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Endogeneity and other problems in curvilinear income-waste response function estimations

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Abstract

Socio-ecological theories have long been in search of general principles to characterise anthropogenic activity-environmental change dynamics. Besides allowing for more flexible hypothesis testing, stochastic-extended IPAT and ImPACT baselines opened the door to multiple environmental applications in which solid waste generation took a growing stage. This paper surveys Waste Kuznets Curve’s original foundations and underlines why the nature and shape of the hypothetical curvilinear income-waste response function tend to compare to a “black-box”. It then stresses why diverging conclusions are linked to heterogeneous estimators’ choices differing in their statistical assumptions and powers; whereas generic patterns hardly emerge (e.g., income elasticities of waste generation vary even when the mathematical functional form does not; population elasticities are sensitive to time-varying data and income groups). Next, we identify persisting biases of endogeneity which threaten the internal validity of WKC conclusions, if uncontrolled for (e.g., simultaneity, waste measurement errors and garbage policy confounding effect); along with other identification problems including within-panel heterogeneity with systematic slope variations and cross-sectional and spatially dependent income series. Although we propose a set of theoretically justified instrumental variables to exogenously predict income levels and ensure unbiased elasticities, we also detect and underline that additional threats to external invalidity do play out in practice (e.g., asymmetric geographical coverage and bias of case study selection due to environmental data constraints; missing policy-realm; within-waste heterogeneity hidden by widely aggregated indicators; and a non-systematic treatment of the technological effect). All prevent the waste literature from converging and should be considered by future empirical assessments.

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Fig. 1

Source: our elaboration

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Data availability

Data is available upon request to the authors.

Code availability

Codes are available upon request to the authors.

Notes

  1. Including but not limited to: chlorinated solvents, heavy metals, poly-cyclic aromatic and aromatic hydrocarbons, and vinyl chlorides.

  2. For an more exhaustive discussion on this topic, see Roca (2002).

  3. Recent applications of time-domain and frequency causality methods [e.g., Granger (1966, 1988), Toda and Yamamoto (1995), Dumitrescu and Hurlin (2012) causality tests] on the GDP-MSW nexus can be found in Lee et al. (2016) for the US, Magazzino et al. (2020) for Switzerland, and Mele et al. (2022) for Korea.

  4. Beckerman (1992) outlines the basic EKC philosophy as: “although economic growth usually leads to environmental deterioration in the early stages of the process, in the end, the best and probably the only-way to attain a decent environment in most countries is to become rich” (p.482).

  5. The concept of waste leakages set up here is a direct reference to the more general concept of carbon leakages developed by the environmental and trade economics literature.

  6. See Lieb (2013) for a review of symmetric economic mechanisms explaining the emergence of a turning point in the broader income-atmospheric polluting emissions response function.

  7. See Ben Jebli et al. (2022) for a review of the CKC literature with similar conclusions.

  8. For a wider overview of this topic, we recommend some complementary notes offered in Gomez-Sanabria et al. (2021).

  9. Best Linear Unbiased Estimator.

  10. See Quental et al. (2011) for an excellent review on the relationship between environmental reforms and political cycles. See Lipford and Yandle (2010) for an attempt to bridge traditional frameworks derived from the School of the Public Choice and environmental constraints.

  11. Information related to “Hot spots” which symptom failed attempts from political and industrial organisations in setting-up a waste management trajectories leading to an equilibrium, are ignored by empirical modellers (D’Alisa et al. 2010). For an exhaustive review of waste management practices in spatial settings, we highly recommend D’Amato et al. (2013).

  12. UNEP and the Green Customs Initiative (GCI) underlined that “national and international crime syndicates worldwide earn an estimated US 20–30 billion dollars annually from hazardous waste dumping, smuggling proscribed hazardous materials, and exploiting and trafficking protected natural resources” (http://www.greencustoms.org/background/). In Italy alone, more than 3 million tons of illegal garbage have been seized over the year 2015 (Peluso 2016).

  13. Assuming \(z_{k}\) (where k ranges from 1 to k, the total number of instrumental variables), denote the selected instrumental variables for x, as long as \(z_{1}\), \(z_{2}\),..., \(z_{k}\) are uncorrelated with the error term \(\epsilon\), any linear combination of the exogenous variables is a valid Instrumental variable.

