sou · GWB325 · 2009-01-01 00:00:00 — The regression will yield a reasonably high value of R2 indicating that the model fits well and the unrelated variable will appear to be significant according to the t-statistics, even though there is no causal relationship between the variables. Basically, this means that we must be extra careful to specify them correctly when working with non-stationary variables. Stationarity is important for empirical work because standard inference procedures do not apply to estimates of models containing non-stationary variables. In particular, the standard t- tests will be biased, so that traditional hypothesis tests will be misleading. The stationarity of the variables is examined using Augmented Dickey-Fuller (ADF) unit root tests (Appendix I). Tests are carried out on the logarithms of the variables, since the model specification assumes that the variables all enter the model in log form. The ADF tests are carried out by estimating the difference equation, allowing for a , trend and three lags of the dependent variable. The model is sequentially simplified on the basis of statistical significance tests. To test for higher levels of integration, the first differences of the variables are also examined using similar procedures. The significance level of the test statistics is based on the critical values for unit root tests. From these tests, we conclude that the variables are either I(0) or I(1), that is some are stationary and some are not. In summary, (the logs of) the variables relating to transport are generally non- stationary, while those relating to residential energy use are stationary. Real income and GDP are both non-stationary, as expected. Given this latter result, a long-run relationship between residential energy use and income cannot be estimated using the data available. This is also apparent from visual inspection of the residential energy use data which is seen to vary around a mean. This is likely to be a feature of the data sample, which only covers the period from 1980 to 2005, rather than of a longer-term relationship. As discussed in Appendix II, a long-run relationship between non-stationary variables will only exist if the variables are cointegrated, that is to say that there is a coefficient vector such that a linear combination of the dependent and independent variables is stationary. For non-stationary variables, cointegration is tested using a procedure. As mentioned above, fuel use in cars was estimated for petrol and diesel cars separately. The long-run relationship was specified as in equation (2) with all variables in log form and expressed in prices by deflating using the Consumer Price Index. Since fuel use and the explanatory variables were found to be non- stationary, it was necessary to test for the existence of a long-run relationship (cointegration). A long-run relationship between the fuel use and the explanatory variables was confirmed by the method in both cases. The dynamic specification was estimated as an autoregressive distributed lag model, with up to 3 lags on all variables and insignificant lags and variables were omitted sequentially. The estimates are reported in Table A1 in Appendix III. All of the estimates are significant at the level or better, the estimated equations explain the data well and no problems are detected on the basis of the various statistical tests employed. The resulting long-run elasticities are shown in Table 1. Price elasticities for petrol and diesel use in cars. Note: all estimates are significant at the confidence level or greater, with the exception of * The elasticities are of the correct sign and generally of a reasonable magnitude. The own price and taxation effects are negative and the cross-price and taxation effects are positive suggesting that prices and taxation have encouraged a substitution between fuel types. The cross-price elasticity of diesel demand with respect to the price of petrol appears rather large. However, as diesel is such a small share of total fuel use for cars (about in 2006), a large value is to be expectedTPF5FPT. The results also indicate that car taxes have had some effect on fuel demand, but the elasticities are of a smaller magnitude than the fuel-price elasticities. It appears that petrol is more price sensitive than diesel and has responded more to vehicle taxation. In fact, no significant relationship could be found between diesel consumption and diesel car taxation. A reason for this may be that the increase in diesel cars was coincident with the increase in diesel car tax in 1993 when the kilometre tax on diesel cars was withdrawn. However, estimating the model for different time periods (1970-90, 70-95) produces the same results. It can also be argued that technical improvements in diesel vehicles are partially responsible for the increasing demand for diesel cars and hence diesel fuel since 2000. Inclusion of a linear time trend for the period from 2000 onwards indicates a significant exogenous increase of diesel demand of per year. Although there are small differences between the elasticities estimated from the models with and without the trend, there are only two cases where the difference is statistically significant: the cross-price elasticity for diesel, which is reduced from 1.34 to 1.00 in the long run, and the cross-elasticity for diesel with respect to the tax on petrol cars, which is reduced from 0.70 to 0.49 in the long rum. The elasticity of diesel consumption with respect to diesel car tax remains insignificant. The own-price elasticities are slightly smaller than the interval of between -0.6 to -0.8 often quoted in the literatureTPF6FPT. However, it must be stressed that the average interval reported in literature reviews has a considerable variation, with individual estimates ranging from 0 to nearly -2. It can be argued that might have a lower than average elasticity, because of its low population density, which makes alternative modes less competitive. importantly, there is considerable empirical evidenceTPF7FPT that suggests that the response to the fuel price increases of the seventies was far stronger than the response to fuel price changes previously or since, that prices have had an asymmetric effect on demand. 