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help: spregrext                                                   dialog: spreg
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+-------+ ----+ Title +------------------------------------------------------------

spregrext: Spatial Panel Random Effects Regression: Lag and Durbin Models

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

*** Examples

Authors

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

spregrext depvar indepvars , nc(#) wmfile(weight_file) model(sar, sdm) [ lmspac lmhet lmnorm diag tests stand inv inv2 mfx(lin, log) aux(varlist) predict(new_var) resid(new_var) level(#) noconstant coll zero tolog vce(vcetype) ]

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

spregrext estimates Spatial Panel MLE Random-Effects Regression with both Lag and Durbin Models

spregrext can generate: - Binary / Standardized Weight Matrix. - Inverse / Inverse Squared Standardized Weight Matrix.

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).

*** Important Notes: spregrext 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 +----------------------------------------------------

1- model(sar) Spatial Lag Model 2- model(sdm) Spatial Durbin Model

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

* nc(#) Number of Cross Sections Units Time series observations must be Balanced in each Cross Section

wmfile(weight_file) Open CROSS SECTION weight matrix file. spregrext will convert automatically spatial cross section w > eight matrix to spatial PANEL weight matrix.

Spatial Weight Matrix file must be: 1- [SxS] Cross Sections units Dimentions, and not Panel dimentions 2- Square Matrix 3- Symmetric Matrix

Spatial Panel Weight Matrix has two types: Standardized and binary weight mat > rix.

stand Use Standardized Panel Weight Matrix, (each row sum equals 1 > ) Default is Binary spatial panel weight matrix which each ele > ment is 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.

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

noconstant Exclude Constant Term from Equation

tests display ALL lmh, lmn, lmsp, diag tests

mfx(lin, log) functional form: Linear model (lin), or Log-Log model (log), to compute Total, Direct, and InDirect 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 ; that is known as combined residual: [Ue = > U_i + E_it] in xtreg models overall error component is computed as: [E_it] see: xtreg postestimation##predict

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

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

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

lmspac Spatial Panel 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

+-------------------------------------------+ ----+ Panel Model Selection Diagnostic Criteria +------------------------

diag Spatial Panel Model Selection Diagnostic Criteria: - Log Likelihood Function LLF - Akaike Final Prediction Error AIC - Schwartz Criterion SC - Akaike Information Criterion ln AIC - Schwarz Criterion ln SC - Amemiya Prediction Criterion FPE - Hannan-Quinn Criterion HQ - Rice Criterion Rice - Shibata Criterion Shibata - Craven-Wahba Generalized Cross Validation-GCV

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

lmhet Spatial Panel Heteroscedasticity Tests: * Ho: Panel Homoscedasticity - Ha: Panel Heteroscedasticity - Engle LM ARCH Test AR(1) E2 =E2_1 - 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 - Breusch-Godfrey Test: E = E_1 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

*** Groupwise Panel Heteroscedasticity Tests * Ho: Panel Homoscedasticity - Ha: Panel Groupwise Heteroscedasticity - Lagrange Multiplier LM Test - Likelihood Ratio LR Test - Wald Test

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

lmnorm Spatial Panel Non Normality Tests: * Ho: Panel Normality - Ha: Panel 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)]

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

Depending on the model estimated, spregrext saves the following results in e():

Scalars

*** Spatial Panel 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

*** Spatial Panel 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 e(aic) Akaike Final Prediction Error AIC e(sc) Schwartz Criterion SC e(laic) Akaike Information Criterion ln AIC e(lsc) Schwarz Criterion Log SC e(fpe) Amemiya Prediction Criterion FPE e(hq) Hannan-Quinn Criterion HQ e(shibata) Shibata Criterion Shibata e(rice) Rice Criterion Rice e(gcv) Craven-Wahba Generalized Cross Validation-GCV e(df1) DF1 e(df2) DF2 e(rmse) Root Mean Squared Error e(rss) Residual Sum of Squares e(wald) Wald Test e(waldp) Wald Test P-Value

*** Spatial Panel Heteroscedasticity Tests: e(lmharch) Engle LM ARCH Test AR(1) e(lmharchp) Engle LM ARCH Test AR(1) P-Value 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(lmhbg) Breusch-Godfrey Test e(lmhbgp) Breusch-Godfrey Test 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

*** Spatial Panel Groupwise Heteroscedasticity Tests: e(lmhglm) Lagrange Multiplier LM Test e(lmhglmp) Lagrange Multiplier LM Test P-Value e(lmhglr) Likelihood Ratio LR Test e(lmhglrp) Likelihood Ratio LR Test P-Value e(lmhgw) Wald Test e(lmhgwp) Wald Test P-Value

*** Spatial Panel 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)]

Matrixes e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(mfx) Marginal Effect e(mfxe) Elasticity

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

Anderson T.W. & Darling D.A. (1954) "A Test of Goodness of Fit", Journal of the American Statisical Association, 49; 765–69.

