Estimation Framework

The investigation approach in this chapter is to measure the contribution of ICT infrastructure to long-term economic growth within the framework of a cross-country growth analysis in the 1980-2010 period. For this purpose we include the variable for ICT infrastructure (as constructed in section 3.2) to the commonly used cross-country regression model of MRW (see MRW 1992).

The MRW model augments the neoclassical model of Solow (1956) by considering human capital.

By including the ICT infrastructure variable we, in turn, extend the MRW model.

Being a popular structural model for the evaluation of long-term growth across countries, the MRW model has been modied by several authors since its appearance in 1992. These modi-cations concerned either the model structure or the usage of dierent methods and approaches to solve the model. Extensions of the MRW model have been conducted by several authors, e.g.

Knowles and Owen (1995) by adding health capital, Ram (2007) by including IQ measure or Aixalá and Fabro (2007) by institutional indicators. The objective of these modications has often been to increase the explanatory power of the model.

The standard Solow model of growth is based on the aggregated production function of Cobb-Douglas type with constant returns to scale. MRW augment the model by adding human capital as further production input. The extended production function is of the form:

Yit=AitK_it^ψH_it^ηL^1−ψ−η_it , (16)

where Yit denotes the real output, Kit denotes the stock of physical capital, Hit represents the stock of human capital,L_itdenotes the supply of labor, whileA_itrepresents the technical progress of country iin time period t. Furthermore ψ and η measure the output elasticity with respect to physical capital and human capital, respectively. MRW assume constant exponential rates for labor and technology:

L_it=L_i0·e^nit, (17)

A_it=A_t=A₀·e^gt, (18)

where ni is the exogenous rate of growth of the labor force in countryi and g is the exogenous rate of technology growth. The latter is assumed to be constant across countries. Thus, it can be derived that physical capital and human capital expressed in eective units of labor evolves as follows:

k˙it =skiyit−(nit+gt+δt)kit, (19) h˙it =shiyit−(nit+gt+δt)hit, (20) where the small letters kit= _A^Kit

itLit,hit = _A^Hit

itLit andyit= _A^Yit

itLit denote quantities per eective labor unit. skiandshipresent the rate of accumulation of physical and human capital of country

i, respectively. Additionally, both types of capital depreciate at the same rateδi. The existence of diminishing returns to capital implies that ψ+η < 1. Under these initial conditions, the capital follows a convergence path to the steady state (k^∗_i, h^∗_i) given by the system of equations:

k^∗_i = s^1−η_ki s^η_hi ni+g+δ

!_1−ψ−η¹

, (21)

h^∗_i = s^ψ_kis^1−ψ_hi ni+g+δ

!_1−ψ−η¹

. (22)

Substituting equation (21) and equation (22) into the production function and taking logs we could express the equilibrium level of income per capita in two alternative ways. Firstly, as a function of investments in human capitalsh:

ln Y_it

Lit

= lnA₀+gt− ψ+η

1−ψ−ηln (n_i+g+δ)_i+ ψ

1−ψ−ηln (s_ki)+ η

1−ψ−ηln (s_hi). (23) Secondly, as a function of the human capital level h^∗_i:

ln Y_it

Lit

= lnA0+gt− ψ

1−ψln (ni+g+δ)_i+ ψ

1−ψln (ski) + η

1−ψln (h^∗_i). (24) For estimation the choice between equation (23) and equation (24) depends on whether the available data on human capital correspond more closely to the rate of accumulation [...] or to the level of human capital (MRW 1992, p. 418).

The short-run dynamics that is the convergence of income per eective labor to its steady-state level is given by:

ln (yit)−ln (yi0) =θln (y^∗_i)−θln (yi0), (25) where θ = 1−e^−λit

, and λi measures the rate of convergence to the long-term equilibrium.