5TP PT Cross-elasticities can be related by the shares of the fuels used. A diesel price cross elasticity of 1.33 is equivalent to a petrol price cross elasticity of 1.33*0.16/0,84=0.25 which is not very different from the estimated elasticity of 0.18. 6TP PT Most recently, , Dargay and Hanly (2004). 7TP PT Dargay and Gately (1997). for this asymmetry in the demand model considerably reduces the price elasticity. As very few of the studies covered by literature reviews allow for this effect, they tend to overestimate the price elasticity. In addition, the majority of studies reviewed do not include very recent data, so the effect of the price rises of the seventies will make a large contribution to the estimated elasticities. The same model as used for cars was estimated for goods vehicles, with the exception that disposable income was replaced by GNP. Models were estimated for heavy and light goods vehicles separately and for petrol and diesel separately and combined for light goods vehicles. Petrol heavy goods vehicles were excluded because they comprise such a small share of the market. Fuel demand in all cases was found to be highly related to GDP, but no significant fuel price elasticities could be estimated. Vehicle taxation appears to have some impact on fuel use, but the estimates are highly uncertain and are thus not reported. As mentioned earlier, models were estimated for single and multi- family houses separately, with a separate equation for each energy product, which included own prices and the prices of substitute energy sources. The resulting elasticities were generally of the wrong sign and/or insignificant. In one single case were we able to find a significant elasticity: the demand for district heating with respect to the price of heating oil. The estimation results are shown in Table A2 in Appendix III. The long-run cross-price elasticity of +0.52 shown in Table 2, is of an acceptable magnitude, but the slow estimated speed of adjustment indicates that the response will take a substantial time; in fact, the estimate indicates that of the total response will take 13 years. This is not surprising given the lifetime of residential heating systems. It also suggests that the increase in district heating noted in the eighties and nineties was a delayed response to earlier price rises. Unfortunately we were unable to estimate the own-price effect. However, the effect of oil prices on district heating will only come about through a substitution away from oil to district heating, so that oil prices must necessarily have an effect on oil demand as well. Table 2 Price elasticity multi-unit dwellings. Estimation period 1984 2005 Light fuel oil price Note: the estimate is significant at confidence or greater. We had more success in estimating elasticities for heating in single- family dwellings, but only a small group of elasticities could be estimated. The estimated equations are shown in Table A3 in Appendix III and the long-run elasticities in Table 3. The own- price elasticity for oil is very large, and there is a small cross-price effect for district heating in relation to the oil price. The electricity price has a small effect on electric heating demand, but a larger effect than would be expected on electricity used for purposes other than heating. Table 3 Price elasticities single-family dwellings. Estimation period 1984 2005 Light fuel oil price Note: all estimates significant at the confidence or greater. 5 Calculation of energy savings The reduction in energy use resulting from changes in taxation is calculated on the basis of the econometric results. This is done by using the estimated models to produce dynamic forecasts of energy use under two scenarios and comparing the results. involves using the actual values of energy demand for the period for which we have data – 2006 for transport and 2005 for . Forecasts for subsequent years are based on the estimated models under the assumption that real prices and income remain . Four different cases are examined. The results are shown in table 4. The first considers the effects of all taxation measures introduced since 1991. The reference case, with taxation, uses actual taxation and income and assumes these remain at 2006 levels in real terms until 2016. The no taxation case uses 1990 taxation levels and assumes these had remained the same in nominal terms until 2006, after which they are assumed to stay at 2006 levels in real terms until 2016. This case thus in effect removes all taxation measures introduced since 1990. The difference in energy use between the reference case and the no taxation case measures the energy savings. The taxes removed in the no taxation case are all changes in fuel and vehicle taxation since 1990 and VAT charged on this tax, and any VAT increases resulting from price changes. The estimated savings are shown in the first row of Table 4. The estimated effect of all changes in taxation is a saving of in 2005, increasing to in 2016. By this time the total effects of all these measures have just about been complete. According to the model, the savings have been a result of an 8.8 reduction in petrol consumption and an increase in diesel consumption of , as motorists have switched from petrol to diesel vehicles. The remainder can be explained as improvements in the efficiency of vehicles, either by substitution of larger for smaller, more energy efficient ones, or by the early retirement of older less energy-efficient cars. The overall savings are illustrated in Figure 5. As shown in Figure 6, this is composed of a larger savings in petrol and an increase in diesel consumption. The second case shows the impact of taxation changes between 2005 and 2007. The increase in vehicle taxation in 2005 is included and fuel tax increases up until 2007. The effect of this is seen to be by 2016, a reduction in petrol by and increase in diesel by . The last two cases show the impacts of an increase in fuel tax by 75 and 50 ore per litre, respectively (rows 3 and 4). Table 4 Energy savings (TWh) in car transport resulting from taxation changes since 1990. Percent of average energy consumption 2000-2005 in parentheses. 