{smcl} {hline} {cmd:help: {helpb r2reg3}}{space 50} {cmd:dialog:} {bf:{dialog r2reg3}} {hline} {bf:{err:{dlgtab:Title}}} {bf:r2reg3: (3SLS-SUR) Overall System R2 - Adjusted R2 - F Test - Chi2 Test} {marker 00}{bf:{err:{dlgtab:Table of Contents}}} {p 4 8 2} {p 5}{helpb r2reg3##01:Syntax}{p_end} {p 5}{helpb r2reg3##02:Description}{p_end} {p 5}{helpb r2reg3##03:Saved Results}{p_end} {p 5}{helpb r2reg3##04:References}{p_end} {p 1}*** {helpb r2reg3##05:Examples}{p_end} {p 5}{helpb r2reg3##06:Author}{p_end} {marker 01}{bf:{err:{dlgtab:Syntax}}} {cmd: r2reg3} {marker 02}{bf:{err:{dlgtab:Description}}} {p 2 2 2}{cmd:r2reg3} computes Overall System R-squared (R2), Adjusted R2, and the overall significance of F-Test, and Chi2-Test, after:{p_end} {p 3 2 2}- {helpb reg3}: (3SLS) Three-Stage Least Squares for systems of simultaneous equations.{p_end} {p 3 2 2}- {helpb sureg}: (SUR) Seemingly Unrelated Regression for sets of equations.{p_end} {p 2 2 2}{cmd:r2reg3} used 5 types of criteria and tests, as discussed in:{p_end} {p 2 2 2}{cmd: McElroy(1977), Judge et al(1985), Dhrymes(1974), Greene(1993), and Berndt(1991)}.{p_end} {p 6 2 2}see eq.12.1.33-36 in Judge et al(1985, p.477).{p_end} {cmd:1- Berndt System R2} = 1-|E'E| / |Yb'Yb| {cmd:2- McElroy System R2} = 1-(U'W*U)/ (Y'W*Y) {cmd:3- Judge System R2} = 1-(U'U) / (Y'Y) Q {cmd:4- Dhrymes System R2} = Sum [R2i (yi' Dt yi']/[Y(I(Q) # Dt)Y] i=1 {cmd:5- Greene System R2} = 1-(Q/trace(inv(Sig))*SYs) {p 2 2 2}From each type of these system R2's, {cmd:r2reg3} can calculate Adjusted R2, F-Test, and Chi2-Test:{p_end} {cmd:Adjusted R2} = 1-(1-R2)*((QN-Q)/(QN-K)) {cmd:F-Test} = R2/(1-R2)*[(QN-K)/(K-Q)] {cmd:Chi2-Test} = -N*(log(1-R2)) where |E'E| = determinant of residual matrix (NxQ) |Yb'Yb| = determinant of dependent variables matrix in deviation from mean (NxQ) yi = dependent variable of eq. i (Nx1) Y = stacked vector of dependent variables (QNx1) U = stacked vector of residuals (QNx1) W = variance-covariance matrix of residuals (W=inv(Omega) # I(N)) N = number of observations K = Number of Parameters Q = Number of Equations R2i = R2 of eq. i Dt = I(N)-JJ'/N, with J=(1,1,...,1)' (Nx1) SYs = (Yb1*Yb2*...Ybq)/N Sig = Sigma hat Matrix Degrees of Freedom F-Test = (K-Q), (QN) Degrees of Freedom Chi2-Test = (K-Q) Log Determinant of Sigma = log|Sigma matrix| Log Likelihood Function LLF =-(N*Q/2)*(1+log(2*_pi))-(N/2*abs(log(Sigma))) {marker 03}{bf:{err:{dlgtab:Saved Results}}} {pstd} {cmd:r2reg3} saves the following in {cmd:r()}: {synoptset 15 tabbed}{...} {p2col 5 15 15 2: Scalars}{p_end} {col 4}{cmd:r(N)}{col 20}Number of Observations {col 4}{cmd:r(k)}{col 20}Number of Parameters {col 4}{cmd:r(k_eq)}{col 20}Number of Equations {col 4}{cmd:r(chi_df)}{col 20}DF chi-squared {col 4}{cmd:r(f_df1)}{col 20}F-Test DF1 Numerator {col 4}{cmd:r(f_df2)}{col 20}F-Test DF2 Denominator {col 4}{cmd:r(r2_b)}{col 20}Berndt R-squared {col 4}{cmd:r(r2_j)}{col 20}Judge R-squared {col 4}{cmd:r(r2_m)}{col 20}McElroy R-squared {col 4}{cmd:r(r2_d)}{col 20}Dhrymes R-squared {col 4}{cmd:r(r2_g)}{col 20}Greene R-squared {col 4}{cmd:r(r2a_b)}{col 20}Berndt Adjusted R-squared {col 4}{cmd:r(r2a_j)}{col 20}Judge Adjusted R-squared {col 4}{cmd:r(r2a_m)}{col 20}McElroy Adjusted R-squared {col 4}{cmd:r(r2a_d)}{col 20}Dhrymes Adjusted R-squared {col 4}{cmd:r(r2a_g)}{col 20}Greene Adjusted R-squared {col 4}{cmd:r(f_b)}{col 20}Berndt F Test {col 4}{cmd:r(f_j)}{col 20}Judge F Test {col 4}{cmd:r(f_m)}{col 20}McElroy F Test {col 4}{cmd:r(f_d)}{col 20}Dhrymes F Test {col 4}{cmd:r(f_g)}{col 20}Greene F Test {col 4}{cmd:r(chi_b)}{col 20}Berndt Chi2 Test {col 