Stochastic Analysis and Forecasts of the Patterns ... - ACS Publications

Feb 29, 2016 - Despite the importance of physical stocks in society, the empirical assessment of total material stock of buildings and infrastructure ...
2 downloads 9 Views 1019KB Size
Subscriber access provided by NEW YORK UNIV

Article

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

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Environmental Science & Technology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 30

Environmental Science & Technology

1

Stochastic Analysis and Forecasts of the Patterns of

2

Speed, Acceleration, and Levels of Material Stock

3

Accumulation in Society

4

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

5

a

6

ku, Nagoya, 464-8601 Japan.

7 8

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.

9 10

Corresponding Author

11

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

12

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

13

[email protected]

14 15

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

16

sustainable materials management.

ACS Paragon Plus Environment

1

Environmental Science & Technology

Page 2 of 30

17

ABSTRACT

18

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

19

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

20

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

21

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

22

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

23

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

24

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

25

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

26

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

28

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

29

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

30

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

31

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

32

ACS Paragon Plus Environment

2

Page 3 of 30

Environmental Science & Technology

33

1. Introduction

34

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

35

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

36

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

37

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

38

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

39

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

40

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

41

material consumption

42

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

,

45

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

46

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

48

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

49

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

50

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

51

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

52

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

53

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

54

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

55

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

14,15

13

, and

, and as such

ACS Paragon Plus Environment

3

Environmental Science & Technology

Page 4 of 30

56

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

57

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

58

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

59

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

60

increasing use of mineral materials are fundamental to modernity.

61

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

62

and show that the flows have been steadily increasing

63

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

64

output (material efficiency)

65

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

66

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

67

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

68

accounting methods

69

uses, and their locations

70

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

71

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

72

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

73

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

74

eventual level of saturation

75

and outflow trends

76

projections of social indicators such as population growth and affluence trends

77

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

78

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

ACS Paragon Plus Environment

4

Page 5 of 30

Environmental Science & Technology

79

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

80

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

81

process approaches have some inherent limitations:

82



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

85

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

86

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

87

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

88

account;

89



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

90

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

91

decisions;

92



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

93

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

94

the possible range of outputs;

95 96



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

97

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

98

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

99

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

ACS Paragon Plus Environment

5

Environmental Science & Technology

Page 6 of 30

100

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

101

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

102

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

103

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

104

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

105

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

106

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

107

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

108

common growth patterns.

109

2. Methodology

110

2.1. Framework: level, speed, and acceleration

111

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

112

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

113

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

114

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

115

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

116

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

117

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

118

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

119

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

120

levels.

ACS Paragon Plus Environment

6

Page 7 of 30

Environmental Science & Technology

121

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

122

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

123

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

124

totaling yearly material flows and stocks has been established

125

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

126

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

127

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

128

same relations for speed and acceleration).

129 130

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

131

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

132

panel).

33

and so the discrete equivalents

ACS Paragon Plus Environment

7

Environmental Science & Technology

133

Page 8 of 30

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)

134

ACS Paragon Plus Environment

8

Page 9 of 30

Environmental Science & Technology

135

2.2. Stochastic analysis using ARIMA

136

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

137

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

138

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

139

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

140

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

141

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

142

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

143

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

144

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

145

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

146

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

147

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

148

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

149

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

150

series at once.

34,35

. The

151

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

152

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

153

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

154

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

155

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

156

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

157

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

ACS Paragon Plus Environment

9

Environmental Science & Technology

Page 10 of 30

158

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

159

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

160

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

161

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

162

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

163

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

164

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

165

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

166

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

167

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

168

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

169

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

170

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

171

supporting information) have validated the viability of the method.

172 173

2.3. Data and analysis procedures

174

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

175

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

176

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

177

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

178

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

179

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

16

and which we

ACS Paragon Plus Environment

10

Page 11 of 30

Environmental Science & Technology

180

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

181

(UNEP) International Resource Panel

182

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

183

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

184

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

185

populations of over 10 million in 1970

186

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

187

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

188

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

189

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

190

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

191

references

192

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

193

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

194

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

195

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

196

3. Results

197

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

198

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

199

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

200

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

201

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

ACS Paragon Plus Environment

11

Environmental Science & Technology

Page 12 of 30

202

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

203

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

204 205

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

206

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

207

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

208

acceleration of accumulation speed.

209

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

210

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

211

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

212

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

213

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

214

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

215

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

ACS Paragon Plus Environment

12

Page 13 of 30

Environmental Science & Technology

216

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

217

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

218

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

219

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

220

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

221

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

222

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

223

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

224

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

225

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

226

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

227

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

228

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

229

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

230

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

231

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

232

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

233

and will see further growth occurring until 2030.

234

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

235

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

236

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

237

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

238

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

ACS Paragon Plus Environment

13

Environmental Science & Technology

Page 14 of 30

239

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

240

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

241

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

242

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

243

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

244

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

245

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

246

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

247

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

248

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

249

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

250

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

251

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

252

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

253

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

254

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

255

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

256

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

257

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

258

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

259

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

260

to stock – a dematerialization.

