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Title

almon: Shirley Almon Generalized Polynomial Distributed Lag Model

Table of Contents

Syntax

Description

Model Options

Almon Options

GMM Options

Ridge Options

Weight Options

Weighted Variable Type Options

Other Options

Model Selection Diagnostic Criteria

Autocorrelation Tests

Heteroscedasticity Tests

Non Normality Tests

Saved Results

References

*** Examples

Author

Syntax

almon depvar indepvars [if] [in] [weight] , zlag(vars) pdl(#) endpr(#)

[ model(als, arch, bcox, gls, gmm, ols, qreg, rreg)

weights(yh|yh2|abse|e2|le2|x|xi|x2|xi2) wvar(varname) techn(str) condition

ridge(orr|grr1|grr2|grr3) kr(#) tune(#) hetcov(type)

lmauto lmhet lmnorm sig diag dn tolog nolag

mfx(lin, log) noconstant tests lag(#) dlag(#) hetcov(gmm_type)

lamp(lhs|rhs|alls|alld) vce(str) techn(str) iter(#)

ar(#) tolerance(#) predict(new_var) resid(new_var) twostep quantile(#) level(#) ]

Description

almon estimates Shirley Almon Polynomial Distributed Lag Model for many variables with different lag order, endpoint restrictions, and polynomial degree order via (ALS - ARCH - Box-Cox - GLS - GMM - OLS - QREG - RREG - Ridge) Regression models,
and computes Autocorrelation, Heteroscedasticity, and Non Normality Tests. Model Selection Diagnostic Criteria,
and Marginal effects and elasticities in both short and long run.

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).

Model Options

model description

als Autoregressive Least Squares (ALS)

arch Autoregressive Conditional Heteroskedasticity (ARCH)

bcox Box-Cox Regression Model (Box-Cox)

gls Generalized Least Squares (GLS)

gmm Generalized Method of Moments (GMM)

ols Ordinary Least Squares (OLS)

qreg Quantile Regression (QREG)

rreg Robust Regression (RREG)

Almon Options

pdl(#) Polynomial Degree (Must be Specified)

endpr(#) Endpoint Restriction Range Must be Specified as (0, 1, 2, 3)

endpr(0) No Endpoint Polynomial Restrictions

endpr(1) Left Side Endpoint Polynomial Restrictions

endpr(2) Right Side Endpoint Polynomial Restrictions

endpr(3) Left & Right Side Endpoint Restrictions of Polynomial

zlag(vars) Polynomial Variables (Must be Specified)

Number of zlag(#) must Equal Number of endpr(#)

GMM Options

hetcov Options Description

hetcov(white) White Method

hetcov(bart) Bartlett Method

hetcov(crag) Cragg (1983) Auxiliary Variables Method

hetcov(dan) Daniell Method

hetcov(hdun) Horn-Duncan (1975) Method

hetcov(hink) Hinkley (1977) Method

hetcov(jack) Jackknife Mackinnon-White (1985) Method

hetcov(nwest) Newey-West Method

hetcov(parzen) Parzen Method

hetcov(quad) Quadratic Spectral Method

hetcov(tent) Tent Method

hetcov(trunc) Truncated Method

hetcov(tukey) Tukey Method

hetcov(tukeym) Tukey-Hamming Method

hetcov(tukeyn) Tukey-Hanning Method

Ridge Options

kr(#) Ridge k value, must be in the range (0 < k < 1).

IF kr(0) in ridge(orr, grr1, grr2, grr3), the model will be an OLS regression.

ridge(orr) : Ordinary Ridge Regression [Judge,et al(1988,p.878) eq.21.4.2]

ridge(grr1): Generalized Ridge Regression [Judge,et al(1988,p.881) eq.21.4.12]

ridge(grr2): Iterative Generalized Ridge [Judge,et al(1988,p.881) eq.21.4.12]

ridge(grr3): Adaptive Generalized Ridge [Strawderman(1978)]

almon estimates Ordinary Ridge regression as a multicollinearity remediation method.

General form of Ridge Coefficients and Covariance Matrix are:

Br = inv[X'X + kI] X'Y

Cov=Sig^2 * inv[X'X + kI] (X'X) inv[X'X + kI]

where:
Br = Ridge Coefficients Vector (k x 1).
Cov = Ridge Covariance Matrix (k x k).
Y = Dependent Variable Vector (N x 1).
X = Independent Variables Matrix (N x k).
k = Ridge Value (0 < k < 1).
I = Diagonal Matrix of Cross Product Matrix (Xs'Xs).
Xs = Standardized Variables Matrix in Deviation from Mean.
Sig2 = (Y-X*Br)'(Y-X*Br)/DF

