Identifying reduced-form relations with panel data: The case of pollution and income

Abstract

In this paper we propose a solution to the non-robustness that plagues the estimation of inverted U-shaped relationships using panel data, such as the relation between pollution and income. When dependent and independent variable (like pollution and income) are both time related, separating the effect of the independent variable from time effects brings about a fundamental identification dilemma: the imposition of restrictions on the controls might drive the shape of the relationship between the dependent (pollution) and independent (income) variables. Our solution consists of imposing the very weak constraint that arbitrary cross-sectional units have the same relationship. We apply our methodology to two widely studied cases, namely, ${\mathrm{SO}}_2$ and ${\mathrm{CO}}_2$ emissions. Interestingly, our estimates are insensitive to the required subjective choices, but also strongly differ from the literature so far. We find consistent positive income effects for both cases and time effect estimates with a clear U-shaped trend for ${\mathrm{SO}}_2$-emissions but only slightly so for ${\mathrm{CO}}_2$-emissions.

Introduction

The literature on the inverted U-shaped relationship between economic growth and the environment, the so-called environmental Kuznets curve (EKC), has come to a dead end. The main reason is that the empirical literature has produced fundamentally different patterns even for the same type of emissions. For example, in the literature on the EKC for ${\mathrm{CO}}_2$, parametric and non-parametric techniques—applied even to the same data set—yield very different outcomes. For instance, a spline-based approach found a so-called within-sample turning point (TP) implying that ${\mathrm{CO}}_2$-emissions are already declining for currently existing highest income countries [26], while non-parametric panel data estimations report the non-existence of an inverted U shape [3]. Similar observations apply to other attempts to estimate income–emission relationships, such as those for ${\mathrm{SO}}_2$. Clearly, this is an unsatisfying state of affairs that fuels distrust in the econometric approach as well as in the underlying intuition [8], [29]. Scientists and policy makers alike are left with the idea that we still know little about the long run relationship between economic growth and the environment.

A fundamental, though seldom questioned, point of departure of this literature is the assumed identification of the inverted U relationship between economic growth and the environment. Although [7] explicitly point at the potential importance of the specification of the time effect in their reduced form approach, they focus on the role of the income variable. The subsequent theoretical and empirical literature has also entirely focused on an inverted U relationship between emissions as the dependent and income as the independent variable, implicitly assuming that this relationship is identified. However, separating the correlation between pollution and income from the correlation between pollution and the passage of time can be difficult because income is correlated with time. Indeed, because pollution and income are both time related, separating income from time effects in a panel framework brings about a fundamental identification dilemma as to how much flexibility one should allow in these time effects. For instance, in traditional parametric approaches inference is based on imposing rather restrictive assumptions, like a typical homogeneous time effect, or on the imposition of a second or third degree polynomial. It would be unfortunate if the imposition of such identifying assumptions on the controls affects the estimation results, such as acceptance or rejection of the existence of the postulated reduced-form relationship. But, this is precisely the problem that hinders estimation in the type of reduced-form models studied in this paper, causing the non-robustness. That different a priori restrictive choices are likely to result in different inferences raises the potential for inferences to become subjectively based, instead of data driven. Accordingly, different ex ante subjective choices of flexibility might explain the sometimes widely divergent empirical findings based on the same data.¹

In this paper we argue that the essential step forward to proper estimation of an EKC is to make the identification requirement explicit, to impose the bare minimum requirement on the income/time relationship in a panel, and to investigate robustness properties of different possible, but equally plausible requirements. Given the assumption that the effects of the income-related effect can be separated from the time effect, we study the minimum requirement that each country has the same time effect as at least one other country. Thus we allow for full flexibility in this common time effect as well as for full flexibility and heterogeneity in the income variable. We apply this methodology to two widely studied emissions: ${\mathrm{SO}}_2$ and ${\mathrm{CO}}_2$ emissions. The different identifications provide robust reduced form estimates for both cases and also match basic intuition. Our estimations provide consistent positive results for the income variable, and therefore suggest that higher income drives emissions upward. However, we also produce plausible estimates of the time effect—which captures unobserved heterogeneity across countries correlated with pollution—with a clear U-shaped trend for ${\mathrm{SO}}_2$-emissions but only slightly so for ${\mathrm{CO}}_2$-emissions. Together, these effects provide overwhelming evidence for an inverted U for ${\mathrm{SO}}_2$-emissions, but not for ${\mathrm{CO}}_2$-emissions. Accordingly, our results both corroborate theoretical models that explicitly distinguish between scale, composition, and technique effects [5], and re-establish the empirical search for inverted U relationships on solid grounds.