3.1.2A General Empirical Framework for Measuring the Returns to IT capital

As stated by Brynjolfsson and Hitt (1995), most of the empirical literature on IT and productivity has used a production function framework to econometrically estimate the effects of IT capital on output and productivity. In general, the theory of production states that firms transform inputs (Z) into output (Y) via a production function (F), with embodied technical progress

Y = A F (Z)(3.6)

where A represents the Solow residual, which captures the effects on output not explained by the explicit use of inputs (e.g., capital and labor). To estimate the specific effects of IT capital input on output, many authors have separated total capital into IT capital (KIT) and traditional or “non-IT capital” (KNIT). If L denotes labor input², then

Y = F (KIT, KNIT,L)(3.7)

A conventional form of the production function is Cobb-Douglas. Brynjolfsson and Hitt (1995) have shown that the use of a less restrictive translog production function does not significantly change estimates of IT elasticity and marginal product. Thus, the following Cobb-Douglas production function is frequently used in the literature

Y = A.KNIT α 0 KIT α 1 Lβ(3.8)

where α0, α1 and β represent the output elasticities of traditional and IT capital and labor hours, respectively. Hence, α1 is also the marginal product of IT capital, which represents the percent change in output due to a 1% change in IT capital input. Taking logarithms and adding an error term (ε), the econometric form of (3.8) is

ln(Y)= ln(A) + α0 ln(KNIT) + α1 ln(KIT) + β ln(L) + ε(3.9)

Using national, industry or firm specific datasets, authors have been able to empirically estimate the parameters of this equation (α0, α1 and β). To determine the effect of IT capital on productivity, both sides of equation 3.8 are divided by L, assuming constant returns to scale (α0 + α1 + β = 1):

ln(Y /L) ≅ TFP + α0 ln(KNIT/L) + α1 ln(KIT/L)(3.10)

where TFP stands for Total Factor Productivity. Thus, information technology capital can boost labor productivity in three ways: (1) accumulating IT capital, which increases capital deepening (K/L,) (2) increasing TFP in the computer-producing sector, (3) increasing TFP in the computer-using sector. Later in this chapter I will describe some empirical studies that have adopted this way of measuring the return to IT capital.

This framework is very simple for the sake of clarity. Various authors have considered different extensions. For instance, computers might earn a “supernatural” rate of return, which will increase the contribution of computers to output growth even if the share of computers is small. Furthermore, the social return to computers might be greater than the private return because of externalities associated with investment in information technology such as knowledge spillovers. Assuming these spillovers are greater when IT activity is denser, I will investigate this hypothesis in the second part of this dissertation (chapters 6,7 and 8). I will then measure the impact of the density of information technology on labor productivity at the county and state levels. In the next section I discuss the different theoretical explanations of the productivity paradox.