Irish Scrappage Scheme - Essay Example

? Scrappage programs have a dual aim of stimulating the private car industry and removing inefficient, high emitting vehicles from the road. More specifically the performance of the Irish scrappage scheme (2010 - 2011) will be assessed in this paper by whether the scheme promoted the purchase of cars which produce carbon emissions of 140g/km or less, relative to higher emitting cars and if the overall sale of cars increased during this time. Two separate regressions are run for each hypothesis. In each case this paper tests to see has there been a structural break in both data sets from Q1 2004 - Q2 2011 at the point of the policy implementation. Using a dummy variable when regressing the time-series data, results show that as forecasted, the introduction of the scrappage scheme did indeed lead to a much needed boost to demands since the sales of total cars increased. Even after controlling for various other factors that exert significant influences on the sales of cars such as inflation of car prices, GDP per capita etc, we find that the time period of the scrappage scheme still exhibits a rise in the car sales thereby reflecting a positive impact of the scheme on car sales over the long run. We did not find any impact of the scheme on the short run dynamics of car sales. We fail to find any evidence that there was an increase in sales of cars that emit lower than 140g/Km of carbon caused by the scrappage scheme. We do however find evidence that sales of more environmentally friendly cars significantly depends on the extent of car price inflation in the long run. 1. Methodology Recall that the questions we are concerned with are (i) whether the scrappage scheme has had a positive impact on the aggregate sales of cars in the domestic market and (ii) whether the introduction of the scrappage scheme has created a substitution effect from G and C band vehicles to A and B brand vehicles. 1.1 The hypothesis and the basic setup In order to empirically examine these questions, the easiest and simplest methodology adoptable is that of using two different OLS regressions for cases (i) and (ii) to test whether the introduction of the scheme led to any significant departures in the time series observations of our dependent variables. As mentioned earlier, our dependent variable for case (i) are the quarterly car sales over the sample period of 2003 to 2010. Incorporating an indicator variable for the time periods which were under the coverage of the scrappage scheme as an independent variable, one can conceive an OLS specification to see if the there was a significant impact of the dummy on the dependent variable. However, in order to obtain precise, valid estimates it is crucial to control for other factors that may have influenced car sales during the sample period. To better understand the reasoning, consider the following regression: (1) represents the dependent variable, denotes the constant, i.e., the intercept, denotes the dummy for the scrappage scheme, represents a vector of controls and is the stochastic disturbance or the error term . can be defined as : And Thus, the coefficient signifies the impact of the scrappage scheme on the dependent variable . If we find is statistically significant from zero, the implication will be that the scrappage scheme had an impact. The sign on the coefficient will indicate the direction of the impact. Therefore, if the coefficient is found to be significant and positive, that will imply that the scrappage scheme led to an increase in the dependent variable . If on the other hand we find the coefficient to be negative, that will imply that the scrappage scheme led to a decline on the dependent variable. The coefficient vector includes the coefficients on the individual variables included as controls. The signs and significances of these coefficients will reveal the direction and importance of the control variables for the determination of the dependent variable. Therefore, for case (i), we can take the time series of car sales as our dependent variable and specify the regression as follows: And for case (ii), our regression specification will be: The in equation (3) represents the ratio of the sum of A and B band cars to the sum of the residual bands. Since we are interested in exploring the impact of the scrappage scheme, provided the control variables effectively control for other factors that may lead to variations in the dependent variables, the are the parameter of interest in both the specifications. If is significantly different from zero, then we shall conclude that the scrappage scheme has had an impact on the dependent variable. We are therefore fundamentally interested in identifying whether it is significantly different from zero or not. Therefore, testing our hypotheses boils down to a t-test of significance for the respective . 