Stochastic Analysis and Forecasts of the Patterns of Speed

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Stochastic Analysis and Forecasts of the Patterns of Speed, Acceleration, and Levels of Material Stock Accumulation in Society Tomer Fishman, Heinz Schandl, and Hiroki Tanikawa Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b05790 • Publication Date (Web): 29 Feb 2016 Downloaded from http://pubs.acs.org on March 3, 2016

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Environmental Science & Technology

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Stochastic Analysis and Forecasts of the Patterns of

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Speed, Acceleration, and Levels of Material Stock

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Accumulation in Society

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Tomer Fishman a *, Heinz Schandl a, b, and Hiroki Tanikawa a

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a

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ku, Nagoya, 464-8601 Japan.

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Nagoya University, Graduate School of Environmental Studies, D2-1(510) Furo-cho, Chikusa-

b

Commonwealth Scientific and Industrial Research Organisation (CSIRO), Black Mountain

Laboratories, Clunies Ross Street, Acton, 2601 ACT, Australia.

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Corresponding Author

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* Tomer Fishman, Nagoya University, Graduate School of Environmental Studies, D2 1(510)

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Furo-cho, Chikusa-ku, Nagoya, 464-8601 Japan. Telephone +81-52-789-3840. Email

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[email protected]

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Keywords: Industrial ecology, material stock, stochastic modeling, uncertainty analysis,

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sustainable materials management.

ACS Paragon Plus Environment

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ABSTRACT

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The recent acceleration of urbanization and industrialization of many parts of the developing

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world, most notably in Asia, has resulted in a fast-increasing demand for and accumulation of

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construction materials in society. Despite the importance of physical stocks in society, the

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empirical assessment of total material stock of buildings and infrastructure and reasons for its

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growth have been underexplored in the sustainability literature. We propose an innovative

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approach for explaining material stock dynamics in society and create a country typology for

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stock accumulation trajectories using the ARIMA (Autoregressive Integrated Moving Average)

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methodology, a stochastic approach commonly used in business studies and economics to inspect

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and forecast time series. This enables us to create scenarios for future demand and accumulation

27

of building materials in society, including uncertainty estimates. We find that the so-far

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overlooked aspect of acceleration trends of material stock accumulation holds the key to

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explaining material stock growth, and that despite tremendous variability in country

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characteristics, stock accumulation is limited to only four archetypal growth patterns. The ability

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of nations to change their pattern will be a determining factor for global sustainability.

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1. Introduction

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Interest in quantifying and analyzing societal material consumption has been rising recently

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under terms such as socio-economic metabolism 1 and circular economy 2–4, and plays a central

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role in ecological economics debates and steady-state economic theories 5. Construction

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materials in buildings and infrastructure, including minerals such as cement, gravel, sand, and

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asphalt, as well as timber and metals such as iron and copper, are durable and immobile, and

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remain in society as in-use stocks for decades. The efficient usage of this material stock to

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provide services to society is thus key to sustainability: long-lifespan stock reduces future raw

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material consumption

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energy efficient stock requires less fossil fuel consumption 11,12, and so forth. On the other hand,

43

infrastructure and buildings that don’t satisfy society’s needs cause further demand for

44

replacement and expansion.

6,7

, high quality stock requires less refurbishment over its lifetime

8–10

,

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Construction materials, especially non-metallic minerals for construction, are high volume,

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low value and low environmental impact per unit of use, and have relatively high recyclability.

47

However, the sheer amount of construction minerals excavated globally is huge and fast

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growing, responsible for about 40% of the yearly global consumption of raw materials

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has very low yearly consumption-to-waste ratios even in developed economies

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the net balance of in-use stock is positive: construction material stocks are growing 16. Globally,

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almost 600 Gt (billion tonnes) of construction minerals were added to physical stocks of

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buildings and transport infrastructure between 1970 and 2010 and we forecast an additional

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inflow of over 800 Gt over the next two decades (2010 to 2030) with a high level of certainty.

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The accumulated environmental effects are formidable, including rapid land use change through

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urbanization, excavation, and demolition waste sites, and high energy and emissions related to

14,15

13

, and

, and as such


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the extraction, transport and manufacturing of these materials, especially cement and bricks.

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Construction minerals are considered less important in the analysis of economic demand for

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materials when compared to fossil fuels (energy) and metals, and yet they exemplify best that

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materials form the physical basis of society and that rising per-capita use of materials and

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increasing use of mineral materials are fundamental to modernity.

