```-------------------------------------------------------------------------------
help: gs3sls                                                   dialog: gs3sls
-------------------------------------------------------------------------------

+-------+
----+ Title +------------------------------------------------------------

gs3sls: Generalized Spatial Autoregressive Three Stage Least Squares (3SLS)
Cross Sections Regression

+-------------------+

Syntax
Description
Model Options
Options
Spatial Aautocorrelation Tests
Model Selection Diagnostic Criteria
Heteroscedasticity Tests
Non Normality Tests
Saved Results
References

*** Examples

Author

+--------+
----+ Syntax +-----------------------------------------------------------

gs3sls depvar indepvars [weight] , wmfile(weight_file) var2(varlist)
eq(1, 2)

[ ols 2sls 3sls sure mvreg lmspac lmhet lmnorm diag tests stand inv
inv2

aux(varlist) mfx(lin, log) order(#) coll zero tolog noconstant

predict(new_var) resid(new_var) level(#) vce(vcetype) ]

+-------------+
----+ Description +------------------------------------------------------

gs3sls estimates Generalized Spatial Autoregressive
Three Stage Least Squares (3SLS) for Cross Sections Regression

gs3sls can generate:
- Binary / Standardized Weight Matrix.
- Inverse  / Inverse Squared Standardized Weight Matrix.
- Binary / Standardized / Inverse Eigenvalues Variable.
- Spatial lagged variables up to 4th order.

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).

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

Buse(1973) R2 in (gs3sls) may be negative, to avoid negative R2, you
can increase number on instrumental variables by choosing order more
than 1 order(2, 3, 4)

*** Important Notes:
gs3sls generates some variables names with prefix:
w1x_ , w2x_ , w3x_ , w4x_ , w1y_ , w2y_ , mstar_ , spat_
So, you must avoid to include variables names with thes prefixes

+---------------+
----+ Model Options +----------------------------------------------------

3sls             Three-Stage Least Squares (3SLS)
2sls             Two-Stage Least Squares (2SLS)
sure             Seemingly Unrelated Regression Estimation (SURE)
ols              Ordinary Least Squares (OLS)
mvreg            SURE with OLS DF adjustment (MVREG)

+---------+
----+ Options +----------------------------------------------------------

* wmfile(weight_file) Open CROSS SECTION weight matrix file.

Spatial Cross Sections Weight Matrix file must be:
1- Square Matrix [NxN]
2- Symmetric Matrix (Optional)

Spatial Weight Matrix has two types: Standardized and binary weight matrix.

stand            Use Standardized Weight Matrix, (each row sum equals 1)
Default is Binary spatial Weight Matrix which each element i
> s 0 or 1

inv              Use Inverse Standardized Weight Matrix (1/W)

inv2             Use Inverse Squared Standardized Weight Matrix (1/W^2)

zero             convert missing values observations to Zero

aux(varlist)     add Auxiliary Variables into regression model
without converting them to spatial lagged variables,
or without log form, i.e., dummy variables.

order(1, 2, 3, 4) Order of lagged independent variables up to maximum 4th ord
> er.

eq(1, 2)         Tests for equation (#), default is 1.

var2(varlist)    Dependent-Independent Variables for the second equation.

var2(varlist) must be combine.
if you have system of 2 Equations:
Y1 = Y2 X1 X2
Y2 = Y1 X3 X4
Variables of Eq. 1 will be Dep. & Indep. Variables
Variables of Eq. 2 will be Dep. & Indep. Variables in option var2( ); i
> .e,
gs3sls y1 x1 x2 , wmfile(SPWcs) var2(y2 x3 x4) eq(1)
gs3sls y1 x1 x2 , wmfile(SPWcs) var2(y2 x3 x4) eq(2)

coll             keep collinear variables; default is removing collinear vari
> ables.

noconstant       Exclude Constant Term from RHS Equation

tests            display ALL lmh, lmn, lmsp, diag tests

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

iter(#)          maximum iterations; default is 100
if iter(#) is reached (100), this means convergence not ach
> ieved yet,
so you can exceed number of maximum iterations more than 10
> 0.

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

level(#)         confidence intervals level; default is level(95)

+--------------------------------+
----+ Spatial Aautocorrelation Tests +-----------------------------------

lmspac Spatial Aautocorrelation Tests:
* Ho: Error has No Spatial AutoCorrelation
Ha: Error has    Spatial AutoCorrelation
- GLOBAL Moran MI Test
- GLOBAL Geary GC Test
- GLOBAL Getis-Ords GO Test
- Moran MI Error Test
- LM Error [SEM] (Burridge) Test
- LM Error [SEM] (Robust) Test
* Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has    Spatial AutoCorrelation
- LM Lag [SAR]  (Anselin) Test
- LM Lag [SAR]  (Robust) Test
* Ho: No General Spatial AutoCorrelation
Ha:    General Spatial AutoCorrelation
- LM SAC   (LMErr+LMLag_R) Test
- LM SAC   (LMLag+LMErr_R) Test

Definitions:

- Spatial autocorrelation: chock in one country affects neighboring countrie
> s

- Spatial autocorrelation: is correlation of a variable with itself in space
> .

