Consider a neoclassical growth model with R&D; investment. Output is produced wi

Question

Consider a neoclassical growth model with R&D; investment. Output is produced with a Cobb-Douglas production function Y = K^alpha (AhL)^1 - alpha, alpha Element (0, 1) where Y is total output, K is physical capital stock, h is human capital per worker, L is total number of workers, and A is a technology index. Assume h is constant and exogenous. Total output can be used for consumption (C), capital investment (I) and research (R). Capital is accumulated according to K = I - delta K, 0 0. Assume that there is no population growth in this economy. (a) What is the role of the terms (1 - A/A*) and epsilon in equation (5)? Why it would be a better way for the total R&D; expenditure (R) to enter the evolution of technology in a per worker term? Explain. (b) Set up the Current-Value Hamiltonian for the representative worker and then derive the associated first-order conditions as well as the Euler equations for the representative agent. (c) Define a = A/A* as the relative productivity of the country. Define the balanced growth path (BGP) in this economy and solve the system. What is the BGP value of the relative technology of the country, A/A*? (d) Suppose that due to the development of internet, epsilon becomes larger. How would this affect the BGP investment in R&D;?

Explanation / Answer

Ans-

Endogenous growth model stresses the role of education for sustained growth. Lucas presents human capital for explaining unlimited growth by increasing the efficiency of education. Jones also gives similar model incorporating human capital. So-called Lisbon Agenda set by EU features the growth gap between EU and the U.S. The first look at the European case reveals the deficit in tertiary education investment.

We examine simple model and derive important implications [1-5].

Some data exist on the relationship between research and development (R&D) and input to education (years to schooling, expenditures). R&D is presumably a very important input to the production function for knowledge. We can also see plots of R&D intensities showing increasing trends in the five most highly developed countries (G-5 countries) from the 1960s to 2005.1 During this period, resources devoted to R&D (relative to GDP) steadily increased. Not only has the share of R&D in terms of goods increased, but the share in terms of labor has also increased.2 We want to know the relationship between research input and human capital.

In Romer’s endogenous growth model, physical capital itself is viewed as knowledge.3 Knowledge is created via a R&D process [6]. In R&D based growth models, imperfect competition is necessary for compensating the rewards for successful innovations. Funke and Strulik argue that instead of R&D, only human capital affects steady-state growth. Sequeira develop this idea and derive the fact that education is most welfare improving. In this study, we seek this hypothesis by theoretical and empirical study. In addition, we compare the growth effect of research with that of human capital. We performed similar study using East Asian economies’ data set [3].4

Mankiw, Romer and Weil belong to the latter group. In this study, we are interested in the second issue [7]. They included human capital into aggregate production function, and broad concept of physical capital, then find the speed of convergence to be relatively lower than that of Solow’s. Mankiw, Romer and Weil have argued that the augmented Solow model is right in including diminishing returns and in forecasting the same rate of (efficiency) growth across countries. Aghion and Howitt, they include human capital into the category of capital as broad capital. With them, Lucas also emphasizes human capital accumulation as a source of growth [8].

Nelson and Phelps5 and subsequent empirical work by Benhabib and Spiegel describe growth as being driven by the stock of human capital. Krueger and Lindahl provide the implication that human capital stocks only matter for catching up, since their correlation disappears when restricting to OECD countires. Hanushek and Woessmann emphasize the significance of the quality of education like conditional test score. Acemoglu delivers the issue of low-development traps by the complementarity between R&D and education investments [9,10]. Barro and Sala-i-Martin analyzed the empirical determinants of growth. They used an empirical framework that considered the growth from two kinds of factors: initial levels of steady-state variables and control variables (e.g., the ratio investment, infrastructure, life expectancy, degree of democracy etc.), using cross-sectional regression methods. Cross-country growth regressions concern the significant correlations between the growth rate of per capita income, the initial value of income, and structural variables [1,11]. Jones showed that U.S. growth rates do not exhibit large persistent changes, although the determinants of long-run growth highlighted by the endogenous growth model do exhibit these changes [12].6

Jones, Kim decomposed the growth rate of the US and South Korea considering education, and concluded that average growth rate consists of transition dynamics and long-run equilibrium growth rate [13]. This paper is organized: Section 2 devotes to search of previous studies and presents basic econometric models. Section-3 performs diverse estimation methods for detecting research effort on growth and get more reliable estimates for convergence. Section 4 summarizes and concludes.

