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Title

alsmle: Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation

Table of Contents

Syntax

Options

Description

Saved Results

References

*** Examples

Acknowledgment

Author

Syntax

alsmle depvar indepvars [if] [in] [weight] , [ noconstant diag mfx(lin, log) dn

log tolog twostep iter(#) tolerance(#) predict(new_var) resid(new_var)

level(#) vce(vcetype) ]

Options

noconstant Exclude Constant Term from Equation

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

log display iteration of Log Likelihood

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

iter(#) number of iterations; Default is iter(50)

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

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

predict(new_var) Predicted values variable

resid(new_var) Residuals values variable

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

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

mfx(lin, log) Type of functional form, either Linear model (lin), or Log-Log model (log), to compute Marginal Effects and Elasticities.

- In Linear model marginal effects are the transformed coefficients (Bm), and elasticities are (Es=Bm X/Y).

- In Log-Log model the transformed coefficients are elasticities, and the marginal effects are (Bm =Es Y/X).

- Using mfx(log) requires tolog option, to trnsform variables to log form.

diag 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

Description

alsmle estimates Autoregressive Least Squares (ALS) via Maximum Likelihood Estimation (MLE), according to Beach-Mackinnon (1978) method for Autocorrelated Errors with first order AR(1).

alsmle can also estimate weighted Autoregressive Maximum Likelihood Estimation weight, with or without constant term.

alsmle can compute model selection diagnostic criteria, marginal effects, and elasticities.

Saved Results

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

Scalars:
e(N) number of observations
e(r2c) R-squared
e(r2c_a) Adjusted R-squared
e(r2u) Raw Moments R-squared
e(r2u_a) Raw Moments Adjusted R2
e(f) F-test
e(fp) F-test P-Value
e(wald) Wald-test
e(waldp) Wald-test P-Value
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

Matrixes:
e(b) coefficient vector
e(V) variance-covariance matrix of the estimators
e(mfx) Beta and Marginal Effect

References

Beach, Charles & James G. Mackinnon (1978)
"A Maximum Likelihood Procedure for Regression with Autocorrelated Errors",
Econometrica, Vol. 46, No. 1, Jan.; 51-58.

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.

Examples

clear all

sysuse alsmle.dta, clear

db alsmle

alsmle y x1 x2

alsmle y x1 x2 , iter(1)

alsmle y x1 x2 , twostep

alsmle y x1 x2 , iter(10)

alsmle y x1 x2 , noconstant

alsmle y x1 x2 , mfx(lin) log

alsmle y x1 x2 [weight=x1]

alsmle y x1 x2 [aweight=x1]

alsmle y x1 x2 [iweight=x1]

alsmle y x1 x2 [pweight=x1]

alsmle y x1 x2 in 2/16 [weight=x1] , noconstant

alsmle y x1 x2 , mfx(lin) diag predict(Yh) resid(Ue)

alsmle y x1 x2 , mfx(log) diag tolog predict(Yh) resid(Ue)

alsmle y x1 x2 , mfx(log) log tolog

. clear all
. sysuse alsmle.dta, clear
. alsmle y x1 x2 , mfx(lin) diag log

==============================================================================
* Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation
==============================================================================
Iteration Rho LLF SSE
0 0.000000 -51.6471 433.3130
1 -0.184911 -51.6645 419.9530
2 -0.197405 -51.4007 419.7750
3 -0.197972 -51.3972 419.7692
4 -0.197997 -51.3971 419.7691
------------------------------------------------------------------------------
Number of Obs = 17
Wald Test = 457.1243 P-Value > Chi2(2) = 0.0000
F Test = 228.5621 P-Value > F(2 , 14) = 0.0000
R-squared = 0.9528 Raw Moments R2 = 0.9987
R-squared Adj = 0.9461 Raw Moments R2 Adj = 0.9985
Root MSE (Sigma) = 5.4757 Log Likelihood Function = -51.3971
Autoregressive Coefficient (Rho) Value = -0.1979982
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1.065033 .2067004 5.15 0.000 .6217044 1.508361
x2 | -1.375032 .0643558 -21.37 0.000 -1.513061 -1.237002
_cons | 129.6105 20.87587 6.21 0.000 84.83621 174.3848
------------------------------------------------------------------------------

==============================================================================
* Model Selection Diagnostic Criteria
==============================================================================
Log Likelihood Function LLF = -51.3971
Akaike Final Prediction Error AIC = 32.3009
Schwartz Criterion SC = 35.6275
Akaike Information Criterion ln AIC = 3.4751
Schwarz Criterion ln SC = 3.5731
Amemiya Prediction Criterion FPE = 34.6460
Hannan-Quinn Criterion HQ = 32.6171
Rice Criterion Rice = 33.3836
Shibata Criterion Shibata = 31.5353
Craven-Wahba Generalized Cross Validation GCV = 32.7901
---------------------------------------------------------------

* Linear: Marginal Effect - Elasticity

+-----------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|--------------+--------------------+--------------------+--------------------|
| x1 | 1.0650 | 0.8154 | 102.9824 |
| x2 | -1.3750 | -0.7801 | 76.3118 |
+-----------------------------------------------------------------------------+
Mean of Dependent Variable = 134.5059

Acknowledgment

I would like to thank Professor James G. Mackinnon
for sending to me his reference paper (1978)

Author

Emad Abd Elmessih Shehata
Assistant Professor
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

alsmle Citation

Emad Abd Elmessih Shehata (2012)

ALSMLE: "Stata Module to Estimate Beach-Mackinnon First Order AR(1) Autoregressive Maximum Likelihood Estimation"

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