help: sptobitsemxt dialog:

Title

sptobitsemxt: Tobit MLE Spatial Error Panel Regression

Table of Contents

Syntax

Description

Options

Spatial Panel Aautocorrelation Tests

Model Selection Diagnostic Criteria

Heteroscedasticity Tests

Non Normality Tests

Saved Results

References

*** Examples

Authors

Syntax

sptobitsemxt depvar indepvars [weight] , nc(#) wmfile(weight_file) ll(#)

[lmspac lmhet lmnorm tests stand inv inv2 coll zero tolog nolog robust diag

dist(norm|exp|weib) mfx(lin, log) predict(new_var) resid(new_var) iter(#)

tech(name) level(#) vce(vcetype) maximize other maximization options ]

Description

sptobitsemxt estimates Tobit MLE Spatial Error Panel Regression Models

sptobitsemxt can estimate the following models:
1- Heteroscedastic Regression Models in disturbance term.
2- Non Normal Regression Models in disturbance term.

sptobitsemxt can generate:

- Binary / Standardized Weight Matrix.
- Inverse / Inverse Squared Standardized Weight Matrix.
- Binary / Standardized / Inverse Eigenvalues Variable.

sptobitsemxt predicted values are obtained from conditional expectation expression.

Yh = E(y|x) = inv(I-Rho*W) * X*Beta

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:
sptobitsemxt 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

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.
sptobitsemxt will convert automatically spatial cross section weight 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 (Optional)

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

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

coll keep collinear variables; default is removing collinear variables.

tests display ALL lmh, lmn, lmsp, diag tests

ll(#) value of minimum left-censoring dependent variable with (tobit).

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.

mfx(lin, log) calculates:

- Total Marginal Effects and Elasticities.
- Direct Marginal Effects and Elasticities.
- InDirect Marginal Effects and Elasticities.

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

dist(norm, exp, weib) Distribution of error term:

1- dist(norm) Normal distribution; default.

2- dist(exp) Exponential distribution.

3- dist(weib) Weibull distribution.

dist option is used to remedy non normality problem, when the error term has non normality distribution.

dist(norm) is the default distribution.

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

robust Huber-White standard errors

tech(name) technique algorithm for maximization of the log likelihood function LLF
tech(nr) Newton-Raphson (NR) algorithm; default
tech(bhhh) Berndt-Hall-Hall-Hausman (BHHH) algorithm
tech(dfp) Davidon-Fletcher-Powell (DFP) algorithm
tech(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm

iter(#) maximum iterations; default is 100
if iter(#) is reached (100), this means convergence not achieved yet,
so you can use another technique algorithm to converge LLF function
or exceed number of maximum iterations more than 100.

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

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

Other maximization_options allows the user to specify other maximization options (e.g., difficult, trace, iterate(#), etc.).
However, you should rarely have to specify them, though they may be helpful if parameters approach boundary values.

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 countries

- 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: Y = BX + rWy + LW1y + e ; e = lW1e+u

- General Spatial Model is used to deal with both types of spatial dependence,
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 information,
which is related to greater uncertainty, less precision, and larger standard 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 error,
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 specification
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 dependence,
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 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

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

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)]
*** Tobit Panel 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

Depending on the model estimated, sptobitsemxt 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 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

*** 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)]

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

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

References

Anderson, T.W. & C. Hsiao (1982)
"Formulation and Estimation of Dynamic Models Using Panel Data",
Journal of Econometrics, 18; 47–82.

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.

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.

Anselin L., Le Gallo J. & Jayet H (2006)
"Spatial Panel Econometrics"
In: Matyas L, Sevestre P. (eds) The Econometrics of Panel Data, Fundamentals and Recent Developments in Theory and Practice, 3rd edn. Kluwer, Dordrecht; 901-969.

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.