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National material flow accounts (MFA) include extraction and trade of construction materials 17–21

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and show that the flows have been steadily increasing

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analysis of national values of construction material use per-capita and per unit of economic

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output (material efficiency)

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these metabolic profiles fail to capture the quantitative and qualitative states of the existing

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material stock and its influence on further consumption and stock accumulation. On the other

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hand, more and more stock accounts are being published at various scales and using various

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accounting methods

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uses, and their locations

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accumulation 27.

25

22–24

. MFA also provides comparative

over time. However, by focusing solely on material throughput

, improving our understanding of the types of materials used, their end 7,25,26

as well as identifying the socio-economic drivers of stock

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Linking material throughput to stocks, various models have been put forward aiming to model

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historical and future in-use stocks of construction materials. These include fitting to s-shaped

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curves whose equations are constructed to approach a fixed upper limit designated as the

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eventual level of saturation

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and outflow trends

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projections of social indicators such as population growth and affluence trends

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models have two traits in common: (1) they are deterministic, using predetermined variable

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values and pre-set scenarios for their initial state and therefore produce non-random outcomes;

10,16,30

28,29

, dynamic forecasts based on scenarios of pre-set future inflow

, and dynamic forecast models linking the growth of stocks to existing 6,31,32

. All these


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and (2) they have a substantial reliance on model variables from exogenous processes, i.e. data

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other than the endogenous material stock statistics. These deterministic model – exogenous

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process approaches have some inherent limitations:

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•

83 84

Exogenous variables are subject to their own uncertainties which permeate into material stock projections;

•

Results are influenced by choices in the selection of variables and definition of their

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relations, and misidentifications or omissions of variables or relations may occur. For

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example, some factors which can be expected to have a direct influence on the amount of

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stocked construction material, such as geography and distances, have yet to be taken into

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account;

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•

Relations with exogenous processes must be definable mathematically. This is especially

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challenging with qualitative factors such as cultural preferences, fashions, or political

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decisions;

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•

Uncertainty analysis of deterministic models, such as sensitivity analysis, is limited and

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even methods like Monte Carlo simulations require initial decisions by the user, which limit

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the possible range of outputs;

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•

The focus on external variables overlooks the endogenous effects of the existing stock on its own future state.

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In light of these limitations, in this study we undertake a different approach. Rather than

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explain and forecast material stock accumulation trends through exogenous variables, we exploit

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the time-related characteristics of historical material stock accumulation as a sole endogenous


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variable and stochastically analyze its trends. This approach relies on what the historical

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accumulation of material stock can tell about future growth patterns, making no presumptions

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about drivers, assumed growth patterns, saturation levels, or any other exogenous variables. The

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analysis provides a deeper understanding of historical growth patterns and a stochastic-

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endogenous method to extend the time series into the future, which can be used as business-as-

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usual or baseline forecasts. We first employ this approach for two case studies, Japan and the

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United States, for the period of 1950–2010 and forecast until 2030. In a second step we extend

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the analysis to a further 43 countries and the entire world for 1970–2030 with the aim of finding

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common growth patterns.

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2. Methodology

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2.1. Framework: level, speed, and acceleration

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The analysis revolves around the examination of the amount, or level, of material stocked in

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society through observation of its speed and acceleration of accumulation. The three terms of

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level, speed, and acceleration of material stock have been used, somewhat casually and

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sometimes interchangeably, in the material flow and stock literature to describe flow patterns and

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the evolution of material stock. We formalize the usage of these terms by adopting their

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established meanings in classical mechanics as the differentials and integrations of each other:

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the change, or differential, in the level of material stock over time is the speed; acceleration is the

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differential of speed. In the opposite direction, integration of acceleration over consecutive

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periods up to a point in time provides the value of speed at that point, and the same for speed and

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levels.


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The processes of accumulation of material stock at the national and global scale are virtually

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continuous, occurring constantly through the day-to-day construction of buildings and

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infrastructure projects. For practical accounting of material flows and stocks a standard of

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totaling yearly material flows and stocks has been established

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of differentials and integrations, i.e. differences and summations, are used throughout our

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analysis. Table 1 details the relations of the three orders of differences and summations used in

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this study, and Figure 1 graphically exemplifies the relations of levels and speeds (which are the

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same relations for speed and acceleration).

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Figure 1. Graphical representation of the mathematical relations of the level of material stock

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(MS, top panel) and the speed of accumulation of that stock (NAS, net addition to stock, bottom

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panel).

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and so the discrete equivalents


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Table 1. The mathematical relations of level, speed, and acceleration of material stocks.