- Spatial Lag Model:     Y = BX + rWy + e         ; e = lWe+u
- Spatial Error Model:   Y = BX + e               ; e = lWe+u
- Spatial Durbin Model:  Y = BX + aWX* + rWy + e  ; e = lWe+u
- General Spatial Model: Y = BX + rWy  + LW1y + e ; e = lW1e+u

- General Spatial Model is used to deal with both types of spatial dependenc
> e,
namely Spatial Lag Dependence and Spatial Error Dependence

- Spatial Error Model is used to handle the spatial dependence due to
the omitted variables or errors in measurement through the error term

- Spatial Autoregressive Model (SAR) is also known as Spatial Lag Model

- Positive spatial autocorrelation exists when high values correlate
with high neighboring values or when low values correlate with low
neighboring values

- Negative spatial autocorrelation exists when high values correlate
with low neighboring values and vice versa.

- presence of positive spatial autocorrelation results in a loss of informat
> ion,
which is related to greater uncertainty, less precision, and larger standa
> rd errors.

- Spatial autocorrelation coefficients (in contrast to their counterparts in
>  time)
are not constrained by -1/+1. Their range depends on the choice of weights
>  matrix.

- Spatial dependence exists when the value associated with one location
is dependent on those of other locations.

- Spatial heterogeneity exists when structural changes related to location
exist in a dataset, it can result in non-constant error variance
(heteroscedasticity) across areas, especially when scale-related
measurement errors are present.

- Spatial regression models are statistical models that account for
the presence of spatial effects, i.e., spatial autocorrelation
(or more generally spatial dependence) and/or spatial heterogeneity.

- if LM test for spatial lag is more significant than LM test for spatial er
> ror,
and robust LM test for spatial lag is significant but robust LM test for
spatial error is not, then the appropriate model is spatial lag model.
Conversely, if LM test for spatial error is more significant than LM test
for spatial lag and robust LM test for spatial error is significant
but robust LM test for spatial lag is not, then the appropriate specificat
> ion
is spatial error model, [Anselin-Florax (1995)].

- robust versions of Spatial LM tests are considered only when
standard versions (LM-Lag or LM-Error) are significant

- General Spatial Model is used to deal with both types of spatial dependenc
> e,
namely spatial lag dependence and spatial error dependence

- Spatial Error Model is used to handle spatial dependence due to omitted
variables or errors in measurement through the error term

- Spatial Autoregressive Model (SAR) is also known as Spatial Lag Model

+-------------------------------------+
----+ 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

+--------------------------+
----+ Heteroscedasticity Tests +-----------------------------------------

lmhet Heteroscedasticity Tests:
* Ho: Homoscedasticity - Ha: Heteroscedasticity
- Hall-Pagan LM Test:  E2 = Yh
- Hall-Pagan LM Test:  E2 = Yh2
- Hall-Pagan LM Test:  E2 = LYh2
- Harvey LM Test:    LogE2 = X
- Wald Test:         LogE2 = X
- Glejser LM Test:    |E| = X
- Machado-Santos-Silva LM Test: Ev= Yh Yh2
- Machado-Santos-Silva LM Test: Ev= X
- White Test - Koenker(R2): E2 = X
- White Test - B-P-G (SSR): E2 = X
- White Test - Koenker(R2): E2 = X X2
- White Test - B-P-G (SSR): E2 = X X2
- White Test - Koenker(R2): E2 = X X2 XX
- White Test - B-P-G (SSR): E2 = X X2 XX
- Cook-Weisberg LM Test E = Yh
- Cook-Weisberg LM Test E = X
*** Single Variable Tests
- Cook-Weisberg LM Test: E = xi
- King LM Test: E = xi

*** Tobit Model Heteroscedasticity LM Tests
- Separate LM Tests - Ho: Homoscedasticity
- Joint LM Test     - Ho: Homoscedasticity

+---------------------+
----+ Non Normality Tests +----------------------------------------------

lmnorm Non Normality Tests:
* Ho: Normality - Ha: Non Normality
*** Non Normality Tests:
- Jarque-Bera LM Test
- White IM Test
- Doornik-Hansen LM Test
- Geary LM Test
- Anderson-Darling Z Test
- D'Agostino-Pearson LM Test
*** Skewness Tests:
- Srivastava LM Skewness Test
- Small LM Skewness Test
- Skewness Z Test
- Skewness Coefficient - Standard Deviation
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test
- Small LM Kurtosis Test
- Kurtosis Z Test