261

ACS Paragon Plus Environment

14

Page 15 of 30

Environmental Science & Technology

262

3.2 International comparisons and material accumulation profiles

263

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

264

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

265

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

266

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

267

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

268

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

269

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

270

information.

271

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

272

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

273

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

274

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

275

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

276

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

277

considered to be archetypal material stock accumulation profiles:

278

(I)

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

279

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

280

growth;

281

(II)

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

282

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;

ACS Paragon Plus Environment

15

Environmental Science & Technology

284

(III)

Page 16 of 30

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.

287

(IV)

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

288

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

289

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

292

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

293

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.

ACS Paragon Plus Environment

16

Page 17 of 30

Environmental Science & Technology

295 296

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

297

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

298

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

299

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.

301

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

304

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

ACS Paragon Plus Environment

17

Environmental Science & Technology

Page 18 of 30

305

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

306

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

307

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

308

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

ACS Paragon Plus Environment

18

Page 19 of 30

Environmental Science & Technology

327

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

328

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.

ACS Paragon Plus Environment

19

Environmental Science & Technology

Page 20 of 30

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

ACS Paragon Plus Environment

20

Page 21 of 30

Environmental Science & Technology

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.

ACS Paragon Plus Environment

21

Environmental Science & Technology

Page 22 of 30

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

ACS Paragon Plus Environment

22

Page 23 of 30

Environmental Science & Technology

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

ACS Paragon Plus Environment

23

Environmental Science & Technology

Page 24 of 30

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?

ACS Paragon Plus Environment

24

Page 25 of 30

Environmental Science & Technology

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

ACS Paragon Plus Environment

25

Environmental Science & Technology

Page 26 of 30

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

ACS Paragon Plus Environment

26

Page 27 of 30

Environmental Science & Technology

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

ACS Paragon Plus Environment

27

Environmental Science & Technology

Page 28 of 30

515

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

516

of the Ministry of the Environment, Japan.

517 518

REFERENCES

519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554

(1)

(2) (3) (4)

(5) (6) (7) (8)

(9)

(10)

(11) (12)

(13)

(14)

Schandl, H.; Müller, D. B.; Moriguchi, Y. Socioeconomic Metabolism Takes the Stage in the International Environmental Policy Debate: A Special Issue to Review Research Progress and Policy Impacts. J. Ind. Ecol. 2015, 19 (5), 689–694. Yuan, Z.; Bi, J.; Moriguichi, Y. The Circular Economy: A New Development Strategy in China. J. Ind. Ecol. 2006, 10 (1-2), 4–8. Preston, F. A Global Redesign? Shaping the Circular Economy; Chatham House: London, 2012. O’Brien, M.; Miedzinski, M.; Giljum, S.; Doranova, A. Eco-innovation and competitiveness: enabling the transition to a resource-efficient circular economy ; annual report 2013; Publications Office of the European Union: Luxembourg, 2014; p 54. O’Neill, D. W. What Should Be Held Steady in a Steady-State Economy?: Interpreting Daly’s Definition at the National Level. J. Ind. Ecol. 2015, 19 (4), 552–563. Müller, D. B. Stock dynamics for forecasting material flows—case study for housing in The Netherlands. Ecol. Econ. 2006, 59 (1), 142–156. Reyna, J. L.; Chester, M. V. The Growth of Urban Building Stock. J. Ind. Ecol. 2014, 19 (4), 524–537. Power, A. Does demolition or refurbishment of old and inefficient homes help to increase our environmental, social and economic viability? Energy Policy 2008, 36 (12), 4487– 4501. Pincetl, S.; Chester, M.; Circella, G.; Fraser, A.; Mini, C.; Murphy, S.; Reyna, J.; Sivaraman, D. Enabling Future Sustainability Transitions. J. Ind. Ecol. 2014, 18 (6), 871– 882. Wiedenhofer, D.; Steinberger, J. K.; Eisenmenger, N.; Haas, W. Maintenance and Expansion: Modeling Material Stocks and Flows for Residential Buildings and Transportation Networks in the EU25. J. Ind. Ecol. 2015, 19 (4), 538–551. Pérez-Lombard, L.; Ortiz, J.; Pout, C. A review on buildings energy consumption information. Energy Build. 2008, 40 (3), 394–398. Chester, M. V.; Sperling, J.; Stokes, E.; Allenby, B.; Kockelman, K.; Kennedy, C.; Baker, L. A.; Keirstead, J.; Hendrickson, C. T. Positioning infrastructure and technologies for low-carbon urbanization. Earths Future 2014, 2 (10), 533–547. Krausmann, F.; Gingrich, S.; Eisenmenger, N.; Erb, K.-H.; Haberl, H.; Fischer-Kowalski, M. Growth in global materials use, GDP and population during the 20th century. Ecol. Econ. 2009, 68 (10), 2696–2705. Hashimoto, S.; Tanikawa, H.; Moriguchi, Y. Where will large amounts of materials accumulated within the economy go?–a material flow analysis of construction minerals for Japan. Waste Manag. 2007, 27 (12), 1725–1738.