5.2 (10.5) Tax 75 ore 2009 Tax 50 ore 2009 Figure 5 Energy savings in fuel consumption for car transport resulting from taxation changes since 1990 Tax at 1990 level Figure 6 Energy savings in petrol and diesel use for car transport resulting from taxation changes since 1990 Petrol - without tax changes from 1990 Diesel - without tax changes from 1990 The savings are much smaller in the residential sector, but the results are in line with the figures shown earlier. Oil prices induced a switch to bio-fuel in single-family houses and to district heating in flats. The savings of oil and electricity are reduced by an increase in district heating and bio-fuels, but there is still a net saving of . However, assuming that the switch to district heating in multifamily dwellings was combined with an equal reduction in oil use the savings increase to . The saving in single-family houses is shown graphically in Figure 7. SOU 2008:25 Bilaga 5 Energy savings (TWh) for heating resulting from taxation since Electricity due to electricity prices Oil due to oil prices Bio-fuels due to oil prices District heating due to oil price Figure 7 Energy Savings in Single family houses Tax at 1990 level The calculations based on the econometric results indicate that by 2016 a savings of will have resulted from taxation measures carried out since 1990. This includes changes in all types of fuel taxes, increases in VAT resulting from these and from non-tax fuel price increases. This represents a minimum value since it only relates energy use for car transport and residential heating, and thus does not include any savings in other sectors – rail, air and sea transport, industry, etc. By using a dynamic model, the effects of these measures over time can be determined. It is seen that the effects on person transport by car are more rapid than the effects one residential heating, which is not surprising given the longevity of heating systems as compared to cars. By 2016, most of the impact of the taxation measures has been complete, whereas for heating, the effects are expected to grow for some years thereafter. The results appear intuitive. There has been a substitution of diesel for petrol in private cars, and for heating, a switch from oil to electricity and bio-fuels in single-family houses and to district heating in flats. The results for the residential sector are less complete than for the transport sector, since reliable estimates could not be obtained for all own- and cross-price elasticities. Despite this, there is sufficient evidence that taxation policy has had significant effects on energy efficiency and that the effects calculated here represent a lower bound for these effects. APPENDIX I: Econometric Background Standard classical estimation methods are based on the assumption that the variables included in the model are stationary. In simple terms, this requires that the means and variances of the variables are over time. If, on the other hand, the means and variances change over time, the variables are non-stationary or in other words, contain a unit root. An implication of such non- stationarity is that the estimates obtained of models including such variables may be inconsistent and the standard significance tests misleading. Since many economic time series are increasing over time, there is reason to suspect that they may be non-stationary. Before embarking on an econometric study based on time series data, it is thus a useful to explore the stationarity or non- stationarity of the variables of interest. Knowledge of the time- series characteristics of the data can also contribute to model specification since, as will be seen below, the time series properties of the variables place constraints on the relationships between them. Related to the concept of stationarity is the level of integration of a time series. This is determined by the number of times a variable must be differenced to become stationary. For a non- stationary variable, if the first difference is stationary, the variable is said to be integrated of order 1, denoted as I(1). Similarly, if second differences are required, the series is I(2). For an I(2) series, the first difference is I(1) and the second difference is stationary. A stationary variable is said to be integrated of order zero, or I(0). The level of integration of a time series can be examined by visual inspection of the graphs of the series, examination of their autocorrelation functions and by formal tests such as the Dickey- Fuller (DF) and Augmented Dickey-Fuller (ADF). Non- stationary series increase or decrease over time, i.e., their means and variances are non-constant and they have autocorrelation functions that do not dampen over time. Of the formal tests, the ADF is employed in this study since it more general than the DF test. Both tests are based on an autoregressive representation of a variable xtB B xt = 0 + 1 xt 1 + 2 xt 2 + + n+1 xt n 1 + t The test equation is based on the reparameterisation: xt = 0 + xt 1 + i xt i + t where = iB B –1. For stationarity, we require < 0, while if x is non-stationary, = 0, which implies the sum of the autoregressive parameters in (A1), i.e. 1B B to Bn+1,B is unity and thus x contains a unit root. The ADF test is implemented by estimating (A2) and testing the null hypothesis = 0, using the ratio of the estimated value to its standard error. The significance level of the test statistics is based on the critical values for unit root