- Kurtosis Coefficient - Standard Deviation
*** Runs Tests:
- Runs Test:
- Standard Deviation Runs Sig(k) - Mean Runs E(k)
- 95% Conf. Interval [E(k)+/- 1.96* Sig(k)]
*** Tobit cross section Non Normality Tests
*** LM Test - Ho: No Skewness
*** LM test - Ho: No Kurtosis
*** LM Test - Ho: Normality (No Kurtosis, No Skewness)
- Pagan-Vella LM Test
- Chesher-Irish LM Test

+---------------+
----+ Saved Results +----------------------------------------------------

gs3sls saves the following results in e():

Scalars

*** Spatial Aautocorrelation Tests:
e(mig)          GLOBAL Moran MI Test
e(migp)         GLOBAL Moran MI Test P-Value
e(gcg)          GLOBAL Geary GC Test
e(gcgp)         GLOBAL Geary GC Test P-Value
e(gog)          GLOBAL Getis-Ords Test GO
e(gogp)         GLOBAL Getis-Ords GO Test P-Value
e(mi1)          Moran MI Error Test
e(mi1p)         Moran MI Error Test P-Value
e(lmerr)        LM Error (Burridge) Test
e(lmerrp)       LM Error (Burridge) Test P-Value
e(lmerrr)       LM Error (Robust) Test
e(lmerrrp)      LM Error (Robust) Test P-Value
e(lmlag)        LM Lag (Anselin) Test
e(lmlagp)       LM Lag (Anselin) Test P-Value
e(lmlagr)       LM Lag (Robust) Test
e(lmlagrp)      LM Lag (Robust) Test P-Value
e(lmsac1)       LM SAC (LMLag+LMErr_R) Test
e(lmsac1p)      LM SAC (LMLag+LMErr_R) Test P-Value
e(lmsac2)       LM SAC (LMErr+LMLag_R) Test
e(lmsac2p)      LM SAC (LMErr+LMLag_R) Test P-Value

*** Model Selection Diagnostic Criteria:
e(N)            number of observations
e(r2bu)         R-squared (Buse 1973)
e(r2raw)        Raw Moments R2
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(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(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

*** Heteroscedasticity Tests:
e(lmhhp1)       Hall-Pagan LM Test E2 = Yh
e(lmhhp1p)      Hall-Pagan LM Test E2 = Yh P-Value
e(lmhhp2)       Hall-Pagan LM Test E2 = Yh2
e(lmhhp2p)      Hall-Pagan LM Test E2 = Yh2 P-Value
e(lmhhp3)       Hall-Pagan LM Test E2 = Yh3
e(lmhhp3p)      Hall-Pagan LM Test E2 = Yh3 P-Value
e(lmhw01)       White Test - Koenker(R2) E2 = X
e(lmhw01p)      White Test - Koenker(R2) E2 = X P-Value
e(lmhw02)       White Test - B-P-G (SSR) E2 = X
e(lmhw02p)      White Test - B-P-G (SSR) E2 = X P-Value
e(lmhw11)       White Test - Koenker(R2) E2 = X X2
e(lmhw11p)      White Test - Koenker(R2) E2 = X X2 P-Value
e(lmhw12)       White Test - B-P-G (SSR) E2 = X X2
e(lmhw12p)      White Test - B-P-G (SSR) E2 = X X2 P-Value
e(lmhw21)       White Test - Koenker(R2) E2 = X X2 XX
e(lmhw21p)      White Test - Koenker(R2) E2 = X X2 XX P-Value
e(lmhw22)       White Test - B-P-G (SSR) E2 = X X2 XX
e(lmhw22p)      White Test - B-P-G (SSR) E2 = X X2 XX P-Value
e(lmhharv)      Harvey LM Test
e(lmhharvp)     Harvey LM Test P-Value
e(lmhwald)      Wald Test
e(lmhwaldp)     Wald Test P-Value
e(lmhgl)        Glejser LM Test
e(lmhglp)       Glejser LM Test P-Value
e(lmhmss1)      Machado-Santos-Silva  LM Test: Ev=Yh Yh2
e(lmhmss1p)     Machado-Santos-Silva LM Test: Ev=Yh Yh2 P-Value
e(lmhmss2p)     Machado-Santos-Silva LM Test: Ev=X P-Value
e(lmhcw1)       Cook-Weisberg LM Test E = Yh
e(lmhcw1p)      Cook-Weisberg LM Test E = Y P-Valueh
e(lmhcw2)       Cook-Weisberg LM Test E = X
e(lmhcw2p)      Cook-Weisberg LM Test E = X P-Value

*** Non Normality Tests:
e(lmnjb)        Jarque-Bera LM Test
e(lmnjbp)       Jarque-Bera LM Test P-Value
e(lmnw)         White IM Test
e(lmnwp)        White IM Test P-Value
e(lmndh)        Doornik-Hansen LM Test
e(lmndhp)       Doornik-Hansen LM Test P-Value
e(lmng)         Geary LM Test
e(lmngp)        Geary LM Test P-Value
e(lmndp)        D'Agostino-Pearson LM Test
e(lmndpp)       D'Agostino-Pearson LM Test P-Value
e(lmnsvs)       Srivastava LM Skewness Test
e(lmnsvsp)      Srivastava LM Skewness Test P-Value
e(lmnsms1)      Small LM Skewness Test
e(lmnsms1p)     Small LM Skewness Test P-Value
e(lmnsms2)      Skewness Z Test
e(lmnsms2p)     Skewness Z Test P-Value
e(lmnsvk)       Srivastava Z Kurtosis Test
e(lmnsvkp)      Srivastava Z Kurtosis Test P-Value
e(lmnsmk1)      Small LM Kurtosis Test
e(lmnsmk1p)     Small LM Kurtosis Test P-Value
e(lmnsmk2)      Kurtosis Z Test
e(lmnsmk2p)     Kurtosis Z Test P-Value
e(sk)           Skewness Coefficient
e(sksd)         Skewness Standard Deviation
e(ku)           Kurtosis Coefficient
e(kusd)         Kurtosis Standard Deviation