Anderson, T. W. & H. Rubin (1950) "The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations", Annals of Mathematical Statistics, Vol. 21; 570-82.

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.

Baltagi, B.H. (2006) "Random Effects and Spatial Autocorrelation with Equal Weights" Econometric Theory 22(5); 973-984.

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.

Elhorst, J. Paul (2003) "Specification and Estimation of Spatial Panel Data Models" International Regional Science review 26, 3; 244–268.

Elhorst, J. Paul (2009) "Spatial Panel Data Models" in Mandfred M. Fischer and Arthur Getis, eds., Handbook of Applied Spatial Analysis, Berlin: Springer.

Engle, Robert (1982) "Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation" Econometrica, 50(4), July; 987-1007.

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.

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

James LeSage and R. Kelly Pace (2009) "Introduction to Spatial Econometrics", Publisher: Chapman & Hall/CRC.

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.

White, Halbert (1980) "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity", Econometrica, 48; 817-838.

Wooldridge, Jeffrey M. (2002) "Econometric Analysis of Cross Section and Panel Data", The MIT Press, Cambridge, Massachusetts, London, England.

+----------+ ----+ 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 spregrext. Note 4: xtset is included automatically in spregrext models. -------------------------------------------------------------------------------

clear all

sysuse spregrext.dta, clear

db spregrext

* (1) Spatial Panel Random Effects Lag Model spregrext y x1 x2 , nc(7) wmfile(SPWxt) model(sar) mfx(lin) tests

* (2) Spatial Panel Random Effects Durbin Model spregrext y x1 x2 , nc(7) wmfile(SPWxt) model(sdm) mfx(lin) tests

spregrext y x1 x2 , nc(7) wmfile(SPWxt) model(sdm) aux(dcs1 dcs2 dcs3) tests

spregrext y x1 x2 dcs1 dcs2 dcs3 , nc(7) wmfile(SPWxt) model(sdm) mfx(lin) tes > ts -------------------------------------------------------------------------------

. clear all . sysuse spregrext.dta, clear . spregrext y x1 x2 , nc(7) wmfile(SPWxt) model(sar) mfx(lin) tests

============================================================================== *** Binary (0/1) Weight Matrix: 49x49 - NC=7 NT=7 (Non Normalized) ============================================================================== ============================================================================== * Spatial Panel Random-Effects Lag Regression (SAR) ============================================================================== y = w1y_y + x1 + x2 ------------------------------------------------------------------------------ Sample Size = 49 | Cross Sections Number = 7 Wald Test = 59.6853 | P-Value > Chi2(3) = 0.0000 F-Test = 19.8951 | P-Value > F(3 , 39) = 0.0000 (Buse 1973) R2 = 0.7981 | Raw Moments R2 = 0.9633 (Buse 1973) R2 Adj = 0.7515 | Raw Moments R2 Adj = 0.9548 Root MSE (Sigma) = 8.3417 | Log Likelihood Function = -167.8776 ------------------------------------------------------------------------------ - R2h= 0.4981 R2h Adj= 0.3822 F-Test = 14.88 P-Value > F(3 , 39) 0.0000 - R2v= 0.4324 R2v Adj= 0.3014 F-Test = 11.43 P-Value > F(3 , 39) 0.0000 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- w1y_y | -.0970908 .0624423 -1.55 0.128 -.2233922 .0292106 x1 | -.2627951 .0800613 -3.28 0.002 -.4247343 -.1008559 x2 | -1.065928 .2860726 -3.73 0.001 -1.644564 -.4872913 _cons | 70.26203 7.203419 9.75 0.000 55.69174 84.83232 ------------------------------------------------------------------------------ Rho Value = -0.0971 Chi2 Test = 2.418 P-Value > Chi2(1) 0.1281 ------------------------------------------------------------------------------