Name

Main notation

Level of material stock

Speed of material stock accumulation

∆

Acceleration of material stock accumulation

∆

Alternative notations

Description

Unit

Total societal material stocks at year t

Mass (tonnes) 1 ∑

The change in material stock between two consecutive years

Mass per year

The change in speed between two consecutive years, or the second order of difference of the level of material stock

Mass per year, per year

2 + ∑

(t/y)

Notes Alternative notation 1 may be hypothetical in the vast majority of material stock cases, as data for a “year zero” are unobtainable for most practical cases. In the second alternative notation τ is a base year with a certain level of existing material stock and ∑ is the sum of all net additions from base year τ to year t. NAS is the Net Addition to Stock, also equivalent to inflows minus outflows in year t 33.

∆

(t/y2)

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2.2. Stochastic analysis using ARIMA

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We analyze level, speed, and acceleration simultaneously using the ARIMA (Autoregressive

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Integrated Moving Average) methodology, commonly used in business and economics analysis

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to inspect and forecast time series 34. This stochastic method to analyze the endogenous effects of

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previous periods on the current period is explained in detail in the supporting information. A

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central notion of the ARIMA method is the requirement to employ it on a stationary time series,

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i.e. on data whose mean and variance are time-independent. In cases of non-stationarity,

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sufficient orders of differencing are applied to achieve a stationary time series

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statistical analysis and forecasts are conducted on the differenced stationary series and the

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results, including the associated uncertainties, are re-integrated into the original series. This trait

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of ARIMA is beneficial to our aims since these differentiation and integration mechanics of the

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ARIMA method fit well with the framework of level, speed, and acceleration described above. In

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practice this means that once a stationary series is identified, for example the series of

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acceleration, the resulting model, coefficients, and uncertainties can be re-integrated to the two

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other series of speed and levels, which provides the manifestation of the same model on all three

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series at once.

34,35

. The

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Furthermore, the ARIMA time series analysis distinguishes between intrinsic growth trends

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and exogenous shocks. In the case of material stock growth, trends may be driven by any of a

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wide range of conceivable processes such as population growth, economic growth, and

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government policy. Shocks may also manifest in a multitude of ways: economic surges or

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downturns, international crises, political decisions, changes in technology and design standards,

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changes in prices, or any other reason. The advantage of the framework is the ability to form

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forecasts of time series data without detailing the effects of exogenous processes, as it does not


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require clear identification of the causes of such trends and shocks. Forecasts are stochastic,

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endogenous one-period-ahead and based only on the intrinsic trends and influence of the lagged

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terms found by the ARIMA analysis, which together with historical variance and historical

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response to shocks contribute to the model’s forecast uncertainty ranges.

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The ARIMA model has some assumptions and limitations. As with other stochastic methods

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such as Ordinary Least Squares (OLS) regressions, results are only as good as the data on which

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they are based and may change with the addition or alteration of data. Specifically, since the

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explanatory variables are the time series’ own lagged values, not only the coefficients but also

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the number and type of variables may change with new data. This is further corroborated by the

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mathematical equivalency of Autoregressive and Moving Average terms in some cases, which

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may make model selection ambiguous. We minimize these issues by adhering to best-practice

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methods and rigorous statistical testing during model selection. Comparisons of the ARIMA

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forecasts to previously published deterministic forecasts and historical statistics (detailed in the

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supporting information) have validated the viability of the method.

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2.3. Data and analysis procedures

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The analysis is conducted on the trends of accumulation of construction minerals. We use the

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aggregate of all non-metallic minerals for construction, including cement, gravel, aggregate,

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sand, and bitumen, which is referred to simply as material stock for the rest of this article unless

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otherwise stated. Data for material stock levels, in tonnes, of the construction minerals in Japan

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and the United States are based on previous research that established historical material stock

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accumulation for the United States and Japan from the post-war era until 2005

16

and which we


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extended to 2010 using newly available data from the United Nations Environment Programme

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(UNEP) International Resource Panel

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material consumption (DMC) for 233 countries and territories and for the world, which in the

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case of construction minerals can be regarded as yearly gross additions to stock, and which was

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found to closely approximate the yearly speed of accumulation. Forty-nine countries having

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populations of over 10 million in 1970

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Ukraine, Uzbekistan and Kazakhstan were omitted because of a lack of country-level material

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statistics before the dissolution of the Soviet Union. The analysis was conducted for the

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remaining 45 countries which together account for about 80% of the global population, and for

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the world. For each country and the world an ARIMA model was selected and fitted using the

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Box-Jenkins approach with the R statistics package (see the supporting information and

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references

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stationarity, the inclusion or lack of a constant, the type (autoregressive or moving average) and

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number of lag terms along with their coefficients and statistical confidence, and related statistics

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which together produce the forecasts. The country models were then investigated individually

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and for commonalities among countries.