4}{cmd:r(chi_j)}{col 20}Judge Chi2 Test {col 4}{cmd:r(chi_m)}{col 20}McElroy Chi2 Test {col 4}{cmd:r(chi_d)}{col 20}Dhrymes Chi2 Test {col 4}{cmd:r(chi_g)}{col 20}Greene Chi2 Test {col 4}{cmd:r(lsig2)}{col 20}Log Determinant of Sigma {col 4}{cmd:r(llf)}{col 20}Log Likelihood Function{col 62}LLF {marker 04}{bf:{err:{dlgtab:References}}} {p 4 8 2}Berndt, Ernst R. (1991) {cmd: "The practice of econometrics: Classical and contemporary",} {it:Addison-Wesley Publishing Company}; 468. {p 4 8 2}Dhrymes, Phoebus J. (1974) {cmd: "Econometrics: Statistical Foundations and Applications",} {it:2ed edition Springer- Verlag New York, USA.}. {p 4 8 2}Greene, William (1993) {cmd: "Econometric Analysis",} {it:2nd ed., Macmillan Publishing Company Inc., New York, USA.}; 490-491. {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}; 477-478. {p 4 8 2}Kmenta, Jan (1986) {cmd: "Elements of Econometrics",} {it:2nd ed., Macmillan Publishing Company, Inc., New York, USA}; 645. {p 4 8 2}McElroy, Marjorie B. (1977) {cmd: "Goodness of Fit for Seemingly Unrelated Regressions: Glahn's R2y,x and Hooper's r~2",} {it:Journal of Econometrics, 6(3), November}; 381-387. {marker 05}{bf:{err:{dlgtab:Examples}}} {stata clear all} {stata sysuse r2reg3.dta , clear} {cmd:* (1) SUR Model:} {stata sureg (y1 y2 x1 x2) (y2 y1 x3 x4)} {stata r2reg3} {stata return list} {cmd:* (2) 3SLS Model:} {stata reg3 (y1 y2 x1 x2) (y2 y1 x3 x4) , exog(x1 x2 x3 x4)} {stata r2reg3} {stata return list} * If you want to use dialog box: Press OK to compute r2reg3 {stata db r2reg3} {hline} . clear all . sysuse r2reg3.dta , clear . * (1) SUR Model: . sureg (y1 y2 x1 x2) (y2 y1 x3 x4) Seemingly unrelated regression ---------------------------------------------------------------------- Equation Obs Parms RMSE "R-sq" chi2 P ---------------------------------------------------------------------- y1 17 3 8.827101 0.8628 106.88 0.0000 y2 17 3 10.71362 0.8332 84.91 0.0000 ---------------------------------------------------------------------- ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y1 | y2 | .1440474 .1473363 0.98 0.328 -.1447264 .4328211 x1 | .3736436 .4464905 0.84 0.403 -.5014617 1.248749 x2 | -1.17085 .2398822 -4.88 0.000 -1.64101 -.7006895 _cons | 159.7348 48.37047 3.30 0.001 64.93046 254.5392 -------------+---------------------------------------------------------------- y2 | y1 | -.0911744 .2613464 -0.35 0.727 -.6034038 .4210551 x3 | -.3973436 .2758714 -1.44 0.150 -.9380417 .1433545 x4 | 2.480269 1.01631 2.44 0.015 .4883381 4.472201 _cons | 40.22012 31.80722 1.26 0.206 -22.12087 102.5611 ------------------------------------------------------------------------------ . r2reg3 ============================================================================== * Simultaneous Equations (3SLS-SUR) - Method = (sure) * (3SLS-SUR) Overall System R2 - Adjusted R2 - F Test - Chi2 Test ============================================================================== +----------------------------------------------------------------------------------------+ | Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value | |----------+------------+------------+------------+------------+------------+------------| | Berndt | 0.9326 | 0.9171 | 59.9838 | 0.0000 | 45.8573 | 0.0000 | | McElroy | 0.8506 | 0.8161 | 24.6660 | 0.0000 | 32.3159 | 0.0000 | | Judge | 0.8466 | 0.8111 | 23.9065 | 0.0000 | 31.8647 | 0.0000 | | Dhrymes | 0.9292 | 0.9128 | 56.8570 | 0.0000 | 45.0101 | 0.0000 | | Greene | 0.8173 | 0.7751 | 19.3807 | 0.0000 | 28.8954 | 0.0001 | +----------------------------------------------------------------------------------------+ Number of Parameters = 8 Number of Equations = 2 Degrees of Freedom F-Test = (6, 34) Degrees of Freedom Chi2-Test = 6 Log Determinant of Sigma = 9.0985 Log Likelihood Function = -125.5810 ------------------------------------------------------------------------------ . * (2) 3SLS Model: . reg3 (y1 y2 x1 x2) (y2 y1 x3 x4) , exog(x1 x2 x3 x4) Three-stage least-squares regression ---------------------------------------------------------------------- Equation Obs Parms RMSE "R-sq" chi2 P ---------------------------------------------------------------------- y1 17 3 8.947416 0.8590 104.54 0.0000 y2 17 3 11.93733 0.7929 69.52 0.0000 ---------------------------------------------------------------------- ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y1 | y2 | .2398091 .2116599 1.13 0.257 -.1750367 .6546549 x1 | .2592727 .4671355 0.56 0.579 -.6562961 1.174842 x2 | -1.04074 .3167524 -3.29 0.001 -1.661563 -.4199164 _cons | 147.5251 53.59456 2.75 0.006 42.48173 252.5685 -------------+---------------------------------------------------------------- y2 | y1 | -.6287858 .6029723 -1.04 0.297 -1.81059 .5530181 x3 | -.5226034 .332618 -1.57 0.116 -1.174523 .129316 x4 | 3.42094 1.484046 2.31 0.021 .5122637 6.329616 _cons | 62.49335 40.3145 1.55 0.121 -16.52163 141.5083 ------------------------------------------------------------------------------ Endogenous variables: y1 y2 Exogenous variables: x1 x2 x3 x4 ------------------------------------------------------------------------------ . r2reg3 ============================================================================== * Simultaneous Equations (3SLS-SUR) - Method = (3sls) * (3SLS-SUR) Overall System R2 - Adjusted R2 - F Test - Chi2 Test ============================================================================== +----------------------------------------------------------------------------------------+ | Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value | |----------+------------+------------+------------+------------+------------+------------| | Berndt | 0.9191 | 0.9004 | 49.2299 | 0.0000 | 42.7469 | 0.0000 | | McElroy | 0.8042 | 0.7590 | 17.7985 | 0.0000 | 27.7216 | 0.0001 | | Judge | 0.8228 | 0.7819 | 20.1180 | 0.0000 | 29.4159 | 0.0001 | | Dhrymes | 0.9050 | 0.8831 | 41.3032 | 0.0000 | 40.0243 | 0.0000 | | Greene | 0.8104 | 0.7666 | 18.5204 | 0.0000 | 28.2672 | 0.0001 | +----------------------------------------------------------------------------------------+ Number of Parameters = 8 Number of Equations = 2 Degrees of Freedom F-Test = (6, 34) Degrees of Freedom Chi2-Test = 6 Log Determinant of Sigma = 9.2772 Log Likelihood Function = -127.1003 ------------------------------------------------------------------------------ {marker 06}{bf:{err:{dlgtab:Author}}} - {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"}} {bf:{err:{dlgtab:R2REG3 Citation}}} {p 1}{cmd:Shehata, Emad Abd Elmessih (2012)}{p_end} {p 1 10 1}{cmd:R2REG3: "Stata Module to Compute (3SLS-SUR) Overall System R2 - Adjusted R2 - F Test - Chi2 Test"}{p_end} {browse "http://ideas.repec.org/c/boc/bocode/s457322.html"} {browse "http://econpapers.repec.org/software/bocbocode/s457322.htm"} {title:Online Help:} {bf:{err:* (1) (3SLS-SUR) * Simultaneous Equations:}} {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:* (2) (SEM-FIML) * Structural Equation Modeling:}} {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:* (3) (NL-SUR) * Non Linear Seemingly Unrelated Regression:}} {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:* (4) (VAR) * Vector Autoregressive Model:}} {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}