Model selection

The exogenous variables included, the type of model and lag structure chosen, as well as the functional form used, have been the subject of much debate. For a detailed discussion of gasoline demand modelling the reader is referred to Bohi (1981) or Sterner and Dahl (1991). The purpose of this section is briefly to present the functional forms and models chosen, concentrating primarily on the issue of lag structure.

The simple static model (M0) in which G is gasoline consumption per capita, Y is deflated per capita income and P is deflated gasoline price is chosen initially. All the variables are in logarithms.

where i=1,..., N are the countries; t=1,..., T are the years. However, static models cannot in general (i.e. at least not with time-series data) be relied upon to capture the complex process of adaptation to changes in prices and income. The way dynamic adaptation is modelled depends upon the lag structure assumed. One particular form of lag structure is the geometrically declining lag. By using the Koyck transformation, geometric lags on the exogenous variables can be modelled through the inclusion of a lagged endogenous variable:

This is referred to as the lagged endogenous model Mj. Although geometrically decreasing lags may be a fairly strong restriction,3 the ease of estimation and the difficulty of obtaining sufficiently long series of data for the estimation of other more complicated lag structures have given the lagged endogenous model considerable popularity.

A slightly less restrictive lag structure can be obtained through the further inclusion of lagged exogenous variables as in (4.3). Model M2 is often referred to as an inverted-V lag4 because it allows for an adjustment that is first low but increasing (because of a 'perception lag') and then geometrically decreasing.

G„ = c + aP „ + pYll + (iGu_x + >#Vl + + P* (4.3)

Equation (4.4) is another form of inverted-V lag that will be referred to as model M3 and which can be derived by assuming that the lags follow a Pascal distribution.

Gu = c 4- aPt, + PY.+ £Glt_, - x/J52Gi t_2 + (4.4)

The final form of dynamic model used here is the polynomial distributed lag model M4 in which only lagged observations of the exogenous variables are included but the ai and fai are constrained by some form of polynomial.

In this model the short-run elasticities are a0 and fa0 while the long-run elasticities are given by the sums of all the as and fas. In the lagged endogenous model M1 the short run is given by a and fa while the long run is given by a and fa divided by 1-A.

Time series, cross-sections and pooled estimators

All the above models can be seen as special cases of a general gasoline demand model with error components such as

where fit=u+vt+sit and &=1,..., K are various explanatory variables (exogenous or endogenous, current or lagged). In (4.6) the logarithm of gasoline demand depends on the vector X of explanatory variables but may also be affected by time-invariant country-specific effects ui and time-specific effects for particular years, Vf

Turning to the issue of how best to use the data, it can be seen that one possibility is to assume that Piat=Pki and estimate separate elasticities pk for each country. This is the time-series approach in which each country data set is analysed separately. This approach highlights the individual country specifics but does not fully use the information implied by the comparison between countries. Another method of estimating is the pure cross-section which amounts to assuming that Pkit=Pkt Thus separate elasticities pkt are estimated for each year on a cross-section of countries.

However, many researchers, such as Baltagi and Griffin (1983), have asserted that the most efficient way to use the variation both along time and across countries in a data set simultaneously is to base estimations on combined cross-section time-series analyses. This can be done by assuming that Put=Ph such that there is one unique elasticity for each explanatory variable estimated for the whole data set. There are many ways of doing this, however (for instance, with or without common intercepts), and furthermore, as should be clear from the analysis by Pesaran and Smith in Chapter 2, the choice of model must take into account the character of the data used. The use of dynamic models such as M1 and M2 with pooled estimators may result in large biases. The approach here will follow that of Chapter 2 and a number of different estimators will be considered, such as the mean group estimates which are averages of individual country time series along with pure cross-section estimates and various pooled estimators.