e(sn)           Standard Deviation Runs Sig(k)
e(en)           Mean Runs E(k)
e(lower)        Lower 95% Conf. Interval [E(k)- 1.96* Sig(k)]
e(upper)        Upper 95% Conf. Interval [E(k)+ 1.96* Sig(k)]

e(lmnpv)        Pagan-Vella LM Test (Tobit Model)
e(lmnpvp)       Pagan-Vella LM Test (Tobit Model) P-Value
e(lmnci)        Chesher-Irish LM Test (Tobit Model)
e(lmncip)       Chesher-Irish LM Test (Tobit Model) P-Value

Macros
e(cmd)          name of the command
e(cmdline)      command as typed
e(depvar)       Name of dependent variable
e(predict)      program used to implement predict
e(wmat)         name of spatial weight matrix
e(dlmat)        name of spmat object in dlmat()
e(elmat)        name of spmat object in elmat()
e(endog)        names of endogenous variables
e(eqnames)      names of equations
e(het)          heteroskedastic or homoskedastic
e(technique)    maximization technique from technique() option
e(title)        title in estimation output

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

e(ilog)         iteration log (up to 20 iterations)
e(ml_h)         derivative tolerance, (abs(b)+1e-3)*1e-3
e(ml_scale)     derivative scale factor
e(Sigma)        Sigma hat matrix
e(first)        First-stage regression results

Functions
e(sample)       marks estimation sample

+------------+
----+ References +-------------------------------------------------------

Anselin, L. (2001) "Spatial Econometrics", In Baltagi, B. (Ed).: A
Companion to Theoretical Econometrics Basil Blackwell: Oxford, UK.

Anselin, L. (2007) "Spatial Econometrics", In T. C. Mills and K.
Patterson (Eds).: Palgrave Handbook of Econometrics. Vol 1,
Econometric Theory. New York: Palgrave MacMillan.

Anselin, L. & Kelejian, H. H. (1997) "Testing for Spatial Error
Autocorrelation in the Presence of Endogenous Regressors",
International Regional Science Review, (20); 153-182.

Anselin, L. & Florax RJ. (1995) "New Directions in Spatial Econometrics:
Introduction. In New Directions in Spatial Econometrics", Anselin L,
Florax RJ (eds). Berlin, Germany: Springer-Verlag.

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

C.M. Jarque & A.K. Bera (1987) "A Test for Normality of Observations and
Regression Residuals" International Statistical Review , Vol. 55;
163-172.

Cook, R.D., & S. Weisberg (1983) "Diagnostics for Heteroscedasticity in
Regression", Biometrica 70; 1-10.

D'Agostino, R. B., & Rosman, B. (1974) "The Power of Geary’s Test of
Normality", Biometrika, 61(1); 181-184.

Damodar Gujarati (1995) "Basic Econometrics" 3rd Edition, McGraw Hill,
New York, USA.

Geary R.C. (1947) "Testing for Normality" Biometrika, Vol. 34; 209-242.

Geary R.C. (1970) "Relative Efficiency of Count of Sign Changes for
Assessing Residuals Autoregression in Least Squares Regression"
Biometrika, Vol. 57; 123-127.

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

Griffiths, W., R. Carter Hill & George Judge (1993) "Learning and
Practicing Econometrics", John Wiley & Sons, Inc., New York, USA.

Harry H. Kelejian and Ingmar R. Prucha (2004) "Estimation of Simultaneous
Systems of Spatially Interrelated Cross Sectional Equations", Journal
of Econometrics, (118); 27-50.
http://econweb.umd.edu/~prucha/Papers/JE118(2004).pdf

Harvey, Andrew (1990) "The Econometric Analysis of Time Series", 2nd
edition, MIT Press, Cambridge, Massachusetts.

Judge, Georege, R. Carter Hill, William . E. Griffiths, Helmut Lutkepohl,
& Tsoung-Chao Lee (1988) "Introduction To The Theory And Practice Of
Econometrics", 2nd ed., John Wiley & Sons, Inc., New York, USA.

Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, &
Tsoung-Chao Lee(1985) "The Theory and Practice of Econometrics", 2nd
ed., John Wiley & Sons, Inc., New York, USA.

Kmenta, Jan (1986) "Elements of Econometrics", 2nd ed., Macmillan
Publishing Company, Inc., New York, USA; 618-625.

Koenker, R. (1981) "A Note on Studentizing a Test for
Heteroskedasticity", Journal of Econometrics, Vol.17; 107-112.

Pagan, Adrian .R. & Hall, D. (1983) "Diagnostic Tests as Residual
Analysis", Econometric Reviews, Vol.2, No.2,. 159-218.

Pearson, E. S., D'Agostino, R. B., & Bowman, K. O. (1977) "Tests for
Departure from Normality: Comparison of Powers", Biometrika, 64(2);
231-246.

Szroeter, J. (1978) "A Class of Parametric Tests for Heteroscedasticity
in Linear Econometric Models", Econometrica, 46; 1311-28.