35,38

36

. This source provides data for the yearly domestic

37

were selected for the analysis and of these, Russia,

for details). Country models include the number of orders of difference to reach

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3. Results

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3.1 Simultaneous analysis of Levels, Speed, and Acceleration for Japan and the USA

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The availability of long-term material stock statistics enables demonstration of the framework

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for the analysis of the level, speed, and acceleration of stock accumulation of the United States

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and Japan (Figure 2). In both cases lagged variables, either autoregressive terms or moving-

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average terms, were statistically found to have a correlation with those of the following periods.


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This indicates that past material stock trends can be used to forecast future trends. The details of

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these variables, along with their coefficients, are specified in the supporting information.

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Figure 2. The accumulation of construction material stock in the USA (left) and Japan (right),

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1950–2030, with forecast intervals of 80% and 95%. Top panels: total stock levels. Middle

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panels: speed of accumulation (also termed the net addition to stock). Bottom panels:

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acceleration of accumulation speed.

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The level of construction material stock of the United States in 1950 was about 19 Gt 16 and by

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2010 it had reached about 114 Gt. The time series for accumulated material stock (Figure 2, top

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panel), suggests smooth linear growth, however the middle panel reveals that material stock

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growth was in fact achieved through fluctuating yearly additions – the United States experienced

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long periods of gradually increasing accumulation speed interrupted by temporary slowdowns,

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and growth speeds recovered on each occasion after only a few years. Although these trends

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visually appear somewhat cyclical, they do not follow a predictable periodic pattern. Slowdown


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occurred in the 1970s, the early 1980s, and again in 2008–09, years which marked important

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global economic events. This can best be seen in the acceleration time series (bottom panel): in

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the 60 years examined, the United States experienced mostly positive acceleration. Years of

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positive acceleration were usually followed by similar trends, but occasionally external shocks

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occurred with strong negative acceleration “dips” (i.e. deceleration), coinciding with economic

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downturn events. The acceleration series seems to be following a long-term trend of reversion to

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a mean, and these shock-induced dips behave somewhat as regulators that keep the mean level of

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acceleration at or just slightly above zero. The acceleration time series, the 2nd order of

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difference, was found to be stationary and therefore the forecasts are generated at this order of

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differencing, under the modeling assumption that this series will again revert to its mean. The

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manifestation of this reversion in terms of speed is that the slowdown following the recent crisis

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will again be short and speed would stabilize at about 1.4 Gt per year, culminating in a level of

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143 Gt of material stock by 2030. The low, slowly diverging uncertainties of the stationary

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acceleration series are re-integrated to produce uncertainty ranges for speed and levels, which

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result in a relatively low uncertainty range of 128 Gt to 157 Gt at the 95% confidence level in

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2030. The United States hence presents an example of an advanced and wealthy economy that

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has not slowed its demand for physical stock accumulation at any time over the past four decades

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and will see further growth occurring until 2030.

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The historical evolution of construction material stock in Japan has followed a remarkably

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different pattern. Starting from a low level of about 1.4 Gt in the years after World War II,

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material stocks have increased to 38 Gt by 2010. Speed has been positive throughout the

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historical time period, explaining the ongoing accumulation of in-use stock levels. However, the

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historical speed profile shows three distinct phases: accumulation picked up speed until the


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beginning of the 1970s, followed by a regulated and more or less constant speed until the 1990s.

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Since then there has been a continuous slowdown, and the speed of accumulation in 2010

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decreased to its 1960 rate. Unlike the case of the United States, the trend of acceleration has not

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been stationary. It was positive and growing until the early 1970s, then fluctuated around a near-

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zero mean for the next two decades, and most years since the early 1990s have experienced

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negative acceleration, i.e. a clear deceleration of stock growth. The length of each period varies,

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and the change from one acceleration episode to the next coincided with external shocks – the

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oil crises in the 1970s and the burst of the Japanese economic bubble in the 1990s. Since the

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acceleration time series of Japan is time-dependent and does not revert to a global mean, a third

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order of differencing was conducted and found to be stationary, as required for ARIMA

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modeling for this country (the supporting information provides a visualization of this 3rd order

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of difference). The forecast for Japan is therefore not based on an overarching long-term

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acceleration trend as in the United States but instead Japan’s model extends the most recent trend

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into the future for the length of our forecast horizon, since the timing of any random future shock

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and its influence on the acceleration trend cannot be predicted by the model. The erratic

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historical year-on-year behavior, unpredictability of the response to external shocks, and re-

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integration of three orders of difference manifest as wide and rapidly diverging uncertainty

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ranges in all three series. This is illustrated most interestingly in the top confidence bands of the

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levels series which even at the 80% confidence level show a possibility of a return to stock

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growth. The point forecasts suggest that material stock levels will peak at nearly 40 Gt around

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the year 2020 before the accumulation speed drops below zero, i.e. negative yearly net additions

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to stock – a dematerialization.

