Choice of the effect size and reduction to a common metric

The second step of the meta-analytical approach is twofold. First, an effect size measure has to be chosen according to the empirical question examined. Then, the effect size measure considered needs to be reduced to a common metric in order to ensure its comparability across studies. Choosing an appropriate effect size rests on the empirical questions at sake. As explained in the first chapter of

21 This happened mainly for quite old papers, whose authors have left the institutions in which the paper is referenced.

Sometimes, it might also be due to the fact that female authors have changed their surname as a consequence of their marital status.

22 However, this number may vary since some working papers might be published in the future.

this dissertation, the empirical studies on the EKC mainly examined the two following research questions:

• Does the EKC exist, i.e. do we systematically find an inverted U shaped PIR? If not, which pollution income path is found?

• When an EKC exists, what is the value of the income turning point (ITP), i.e. at which income levels do emissions start declining?

In order to address both questions, we construct two effects sizes. The first captures the shape of the pollution-income path found by each observation. The second considers the value of the ITP (when the latter exists).

3.2.1 Shape of the pollution–income path

Figure 1.III in chapter 1 listed the six possible shapes of the pollution-income path emanating from empirical EKCs. From these six possibilities, we constructed 4 categories:

I. The observation confirms the existence of an EKC.

II. The observation does not lead to an EKC but a monotonically decreasing relationship between pollution and income per capita (monotonically decreasing environmental quality).

III. The observation does not lead to an EKC but a monotonically increasing relationship between pollution and income per capita (monotonically increasing environmental quality).

IV. The observation does not lead to an EKC and no other statistically significant relationship is observed (the pollution income path is flat).

In order to ensure a homogeneous categorization of the primary studies, we used two rules. First, we took into consideration only the statistically significant income parameters (10% confidence level).

Secondly, an observation belongs to the first category only if the observed ITP lies inside the income range considered by the study. If the ITP is higher than the maximum income level of the sample, the relationship is considered monotonically increasing (category 3). Identically, if the ITP is lower than the minimum income level of the sample, the relationship is considered monotonically decreasing (category 2). The strict application of these rules allowed to categorize every observation. Figure 2.III indicates the number of observations in each of the four categories.

The following elements deserve attention. First, choosing a 10 % confidence level is subjective and not usual. However, doing so ensures a good consistency with the authors’ primary study conclusions on the EKC. If we had chosen a more restrictive level, several observations would be classified in the fourth category whereas the primary study, even if the non-significance of the parameter is observed, calculates an ITP and seems to conclude to the existence of the EKC (see for example, Grossman and Krueger, 1995).

Furthermore, several observations conclude that the PIR follows a U, an N or an inversed N path. In those cases, we classified these observations by examining where the ITPs are located. In most cases, one of the ITPs lies outside the pertinent income range and the relationship could be put in one of the categories. However, 5 observations (2 from Panayotou, 1997 and 3 from Kaufman et al., 1998) on SO₂ concentrations follow an unambiguous U path. We classified these 5 observations in the

second category since the pollution growth rate appears to be positive on the largest part of the income range examined.

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83

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40

0 20 40 60 80 100 120 140 160

EKC increasing decreasing flat

Fig. 2.III Pollution income path

3.2.2 Income turning point (ITP)

The second effect size measure captures the value of the ITPs. When primary studies did not explicitly compute the ITP, we calculated it by partially differentiating the estimated equation with respect to income, setting the equation to zero and solving. Cavlovic et al. (2000) proceed quite identically.

However, they ignored all higher income terms than the quadratic. We did not take such a shortcut because ignoring higher income terms had a considerable impact on the value of the calculated ITP.

When no income turning point can be calculated, the observation is described as either positive, negative or flat by the first effect size measure.

The ITPs are expressed in 1985 U.S.-$. ITPs were converted to 1985 U.S.-$ using the U.S. GDP deflator²³. As shown in Figure 2.IV²⁴, the estimated ITP vary considerably between a few hundred to millions of dollars. Note that when one looks at the database, it might be confusing to see that an ITP had been calculated whereas the pollution-income path is considered monotonically increasing. This is due to the fact that, even if an ITP can be calculated, the relationship is unambiguously positive when we consider only the pertinent income range. For example, the ITP calculated in Shafik (1994) amounts to $102 millions. As the highest income level considered in this study is around $30'000, the estimated ITP lies well outside the pertinent income range and the relationship is considered monotonically increasing.

23 Source: Economic Report of the President 1993 Table B-3

24 As the ITPs vary considerably across pollutant types, we present the logarithmic transformation of the ITPs and group them according to pollutant categories (these categories are described in section 3.3.3).

The two effects sizes summarize the principal results of the 49 primary studies. However, at this stage, the statistical power of these measures is not taken into consideration. In other words, nothing distinguishes a highly significant result from a poorly significant one. One possible approach used by Cavlovic et al. (2000) consists in estimating the variance of each ITP²⁵. Since ITP are calculated from parameter estimates from econometric studies whose estimated standard errors are available, estimated variances may also be calculated using the Delta method (see Greene, 1997 and appendix 1 for further details). These variances may then be used for weighting observations. However, in order to apply the Delta method properly, one needs to know the covariance between parameter estimates.

This information is usually lacking and this gap prevents us from using the Delta method. Cavlovic et al. (2000) overcome this problem by assuming zero covariance between income parameter estimates.

As pointed out by Plassman and Khanna (2002), the income parameters are usually highly correlated in a polynomial regression and setting covariance to zero will give unreliable estimations²⁶.

5.6058 18.2143

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Fig. 2.IV Income turning point (logarithmic scale) by pollutant categories

25 The majority of studies have not calculated the variance of the ITPs. However, Cole et al. (1997) and Grossman and Krueger (1995) report standard errors for their ITP estimates that are derived from linear approximations of the turning point estimators (Delta method). List and Gallet (1999) mention the use of 95 % confidence intervals around their ITPs, but they neither report them nor do they explain how they constructed these intervals.

26 We thank Florenz Plassman (State University of Birghamton) for helpful and valuable explanations and comments on this issue.

global local resource toxic waste SO2 water

Ln (ITPs)