Weight Options

wvar(varname) Weighted Variable Name

Weighted Variable Type Options

weights Options Description

weights(yh) Yh - Predicted Value

weights(yh2) Yh^2 - Predicted Value Squared

weights(abse) abs(E) - Absolute Value of Residual

weights(e2) E^2 - Residual Squared

weights(le2) log(E^2) - Log Residual Squared

weights(x) (x) Variable

weights(xi) (1/x) Inverse Variable

weights(x2) (x^2) Squared Variable

weights(xi2) (1/x^2) Inverse Squared Variable

Other Options

lamp( ) Transformation Type in model(bcox)

lamp(lhs) Power Transformations on (LHS) Left Hand Side Only; default

lamp(rhs) Power Transformations on (RHS) Right Hand Side Only

lamp(alls) Power Transformations on both (LHS) & (RHS) are the Same

lamp(alld) Power Transformations on both (LHS) & (RHS) are Different

techn(name) Maximization of Log Likelihood Function (LLF) Technique Algorithm

techn(nr) Newton-Raphson (NR); default

techn(bhhh) Berndt-Hall-Hall-Hausman (BHHH)

techn(dfp) Davidon-Fletcher-Powell (DFP)

techn(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS)

dlag(#) Location of Lagged Dependent Variable

lag(#) Lag Length Order Tests; Autocorrelation, Heteroscedasticity, and Unit Roots

ar(#) Autoregressive Variables Lag Length

condition use conditional MLE instead of full MLE with model(als)

dn Use (N) divisor instead of (N-K) for Degrees of Freedom (DF)

quantile(#) Quantile Value

tune(#) use # as the biweight tuning constant;
default is tune(7) with model(qreg)

twostep Two-Step estimation, stop after first iteration, same as iter(1)

iter(#) number of iterations; Default is iter(200)

tolerance(#) tolerance for coefficient vector; Default is tol(0.00001)

tests Display ALL lma, lmh, lmn, lmi, lmcl, diag, reset tests

noconstant Exclude Constant Term from Equation

nolag Use Independent Variables in current period X(t), instead of lag X(t-1)

predict(new_var) Predicted values variable

resid(new_var) Residuals values variable

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 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

sig print significance level for each entry in Correlation Matrix

level(#) Confidence Intervals Level; default is level(95)

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

techn(name) Maximization of Log Likelihood Function (LLF) Technique Algorithm

techn(nr) Newton-Raphson (NR); default

techn(bhhh) Berndt-Hall-Hall-Hausman (BHHH)

techn(dfp) Davidon-Fletcher-Powell (DFP)

techn(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS)

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

lmauto: Autocorrelation Tests

Ho: No Autocorrelation - Ha: Autocorrelation
- Durbin h Test (Lag DepVar)
- Durbin h Test after ALS(1)
- Harvey LM Test (Lag DepVar)
- Harvey LM Test after ALS(1)
- Wald T Test
- Wald Chi2 Test
- Berenblut-Webb Test
- King Test (MA)
- Rho Value for
- Durbin-Watson Test
- Von Neumann Ratio Test
- Durbin m Test (drop 1 obs)
- Durbin m Test (keep 1 obs)
- Breusch-Godfrey LM Test (drop 1 obs)
- Breusch-Godfrey LM Test (keep 1 obs)
- Breusch-Pagan-Godfrey LM Test
- Ljung-Box LM Test
- Box-Pierce LM Test
- Z Test

lmhet: Heteroscedasticity Tests

Ho: Homoscedasticity - Ha: Heteroscedasticity
- Engle LM ARCH Test
- Hall-Pagan LM Test: E2 = Yh
- Hall-Pagan LM Test: E2 = Yh2
- Hall-Pagan LM Test: E2 = LYh2
- Harvey LM Test: LogE2 = X
- Wald LM Test: LogE2 = X
- Glejser LM Test: |E| = X
- Breusch-Godfrey Test: E2 = E2_1 X
- Machado-Santos-Silva Test: Ev=Yh Yh2
- Machado-Santos-Silva 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 E2/Sig2 = Yh
- Cook-Weisberg LM Test E2/Sig2 = X

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
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test
- Small LM Kurtosis Test
- Kurtosis Z Test
- Runs Test

Saved Results

almon saves the following in e():

*** 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

*** Autocorrelation Tests:
e(rho#) Rho Value for AR(i)
e(lmabgd#) Breusch-Godfrey LM Test (drop i obs)
e(lmabgdp#) Breusch-Godfrey LM Test (drop i obs) P-Value
e(lmabgk#) Breusch-Godfrey LM Test (keep i obs)
e(lmabgkp#) Breusch-Godfrey LM Test (keep i obs) P-Value
e(lmabpg#) Breusch-Pagan-Godfrey LM Test AR(i)
e(lmabpgp#) Breusch-Pagan-Godfrey LM Test AR(i) P-Value
e(lmabp#) Box-Pierce LM Test AR(i)
e(lmabpp#) Box-Pierce LM Test AR(i) P-Value
e(lmadho) Durbin h Test (Lag DepVar)
e(lmadhop) Durbin h Test (Lag DepVar) P-Value
e(lmadha) Durbin h Test after ALS(1)
e(lmadhap) Durbin h Test after ALS(1) P-Value
e(lmadmd#) Durbin m Test (drop i obs) AR(i)
e(lmadmdp#) Durbin m Test (drop i obs) AR(i) P-Value
e(lmadmk#) Durbin m Test (keep i obs) AR(i)
e(lmadmkp#) Durbin m Test (keep i obs) AR(i) P-Value
e(lmadw#) Durbin-Watson Test AR(i)
e(lmahho) Harvey LM Test (Lag DepVar)
e(lmahhop) Harvey LM Test (Lag DepVar) P-Value
e(lmahha) Harvey LM Test after ALS(1)
e(lmahhap) Harvey LM Test after ALS(1) P-Value
e(lmalb#) Ljung-Box LM Test AR(i)
e(lmalbp#) Ljung-Box LM Test AR(i) P-Value
e(lmawt) Wald T Test
e(lmawtp) Wald T Test P-Value
e(lmawc) Wald Chi2 Test
e(lmawcp) Wald Chi2 Test P-Value
e(lmabw) Berenblut-Webb Test
e(lmakg) King Test (MA)
e(lmavon#) Von Neumann Ratio Test AR(i)
e(lmaz#) Z Test AR(i)
e(lmazp#) Z Test AR(i) P-Value

