sou · GWB325 · 2009-01-01 00:00:00 — Further, if the ECM is the correct specification, the estimates obtained from the Partial Adjustment Model will suffer from biases, since it omits XB t-1B which is often highly correlated with XtB .B Another advantage over occurs if the dependent variable is non-stationary, which may be the case with economic series that continually increase (or decrease) over time. APPENDIX II: Description of Test Statistics The statistic is a test for first-order serial correla- tion. If there is no serial correlation, the DW statistic will be around 2. The DW statistic will fall below 2 if there is positive serial correlation (in the worst case it will be near zero). If there is negative serial correlation, the statistic will lie somewhere between 2 and 4. The DW statistic is not valid for a regression containing a lagged dependent variable. In this case, the test is preferable, which provides a more general testing framework that the test. Akaike Information Criterion (AIC) The Akaike Information Criterion is often used in model selection for non-nested alternatives – smaller values of the AIC are preferred. For example, you can choose the length of a lag distri- bution by choosing the specification with the lowest value of the AIC. The is an alternative to the Akaike Information Criterion that imposes a larger penalty for additional coefficients. is a test statistic for testing whether the residuals are normally distributed. The test statistic measures the difference of the skewness and kurtosis of the residuals with those from the normal distribution. Under the null hypothesis of a normal distribution, the statistic is distributed as X2P P with 2 degrees of freedom. If the residuals are normally distributed, the statistic should not be significant. Unlike the statistic for AR(1) errors, the Breusch- test may be used to test for higher order ARMA errors and is applicable whether or not there are lagged dependent variables. It is recommended in preference to the DW statistic when testing for autocorrelation in errors. The null hypothesis of the LM test is that there is no serial correlation up to lag order p, where p is a pre-specified integer. The local alternative is ARMA(r, q) errors, where the number of lag terms p = max (r, q). Note that this alternative includes both AR(p) and MA(p) error processes, so that the test may have power against a variety of alternative autocorrelation structures. The test is performed by regressing the residuals on the original regressors and lagged residuals up to order p. The Obs*R-squared statistic is the test statistic and is computed as the number of observations times the (uncentred) R2P P from the test regression. Under quite general conditions, the LM statistic is asymptotically distributed as X2P (p)P . This is a Lagrange Multiplier (LM) test for autoregressive conditional heteroscedasticity (ARCH) in the residuals. This particular specification of heteroscedasticity was motivated by the observation that in many financial time series, the magnitude of residuals appeared to be related to the magnitude of recent residuals. ARCH in itself does not invalidate standard LS inference. However, ignoring ARCH effects may result in loss of efficiency. This is a test for heteroscedasticity in the residuals from a least squares regression. Ordinary least squares estimates are consistent in the presence of heteroscedasticity, but the conventional computed standard errors are no longer valid. Whites test is a test of the null hypothesis of no heteroscedasticity against heteroscedasticity of some unknown general form. The test statistic is computed by an auxiliary regression where the squared residuals are regressed on all possible (non-redundant) cross products of the regressors. Two statistics are reported. The F-statistic is an omitted variable test for the joint significance of all cross products, excluding the . It is presented for comparison purposes. The Obs*R- squared statistic is Whites test statistic, computed as the number of observations times the centred R2P P from the test regression, and is asymptotically distributed as X2P P with degrees of freedom equal to the number of slope coefficients (excluding the ) in the test regression. also describes this approach as a general test for model misspecification, since the null hypothesis underlying the test assumes that the errors are both homoscedastic and independent of the regressors, and that the linear specification of the model is correct. Failure of any one of these conditions could lead to a significant test statistic. Conversely, a non-significant test statistic implies that none of the three conditions is violated. The Chow forecast test first estimates the model for a subsample comprised of the first TB1B observations. This estimated model is then used to predict the values of the dependent variable in the remaining T2B B data points. A large difference between the actual and predicted values casts doubt on the stability of the estimated relation over the two subsamples. The F-statistic follows an exact finite sample F-distribution if the errors are independent, and identically, normally distributed. The log likelihood ratio statistic has an asymptotic X2 distribution with degrees of freedom equal to the number of forecast points