ECONOMETRICS
Error-Correction Modeling (ECM)
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
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.
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?
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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].
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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
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t LFOOD LRGDP LWTID
ECT [ 2 . 422 0 . 528 0 . 044
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LRGDP LFOOD
LFOOD
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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