*** Heteroscedasticity Tests:
e(lmharch) Engle LM ARCH Test AR(i)
e(lmharchp) Engle LM ARCH Test AR(i) P-Value
e(lmhhp1) Hall-Pagan LM Test
e(lmhhp1p) Hall-Pagan LM Test P-Value
e(lmhhp2) Hall-Pagan LM Test
e(lmhhp2p) Hall-Pagan LM Test P-Value
e(lmhhp3) Hall-Pagan LM Test
e(lmhhp3p) Hall-Pagan LM Test P-Value
e(lmhharv) Harvey LM Test
e(lmhharvp) Harvey LM Test P-Value
e(lmhwald) Wald LM Test
e(lmhwaldp) Wald LM Test P-Value
e(lmhgl) Glejser LM Test
e(lmhglp) Glejser LM Test P-Value
e(lmhmss1) Machado-Santos-Silva Test: Ev=Yh Yh2 LM Test
e(lmhmss1p) Machado-Santos-Silva Test: Ev=Yh Yh2 LM Test P-Value
e(lmhmss2) Machado-Santos-Silva Test: Ev=X LM Test
e(lmhmss2p) Machado-Santos-Silva Test: Ev=X LM Test P-Value
e(lmhbg) Breusch-Godfrey Test
e(lmhbgp) Breusch-Godfrey Test P-Value
e(lmhw01) White Test (X) - Koenker(R2)
e(lmhw01p) White Test (X) - Koenker(R2) P-Value
e(lmhw02) White Test (X) - B-P-G (SSR)
e(lmhw02p) White Test (X) - B-P-G (SSR) P-Value
e(lmhw11) White Test (X X2) - Koenker(R2)
e(lmhw11p) White Test (X X2) - Koenker(R2) P-Value
e(lmhw12) White Test (X X2) - B-P-G (SSR)
e(lmhw12p) White Test (X X2) - B-P-G (SSR) P-Value
e(lmhw21) White Test (X X2 XX) - Koenker(R2)
e(lmhw21p) White Test (X X2 XX) - Koenker(R2) P-Value
e(lmhw22) White Test (X X2 XX) - B-P-G (SSR)
e(lmhw22p) White Test (X X2 XX) - B-P-G (SSR) P-Value
e(lmhcw1) Cook-Weisberg LM Test E2/Sig2n = Yh
e(lmhcw1p) Cook-Weisberg LM Test E2/Sig2n = Yh P-Value
e(lmhcw2) Cook-Weisberg LM Test E2/Sig2n = X
e(lmhcw2p) Cook-Weisberg LM Test E2/Sig2n = 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(lmnsms) Small LM Skewness Test
e(lmnsmsp) Small LM Skewness Test P-Value
e(lmnsz) Skewness Z Test
e(lmnszp) Skewness Z Test P-Value
e(lmnsvk) Srivastava Z Kurtosis Test
e(lmnsvkp) Srivastava Z Kurtosis Test P-Value
e(lmnsmk) Small LM Kurtosis Test
e(lmnsmkp) Small LM Kurtosis Test P-Value
e(lmnsmk) Kurtosis Z Test
e(lmnsmkp) Kurtosis Z Test P-Value
e(sk) Skewness Coefficient
e(sksd) Skewness Standard Deviation
e(ku) Kurtosis Coefficient
e(kusd) Kurtosis Standard Deviation
e(en) Mean Runs E(k)
e(sn) Standard Deviation Runs Sig(k)
e(lower) 95% Lower Conf. Interval
e(upper) 95% Upper Conf. Interval

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(restc) Restriction Matrix

References

Shirley Montag Almon (1935–1975)
http://en.wikipedia.org/wiki/Shirley_Montag_Almon

Almon, Shirley (1965)
The Distributed Lag Between Capital Appropriations and Expenditures,
Econometrica, Vol. 33, No. 1, Jan.; 178-196.

Almon, Shirley (1968)
Lags Between Investment Decisions and Their Causes,
Rev. Econ. Stat., Vol. 50; 193-206.