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 .
Note 4: xtset is included automatically in sptobitsemxt models.

clear all

sysuse sptobitsemxt.dta, clear

db sptobitsemxt

* (1) Tobit MLE Spatial SAC Panel Normal Regression Model
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(norm) predict(Yh) resid(Ue) ll(3)
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(norm) mfx(lin) test ll(3)
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(norm) mfx(log) test ll(3) tolog

* (2) Tobit MLE Spatial SAC Panel Exponential Regression Model
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(exp) mfx(lin) test ll(3)
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(exp) mfx(log) test ll(3) tolog

* (3) Tobit MLE Spatial SAC Panel Weibull Regression Model
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(weib) mfx(lin) test ll(3)
sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(weib) mfx(log) test ll(3) tolog

* (4) Tobit MLE Weighted Spatial SAC Panel Regression Model
sptobitsemxt y x1 x2 [weight = x1], nc(7) wmfile(SPWxt) mfx(lin) test ll(3)
sptobitsemxt y x1 x2 [aweight = x1], nc(7) wmfile(SPWxt) mfx(lin) test ll(3)
sptobitsemxt y x1 x2 [iweight = x1], nc(7) wmfile(SPWxt) mfx(lin) test ll(3)

. clear all
. sysuse sptobitsemxt.dta, clear
. sptobitsemxt y x1 x2 , nc(7) wmfile(SPWxt) dist(norm) mfx(lin) test ll(3)

==============================================================================
*** Binary (0/1) Weight Matrix: 49x49 - NC=7 NT=7 (Non Normalized)
==============================================================================
*** ys Lower Limit = 0
*** ys Left- Censored Observations = 9
*** ys Left-UnCensored Observations = 40
------------------------------------------------------------
==============================================================================
* Tobit MLE Spatial Error Panel Normal Model (SEM)
==============================================================================
ys = x1 + x2
------------------------------------------------------------------------------
Sample Size = 49 | Cross Sections Number = 7
Wald Test = 43.4952 | P-Value > Chi2(2) = 0.0000
F-Test = 21.7476 | P-Value > F(2 , 40) = 0.0000
(Buse 1973) R2 = 0.4860 | Raw Moments R2 = 0.8249
(Buse 1973) R2 Adj = 0.3832 | Raw Moments R2 Adj = 0.7898
Root MSE (Sigma) = 16.5476 | Log Likelihood Function = -152.4694
------------------------------------------------------------------------------
- R2h= 0.4347 R2h Adj= 0.3216 F-Test = 17.68 P-Value > F(2 , 40) 0.0000
- R2v= 0.4142 R2v Adj= 0.2971 F-Test = 16.26 P-Value > F(2 , 40) 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ys |
x1 | -.4443557 .1177555 -3.77 0.000 -.6751522 -.2135592
x2 | -1.305814 .3377474 -3.87 0.000 -1.967787 -.6438415
_cons | 69.42618 4.994364 13.90 0.000 59.6374 79.21495
-------------+----------------------------------------------------------------
Lambda | .0073434 .0239708 0.31 0.759 -.0396385 .0543253
Sigma | 10.73 1.186894 9.04 0.000 8.403725 13.05627
------------------------------------------------------------------------------
LR Test SEM vs. OLS (Lambda=0): 0.0938 P-Value > Chi2(1) 0.7593
Acceptable Range for Lambda: -0.5201 < Lambda < 0.3115
------------------------------------------------------------------------------

==============================================================================
* Panel Model Selection Diagnostic Criteria
==============================================================================
- Log Likelihood Function LLF = -152.4694
- Akaike Final Prediction Error AIC = 310.9387
- Schwarz Criterion SC = 316.6142
- Akaike Information Criterion ln AIC = 5.5320
- Schwarz Criterion ln SC = 5.6478
- Amemiya Prediction Criterion FPE = 290.5895
- Hannan-Quinn Criterion HQ = 263.9977
- Rice Criterion Rice = 254.7206
- Shibata Criterion Shibata = 250.9014
- Craven-Wahba Generalized Cross Validation-GCV = 253.6372
------------------------------------------------------------------------------

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

- GLOBAL Moran MI = -0.0995 P-Value > Z(-0.693) 0.4883
- GLOBAL Geary GC = 1.0465 P-Value > Z(0.326) 0.7442
- GLOBAL Getis-Ords GO = 0.2843 P-Value > Z(0.693) 0.4883
------------------------------------------------------------------------------
- Moran MI Error Test = -0.1053 P-Value > Z(-0.744) 0.9162
------------------------------------------------------------------------------
- LM Error (Burridge) = 0.4620 P-Value > Chi2(1) 0.4967
- LM Error (Robust) = 0.1846 P-Value > Chi2(1) 0.6675
------------------------------------------------------------------------------
Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has Spatial AutoCorrelation