1.2 Stationarity Concerns – the error correction model However, a central concern when dealing with time series data particularly in smaller samples is non-stationarity. If processes that underlie the data are not stationary, then running simple OLS regressions can lead to spurious estimates. These in turn can lead to fallacious inferences and conclusions if we are not careful. Thus, if there is a problem of non-stationarity in our data series, it is possible we may obtain significant estimates which in truth are spurious. Thus, we may potentially be misled if we do not explicitly deal with possible non-stationarity of our data. While the presence of unit roots can prove to be confounding for precision of estimation and even the validity of them if not specifically tended to, it can also reveal substantial nuances of the underlying data generating process that would remain unknown otherwise in certain cases. An instance of such a convenience is if we have co-integrated variables. In that case, by using error correction methodology it is possible to demarcate the short run and long run dynamics of the model. Co-integrated variables follow the same order of integration. Therefore, in order to identify whether the variables are cointegrated the first step is identifying their orders of integration. In fact, there are two alternatives that we shall use to figure out the nature of stationarity in our data. First, we shall use Johansen’s test for co-integration that shall identify whether any of the variables are co-integraged and if they are then how many are. Secondly, we shall utilize unit root tests on the levels and the differences of the series of higher orders until we are able to reject non-stationarity of the series in question. This will allow us to identify what the order of integration is for each respective variable. For all the variables that share same orders of integration we will explore the possibility of co-integration using the Engle and Granger (1987) 2 step process. In fact, the Engle and Granger methodology is an instance where additional information can be extracted by utilising co-integration of the data. The Engle and Granger (1988) 2 step error correction methodology essentially incorporates the co-integration test in its first stage. The first stage is simply running the OLS regression in levels of the non-stationary variables. The estimated relationship is valid and reflects the long run dynamics of the model as long as the series of estimated errors is stationary. If the fitted errors are found to be stationary, the non-stationary variables in levels are said to be co-integrated. The 2nd stage is to estimate the short run dynamics by regressing the model in the order of differences that made the series stationary on same order differenced series of the explanatory variables and the fitted residual with a lag order equal to the order of integration. Thus, as the first step, we shall run the case specific variants (2) and (3) of the regression specified in (1) as the long run model. Then, if the fitted errors are found to be stationary, we shall run the following model to gauge the short run dynamics: (4) Where, the dependent variable is found to be integrated of the order i and is the error correction term. It is the lagged value of the fitted residual from the long run model. 2. Results and Discussion This section presents the results of running the regressions specified in the methodology section and discusses the implications in the context of our hypotheses. It would be convenient to note the following notations that are used in the tables: MACS: moving average of car sales (dependent variable for OLS specification denoted by equation 2) SCRAP: scrappage dummy (independent variable of primary interest) OP: Crude oil price per barrel (Control variable) CARINF: Inflation of car prices (Control variable) INFCARIN: inflation of car insurance (Control Varible) GDPPC: GDP per capita (Control Variable) ABRES: ratio of the sum of A & B bands to the sum of the residual bands (Dependent variable is OLS specification denoted by equation 3) 2.1 Impact of Scrappage Scheme on quarterly average car sales - OLS specification, equation (2) Table 1 presents the results of the 1st stage OLS model specified as equation (2). Table 1: Estimation results - Long run model (equation 2) The first point to note from table 1 is that the coefficient on indicator variable scrap is significant and positive. The t-statistic takes a value of 2.37 > 1.96, which is the 5% critical value. This implies that introduction of the Scrappage scheme has had a positive impact on the moving averages of total car sales. Therefore, as expected, the introduction of the Scrappage Scheme seems to have served its purpose in increasing the overall demand for cars. Apart from the Oil prices, all the variables included in the specification as controls turn out to be significant and the coefficients are positive. Thus, the implication is that all the control variables from oil prices exert a positive influence on car sales. Figure 2.1: Time plot of the fitted residuals However, these estimates are valid and do reflect the long run relationships between the independent variables and the dependent variable only if the residuals or the fitted errors from the model are stationary. Figure 1 above presents the time plot of the fitted errors. Observe that there is no evidence of any particular trend or pattern in the time plots. Therefore it can be expected that the errors are stationary. However, formal proof for this fact is provided in table 2. Table 2: Stationarity of the fitted residuals - results of and ADF test Table 2 presents the results of a unit root test on the residuals from the model. Note that since the regression specification for the Augmented Dickey Fuller test specifies that there is no constant or trend, the typical Dickey Fuller critical values are inappropriate to gauge the significance of the test statistic. From MacKinnon’s (1999) table we find that the 5% critical value for a model with the characteristics of equation (2) is 3.61. Observe that the absolute value of the computed statistic is 4.003, which is greater than the critical value. Therefore, we reject the null hypothesis of a unit