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

Box, George & Pierce D. (1970)
"Distribution of Residual Autocorrelations in Autoregressive Integrated Moving Average Time Series Models",
Journal of the American Statisical Association, 65; 1509-1526.

Breusch, Trevor (1978)
"Testing for Autocorrelation in Dynamic Linear Models",
Aust. Econ. Papers, Vol. 17; 334-355.

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. Belsley (1991)
"Conditioning Diagnostics, Collinearity and Weak Data in Regression",
John Wiley & Sons, Inc., New York, USA.

D. Belsley, E. Kuh, and R. Welsch (1980)
"Regression Diagnostics: Identifying Influential Data and Sources of Collinearity",
John Wiley & Sons, Inc., New York, USA.

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.

DeBenedictis, L. F. & Giles D. E. A. (1998)
"Diagnostic Testing in Econometrics: Variable Addition, RESET and Fourier Approximations",
In: A. Ullah & D. E. A. Giles (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York; 383-417.

Durbin, James (1970a)
"Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables",
Econometrica, vol.38, no.3, May; 410-421.

Durbin, James (1970b)
"An Alternative to the Bounds Test for Testing for Serial Correlation in Least Square Regression",
Econometrica, Vol. 38, No. 2, May; 422-429.

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

Evagelia, Mitsaki (2011)
"Ridge Regression Analysis of Collinear Data",
http://www.stat-athens.aueb.gr/~jpan/diatrives/Mitsaki/chapter2.pdf

Farrar, D. and Glauber, R. (1976)
"Multicollinearity in Regression Analysis: the Problem Revisited",
Review of Economics and Statistics, 49; 92-107.

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.

Godfrey, L. (1978)
"Testing for Higher Order Serial Correlation in Regression Equations when the Regressors Include Lagged Dependent Variables",
Econometrica, Vol., 46; 1303-1310.

Greene, William (1993)
"Econometric Analysis",
2nd ed., Macmillan Publishing Company Inc., New York, USA; 616-618.

Greene, William (2007)
"Econometric Analysis",
6th ed., Upper Saddle River, NJ: Prentice-Hall; 387-388.

Griffiths, W., R. Carter Hill & George Judge (1993)
"Learning and Practicing Econometrics",
John Wiley & Sons, Inc., New York, USA; 602-606.

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

Hoerl A. E. (1962)
"Application of Ridge Analysis to Regression Problems",
Chemical Engineering Progress, 58; 54-59.

Hoerl, A. E. and R. W. Kennard (1970a)
"Ridge Regression: Biased Estimation for Non-Orthogonal Problems",
Technometrics, 12; 55-67.

Hoerl, A. E. and R. W. Kennard (1970b)
"Ridge Regression: Applications to Non-Orthogonal Problems",
Technometrics, 12; 69-82.

Hoerl, A. E. ,R. W. Kennard, & K. Baldwin (1975)
"Ridge Regression: Some Simulations",
Communications in Statistics, A, 4; 105-123.

Hoerl, A. E. and R. W. Kennard (1976)
"Ridge Regression: Iterative Estimation of the Biasing Parameter",
Communications in Statistics, A, 5; 77-88.

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; 615.

Kmenta, Jan (1986)
"Elements of Econometrics",
2nd ed., Macmillan Publishing Company, Inc., New York, USA; 718.

Ljung, G. & George Box (1979)
"On a Measure of Lack of Fit in Time Series Models",
Biometrika, Vol. 66; 265–270.

Machado, J.A.F. and Santos Silva, J.M.C. (2000)
"Glejser's Test Revisited",
Journal of Econometrics, 97(1); 189-202.

Maddala, G. (1992)
"Introduction to Econometrics",
2nd ed., Macmillan Publishing Company, New York, USA; 358-366.

Marquardt D.W. (1970)
"Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation",
Technometrics, 12; 591-612.

Marquardt D.W. & R. Snee (1975)
"Ridge Regression in Practice",
The American Statistician, 29; 3-19.

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

Pidot, George (1969)
"A Principal Components Analysis of the Determinants of Local Government Fiscal Patterns",
Review of Economics and Statistics, Vol. 51; 176-188.

Ramsey, J. B. (1969)
"Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis",
Journal of the Royal Statistical Society, Series B 31; 350-371.

Rencher, Alvin C. (1998)
"Multivariate Statistical Inference and Applications",
John Wiley & Sons, Inc., New York, USA; 21-22.

Strawderman, W. E. (1978)
"Minimax Adaptive Generalized Ridge Regression Estimators",
Journal American Statistical Association, 73; 623-627.

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

Theil, Henri (1971)
"Principles of Econometrics",
John Wiley & Sons, Inc., New York, USA.

Von, Neumann (1941)
"Distribution of the Ratio of the Mean Square Successive Difference to the Variance",
Annals Math. Stat., Vol. 12; 367-395.