============================================================================== * Panel Model Selection Diagnostic Criteria ============================================================================== - Log Likelihood Function LLF = -167.8776 - Akaike Final Prediction Error AIC = 349.7552 - Schwartz Criterion SC = 362.9979 - Akaike Information Criterion ln AIC = 4.3000 - Schwarz Criterion ln SC = 4.5702 - Amemiya Prediction Criterion FPE = 79.5240 - Hannan-Quinn Criterion HQ = 81.6563 - Rice Criterion Rice = 77.5359 - Shibata Criterion Shibata = 71.2064 - Craven-Wahba Generalized Cross Validation-GCV = 75.3821 ------------------------------------------------------------------------------

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

- GLOBAL Moran MI = 0.1581 P-Value > Z( 1.573) 0.1158 - GLOBAL Geary GC = 0.7908 P-Value > Z(-1.482) 0.1384 - GLOBAL Getis-Ords GO = -0.4517 P-Value > Z(-1.573) 0.1158 ------------------------------------------------------------------------------ - Moran MI Error Test = 0.7232 P-Value > Z(6.540) 0.4695 ------------------------------------------------------------------------------ - LM Error (Burridge) = 1.1082 P-Value > Chi2(1) 0.2925 - LM Error (Robust) = 4.1311 P-Value > Chi2(1) 0.0421 ------------------------------------------------------------------------------ Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation Ha: Spatial Lagged Dependent Variable has Spatial AutoCorrelation

- LM Lag (Anselin) = 0.1502 P-Value > Chi2(1) 0.6984 - LM Lag (Robust) = 3.1731 P-Value > Chi2(1) 0.0749 ------------------------------------------------------------------------------ Ho: No General Spatial AutoCorrelation Ha: General Spatial AutoCorrelation

- LM SAC (LMErr+LMLag_R) = 4.2813 P-Value > Chi2(2) 0.1176 - LM SAC (LMLag+LMErr_R) = 4.2813 P-Value > Chi2(2) 0.1176 ------------------------------------------------------------------------------

============================================================================== *** Panel Heteroscedasticity Tests ============================================================================== Ho: Panel Homoscedasticity - Ha: Panel Heteroscedasticity

- Engle LM ARCH Test AR(1): E2 = E2_1 = 0.2763 P-Value > Chi2(1) 0.5992 ------------------------------------------------------------------------------ - Hall-Pagan LM Test: E2 = Yh = 0.0280 P-Value > Chi2(1) 0.8672 - Hall-Pagan LM Test: E2 = Yh2 = 0.0148 P-Value > Chi2(1) 0.9030 - Hall-Pagan LM Test: E2 = LYh2 = 0.0725 P-Value > Chi2(1) 0.7878 ------------------------------------------------------------------------------ - Harvey LM Test: LogE2 = X = 1.6048 P-Value > Chi2(2) 0.4483 - Wald Test: LogE2 = X = 3.9596 P-Value > Chi2(1) 0.0466 - Glejser LM Test: |E| = X = 7.0870 P-Value > Chi2(2) 0.0289 - Breusch-Godfrey Test: E = E_1 X = 9.1582 P-Value > Chi2(1) 0.0025 ------------------------------------------------------------------------------ - Machado-Santos-Silva Test: Ev=Yh Yh2 = 0.2813 P-Value > Chi2(2) 0.8688 - Machado-Santos-Silva Test: Ev=X = 6.3181 P-Value > Chi2(3) 0.0971 ------------------------------------------------------------------------------ - White Test - Koenker(R2): E2 = X = 8.1716 P-Value > Chi2(3) 0.0426 - White Test - B-P-G (SSR): E2 = X = 11.7901 P-Value > Chi2(3) 0.0081 ------------------------------------------------------------------------------ - White Test - Koenker(R2): E2 = X X2 = 9.8556 P-Value > Chi2(6) 0.1309 - White Test - B-P-G (SSR): E2 = X X2 = 14.2198 P-Value > Chi2(6) 0.0273 ------------------------------------------------------------------------------ - White Test - Koenker(R2): E2 = X X2 XX= 27.4331 P-Value > Chi2(9) 0.0012 - White Test - B-P-G (SSR): E2 = X X2 XX= 39.5809 P-Value > Chi2(9) 0.0000 ------------------------------------------------------------------------------ - Cook-Weisberg LM Test: E2/S2n = Yh = 0.0404 P-Value > Chi2(1) 0.8408 - Cook-Weisberg LM Test: E2/S2n = X = 11.7901 P-Value > Chi2(3) 0.0081 ------------------------------------------------------------------------------ *** Single Variable Tests (E2/Sig2): - Cook-Weisberg LM Test: w1y_y = 0.0011 P-Value > Chi2(1) 0.9733 - Cook-Weisberg LM Test: x1 = 2.8006 P-Value > Chi2(1) 0.0942 - Cook-Weisberg LM Test: x2 = 2.9608 P-Value > Chi2(1) 0.0853 ------------------------------------------------------------------------------ *** Single Variable Tests: - King LM Test: w1y_y = 0.0166 P-Value > Chi2(1) 0.8975 - King LM Test: x1 = 0.0815 P-Value > Chi2(1) 0.7752 - King LM Test: x2 = 3.0773 P-Value > Chi2(1) 0.0794 ------------------------------------------------------------------------------

