# International Futures Help System

## The Production Function: Basic Overview

Cobb-Douglas production functions involving sector-specific technology or multifactor productivity (TEFF), capital (KS) and labor (LABS) provide potential value added (VADDP) in each sector, taking into account the level of capacity utilization (CAPUT), initially set exogenously (**
caputtar
**). In a multi-sector model the functions require sectoral exponents for capital (CDALFS) and labor that, assuming constant returns to scale, sum to one within sectors.

Solow (1956) long ago recognized that the standard Cobb-Douglas production function with a constant scaling coefficient in front of the capital and labor terms was inadequate because the expansion of capital stock and labor supply leave a large portion of economic growth unexplained. It then became standard practice to represent an exogenously specified growth of technology term in front of the capital and labor terms as "disembodied" technological progress (Allen 1968: Chapter 13). Romer (1994) began to show the value of unpacking such a term and specifying its elements in the model, thereby endogenously representing this otherwise very large residual, which we can understand to represent the growth of multifactor productivity (MFP).

In IFs that total endogenous productivity growth factor (TEFF) is the accumulation over time (hence a stock like labor and capital) of annual values of growth in multifactor productivity (MFPGRO). There are many components contributing to growth of productivity, and there is a vast literature around them. See, for example, Barro and Sala-i-Martin (1999) for theoretical and empirical treatment of productivity drivers; also see Barro (1997) for empirical analysis (or McMahon 1999) for a focus on education.

In the development of IFs there was a fundamental philosophic choice to make. One option was to keep the multi-factor productivity function very simple, perhaps to restrict it to one or two key drivers, and to estimate the function as carefully as possible. Suggestions included focusing on the availability/price of energy and the growth in electronic networking and the knowledge society.

The second option was to develop a function that included many more factors known or strongly suspected to influence productivity and to attempt a more stylistic representation of the function, using empirical research to aid the effort as much as possible. The advantages of the second approach include creating a model that is much more responsive to a wide range of policy levers over the long term. The disadvantages include some inevitable complications with respect to overlap and redundancy of factor representation, as well as some considerable complexity of presentation.

Because IFs is a thinking tool and an extensively integrated multi-model system, the second approach was adopted, and the production function has become an element of the economic model that will be subject to regular revision and enhancement. IFs groups the many drivers of multifactor productivity into five categories, recognizing that even the categories overlap somewhat. The base category is one that represents core technological development and transfer elements of convergence theory, with less developed countries gradually catching up with more developed ones. The four other categories incorporate factors that can either retard or accelerate such convergence, transforming the overall formulation into one of conditional convergence.

**
The convergence base
**
**.** The base rate of multifactor productivity growth (MFPRATE) is the sum of the growth rate for technological advance or knowledge creation of a technological leader in the global system (**
mfpleadr
**) and a convergence premium (MFPPrem) that is specific to each country/region. The basic concept is that it can be easier for less developed countries to adopt existing technology than for leading countries to develop it (assuming some basic threshold of development has been crossed). The base rate for the leader remains an unexplained residual in the otherwise endogenous representation of MFP, but that has the value of making it available to model users to represent, if desired, technological cycles over time (e.g. Kondratief waves). The base also includes a correction term (MFPCor) that is initially set to the difference between empirical growth of MFP (calculated the first year as a residual between factor growth and output growth) and the sum of the technological leader and convergence premium terms. Over time, the correction term is phased out, but the four other terms (below) become key drivers of country-specific productivity. In fact, significant change in the other terms can either undercut the foundational convergence process or greatly augment it.

**
Human capital
**
**.** This term has multiple components, including changes in educational spending as a portion of GDP, educational attainment of adults, and changes in health expenditure. For example, Barro and Sala-i-Martin (1999: 433) estimated that a 1.5% increase in government expenditures on education translates into approximately a 0.3% increase in annual economic growth.

**
Social capital
**
**.** Similarly, social capital representation aggregates several components including economic freedom and absence of overt social conflict. Illustratively, the value of the parameter for economic freedom (**
elgref
**) was estimated in a cross-sectional relationship of change in GDP level from 1985 to 1995 with the level of economic freedom. Similarly, Barro places great emphasis in his estimation work on the "rule of law".

**
Physical capital
**
**.** In collaborative work with the IFs project, Robert Ayres correctly emphasized the close relationship between energy supply availability and economic growth. For instance, a rapid increase in world energy prices (WEP) essentially makes much capital stock less valuable. IFs uses world energy price relative to world energy prices in the previous year to compute an energy price term. The physical capital term also represents the extent of various types of infrastructure in a society.

**
Knowledge Capital
**
**.** This fourth term includes changes in the R&D spending, computed from government spending (GDS) on R&D as a portion of total government spending (GOVCON) contribute to knowledge creation, notably in the more developed countries. Globerman (2000) reviewed empirical work on the private and social returns to R&D spending and found them to be in the 30-40% range; see also Griffith, Redding, and Van Reenen (2000). Many other factors undoubtedly contribute to superior knowledge development diffusion. This term represents especially the extent of economic integration with the global economy via trade.

All of the elements computed in the human, social, physical and knowledge capital terms are used in shaping economic productivity and growth rates of the model on a differential basis–that is, they are computed and evaluated relative to underlying "expected" patterns given overall economic development levels. Their actual levels can be above or below expected ones and they can therefore either add to or slow down the productivity growth rate. See the detailed equations of the production function for elaboration.