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

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

Examples

clear all

sysuse almon.dta , clear

gen lx1=log(x1)
gen lx2=log(x2)

* (1) Ordinary Least Squares (OLS)
almon y l(0/3).x1 , zlag(x1) pdl(2) end(0) model(ols) nolag

almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(log) test tolog
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(3)

almon y l.y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(1) dlag(1)
almon y l(0/3).x1 l.y l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(1) dlag(2)
almon y l(0/3).x1 l(0/3).x2 l.y , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) lma lag(1) dlag(3)

* (2) Autoregressive Least Squares (ALS)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(als) mfx(lin) test
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(als) mfx(log) test tolog
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(als) mfx(lin) test twostep

almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(als) mfx(lin) ar(1) test
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(als) mfx(lin) ar(2) test

* (3) Quantile Regression (QREG)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(qreg) mfx(lin) test
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(qreg) mfx(log) test tolog

* (4) Robust Regression (RREG)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(rreg) mfx(lin) test
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(rreg) mfx(log) test tolog

* (5) Generalized Method of Moments (GMM)
White:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white)
Bartlett:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(bart)
Cragg:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(crag)
Daniell:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(dan)
Horn-Duncan:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(hdun)
Hinkley:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(hink)
Jackknife:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(jack)
Newey-West:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(nwest)
Parzen:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(parzen)
Quadratic Spectral:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(quad)
Tent:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(tent)
Truncated:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(trunc)
Tukey:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(tukey)
Tukey-Hamming:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(tukeym)
Tukey-Hanning:
almon y l(0/3).x1 l(0/3).x2, zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(tukeyn)

* (6) Weighted OLS & GMM Regression
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(yh)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(yh2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(abse)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(e2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(le2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(x) wvar(x1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(xi) wvar(x1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(x2) wvar(x1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test weights(xi2) wvar(x1)

almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0)model(gmm) mfx(lin) test hetcov(white) weights(yh)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0)model(gmm) mfx(lin) test hetcov(white) weights(x) wvar(x1)

* (7) Ridge Regression
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test ridge(orr) kr(0.5)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test ridge(orr) kr(0.5) weights(x) wvar(x1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test ridge(grr1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test ridge(grr2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) mfx(lin) test ridge(grr3)

almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white) ridge(orr) kr(0.5)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white) ridge(orr) kr(0.5) weights(x) wvar(x1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white) ridge(grr1)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white) ridge(grr2)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(gmm) mfx(lin) test hetcov(white) ridge(grr3)

* (8) Box-Cox Regression (Box-Cox)
almon y l(0/3).lx1 l(0/3).lx2 , zlag(x1 x2) pdl(2 2) end(0 0) model(bcox) test mfx(lin) lag(3) lamp(lhs)
almon y l(0/3).lx1 l(0/3).lx2 , zlag(x1 x2) pdl(2 2) end(0 0) model(bcox) test mfx(lin) lag(3) lamp(rhs)
almon y l(0/3).lx1 l(0/3).lx2 , zlag(x1 x2) pdl(2 2) end(0 0) model(bcox) test mfx(lin) lag(3) lamp(alls)
almon y l(0/3).lx1 l(0/3).lx2 , zlag(x1 x2) pdl(2 2) end(0 0) model(bcox) test mfx(lin) lag(3) lamp(alld)

* (9) Autoregressive Conditional Heteroskedasticity (ARCH)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(arch) lag(1) test diag mfx(lin)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(arch) lag(2) test diag mfx(lin)
almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(arch) lag(1) test diag mfx(log) tolog

almon y l(0/3).x1 l(0/3).x2 , model(ols) zlag(x1 x2) pdl(2 2) end(0 0) mfx(lin)

almon y l(0/3).x1 , model(ols) zlag(x1) pdl(2) end(0)
almon y l(0/3).x1 l(0/3).x2 , model(ols) zlag(x1 x2) pdl(2 2) end(1 1)
almon y l(0/4).x1 l(0/3).x2 x3 , model(ols) zlag(x1 x2) pdl(2 2) end(3 2)

tsset t
constr def 1 x1 - 3*L.x1 + 3*L2.x1 - L3.x1 = 0
cnsreg y l(0/3).x1 l(0/3).x2 , c(1)
almon y l(0/3).x1 , model(ols) zlag(x1) pdl(2) end(0) mfx(lin)

tsset t
constr def 1 x2 - 3*L.x2 + 3*L2.x2 - L3.x2 = 0
cnsreg y l(0/3).x2 , c(1)
almon y l(0/3).x2 , model(ols) zlag(x2) pdl(2) end(0) mfx(lin)

tsset t
constr def 1 x1 - 3*L.x1 + 3*L2.x1 - L3.x1 = 0
constr def 2 x2 - 3*L.x2 + 3*L2.x2 - L3.x2 = 0
cnsreg y l(0/3).x1 l(0/3).x2 , c(1-2)
almon y l(0/3).x1 l(0/3).x2 , model(ols) zlag(x1 x2) pdl(2 2) end(0 0) mfx(lin)

. clear all
. sysuse almon.dta , clear
. almon y l(0/3).x1 l(0/3).x2 , zlag(x1 x2) pdl(2 2) end(0 0) model(ols) test mfx(lin)

