ERROR CORRECTION MODEL Yule (1936) and Granger and Newbold (1974) were the first to draw attention to the problem of false correlations and find solutions about how to overcome them in time series analysis. Providing two time series that are completely unrelated but integrated (not stationary), regression analysis with each other will tend to produce relationships that appear to be statistically significant and a researcher might think he has found evidence of a correct relationship between these variables. Ordinary least squares are no longer consistent and the test statistics commonly used are invalid. Specifically, the Monte Carlo simulation shows that one will get very high t-squared R statistics, very high and low Durbin- Watson statistics. Technically, Phillips (1986) proves that parameter estimates will not converge in probability, intercepts will diverge and slope will have a distribution that does not decline when the sample size increases. However, there may be a general stochastic tendency for both series that a researcher is really interested in because it reflects the long-term relationship between these variables. Because of the stochastic nature of trends, it is not possible to break integrated series into deterministic trends (predictable) and stationary series that contain deviations from trends. Even in a random walk detrended detrended random correlation will finally appear. So detrending doesn't solve the estimation problem. To keep using the Box-Jenkins approach, one can differentiate series and then estimate models such as ARIMA, given that many of the time series that are commonly used (eg in economics) seem stationary in the first difference. Forecasts from such models will still reflect the cycles and seasonality in the data. However, any information about long-term adjustments that may contain data at the level level and long-term estimates will not be reliable. This prompted Sargan (1964) to develop an ECM methodology, which maintains level information Before carrying out ECM estimation and descriptive analysis, several stages must be carried out such as data stationarity test, and degree of cointegration test. After the data is estimated using ECM. The steps in formulating the ECM model are as follows: 1. Specify the expected relationship in the model under study. GDPt = f(INF, LIR, KURS, AK, GFCF, IVA, TRADE, POP, TR) GDPt = 0 + 1INFt + 2LIRt + 3KURSt + 5GFCFt + 6IVAt + 7TRADEt + 8AKt + 9TRt ....................................................... (1) Information: GDPt : Gross Domestic Product per year in period t INFt : Inflation, consumer prices (annual%) in period t LIRt : Lending interest rate (%) period t Kurst : Rupiah Exchange Rate against US dollar period t GFCFt : Gross Fixed Capital Formation in period t IVAt : Industry, value added (constant LCU) in period t TRADEt : Total Trade Value in period t Akt : Labor Force in period t ECM Model Regression Teaching Materials Agus Tri Basuki, M.Sc. TRt : Tax Revenue (current LCU) in period t 0, 1, 2,.... 9 : Coeffisient in the long-term 2. Establish a single cost function in the error correction method: }2 Ct = b1 (GDPt – GDPt*) + b2 {(GDPt - GDPt-1)– ft (Zt - Zt-1) …........... (2) Based on the data above Ct is a quadratic cost function, GDPt is gross domestic income in period t, whereas Zt is a vector variable that affects gross domestic income and is considered to be affected linearly by inflation, interest rates, exchange rates, labor force, total investment in the country's economy host, Industry, value added, total trade value, total population, and tax revenue. b1 and b2 are row vectors that give weight to Zt - Zt-1. The first component of the single cost function above is the imbalance cost and the second component is the adjustment cost component. Whereas B is a time lag operation. Zt is a variable factor that influences currency demand. a. Minimizing the cost function of the equation with respect to Rt, you will get: GDPt = GDPt + (1- e) GDPt-1 – (1 – e) ft (1-B) Zt ......................................... ( 3) b. Substitute GDPt - GDPt-1 so that it is obtained: LogGDPt = b0 + b1INFt + b2LIRt + b3LogKURSt + b5LogGFCFt + b6LogIVAt + B7LogTRADEt + b8LogAKt + b9Log0TRt ..................................................... (4) While the short-term relationship is expressed by the following equation: DLogGDPt = b0 + b1DINFt + b2DLIRt + b3DLogKURSt + b5DLogGFCFt + b6DLogIVAt + B7DLogTRADEt + b8DLogAKt + b9DLog0TRt ..................... (5) From the results of parameterization of the short-term equation can produce a new equation form, the equation was developed from the previous equation to measure the long-term parameters by using ECM model econometric regression: DLogGDPt = β0 + b1DINFt + β2DLIRt + β3DLogKURSt + β5DLogGFCFt + β6 