+----------+
----+ Examples +---------------------------------------------------------

Note 1: you can use: spweight, spweightcs, spweightxt to create Spatial Weight
> Matrix.
Note 2: Remember, your spatial weight matrix must be:
*** 1-Cross Section Dimention  2- Square Matrix 3- Symmetric Matrix
Note 3: You can use the dialog box for gs3sls.
-------------------------------------------------------------------------------

clear all

sysuse gs3sls.dta, clear

* Y1 = Y2 X1 X2
* Y2 = Y1 X3 X4

* (1) Generalized Spatial Autoregressive 3SLS - AR(1) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(1) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test aux
> (x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(log) test tol
> og
-------------------------------------------------------------------------------

* (2) Generalized Spatial Autoregressive 3SLS - AR(2) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(2) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test aux
> (x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(log) test tol
> og
-------------------------------------------------------------------------------

* (3) Generalized Spatial Autoregressive 3SLS - AR(3) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(3) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test aux
> (x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(log) test tol
> og
-------------------------------------------------------------------------------

* (4) Generalized Spatial Autoregressive 3SLS - AR(4) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(4) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test aux
> (x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(log) test tol
> og
-------------------------------------------------------------------------------

* Generalized Spatial Autoregressive 3SLS (GS3SLS) (Cont.)
* This example is taken from Prucha data about:
* Estimation of Simultaneous Systems of Spatially Interrelated Cross Sectional
> Equations
* More details can be found in:
* http://econweb.umd.edu/~prucha/Research_Prog4.htm
* Results of (gs3sls) with order(2) is identical to:
* http://econweb.umd.edu/~prucha/STATPROG/SIMEQU/PROGRAM4.log

clear all
sysuse gs3sls1.dta , clear
gs3sls y1 x1 , var2(y2 x2) wmfile(SPWcs1) order(2)
-------------------------------------------------------------------------------

. clear all
. sysuse gs3sls.dta, clear
. gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test

==============================================================================
*** Binary (0/1) Weight Matrix: 49x49 (Non Normalized)
==============================================================================
==============================================================================
* Generalized Spatial Autoregressive Three Stage Least Squares (GS3SLS)
==============================================================================
y1 = w1y_y1 + w1y_y2 + y2 + x1 + x2
------------------------------------------------------------------------------
y2 = w1y_y2 + w1y_y1 + y1 + x3 + x4
------------------------------------------------------------------------------

Three-stage least-squares regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"     F-Stat        P
----------------------------------------------------------------------
y1_1               49      6    8.882384    0.9859     599.50   0.0000
y2_2               49      6    7.868505    0.9745     415.59   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
|      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
y1_1         |
wy11_y1 |   .1940849   .1183821     1.64   0.105     -.041251    .4294208
wy21_y2 |  -.1654769   .1140357    -1.45   0.150    -.3921724    .0612186
y2_1 |   .9109229   .0936462     9.73   0.000     .7247603    1.097085
x1 |  -.0418041   .0648295    -0.64   0.521    -.1706809    .0870727
x2 |  -.0158608   .2087922    -0.08   0.940    -.4309259    .3992043
_cons1 |  -.7531394   6.884779    -0.11   0.913    -14.43963    12.93335
-------------+----------------------------------------------------------------
y2_2         |
wy22_y2 |   .0825191   .1061625     0.78   0.439    -.1285249    .2935632
wy12_y1 |  -.0993446   .1111537    -0.89   0.374    -.3203108    .1216216
y1_2 |   .6226907   .1553474     4.01   0.000     .3138704    .9315111
x3 |   .0317989    .073177     0.43   0.665    -.1136722      .17727
x4 |    .253528   .0736226     3.44   0.001      .107171    .3998849
_cons2 |   3.050447   3.564239     0.86   0.394    -4.035025    10.13592
------------------------------------------------------------------------------
Endogenous variables:  y1_1 y2_2 wy11_y1 wy21_y2 y2_1 wy12_y1 wy22_y2 y1_2
Exogenous variables:   x1 x2 _cons1 x3 x4 _cons2 w1x_x1 w1x_x2 w1x_x3 w1x_x4
w2x_x1 w2x_x2 w2x_x3 w2x_x4
------------------------------------------------------------------------------
EQ1: R2= 0.9859 - R2 Adj.= 0.9843  F-Test =  589.235   P-Value> F(5, 42)
LLF =  -173.347   AIC =  358.694    SC =  370.045   Root MSE =  8.8824

EQ2: R2= 0.9745 - R2 Adj.= 0.9715  F-Test =  321.068   P-Value> F(5, 42)
LLF =  -167.408   AIC =  346.817    SC =  358.168   Root MSE =  7.8685
Yij = LHS Y(i) in Eq.(j)
------------------------------------------------------------------------------

