help: xtreghet dialog:

Title

xtreghet: MLE Random-Effects with Multiplicative Heteroscedasticity Panel Data Regression

Table of Contents

Syntax

Description

Model

Options

Model Selection Diagnostic Criteria

Groupwise Heteroscedasticity Tests

Saved Results

References

*** Examples

Author

Syntax

xtreghet depvar indepvars [if] [in] , id(var) it(var) [ model(xtmln|xtmlh) mhet(varlist)

mfx(lin|log) lmhet diag predict(new_var) resid(new_var)

iter(#) tech(name) noconstant coll zero tolog nolog level(#) vce(vcetype) ]

Description

xtreghet Stata Module to Estimate MLE Random-Effects with Multiplicative Heteroscedasticity Panel Data Regression, and calculate Heteroscedasticity tests, Model Selection Diagnostic Criteria, and Marginal Effects and Elasticities

R2, R2 Adjusted, and F-Test, are obtained from 4 ways:

1- (Buse 1973) R2.

2- Raw Moments R2.

3- squared correlation between predicted (Yh) and observed dependent variable (Y).

4- Ratio of variance between predicted (Yh) and observed dependent variable (Y).

- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).

- F-Test=R2/(1-R2)*(N-K-1)/(K).

Model

1- model(xtmln) MLE Random-Effects Panel Regression
* Normal Model
2- model(xtmlh) MLE Random-Effects Panel Regression
* Multiplicative Heteroscedasticity Normal Model

Options

* id(var) Cross Sections ID variable name
* it(var) Time Series ID variable name

zero convert missing values observations to Zero

coll keep collinear variables; default is removing collinear variables.

noconstant Exclude Constant Term from Equation

mhet(varlist) Set variable(s) that will be included in:
Panel Multiplicative Heteroscedasticity with model(xtmlh)
to remidy Heteroscedasticity, option [weight], can not be used here.

iter(#) number of iterations; Default is iter(100)

tech(name) technique algorithm for maximization of the log likelihood function LLF
tech(nr) Newton-Raphson (NR) algorithm, , Default
tech(bhhh) Berndt-Hall-Hall-Hausman (BHHH) algorithm
tech(dfp) Davidon-Fletcher-Powell (DFP) algorithm
tech(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm

tolerance(#) tolerance for coefficient vector; Default is tol(0.00001)

nolog suppress iteration of the log likelihood

level(#) confidence intervals level. Default is level(95)

mfx(lin, log) functional form: Linear model (lin), or Log-Log model (log),
to compute Marginal Effects and Elasticities
- In Linear model: marginal effects are the coefficients (Bm),
and elasticities are (Es = Bm X/Y).
- In Log-Log model: elasticities are the coefficients (Es),
and the marginal effects are (Bm = Es Y/X).
- mfx(log) and tolog options must be combined, to transform linear variables to log form.

tolog Convert dependent and independent variables
to LOG Form in the memory for Log-Log regression.
tolog Transforms depvar and indepvars
to Log Form without lost the original data variables

predict(new_variable) Predicted values variable

resid(new_variable) Residuals values variable
computed as Ue=Y-Yh ; that is known as combined residual: [Ue = U_i + E_it]
overall error component is computed as: [E_it]
see: xtreg postestimation

vce(vcetype) ols, robust, cluster, bootstrap, jackknife, hc2, hc3

Model Selection Diagnostic Criteria

diag Model Selection Diagnostic Criteria:

- Log Likelihood Function LLF
- Akaike Information Criterion (1974) AIC
- Akaike Information Criterion (1973) Log AIC
- Schwarz Criterion (1978) SC
- Schwarz Criterion (1978) Log SC
- Amemiya Prediction Criterion (1969) FPE
- Hannan-Quinn Criterion (1979) HQ
- Rice Criterion (1984) Rice
- Shibata Criterion (1981) Shibata
- Craven-Wahba Generalized Cross Validation (1979) GCV

Groupwise Heteroscedasticity Tests

lmhet Groupwise Panel Heteroscedasticity Tests:

* Ho: Panel Homoscedasticity - Ha: Panel Groupwise Heteroscedasticity
- Lagrange Multiplier LM Test
- Likelihood Ratio LR Test
- Wald Test

Saved Results

xtreghet saves the following results in e():

*** Panel Model Selection Diagnostic Criteria:
e(N) number of observations
e(r2bu) R-squared (Buse 1973)
e(r2bu_a) R-squared Adj (Buse 1973)
e(r2raw) Raw Moments R2
e(r2raw_a) Raw Moments R2 Adj
e(f) F-test
e(fp) F-test P-Value
e(wald) Wald-test
e(waldp) Wald-test P-Value

e(r2h) R2 Between Predicted (Yh) and Observed DepVar (Y)
e(r2h_a) Adjusted r2h
e(fh) F-test due to r2h
e(fhp) F-test due to r2h P-Value

e(r2v) R2 Variance Ratio Between Predicted (Yh) and Observed DepVar (Y)
e(r2v_a) Adjusted r2v
e(fv) F-test due to r2v
e(fvp) F-test due to r2v P-Value

e(sig) Root MSE (Sigma)
e(llf) Log Likelihood Function LLF
e(aic) Akaike Information Criterion (1974) AIC
e(laic) Akaike Information Criterion (1973) Log AIC
e(sc) Schwarz Criterion (1978) SC
e(lsc) Schwarz Criterion (1978) Log SC
e(fpe) Amemiya Prediction Criterion (1969) FPE
e(hq) Hannan-Quinn Criterion (1979) HQ
e(rice) Rice Criterion (1984) Rice
e(shibata) Shibata Criterion (1981) Shibata
e(gcv) Craven-Wahba Generalized Cross Validation (1979) GCV

*** Panel Groupwise Heteroscedasticity Tests:
e(lmhglm) Lagrange Multiplier LM Test
e(lmhglmp) Lagrange Multiplier LM Test P-Value
e(lmhglr) Likelihood Ratio LR Test
e(lmhglrp) Likelihood Ratio LR Test P-Value
e(lmhgw) Wald Test
e(lmhgwp) Wald Test P-Value

Matrixes
e(b) coefficient vector
e(V) variance-covariance matrix of the estimators
e(mfxlin) Marginal Effect and Elasticity in Lin Form
e(mfxlog) Marginal Effect and Elasticity in Log Form

References

Breusch, Trevor (1987)
"Maximum Likelihood Estimation of Random Effects Models",
Journal of Econometrics, 36; 383–389.

Breusch, Trevor & Adrian Pagan (1980)
"The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics",
Review of Economic Studies 47; 239-253.

Greene, William (2007)
"Econometric Analysis",
6th ed., Macmillan Publishing Company Inc., New York, USA..

Examples

clear all

sysuse xtreghet.dta, clear

db xtreghet

* MLE Random-Effects Regression - Normal Model

xtreghet y x1 x2 , id(id) it(t) model(xtmln) mfx(lin) diag lmhet

* MLE Random-Effects Regression - Multiplicative Heteroscedasticity Model

xtreghet y x1 x2 , id(id) it(t) model(xtmlh) mhet(x1 x2) mfx(lin) diag lmhet

xtreghet y x1 x2 x3 x4 , id(id) it(t) model(xtmlh) mhet(x1 x2) diag lmhet

. clear all
. sysuse xtreghet.dta, clear
. xtreghet y x1 x2 , id(id) it(t) model(xtmlh) mhet(x1 x2) mfx(lin) diag lmhet