root in the series of fitted errors. Therefore, the obtained estimates in table 1 are valid as a representation of the long run dynamics of car sales. This proves that the scrappage scheme does have a positive long run impact. Therefore the null hypothesis that the scrappage scheme does not have an impact, or that it has a negative impact on car sales is rejected at the 5% level of significance. Additionally, it is important to note that the fitted errors being stationary also implies the existence of co-integrated variables within the specification. Table 3 formally proves this. It presents the results of a Johansen cointegration test. Table 3: Co-integration test for variables in specification denoted as equation 2 Observe that we fail to reject upto a maximum rank of 3 from the trace statistic. Therefore, the test implies cointegration between 3 of the variables in our specification. It is this co-integration that leads to our estimates being non-spurious in spite of non-stationarity. 2.2 Short run dynamics In this section we shall examine the short run dynamics of car sales. As noted in the methodology section, the 2nd step of the Engle and Granger error correction methodology is to run a regression in differences of the order that makes the dependent variable stationary. Thus, the first step is to identify the order of integration of the variables we are interested in. Table 4: Testing for unit roots in levels of MACS Table 5: Testing for unit roots in the 1st differences of MACS Table 6: Testing for unit roots in 2nd differences of MACS Table 7: Testing for unit roots in the 3rd differences of MACS Recall that the null hypothesis in the Augmented Dickey Fuller (ADF) is that the series being investigated contains a unit root. If the test statistic exceeds the critical value in absolute terms, then we reject the null hypothesis in favour of the alternative: there is no unit root in the series. Tables 4 through 7 show that MACS or the moving averages of car sales is a series that is integrated of order 3, i.e., it is {I(3)}. We fail to reject the presence of a unit root in the levels, 1st and 2nd differences of the series. The ADF test rejects non-stationarity of the series in 3rd differences. Table 8: Testing for unit roots in levels of Oil prices Table 9: Testing for unit roots in 1st differences of oil prices Tables 8 and 9 show that Oil prices follow an I(1) process. While we fail to reject the presence of a unit root in the levels of the series, the test rejects a unit root in the 1st differences of the series. Table 10: Testing for unit roots in Car price inflation Table 11: Testing for unit roots in 1st differences of car price inflation Table 12: Testing for unit roots in 2nd differences of car price inflation Observe from tables 10 through 12 that car price inflation seems to follow an {I(2)} process. While we fail to reject non-stationarity of car price inflation in its levels, the ADF test rejects the presence of a unit root in the 1st differences of the series. Therefore it is integrated of the 2nd order. Tables 13, 14, and 15 tests for the presence of unit roots in levels and successively higher orders of differences of the control variable price inflation for car insurance. Table 13: Testing for unit roots in car insurance price inflation Table 14: Testing for unit roots in 1st differences of car insurance inflation Table 15: Testing for unit roots in 2nd differences of car insurance inflation Observe that stationarity is obtained at the 2nd differences of car price inflation. Therefore the series is {I(2)}. Table 16: Testing for unit roots in GDP per capita Table 17: Testing for unit roots in 1st differences of GDP per capita Table 18: PP test for unit roots in 1st differences of GDP per capita In tables 16 through 18 we examine the stationarity properties of GDP per capita. As can be noted from the time plot of the series presented in the data section, there is a substantial spike at the end which seemingly deceives the ADF tests which fails to detect stationarity in the series at even 5th order of differences. However, using both a Dickey Fuller test and a Phililps-Perron test we ascertain that the series is actually {I(1)}. It should be noted however that dropping the outlier of the first quarter of 2011, we found that the ADF test provided evidence to the fact that GDP per capita series was {I(1)} as well. Table 19: Testing for unit roots in 2nd differences of AB to residuals ratio Table 20: Testing for unit roots in 3rd differences of AB to residuals ratio Finally, in tables 19 and 20, we turn to the results of running an ADF test on the ratio variable that we constructed to measure the incidence of substitution from G and C bands into A and B bands which is the dependent variable in regression specification denoted by equation (3). Our results indicate that this variable, like the other dependent variable is also {I(3)}. That is it becomes stationary at 3rd order of differencing. Now, since we are aware about the exact stationarity properties, i.e., the orders of integration of the variables of interest, we turn to exploring the short run dynamics of the dependent variables which constitutes the 2nd stage of the Engle and Granger methodology. 