- Overall System R2 - Adjusted R2 - F Test - Chi2 Test

+----------------------------------------------------------------------------+
|     Name |       R2 |   Adj_R2 |        F |  P-Value |     Chi2 |  P-Value |
|----------+----------+----------+----------+----------+----------+----------|
|   Berndt |   0.9687 |   0.9651 | 272.4818 |   0.0000 | 169.7657 |   0.0000 |
|  McElroy |   0.9807 |   0.9785 | 448.0609 |   0.0000 | 193.5317 |   0.0000 |
|    Judge |   0.7160 |   0.6830 |  22.1851 |   0.0000 |  61.6789 |   0.0000 |
+----------------------------------------------------------------------------+
Number of Parameters         =          12
Number of Equations          =           2
Degrees of Freedom F-Test    =      (10, 88)
Degrees of Freedom Chi2-Test =          10
Log Determinant of Sigma     =     -6.4948
Log Likelihood Function      =   -298.1795
------------------------------------------------------------------------------

y1 = w1y_y1 + w1y_y2 + y2 + x1 + x2
------------------------------------------------------------------------------
Sample Size       =          49
Wald Test         =    307.5420   |   P-Value > Chi2(5)       =      0.0000
F-Test            =     61.5084   |   P-Value > F(5 , 43)     =      0.0000
(Buse 1973) R2     =      0.6580   |   Raw Moments R2          =      0.9378
(Buse 1973) R2 Adj =      0.6182   |   Raw Moments R2 Adj      =      0.9306
Root MSE (Sigma)  =     10.3385   |   Log Likelihood Function =   -173.3472
------------------------------------------------------------------------------
- R2h= 0.6824   R2h Adj= 0.6455  F-Test =   18.48 P-Value > F(5 , 43)  0.0000
- R2v= 0.9650   R2v Adj= 0.9609  F-Test =  236.84 P-Value > F(5 , 43)  0.0000
------------------------------------------------------------------------------
y1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
y1_1         |
w1y_y1 |   .1940849   .1183821     1.64   0.108    -.0446554    .4328252
w1y_y2 |  -.1654769   .1140357    -1.45   0.154    -.3954518     .064498
y2 |   .9109229   .0936462     9.73   0.000     .7220672    1.099778
x1 |  -.0418041   .0648295    -0.64   0.522    -.1725452    .0889371
x2 |  -.0158608   .2087922    -0.08   0.940    -.4369304    .4052088
_cons |  -.7531394   6.884779    -0.11   0.913    -14.63762    13.13134
------------------------------------------------------------------------------
Rho Value  =  0.1941       F Test =     2.688    P-Value > F(1, 43)   0.1084
------------------------------------------------------------------------------

==============================================================================
*** Spatial Aautocorrelation Tests
==============================================================================
Ho: Error has No Spatial AutoCorrelation
Ha: Error has    Spatial AutoCorrelation

- GLOBAL Moran MI            =  -0.2035     P-Value > Z(-2.147)   0.0318
- GLOBAL Geary GC            =   1.1490     P-Value > Z(1.168)    0.2427
- GLOBAL Getis-Ords GO       =   0.9803     P-Value > Z(2.147)    0.0318
------------------------------------------------------------------------------
- Moran MI Error Test        =  -0.0764     P-Value > Z(-0.653)   0.9391
------------------------------------------------------------------------------
- LM Error (Burridge)        =   3.7644     P-Value > Chi2(1)     0.0524
- LM Error (Robust)          =  22.3153     P-Value > Chi2(1)     0.0000
------------------------------------------------------------------------------
Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has    Spatial AutoCorrelation

- LM Lag (Anselin)           =   0.3598     P-Value > Chi2(1)     0.5486
- LM Lag (Robust)            =  18.9108     P-Value > Chi2(1)     0.0000
------------------------------------------------------------------------------
Ho: No General Spatial AutoCorrelation
Ha:    General Spatial AutoCorrelation

- LM SAC (LMErr+LMLag_R)     =  22.6752     P-Value > Chi2(2)     0.0000
- LM SAC (LMLag+LMErr_R)     =  22.6752     P-Value > Chi2(2)     0.0000
------------------------------------------------------------------------------

==============================================================================
* Model Selection Diagnostic Criteria
==============================================================================
- Log Likelihood Function       LLF               =  -173.3472
- Akaike Final Prediction Error AIC               =   358.6944
- Schwarz Criterion             SC                =   370.0454
- Akaike Information Criterion  ln AIC            =     4.7860
- Schwarz Criterion             ln SC             =     5.0177
- Amemiya Prediction Criterion  FPE               =   119.9732
- Hannan-Quinn Criterion        HQ                =   130.8329
- Rice Criterion                Rice              =   124.2179
- Shibata Criterion             Shibata           =   116.7680
- Craven-Wahba Generalized Cross Validation-GCV   =   121.7994
------------------------------------------------------------------------------

==============================================================================
* Heteroscedasticity Tests
==============================================================================
Ho: Homoscedasticity - Ha: Heteroscedasticity
------------------------------------------------------------------------------