==============================================================================
*** Shirley Almon Generalized Polynomial Distributed Lag Model ***
==============================================================================
*** Ordinary Least Squares (OLS) ***
-------------------------------------------------------
- Polynomial Variables: x1 x2
- Lag Length: l(0/3).x1 l(0/3).x2
- Polynomial Degree: PDL(2 2)
- Endpoint Restriction: End(0 0)
* x1: No Endpoint Polynomial Restrictions
* x2: No Endpoint Polynomial Restrictions
------------------------------------------------------------------------------
y = x1 L.x1 L2.x1 L3.x1 x2 L.x2 L2.x2 L3.x2
------------------------------------------------------------------------------
* Restrictions:
1: x1 - 3*L.x1 + 3*L2.x1 - L3.x1 = 0
2: x2 - 3*L.x2 + 3*L2.x2 - L3.x2 = 0
------------------------------------------------------------------------------
Sample Size = 32 | Sample Range = 1 - 36
Wald Test = 1800.8301 | P-Value > Chi2(6) = 0.0000
F-Test = 300.1384 | P-Value > F(6 , 25) = 0.0000
R2 (R-Squared) = 0.9863 | Raw Moments R2 = 0.9999
R2a (Adjusted R2) = 0.9830 | Raw Moments R2 Adj = 0.9999
Root MSE (Sigma) = 2.8840 | Log Likelihood Function = -75.3504
------------------------------------------------------------------------------
- R2h= 0.9863 R2h Adj= 0.9830 F-Test = 300.14 P-Value > F(6 , 25) 0.0000
- R2v= 0.9863 R2v Adj= 0.9830 F-Test = 300.14 P-Value > F(6 , 25) 0.0000
- R2r= 0.9999 R2r Adj= 0.9999 F-Test =68028.22 P-Value > F(7 , 25) 0.0000
------------------------------------------------------------------------------
Akaike Criterion AIC = 162.7009 | Schwarz Criterion SC = 171.4953
------------------------------------------------------------------------------
- Joint F-Test Restriction: x1 = 23.876 P > F(3, 25) 0.0000
- Joint F-Test Restriction: x2 = 0.748 P > F(3, 25) 0.5340
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 |
--. | 1.224306 .3235994 3.78 0.001 .5578402 1.890771
L1. | .5102923 .3001897 1.70 0.102 -.10796 1.128544
L2. | .0228886 .3091815 0.07 0.942 -.6138825 .6596598
L3. | -.2379053 .4256806 -0.56 0.581 -1.114611 .6388004
|
x2 |
--. | -.0057917 .2024303 -0.03 0.977 -.4227048 .4111214
L1. | .1321913 .1463322 0.90 0.375 -.1691856 .4335681
L2. | .0477574 .1419953 0.34 0.739 -.2446875 .3402022
L3. | -.2590934 .180877 -1.43 0.164 -.6316165 .1134297
|
_cons | 70.12386 9.369416 7.48 0.000 50.82719 89.42053
------------------------------------------------------------------------------

==============================================================================
*** Model Selection Diagnostic Criteria - (Model= OLS)
==============================================================================
- Log Likelihood Function LLF = -75.3504
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 10.0646
- Akaike Information Criterion (1973) Log AIC = 2.3090
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 13.8690
- Schwarz Criterion (1978) Log SC = 2.6297
---------------------------------------------------------------------------
- Amemiya Prediction Criterion (1969) FPE = 10.1372
- Hannan-Quinn Criterion (1979) HQ = 11.1932
- Rice Criterion (1984) Rice = 11.5524
- Shibata Criterion (1981) Shibata = 9.3412
- Craven-Wahba Generalized Cross Validation (1979) GCV = 10.6467
------------------------------------------------------------------------------

==============================================================================
*** Autocorrelation Tests - (Model= OLS)
------------------------------------------------------------------------------
Ho: No Autocorrelation - Ha: Autocorrelation
------------------------------------------------------------------------------
- Durbin h Test cannot be computed
- Durbin h Test after ALS(1) AR(1)= 1.7480 P-Value >Z(0,1) 0.0805
------------------------------------------------------------------------------
- Harvey LM Test (Lag DepVar) AR(1)= -3.2482 P-Value >Chi2(1) 0.0715
- Harvey LM Test after ALS(1) AR(1)= 3.0553 P-Value >Chi2(1) 0.0805
------------------------------------------------------------------------------
- Wald T Test AR(1)= 3.1693 P-Value >Z(0,1) 0.0015
- Wald Chi2 Test AR(1)= 10.0443 P-Value >Z(0,1) 0.0015
------------------------------------------------------------------------------
- Berenblut-Webb Test AR(1)= 0.8549 df: (8 , 32)
- King Test (MA) AR(1)= 0.6983 df: (8 , 32)
------------------------------------------------------------------------------
- Rho Value for Lag(1) AR(1)= 0.4548
- Z Test AR(1)= 2.5726 P-Value >Chi2(1) 0.1087
- Box-Pierce LM Test AR(1)= 6.6181 P-Value >Chi2(1) 0.0101
- Ljung-Box LM Test AR(1)= 7.2586 P-Value >Chi2(1) 0.0071
- Durbin-Watson Test AR(1)= 1.0210 df: (8 , 32)
- Von Neumann Ratio Test AR(1)= 1.0539 df: (8 , 32)
- Durbin m Test (drop 1 obs) AR(1)= 7.6611 P-Value >Chi2(1) 0.0056
- Durbin m Test (keep 1 obs) AR(1)= 7.3202 P-Value >Chi2(1) 0.0068
- Breusch-Godfrey LM Test (drop 1 obs) AR(1)= 8.9446 P-Value >Chi2(1) 0.0028
- Breusch-Godfrey LM Test (keep 1 obs) AR(1)= 9.2076 P-Value >Chi2(1) 0.0024
* Breusch-Pagan-Godfrey LM Test AR(1)= 3.0344 P-Value >Chi2(1) 0.0815
------------------------------------------------------------------------------

