=arg (default=“aic”)	Information criterion for automatic selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn) (if “lrvarlag=a”).
panwgtmaxlag=integer	Maximum lag-length for automatic selection (optional) (if “lrvarlag=a”). The default is an observation-based maximum.
panwgtkern=arg (default=“bart”)	Kernel shape: “none” (no kernel), “bart” (Bartlett, default), “bohman” (Bohman), “daniell” (Daniell), “parzen” (Parzen), “parzriesz” (Parzen-Riesz), “parzgeo” (Parzen-Geometric), “parzcauchy” (Parzen-Cauchy), “quadspec” (Quadratic Spectral), “trunc” (Truncated), “thamm” (Tukey-Hamming), “thann” (Tukey-Hanning), “tparz” (Tukey-Parzen).
panwgtbw=arg (default=“nwfixed”)	Bandwidth:: “fixednw” (Newey-West fixed), “andrews” (Andrews automatic), “neweywest” (Newey-West automatic), number (User-specified bandwidth).
panwgtnwlag=integer	Newey-West lag-selection parameter for use in nonparametric bandwidth selection (if “bw=neweywest”).
panwgtbwoffset=integer (default=0)	Apply offset to automatically selected bandwidth. For settings where “cov=hac”, “covkern=” is specified, and “covbw=” is not user-specified.
panwgtbwint	Use integer portion of bandwidth chosen by automatic selection method (“bw=andrews” or “bw=neweywest”).

For the coefficient covariance estimation we have:

lrvar=ordinary	Compute DOLS estimates of the long-run residual variance used in covariance calculation using the ordinary variance.
lrvarlag=arg (default=0)	For DOLS estimates of the long-run residual variance used in covariance calculation, lag specification: integer (user-specified lag value), “a” (automatic selection).
lrvarinfosel=arg (default=“aic”)	For DOLS estimates of the long-run residual variance used in covariance calculation, information criterion for automatic selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn) (if “lrvarlag=a”).
lrvarmaxlag=integer	For DOLS estimates of the long-run residual variance used in covariance calculation, maximum lag-length for automatic selection (optional) (if “lrvarlag=a”). The default is an observation-based maximum.
lrvarkern=arg (default=“bart”)	For DOLS estimates of the long-run residual variance used in covariance calculation, Kernel shape: “none” (no kernel), “bart” (Bartlett, default), “bohman” (Bohman), “daniell” (Daniell), “parzen” (Parzen), “parzriesz” (Parzen-Riesz), “parzgeo” (Parzen-Geometric), “parzcauchy” (Parzen-Cauchy), “quadspec” (Quadratic Spectral), “trunc” (Truncated), “thamm” (Tukey-Hamming), “thann” (Tukey-Hanning), “tparz” (Tukey-Parzen).
lrvarbw=arg (default=“nwfixed”)	For DOLS estimates of the long-run residual variance used in covariance calculation, bandwidth:: “fixednw” (Newey-West fixed), “andrews” (Andrews automatic), “neweywest” (Newey-West automatic), number (User-specified bandwidth).
lrvarnwlag=integer	For DOLS estimates of the long-run residual variance used in covariance calculation, Newey-West lag-selection parameter for use in nonparametric bandwidth selection (if “bw=neweywest”).
lrvarbwoffset=integer (default=0)	For DOLS estimates of the long-run residual variance used in covariance calculation, apply offset to automatically selected bandwidth. For settings where “cov=hac”, “covkern=” is specified, and “covbw=” is not user-specified.
lrvarbwint	For DOLS estimates of the long-run residual variance used in covariance calculation, use integer portion of bandwidth.

Examples

FMOLS and CCR

To estimate, by FMOLS, the cointegrating equation for LC and LY including a constant, you may use:

cointreg(nodf, bw=andrews) lc ly

The long-run covariances are estimated nonparametrically using a Bartlett kernel and a bandwidth determined by the Andrews automatic selection method. The coefficient covariances are estimated with no degree-of-freedom correction.

To include a linear trend term in a model where the long-run covariances computed using the Quadratic Spectral kernel and a fixed bandwidth of 10, enter:

cointreg(trend=linear, nodf, bw=10, kern=quadspec) lc ly

A model with a cubic trend may be estimated using:

cointreg(trend=linear, lags=2, bw=neweywest, nwlag=10, kernel=parzen) lc ly @determ @trend^3

Here, the long-run covariances are estimated using a VAR(2) prewhitened Parzen kernel with Newey-West nonparametric bandwidth determined using 10 lags in the autocovariance calculations.

cointreg(trend=quadratic, bw=andrews, lags=a, infosel=aic, kernel=none, regdiff) lc ly @regdeterm @trend^3

estimates a restricted model with a cubic trend term that does not appear in the cointegrating equation using a parametric VARHAC with automatic lag length selection based on the AIC. The residuals for the regressors equations are obtained by estimating the difference specification.

To estimate by CCR, we provide the “method=ccr” option. The command

cointreg(method=ccr, lag=2, bw=andrews, kern=quadspec) lc ly

estimates, by CCR, the constant only model using a VAR(2) prewhitened Quadratic Spectral and Andrews automatic bandwidth selection.

cointreg(method=ccr, trend=linear, lag=a, maxlag=5, bw=andrews, kern=quadspec) lc ly

modifies the previous estimates by adding a linear trend term to the cointegrating and regressors equations, and changing the VAR prewhitening to automatic selection using the default SIC with a maximum lag length of 5.

cointreg(method=ccr, trend=linear, regtrend=quadratic, lag=a, maxlag=5, bw=andrews) lc ly

adds a quadratic trend term to the regressors equations only, and changes the kernel to the default Bartlett.

DOLS

cointreg(method=dols, trend=linear, nodf, lag=4, lead=4) lc ly

estimates the linear specification using DOLS with four lags and leads. The coefficient covariance is obtained by rescaling the no d.f.-correction OLS covariance using the long-run variance of the residuals computed using the default Bartlett kernel and default fixed Newey-West bandwidth.

cointreg(method=dols, trend=quadratic, nodf, lag=4, lead=2, covkern=bohman, covbw=10) lc ly @determ @trend^3

estimates a cubic specification using 4 lags and 2 leads, where the coefficient covariance uses a Bohman kernel and fixed bandwidth of 10.

cointreg(method=dols, trend=quadratic, nodf, lag=4, lead=2, cov=hac, covkern=bohman, covbw=10) lc ly @determ @trend^3

estimates the same specification using a HAC covariance in place of the scaled OLS covariance.

cointreg(method=dols, trend=quadratic, lltype=none, cov=ols) lc ly @determ @trend^3

computes the Static OLS estimates with the usual OLS d.f. corrected coefficient covariance.

Cross-references

See “Cointegrating Regression” for a discussion of single equation cointegrating regression. See “Panel Cointegration Estimation” for discussion of estimation in panel settings.

See “Technical Discussion” for a discussion of VEC estimation.