Estimate a vector error correction model (VEC).
Syntax
var_name.ec(options) lag_pairs endog_list [@ x1 x2 x3 ...] [@exogsr sx1 sx2 sx3 ...] [@exoglr lx1 lx2 lx3 ...] [@exogboth bx1 bx2 bx3 ...]
Specify the order of the VEC by entering lag_pairs consisting of one or more pairs of lag intervals, and then list the series or groups to be used as endogenous variables.
Note that the lag orders are for the differences in the error correction representation of the VEC, not the levels representation of the VAR. If you are comparing results obtained elsewhere, you should be certain that the specifications for the lag orders are comparable.
In addition, you may optionally provide:
• an “@”-sign or “@exogsr” followed by a list of exogenous variables in the short-run equation only
• “@exoglr” followed by a list of exogenous variables in the long-run relation only
• “@exogboth” followed by a list of exogenous variables in both the long-run relation and the short-run equations
Do not include an intercept or trend in the VEC specification, these deterministic trend terms should be specified using the “determ=” option, as described below.
Options
Deterministic Trend Option
There are 8 different deterministic trend assumptions that you may specify using the “determ=arg” option.
These cases correspond to whether the intercept (“c”) and the trend (“t”) are either
• not included (“n”)
• in the long-run cointegrating relation only (“l”)
• in the short-run equation only (“s”)
• in both the long and short-run equations (“b”)
The values of arg are text shortcuts formed by joining a text shortcut for the intercept specification with a text shortcut for the trend specification.
The individual intercept and trend specifications are formed by joining the “c” and the “t” with the appropriate letter describing inclusion in the long and short-run equations.
For example,
• “cb” indicates that the constant is in both the long and short-run equation
• “tl” indicates that the trend is in the long-run cointegrating equation only
so that
• “cbtl” indicates that the constant is in both the long and short-run and the trend is in the long-run only
Using this convention (along with a special “none” option), we may easily describe options arguments for all 8 deterministic cases:
cntn, none | Case 1: No deterministic terms. Corresponding VAR model has no deterministic terms. |
cltn | Case 2: Restricted constant. Constant only in the cointegrating relations. Corresponding VAR has a constant. |
cbtn (default) | Case 3 (JHJ): Unrestricted constant Constant included both in the short-run equation and (artificially) in the cointegrating relations via orthogonalization. Corresponding VAR has a constant and trend. |
cstn | Case 3: Unrestricted constant Constant only in the short-run equation. Corresponding VAR has a trend. |
cbtl | Case 4 (JHJ): Unrestricted constant and restricted trend Constant included both in the short-run equation and (artificially) in the cointegrating relations via orthogonalization, and trend included only in the cointegrating relations. Corresponding VAR has a constant and trend. |
cstl | Case 4: Unrestricted constant and restricted trend Constant only in the short-run equation, and trend only in the cointegrating relation. Corresponding VAR has a trend. |
cbtb | Case 5 (JHJ): Unrestricted constant and trend Constant and trend both included in the short-run equation and (artificially) in the cointegrating relations via orthogonalization. Corresponding VAR has a constant, linear, and quadratic trend. |
csts | Case 5: Unrestricted constant and trend Constant and trend both included in the short-run equation. Corresponding VAR has a linear and quadratic trend. |
Other Options
rank = integer (default = 1) | Number of cointegrating relationships. |
restrict | Impose restrictions as specified by the
Var::append proc, or the “restspec=” option. |
restspec="spec" | Define the restricted VEC specification where spec is a space a space delimited list of VEC coefficient restrictions. |
m = integer, maxit = integer | Maximum number of iterations for restricted estimation (only valid if you choose the restrict option). |
c = scalar, cvg = scalar | Convergence criterion for restricted estimation. (only valid if you choose the restrict option). |
prompt | Force the dialog to appear from within a program. |
p | Print the results view. |
Examples
var macro1.ec 1 4 m1 gdp tb3
declares a var object MACRO1 and estimates a VEC with four lagged first differences, three endogenous variables and one cointegrating equation using the default trend option “c”.
var term.ec(determ=cstl, rank=2) 1 2 4 4 tb1 tb3 tb6 @ d2 d3 d4
declares a var object TERM and estimates a VEC with lagged first differences of order 1, 2, 4, three endogenous variables, three exogenous variables, and two cointegrating equations using deterministic trend option “determ=cstl” for a model with a constant in the short-run equation, and a trend in the long-run cointegrating relation.
var macro1.ec(determ=cstl, rank=2) 1 2 4 4 tb1 tb3 tb6 @exogsr exog1 @exoglr exog2 @exogdual exog3
The line above declares a VAR object MACRO01 with the same basic specification as TERM, but with an additional short-run exogenous variable EXOG1, a long-run exogenous variable EXOG2, and a dual exogenous variable EXOG3.
Cross-references
See
Var::ls and
Var::bvar for estimation of ordinary VARs and Bayesian VAR models. See also
Var::coint and
Var::append.