==============================================================================
*** Heteroscedasticity Tests - (Model= OLS)
------------------------------------------------------------------------------
Ho: Homoscedasticity - Ha: Heteroscedasticity
------------------------------------------------------------------------------
- Engle LM ARCH Test AR(1) E2=E2_1-E2_1= 0.4052 P-Value > Chi2(1) 0.5244
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 0.2690 P-Value > Chi2(1) 0.6040
- Hall-Pagan LM Test: E2 = Yh2 = 0.2638 P-Value > Chi2(1) 0.6075
- Hall-Pagan LM Test: E2 = LYh2 = 0.2747 P-Value > Chi2(1) 0.6002
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 4.7756 P-Value > Chi2(2) 0.0918
- Wald LM Test: LogE2 = X = 11.7834 P-Value > Chi2(1) 0.0006
- Glejser LM Test: |E| = X = 8.0715 P-Value > Chi2(2) 0.0177
- Breusch-Godfrey Test: E2 = E2_1 X = 11.3301 P-Value > Chi2(1) 0.0008
------------------------------------------------------------------------------
- Machado-Santos-Silva Test: Ev=Yh Yh2 = 0.3817 P-Value > Chi2(2) 0.8263
- Machado-Santos-Silva Test: Ev=X = 8.9885 P-Value > Chi2(8) 0.3433
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X = 9.8833 P-Value > Chi2(8) 0.2733
- White Test -B-P-G (SSR): E2 = X = 7.2499 P-Value > Chi2(8) 0.5099
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2 = 19.0564 P-Value > Chi2(16) 0.2657
- White Test -B-P-G (SSR): E2 = X X2 = 13.9787 P-Value > Chi2(16) 0.6003
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2 XX= 32.0000 P-Value > Chi2(31) 0.4167
- White Test -B-P-G (SSR): E2 = X X2 XX= 23.4735 P-Value > Chi2(31) 0.8314
------------------------------------------------------------------------------
- Cook-Weisberg LM Test E2/Sig2 = Yh = 0.1973 P-Value > Chi2(1) 0.6569
- Cook-Weisberg LM Test E2/Sig2 = X = 7.2499 P-Value > Chi2(8) 0.5099
------------------------------------------------------------------------------

==============================================================================
*** Non Normality Tests - (Model= OLS)
------------------------------------------------------------------------------
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
*** Non Normality Tests:
- Jarque-Bera LM Test = 0.5171 P-Value > Chi2(2) 0.7722
- White IM Test = 1.0258 P-Value > Chi2(2) 0.5988
- Doornik-Hansen LM Test = 0.2038 P-Value > Chi2(2) 0.9031
- Geary LM Test = -2.1426 P-Value > Chi2(2) 0.3426
- Anderson-Darling Z Test = 0.1895 P > Z( 1.371) 0.9147
- D'Agostino-Pearson LM Test = 0.3501 P-Value > Chi2(2) 0.8394
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test = 0.1385 P-Value > Chi2(1) 0.7098
- Small LM Skewness Test = 0.1859 P-Value > Chi2(1) 0.6663
- Skewness Z Test = 0.4312 P-Value > Chi2(1) 0.6663
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = -0.6154 P-Value > Z(0,1) 0.5383
- Small LM Kurtosis Test = 0.1641 P-Value > Chi2(1) 0.6854
- Kurtosis Z Test = -0.4051 P-Value > Chi2(1) 0.6854
------------------------------------------------------------------------------
Skewness Coefficient = 0.1611 - Standard Deviation = 0.4145
Kurtosis Coefficient = 2.4671 - Standard Deviation = 0.8094
------------------------------------------------------------------------------
Runs Test: (11) Runs - (15) Positives - (17) Negatives
Standard Deviation Runs Sig(k) = 2.7712 , Mean Runs E(k) = 16.9375
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (11.5059 , 22.3691 )
------------------------------------------------------------------------------

