Equation—157
Equation
Equation object. Equations are used for single equation estimation, testing, and forecasting.
Equation Declaration
equation ............... |
declare equation object (p. 286). |
To declare an equation object, enter the keyword equation, followed by a name:
equation eq01
and an optional specification:
equation r4cst.ls r c r(-1) div
equation wcd.ls q=c(1)*n^c(2)*k^c(3)
Equation Methods
arch...................... |
autoregressive conditional heteroskedasticity (ARCH and GARCH) |
|
(p. 206). |
binary................... |
binary dependent variable models (includes probit, logit, gompit) |
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models (p. 222). |
censored ............... |
censored and truncated regression (includes tobit) models |
|
(p. 238). |
count.................... |
count data modeling (includes poisson, negative binomial and |
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quasi-maximum likelihood count models) (p. 258). |
gmm..................... |
generalized method of moments (p. 310). |
logit...................... |
logit (binary) estimation (p. 344). |
ls.......................... |
linear and nonlinear least squares regression (includes weighted |
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least squares and ARMAX) models (p. 345). |
ordered ................. |
ordinal dependent variable models (includes ordered probit, |
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ordered logit, and ordered extreme value models) (p. 378). |
probit ................... |
probit (binary) estimation (p. 410). |
tsls ....................... |
linear and nonlinear two-stage least squares (TSLS) regression |
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models (includes weighted TSLS, and TSLS with ARMA errors) |
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(p. 515). |
Equation Views
archtest................. |
LM test for the presence of ARCH in the residuals (p. 210). |
arma..................... |
Examine ARMA structure of estimated equation (p. 214). |
auto...................... |
Breusch-Godfrey serial correlation Lagrange Multiplier (LM) test |
|
(p. 216). |
158—Appendix A. Object, View and Procedure Reference
cellipse ................ |
Confidence ellipses for coefficient restrictions (p. 236). |
chow ................... |
Chow breakpoint and forecast tests for structural change (p. 241). |
coefcov ................ |
coefficient covariance matrix (p. 244). |
correl ................... |
correlogram of the residuals (p. 256). |
correlsq................ |
correlogram of the squared residuals (p. 257). |
derivs .................. |
derivatives of the equation specification (p. 273). |
fixedtest ............... |
test significance of estimates of fixed effects (p. 299). |
garch ................... |
conditional standard deviation graph (only for equations estimated |
|
using ARCH) (p. 308). |
grads ................... |
examine the gradients of the objective function (p. 315). |
hist ...................... |
histogram and descriptive statistics of the residuals (p. 322). |
label .................... |
label information for the equation (p. 330). |
means.................. |
descriptive statistics by category of the dependent variable (only |
|
for binary, ordered, censored and count equations) (p. 367). |
output.................. |
table of estimation results (p. 380). |
predict ................. |
prediction (fit) evaluation table (only for binary and ordered equa- |
|
tions) (p. 408). |
ranhaus ............... |
Hausman test for correlation between random effects and regres- |
|
sors (p. 413). |
representations..... |
text showing specification of the equation (p. 417). |
reset .................... |
Ramsey’s RESET test for functional form (p. 420). |
resids ................... |
display, in tabular form, the actual and fitted values for the depen- |
|
dent variable, along with the residuals (p. 422). |
results.................. |
table of estimation results (p. 423). |
rls........................ |
recursive residuals least squares (only for non-panel equations |
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estimated by ordinary least squares, without ARMA terms) |
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(p. 423). |
testadd ................. |
likelihood ratio test for adding variables to equation (p. 500). |
testdrop ............... |
likelihood ratio test for dropping variables from equation (p. 503). |
testfit ................... |
performs Hosmer and Lemeshow and Andrews goodness-of-fit |
|
tests (only for equations estimated using binary) (p. 505). |
wald .................... |
Wald test for coefficient restrictions (p. 530). |
white ................... |
White test for heteroskedasticity (p. 542). |
Equation Procs
displayname......... |
set display name (p. 276). |
fit ........................ |
static forecast (p. 297). |
forecast ................ |
dynamic forecast (p. 300). |
|
Equation—159 |
|
|
makederivs ........... |
make group containing derivatives of the equation specification |
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(p. 351). |
makegarch............ |
create conditional variance series (only for ARCH equations) |
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(p. 352). |
makegrads ............ |
make group containing gradients of the objective function |
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(p. 353). |
makelimits............ |
create vector of estimated limit points (only for ordered models) |
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(p. 357). |
makemodel........... |
create model from estimated equation (p. 358). |
makeregs .............. |
make group containing the regressors (p. 359). |
makeresids ........... |
make series containing residuals from equation (p. 359). |
updatecoefs........... |
update coefficient vector(s) from equation (p. 521). |
Equation Data Members
Scalar Values
@aic..................... |
Akaike information criterion. |
@coefcov(i,j) ....... |
covariance of coefficient estimates i and j. |
@coefs(i).............. |
i-th coefficient value. |
@dw .................... |
Durbin-Watson statistic. |
@f........................ |
F-statistic. |
@hq ..................... |
Hannan-Quinn information criterion. |
@jstat................... |
J-statistic — value of the GMM objective function (for GMM). |
@logl ................... |
value of the log likelihood function. |
@meandep ........... |
mean of the dependent variable. |
@ncoef................. |
number of estimated coefficients. |
@r2...................... |
R-squared statistic. |
@rbar2................. |
adjusted R-squared statistic. |
@regobs ............... |
number of observations in regression. |
@schwarz ........... |
Schwarz information criterion. |
@sddep ................ |
standard deviation of the dependent variable. |
@se...................... |
standard error of the regression. |
@ssr..................... |
sum of squared residuals. |
@stderrs(i) ........... |
standard error for coefficient i. |
@tstats(i) ............. |
t-statistic value for coefficient i. |
c(i) ....................... |
i-th element of default coefficient vector for equation (if applica- |
|
ble). |
160—Appendix A. Object, View and Procedure Reference
Vectors and Matrices
@coefcov ............. |
covariance matrix for coefficient estimates. |
@coefs................. |
coefficient vector. |
@stderrs .............. |
vector of standard errors for coefficients. |
@tstats ................ |
vector of t-statistic values for coefficients. |
Equation Examples
To apply an estimation method (proc) to an existing equation object:
equation ifunc
ifunc.ls r c r(-1) div
To declare and estimate an equation in one step, combine the two commands:
equation value.tsls log(p) c d(x) @ x(-1) x(-2) equation drive.logit ifdr c owncar dist income equation countmod.count patents c rdd
To estimate equations by list, using ordinary and two-stage least squares:
equation ordinary.ls log(p) c d(x)
equation twostage.tsls log(p) c d(x) @ x(-1) x(-2)
You can create and use other coefficient vectors:
coef(10) a
coef(10) b
equation eq01.ls y=c(10)+b(5)*y(-1)+a(7)*inc
The fitted values from EQ01 may be saved using,
series fit = eq01.@coefs(1) + eq01.@coefs(2)*y(-1) + eq01.@coefs(3)*inc
or by issuing the command:
eq01.fit fitted_vals
To perform a Wald test:
eq01.wald a(7)=exp(b(5))
You can save the t-statistics and covariance matrix for your parameter estimates:
vector eqstats=eq01.@tstats
matrix eqcov=eq01.@coefcov