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3.2 International comparisons and material accumulation profiles

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Models and forecasts until 2030 were produced for the stock accumulation of a further 43

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countries and the World. Japan and the United States are the only two countries for which

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historical data for accumulated material stock levels exist. For the 43 additional countries the

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data analyzed is the yearly speed of consumption since 1970. The drawback is that without data

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for the base level of stock in 1970 ( ) only total accumulated additions to stock in the years

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since 1970 (∑ ) can be calculated. The emphasis in this section is on the common

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traits found between countries. Individual country results can be found in the supporting

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information.

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No conspicuous similarities were found among the different country models’ lagged terms, but

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the order of difference at which the time series is stationary was found to be a meaningful

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criterion for the grouping of countries. Each of the 45 examined nations (including Japan and the

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USA) and the world can be classified as one of only four stock accumulation profiles based

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solely on the pattern and stationarity (or lack of stationarity) of their acceleration time series.

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These profiles can be viewed as idealized growth paths which countries follow, and so can be

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considered to be archetypal material stock accumulation profiles:

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(I)

Countries whose acceleration is stationary around zero, i.e. exhibit no acceleration, and

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thus their speed of stock accumulation is stationary and levels approximate linear

280

growth;

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(II)

Countries whose acceleration is stationary with a positive value, and as such their speed

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increases at a fixed rate per year (linear increases), and the growth of the levels of stock

283

is increasing from one period to the next in a parabolic shape;


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(III)

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Countries with non-stationary speed or acceleration, and the acceleration has a general

285

increasing trend throughout time, resulting in increasing speeds and more pronounced

286

increases of levels compared to category II.

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(IV)

Countries with non-stationary speed or acceleration, and the acceleration exhibits

288

varying phases, including negative acceleration phases (deceleration). These varying

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acceleration phases manifest as periods of increasing, stable, and decreasing speeds,

290

which may culminate in s-shaped stock level patterns.

291

These profiles also help to describe how countries essentially respond to external shocks to

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their material accumulation trends, with the specific response also determined by each individual

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country’s own lag terms. The four growth profiles are presented in Figure 3 together with the

294

allocation of the analyzed countries into each group.


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Figure 3. The four growth pattern archetypes as they appear on the time series of three orders of

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level, speed, and acceleration, and the countries found to exhibit these patterns. The conceptual

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patterns (dashed lines) are superimposed on patterns derived from exemplary cases from each

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category (solid lines) to demonstrate how real historical data may deviate from the ideal

300

archetypal pattern. The countries from which the patterns are derived are marked in bold letters.

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Countries in italics exhibit unique patterns within their groups, refer to the main text for details.

302 303

The first group includes a single country, the Netherlands. Its historical speed of stock

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accumulation appears to undergo aperiodic cycles around a mean of about 44 million tonnes of


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additional stock per year, which culminated in a total increase to stock of over 1.8 Gt in the last

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40 years, equivalent to the area below the speed trend in Figure 4, panel I. The model found an

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autoregressive relation between past years and the current time period, and based on this and the

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stationary trend, the forecast is of a slow reversion to the mean of the historical series, resulting

309

in a further addition of almost a billion tonnes to stocked construction material in the next 20

310

years. The confidence interval bands are wide due to historical fluctuations, and grow due to the

311

accumulation of uncertainties from year to year in this one-period-ahead forecast. Given the

312

Netherlands’ characteristics as a wealthy, mature economy, with very low population growth and

313

already quite dense infrastructure, it may well be that inflows are used merely to maintain

314

existing stock especially considering the very low amounts of materials used yearly. The

315

Netherlands may be representative of other smaller or less populated European Union countries

316

with similar profiles. This is corroborated by recent findings on construction mineral usage

317

trends in the EU25 in other studies 10.

318

Unlike the first group, the speed of material stock accumulation of the countries in the second

319

group grows over time. Common to these 20 countries is that their rates of acceleration revert to

320

a mean with a positive value independent of time. This constant and positive acceleration means

321

that material stock accumulation picks up speed year-on-year at a linear rate, forecast to continue

322

into the future with confidence bands characterized by sideways-parabolic shapes. Figure 4

323

shows two examples from this category. Turkey’s addition to its stock in 1970 was about 75

324

million tonnes but accelerated at an average yearly rate of additional 8.5 million tonnes, and by

325

2010 growth had sped up to more than 400 million tonnes per year totaling to an increase of over

326

8 Gt in 40 years. If these rates continue as the model forecast suggests, the speed of growth will


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reach over 580 million tonnes per year in 2030, an addition of a further 10 Gt of stock (Figure 4,

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panel IIa).