- Hall-Pagan LM Test:      E2 = Yh     =   0.3919    P-Value > Chi2(1)  0.5313
- Hall-Pagan LM Test:      E2 = Yh2    =   0.3253    P-Value > Chi2(1)  0.5685
- Hall-Pagan LM Test:      E2 = LYh2   =   0.6108    P-Value > Chi2(1)  0.4345
------------------------------------------------------------------------------
- Harvey LM Test:       LogE2 = X      =   5.9461    P-Value > Chi2(2)  0.0511
- Wald LM Test:         LogE2 = X      =  14.6713    P-Value > Chi2(1)  0.0001
- Glejser LM Test:        |E| = X      =   4.1401    P-Value > Chi2(2)  0.1262
------------------------------------------------------------------------------
- Machado-Santos-Silva Test: Ev=Yh Yh2 =   0.5182    P-Value > Chi2(2)  0.7718
- Machado-Santos-Silva Test: Ev=X      =   4.0117    P-Value > Chi2(5)  0.5477
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X      =   5.0945    P-Value > Chi2(5)  0.4045
- White Test -B-P-G (SSR): E2 = X      =   6.5695    P-Value > Chi2(5)  0.2547
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2   =  21.4646    P-Value > Chi2(10) 0.0181
- White Test -B-P-G (SSR): E2 = X X2   =  27.6792    P-Value > Chi2(10) 0.0020
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2 XX=  31.7945    P-Value > Chi2(20) 0.0455
- White Test -B-P-G (SSR): E2 = X X2 XX=  41.0001    P-Value > Chi2(20) 0.0037
------------------------------------------------------------------------------
- Cook-Weisberg LM Test  E2/Sig2 = Yh  =   0.5054    P-Value > Chi2(1)  0.4771
- Cook-Weisberg LM Test  E2/Sig2 = X   =   6.5695    P-Value > Chi2(5)  0.2547
------------------------------------------------------------------------------
*** Single Variable Tests (E2/Sig2):
- Cook-Weisberg LM Test: w1y_y1            =   0.2467 P-Value > Chi2(1) 0.6194
- Cook-Weisberg LM Test: w1y_y2            =   0.3666 P-Value > Chi2(1) 0.5449
- Cook-Weisberg LM Test: y2                =   0.5147 P-Value > Chi2(1) 0.4731
- Cook-Weisberg LM Test: x1                =   0.8640 P-Value > Chi2(1) 0.3526
- Cook-Weisberg LM Test: x2                =   1.0129 P-Value > Chi2(1) 0.3142
------------------------------------------------------------------------------
*** Single Variable Tests:
- King LM Test: w1y_y1                     =   0.3881 P-Value > Chi2(1) 0.5333
- King LM Test: w1y_y2                     =   0.7501 P-Value > Chi2(1) 0.3865
- King LM Test: y2                         =   0.2827 P-Value > Chi2(1) 0.5949
- King LM Test: x1                         =   1.1674 P-Value > Chi2(1) 0.2799
- King LM Test: x2                         =   1.5140 P-Value > Chi2(1) 0.2185
------------------------------------------------------------------------------

==============================================================================
* Non Normality Tests
==============================================================================
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
*** Non Normality Tests:
- Jarque-Bera LM Test                  =   4.0039     P-Value > Chi2(2) 0.1351
- White IM Test                        =   8.5980     P-Value > Chi2(2) 0.0136
- Doornik-Hansen LM Test               =   3.7484     P-Value > Chi2(2) 0.1535
- Geary LM Test                        =  -1.7693     P-Value > Chi2(2) 0.4129
- Anderson-Darling Z Test              =   0.6900     P > Z( 1.468)     0.9289
- D'Agostino-Pearson LM Test           =   5.1472     P-Value > Chi2(2) 0.0763
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test          =   3.3193     P-Value > Chi2(1) 0.0685
- Small LM Skewness Test               =   3.6765     P-Value > Chi2(1) 0.0552
- Skewness Z Test                      =   1.9174     P-Value > Chi2(1) 0.0552
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava  Z Kurtosis Test          =   0.8274     P-Value > Z(0,1)  0.4080
- Small LM Kurtosis Test               =   1.4708     P-Value > Chi2(1) 0.2252
- Kurtosis Z Test                      =   1.2128     P-Value > Chi2(1) 0.2252
------------------------------------------------------------------------------
Skewness Coefficient =  0.6375     - Standard Deviation =  0.3398
Kurtosis Coefficient =  3.5791     - Standard Deviation =  0.6681
------------------------------------------------------------------------------
Runs Test: (19) Runs -  (28) Positives - (21) Negatives
Standard Deviation Runs Sig(k) =  3.3912 , Mean Runs E(k) = 25.0000
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (18.3533 , 31.6467 )
------------------------------------------------------------------------------

* Linear: Marginal Effect - Elasticity *

+-----------------------------------------------------------------------------+
|     Variable | Marginal_Effect(B) |     Elasticity(Es) |               Mean |
|--------------+--------------------+--------------------+--------------------|
|y1_1          |                    |                    |                    |
|       w1y_y1 |             0.1941 |             0.9415 |           170.4034 |
|       w1y_y2 |            -0.1655 |            -0.8735 |           185.4260 |
|           y2 |             0.9109 |             1.0055 |            38.7779 |
|           x1 |            -0.0418 |            -0.0457 |            38.4362 |
|           x2 |            -0.0159 |            -0.0065 |            14.3749 |