tests, and are dependent on the form of the equation, i.e. whether a or trend is included and the number of lagged difference terms. The difference between the DF and the ADF test is that the former assumes that x is a 1stP P order autoregressive process so that the test equation does not include lagged differenced terms. The ADF allows the process to be of any order. To test for higher levels of integration, the first differences of the variables can be examined using similar procedures. If x is found to be non-stationary, the 1stP P differenced series must be tested for stationarity. If it is found to be stationary, x is I(1), otherwise x may be I(2). To determine this, the 2ndP P differences must be tested. It should be stressed that unit root tests in general do not produce unambiguous results. They are large sample tests and their behaviour in small samples is questionable. It is well known that the commonly used tests, as the ADF test, which have a unit root as the null hypothesis, tend in general not to reject a unit root. Other tests, using stationarity as the null, tend not to reject stationarity. Thus contradictory results can be obtained using different tests. In addition, the tests have very low power against a trend stationary alternative. This is particularly the case where the time series has a structural break. Given these problems, any results regarding the stationarity or non-stationarity of a particular series must be treated with caution. As mentioned above, the order of integration of the variables has implications for the estimation of the econometric model. Particularly, if the variables are non-stationary, the least squares estimators and significance tests are invalid. Also, since the error term of the regression equation must be stationary, this requires a coefficient vector such that a linear combination of the dependent and independent variables is stationary. If such a linear combination exists the variables are cointegrated. If we have only two variables, this will only be possible if they are integrated of the same order. For example, if y is I(1) and x is I(0), y would drift either upwards or downwards over time while x would vary around a mean, so that the difference between them would become greater over time. There will thus be no long-run relationship between them. However, if we have three or more variables, a subset of the higher-order series can cointegrate to the order of the lower-order series, which in turn can cointegrate with the remaining series. Thus if y is I(1), and x and z are I(2), x and z may cointegrate to I(1), which can then cointegrate with y. Similarly if y and x are I(1) and z is I(0), y and x can cointegrate to I(0) so that z can be related to y while the error term remains stationary. The important thing is that the linear combination of the variables maintains a stationary error term. Cointegration is related to the concept of the long run, in that it indicates that the observed relationship between the variables has been maintained for a long period. Cointegrated non-stationary variables define a long-run relationship. Other stationary or I(0) variables may affect the dependent variable in the long run through their means or through their means around deterministic trends. Various methods have been suggested to test for cointegration. One method is to estimate the cointegrating relationship separately. Qt = + Xt by and testing whether the residual is stationary. This can be done using the statistic, DF or ADF tests. Appropriate critical values are given by . Another method, the test, uses a vector autoregressive approach and maximum likelihood procedures to estimate all possible cointegrating equations. According to the Granger Representation Theorem, cointegrated series can be represented by an . The dependent variable in an Error-Correction Model (ECM) is specified in terms of differences, rather than levels. This has certain advantages for statistical estimation, as will be discussed below. A simple form of the ECM can be written as: Qt = ( 1)Qt 1 + 0 Xt + ( 0 + 1 ) Xt 1 where X is a vector of explanatory variables. general forms could include higher order lagged differenced terms of the independent variables and lagged differences of the dependent variables. The model in (A4) can alternatively be written as: + ( 1) Qt 1 The parameter 0B B is the impact, or short-term, effect and (1- ) is the feedback effect, which is similar to the adjustment coefficient,, in the Partial Adjustment Model. The long-run response is given by ( o + 1) In the ECM, the dependent variable is in differenced form, and is thus generally stationary. Since both sides of the equation must have the same time series properties, the relationship between variables on the right hand side of the equation must also be stationary. If all or some of the level variables in the brackets are non-stationary, this requires that the linear combination of these variables as indicated in the brackets is stationary, i.e. that the variables are cointegrated. The allows estimation of both short- and long-run parameters simultaneously. If the error-correction term ( - 1) is significantly different from zero and negative (since 0 < < 1) the variables are cointegrated and the estimated parameters of the lagged level variables define the long-run relationship. It has been shown that this method results in efficient estimates of the long-run parameters. The ECM can be estimated by non-linear least squares as expressed in (A5). Alternatively, the terms in the brackets can be multiplied by ( - 1) Qt = 0 Xt + ( 1)Qt 1 + ( 0 + 1) Xt 1 and the equation estimated by . The imposes a less restrictive lag structure than the Partial Adjustment Model by including lagged independent variables (and perhaps higher order lags of the dependent variable). The short-run (or first period) response is thus not necessarily the same proportion of the long-run response for all independent variables.