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# Technological Progress, Skill Bias

BIBLIOGRAPHY

This entry will discuss the different approaches to total factor productivity measurement and define skill-biased technical change. Let t denote a technology index and x and y denote inputs and output, respectively. Then the production function can be written as

y=f(x,t).

Technological change is then defined as a change in the technology index t that affects the relationship between inputs x and output y. Given a change in t (say from t 1 to t 2), technological change is said to take place if

Assuming that t 2 > t 1, technological change is called technological progress if

that is, if technological change allows the production of more output y with the same quantity of inputs x. Alternatively, technological change is called technological regress if

Technological progress is usually measured in terms of the rate of technological progress

Under the assumption of constant returns to scale (which is the maintained assumption in this article), the rate of technological progress is also referred to as the growth rate of total factor productivity (TFP) or total factor productivity growth.

There are four alternative approaches to the measurement of the rate of technological progress: growth accounting, the index number approach, the econometric approach, and the distance function approach.

The growth accounting approach to the measurement of the rate of technological progress was pioneered by Moses Abramovitz (1956) and Robert M. Solow (1957). It requires the specification of a neoclassical production function, y = f(x, t). Totally differentiating the production function with respect to t and rearranging yields the rate of technological progress

As an example, consider the Cobb-Douglas production function Y=AKαL1-α, where K is capital, L is labor, α is the share of capital in output, and A is a measure of the current level of technology, referred to as total factor productivity. With this production function, equation (2) implies

according to which the rate of growth of A is just the rate of technological progress (under constant returns to scale). Intuitively, A /A is the growth in output that cannot be accounted for by growth in capital and labor and is often called the Solow residual, after Robert Solow, who suggested this method of estimating the rate of total factor productivity growth.

Pioneered by W. Erwin Diewert (1976), the index number approach is an extension of growth accounting (from a continuous-time framework to a discrete-time framework). Under the assumption of cost minimization and constant returns to scale, equation (2) can be rewritten as

where Iy is a (real) output quantity index and Ix an input quantity index. Equivalently,

according to which the rate of technological progress is a function of the ratio of an output quantity index to an input quantity index. Clearly, the index number approach does not require the specification of a production function, although we did use it above to establish the equivalency between the growth accounting approach and the index number approach.

The index number approach is widely used by the majority of statistical agencies that produce productivity statistics (see Diewert and Nakamura 2003 for details). One critical issue regarding this approach is the selection of the appropriate indexes. Statistical indexes are mainly characterized by their statistical properties. These properties were examined in great detail by Irving Fisher (1922) and serve as tests in assessing the quality of a particular statistical index. They have been named, after Fisher, as Fishers system of tests (see Eichhorn 1976 for a detailed analysis as well as a comprehensive bibliography of Fisher s test or axiomatic approach to index numbers).

The econometric approach involves estimating the parameters of a production, cost, or profit function. With a production function, the rate of technological progress can be measured directly using equation (1). With a cost function, C(r, y, t ), where r is the vector of input prices and the assumption of constant returns to scale, the rate of technological change can be shown to be

where ln C(r, y, t)/t is the dual rate of cost diminution. With a profit function, π(r, y, t ), and the assumption of constant returns to scale, the rate of technological progress can be shown to be the product of the dual rate of profit growth and the ratio of profit to revenue, as follows,

where p is the price of output. While the econometric approach provides deep insights into the production structure (i.e., the price elasticities as well as the elasticities of substitution), it assumes that the firms or industries in question are fully efficient (i.e., operating on the production frontier), which has been proved not to be the case by studies on technical and allocative efficiency.

Finally, the distance function approach to measuring total factor productivity, introduced separately by Ronald Shephard (1953) and Sten Malmquist (1953), seeks to separate total factor productivity into two components: changes resulting from a movement toward the production frontier and shifts in the frontier. Mathematically, the Malmquist total factor productivity index is given by

where the term outside the brackets on the right-hand side measures the change in relative efficiency between years t and t + 1 and the geometric mean of the two ratios inside the brackets measures the shift in technology (technological progress) between the two periods evaluated at xt and xt + 1. This approach has several advantages. It does not require a specific functional form, and it does not assume that firms are operating at their efficient level. However, implicit in the approach is the assumption that all units (firms, industries, or countries) being compared have the same production function, when in fact evidence suggests that even firms in the same industry do not have identical production functions.

In our discussion so far of the four approaches to the measurement of technological progress, we implicitly assumed that technological progress is factor-neutral in the sense that the marginal rate of substitution between any two inputs (measured along a ray through the origin) is not affected by technological progress. Studies, however, find that technological progress is not factor-neutral; rather, it is skill-biased. Skill bias occurs when a shift in the production function (technological change) favors skilled over unskilled labor by increasing its relative productivity and therefore its relative demand and skill premium.

SEE ALSO Growth Accounting; Machinery; Production Function; Returns to Scale; Technological Progress, Economic Growth; Technology; Technology, Adoption of

## BIBLIOGRAPHY

Abramovitz, Moses. 1956. Resource and Output Trends in the United States since 1870. American Economic Review 46: 523

Diewert, W. Erwin. 1976. Exact and Superlative Index Numbers. Journal of Econometrics 4: 115145.

Diewert, W. Erwin, and Alice Nakamura. 2003. Index Number Concepts, Measures of Decompositions of Productivity.Journal of Productivity Analysis 19: 127159.

Eichhorn, W. 1976. Fishers Tests Revisited. Econometrica 44 247256.

Fisher, Irving. 1922. The Making of Index Numbers: A Study of Their Varieties, Tests, and Reliability. Boston: Houghton Mifflin.

Malmquist, Sten. 1953. Index Numbers and Indifference Surfaces. Trabajos de Estadistica 4: 209242.

Shephard, Ronald W. 1953. Cost and Production Functions. Princeton, NJ: Princeton University Press.

Solow, Robert M. 1957. Technical Change and the Aggregate Production Function. Review of Economics and Statistics 39: 312320.

Apostolos Serletis