4.1The Model

This section describes the empirical model used to estimate the returns to IT capital stock and to evaluate the possibility of excess returns. It also discusses the procedure used to estimate the output and productivity growth contributions of IT capital.

4.1.1Estimation of the Returns to IT Capital Stock

The data presented in chapter 2 showed that U.S. businesses have invested heavily in IT equipment during the last two decades. At the origin of this massive investment was there certainly the premise that computer and information technology equipment in general could eventually increase firms’ productivity, simply because this type of equipment was assumed to be more productive than traditional capital. This premise was empirically tested and authors reached different conclusions. On one hand, Berndt and Morrison (1995) argued that aggregate returns from IT investment were not significantly different from that of other types of capital. On the other hand, at the firm level, Brynjolfsson and Hitt (1993) estimated returns to IT investment between 50% and 60%. I intend to use a model derived from the work of Lehr and Lichtenberg (1999) to test whether returns from IT equipment are greater than that of traditional capital. This section describes this model.

To start with, assume that at time t, within state s, industry i transforms capital (K) and Labor (L) into output (Y) according to a constant returns to scale Cobb-Douglas production function and embodied technical progress:

Yits = A Kits α Lits 1- α(4.1)

The parameter α represents the elasticity of output with respect to capital. Next, decompose total capital into information technologyy capital (KIT) and other types of capital aggregated into “traditional” or “non-IT” capital (KNIT). Thus

Kits = KNITits + KITits(4.2)

Equation 4.1, given equation 4.2, now becomes

Yits = A (KNITits + KITits)α Lits 1- α(4.3)

The neoclassical theory postulates that all types of capital earn the same marginal returns. This argument constitutes the null hypothesis that will be tested using this model. Under the alternative hypothesis, the return to IT capital differs from the return to traditional capital and is most likely greater. Let parameter θ capture the “excess productivity” from IT capital. Thus equation (4.3) becomes

Yits = A.[KNITits + (1+θ ). KITits]α.Lits 1- α(4.4)

I will test the “excess returns” from IT capital hypothesis H1, which is derived next.

Replacing KNIT by K – KIT in equation 4.4 and dropping the subscripts for the sake of simplicity leads to

Y = A [ K- KIT + (1+θ) KIT ] α L1- α ⇔

⇔Y = A [K + θKIT ] α L1- α

⇔Y = A [K (1+ θKIT/K)] α L1- α(4.5)

Taking logarithms, we can write

⇔ln(Y) = ln(A) + α ln [ K (1+ θKIT/K)] + (1-α) L(4.6)

Finally, letting IT% represent the ratio of IT capital to total capital (KIT/K)

ln(Y) = ln(A) + αln(K) + αln[1+ θ.IT%] + (1-α)ln(L)(4.7)

The null hypothesis states that all types of capital earn the same returns, net of depreciation and other costs associated with each type of capital asset. The first order condition for profit maximization requires that the ratio of the marginal products of IT capital to traditional capital be equal to the ratio of the user costs of these types of capital. This hypothesis refers to the equilibrium point A in figure 3.1. If the ratio of returns were not equal to the ratio of user costs, then firms would be better off investing in the type of capital that had higher returns, and less on capital equipment with lower returns. Thus,

MPKIT / MPKNIT = RKIT/ RKNIT

⇔1+θ = [(r + δKIT - πKIT) pKIT ] / [(r + δKNIT - πKNIT) pKNIT ](4.8)

where MP is the marginal product, R is the user cost of capital, r measures the discount rate common to all types of capital, δ is the depreciation rate, π is the expected rate of capital gain (or loss in the case of IT capital), and p is the purchase price per unit of capital. Various authors have reported different estimates of user costs, mainly because they considered different values for r, δ and π. The ratio pKIT/pKNIT is set to unity because the two types of capital are measured in dollar values so that their prices are both $1. Table 4.1 reports various estimates of the elements of the user costs according to different authors’ calculations. Averaging these estimates and replacing them in equation 4.8 leads to a value for the ratio of user costs of capital between 3 and 6, which is also equal to 1+θ. Lehr and Lichtenberg chose 5 as an upper bound estimate of θ. The null hypothesis of no excess returns then becomes a test of θ=5. If θ is significantly greater than 5, then the null hypothesis is rejected and the alternative hypothesis of excess returns to IT capital cannot be rejected.

Interestingly, Lehr and Lichtenberg argued that as long as IT% is small (in the order of 2%), it is possible to substitute αθ (IT%) for α ln(1 + θIT%).³ Consequently, equation 4.7 becomes:

ln(Y) = ln(A) + α ln(K) + αθIT% + (1-α) ln(L)(4.9)

From equation 4.1, the growth in productivity not explained by inputs or total factor productivity (TFP) is

TFP = A = Y/ (Kα L1- α)(4.10)

Taking logarithms and replacing TFP in equation 4.9 leads to

ln(TFP) = ln(A) + αθIT%(4.11)

Also, dividing both sides of equation 4.5 by L and taking logarithms

ln(Y/L) = ln(A) + α ln(K/L) + αθIT%(4.12)

Table 4.1Values of Discount Rate, Depreciation and Price Appreciation Estimated from Various Sources

Variable	Source	Estimates	Mean
Risk-adjusted discount rate r	Lau & Tokutsu (1992) Oliner & Sichel (1994)	0.07 0.12	0.10
IT capital Depreciation rate δKIT	Kiley (1999) Lau & Tokutsu (1992) Whelan (1999) Oliner & Sichel (2000)	0.12 0.20 0.22 0.30	0.21
Non-IT capital Depreciation rate δKNIT	Whelan (1999) Lau & Tokutsu (1992)	0.13 0.05	0.09
Rate of price depreciation for IT capital πKIT	Lau & Tokutsu (1992) Kiley (1999) Oliner & Sichel (2000)	-0.15 -0.24 -0.34	-0.24
Rate of price appreciation for non-IT capital πKNIT	Lau & Tokutsu (1992)	0.05	0.05

Under the null hypothesis of no excess returns to IT capital, the share of IT capital (IT% or IT ratio) will not increase TFP and labor productivity according to equations 4.11 and 4.12, respectively (αθ = 0). However, if the null hypothesis is rejected, then TFP and labor productivity might increase with the share of IT capital (αθ > 0).

In this study, I use a pooled cross-section dataset on industry variables at the state level between 1977 and 1997. Econometric analysis of pooled data requires the introduction of fixed effects or dummy variables for years, industries and states. These fixed effects will control for exogenous differences among years (γt), industries (λi), and states (νs). The first Cobb-Douglas production function that will be estimated at the national, industry and state levels is

Yits = A KNITits α 0 KITits α 1 Lits β (4.13)

Taking logarithms and introducing dummy variables to control for fixed effects, the least squares dummy variables (LSDV) functional form is:

ln(Yits) = Σγt-1 + Σλi-1 + Σνs-1 + α0 ln(KNITits) + α1 ln(KITits) + β.ln(Lits) + εits(4.14)

A simple test of whether IT capital is productive is to test the null hypothesis H0: α1 >0. Then, equation 4.9 needs to be estimated. Its econometric form is:

ln (Yits) = γt-1 + λi + νs + α.ln (Kits) + α.θ.(IT%)its + (1-α) ln (Lits) + εits(4.15)

where α0 and α1 measure the output elasticities of traditional and IT capital respectively. If θ is significantly greater than 5 then the hypothesis H0 of similar returns for IT and traditional capital would be rejected.