Economic growth and economic development 118

Introduction to Modern Economic Growth markets, also gives us a framework for accounting for the sources of economic growth In particular, Solow (1957) developed what has become one of the most common tools in macroeconomics, the growth accounting framework For our purposes, it is sufficient to expose the simplest version of this framework Consider a continuous-time economy and differentiate the production function (2.1) with respect to time Dropping time dependence and denoting the partial derivatives of F with respect to its arguments by FA , FK and FL , this yields (3.1) Y˙ FA A A˙ FK K K˙ FL L L˙ = + + Y Y A Y K Y L Now denote the growth rates of output, capital stock and labor by g ≡ Y˙ /Y , ˙ ˙ and gL ≡ L/L, and also define gK ≡ K/K x≡ FA A A˙ Y A as the contribution of technology to growth Next, recall from the previous chapter that with competitive factor markets, we have w = FL and R = FK (equations (2.5) and (2.6)) and define the factor shares as αK ≡ RK/Y and αL ≡ wL/Y Putting all these together, (3.1) can be written as (3.2) x = g − αK gK − αL gL This is the fundamental growth accounting equation At some level it is no more than an identity However, it also allows us to estimate the contribution of technological progress to economic growth using data on factor shares, output growth, labor force growth and capital stock growth This contribution from technological progress is typically referred to as Total Factor Productivity (TFP) or sometimes as Multi Factor Productivity In particular, denoting an estimate by “ˆ”, we have the estimate of TFP growth at time t as: (3.3) xˆ (t) = g (t) − αK (t) gK (t) − αL (t) gL (t) we only put the “ˆ” on x, but one may want to take into account that all of the terms on the right hand side are also “estimates” obtained with a range of assumptions from national accounts and other data sources 104