THE RESULTS 4.2.1

Cross-section estimates

Table 4.1 shows a series of cross-section estimates for different years. The model used is the simple static model M0 and the values obtained average around -1 for price and +1 for income, which concurs rather well with earlier estimates of long-run elasticities (see Dahl and Sterner 1991a). One advantage with the pure cross-section studies is that they permit the use of such simple models that still appear to pick up longrun elasticities. Note also that the use of dynamic models (the lagged endogenous model M1) with cross-section data gives rather strange values (see Table 4.1, note).

It is interesting to note that the development of the elasticities over time turns out to be moderately stable between most individual pairs of years but that over longer intervals of time there are some appreciable variations. In particular, between 1972 and 1977 there is a constant decline in price elasticities, which reverses after 1977 and increases thereafter, particularly until 1982. One possible explanation is that the international price increase in 1972-3 had strongly varying effects on the domestic price levels in different

OECD countries. These differences depended on the degree of energy self-sufficiency and on whether or not the government tried to accommodate price changes through tax policy. In any event, consumption adjusted very slowly for two reasons: first, lags are always important as has already been emphasized, and second, there was less preparedness for this first oil shock. Between 1972 and 1977 price differentiation between countries increased

Table 4.1 Elasticity estimates with pure cross-sections

Year

Price elasticity t

Income elasticity

t

N

R2

1970

-1.27

-4.92

1.15

6.16

23

0.91

1971

-1.14

-4.84

1.25

6.86

23

0.91

1972

-1.19

-5.28

1.23

7.15

23

0.91

1973

-0.95

-4.55

1.39

8.50

23

0.89

1974

-0.91

-4.80

1.28

6.95

23

0.88

1975

-0.87

-3.69

1.20

5.62

23

0.85

1976

-0.78

-3.79

1.25

6.12

23

0.85

1977

-0.77

-4.27

1.26

6.80

23

0.86

1978

-1.08

-5.31

0.92

4.68

23

0.90

1979

-1.13

-4.33

0.92

3.96

23

0.88

1980

-1.25

-6.24

0.88

4.83

23

0.91

1981

-1.20

-5.10

1.08

5.93

23

0.89

1982

-1.34

-5.64

0.82

3.98

23

0.89

1983

-1.05

-4.78

1.00

4.90

23

0.87

1984

-1.20

-4.93

0.82

3.79

22

0.88

1985

-0.98

-3.92

1.02

4.60

19

0.85

Meana

-1.09

1.08

Notes: These results were obtained using the simple static model.

aThis is the weighted mean (using the inverse of standard deviations as weights). The simple averages were -1.07 and 1.09 respectively. When using a static vehicle model G=f(Y, P, V), where V is the vehicle stock, the mean price elasticity was -1.18 but the mean income elasticity was practically zero, this effect being picked up by the vehicle variable. When using the dynamic model Mj the mean short-run price elasticity was -0.15 and the income elasticity 0.04. X was 0.85 and thus long-run elasticities can be calculated as -1.0 and 0.27. The values varied markedly between individual years.

with little immediate effect on consumption. After 1977 this process was gradually reversed with consumption finally adjusting but price policies (in most OECD countries) becoming increasingly harmonized in line with international price levels (although with large differences remaining due to fiscal and environmental considerations).

Time-series estimates

Using the data as time series allows for the study of possible variations between different countries, which may be very useful in itself since there is no particular reason why the elasticities should be identical between countries. If, however, an overall estimate for the whole group of countries is still considered desirable, there are two ways of using the time-series estimates to give such a global estimate, as pointed out in Chapter 2. First, data for all the individual countries can be aggregated and an aggregate time-series analysis can be conducted. (Note that this is, in a sense, no different from treating the United States as a single-country observation since it is already an aggregation of the various states.) Second, (weighted) averages of the individual time-series estimates for each country can be taken, yielding the 'mean group estimates'.

Table 4.2 lists a set of such individual estimates and the corresponding averages for the lagged endogenous (Mj) model. A quick glance at Table 4.2 will convince the reader that there is a considerable difference between the time-series and the cross-section results. The time-series estimates of long-run price elasticities (+0.1 and -2.3) vary more between countries than the cross-section estimates (-0.8 to -1.3). The significance levels are also generally lower.

