The Role Of Extrapolation In Integrated Assessment Models

Integrated assessment (IA) models are at the heart of current efforts to assess policies and prospects for the future. The relationships between technological progress, economic activity and global environment are the focus of most of this area of research. Each model is designed to address different policy questions, for example, to quantify the potential costs of climate stabilization policies such as the Kyoto Protocol (Manne and Wene 1994; Weyant 1999), or to assess our ability to meet future energy demands (Nakicenovic 1993) and maintain future rates of economic growth (Gerlagh and van der Zwaan 2003).

Examples of 'top-down' (or macroeconomic) models, include GEMINI-E3, MERGE, CETA, DICE and RICE (Bernard and Vielle 2003; Manne and Wene 1994; Manne and Richels 2004; Nordhaus 1993, 2004). Examples of 'bottom-up' (energy system) models, include MESSAGE, DEMETER or FREE (Messner and Strubegger 1994; Fiddaman 1998; Gerlagh and van der Zwaan 2003).

Whether bottom-up or top-down, most share a common set of assumptions based on Robert Solow's neoclassical model of economic growth (Solow 1956, 1957). One of the simpler integrated assessment models, the top-down DICE model, was specifically focused on the economics of climate change (Nordhaus 1992, 1998). Nordhaus concluded that the costs of mitigating climate change today would cause a reduction in the rate of future economic growth. The logic underlying this conclusion is that (by assumption) the economy is currently on an optimal trajectory. It follows that any interference by government must inevitably force a departure from the optimal path. That would presumably cause a reduction in the growth rate. But is the current trajectory really optimal?

Gross output in DICE was given by a two-factor (capital and labor) Cobb-Douglas production function, together with an assumed rate of total factor productivity (TFP) and an assumed rate of decline in the energy intensity of the economy. The utility of future consumption was discounted at an assumed rate.1 All of these parameters are essentially extrapolations. This is equally true of other large-scale models. For instance, the TFP assumption is a direct extrapolation based on an exponential fit of the ratio between the actual GDP (adjusted for inflation) and the 'naked' Cobb-Douglas model (assuming A(t) = 1) for the US economy from 1900 through 2004. The residual (TFP) grew at an average rate of 1.6 percent per annum while the 'naked' C-D function of capital and labor grew at an average annual rate of 1.67 percent. Adding the two rates together, the GDP increased at an average annual rate of about 3.3 percent per annum from 1900 through 2004. Most models, like DICE, simply assume that the TFP - a measure of technological progress - will continue to grow at the same rate, or slightly less, in the future. They also extrapolate standard labor force growth rates to estimate the labor component of the C-D function. Finally, they extrapolate an average historical savings rate and depreciation rate to estimate future capital stock growth.

Nordhaus also assumed that the energy/GDP ratio (known as 'energy intensity') would continue to decline at a fixed rate. This again is an extrapolation of past behavior, obtained from a similar exponential fit to an historical time series. The assumed social discount or time preference rate is somewhat open to debate, but the most common choice by economists would be to equate it with the 'prime' rate of interest or the average historical GDP growth rate (Hanke and Anwyll 1980; Markandya and Pearce 1988; Gerlagh 2000).

These are all extrapolations and, consequently, they all assume implicitly that the structure of the economy and the behavior of consumers will not change in the foreseeable future. Yet many of the underlying trends have actually changed significantly in the past several decades. Examples include family size, retirement ages, working hours per week, female participation in the labor force, household savings, investment, the decline of manufacturing in the US, the increasing US trade gap, and the increasing national debt, among others.

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