6.2.2Empirical Evidence on Productivity Measurement Across Space

Gerking (1994) provides a complete survey on later empirical evidence concerning measurement of productivity levels and patterns of changes in these levels over time. Most of the empirical studies use the same methodology. The model usually starts with a production function of the form:

Q = g (Z) f (K,L) (6.2)

where g() represents Hicks-neutral productivity, Z is a vector of variables affecting productivity and f() is a Cobb-Douglas or CES production function. The variable L is easy to measure, it is merely the number of employees, sometimes weighted by average years of education to add some quality aspects to the labor force variable. Z contains variables that reflect agglomeration economies (population, size of the industry) as well as dummies for the geographical unit of analysis (region, state or city). However, there is usually no good measure of capital services at the level of these geographical units. Authors have adopted several options to conduct their studies: (1) avoid the use of K, (2) constructing their own measures of K, or (3) use some proxies:

1. Sveikauskas (1975) introduced the notion that productivity may be systematically higher in large urban areas. He was only concerned with the size of cities, measured by population. He separated estimates of g() and f(). His concern was to study the effect of Z on Q and therefore he omitted K, the capital variable. Using a CES production function and manufacturing data, his results indicate that Hicks-neutral productivity increases by about 6 % with a doubling of the population size. Segal (1976) considered a Cobb-Douglas production function and economy-wide data on a set of SMSAs and found that productivity is 8% higher in larger SMSAs (population is more than 2 million) compared to smaller SMSAs (with a population less than 250,000). Finally, Moomaw (1981) criticized these two studies, arguing that their results are both biased upward for different reasons. First, Sveikauskas omitted K, which is probably positively correlated with population size, explaining the overestimation. Then, the upward bias to Segal’s productivity estimates might have been due to underestimation of the capital stock. Moomaw re-estimated these results introducing a theory of firm behavior that incorporates the firm’s choice of city size. He found that a doubling in population size would increase productivity by only 2.5%.

2. The Annual Survey of Manufacturers from the U.S. Census Bureau (1990) reports book value of capital assets for 2-digit industries by state. However, this measure is not corrected for price level changes. An alternative is to estimate the level of capital stock by summing investment of different vintages after adjustment for depreciation rate, technical change and inflation. This is also called the perpetual inventory method as used by Hulten and Schwab (1984) at the regional level, and Segal (1976) at the city level, and discussed further below.

3. The last method of capital stock estimation assumes that non-labor costs, which are equal to the value of capital services, are simply the difference between value added and labor cost. Unfortunately, this method is not better than the perpetual inventory approach, because labor costs are themselves proxies.