For some countries the results are rather unexpected. This is the case, for instance, with the positive price elasticity in Switzerland. However, it appears that transit traffic and cross-border purchasing of gasoline between Switzerland, Austria, Germany and Italy is very significant and distorts the results for the relatively small Swiss market. Another country with which problems were encountered was Japan, where an unrestricted estimate of 0.93 for X and (insignificantly) negative income elasticities was obtained. Since such a value for the lagged endogenous variable implies an unreasonably slow adjustment (adjustment would be only 75 per cent complete twenty years after a change in gasoline price!) this parameter was arbitrarily set to 0.8 (which is still higher than the average of 0.69).

Naturally there are many other country particularities that may help to explain variations for individual countries. The case of Sweden, which has been analysed in greater detail elsewhere (see Sterner 1990), will be discussed. Throughout most of the period under discussion Sweden has had uniquely high rates of marginal income taxation. These have been combined, however, with very generous allowances for deducting driving expenses, and thus the companies have had a strong incentive to give their employees cars instead of cash and the latter have had a strong incentive to drive long distances to work. Naturally the incentive effect of gasoline prices has been relatively low and thus also the price elasticities were low (see Table 4.3).

In spite of the variations discussed above, as well as others that are apparent from the table, one may want to consider, with more or less confidence, the mean group estimates as an overall estimate for the OECD as a whole during this period. As noted in Chapter 2 there are two ways of calculating such averages: either by taking (weighted) averages of the long-run elasticity estimates directly or by taking averages of the individual country parameters (short-run elasticities and Xs) and then calculating a long-run elasticity from these means using, as usual, esr/(1-X). The choice depends on which hypothesis is made about the distribution of a, ft and X (see Chapter 2).

As it turns out the results do not vary very much between these two hypotheses, but the income elasticity is very sensitive to the difference between weighted and simple means. The simple average of the price elasticities is -0.85, or -0.81 when calculated as the mean of the short-run

Table 4.2 Individual country elasticities (model Mj)a

e/sr)

e/Ir)

e/sa}

e/Ir)

X

DF

r2

DH

Canada

-0.25

-1.07

0.12

0.53

0.77

19

0.97

-1.01

(-4.48)

(0.35)

(1.34)

(0.17)

(7.05)

United States

-0.18

-1.00

0.18

1.00

0.82

21

0.98

0.11

(-6.59)

(0.41)

(2.62)

(0.17)

(12.44)

e/si-)

ep(Ir)

er(sr)

ey(Ir)

X

DF R2

DH

Austria

-0.25

-0.59

0.51

1.19

0.57

18 0.97

-0.52

(-2.30)

(0.26)

(2.19)

(0.19)

(3.69)

Belgium

-0.36

-0.71

0.63

1.25

0.49

21 0.99

0.14

(-7.54)

(0.17)

(3.24)

(0.06)

(3.54)

Denmark

-0.30

-0.64

0.25

0.52

0.52

20 0.97

b

(-7.94)

(0.08)

(4.63)

(0.05)

(8.32)

Finland

-0.32

-1.23

0.32

1.22

0.74

20 0.98

b

(-2.90)

(0.39)

(2.17)

(0.18)

(8.31)

France

-0.36

-0.70

0.64

1.23

0.48

21 0.99

0.00

(-4.60)

(0.17)

(2.83)

(0.07)

(3.00)

Germany

-0.05

-0.57

0.04

0.48

0.92

21 0.99

0.63

(-0.68)

(1.01)

(0.25)

(1.43)

(11.86)

Greece

-0.23

-1.12

0.41

2.03

0.80

16 0.99

0.20

(-2.15)

(0.74)

(2.19)

(0.26)

(7.56)

Ireland

-0.21

-1.68

0.12

0.93

0.87

21 0.99

0.82

(-4.88)

(1.14)

(0.88)

(0.44)

(9.70)

