6.2.3The Sources of Growth Framework

The sources of growth framework was introduced by Hulten and Schwab (1984). It represents an alternative to econometric cross-sectional analyses, which measures productivity level differences. This method focuses on measuring factor accumulation and productivity growth rate over time. Hulten and Schwab (1984) were the first authors to apply this technique at the regional level. They looked at the regional productivity growth in U.S. manufacturing for the period 1951-1978. Using a Hicks-neutral production function, the growth rate of real product is partitioned into the share-weighted growth rates of inputs (capital, labor and intermediate input), and a residual representing total factor productivity.

Qt = F (A t V (K t , L t ) , M t )(6.3)

where gross manufacturing output in period t, Q t, is a function of capital K t , labor L t, intermediate input M t, and technology A t. Under profit maximization, the marginal product conditions imply:

δQt / δM t = pt M / pt ; δQt / δK t = pt K / pt ; δQt / δL t = pt L / pt (6.4)

where pt is the price of output at time t, and pt M , pt K , pt L the relevant factor prices. Combining these marginal products with the logarithmic differentiation of (6.2) leads to

gr(v) = St k gr(k) + St L gr(l) + gr(A)(6.5)

where gr(.) represents the growth rate of the variable in parenthesis. St j represents factor shares in value added such that St k + St L = 1 (constant returns to scale) and

St k = pt K K t/ Qt and St L = pt L L t/ Qt (6.6)

Finally, gr(A) is the growth rate of technical progress, or total factor productivity (TFP). It represents here the growth rate in output not attributable to growth in inputs. It could include things such as better education quality and quantity, intensive training of the workforce, better health and safety measures, quality of equipment, communication and transportation. The main problem with this framework is that it leaves most of the national growth in productivity unexplained, under the form of total factor productivity.

Williams (1985) allowed technical progress to be factor augmenting instead of Hicks-neutral, which means that there is a factor augmenting parameter associated with each input instead of the production function F(.) itself. The production function becomes:

Vit = F (αtKit, βtLit ) (6.7)

where i stands for region, t for time, αt and βt are factor augmenting parameters that convert the quantity of capital and labor (Kit and Lit) into efficiency units, and Vit represents value added in manufacturing. Equation 6.6 expressed in relative rates of change over time becomes:

gr(v) = St k [gr(k) + gr(α)] + St L [gr(l) + gr(β)] + gr(A)(6.8)

Setting equation 6.5 equals to equation 6.8, the share-weighted sum of factor-specific efficiency growth rates could then serve as an estimate of total factor productivity:

gr(A) = St k gr(α) + St L gr(β)(6.9)

Assuming competitive factor markets, Williams was able to estimate gr(α) and gr(β) and therefore it was possible to estimate gr(A) directly instead of indirectly as a residual. This is known as Sato’s method, which is an alternative to Hulten and Schwab’s method using residuals only.

Beeson (1990) used data on 42 states and 45 large SMSAs so that sources of growth could be compared between, as well as within, regions. Total factor productivity was computed using the residual method and capital stock figures were estimated by the perpetual inventory method. The author found smaller growth rates in real manufacturing value added within SMSAs than outside large SMSAs.

Fogarty and Garofalo (1988) used the total factor productivity methodology to identify the contribution of agglomeration economies to productivity differentials. First, they estimated a variable elasticity of substitution (VES) production function, and used it to calculate the sources of total factor productivity growth. Value added was significantly related to agglomeration economy variables such as the density of the manufacturing sector. Their results indicate that total factor productivity was the dominant source of growth. Agglomeration economy variables were positively and significantly related to total factor productivity growth.

Williams and Moomaw (1989) used a translog production function to compare estimates of total factor productivity for 48 states. Their findings indicate higher growth rates of manufacturing value added in Southern and Western states. Overall, they found a greater interstate variation in total factor productivity than estimated by Hulten and Schwab. These results come from a single equation regression model, which explains 50% of interstate TFP variation. The most significant positive explanatory variables were: the rate of change in R&D spending, the rate of growth in manufacturing output, the rate of growth of the capital/labor ratio and the rate of growth of production workers as a percentage of all workers in manufacturing. The rate of unionization was found to be negatively correlated to growth in TFP.

Whereas most of the previous literature focused on manufacturing productivity, Carlino and Voith (1992) were the first to study state variations in aggregate productivity using Gross State Product (GSP) data. Value added at the metropolitan, state or regional level has been available previously only for manufacturing industries. Then, the U.S. Commerce Department’s Bureau of Economic Analysis (BEA) introduced annual gross state product in May of 1988. In their model, Carlino and Voith consider several determinants of state-to-state variations in productivity. They found that a state’s industry mix, infrastructure, education level, and metropolitan structure all significantly affect productivity. Another important finding is that a ranking of states by productivity gains based on GSP data differs markedly from a ranking based solely on manufacturing data. This raises reservations regarding previous studies and their inferences regarding aggregate productivity at the regional level based on manufacturing data.