==============================================================================

* Marginal Effect - Elasticity - Standardized Beta (Model= OLS): Linear *

+----------------------------------------------------------------------------+
| y | Margin | Elasticity | St_Beta | Mean |
|----------------+--------------+--------------+--------------+--------------|
|y | | | | |
| x1 | 1.2243 | 0.6857 | 0.8374 | 196.6850 |
| L.x1 | 0.5103 | 0.2834 | 0.3436 | 194.9896 |
| L2.x1 | 0.0229 | 0.0126 | 0.0151 | 193.2746 |
| L3.x1 | -0.2379 | -0.1299 | -0.1551 | 191.6763 |
| x2 | -0.0058 | -0.0037 | -0.0042 | 224.8154 |
| L.x2 | 0.1322 | 0.0839 | 0.0933 | 222.9883 |
| L2.x2 | 0.0478 | 0.0301 | 0.0333 | 221.1494 |
| L3.x2 | -0.2591 | -0.1618 | -0.1807 | 219.3559 |
+----------------------------------------------------------------------------+
Mean of Dependent Variable = 351.1539

------------------------------------------------------------------------------
* Variable Mean Lag Full Lag SUM(Coefs.) Std. Err. T-Test P>|t|
------------------------------------------------------------------------------
x1 -0.1037 0.8963 1.5196 0.3592 4.230 0.0003
------------------------------------------------------------------------------
x2 6.4704 7.4704 -0.0849 0.3373 -0.252 0.8033
------------------------------------------------------------------------------

------------------------------------------------------------------------------
* Variable Marginal Effect (B) | Elasticity (Es)
Short Run Long Run | Short Run Long Run
------------------------------------------------------------------------------
x1 1.2243 1.5196 | 0.6857 0.8518
------------------------------------------------------------------------------
x2 -0.0058 -0.0849 | -0.0037 -0.0515
------------------------------------------------------------------------------

Author

Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

ALMON Citation

Shehata, Emad Abd Elmessih (2016)

ALMON: "Stata Module to Estimate Shirley Almon Generalized Polynomial Distributed Lag Model"

Online Help:

*** Distributed Lag Models
almon1 Shirley Almon Polynomial Distributed Lag Model (ALMON1)
almon Shirley Almon Generalized Polynomial Distributed Lag Model (ALMON)
dlagft Alt France-Jan Tinbergen Distributed Lag Model (DLAGFT)
dlagdj Dale Jorgenson Rational Distributed Lag Model (DLAGDJ)
dlagfd Frank De Leeuw Inverted V Distributed Lag Model (DLAGFD)
dlagif Irving Fisher Arithmetic Distributed Lag Model (DLAGIF)
dlagmf Milton Fridman Partial Adjustment-Adaptive Expectations
Distributed Lag Model (DLAGMF)
dlagmn Marc Nerlove Partial Adjustment Distributed Lag Model (DLAGMN)
dlagrs Robert Solow Pascal Triangle Distributed Lag Model (DLAGRS)
dlagrw Rudolf Wolffram Segmenting Partial Adjustment Distributed Lag (DLAGRW)
dlagtq Tweeten-Quance Partial Adjustment Distributed Lag Model (DLAGTQ)

*** Demand System Models
dles Linear Expenditure System (LES) (DLES)
deles Extended Linear Expenditure System (ELES) (DELES)
dqes Quadratic Expenditure System (QES) (DQES)
drot Rotterdam Demand System (DROT)
droti Inverse Rotterdam Demand System (DROTI)
daidsla Linear Approximation Almost Ideal Demand System (AIDS-LA) (DAIDSLA)
daidsfd First Difference Almost Ideal Demand System (AIDS-FD) (DAIDSFD)
daidsi Inverse Almost Ideal Demand System(AIDS-I) (DAIDSI)
daidsq Quadratic Almost Ideal Demand System (QAIDS) (AIDSQ)
darmin Primal Armington Demand System (DARMIN)
dengel Engel Demand System (DENGEL)
dgads Generalized AddiLog Demand System (GADS) (DGADS)
dtlog Transcendental Logarithmic Demand System (DTLOG)
dwork Working Demand System (DWORK)

prodfm Production Function Models (PRODFM)

proffm Profit Function Models (PROFFM)

costfm Cost Function Models (COSTFM)
cost3 Quadratic and Cubic Cost Functions (COST3)

iic Investment Indicators Criteria (IIC)

iot Leontief Input - Output Table (IOT)

index Index Numbers (INDEX)

mef Marketing Efficiency Models (MEF)

pam Policy Analysis Matrix (PAM)
pem Partial Equilibrium Model (PEM)

*** Financial Analysis Models
fam Financial Analysis Models (FAM)
xbcr Benefit-Cost Ratio (XBCR)
xirr Internal Rate of Return (XIRR)
xmirr Modified Internal Rate of Return (XMIRR)
xnfv Net Future Value (XNFV)
xnpv Net Present Value (XNPV)
xpp Payback Period (XPP)

*** Trade Models
wtm World Trade Models (WTM)
wtic World Trade Indicators Criteria (WTIC)
wtrca World Trade Revealed Comparative Advantage (WTRCA)
wtrgc World Trade Regional Geographical Concentration (WTRGC)
wtsgc World Trade Sectoral Geographical Concentration (WTSGC)