Italy

-0.37

-1.15

0.40

1.25

0.68

21 0.97

-0.97

(-2.94)

(0.33)

(2.41)

(0.28)

(8.40)

Netherlands

-0.57

-2.29

0.14

0.57

0.75

21 0.98

-1.43

(-5.01)

(0.76)

(1.09)

(0.30)

(6.97)

Norway

-0.43

-0.90

0.63

1.32

0.52

21 0.97

-0.83

-3.22)

(0.31)

(3.13)

(0.11)

(3.64)

Portugal

-0.13

-0.67

0.37

1.93

0.81

15 0.98

b

(-1.96)

(0.38)

(2.05)

(0.36)

(11.18)

Spain

-0.14

-0.30

0.96

2.08

0.54

13

0.97

c

(-0.82)

(0.46)

(2.12)

(0.27)

(2.92)

Sweden

-0.13

-0.46

0.33

1.16

0.72

32

0.99

-1.41

(-2.07)

(0.21)

(3.10)

(0.11)

(10.38)

Switzerlan

0.05

0.09

0.85

1.54

0.45

22

0.98

1.30

d

(0.32)

(0.28)

(2.92)

(0.15)

(3.08)

Great

-0.11

-0.45

0.36

1.47

0.75

21

0.98

-0.87

Britain

(-1.66)

(0.37)

(1.81)

(0.24)

(6.37)

Australia

-0.05

-0.18

0.18

0.71

0.75

20

0.99

0.10

(-2.57)

(0.08)

(2.44)

(0.09)

(9.97)

Japan

-0.15 (-4.37)

-0.76

0.15 (11.86)

0.77

0.80d

21

0.90

d

Turkey

-0.31

-0.61

0.65

1.29

0.50

15

0.95

-0.90

-5.31)

(0.22)

(4.01)

(0.17)

(3.91)

Mean

-0.25

-0.85

0.37

1.15

0.69

Weighted

-0.76

0.79

meane

Aggregate

-0.31

-1.28

0.29

1.19

0.76

25

0.99

time series

Notes: The long-run standard deviation for the OLS estimations is calculated using the Bardsen (1989) method.

Notes: The long-run standard deviation for the OLS estimations is calculated using the Bardsen (1989) method.

aThe time period is 1960-86; for Sweden 1950-86; for Spain 1965-86. bRe-estimated with GLS because of high degree of autocorrelation. cDurbin H could not be calculated.

dThe Japanese results are estimated with the restriction that the speed of adjustment is 0.2. Hence the missing t values. ^Weighted by the inverse of the standard deviation for long-run elasticities. Switzerland not included. Japan given average weights.

Note that long-run elasticities can also be calculated from the means of the short-run elasticities and the lag-end parameter. With unweighted means this method give us values of -0.81 and 1.19 respectively.

elasticities divided by (one minus) the mean of the As. The weighted average of the long-run elasticities is -0.76. For the income elasticities the corresponding figures are 1.15, 1.19 and 0.79 respectively. The reason the weighted estimate is so much lower is mainly the effect of Germany which has a very low long-run income elasticity combined with very high levels of significance (and thus a very heavy weight). The unweighted income elasticity, however, concurs well with the cross-sectional evidence found above, while average long-run price elasticities are, as expected, somewhat lower. The same also applies to the aggregate estimates (time series on the sum of all observations) of -1.28 and 1.19 respectively; however, in this case the price elasticity is very high.