329

Except for the United States, the countries of this category respond to shocks – either sudden

330

drops or surges – by rapid reversion to their previous trends of acceleration. In effect, this means

331

that external shocks have only a minor effect on the long-term accumulation of material stocks in

332

these countries. They seem to be locked into a particular growth trend. However, these countries

333

differ by the nature of the shocks they have experienced. Some, like Turkey and notably many

334

Latin American countries (Argentina, Colombia, Mexico and Venezuela), were mostly subjected

335

to intermittent drops in their otherwise constant increase of speed, showing resilience to

336

economic downturns and other shocks which hints that there is ongoing demand for further stock

337

increases and that the socio-economic structure of these countries can withstand temporary

338

setbacks. This observation may also relate to policy settings that have enabled anticyclical

339

investment into construction activities to counterbalance years with slow economic growth. In

340

sharp contrast, some countries had undergone “shocks” of short surges of positive acceleration,

341

after which they resumed their linear trend. The case of Thailand in Figure 4, panel IIb is one

342

such example which had two surge periods, in the 1990s and again in the early 2000s. Some

343

other Southeast Asian countries (the Philippines and Malaysia) exhibit similar patterns, as well

344

as European late developers Spain and Romania, whose recent growth spurts and plunges are

345

remarkable in their scale and rapidity. It would seem that all these countries attempted to hasten

346

their growth but could not withstand long-term stresses and eventually were pulled back to their

347

previous slow linear growth trends. Other countries like Indonesia, Nigeria, and South Africa

348

have experienced a mix of both positive and negative surges since the 1970s, and in any case

349

rapidly returned to their intrinsic growth trends.


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350

The United States is unique in this category, as even though it has a stationary acceleration

351

trend which places it in this group, its response mechanism to external shocks is quite different

352

from the previously described ones – it does not quickly return to pre-shock speeds, but instead

353

slowly starts to increase its speed of accumulation from the new minimum. We interpret this to

354

mean that the socio-economic structure of the United States causes its stock growth pattern to be

355

characterized by cycles of slow growth that overshoot actual demand and culminate in external

356

shocks that pull growth rates down to undersupplied levels. One reason for this may be the role

357

the housing sector plays in the United States in bolstering domestic demand in years where

358

growth driven by export industries has slumped.

359

The third group and fourth group include those countries for which, like Japan, acceleration

360

was not stable or mean-reverting throughout 1970 to 2010. They thus all share several

361

characteristics: as there is no overarching global mean acceleration trend to which they revert,

362

their forecasts are based on trends from recent years and their uncertainty levels rapidly expand

363

with funnel-shaped confidence bands. However the two groups’ trends are remarkably different.

364

The third group includes 15 developing economies whose material stock accumulation has been

365

accelerating year on year. Unlike the countries in category II, which follow a steady acceleration

366

trend that causes a linear increase in speed, here speed is increasing faster and faster due to

367

acceleration surging from one year to the next. China is the most pronounced example (Figure 4,

368

panel III a). In the 1970s, its range of acceleration was in the magnitude of tens of thousands of

369

tonnes/y2. By the 1980s it grew to hundreds of millions t/y2 and most years since 2003 have had

370

acceleration of over a billion t/y2. This surging acceleration is apparent in the total accumulated

371

stock. From 1970 to 2010 China increased its construction mineral stock by over 146 Gt, of

372

which over 50% was added in the last few years, from 2004 to 2010. The 14.5 Gt added to the


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373

stock in 2010 are equivalent to the total addition to stock from 1970 to 1988. Although not as

374

massive as in China’s case, the rest of the countries in this group all experienced similar surging

375

growth, and their forecasts are therefore for further acceleration. However, the forecast profiles

376

of these countries differ in their unique uncertainties. Like China, some countries had more

377

assured acceleration resulting in narrower levels of uncertainty, but others such as Brazil (Figure

378

4, panel III b) experienced more setbacks in their recent growth, manifesting as higher

379

uncertainties in their forecasts and therefore wider and more divergent confidence bands.