T2 under the null hypothesis of no structural change. If the statistic is not significant, then the null hypothesis of no structural change is rejected. RESET stands for Regression Specification . Specification error is an omnibus term which covers any departure from the assumptions of the maintained model. heteroscedasticity, or non-normality of the residuals all violate the assumption that the disturbances are distributed N(0, 2P IP ). RESET is a general test for the following types of specification errors: Incorrect functional form; Correlation between the independent variables and the disturbances which may be caused by, among other things, measurement error in the independent variables, the presence of lagged dependent variables in the regressors, and serially correlated disturbances. APPENDIX III: Econometric results Table A1 Estimation Results: Petrol and Diesel Consumption in Definition (all variables in logs) Petrol consumption in cars, mP Diesel consumption In cars, mP Real price petrol, ore/litre Petrol vehicle tax, cars, Kr Real price diesel, ore/litre Real vehicle tax diesel, cars, Kr Variable(-1) Variable at period (t-1) System: _DRIV Estimation Method: Seemingly Unrelated Regression Sample: 1973 2006 Included observations: 34 Total system (balanced) observations 68 Linear estimation after one-step weighting matri C(11) C(12) C(13) C(14) C(15) C(16) C(17) C(21) C(23) C(24) C(25) Determinant residual covariance 1.29E-06 Equation: LBENB = C(11) + C(12)*LRDINK + C(13)*LRPBEN + C(14) *LRFSB + C(15)*LRPDIEKB + C(16)*LRFSD + C(17)*LBENB(-1) Equation: LDIEB = C(21) + C(12)*LRDINK + C(23)*LRPBEN + C(24) *LRFSB+ C(25)*LRPDIEKB + 0*LRFSD + 0.503*LDIEB(-1) Estimation results – Multi-family houses Log of district heating in TWn LRPO(-2) Log of real oil price two years previous a) District Heating Dependent Variable: LTWHFHCF Method: Least Squares Sample (adjusted): 1984 2005 Included observations: 22 after adjustments LRPO(-2) LTWHFHCF(-1) Prob(F-statistic) Bilaga 5 SOU 2008:25 Estimation results – Single-family houses Log heating oil in TWh Log electricity in TWh Log of bio-fuel in TWh Log of household electricity in TWh Log real oil price, ore/kWh Log real electricity price, ore/kWh a) Heating: Oil Dependent Variable: LTWHSHCO Method: Least Squares Sample (adjusted): 1984 2005 Included observations: 22 after adjustments LTWHSHCO(-1) Prob (F-statistic) b) Heating: electricity Dependent Variable: LTWHSHCE Method: Least Squares Sample (adjusted): 1984 2005 Included observations: 22 after adjustments LTWHSHCE(-1) Prob (F-statistic) c) Heating: Bio-fuels Dependent Variable: LTWHSHCV Method: Least Squares Sample (adjusted): 1984 2005 Included observations: 22 after adjustments LTWHSHCV(-1) Bilaga 5 SOU 2008:25 Prob (F-statistic) d) Household electricity Dependent Variable: LHELSH Method: Least Squares Sample (adjusted): 1979 2004 Included observations: 26 after adjustments LHELSH(-1) Prob (F-statistic) , R. and R. 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Bedömningar och förslag. 4.Omreglering av apoteksmarknaden. Kränkande utformning av kommersiella meddelanden. 6.Fastighetsmäklaren och konsumenten. Åtgärdsplan för den kliniska forskningen. 8.Bidrag på lika villkor. En myndighet för all trafik. 11.Frihet för studenter – om hur kår- och nationsobligatoriet kan avskaffas. 12.Finansiella sektorn bär frukt. Analys av finansiella sektorn ur ett svenskt perspektiv. 13.Bättre kontakt via nätet – om anslutning av förnybar elproduktion. + : issues for electricity production based on renewable energy sources in , , , and . 14.Timmar, kapital och teknologi – vad betyder mest? En analys av produktivitetsutvecklingen med hjälp av tillväxtbokföring. 15.LOV att välja – Lag Om Valfrihetssystem. 16.Förtursförklaring i domstol. 17.Frivux – valfrihet i vuxenutbildningen. 18.Evidensbaserad praktik inom social tjänsten– till nytta för brukaren. 19.Att slutförvara långlivat farligt avfall i undermarksdeponi i berg. 20.Patentskydd för biotekniska upp- finningar. Globalisering, strukturomvandling och sysselsättningsdynamik. 22.Ett stabsstöd i tiden. 25.Ett energieffektivare +Bilaga. Skyddet för den personliga integriteten. Bedömningar och förslag. Fastighetsmäklaren och konsumenten. [6] Förtursförklaring i domstol. Patentskydd för biotekniska uppfinningar. Immunitet för stater och deras egendom. [2] Konsulär katastrofinsats. Omreglering av apoteksmarknaden. LOV att välja – Lag Om Valfrihetssystem. – till nytta för brukaren. Finansiella sektorn bär frukt. Analys av finansiella sektorn ur ett svenskt perspektiv. Timmar, kapital och teknologi – vad betyder mest? En analys av produktivitetsutvecklingen med hjälp av tillväxtbokföring. Globalisering, strukturomvandling och sysselsättningsdynamik. Ett stabsstöd i tiden. Åtgärdsplan för den kliniska forskningen. Bidrag på lika villkor. Frihet för studenter – om hur kår- och nationsobligatoriet kan avskaffas. Frivux – valfrihet i vuxenutbildningen. Att slutförvara långlivat farligt avfall i under- marksdeponi i berg. Barlastvattenkonventionen – om anslutning. En myndighet för all trafik. Bättre kontakt via nätet – om anslutning av förnybar elproduktion. + : issues for electricity production based on renewable energy sources in , , , and . Ett energieffektivare + Bilaga. Kränkande utformning av kommersiella meddelanden.