As noted earlier a number of other dynamic5 models M2, M3 and M4 can be postulated. M2 is the only functional form for which any tests could be readily conducted (since M1 is nested in M2). In fact it was found that the addition, in M2, of the lagged exogenous variables did not appear to add much, and the more restricted model M1 could not be rejected. The results for M2, which were similar to the other 'inverted-V' lag model (M3) in any case,

Table 4.3 Comparison of long-run elasticities

Price elasticities

Income elasticities

m4

M1

m2

m4

M1

M2

Canada

-2.0

-1.1

-0.9

0.6

0.5

0.6

United States

-1.2

-1.0

-0.6

1.2

1.0

0.8

Austria

-1.2

-0.6

-0.7

0.9

1.2

1.2

Belgium

-1.5

-0.7

-0.6

1.0

1.3

1.3

Denmark

-0.8

-0.6

-0.6

0.3

0.6

0.6

Finland

-1.2

-1.0

-0.9

1.2

1.4

1.4

France

-0.4

-0.7

-0.6

0.9

1.2

1.1

Germany

+0.1

-0.6

+0.3

1.6

0.5

1.9

Greece

+0.2

-1.1

-0.6

1.8

2.0

1.9

Ireland

-1.0

-1.7

-0.8

1.3

0.9

1.3

Italy

-0.7

-1.2

-0.9

0.9

1.3

1.2

Netherlands

-3.2

-2.3

-1.5

0.4

0.6

0.8

Norway

-2.5

-0.9

-0.8

1.3

1.3

1.3

Portugal

-0.7

-0.3

-0.1

1.1

2.1

2.2

Spain

-1.2

-0.3

-0.1

1.4

2.1

2.4

Sweden

-0.1

-0.45

-0.43

1.2

1.2

1.3

Switzerland

+0.15

+0.1

+0.1

1.8

1.5

1.6

Great Britain

-1.4

-0.5

-0.4

1.6

1.5

1.6

Price elasticities

Income elasticities

m4

Mj

m2

m4

Mj

M2

Australia

-0.2

-0.2

-0.1

1.2

0.7

0.8

Japan

-0.3

-0.8

-0.8

0.8

0.8

0.8

Turkey

-1.1

-0.6

-0.5

1.1

1.3

1.2

Mean

-1.0

-0.8

-0.6

1.1

1.2

1.3

will not, therefore, be reported. Table 4.3 summarizes the long-run elasticities for the remaining models Mj, M3 and M4, again indicating that the estimates are not all that robust to changes in functional form and showing that more work is required on at least some of the individual countries.

4.2.3 Pooled estimates

And finally, the results obtained from the use of pooled estimators will be discussed and the results will be compared with the averages obtained from cross-sections and time series. Table 4.4 contains a number of estimates. These include the ordinary pooled OLS estimator with common intercepts, the fixed effects or so-called 'within' estimator6 that allows for individual country intercepts, and the generalized least squares estimator (GLS). For the last-mentioned the results of several models are reported. For comparison, the aggregate cross-section or so-called 'between' estimator is also reported, together with both the aggregate time-series and the mean group estimates.

One of the principal points raised in Chapter 2 concerned the risks for sizeable bias when using the lagged endogenous dynamic model with pooled data. The X will tend to be biased towards unity and the short-run elasticities towards zero. This is indeed clearly found in the OLS estimate even if the results are somewhat less dramatic than in the empirical example used in Chapter 2. A X estimate of 0.91, however, implies that only one-tenth of the adaptation occurs in the first year and is indeed difficult to justify intuitively. In addition, the short-run income elasticity has an implausibly low value of 0.05. As in Chapter 2 both these results remain largely true, but to a somewhat lesser extent, with the fixed effects estimator.

The estimated price elasticity, listed in Table 4.2, is -1.3, which is in fact higher than the typical time-series values. To illustrate graphically, the relationship between pooled and time-series estimates is complicated by the fact that there are two exogenous variables (as well as lagged variables). However, the assumption that the income elasticity is close to unity (which it tends to be) allows price elasticities to be more closely examined. Figure 4.1 is intended to capture the difference (under this assumption) between different types of estimates by plotting Q/Y against P. The figure shows that the pooled (OLS) estimate will indeed be steeper (more price elastic) than the individual time series for the two countries selected, Sweden and Canada.

The 'between' estimator highlights, as the name suggests, the variation between countries. It is a cross-section of the averages over time for each country. The results are not far from the pure cross-section estimates in Table 4.1. The reason why this estimate is lower than the 'within' estimate in Table 4.2 is that the 'between' estimate is based on a static model. Indeed, 'within' estimation of the static model gives values of around -0.4.

