8.1The Density of Employment and Productivity

First, I intend to approximately replicate Ciccone and Hall’s results regarding the effect of county employment density on state labor productivity, as proposed in section 7.3. The equation to be estimated is:

lnps = lnA + ε lnedus + lnDs(θ)(8.1)

It can by estimated by nonlinear least squares. The parameter θ to be estimated reflects the product of a congestion and an agglomeration effect due to increasing employment density. Estimates appear in Table 8.1. In order to test my capital stock data, I also added the capital per employee variable to the labor productivity regression as:

lnps = lnA + α.lnkns + ε.lneds + lnDs(θ)(8.2)

where Ds(θ) is defined as:

Ds(θ) = [ Σc (nc θ.ac 1- θ)] / ns(8.3)

The estimated value for parameter θ is similar to the one obtained by Ciccone and Hall, with a 95% confidence interval ranging from1.0492 to 1.0592. CH’s value of 1.051 falls into this confidence interval. Furthermore, they found a value of 0.51 for the elasticity of the education variable, which is not far from 0.30 considering that the capital-to-labor ratio may have captured some effects attributed to education by CH.

Table 8.1Estimates of Elasticities from Equation 8.2

	Constant	Capital/labor	Education	θ (own)	θ (CH)
Coefficient	3.563	0.523	0.298	1.054	1.051
Standard Deviation	0.384	0.025	0.071	0.005	0.008

Thus, using my own datasets at the state and county level, I am able to confirm that doubling employment in a county will increase state labor productivity by almost 6%. This brings more confidence to the results presented in the next sections.