  14. Debt service and age dependency ratio have been extensively used as exogenous predictors to GDP. See for instance Lin and Liscow (2013)

  15. Although the Swamy’s test (Swamy 1970) is efficient for small \(N<T\), Pesaran and Yamagata (2008) offered a test of slope homogeneity for panel setting characterised by large N and T. The null H0 set homogeneous slope coefficients across cross-sectional units, against the alternative H1. This framework presents the advantage of assuming a vector of heterogeneous constants. An updated review of this topic is presented in Breitung and Salish (2021).

  16. This literature often applies the Frees’ and Friedman’s tests of cross sectional independence (Friedman 1937; Frees 1995); the Breusch Pagan LM test of independence (Breusch and Pagan 1980); or the latest Pesaran (2004) Cross-section Dependence (CD) test. An in-depth discussion on their statistical properties, we recommend De Hoyos and Sarafidis (2006).

  17. The United Nations Environmental Program (UNEP, 2018) report on “Single-use plastics: a roadmap for Sustainability” showed that 99% of manufactured products purchased by individuals become garbage over the first five months following their purchase (Ayeleru et al. 2020). Bulk of this MSW happens to be non-biodegradable plastic waste (PW, 300 million tonnes yearly generated worldwide) (Tulashie et al. 2020). Emerging countries concentrate a growing attention from environmental scientists as some of them simultaneously face: a booming waste generation and demography (i); a lack of waste treatment, recycling and waste-to-energy technology transfers (ii); relatively more lenient environmental regulations (iii) which condition an over-reliance over landfills for which there is already a shortage since using land surface for crop competes with other economic purposes such as energy generation, resource extraction and waste land-filling (Jambeck et al. 2018).

  18. This methodological point is discussed in Sects. 5.3 and 5.4.

  19. It is important to mention that very recent papers used astronomical and meteorological seasons to model municipal solid waste disposal rates. General outputs derived from Recurrent Neural Network (RNN) and Long short-term Memory (LSTM) tools showed how seasonality contributes to predict MSW generation rates (larger in summer than winter). For an exhaustive review of this topic, see Adusei et al. (2022).

  20. Indeed, using lagged-transformations on linearly extrapolated series would offer outputs that are rather determined by the assumptions laying under the extrapolation technique than the policy information itself.

  21. It is important to mention that there exists an incipient literature assessing the contribution of knowledge capital accumulation on nudged consumer behaviours towards reduced-packaged products or waste nature offering larger value extraction potentials post-consumption. For a macro-level application, see Halkos and Petrou (2020); for a stratified analysis, see Secondi et al. (2015)

  22. The question on how to capture technological dynamics has been subject to intense debates in the more general economic theory literature. Over time, scholars agreed that its nature goes beyond a simple exogenous residu (Solow 1999; Weitzman 1996).

Abbreviations

2SLS:

2-Stage-least-square

ANNs:

Artificial neural networks experiments

BCS-GC:

Breitung-Candelon Spectral Granger-causality

BLUE:

Best linear unbiased estimator

CA:

Cointegration analysis

CCEMG:

Common correlated effects mean group

CEV:

Classical errors-in-variables

CKC:

Carbon Kuznets curve

COE:

Cochrane-Orcutt estimation

D2C:

Causal direction from dependency algorithm

DiD:

Difference-in-differences methodology

DOLS:

Dynamic ordinary least squares

DTM:

Decision tree model

DTPR:

Dynamic threshold panel regression

ECT:

Error correction term

EE:

Ecological elasticities

EEO:

Energy-emissions-output

E-WKC:

Electronic waste Kuznets curve

FF:

Functional form

FGLS:

Fully generalized least squares

FMOLS:

Fully modified ordinary least squares

GAMMs:

Generalized additive mixed models

GGM:

Generalized gamma model

GLS:

Generalized least squares

GMM:

Generalized method of moments

GTWR:

Geographical and temporal weighted regression

GWR:

Geographically weighted regression

IV:

Instrumental variable

MLM:

Maximum likelihood model

MSW:

Municipal solid waste

OLS:

Ordinary least squares

Panel FE:

Panel fixed effects

Panel RE:

Panel random effects

PCA:

Principal component analysis

P-W:

Prais-Winsten method

QMS:

Quadratic Match-Sum method

STIRPAT:

Stochastic impact by regression on population, affluence and technology

TSCS:

Time-series cross-section

UNEP:

United Nations Environmental Program

VAR:

Vector auto-regressive model

WEEE:

Waste electrical and electronic equipment

WKC:

Waste Kuznets curve

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    Nicolas Schneider

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Schneider, N. Endogeneity and other problems in curvilinear income-waste response function estimations. Stoch Environ Res Risk Assess 38, 357–382 (2024). https://doi.org/10.1007/s00477-023-02598-8

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