- LM Lag (Anselin) = 0.2796 P-Value > Chi2(1) 0.5970
- LM Lag (Robust) = 0.0022 P-Value > Chi2(1) 0.9624
------------------------------------------------------------------------------
Ho: No General Spatial AutoCorrelation
Ha: General Spatial AutoCorrelation

- LM SAC (LMErr+LMLag_R) = 0.4642 P-Value > Chi2(2) 0.7929
- LM SAC (LMLag+LMErr_R) = 0.4642 P-Value > Chi2(2) 0.7929
------------------------------------------------------------------------------

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

- Engle LM ARCH Test AR(1): E2 = E2_1 = 0.0338 P-Value > Chi2(1) 0.8541
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 0.1783 P-Value > Chi2(1) 0.6729
- Hall-Pagan LM Test: E2 = Yh2 = 0.1458 P-Value > Chi2(1) 0.7026
- Hall-Pagan LM Test: E2 = LYh2 = 0.1281 P-Value > Chi2(1) 0.7204
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 0.7406 P-Value > Chi2(2) 0.6905
- Wald Test: LogE2 = X = 1.8274 P-Value > Chi2(1) 0.1764
- Glejser LM Test: |E| = X = 0.7796 P-Value > Chi2(2) 0.6772
- Breusch-Godfrey Test: E = E_1 X = 0.5459 P-Value > Chi2(1) 0.4600
------------------------------------------------------------------------------
- Machado-Santos-Silva Test: Ev=Yh Yh2 = 0.2029 P-Value > Chi2(2) 0.9035
- Machado-Santos-Silva Test: Ev=X = 0.8612 P-Value > Chi2(2) 0.6501
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X = 0.6416 P-Value > Chi2(2) 0.7256
- White Test - B-P-G (SSR): E2 = X = 0.9823 P-Value > Chi2(2) 0.6119
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X X2 = 2.1214 P-Value > Chi2(4) 0.7134
- White Test - B-P-G (SSR): E2 = X X2 = 3.2478 P-Value > Chi2(4) 0.5172
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X X2 XX= 2.3805 P-Value > Chi2(5) 0.7944
- White Test - B-P-G (SSR): E2 = X X2 XX= 3.6445 P-Value > Chi2(5) 0.6016
------------------------------------------------------------------------------
- Cook-Weisberg LM Test: E2/S2n = Yh = 0.2729 P-Value > Chi2(1) 0.6014
- Cook-Weisberg LM Test: E2/S2n = X = 0.9823 P-Value > Chi2(2) 0.6119
------------------------------------------------------------------------------
*** Single Variable Tests (E2/Sig2):
- Cook-Weisberg LM Test: x1 = 0.0035 P-Value > Chi2(1) 0.9530
- Cook-Weisberg LM Test: x2 = 0.7856 P-Value > Chi2(1) 0.3754
------------------------------------------------------------------------------
*** Single Variable Tests:
- King LM Test: x1 = 0.1737 P-Value > Chi2(1) 0.6769
- King LM Test: x2 = 1.2443 P-Value > Chi2(1) 0.2646
------------------------------------------------------------------------------

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

- Lagrange Multiplier LM Test = 11.5564 P-Value > Chi2(6) 0.0726
- Likelihood Ratio LR Test = 21.5728 P-Value > Chi2(6) 0.0014
- Wald Test = 974.1185 P-Value > Chi2(7) 0.0000
------------------------------------------------------------------------------