380

The fourth group is made up of countries whose recent trends, and thus their forecasts, are of

381

steady speed or deceleration. It includes Japan and seven other advanced economies plus North

382

Korea. The advanced economies all underwent phases of acceleration, stable speed, and

383

deceleration in recent years as visualized in Figure 3, which culminate in s-shaped growth

384

patterns for the levels of material stocks. Nevertheless, they vary in the timing, length, and

385

strength of each of these phases, and in some cases entire phases were skipped. For instance,

386

Germany (Figure 4, panel IV) had a prolonged acceleration phase that came to an abrupt end in

387

the mid-1990s and has been decelerating since then, never going through a stable speed of

388

material stock accumulation in this 40-year period. Japan and Italy are both forecast to enter a

389

period of dematerialization before 2030, but even the other four advanced economies’ 95%

390

confidence intervals mark some probability of negative speeds by 2030. North Korea, whose

391

material consumption and economic history are markedly different than advanced economies,

392

also belongs to this group for having varying phases of acceleration, although its case is of

393

acceleration-deceleration-stabilization giving rise to a somewhat different speed profile.


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394 395

Figure 4. The speed of accumulation of material stock, 1970–2030 with forecast intervals of

396

80% and 95%, in (I) The Netherlands, (II a) Turkey, (II b) Thailand, (III a) China, (III b) Brazil,

397

(IV) Germany. Note the different vertical scales by country.

398 399

4. Discussion

400

Methodologically, this study introduces two additions to the material stock discourse: the

401

concepts of speed and acceleration, the latter analyzed for the first time; and stochastic time-

402

series analysis to robustly analyze material stock trends and produce forecasts. The analysis was

403

conducted using the total material consumption and stock accumulation of nations, different

404

from per-capita or per-unit of GDP rates which, while useful for cross-country comparisons, may

405

hide the total environmental burden of material stock and which also inherently assume a certain

406

relation to the population at a designated year, hiding any lagged effects. The ARIMA approach

407

was found to be viable for producing forecasts of material stock accumulation using only

408

historical trend data and requiring no assumptions or exogenous variables – a great advantage


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409

over other methods – and can thus serve researchers and decision makers as a baseline or

410

business-as-usual case to compare against other scenarios that describe policy alternatives.

411

Regardless of the stochastic time-series process that underlies each country’s model,

412

uncertainties naturally increase the further the model is extended into the future. Because of this,

413

it would be advisable for policy formulation to focus on the earlier years of the forecasts and to

414

augment the historical time series as new data becomes available, which would improve the

415

precision of the method. The analysis of the behavior of acceleration with the ARIMA method,

416

through which the four archetypal growth profiles were identified, offers a new understanding of

417

how countries may succeed or fail in attempts to bolster their material input, such as in the case

418

of category III countries which manage to sustain constant increases to their yearly consumption

419

and stocking rates compared to category II countries which do not. It also shows how different

420

countries’ accumulation reacted historically to external shocks, which can inform policy around

421

the economics and environmental effects of the construction sector.

422

It is remarkable that only four archetypal profiles of material accumulation pathways were

423

found despite the huge diversity of socio-economic and geographical properties and size of the

424

examined countries. Many other acceleration profiles may be thought of, such as stationary

425

negative acceleration or speeds, but no such cases were found in this study. Previous research 23

426

divided countries into a hierarchy of developing/emerging/industrialized groups at two points in

427

time separated by 25 years. In comparison, the groupings presented here identify common

428

pathways of material accumulation through time, leading to different groupings with some

429

interesting and unexpected results, such as splitting the previous study’s industrialized countries

430

cluster across three of our categories, and emerging and developing countries belonging to two

431

different growth profiles. These groupings thus offer new perspectives that expand our


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432

understanding of long-term material consumption and accumulation in different countries. The

433

finding of stationary acceleration for the countries of categories I and II is significant as it means

434

that shocks, whether positive or negative, might seem dramatic when looking at the time series

435

graph of speed, as done in material flow studies and socio-economic metabolism research so far,

436

but have only a minor effect on long-term growth and may be compensated for by bigger growth

437

in later years. This is even more pronounced in the 15 countries of category III, which include

438

the fast emerging economies of Brazil, India, and China. Their archetypal stock level profile

439

superficially resembles category II yet the underlying rates are much faster due to their ongoing

440

process of acceleration. It would seem that their economic structures provide a sufficient base

441

from which to sustain ongoing demands for more and more material stock increases from year to

442

year.

443

From the viewpoint of sustainability, these results are the most alarming. Due to domination in

444

recent years by highly populated countries like China and India and the aggregation of all

445

countries – which tends to smooth out any “bumps” related to shocks in the time series – the

446

speed of accumulation of the world in total is accelerating at expanding rates and is forecast to

447

continue to increase (Figure 5). Almost 600 Gt were accumulated from 1970 to 2010, of which

448

more than half were added in the last 13 years. The model’s assumption that historical trends will

449

persist year-on-year into the future, a further 800 Gt will be added to stock by 2030. The

450

question is, then, whether such increases can realistically continue unhampered into the future, or

451

whether this accelerating growth will slow down or even stop for either endogenous or

452

exogenous reasons. To rephrase the question, can countries change their paths?