DLogIVAt + β7DLogTRADEt + β8DLogAKt + β9DLog0TRt + ECT + t ….. (6) ECT = DINFt-1 + DLIRt-1 + DLogKURSt-1 + DLogGFCFt-1 + DLogIVAt-1 + DLogTRADEt-1 + DLogAKt-1 + DLog0TRt-1 …................................................. (7) Note : ECT : Error Correction Term ECM Model Regression Teaching Materials Agus Tri Basuki, M.Sc. Decreased Stages of the ECM Model Unit Root Test (unit root test) a. The concept used to test the stationary of a time-consuming data is the unit root test. If a time series data is not stationary, it can be said that the data is facing a unit root problem. b. The existence of the unit root problem can be seen by comparing the t- statistics results of the regression with the value of the Augmented Dickey Fuller test. The equation model is as follows: c. ΔGDPt = a1 + a2 T + ΔGDPt-1 + i ∑mi=1GDPt-1 + et ………............... (9) d. Where ΔGDPt-1 = (ΔGDPt-1 - ΔGDPt-2) and so on, m = length of time lag based on i = 1,2 .... m. The null hypothesis is still δ = 0 or ρ = 1. The t-statistics value of ADF is the same as the t-statistic value of DF. Integration Test a. If the unit root test above the time series data observed is not stationary, then the next step is to test the degree of integration to find out at what degree of integration the data will be stationary. The degree of integration test is carried out with the model: b. ΔGDPt = a1 + δΔGDPt-1 + i ∑mi=1GDPt-1 + et ....................... (10) c. ΔGDPt = β 1 + β 2 T + δΔGDPt-1 + i ∑mi=1GDPt-1 + et …………......... (11) d. The t-statistic value of the regression results of equations (10) and (11) is compared with the t-statistic value in the DF table. If the value of δ in both equations is equal to one, the variable ΔUKRt is said to be stationary at one degree, or symbolized as ΔGDPt ~ I (1). Cointegration Test The cointegration test is most commonly used the engle-Granger (EG) test, the augmented Engle-Granger test (AEG) and the Durbin-Watson cointegrating regression test (CRDW). To get the calculated EG, AEG and CRDW values, the data to be used must have been integrated to the same degree. OLS testing of an equation below: LogGDPt = b0 + b1INFt + b2LIRt + b3 LogKURSt + b5LogGFCFt + b6LogIVAt + B7 LogTRADEt + b8 LogAKt + b9 Log0TRt ............... (12) From equation (12), save the residual (error terms). The next step is to estimate the autoregressive equation model of the residual based on the following equations: Δt = λt-1 ………………..........................................(13) Δt = λt-1 + i t-1 .................................................................(14) ECM Model Regression Teaching Materials Agus Tri Basuki, M.Sc. With the hypothesis test: H0 : = I(1), meaning that there is no cointegration Ha : I(1), meaning that there is cointegration Based on the OLS regression results in equation (12) will obtain a calculated CRDW value (DW value in the equation) to then be compared with the CRDW table. While from equations (13) and (14) EG and AEG values will be obtained which will also be compared with the DF and ADF table values. Error Correction Model If it passes the cointegration test, it will then be tested by using a dynamic linear model to find out the possibility of structural change, because the long- term equilibrium relationship between the independent variable and the dependent variable from the results of the cointegration test will not apply at any time. In brief, the ECM operation process in the currency demand equation (5) has been modified to: DLogGDPt = β0 + b1DINFt + β2DLIRt + β3DLogKURSt + β5DLogGFCFt + β6 DLogIVAt + β7 DLogTRADEt + β8DLogAKt + β9DLog0TRt + ECT(-1) + t ............. (13) ECM Model Regression Teaching Materials Agus Tri Basuki, M.Sc. Literature Study (Previous Theories and Studies) Identification of Research Variables and Modeling Revition Making Hypotheses No Data Collection Process Data processing Fullfil Unit Root Test, Cointegration Test, Short- Term Regression and Classical Assumption Test Yes Model Estimation and Hypothesis test Conclusions and Recommendations Figure 1 Steps for Research with ECM ECM Model Regression Teaching Materials Agus Tri Basuki, M.Sc. Data of GDP, inf, lir, kurs, GFCF, IVA, TRADE, AK and TR Tahun GDP (M) Kurs GFCF (M) LIR INF TR (M) Trade (M) AK (J) IVA (M) 1986 2,047,293 1,283 525,768 21.49 5.83 14,993 819,473 69 798,545 1987 2,155,799 1,644 554,681 21.67 9.28 18,827 998,819 71 848,963 1988 2,292,815 1,686 618,518 22.1 8.04 21,435 1,083,460 73 907,302 1989 2,501,111 1,770 710,782 21.7 6.42 26,678 1,227,592 75 1,053,730 1990 2,726,250 1,843 825,058 20.83 7.81 37,432 1,441,964 76 1,161,956 1991 2,969,644 1,950 931,494 25.53 9.42 39,098 1,628,540 77 1,277,017 1992 3,184,067 2,030 964,891 24.03 7.53 44,500 1,828,528 79 1,503,687 1993 3,415,042 2,087 1,028,570 20.59 9.69 47,344 1,725,393