+-------+ ----+ Title +------------------------------------------------------------
gs3slsar: Generalized Spatial Autoregressive Three Stage Least Squares (3SLS) Cross Sections Regression
+-------------------+ ----+ Table of Contents +------------------------------------------------
Syntax Description Model Options Options Spatial Aautocorrelation Tests Model Selection Diagnostic Criteria Heteroscedasticity Tests Non Normality Tests Saved Results References
*** Examples
Author
+--------+ ----+ Syntax +-----------------------------------------------------------
gs3slsar 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 +------------------------------------------------------
gs3slsar estimates Generalized Spatial Autoregressive Three Stage Least Squares (3SLS) for Cross Sections Regression
gs3slsar 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).
- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1). - F-Test=R2/(1-R2)*(N-K-1)/(K).
Buse(1973) R2 in (gs3slsar) 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: gs3slsar 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, gs3slsar y1 x1 x2 , wmfile(SPWcs) var2(y2 x3 x4) eq(1) gs3slsar 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 +----------------------------------------------------
gs3slsar 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(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
*** 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(lmhmss2) Machado-Santos-Silva LM Test: Ev=X 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(lmnad) Anderson-Darling Z Test e(lmnadp) Anderson-Darling Z 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(gradient) gradient vector 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 gs3slsar. -------------------------------------------------------------------------------
clear all
sysuse gs3slsar.dta, clear
* Y1 = Y2 X1 X2 * Y2 = Y1 X3 X4
* (1) Generalized Spatial Autoregressive 3SLS - AR(1) (GS3SLSAR) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(1) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test a > ux(x5) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(log) test t > olog -------------------------------------------------------------------------------
* (2) Generalized Spatial Autoregressive 3SLS - AR(2) (GS3SLSAR) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(2) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test a > ux(x5) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(log) test t > olog -------------------------------------------------------------------------------
* (3) Generalized Spatial Autoregressive 3SLS - AR(3) (GS3SLSAR) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(3) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test a > ux(x5) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(log) test t > olog -------------------------------------------------------------------------------
* (4) Generalized Spatial Autoregressive 3SLS - AR(4) (GS3SLSAR) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(4) mfx(lin) test gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test a > ux(x5) gs3slsar y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(log) test t > olog -------------------------------------------------------------------------------
* Generalized Spatial Autoregressive 3SLS (GS3SLSAR) (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 (gs3slsar) with order(2) is identical to: * http://econweb.umd.edu/~prucha/STATPROG/SIMEQU/PROGRAM4.log
clear all sysuse gs3slsar1.dta , clear gs3slsar y1 x1 , var2(y2 x2) wmfile(SPWcs1) order(2) -------------------------------------------------------------------------------
. clear all . sysuse gs3slsar.dta, clear . gs3slsar 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 (GS3SLSAR) ============================================================================== 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 +-----------------------------------------------------------
Emad Abd Elmessih Shehata Professor (PhD Economics) Agricultural Research Center - Agricultural Economics Research Institute - Eg > ypt 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
+-------------------+ ----+ GS3SLSAR Citation +------------------------------------------------ Shehata, Emad Abd Elmessih (2012) GS3SLSAR: "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
Online Help:
*** 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 ------------------------------------------------------------------------------- > -