Empirical Analysis: Growth Regression

Previous literatures

Many economists have recently presented sophisticated empirical analysis for cross-country growth regression, including Islam, Caselli, Esquivel, and Lefort, Cellini, and Barro and Sala-i-Martin [1,14-16].

These studies raise two basic methodological issues.

Jones shows conditional convergence by depicting growth rates and relative income levels of each country to that of the US. Relatively poorer countries compared with income levels of their own steady state incomes reveal high growth rate [4,5].

The first objection to Mankiw, Romer, and Weil is that they assume a country’s initial efficiency is uncorrelated with the explanatory variables [7]. Islam solves this problem by using panel data. The estimates are different from previous cross-sectional results, implying that the fixed effects problem is serious. When fixed effects are substantial, OLS yields inconsistent and inefficient estimates. They cannot disentangle the individual effects from trend effects [14].

In this paper, we solve this problem further considering the endogeneity of RHS variables in growth regression by using Arellano and Bond’s GMM estimation [17].

The second objection to standard growth regressions is that they assume a country’s steady-state determinants are fixed over time. Cellini solves this problem by using co-integration and error-correction methods. We apply the same tools to test endogenous growth theory [16]. Sarno also takes ECM approach. He shows that long-run equilibriums of G7 countries follow nonlinear error corrections [18]. In addition, he asserts that there exist significant spillovers within the G7. However, he used R&D data for only measuring productivity (or technology). In contrast to this, in this paper, we explicitly consider R&D data in the framework of endogenous growth theory.

The third extension is that of Liu and Stengos [19]. They recognized the nonlinearity of the effects of education (enrollment in the secondary school) on growth rate, and used semi-parametric approach in growth regression.

In summary, these previous studies neglect the implication of Romer’s endogenous growth theory. The growth of per capita income (or labor productivity) is associated with knowledge creation activity [20]. In this context, Ha and Howitt test the implication of Schumpeterian growth theory by co-integration and simulation. However, they do not use the standard growth equation setting.

Meanwhile, empirical growth studies use human capital variable for explaining cross-country income differences. MRW, Lucas and Jones, Romer are good examples [4,5]. In this study, we compare the effects of education with those of research and development. Benhabib and Spiegel show that growth is correlated with initial level of human capital.

In this paper, we incorporate related variables such as R&D intensity and R&D expenditures into previous neoclassical growth models. According to R&D based growth models, increase in R&D inputs enhances the rate of growth. We examine and test this hypothesis in this empirical study.

Economic growth models: exogenous vs. endogenous

Stylized facts for growth are summarized by Kaldor7. Where y97 is per capita GDP in 1997 (relative to the U.S.), g is the average annual growth rate, sK is the physical investment rate, n is the population growth rate, and y* is the steady state income per capita (relative to the U.S.) (Table 1).

Table 1: Fundamental parameter values.

Closed form solution of the slow models: We first consider a neoclassical growth model with exogenous technological progress. This enables us to understand endogenous growth theory more easily. The production technology for the final-goods sector (Y) is expressed by an aggregate Cobb-Douglas production function. The steady-state growth rate of A (technology) and output are constant and given by:

gA = gy (= gk) (1)

y: output per capita, k: capital per capita

This “Solow model with technological progress” predicts that growth rate is determined by the rate of exogenous technological change. While the two growth rate are the same in this Harrodneutral technological progress case, gy =gA +gk in the Hicks-neutral technological progress case.

But, this model has fatal disadvantage that it cannot explain this source of “manna from heaven” (eg. Exogenous technological progress) Jones incorporates human capital into Solow model [4,5].