==============================================================================
* Panel Non Normality Tests
==============================================================================
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
*** Non Normality Tests:
- Jarque-Bera LM Test = 11.9267 P-Value > Chi2(2) 0.0026
- White IM Test = 12.0792 P-Value > Chi2(2) 0.0024
- Doornik-Hansen LM Test = 11.8797 P-Value > Chi2(2) 0.0026
- Geary LM Test = 0.0976 P-Value > Chi2(2) 0.9523
- Anderson-Darling Z Test = 1.5326 P > Z( 3.226) 0.9994
- D'Agostino-Pearson LM Test = 11.8985 P-Value > Chi2(2) 0.0026
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test = 9.6243 P-Value > Chi2(1) 0.0019
- Small LM Skewness Test = 9.0129 P-Value > Chi2(1) 0.0027
- Skewness Z Test = -3.0022 P-Value > Chi2(1) 0.0027
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = 1.5174 P-Value > Z(0,1) 0.1292
- Small LM Kurtosis Test = 2.8855 P-Value > Chi2(1) 0.0894
- Kurtosis Z Test = 1.6987 P-Value > Chi2(1) 0.0894
------------------------------------------------------------------------------
Skewness Coefficient = -1.0856 - Standard Deviation = 0.3398
Kurtosis Coefficient = 4.0619 - Standard Deviation = 0.6681
------------------------------------------------------------------------------
Runs Test: (25) Runs - (29) Positives - (20) Negatives
Standard Deviation Runs Sig(k) = 3.3440 , Mean Runs E(k) = 24.6735
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (18.1192 , 31.2278 )
------------------------------------------------------------------------------

==============================================================================
*** Tobit Heteroscedasticity LM Tests
==============================================================================
Separate LM Tests - Ho: Homoscedasticity
- LM Test: x1 = 0.0031 P-Value > Chi2(1) 0.9555
- LM Test: x2 = 0.5664 P-Value > Chi2(1) 0.4517

Joint LM Test - Ho: Homoscedasticity
- LM Test = 0.7906 P-Value > Chi2(2) 0.6735

==============================================================================
*** Tobit Non Normality LM Tests
==============================================================================
LM Test - Ho: No Skewness
- LM Test = 16.4995 P-Value > Chi2(1) 0.0000

LM test - Ho: No Kurtosis
- LM Test = 2.7387 P-Value > Chi2(1) 0.0979

LM Test - Ho: Normality (No Kurtosis, No Skewness)
- Pagan-Vella LM Test = 21.1041 P-Value > Chi2(2) 0.0000
- Chesher-Irish LM Test = 48.6938 P-Value > Chi2(2) 0.0000
------------------------------------------------------------------------------

* Linear: Marginal Effect - Elasticity - Spatial Panel *

+---------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|------------+--------------------+--------------------+--------------------|
|ys | | | |
| x1 | -0.4444 | -0.5888 | 38.4362 |
| x2 | -1.3058 | -0.6471 | 14.3749 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable = 29.0070

Authors

- Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
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

SPTOBITSEMXT Citation

Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2012)

SPTOBITSEMXT: "Tobit MLE Spatial Error Panel Regression"

Online Help:

*** Spatial Econometrics Regression Models:

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*** (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 Regression
spmstarxt (m-STAR) Spatial Lag Panel Models
spmstardxt (m-STAR) Spatial Durbin Panel Models
spmstardhxt (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Panel Models
spmstarhxt (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Panel Models
spregdhp Spatial Panel Han-Philips Linear Dynamic Regression: Lag & Durbin Models
spregdpd Spatial Panel Arellano-Bond Linear Dynamic Regression: Lag & Durbin 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)
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*** (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 Sections Models
spmstarh (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Cross Sections 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)
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*** (3) Tobit Spatial Regression Models:

*** (3-1) Tobit Spatial Panel Data Regression Models:
sptobitgmmxt Tobit Spatial GMM Panel Regression
sptobitmstarxt Tobit (m-STAR) Spatial Lag Panel Models
sptobitmstardxt Tobit (m-STAR) Spatial Durbin Panel Models
sptobitmstardhxt Tobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Panel Models
sptobitmstarhxt Tobit (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Panel 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
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*** (3-2) Tobit Spatial Cross Section Regression Models:
sptobitgmm Tobit Spatial GMM Cross Sections Regression
sptobitmstar Tobit (m-STAR) Spatial Lag Cross Sections Models
sptobitmstard Tobit (m-STAR) Spatial Durbin Cross Sections Models
sptobitmstardh Tobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Cross Sections
sptobitmstarh Tobit (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
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*** (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
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