2.3 Short run dynamics of car sales (equation 5) Table 21 presents the results of running the Engle Granger 2nd stage regression in 3rd differences including the error correcting 3rd lag of the residual from the 1st stage (equation 2). Table 21: Estimates from error corrected model - Short run dynamics Observe that only the 3rd difference of car price inflation seems to have an impact on the 3rd difference of the moving averages of car sales. All other variables, including the error correction term turn out to be insignificant. Thus, from this sub-section we find evidence of a positive and significant impact of the scrappage scheme on the average car sales in the long run. The short run dynamics of car sales however seem to be influenced only by the rate of change in the growth of car price inflation. 2.4 The effects on the incidence of substitution to A and B band vehicles from other bands of the Scrappage Scheme - Long run OLS estimates of equation (3) This section presents the results for estimation of equation (3). Recall that the independent variable in this specification is the constructed measure of incidence of substitution from G and C band cars into A and B band cars. Table 22: Long run dynamics of AB to residual ratio, 1st stage OLS From table 22 we find that the indicator variable for the presence of the scrappage scheme turns out to be insignificant. Thus, we fail to find any evidence for the fact that the scheme led to any substitution into A or B band vehicles. The constant, GDP per capita and car price inflation are variables that have coefficients that are significantly different from zero. Car price inflation seems to have an inverse impact on the incidence of substitution while GDP per capita has a very small but positive impact on the ratio. To evaluate the validity of these results and to examine if they could possibly be spurious, we now turn to explore the nature of the fitted errors. Figure 2.2: Time plot of fitted residuals (from regression of equation 3) From the figure above (2.2) we note that there are no evident patterns or trends in the fitted residuals. This seems to imply that the residuals for this regression, like the previous one are stationary as well. Table 23: Testing for unit roots in fitted errors (equation 3) Our anticipation regarding the fitted errors being stationary is validated by the ADF test results shown above. Recall that the critical value from MacKinnon’s (1999) tables is 3.61. Therefore, the test rejects non-stationarity of the residual. Since the residual is stationary, our estimates obtained in table 22 are valid. Therefore, we can conclude that the long run movements of the incidences of substitution into A and B bands from other bands are significantly influenced by the inflation of car prices and GDP per capita. However, we fail to find any evidence of a significant influence of the scrappage scheme. 2. 5 Short Run dynamics of the incidence Turning to short run dynamics, we find that the 3rd differences of car price inflation affect the 3rd differences of the incidence in the short run. No other variables including the error correction term turn out to be significant. Table 24: Short run dynamics, error corrected model Therefore, the conclusion from this subsection is that we fail to find any evidence that the scrappage scheme led to any substitution to A and B band cars from other bands. However, we do find that GDP per capita has a very small but positive impact on the incidence while car price inflation turns out to be a significant determinant in the long run. In the short run, the dynamics of the incidence are influenced only by the dynamics of car price inflation. 3. Summary and Conclusion In this paper, we evaluated the impacts of the Irish Scrappage Scheme in light of its stated objectives. The forecasts, as well as the stated objectives expected that the scheme will stimulate demand in the car market and thus lead to an increase in the car sales and additionally lead to a reduction in the ratio of high carbon emitting cars to lower carbon emitting cars. Our results show that as forecasted, the introduction of the scrappage scheme did indeed lead to a much needed boost to demands since the sales of total cars increased. Even after controlling for various other factors that exert significant influences on the sales of cars such as inflation of car prices, GDP per capita etc, we find that the time period of the scrappage scheme still exhibits a rise in the car sales thereby reflecting a positive impact of the scheme on car sales over the long run. We did not find any impact of the scheme on the short run dynamics of car sales. However, we fail to find any substantiating evidence for the second aspect of the forecast. There is no evidence that there was an increase in sales of cars that emit lower than 140g/Km of carbon caused by the scrappage scheme. We do however find evidence that sales of more environmentally friendly cars significantly depends on the extent of car price inflation in the long run. Additionally, we find that car the 2rd order dynamics of car price inflation turns out to be a significant determinant of the 2nd order dynamics of the incidence of lower to higher carbon emitting cars. It should be noted however, that our study is extremely limited because of the small sample size. Additionally, the introduction of the scheme was so far into the sample that it may well be that the sample ends before true impacts of the scheme are felt. However, our results do indicate that this is an issue worth investigating once substantial data becomes available. References: Engel and Clive Granger (1987) “Cointegration and error correction: Representation, estimation and testing”, Econometrica, 55: 251-276 MacKinnon, J (1991) “Critical Values for Cointegrstion Tests”, in R. Engel and C. Granger, Long-run Economic Relationships, Oxford University Press Read More