ACS Paragon Plus Environment

28

Page 29 of 30

555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600

Environmental Science & Technology

(15) Hashimoto, S.; Tanikawa, H.; Moriguchi, Y. Framework for estimating potential wastes and secondary resources accumulated within an economy–A case study of construction minerals in Japan. Waste Manag. 2009, 29 (11), 2859–2866. (16) Fishman, T.; Schandl, H.; Tanikawa, H.; Walker, P.; Krausmann, F. Accounting for the Material Stock of Nations. J. Ind. Ecol. 2014, 18 (3), 407–420. (17) Gierlinger, S.; Krausmann, F. The Physical Economy of the United States of America. J. Ind. Ecol. 2012, 16 (3), 365–377. (18) Krausmann, F.; Gingrich, S.; Nourbakhch-Sabet, R. The Metabolic Transition in Japan. J. Ind. Ecol. 2011, 15 (6), 877–892. (19) Schandl, H.; West, J. Resource use and resource efficiency in the Asia–Pacific region. Glob. Environ. Change 2010, 20 (4), 636–647. (20) West, J.; Schandl, H.; Krausmann, F.; Kovanda, J.; Hak, T. Patterns of change in material use and material efficiency in the successor states of the former Soviet Union. Ecol. Econ. 2014, 105 (0), 211–219. (21) West, J.; Schandl, H. Material use and material efficiency in Latin America and the Caribbean. Ecol. Econ. 2013, 94, 19–27. (22) Steinberger, J. K.; Krausmann, F. Material and energy productivity. Environ. Sci. Technol. 2011, 45 (4), 1169–1176. (23) Steinberger, J. K.; Krausmann, F.; Getzner, M.; Schandl, H.; West, J. Development and Dematerialization: An International Study. PloS One 2013, 8 (10), e70385. (24) Steinberger, J. K.; Krausmann, F.; Eisenmenger, N. Global patterns of materials use: A socioeconomic and geophysical analysis. Ecol. Econ. 2010, 69 (5), 1148–1158. (25) Tanikawa, H.; Fishman, T.; Okuoka, K.; Sugimoto, K. The weight of society over time and space: a comprehensive account of the construction material stock of Japan, 19452010. J. Ind. Ecol. 2015, 19 (5), 778–791. (26) Tanikawa, H.; Hashimoto, S. Urban stock over time: spatial material stock analysis using 4d-GIS. Build. Res. Inf. 2009, 37 (5-6), 483–502. (27) Fishman, T.; Schandl, H.; Tanikawa, H. The socio-economic drivers of material stock accumulation in Japan’s prefectures. Ecol. Econ. 2015, 113, 76–84. (28) Pauliuk, S.; Milford, R. L.; Müller, D. B.; Allwood, J. M. The Steel Scrap Age. Environ. Sci. Technol. 2013, 47 (7), 3448–3454. (29) Hatayama, H.; Daigo, I.; Matsuno, Y.; Adachi, Y. Outlook of the World Steel Cycle Based on the Stock and Flow Dynamics. Environ. Sci. Technol. 2010, 44 (16), 6457–6463. (30) Elshkaki, A.; Voet, E. van der; Timmermans, V.; Holderbeke, M. V. Dynamic stock modelling: A method for the identification and estimation of future waste streams and emissions based on past production and product stock characteristics. Energy 2005, 30 (8), 1353–1363. (31) Kapur, A.; Keoleian, G.; Kendall, A.; Kesler, S. E. Dynamic Modeling of In-Use Cement Stocks in the United States. J. Ind. Ecol. 2008, 12 (4), 539–556. (32) Huang, T.; Shi, F.; Tanikawa, H.; Fei, J.; Han, J. Materials demand and environmental impact of buildings construction and demolition in China based on dynamic material flow analysis. Resour. Conserv. Recycl. 2013, 72 (0), 91–101. (33) Eurostat. Economy-wide material flow accounts and derived indicators: a methodological guide; European Statistical Office: Luxemburg, 2001. (34) Becketti, S. Introduction to time series using Stata; Stata Press: College Station, Texas, 2013.

ACS Paragon Plus Environment

29

Environmental Science & Technology

601 602 603 604 605 606

(35) (36) (37) (38)

Page 30 of 30

Hyndman, R. J.; Athanasopoulos, G. Forecasting: principles and practice; OTexts, 2014. UNEP. Global material flow and resource productivity; 2015. World Bank. World DataBank databank.worldbank.org. Hyndman, R. J.; Khandakar, Y. Automatic Time Series Forecasting: The forecast Package for R. J. Stat. Softw. 2008, 27 (3), 1–22.

ACS Paragon Plus Environment

30