Equation (25) implies that the change of income per eective labor is a function of the determi-nants of both the steady state y^∗ and the initial initial level yi0 of income per eective unit of labor. Substituting for the steady state expression y^∗ in equation (25) we get:⁶⁸

ln (yit)−ln (yi0) = θψ

1−ψ−ηln (ski) + θβ

1−ψ−ηln (shi)−θ(ψ+η)

1−ψ−ηln (ni+g+δ)_i−θln (yi0), (26) The growth equation (26) has been estimated by MRW in their examination for a cross section of countries in the period 1965-1980. According to Ram (2007), the regression model used by MRW (1992, p. 426, Table V) can be written as:

68 See MRW (1992, pp. 422-423) for a detailed explanation of the procedure.

ln(^Y_Y¹⁹⁸⁵

1960)_i =α+β₁ln(Y₁₉₆₀)_i+β₂ln(n+g+δ)_i+β₃ln(I/GDP)_i+β₄ln(School)_i+u_i, (27) where ^(Y1960)i and (Y1985)_i denote the average income of working-age persons from country i in the years 1960 and 1985. Furthermore, ni is the growth rate of the working-age population, g the rate of technical change and δ the depreciation rate of physical capital. The value of g+δ is usually assumed to be 0.05 and constant across the countries (see e.g, MRW 1992, Knowles and Owen 1995). In the investigation of MRW (1992), (I/GDP)_i denotes the average ratio of investment over the period 1960-1985 as proxy for physical capital investment (s_ki). (School)_i denotes the average percentage of the working-age population in secondary school over the period 1960-1985 as proxy for human capital investment (s_hi). Furthermore,u_i denotes the error term.

In order to serve our purposes, we modify the model equation (27) in three ways. The rst modi-cation concerns the observation period, which we change to 1980-2010. The second modimodi-cation concerns the variable School, which is only available for an insucient number of countries in the context of our research. Other authors, such as Bechetti and Adriani (2005), use the average schooling years as proxy for human capital investment. This indicator, however, does not take potential decreasing returns to years of schooling into account. For this reason, we use the indi-cator of human capital per worker as suggested by Hall and Jones (1999), which is constructed by the average years of schooling and an assumed rate of return to education. This variable will be formally described in section 5.4.

According to the rst two modications, the model equation can be written as:

ln(^Y_Y²⁰¹⁰

1980)i =α+β1ln(Y1980)i+β2ln(n+g+δ)i+β3ln(I/GDP)i (28) +β₄ln(HC)_i+u_i,

where, analogously,(Y1980)_i and(Y2010)_idenote the average income of working-age persons of coun-try iin the years 1980 and 2010, and(HC)_i denotes the human capital per worker.⁶⁹

As a third modication, we introduce the ICT infrastructure variable in the model of equation (28). As one of the rst, Nonneman and Vanhoudt (1996) propose a further augmentation of the model by explicitly including the (endogenous) accumulation of technological know-how. They suggest including other types of capital (e.g., infrastructure, equipment, other physical capital, human capital, know-how) in order to increase the explanatory power of the model. They further suggest considering technological know-how (in the sense of blueprints for production processes and new products) as any other input in production. The ICT variable, as used in this dissertation, applies to several of the extension types named by Nonneman and Vanhoudt (1996).

Thus, the ICT variable is a proxy for infrastructure, equipment (e.g. end-devices such as PCs) and know-how (due to its ability to reduce information asymmetries). For this reason, the addition of ICT is a meaningful extension of the MRW model. By including the ICT infrastructure variable to the model, the model equation is given by:

69 At this point we are leaving open from which year or years the human capital variable will be calculated.

ln(^Y_Y²⁰¹⁰

1980)_i =α+β₁ln(Y₁₉₈₀)_i+β₂ln(n+g+δ)_i+β₃ln(I/GDP)_i (29) +β4ln(HC)i+β5ln(ICT)i+ui.

We use the model equation, as given in equation (29), in the context of our empirical analyses in this chapter to assess the relationship between ICT and economic growth. In order to obtain robust results, we will also include other known growth determinants as control variables in the model. This serves to examine whether ICT inuences growth only under particular economic, nancial, institutional and/or policy environments. We will explain the variable sources in section 5.4.

As previously mentioned, this analysis suggests an endogeneity problem due to reverse causality between GDP and ICT. To prevent the suspected endogeneity problem, we will apply an instru-mental variable approach, as will be explained in subsection 5.3.3. However, a form of reverse causality can also be assumed from the explanatory variables of capital investment and human capital. For instance, Hanushek and Woessmann (2012) suggest that growth provides added resources that can be used to improve schools. Hence, this could lead to higher human capital.

For that reason, we use the values of human capital and the investment ratio from the initial year 1980. This serves to avoid further endogeneity problems and to prevent biased results of the (IV) estimates.⁷⁰