============================================================================== * Panel Groupwise Heteroscedasticity Tests ============================================================================== Ho: Panel Homoscedasticity - Ha: Panel Groupwise Heteroscedasticity

- Lagrange Multiplier LM Test = 6.6534 P-Value > Chi2(6) 0.3541 - Likelihood Ratio LR Test = 6.9317 P-Value > Chi2(6) 0.3272 - Wald Test = 14.6044 P-Value > Chi2(7) 0.0414 ------------------------------------------------------------------------------

============================================================================== * Panel Non Normality Tests ============================================================================== Ho: Normality - Ha: Non Normality ------------------------------------------------------------------------------ *** Non Normality Tests: - Jarque-Bera LM Test = 1.9767 P-Value > Chi2(2) 0.3722 - White IM Test = 8.3237 P-Value > Chi2(2) 0.0156 - Doornik-Hansen LM Test = 4.6284 P-Value > Chi2(2) 0.0988 - Geary LM Test = -1.0081 P-Value > Chi2(2) 0.6041 - Anderson-Darling Z Test = 0.3602 P > Z( 0.112) 0.5447 - D'Agostino-Pearson LM Test = 2.8163 P-Value > Chi2(2) 0.2446 ------------------------------------------------------------------------------ *** Skewness Tests: - Srivastava LM Skewness Test = 0.3753 P-Value > Chi2(1) 0.5401 - Small LM Skewness Test = 0.4612 P-Value > Chi2(1) 0.4971 - Skewness Z Test = -0.6791 P-Value > Chi2(1) 0.4971 ------------------------------------------------------------------------------ *** Kurtosis Tests: - Srivastava Z Kurtosis Test = 1.2654 P-Value > Z(0,1) 0.2057 - Small LM Kurtosis Test = 2.3551 P-Value > Chi2(1) 0.1249 - Kurtosis Z Test = 1.5346 P-Value > Chi2(1) 0.1249 ------------------------------------------------------------------------------ Skewness Coefficient = -0.2144 - Standard Deviation = 0.3398 Kurtosis Coefficient = 3.8856 - Standard Deviation = 0.6681 ------------------------------------------------------------------------------ Runs Test: (22) Runs - (24) Positives - (25) Negatives Standard Deviation Runs Sig(k) = 3.4619 , Mean Runs E(k) = 25.4898 95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (18.7045 , 32.2751 ) ==============================================================================

* Linear: Marginal Effect - Elasticity - Spatial Panel - (Model= sar) *

+---------------------------------------------------------------------------+ | Variable | Marginal_Effect(B) | Elasticity(Es) | Mean | |------------+--------------------+--------------------+--------------------| | w1y_y | -0.0971 | -0.2764 | 100.0064 | | x1 | -0.2628 | -0.2875 | 38.4362 | | x2 | -1.0659 | -0.4362 | 14.3749 | +---------------------------------------------------------------------------+ Mean of Dependent Variable = 35.1288 -------------------------------------------------------------------------------

+---------+ ----+ Authors +----------------------------------------------------------

- 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

- Sahra Khaleel A. Mickaiel Professor (PhD Economics) Cairo University - Faculty of Agriculture - Department of Economics - Egypt Email: sahra_atta@hotmail.com WebPage: http://sahraecon.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/pmi520.html WebPage at EconPapers: http://econpapers.repec.org/RAS/pmi520.htm

+--------------------+ ----+ SPREGREXT Citation +-----------------------------------------------

Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2012) SPREGREXT: "Spatial Panel Random Effects Regression: Lag and Durbin Models"