{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}