==============================================================================
* MLE Random-Effects Panel Data Regression (Normal Distribution)
* Multiplicative Heteroscedasticity
==============================================================================
y = x1 + x2
------------------------------------------------------------------------------
Sample Size = 49 | Cross Sections Number = 7
Wald Test = 52.4642 | P-Value > Chi2(2) = 0.0000
F-Test = 26.2321 | P-Value > F(2 , 40) = 0.0000
(Buse 1973) R2 = 0.5328 | Raw Moments R2 = 0.9151
(Buse 1973) R2 Adj = 0.4394 | Raw Moments R2 Adj = 0.8981
Root MSE (Sigma) = 12.5280 | Log Likelihood Function = -178.6711
------------------------------------------------------------------------------
- R2h= 0.5457 R2h Adj= 0.4548 F-Test = 27.63 P-Value > F(2 , 40) 0.0000
- R2v= 0.3924 R2v Adj= 0.2709 F-Test = 14.86 P-Value > F(2 , 40) 0.0000
------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y |
x1 | -.1619364 .0801844 -2.02 0.043 -.319095 -.0047779
x2 | -1.518764 .2879389 -5.27 0.000 -2.083113 -.9544138
_cons | 62.90976 5.540581 11.35 0.000 52.05043 73.7691
-------------+----------------------------------------------------------------
Hetero |
x1 | -.0095464 .0098502 -0.97 0.332 -.0288525 .0097597
x2 | -.0338743 .0259918 -1.30 0.192 -.0848172 .0170687
-------------+----------------------------------------------------------------
Sigu | 20.79506 12.51326 1.66 0.097 -3.730475 45.3206
Sige | 20.1629 9.211693 2.19 0.029 2.108315 38.21749
------------------------------------------------------------------------------

==============================================================================
* Panel Model Selection Diagnostic Criteria - Model= (xtmlh)
==============================================================================
- Log Likelihood Function LLF = -178.6711
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 177.5970
- Akaike Information Criterion (1973) Log AIC = 5.1795
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 241.8663
- Schwarz Criterion (1978) Log SC = 5.4884
---------------------------------------------------------------------------
- Amemiya Prediction Criterion (1969) FPE = 182.5744
- Hannan-Quinn Criterion (1979) HQ = 199.6770
- Rice Criterion (1984) Rice = 190.2424
- Shibata Criterion (1981) Shibata = 169.9583
- Craven-Wahba Generalized Cross Validation (1979) GCV = 182.9993
------------------------------------------------------------------------------

==============================================================================
* Panel Groupwise Heteroscedasticity Tests
==============================================================================
Ho: Panel Homoscedasticity - Ha: Panel Groupwise Heteroscedasticity

- Lagrange Multiplier LM Test = 7.3373 P-Value > Chi2(6) 0.2908
- Likelihood Ratio LR Test = 7.1253 P-Value > Chi2(6) 0.3094
- Wald Test = 12.4812 P-Value > Chi2(7) 0.0858
------------------------------------------------------------------------------

* Marginal Effect - Elasticity (Model= xtmlh): Linear *

+---------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|------------+--------------------+--------------------+--------------------|
|y | | | |
| x1 | -0.1619 | -0.1772 | 38.4362 |
| x2 | -1.5188 | -0.6215 | 14.3749 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable = 35.1288

Author

Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage: http://emadstat.110mb.com/stata.htm
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

XTREGHET Citation

Shehata, Emad Abd Elmessih (2012)

XTREGHET: "MLE Random-Effects with Multiplicative Heteroscedasticity Panel Data Regression"

http://ideas.repec.org/c/boc/bocode/s457463.html

http://econpapers.repec.org/software/bocbocode/s457463.htm

Online Help:

* Econometric Regression Models:

* (1) (OLS) * Ordinary Least Squares Regression Models:
olsreg OLS Econometric Ridge & Weighted Regression Models: Stata Module Toolkit
ridgereg OLS Ridge Regression Models
gmmreg OLS Generalized Method of Moments (GMM): Ridge & Weighted Regression
chowreg OLS Structural Change Regressions and Chow Test
---------------------------------------------------------------------------
* (2) (2SLS-IV) * Two-Stage Least Squares & Instrumental Variables Regression Models:
reg2 2SLS-IV Econometric Ridge & Weighted Regression Models: Stata Module Toolkit
gmmreg2 2SLS-IV Generalized Method of Moments (GMM): Ridge & Weighted Regression
limlreg2 Limited-Information Maximum Likelihood (LIML) IV Regression
meloreg2 Minimum Expected Loss (MELO) IV Regression
ridgereg2 Ridge 2SLS-LIML-GMM-MELO-Fuller-kClass IV Regression
ridge2sls Two-Stage Least Squares Ridge Regression
ridgegmm Generalized Method of Moments (GMM) IV Ridge Regression
ridgeliml Limited-Information Maximum Likelihood (LIML) IV Ridge Regression
ridgemelo Minimum Expected Loss (MELO) IV Ridge Regression
---------------------------------------------------------------------------
* (3) * Panel Data Regression Models:
regxt Panel Data Econometric Ridge & Weighted Regression Models: Stata Module Toolkit
xtregdhp Han-Philips (2010) Linear Dynamic Panel Data Regression
xtregam Amemiya Random-Effects Panel Data: Ridge & Weighted Regression
xtregbem Between-Effects Panel Data: Ridge & Weighted Regression
xtregbn Balestra-Nerlove Random-Effects Panel Data: Ridge & Weighted Regression
xtregfem Fixed-Effects Panel Data: Ridge & Weighted Regression
xtregmle Trevor Breusch MLE Random-Effects Panel Data: Ridge & Weighted Regression
xtregrem Fuller-Battese GLS Random-Effects Panel Data: Ridge & Weighted Regression
xtregsam Swamy-Arora Random-Effects Panel Data: Ridge & Weighted Regression
xtregwem Within-Effects Panel Data: Ridge & Weighted Regression
xtregwhm Wallace-Hussain Random-Effects Panel Data: Ridge & Weighted Regression
xtreghet MLE Random-Effects Multiplicative Heteroscedasticity Panel Data Regression
---------------------------------------------------------------------------
* (4) (MLE) * Maximum Likelihood Estimation Regression Models:
mlereg MLE Econometric Regression Models: Stata Module Toolkit
mleregn MLE Normal Regression
mleregln MLE Log Normal Regression
mlereghn MLE Half Normal Regression
mlerege MLE Exponential Regression
mleregle MLE Log Exponential Regression
mleregg MLE Gamma Regression
mlereglg MLE Log Gamma Regression
mlereggg MLE Generalized Gamma Regression
mlereglgg MLE Log Generalized Gamma Regression
mleregb MLE Beta Regression
mleregev MLE Extreme Value Regression
mleregw MLE Weibull Regression
mlereglw MLE Log Weibull Regression
mleregilg MLE Inverse Log Gauss Regression
---------------------------------------------------------------------------
* (5) * Autocorrelation Regression Models:
autoreg Autoregressive Least Squares Regression Models: Stata Module Toolkit
alsmle Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation Regression
automle Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation Regression
autopagan Pagan AR(p) Conditional Autoregressive Least Squares Regression
autoyw Yule-Walker AR(p) Unconditional Autoregressive Least Squares Regression
autopw Prais-Winsten AR(p) Autoregressive Least Squares Regression
autoco Cochrane-Orcutt AR(p) Autoregressive Least Squares Regression
autofair Fair AR(1) Autoregressive Least Squares Regression
---------------------------------------------------------------------------
* (6) * Heteroscedasticity Regression Models:
hetdep MLE Dependent Variable Heteroscedasticity
hetmult MLE Multiplicative Heteroscedasticity Regression
hetstd MLE Standard Deviation Heteroscedasticity Regression
hetvar MLE Variance Deviation Heteroscedasticity Regression
glsreg Generalized Least Squares Regression
---------------------------------------------------------------------------
* (7) * Non Normality Regression Models:
robgme MLE Robust Generalized Multivariate Error t Distribution
bcchreg Classical Box-Cox Multiplicative Heteroscedasticity Regression
bccreg Classical Box-Cox Regression
bcereg Extended Box-Cox Regression
---------------------------------------------------------------------------
* (8) (NLS) * Nonlinear Least Squares Regression Regression Models:
autonls Non Linear Autoregressive Least Squares Regression
qregnls Non Linear Quantile Regression
---------------------------------------------------------------------------
* (9) * Logit Regression Models:
logithetm Logit Multiplicative Heteroscedasticity Regression
mnlogit Multinomial Logit Regression
---------------------------------------------------------------------------
* (10) * Probit Regression Models:
probithetm Probit Multiplicative Heteroscedasticity Regression
mnprobit Multinomial Probit Regression
---------------------------------------------------------------------------
* (11) * Tobit Regression Models:
tobithetm Tobit Multiplicative Heteroscedasticity Regression
---------------------------------------------------------------------------

