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Error-Correction Modeling (ECM) ECONOMETRICS

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ECONOMETRICS

Error-Correction Modeling (ECM)

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STEPS IN TIME SERIES ECONOMETRICS

THEORETICAL UNDERPINNINGS

Variables to be Included? Focus? Well-specified Equation or System Dynamics. Motivation?

UNIT ROOT TESTS

COINTEGRATION TESTS

One-equation Focus:

Error Correction Modeling - Specification

- Estimation - Diagnostics - Inferences

Multi-equation modeling

Granger

Causality VAR or VECM

Variance

Decompositions &

Impulse Responses

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ERROR CORRECTION MODELING

Definition:

 Cointegration implies and is implied by the presence of error-correction model (Engle and Granger, 1987)..

 The presence of cointegration rejects non-causality

between the variables. More specifically, there must be a causation in at least one direction.

 Error-correction model allows a variable to respond not only to the changes in other variables but also to the gap between the variable and its determinant. That is, the errors (deviations) are corrected.

 Thus, it conveniently combines the short-run dynamics of

the variables and their adjustments towards the long-run

relationships.

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ERROR CORRECTION MODELING

One-Equation Formulation:

1. Changes in y respond to changes in other variables and to deviation from the long-run (disequilibrium) from last period ( e t-1 )

2.  is the speed of adjustment coefficient [closing the gap]. Its sign must be negative.

NOTE: For multivariate regression – the equation can be extended accordingly.

QUESTION: If the dependent variable is  X, what should be the sign of the adjustment coefficient?

t t

k

i

i t i

k

i

i t i

t Y X u

Y       

 

  

1

1 1



1 1

1 [ ]

   tt

t X

Y   

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ERROR CORRECTION MODELING

One-Equation ECM Estimation:

1. Estimate the Long-run relation to obtain the error terms.

2. Lag length Selection:

- Hendry’s General-to-Specific Procedure - FPE and other Information Criteria.

- Hsiao’s (1981) Sequential procedure based on FPE

- Lags for all RHS variables can be imposed to be the same or to be different.

- If the interest is in ONE EQUATION  lags are not the same for all variables.

- General-to-Specific criteria are normally applied. It fits the PARSIMONY

principles of time series modeling.

3. Estimate the Final Model

4. Diagnostic Tests [Autocorrelation, Heteroskedasticity, RESET, ARCH, Structural Break and so son].

t t

k

i

i t i

k

i

i t i

t Y X u

Y       

 

  

1

1 1



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STEPS IN ERROR CORRECTION MODELING

STEP I: Estimate the Long-run Equation to obtain the error terms, denoted ECT

(Say, we use DOLS Estimates)

STEP II: Estimate the ECM with the maximum lags

STEP III: Use Hendry’s method by sequentially delete insignificant lags

t t

t

t LFOOD LRGDP LWTID

ECT   [  2 . 422  0 . 528  0 . 044

t t

k

i

i t i

k

i

i t i

k

i

i t i

t

u ECT

LWTID

LRGDP LFOOD

LFOOD

  

 

 

1 0

0 1

 

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STEPS IN ERROR CORRECTION MODELING

Dependent Variable: DFOODP Method: Least Squares Date: 06/25/11 Time: 15:46 Sample (adjusted): 1976 2009

Included observations: 34 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.015785 0.016768 0.941413 0.3590

DFOODP(-1) 0.510380 0.230615 2.213127 0.0400

DFOODP(-2) 0.087966 0.169096 0.520213 0.6093

DFOODP(-3) 0.065855 0.138407 0.475808 0.6399

DFOODP(-4) 0.042137 0.112094 0.375907 0.7114

DRGDP -0.070704 0.125447 -0.563614 0.5800

DRGDP(-1) -0.360204 0.202109 -1.782229 0.0916

DRGDP(-2) -0.255671 0.199921 -1.278865 0.2172

DRGDP(-3) -0.112622 0.176136 -0.639405 0.5306

DRGDP(-4) -0.063799 0.174556 -0.365493 0.7190

DWTID 0.006294 0.021128 0.297903 0.7692

DWTID(-1) 0.006298 0.025515 0.246826 0.8078

DWTID(-2) -0.004100 0.025614 -0.160060 0.8746

DWTID(-3) 0.005488 0.019118 0.287082 0.7773

DWTID(-4) 0.012307 0.018435 0.667617 0.5128

ECT(-1) -0.833880 0.272726 -3.057571 0.0068

R-squared 0.632795 Mean dependent var 0.036491

Adjusted R-squared 0.326792 S.D. dependent var 0.027747

S.E. of regression 0.022767 Akaike info criterion -4.421859

Sum squared resid 0.009330 Schwarz criterion -3.703571

Log likelihood 91.17160 F-statistic 2.067933

Durbin-Watson stat 2.234078 Prob(F-statistic) 0.071770

All lag 4 are not significant and can be deleted

Repeat the

process to

arrive at the

most specific

model…

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STEPS IN ERROR CORRECTION MODELING

STEP IV: DIAGNOSTIC STATISTICS

Dependent Variable: DFOODP Method: Least Squares Date: 06/25/11 Time: 15:51 Sample (adjusted): 1973 2009

Included observations: 37 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -0.002985 0.007116 -0.419461 0.6776

DFOODP(-1) 0.224106 0.095529 2.345952 0.0251

DWTID 0.037463 0.016530 2.266347 0.0301

ECT(-1) -0.532816 0.070696 -7.536725 0.0000

R-squared 0.715852 Mean dependent var 0.044788

Adjusted R-squared 0.690021 S.D. dependent var 0.045343 S.E. of regression 0.025245 Akaike info criterion -4.418567

Sum squared resid 0.021031 Schwarz criterion -4.244414

Log likelihood 85.74349 F-statistic 27.71228

Durbin-Watson stat 2.212872 Prob(F-statistic) 0.000000

Final

Model

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EXERCISE

Can we replicate the above, but using Asymmetric Error-Correction Modeling

LET TRY…..

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