{smcl} {hline} {cmd:help: {helpb lmhhp}}{space 50} {cmd:dialog:} {bf:{dialog lmhhp}} {hline} {bf:{err:{dlgtab:Title}}} {bf:lmhhp: OLS Heteroscedasticity Hall-Pagan Test} {marker 00}{bf:{err:{dlgtab:Table of Contents}}} {p 4 8 2} {p 5}{helpb lmhhp##01:Syntax}{p_end} {p 5}{helpb lmhhp##02:Description}{p_end} {p 5}{helpb lmhhp##03:Options}{p_end} {p 5}{helpb lmhhp##04:Saved Results}{p_end} {p 5}{helpb lmhhp##05:References}{p_end} {p 1}*** {helpb lmhhp##06:Examples}{p_end} {p 5}{helpb lmhhp##07:Authors}{p_end} {marker 01}{bf:{err:{dlgtab:Syntax}}} {p 5 5 6} {cmd:lmhhp} {depvar} {it:{help varlist:indepvars}} {ifin} , {err: [} {opt nocons:tant} {opt coll} {err:]}{p_end} {marker 02}{bf:{err:{dlgtab:Description}}} {pstd} {cmd:lmhhp} computes OLS Heteroscedasticity Hall-Pagan Test Ho: Homoscedasticity - Ha: Heteroscedasticity - Hall-Pagan LM Test: E2 = Yh - Hall-Pagan LM Test: E2 = Yh2 - Hall-Pagan LM Test: E2 = LYh2 {p 3 4 2} R2, R2 Adjusted, and F-Test, are obtained from 4 ways:{p_end} {p 5 4 2} 1- (Buse 1973) R2.{p_end} {p 5 4 2} 2- Raw Moments R2.{p_end} {p 5 4 2} 3- squared correlation between predicted (Yh) and observed dependent variable (Y).{p_end} {p 5 4 2} 4- Ratio of variance between predicted (Yh) and observed dependent variable (Y).{p_end} {p 5 4 2} - Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).{p_end} {p 5 4 2} - F-Test=R2/(1-R2)*(N-K-1)/(K).{p_end} {marker 03}{bf:{err:{dlgtab:Options}}} {synoptset 16}{...} {col 3}{opt nocons:tant}{col 20}Exclude Constant Term from Equation {col 3}{opt coll}{col 20}keep collinear variables; default is removing collinear variables. {marker 04}{bf:{err:{dlgtab:Saved Results}}} {pstd} {cmd:lmhhp} saves the following in {cmd:e()}: {err:*** Heteroscedasticity Tests:} {col 4}{cmd:e(lmhhp1)}{col 20}Hall-Pagan LM Test {col 4}{cmd:e(lmhhp1p)}{col 20}Hall-Pagan LM Test P-Value {col 4}{cmd:e(lmhhp2)}{col 20}Hall-Pagan LM Test {col 4}{cmd:e(lmhhp2p)}{col 20}Hall-Pagan LM Test P-Value {col 4}{cmd:e(lmhhp3)}{col 20}Hall-Pagan LM Test {col 4}{cmd:e(lmhhp3p)}{col 20}Hall-Pagan LM Test P-Value {marker 05}{bf:{err:{dlgtab:References}}} {p 4 8 2}Damodar Gujarati (1995) {cmd: "Basic Econometrics"} {it:3rd Edition, McGraw Hill, New York, USA}. {p 4 8 2}Greene, William (1993) {cmd: "Econometric Analysis",} {it:2nd ed., Macmillan Publishing Company Inc., New York, USA}; 616-618. {p 4 8 2}Greene, William (2007) {cmd: "Econometric Analysis",} {it:6th ed., Upper Saddle River, NJ: Prentice-Hall}; 387-388. {p 4 8 2}Judge, Georege, R. Carter Hill, William . E. Griffiths, Helmut Lutkepohl, & Tsoung-Chao Lee (1988) {cmd: "Introduction To The Theory And Practice Of Econometrics",} {it:2nd ed., John Wiley & Sons, Inc., New York, USA}. {p 4 8 2}Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985) {cmd: "The Theory and Practice of Econometrics",} {it:2nd ed., John Wiley & Sons, Inc., New York, USA}; 615. {p 4 8 2}Kmenta, Jan (1986) {cmd: "Elements of Econometrics",} {it: 2nd ed., Macmillan Publishing Company, Inc., New York, USA}; 718. {p 4 8 2}Pagan, Adrian .R. & Hall, D. (1983) {cmd: "Diagnostic Tests as Residual Analysis",} {it:Econometric Reviews, Vol.2, No.2,}. 