Empirical Results And Sensitivity

Sensitivity tests have been performed by varying critical parameters of both the bi-logistic function and the rate of decline of the primary exergy intensity of output. Model parameters were assumed to vary according to a Gaussian distribution. Estimates of suitable minimum, maximum, mean and standard deviation were determined for each model parameter in isolation, while keeping all others at their empirically observed values, used in the REXSH (historical) model (Table 8.2). The parameters of the Gaussian probability distribution functions (pdfs) were chosen to provide plausible distributions about the forecast generated using the empirically observed parameter (Table 8.3). These pdfs were then used in a multivari-ate sensitivity analysis, which involved randomly drawing values for all parameters simultaneously, during 500 successive runs of the REXSF model.

Table 8.2 Forecast GDP growth rates for three alternative technology scenarios

Low

Mid

High

f GDP

f

GDP

f GDP

Minimum

0.16% -2.97%

0.43%

-1.89%

1.11% 1.94%

Average

0.40% -1.29%

0.72%

0.38%

1.18% 2.20%

Maximum

0.62% 0.92%

0.89%

1.75%

1.23% 2.63%

Table 8.3

Sensitivity test Gaussian probability distribution parameters

dt2

m2

K2

Dematerialization

rate

Minimum

8 000

8 000

0.15

0.006

Maximum

12000

16 000

0.4

0.016

Mean

10000

1 2 326

0.2

0.012

St. Dev.

1 000

1 000

0.02

0.002

The results of this (multivariate) sensitivity analysis show how (simultaneous) perturbations of parameter values feed back to produce a range of plausible future trajectories of future output intensity, resource use efficiency and economic growth (Figures 8.8 and 8.9). In particular, Figure 8.10 shows how varying the exogenous assumption about the future rate of output intensity (E/Y) decline alters the accumulation of production experience and consequently the endogenous rate with which exergy conversion efficiency progresses. It is important to bear in mind, however, that one cannot conclude from the graph that accelerating the rate of decline per se will increase the rate of economic growth. On the contrary, what the graph really expresses is the fact that a higher rate of decline simply means that a given input of exergy generates more GDP. How to achieve that result is another question.

It may be of interest to note that the declining ratio E/Y can be interpreted as an indicator of dematerialization, bearing in mind that a major fraction of materials inputs to the economy actually consists of fuels and biomass. It follows that goals such as 'Factor Four' (von Weizsaecker et al. 1998) or 'Factor Ten' (Factor Ten Club 1994 and 1997) can be expressed roughly in terms of the intensity (E/Y) ratio.

Varying each of the parameters of the bi-logistic function produces a plausible spread of future trajectories for efficiency f and output Y, for a constant rate of decline (1.2 percent per annum) of the exergy intensity of

Primary exergy intensity of output

Primary exergy intensity of output

Primary exergy demand

1975 Year

Gross output log

Gross output log

Technical efficiency of primary exergy conversion

2013

Empirical data

Figure 8.8 Sensitivity test results varying the fractional decay rate of output exergy intensity output (Figure 8.11). When both E/Y and f are perturbed simultaneously, the range of possible outcomes is increased dramatically as the full impacts of feedbacks between resource consumption, production experience and end-use efficiency are manifest.

Combining these projections, and using the LINEX production function, corrected for ICT growth, we obtain the GDP projections shown in Figure 8.12. Although these forecasts are highly uncertain, it is very important to observe that the most probable forecast for US GDP is one in which growth ceases sometime between 2030 and 2040. Thus an important future implication of our model is that growth driven by the historical 'engine' is slowing and could possibly come to a halt a few decades hence. The reasons seem straightforward: (1) the efficiency gains in primary exergy conversion (to physical work) are getting harder to achieve (the S-curve has passed its point of inflection) and (2) the opportunities to substitute machines for labor are getting scarcer (because an increasing fraction of the GDP consists of services, where value is essentially equated to cost). In other words, there is a double saturation effect.

In order for economic growth to continue at historical rates without proportional increases in fossil fuel consumption and associated waste and pollution, it is vitally important to exploit new ways of generating value-added

Gross output log 10

Gross output log 10

Primary exergy intensity of output 2

1975 Year

1975 Year

Primary exergy intensity of output 2

1975 Year

Figure 8.9 Sensitivity test results varying both the fractional rate of output exergy intensity and selected parameters of the bi-logistic curve controlling the rate of efficiency growth

RXS_H_SENS_FM-

RXS_H_SENS_DEMAT-

Empirical Data-

1975 Year

Figure 8.9 Sensitivity test results varying both the fractional rate of output exergy intensity and selected parameters of the bi-logistic curve controlling the rate of efficiency growth

Year

Figure 8.10 Historical (1950-2000) and forecast (2000-50) GDP for alternate rates of decline of the energy intensity of output, USA

Year

Figure 8.10 Historical (1950-2000) and forecast (2000-50) GDP for alternate rates of decline of the energy intensity of output, USA

Year

Figure 8.11 Historical (1950-2000) and forecast (2000-50) technical efficiency of energy conversion for alternate rates of technical efficiency growth, USA

Year

Figure 8.11 Historical (1950-2000) and forecast (2000-50) technical efficiency of energy conversion for alternate rates of technical efficiency growth, USA

without doing more physical work. Either basic resource costs must continue to decline relative to wages or it will be necessary to develop ways of reducing fossil fuel inputs per unit of physical work output. But major new cost-reducing resource discoveries seem quite unlikely. Moreover, economies

Year

Figure 8.12 Historical (1950-2000) and forecast (2000-50) GDP for alternate rates of technical efficiency growth, USA

Year

Figure 8.12 Historical (1950-2000) and forecast (2000-50) GDP for alternate rates of technical efficiency growth, USA

of scale and experience are unlikely to compensate for declining resource discovery, and conventional energy conversion technologies are already so high that future improvements are almost certain to be marginal.

The optimistic 'high' growth rate in Figure 8.12 implies a significant increase in the efficiency with which useful work is generated from exergy inputs. This is technically feasible, but it seems unlikely to occur without drastic policy interventions to encourage the adoption of efficient technologies such as combined heat and power (CHP), rooftop photo-voltaics, small mass-produced wind turbines, double and triple glazed windows, domestic heat pumps, battery powered cars and so forth. In virtually all cases, progress is still impeded by anti-competitive behavior on the part of oligopolistic industries, reluctance by lenders to provide mortgages for 'non-standard' construction, reluctance on the part of insurers to insure firms promoting innovative systems, and regulatory hurdles from zoning requirements to safety rules.

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