OLS estimation takes variation both within and between countries into account. However, as pointed out by Baltagi and Griffin (1983), it may be

Table 4.4 Summary of long-run elasticity estimates for the OECDa

Estimation

Model

SR price

LR price

SR income

LR income

Lag-end DFE R2

technique

elasticity

elasticity

elasticity

elasticity

Pooled OLSb

Mj

-0.12

-1.39

0.05

0.58

0.91

479 0.99

(-9.3)

(3.8)

(97.7)

Pooled (fix

Mj

-0.22

-1.27

0.13

0.75

0.83

459 0.99

effects)

(-10.4)

(4.2)

(43.1)

'within'c

Pooled GLS

M1

-0.18

-1.35

0.10

0.73

0.87

479

(Fuller and

(-10.2)

(4.1)

(62.0)

Battese

method)

m2

-0.22

-1.34

0.25

0.69

0.89

477

(-8.5)

(2.4)

(61.4)

m3

-0.15

-1.16

0.14

0.63

0.87

491

(-11.4)

(11.0)

Pooled GLS

M4d

-0.38

-1.05

1.13

1.63

406 0.96

(Yule-Walker

(-7.5)

(27.0)

method)

To compare

Static M0

-1.19

1.09

18 0.90

Betweene

(-5.4)

(6.08)

cross-section

Mean group

M1

-0.76

0.79

estimates

Aggregate

M1

-0.31

-1.28

0.29

1.19

0.76

21

time series

Notes: aOECD except Luxembourg, Iceland and New Zealand, 1963-85. Purchasing power parity used for conversion.

bEven for the static model, OLs produces high price elasticities: -0.98 and 1.26.

cFor the static model, 'within' estimates do give a typical 'intermediate' value of -0.4 for price.

dPDL of second degree, with eight price and four income lags for 1970-85.

e'Between' is a cross-section for the static model on average data.

Notes: aOECD except Luxembourg, Iceland and New Zealand, 1963-85. Purchasing power parity used for conversion.

bEven for the static model, OLs produces high price elasticities: -0.98 and 1.26.

cFor the static model, 'within' estimates do give a typical 'intermediate' value of -0.4 for price.

dPDL of second degree, with eight price and four income lags for 1970-85.

e'Between' is a cross-section for the static model on average data.

influenced too much by 'between' variation since both within-country (between years) and between-country variation are given equal weight, despite the fact that the between-country error term would be expected to have much greater variance. Therefore, the GLS estimator is proposed in order to take into consideration the respective variances of the error components so as to provide a better estimate. Baltagi and Griffin use five different two-stage GLS estimators that give different estimates, but state that there is no suitable way to choose between them. In this case only one estimator has been chosen (following Fuller and Battese 1974; see Drummond and Gallant 1979). Attention is concentrated, instead, on variation due to the model used and the region or time period analysed.

For the lagged endogenous model, a significant gap between the 'within' and the OLS estimators is found. Furthermore the GLS estimate fits neatly in between the two for both price and income elasticities.7 The inverted-V lag, M3, gave slightly lower (and more plausible?) price elasticities.8 This model is subject to the same type of bias as discussed above, however. Of particular interest is the polynomial distributed lag model M4, since it has no lagged endogenous variable. M4 was estimated with a Yule-Walker GLS autoregressive procedure (see Gallant and Goebel 1976). This gives lower price elasticities but much higher

❖ Canada data points and regression line

data points and ^^ "iT«""-- ■ regression line A J,

Overall regression line

Figure 4.1 Gasoline prices and consumption, OECD 1960-88

income elasticities. It must be noted, however, that the period used for estimation is much shorter owing to the data required for the lags on price and income.