159-218. {marker 06}{bf:{err:{dlgtab:Examples}}} {stata clear all} {stata sysuse lmhhp.dta , clear} {stata db lmhhp} {stata lmhhp y x1 x2} {hline} . clear all . sysuse lmhhp.dta , clear . lmhhp y x1 x2 ============================================================================== * Ordinary Least Squares (OLS) ============================================================================== y = x1 + x2 ------------------------------------------------------------------------------ Sample Size = 17 Wald Test = 273.3662 | P-Value > Chi2(2) = 0.0000 F-Test = 136.6831 | P-Value > F(2 , 14) = 0.0000 (Buse 1973) R2 = 0.9513 | Raw Moments R2 = 0.9986 (Buse 1973) R2 Adj = 0.9443 | Raw Moments R2 Adj = 0.9984 Root MSE (Sigma) = 5.5634 | Log Likelihood Function = -51.6471 ------------------------------------------------------------------------------ - R2h= 0.9513 R2h Adj= 0.9443 F-Test = 136.68 P-Value > F(2 , 14) 0.0000 - R2v= 0.9513 R2v Adj= 0.9443 F-Test = 136.68 P-Value > F(2 , 14) 0.0000 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | 1.061709 .2666739 3.98 0.001 .4897506 1.633668 x2 | -1.382986 .0838143 -16.50 0.000 -1.562749 -1.203222 _cons | 130.7066 27.09429 4.82 0.000 72.59515 188.8181 ------------------------------------------------------------------------------ ============================================================================== *** OLS Heteroscedasticity Hall-Pagan Test ============================================================================== Ho: Homoscedasticity - Ha: Heteroscedasticity ------------------------------------------------------------------------------ - Hall-Pagan LM Test: E2 = Yh = 2.4946 P-Value > Chi2(1) 0.1142 - Hall-Pagan LM Test: E2 = Yh2 = 2.6579 P-Value > Chi2(1) 0.1030 - Hall-Pagan LM Test: E2 = LYh2 = 2.3031 P-Value > Chi2(1) 0.1291 ------------------------------------------------------------------------------ {marker 07}{bf:{err:{dlgtab:Authors}}} - {hi:Emad Abd Elmessih Shehata} {hi:Professor (PhD Economics)} {hi:Agricultural Research Center - Agricultural Economics Research Institute - Egypt} {hi:Email: {browse "mailto:emadstat@hotmail.com":emadstat@hotmail.com}} {hi:WebPage at IDEAS:{col 27}{browse "http://ideas.repec.org/f/psh494.html"}} {hi:WebPage at EconPapers:{col 27}{browse "http://econpapers.repec.org/RAS/psh494.htm"}} - {hi:Sahra Khaleel A. Mickaiel} {hi:Professor (PhD Economics)} {hi:Cairo University - Faculty of Agriculture - Department of Economics - Egypt} {hi:Email: {browse "mailto:sahra_atta@hotmail.com":sahra_atta@hotmail.com}} {hi:WebPage at IDEAS:{col 27}{browse "http://ideas.repec.org/f/pmi520.html"}} {hi:WebPage at EconPapers:{col 27}{browse "http://econpapers.repec.org/RAS/pmi520.htm"}} {bf:{err:{dlgtab:LMHHP Citation}}} {p 1}{cmd:Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2014)}{p_end} {p 1 10 1}{cmd:LMHHP: "Stata Module to Compute OLS