PANELDOLS Procedure

@PANELDOLS is a procedure for estimating the cointegrating vectors using the multivariate group mean panel DOLS from Pedroni(2001). A companion procedure for estimating with fully modified OLS (FM OLS) rather than DOLS is @PANELFM.

@PANELDOLS( options ) start end

# list of variables (list dependent variable first)

Parameters

start, end

range for regression. By default, the maximum range permitted by all variables involved in the regression allowing for lags.

Options

DET=NONE/[CONSTANT]/TREND

TDUM/[NOTDUM]

Use TDUM to subtract out common time effects

AVERAGE=[SIMPLE]/SQRT/PRECISION

Determines how the individual estimates are combined to compute the full sample estimate. AVERAGE=SIMPLE takes a simple arithmetic average. This is the default, and the behavior of Pedroni's original program. AVERAGE=SQRT weights each individual by the diagonal matrix formed by taking the square roots of the precision matrix (inverse covariance matrix) of the estimates for that individual. This matches up with the averaging done in computing the t-statistics, that is, the coefficients and covariance matrix from AVERAGE=SQRT will reproduce the average t-statistics. AVERAGE=PRECISION weights each individual by the precision of its estimates.

LAGS=number of lags to use in the Bartlett kernel (for computing the variance) [5]

DLAGS=number of lags and leads on the differences [2]

SMPL=standard SMPL option[not used]

PRINT=NONE/SHORT/[FULL]

Sets the level of printed output. PRINT=FULL includes the estimates for the individuals, while PRINT=SHORT just does the full sample estimates.

TITLE="title of report" ["Mean Group Panel FM Estimation"]

BVEC=VECTOR with hypothesized slope coefficients [all zeros]

The t-statistics reported are for tests against this vector.

Important Note

DOLS can very quickly exhaust the degrees of freedom in a data set. There are 2*DLAGS+1 (by default 5) added regressors in the differences for each right side endogenous variable plus you lose DLAGS*2+1 data points allowing for lags and leads and differences. So 20 observations per individual, two right side endogenous variables, DLAGS=2 leaves you with 15 usable observations, and 13 regressors (constant + 2 current RHS + 2 x 5 additional lags and leads on the differences).

Variables Defined

%BETA	group estimates of coefficients (VECTOR)
%STDERRS	group estimates of standard errors (VECTOR)
%TSTATS	group estimates of t-statistics (for testing BVEC if you include it) (VECTOR)
%XX	estimates of covariance matrix of group estimates (SYMMETRIC)
%RESIDS	cointegrating residuals (computed at the group mean coefficients)
%%IBETAS	individual coefficients (VECTOR[VECTOR] with %%IBETAS(i) the coefficient vector for individual i).
%%ISTDERRS	individual standard errors (VECTOR[VECTOR] with %%ISTDERRS(i) the standard error vector for individual i).
%%ITSTATS	individual t-statistics (for testing BVEC if you include it) (VECTOR[VECTOR] with %%ITSTATS(i) the t-statistic vector for individual i).
%%IXX	individual covariance matrices (VECTOR[SYMM] with %%IXX(i) as the covariance matrix for individual i).

Example

open data pedroni_ppp.xls

calendar(panelobs=246,m) 1973:6

data(format=xls,org=columns) 1//1973:06 20//1993:11 ae rf wpi cpi uswpi $

uscpi country entry year month

set logratio = log(cpi/uscpi)

set logexrate = log(ae)

* The individual tests are done with 4 lags for each

@paneldols(dlags=4,lags=4,bvec=||1.0||,print=full,average=simple,$

ibetas=dolsbeta,itstats=dolststat)

# logexrate logratio

The cointegrating regression is LOGEXRATE on LOGRATIO. Since the theory is that the coefficient should be 1, the BVEC=||1.0|| means that all t-statistics are for tests against that.

Sample Output

Mean Group Panel DOLS Estimation

LHS Variable LOGEXRATE

Individuals 20

Time Periods 246

Dynamic Lags 4

common time dummies NOT included

RHS Variable H0 Coefficient

LOGRATIO 1.000000

Member Variable Coefficient t-Statistic

No.1 LOGRATIO 0.671124 -1.881806

No.2 LOGRATIO 0.230249 -1.925718

No.3 LOGRATIO 1.897945 2.800014

No.4 LOGRATIO 2.210515 7.960324

No.5 LOGRATIO 0.906373 -0.589841

No.6 LOGRATIO 1.084850 1.105162

No.7 LOGRATIO 0.658927 -2.026044

No.8 LOGRATIO 1.156580 0.805709

No.9 LOGRATIO 1.363110 2.213636

No.10 LOGRATIO 1.426408 1.846377

No.11 LOGRATIO 1.748779 4.942346

No.12 LOGRATIO 0.988492 -0.359850

No.13 LOGRATIO 1.093443 2.418046

No.14 LOGRATIO 1.017810 0.177761

No.15 LOGRATIO 1.114728 5.741540

No.16 LOGRATIO 1.023828 0.596723

No.17 LOGRATIO 1.371505 10.773928

No.18 LOGRATIO 1.027841 3.535930

No.19 LOGRATIO 2.063008 7.672863

No.20 LOGRATIO 0.877218 -1.438148

*************

Group LOGRATIO 1.196637 9.921199