Growth regression revisited: R&D promotes convergence?

Abstract

Barro and Sala-i-Martin (2004) analysed the empirical determinants of growth. They used a cross-sectional empirical framework that considered growth from two kinds of factors, initial levels of steady-state variables and control variables (e.g. investment ratio, infrastructure). Recent literature suggests that Generalized Method of Moments (GMM) estimation of dynamic panel data models produce more efficient and consistent estimates than Ordinary Least Squares (OLS) or pooled regression models. Following Cellini (1997), we also consider co-integration and error-correction methods for the growth regression. We extend the previous research for Asian countries of Kim (2009) to developed countries. Following the implications of semi-endogenous growth theory, we regressed output growth on a constant, 1-year lagged output (initial income) and the determinants of steady-state income (investment rate, population growth, the quadratic (or linear) function of Research and Development (R&D) intensity). The regression suggests faster significant convergence. This contradicts with that of Mankiw et al. (1992), which asserts that the speed is lower when considering broad concept of capital including human capital. The coefficients for the determinants of steady-state income, especially for the quadratic function of R&D intensity, are significant and occur in the expected direction. Our results suggest that adopting appropriate growth policy, an economy can grow more rapidly through transition dynamics or changing fundamentals.

Notes

¹ In this article, we consider Canada, France, Japan, UK and US. Germany is substituted for Canada because of structural change of Germany in 1990s.

² The number of US scientists and engineers engaged in R&D increased from about 0.75% of the labour force in 1993 to around 1% in the 2000s.

³ Pioneering studies for growth and R&D were performed by Uzawa (1965), Shell (1966, 1967) and Phelps (1966).

⁴ Caselli et al. (1996) use a GMM estimator in a dynamic panel data model. The first step in the estimation procedure is to eliminate individual effects using the first difference.

⁵ However, per capita output is proportional to the share of R&D in the population of an economy along a balanced growth path. The scale effect exhibited by the model is measured in levels, not in growth. This effect comes from the nonappropriable nature of knowledge. A larger economy provides more potential creators for knowledge.

⁶ A significant negative coefficient on the initial income level coincides with the implications of neoclassical growth theory, as countries close to a steady-state experience a slowdown in growth.

⁷ Generally, scale effects mean that an increase in the number of workers employed in R&D increases the long-run growth rate, as shown in Romer's (1990) model.

⁸ An area of macroeconomic research that has been important is called endogenous growth theory. It focuses on explaining technological growth rather than treating technology as exogenous. However, in Jones’ model, without population growth, per capita income growth eventually stops. For this reason, it is sometimes referred to as a semi-endogenous growth model.

⁹ We mainly focus on the growth rate of output in the process of transition dynamics, and not on the long-term growth rate of output per capita. This makes some difference from the view of Schumpeterian growth theory.

¹⁰ Jones (1995a, 2002b).

¹¹ 1958 Conference on capital accumulation.

¹² World research effort has steadily increased over the last 40 years.

¹³ For example, the average growth rate of the US economy has been very close to 2% per year for the last 100 years.

¹⁴ 

In this equation, we define a new parameter, the speed of convergence: λ = (1 − α)(n + g + d). In between t = 0 and t = ∞, income per capita is the weighted average of its initial and steady-state value. As time goes on, the first term in the bracket has higher weight, since the exponent term 1 − e − λt increases.

¹⁵ Jones (2002b).

¹⁶ Romer (1990) assumed that, in the intermediate sector, firms must pay a sunk cost (price of patent) of product innovation (Jones, 2002a). Aghion and Howitt (2009) assume that successful innovator become an entrepreneur as a monopolist.

¹⁷ We have to decide how much labour works to produce output and knowledge, considering that these two activities employ all of the labour in the economy: L_Y  + L_A  = L. We can denote the equation describing technological progress so that R&D cost is fixed in terms of goods rather than labour. This equation reflects the existence of inter-temporal spillovers ϕ in research activities. All researchers can make use of the accumulated knowledge, A, embodied in existing designs.

¹⁸ To slightly simplify things, assume that λ = 1 and ϕ = 0. None of the results are qualitatively affected by this assumption.

¹⁹ The only difference with the Solow model is the presence of the term (1 − s_R ).

²⁰ A larger economy provides a larger market and has more potential creators of knowledge.

²¹ In this model, per capita output is proportional to the steady-state population. The model exhibits a scale effect in levels. This effect comes from the nonappropriable nature of knowledge.

²² In this article, we consider Canada, France, Japan, UK and US. Germany is substituted for Canada because of structural change in 1990s.

²³ Missing data is very common in panel data sets. For this reason, panels in which group sizes differ are not unusual. These panels are called unbalanced panels.

²⁴ The fixed effects approach takes α_i to be a group (industry) specific constant term in the regression model. The random effects approach specifies that α_i must be a group (industry) specific disturbance in the regression model.

²⁵ Islam (1995) divides the total period into 5-year time increments. The main reasons for this are that errors are less influenced by cycle and less likely to be serially correlated.

²⁶ We explain the derivation of this regression equation in detail again. We assume that the path of income follows:

The first argue that (y − y*) grows at a rate of −λ. The second means that as time passes, y has more component of y*. If we also assume common balanced growth path level of (log) income y*, we get the following growth regression for unconditional convergence:

The value related with long-run level of income is captured by α. This growth regression is considered as the case of unconditional convergence. If we admit the fact that each country converges to his own level of y_i *, the regression function takes the form: If we set the equation for the level of equilibrium output

where X is structural variables, like investment rate, population growth, etc. Then growth regression for unconditional convergence is

If we measure growth per one period, then the regression is

This final equation is mainly used in our panel study. This idea comes from Islam (1995) originally. Again, it is important to distinguish between conditional and unconditional convergence. The former is concerned with the process in which all income levels move to its own long-run target. In our regression, it is expressed as y*. The latter refers to the dynamic transition in which all countries have the same common target. In regression, it is captured by the term α.

²⁷ We use the data for years of schooling and refer to Mincerian wage equation.

²⁸ We can also estimate the growth regression model by SUR with the strong restriction that each coefficient is the same across countries and over time. This estimation is a Generalized Least Squares (GLS) procedure. The result shows that most coefficients are significant (omitted).

²⁹ Sometimes, human capital can be measured in the form of health (Weil, 2008). This includes expected life at birth or nutrition status and so on.

³⁰ To understand this principle, consider an economy that starts out below its steady state. If the share of R&D is permanently increased, the economy is now farther below its balanced growth path and we can expect it to grow rapidly to catch up to this state (Jones, 2002a).

³¹ The time it takes for (y − y*) with a negative growth rate to fall in half is approximately equal to (70/λ in %). The half-life is 70/1.61, or 43 years.

³² In this model, per capita output may be proportional to the world output Y(t) of the economy along a balanced growth path. However, if we assume that the designs for a new product of one country are not fully available in the other countries, Y(t) may denote country-specific output [Y(t) = Y*(t)].

³³ These results also show that in an augmented Solow model, there may be biased estimation from the omission of R&D intensity variables.

³⁴ Kim, 2009.

³⁵ We omit the second term in the RHS of the regression equation because of a problem with insufficient degrees of freedom.

³⁶ In the cases of Japan, UK and Canada, we insert the trend variable into the ADF test equation.

³⁷ To effectively use DF test, we need to have a lot of observations, and this is not very common in panel data sets. We consider the possibility that we do not reject the null hypothesis because we are running these tests on relatively few observations.

³⁸ Originally, they derived the conditional ECMs from the VAR (p) model.

³⁹ Kim (2009).