Heteroscedasticity Hall-Pagan Test"}{p_end} {title:Online Help:} {bf:{err:* Heteroscedasticity Tests:}} {bf:{err:* (1) (OLS) * Ordinary Least Squares Tests:}} {helpb lmhreg}{col 12}OLS Heteroscedasticity Tests {helpb lmharch}{col 12}OLS Heteroscedasticity Engle (ARCH) Test {helpb lmhcw}{col 12}OLS Heteroscedasticity Cook-Weisberg Test {helpb lmhgl}{col 12}OLS Heteroscedasticity Glejser Test {helpb lmhharv}{col 12}OLS Heteroscedasticity Harvey Test {helpb lmhhp}{col 12}OLS Heteroscedasticity Hall-Pagan Test {helpb lmhmss}{col 12}OLS Heteroscedasticity Machado-Santos-Silva Test {helpb lmhwald}{col 12}OLS Heteroscedasticity Wald Test {helpb lmhwhite}{col 12}OLS Heteroscedasticity White Test --------------------------------------------------------------------------- {bf:{err:* (2) (NLS) * Non Linear Least Squares Tests:}} {helpb lmhnls}{col 12}Non Linear Least Squares Heteroscedasticity Tests {helpb lmharchnl}{col 12}NLS Heteroscedasticity Engle (ARCH) Test {helpb lmhcwnl}{col 12}NLS Heteroscedasticity Cook-Weisberg Test {helpb lmhglnl}{col 12}NLS Heteroscedasticity Glejser Test {helpb lmhharvnl}{col 12}NLS Heteroscedasticity Harvey Test {helpb lmhhpnl}{col 12}NLS Heteroscedasticity Hall-Pagan Test {helpb lmhmssnl}{col 12}NLS Heteroscedasticity Machado-Santos-Silva Test {helpb lmhwaldnl}{col 12}NLS Heteroscedasticity Wald Test {helpb lmhwhitenl}{col 12}NLS Heteroscedasticity White Test --------------------------------------------------------------------------- {bf:{err:* (3) (MLE) * Maximum Likelihood Estimation Tests:}} {helpb lmhmle}{col 12}MLE Heteroscedasticity Tests {helpb lmharchml}{col 12}MLE Heteroscedasticity Engle (ARCH) Test {helpb lmhcwml}{col 12}MLE Heteroscedasticity Cook-Weisberg Test {helpb lmhglml}{col 12}MLE Heteroscedasticity Glejser Test {helpb lmhharvml}{col 12}MLE Heteroscedasticity Harvey Test {helpb lmhhpml}{col 12}MLE Heteroscedasticity Hall-Pagan Test {helpb lmhmssml}{col 12}MLE Heteroscedasticity Machado-Santos-Silva Test {helpb lmhwaldml}{col 12}MLE Heteroscedasticity Wald Test {helpb lmhwhiteml}{col 12}MLE Heteroscedasticity White Test --------------------------------------------------------------------------- {bf:{err:* (4) (2SLS-IV) * Two-Stage Least Squares & Instrumental Variables Tests:}} {helpb lmhreg2}{col 12}2SLS-IV Heteroscedasticity Tests {helpb lmharch2}{col 12}2SLS-IV Heteroscedasticity Engle (ARCH) Test {helpb lmhcw2}{col 12}2SLS-IV Heteroscedasticity Cook-Weisberg Test {helpb lmhgl2}{col 12}2SLS-IV Heteroscedasticity Glejser Test {helpb lmhharv2}{col 12}2SLS-IV Heteroscedasticity Harvey Test {helpb lmhhp2}{col 12}2SLS-IV Heteroscedasticity Hall-Pagan Test {helpb lmhmss2}{col 12}2SLS-IV Heteroscedasticity Machado-Santos-Silva Test {helpb lmhwald2}{col 12}2SLS-IV Heteroscedasticity Wald Test {helpb lmhwhite2}{col 12}2SLS-IV Heteroscedasticity White Test --------------------------------------------------------------------------- {bf:{err:* (5) Panel Data Tests:}} {helpb lmhxt}{col 12}Panel Data Heteroscedasticity Tests {helpb lmhgwxt}{col 12}Panel Data Groupwise Heteroscedasticity Tests {helpb ghxt}{col 12}Panel Groupwise Heteroscedasticity Tests {helpb lmhlmxt}{col 12}Panel Data Groupwise Heteroscedasticity Breusch-Pagan LM Test {helpb lmhlrxt}{col 12}Panel Data Groupwise Heteroscedasticity Greene LR Test {helpb lmharchxt}{col 12}Panel Data Heteroscedasticity Engle (ARCH) Test {helpb lmhcwxt}{col 12}Panel Data Heteroscedasticity Cook-Weisberg Test {helpb lmhglxt}{col 12}Panel Data Heteroscedasticity Glejser Test {helpb lmhharvxt}{col 12}Panel Data Heteroscedasticity Harvey Test {helpb lmhhpxt}{col 12}Panel Data Heteroscedasticity Hall-Pagan Test {helpb lmhmssxt}{col 12}Panel Data Heteroscedasticity Machado-Santos-Silva Test {helpb lmhwaldxt}{col 12}Panel Data Heteroscedasticity Wald Test {helpb lmhwhitext}{col 12}Panel Data Heteroscedasticity White Test --------------------------------------------------------------------------- {bf:{err:* (6) (3SLS-SUR) * Simultaneous Equations Tests:}} {helpb lmareg3}{col 12}(3SLS-SUR) Overall System Autocorrelation Tests {helpb lmhreg3}{col 12}(3SLS-SUR) Overall System Heteroscedasticity Tests {helpb lmnreg3}{col 12}(3SLS-SUR) Overall System Non Normality Tests {helpb lmcovreg3}{col 12}(3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix {helpb r2reg3}{col 12}(3SLS-SUR) Overall System R2, F-Test, and Chi2-Test {helpb diagreg3}{col 12}(3SLS-SUR) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- {bf:{err:* (7) (SEM-FIML) * Structural Equation Modeling Tests:}} {helpb lmasem}{col 12}(SEM-FIML) Overall System Autocorrelation Tests {helpb lmhsem}{col 12}(SEM-FIML) Overall System Heteroscedasticity Tests {helpb lmnsem}{col 12}(SEM-FIML) Overall System Non Normality Tests {helpb lmcovsem}{col 12}(SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test {helpb r2sem}{col 12}(SEM-FIML) Overall System R2, F-Test, and Chi2-Test {helpb diagsem}{col 12}(SEM-FIML) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- {bf:{err:* (8) (NL-SUR) * Non Linear Seemingly Unrelated Regression Tests:}} {helpb lmanlsur}{col 12}(NL-SUR) Overall System Autocorrelation Tests {helpb lmhnlsur}{col 12}(NL-SUR) Overall System Heteroscedasticity Tests {helpb lmnnlsur}{col 12}(NL-SUR) Overall System Non Normality Tests {helpb lmcovnlsur}{col 12}(NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test {helpb r2nlsur}{col 12}(NL-SUR) Overall System R2, F-Test, and Chi2-Test {helpb diagnlsur}{col 12}(NL-SUR) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- {bf:{err:* (9) (VAR) * Vector Autoregressive Model Tests:}} {helpb lmavar}{col 12}(VAR) Overall System Autocorrelation Tests {helpb lmhvar}{col 12}(VAR) Overall System Heteroscedasticity Tests {helpb lmnvar}{col 12}(VAR) Overall System Non Normality Tests {helpb lmcovvar}{col 12}(VAR) Breusch-Pagan Diagonal Covariance Matrix Test {helpb r2var}{col 12}(VAR) Overall System R2, F-Test, and Chi2-Test {helpb diagvar}{col 12}(VAR) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- {psee} {p_end}