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453 454

Figure 5. The global speed of accumulation of material stock, 1970–2030, with forecast intervals

455

of 80% and 95%. The areas below the trend line are the total accumulated material 1970–2010

456

and the forecasted total accumulation 2010–2030.

457 458

The answer may lie with the seven developed countries which indeed changed their paths

459

within the examined time period and are already undergoing deceleration that could lead to

460

stagnating levels of material stocks and ultimately dematerialization. Of the four stock growth

461

archetypes found, only the s-shaped growth of category IV countries describes a change towards

462

deceleration. The Japanese and South Korean cases are the most straightforward examples. Their

463

early material stock accumulation profiles (Japan until the early 1970s and South Korea until the

464

end of the 1990s) resemble the surging acceleration seen in the third country group, and their

465

acceleration periods ended in clearly identifiable external shocks – the 1970s oil crises in the

466

case of Japan and the Southeast Asian crisis of 1997 in the case of South Korea. Japan changed

467

its accumulation profile a second time in 1991 coinciding with another discernable exogenous

468

shock, the burst of the economic bubble. Unlike Japan and South Korea, no prominent economic

469

shocks occurred in the other five countries that changed their courses. The UK’s change from

470

acceleration to deceleration occurred in 1989 and Germany’s speed peaked in 1994, while


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471

Canada, Italy, and France changed from acceleration to stable or slowly decreasing speeds in

472

1980, 1983, and 1991 respectively. These were, however, periods marked by the onset of neo-

473

conservative economic policies and an end to anticyclical Keynesian policy settings. The trigger

474

for the change in trends in these countries may thus be a “soft” reason such as the change in

475

economic and social policies. It could also be that these countries reached saturation in their

476

material stocks. Such saturation is probably not purely caused by a physical, spatial limit, but

477

rather a combination of physical and socio-economic conditions under which material stocks

478

reach a level of sufficiency to meet the demands of society and the economy, and further

479

expansion is hence constrained. However, to explore this hypothesis, examining only speed

480

indicators – net additions to stock (NAS) or domestic material consumption (DMC) – is weakly

481

helpful at best since we can now conclude that speed is only a symptom, not the end-point.

482

The logical next step is thus to re-introduce external variables such as the well-studied

483

population and GDP but also other suspected influences such as indicators of government

484

policies, economic structure, trade statistics, energy and commodity prices, or international

485

events. This can be done by expanding the ARIMA method to include exogenous variables as

486

well as by more computationally complex stochastic methods such as vector autoregressions

487

(VAR). In any case, focus should be placed on the specific analysis of the periods of change in

488

acceleration and corresponding material stock levels. The mature economies of category IV and

489

the Netherlands, with their already stable consumption speeds, should be analyzed in this way to

490

determine if acceleration changes due to material stocks reaching any kind of sufficiency and

491

saturation in absolute numbers, or otherwise in any other proportional way – per capita, per unit

492

of GDP, per unit of area, etc. This will be crucial for countries like China, India, and Brazil that

493

need to establish sufficient levels of stock of buildings and infrastructure for their growing


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494

population and economies, and for their growing cities to adapt a new pattern of stock saturation

495

which will be a determining factor for global sustainability. This kind of investigation requires

496

data not only on the speed and acceleration of material stocks, but on the actual levels in more

497

countries, data that unfortunately does not currently exist.

498 499

ASSOCIATED CONTENT

500

Supporting Information. (1) Details of the ARIMA method; (2) Comparison of this study’s

501

stochastic forecasts with deterministic forecasts from previous research; (3) Visualization of the

502

3rd order of difference for Japan; (4) ARIMA models for all 45 examined countries and the

503

world. This material is available free of charge via the Internet at http://pubs.acs.org.

504 505 506

AUTHOR INFORMATION

507

Corresponding Author

508

* Tomer Fishman, Nagoya University, Graduate School of Environmental Studies, D2 1(510)

509

Furo-cho, Chikusa-ku, Nagoya, 464-8601 Japan. Telephone +81-52-789-3840. Email

510

[email protected]

511 512

ACKNOWLEDGMENTS

513

The authors thank Yasushi Kondo for very helpful comments on the early stages of this research,

514

and are grateful to Karin Hosking (CSIRO) for copyediting the manuscript. This research was


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515

financially supported by the Environment Research and Technology Development Fund (1-1402)

516

of the Ministry of the Environment, Japan.

517 518

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Stochastic Analysis and Forecasts of the Patterns of Speed

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