To sum up all the pooled estimates, very low income elasticities (except in the PDL) and high long-run price elasticities (-1.2 to -1.4) are found. Compared with the cross-section estimates the price (but not income) elasticities seem to concur rather well. Compared with aggregate or mean time-series results, however, the price elasticities are indeed higher but the income elasticities still considerably lower.9

And finally, it should be pointed out that the estimates are considerably higher than those reported by Baltagi and Griffin. This has already been discussed by Sterner (1991) who noted two factors explaining the difference. First, Baltagi and Griffin used gasoline per vehicle as an endogenous variable. As they rightly point out this assumes that the number of vehicles is insensitive to the price of gasoline and thus their price elasticities were correspondingly biased. Second, and more interestingly, in the present study a'moving window' approach was used to show that the pooled estimates were rather sensitive to the exact composition of countries and years included. With longer time periods the price elasticities tended to increase and for some,

Table 4.5 Elasticities for different regions and time periods

LR price elasticity

LR income elasticity

Lag-end

1963-78 OECD

0.98

0.84

LR price elasticity

LR income elasticity

Lag-end

EU

-1.01

0.72

0.87

North Europe

-0.78

0.95

0.78

Scandinavia

-0.93

1.06

0.68

Non-Europe

-1.74

0.91

0.83

1963-85

OECD

-1.35

0.73

0.87

EU

-1.41

0.38

0.89

North Europe

-1.28

0.65

0.84

Scandinavia

-1.08

0.96

0.74

Non-Europe

-2.12

0.58

0.88

Notes: This is a generalized 'moving window' approach allowing regions and time periods to vary. The model is M1 estimated with GLS (Fuller and Battese). Regions are defined as follows: OECD except Iceland, Luxembourg and New Zealand; EU is defined as above except Norway, Sweden, Findland and Switzerland; North Europe is defined as above except Spain, Portugal, Belgium, France, Austria and Italy; Scandinavia is Norway, Sweden, Denmark and Finland; Non-Europe is Canada, United States, Australia, Japan and Turkey.

smaller, samples of countries the price elasticities even increased quite dramatically, as shown in Table 4.5.

CONCLUSIONS

In this chapter the focus has been on the long-run price sensitivity of gasoline demand. By comparing time-series, cross-section and pooled estimators using different models it is hoped that yet another empirical illustration of the systematic sources of differences between the estimators analysed in Chapter 2 has been provided. Although pooled estimators appear to be an attractive way of using all the available information, Pesaran and Smith have shown that pooled estimators with dynamic model specifications give biased values and the modeller thus has to turn to other estimators. The findings in this study are, in this respect, fully in accord with those in Chapter 2. Furthermore it was found, as expected, that cross-sections tend to give higher price elasticities than time series. Moreover, they do so even with simple static models, whereas time-series data require the modeller to use dynamic specifications. And finally, the potential importance of which countries and years are actually included in the data set analysed is discussed.

NOTES

1 Other approaches are discussed in Sterner (1990).

2 The main reason for their exclusion is lack of data on vehicle prices, public transport availability and road infrastructure variables etc.

3 This model can be derived by assuming that desired consumption is G? = c + , + + but that adaptation is partial: — , = s((Tt - G, _,) + Ea Note that this implies that fit=sen+et2.

4 The static model and the models M1 and M2 are the same as in Chapter 2 but models M3 and M4 defined here are not used in Chapter 2.

5 The static model could also be used but, as shown in Chapter 2 or in Sterner (1990), static estimates will be biased if the true model does indeed include some form of lag structure. See also Table 4.4, note c.

6 'Within' is basically an estimator designed to pick up elasticities due to variation within countries. It is estimated as an OLS with country dummies on the intercept (for the lagged endogenous model specification).

7 In a single explanatory variable model the GLS estimator must fall between the OLS and the 'within' estimator but this does not necessarily apply in models with several explanatory factors.

8 Note that nested tests cannot be carried out comparing (4.5) and (4.4) because of the restriction on the parameters of gt-1 and gt-2.

9 Except when compared with the weighted average which, however, as we saw above was very heavily influenced by one single country.

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