Panel Data Tests:

* (1) * Autocorrelation Tests:
lmaxt Panel Data Autocorrelation Tests
lmabxt Panel Data Autocorrelation Baltagi Test
lmabgxt Panel Data Autocorrelation Breusch-Godfrey Test
lmabpxt Panel Data Autocorrelation Box-Pierce Test
lmabpgxt Panel Data Autocorrelation Breusch-Pagan-Godfrey Test
lmadurhxt Panel Data Autocorrelation Dynamic Durbin h and Harvey LM Tests
lmadurmxt Panel Data Autocorrelation Dynamic Durbin m Test
lmadwxt Panel Data Autocorrelation Durbin-Watson Test
lmavonxt Panel Data Von Neumann Ratio Autocorrelation Test
lmawxt Panel Data Autocorrelation Wooldridge Test
lmazxt Panel Data Autocorrelation Z Test
---------------------------------------------------------------------------
* (2) * Heteroscedasticity Tests:
lmhxt Panel Data Heteroscedasticity Tests
lmhgwxt Panel Data Groupwise Heteroscedasticity Tests
ghxt Panel Groupwise Heteroscedasticity Tests
lmhlmxt Panel Data Groupwise Heteroscedasticity Breusch-Pagan LM Test
lmhlrxt Panel Data Groupwise Heteroscedasticity Greene LR Test
lmharchxt Panel Data Heteroscedasticity Engle (ARCH) Test
lmhcwxt Panel Data Heteroscedasticity Cook-Weisberg Test
lmhglxt Panel Data Heteroscedasticity Glejser Test
lmhharvxt Panel Data Heteroscedasticity Harvey Test
lmhhpxt Panel Data Heteroscedasticity Hall-Pagan Test
lmhmssxt Panel Data Heteroscedasticity Machado-Santos-Silva Test
lmhwaldxt Panel Data Heteroscedasticity Wald Test
lmhwhitext Panel Data Heteroscedasticity White Test
---------------------------------------------------------------------------
* (3) * Non Normality Tests:
lmnxt Panel Data Non Normality Tests
lmnadxt Panel Data Non Normality Anderson-Darling Test
lmndhxt Panel Data Non Normality Doornik-Hansen Test
lmndpxt Panel Data Non Normality D'Agostino-Pearson Test
lmngryxt Panel Data Non Normality Geary Runs Test
lmnjbxt Panel Data Non Normality Jarque-Bera Test
lmnwhitext Panel Data Non Normality White Test
---------------------------------------------------------------------------
* (4) * Panel Data Error Component Tests:
lmecxt Panel Data Error Component Tests
---------------------------------------------------------------------------
* (5) * Panel Data Diagonal Covariance Matrix Test:
lmcovxt Panel Data Breusch-Pagan Diagonal Covariance Matrix LM Test
---------------------------------------------------------------------------
* (6) * Panel Data ModeL Selection Diagnostic Criteria:
diagxt Panel Data ModeL Selection Diagnostic Criteria
---------------------------------------------------------------------------
* (7) * Panel Data Specification Tests:
lmhausxt Panel Data Hausman Specification Test
resetxt Panel Data REgression Specification Error Tests (RESET)
---------------------------------------------------------------------------
* (8) * Panel Data Identification Variables:
idt Create Identification Variables in Panel Data
xtidt Create Identification Variables in Panel Data
---------------------------------------------------------------------------