Along a balanced growth path, we get:

y*(t) = (sK / n + gA + d)(/1-) h A(t) (2)

where y* is the steady state income per capita, sK is the physical investment rate, gA is the average annual growth rate of productivity, and d is the depreciation rate of physical capital.

hL=H

h=exp(u)

Y=K (AH)1-

where u is years of schooling, is the return to education, H is total amount of human capital.

y(t) = [(sK / n + gA + d) * (1 - e-t ) + (y0 / A0) * (1 - / ) * e-t](/1-) h A(t) (3)

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

Note that income per capita at any time (t) is written as a function of the parameters, percapita human capital and of the exogenous variable A(t).8 This specification leads us to compare cross-country income differences, and gives insight into method for comparing growth rate differences. Neoclassical reference emphasizing (human) capital accumulation is Mankiw, Romer and Weil [7]. Theirs is an augmented version of the Solow model with human capital that slows down the convergence to the steady state by counteracting the effects of diminishing returns of physical capital.

a. Human capital: Lucas presents another version of endogenous model.

Y=K (AH)1-

h=(1-u)h

h/h=g

The increase in human capital per person (h) increases the steady-state income level, and increases growth rate. Human capital accumulates at a speed proportional to the stock of capital. Human capital affects current production, and current schooling time (1-u) affects the accumulation. Finally, education effort produces a positive growth rate in steady state.

We also examine the effects of human capital measured by years of schooling or school enrollment rate on the growth rates.

b. AK: Simultaneous accumulation of human and physical capital: Romer presents another version of endogenous model that consider learning by doing effect. This is called as AK model. Another model that explains non-existence of DRS is as follows [6]

y=k0.5 h0.5

k=sy

h=qy

k=1+(sq) 0.5

The increase in saving rate and investment in human capital per person (h) increases the steady-state income level, and increases growth rate. We can see the saving and investment rate have growth effect as well as level effect.

c. Human capital and R&D in endogenous model: Sequeira presents another version of endogenous model.

h=ahh +bhn1-c

h: human capital per person, hh: schooling, bhn1-c : learning with varieties

Y/Y=(r*-) /

y(t) – y(t - 1) = + y(t - 1) + X(t) + (4)

Here, y*(t) = a+bX, and X is the (row-vector of) determinant of steady-state income, (investment rate, population growth, productivity growth, depreciation rate, etc.).

We estimated the growth regression model by fixed or random effects panel regression with the restriction that each individual country effects exists. In this regression we include the level variable of R&D investment (SR) and human capital (H).9 Their coefficients are positive and significant. We can find that the growth effect of research effort is larger than human capital. Human capital is measured by years of schooling (H, Penn Table) or enrollment in secondary school. SEC, Liu and Stengos10These data can be obtained from Barro and Lee (Table 3) [19,21].11

Table 3: Growth regression including human capital and R&D.

We can see that research has greater effect than degree of education measured by years of schooling or school enrollment rate. A 1% increase in the rate of the square of research intensity causes an 0.02% change in the per capita income.

Table 4 shows that there are causalities from main variables of interest (R&D efforts, lagged dependent values).12 This solves the problem of endogeneity partially, since some lagged variables Grengercause the dependent variables. Whenever the zero-conditional-mean assumption holds for an explanatory variable, we say it is exogenous. In general, a lagged dependent variable model with serial correlation reveals the endogeneity problem. Regression with growth on left-hand side and education on right-hand side raises this problem, too. One way to deal with is to use instrumental varibles (IV) or to proceed to 2SLS. In special, Bils and Klenow emphasize this problem in crosscountry panel regressions for TFP growth equation [22]. We can use sophisticated econometric methods like by Arellano and Bond [17], but we postpone this performance to future research.

Table 4: Granger causality tests.

Contrary to Hausmann and Rodrik, Shleifer and Vishny stress the greater scope for government failure in LDCs, where controls on governments are relatively weaker. We considered the government consumption ration(G)13 as control variables, then estimation results show that the effects of research are smaller, even being negative. The analysis may consider other control variables, such as entrepreneurship and venture capital, and possibly other variables dealing with regulation, in the spirit of Shleifer’s works [23] (Table 5). Shleifer shows the regression output of TFP Growth Equation (Research sR vs. Education SEC). This shows that the effects of research efforts are larger and significant (Table 6), but insignificant when being controlled by the stock of existing human capital (Tables 3-6).

Sample (adjusted): 1999 2006

y97 y60 g(60,97) sK u n (A90)A97 U.S. 1.000 1.000 0.0139 0.204 11.89 0.0096 (1.000)1.000 Korea 0.596 0.111 0.0594 0.326 10.56 0.0110 (0.435)0.750

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.