+-----------------------------------------------------------------------------+
Mean of Dependent Variable =     35.1288

+--------+
----+ Author +-----------------------------------------------------------

Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Eg
> ypt
WebPage at IDEAS:       http://ideas.repec.org/f/psh494.html
WebPage at EconPapers:  http://econpapers.repec.org/RAS/psh494.htm

+-----------------+
----+ GS3SLS Citation +--------------------------------------------------
GS3SLS: "Generalized Spatial Autoregressive Three Stage Least Squares Cross
Sections Regression"

http://ideas.repec.org/c/boc/bocode/s457387.html

http://econpapers.repec.org/software/bocbocode/s457387.htm

*** Spatial Econometrics Regression Models:

-------------------------------------------------------------------------------
> -
*** (1) Spatial Panel Data Regression Models:
spregxt      Spatial Panel Regression Econometric Models: Stata Module Toolkit
gs2slsxt     Generalized Spatial Panel 2SLS Regression
gs2slsarxt   Generalized Spatial Panel Autoregressive 2SLS Regression
spglsxt      Spatial Panel Autoregressive Generalized Least Squares Regression
spgmmxt      Spatial Panel Autoregressive Generalized Method of Moments Regress
> ion
spmstarxt    (m-STAR) Spatial Lag Panel Models
spmstardxt   (m-STAR) Spatial Durbin Panel Models
spmstardhxt  (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Panel Mo
> dels
spmstarhxt   (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Panel Model
> s
spregdhp     Spatial Panel Han-Philips Linear Dynamic Regression: Lag & Durbin
> Models
spregdpd     Spatial Panel Arellano-Bond Linear Dynamic Regression: Lag & Durbi
> n Models
spregfext    Spatial Panel Fixed Effects Regression: Lag & Durbin Models
spregrext    Spatial Panel Random Effects Regression: Lag & Durbin Models
spregsacxt   MLE Spatial AutoCorrelation Panel Regression (SAC)
spregsarxt   MLE Spatial Lag Panel Regression (SAR)
spregsdmxt   MLE Spatial Durbin Panel Regression (SDM)
spregsemxt   MLE Spatial Error Panel Regression (SEM)
-------------------------------------------------------------------------------
> -
*** (2) Spatial Cross Section Regression Models:
spregcs      Spatial Cross Section Regression Econometric Models: Stata Module
> Toolkit
gs2sls       Generalized Spatial 2SLS Cross Sections Regression
gs2slsar     Generalized Spatial Autoregressive 2SLS Cross Sections Regression
gs3sls       Generalized Spatial Autoregressive 3SLS Regression
gs3slsar     Generalized Spatial Autoregressive 3SLS Cross Sections Regression
gsp3sls      Generalized Spatial 3SLS Cross Sections Regression
spautoreg    Spatial Cross Section Regression Models
spgmm        Spatial Autoregressive GMM Cross Sections Regression
spmstar      (m-STAR) Spatial Lag Cross Sections Models
spmstard     (m-STAR) Spatial Durbin Cross Sections Models
spmstardh    (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Cross Se
> ctions Models
spmstarh     (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Cross Secti
> ons Models
spregsac     MLE Spatial AutoCorrelation Cross Sections Regression (SAC)
spregsar     MLE Spatial Lag Cross Sections Regression (SAR)
spregsdm     MLE Spatial Durbin Cross Sections Regression (SDM)
spregsem     MLE Spatial Error Cross Sections Regression (SEM)
-------------------------------------------------------------------------------
> -
*** (3) Tobit Spatial Regression Models:

*** (3-1) Tobit Spatial Panel Data Regression Models:
sptobitgmmxt Tobit Spatial GMM Panel Regression
sptobitmstarxtTobit (m-STAR) Spatial Lag Panel Models
sptobitmstardxtTobit (m-STAR) Spatial Durbin Panel Models
sptobitmstardhxtTobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity
>  Panel Models
sptobitmstarhxtTobit (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Pan
> el Models
sptobitsacxt Tobit MLE Spatial AutoCorrelation (SAC) Panel Regression
sptobitsarxt Tobit MLE Spatial Lag Panel Regression
sptobitsdmxt Tobit MLE Spatial Panel Durbin Regression
sptobitsemxt Tobit MLE Spatial Error Panel Regression
spxttobit    Tobit Spatial Panel Autoregressive GLS Regression
--------------------------------------------------------------
*** (3-2) Tobit Spatial Cross Section Regression Models:
sptobitgmm   Tobit Spatial GMM Cross Sections Regression
sptobitmstar Tobit (m-STAR) Spatial Lag Cross Sections Models
sptobitmstardTobit (m-STAR) Spatial Durbin Cross Sections Models
sptobitmstardhTobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity C
> ross Sections
sptobitmstarhTobit (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Cross
>  Sections
sptobitsac   Tobit MLE AutoCorrelation (SAC) Cross Sections Regression
sptobitsar   Tobit MLE Spatial Lag Cross Sections Regression
sptobitsdm   Tobit MLE Spatial Durbin Cross Sections Regression
sptobitsem   Tobit MLE Spatial Error Cross Sections Regression
-------------------------------------------------------------------------------
> -
*** (4) Spatial Weight Matrix:
spcs2xt      Convert Cross Section to Panel Spatial Weight Matrix
spweight     Cross Section and Panel Spatial Weight Matrix
spweightcs   Cross Section Spatial Weight Matrix
spweightxt   Panel Spatial Weight Matrix
-------------------------------------------------------------------------------
> -

```