7.1.1Model 1: The Concentration of IT Activity and Labor Productivity

States have different profiles regarding the location of their IT activity. This model assumes that the differences in state labor productivity can be explained by differences in the localization patterns of IT activity across states. The concept of “employment concentration” is introduced, as well as the definition of the ratio used to measure it. This ratio is computed for IT and non-IT employment concentration. The purpose is to evaluate the effect of the concentration of IT activity relative to non-IT activity on state labor productivity.

States differ not only in their physical sizes and their total numbers of employees, they also differ in their spatial distributions of population and workers. Neoclassical theory argues that employees should be evenly distributed across all areas, including counties within states and across acres within counties). The concentration ratio represents the deviation of the distribution of employees across counties from the neoclassical distribution given by the state’s global employment density. In other words, it is the ratio of the sum of county employment densities, weighted by their share of state’s employment, and state overall density. For a given state, s, the concentration ratio (CON) is given by:

CONs = Σc [(nc/ac).(nc/ns)] / (ns / as)(7.1)

where nc is employment in county c, ac is the number of acres in county c, ns is total employment in state s and as is the total number of acres in state s. After rearranging,

⇔CONs = (Σc nc 2 / ac) / ns 2 / as(7.2)

A value of 1 for the concentration ratio will indicate an even distribution of employment across counties in state s. The higher the value, the more employment is concentrated into few counties. The maximum value depends on the physical sizes of the counties in state s. Although this measure is not perfect, it has the merit of expressing at the state level what is happening across counties within each state. It is similar to the location quotient, which may be computed at the county level and does not take into account the area of counties (only their shares of employment in a given industry compared to the state’s share).

According to neoclassical theory, with decreasing returns to labor, the higher the concentration ratio is in a given state, the lower should be its labor productivity. Based on the work of Graham (2000), using a simple Cobb-Douglas production function, I intend to test the validity of this neoclassical premise by estimating the following equation:

lnps = lnA + α lnkns + β lnCONs(7.3)

where ps is a measure of labor productivity in state s, namely output per worker, which depends on total factor productivity as captured by the term lnA, the state’s capital to labor ratio represented by kns, and the measure of employment concentration in state s as defined previously by CONs. The elasticity of capital deepening (kns) in state s, represented by the parameter α, is expected to be close to a third, which is the value for the share of capital usually observed nationally. Parameter β, the elasticity of productivity with respect to employment concentration, is expected to be negative under the neoclassical theory of decreasing returns to scale to labor density. If the sign of β is positive and significant, then it must be that there are some externalities associated with employment concentration, which increase labor productivity. According to previous findings in the field of regional economics, I expect to find a positive and significant sign for β.

However, my goal in this study is not to limit my analysis of employment location and productivity to total employment only, but to estimate the effect of IT employment localization relative to traditional employment. In order to do so, I first need to compute the concentration ratios for each type of employment in each state. Using the same definition of concentration as in equation 7.2:

CONs,e = ( Σc nc,e 2 / ac ) / ns,e 2 / as(7.4)

where e indexes IT or non-IT employment (e=1 and e=2, respectively). However, since I am interested in the relative effect of IT vs. non-IT employment concentration on state productivity, I will consider the ratio of those two employment concentration measures as defined by RCON = CONs, IT / CONs, NIT. Using the same production function form as in equation 7.3, I will estimate the effect of RCON on productivity.

ln ps = lnA + αs lnkns + δ lnRCONs(7.5)

A positive sign for δ will indicate that the IT employment concentration has a greater effect on productivity relative to traditional employment concentration. This elasticity δ also indicates by how much state labor productivity will increase if the ratio, RCON, doubles.