Prof. Dr. Thomas Steger Advanced Macroeconomics I Lecture SS 13 5. R&D based Economic Growth: Romer (1990) Introduction The challenge of modeling technological change The structure of the model The long run growth rate The decentralized solution Market imperfections and policy implications
Introduction (1) 2
Introduction (1) Motivation / starting point Neoclassical growth theory: the ultimate engine of growth is technical change (exogenous); Growth accounting: the Solow residual is substantial (qualifications); At the global level there is divergence in international per capita income. 3
Introduction (2) Some empirical evidence (Cameron, Innovation and Growth, 1998) The empirical literature on innovation and growth has found that: The elasticity of output w.r.t the stock of R&D, denoted as β, lies between 0.05 and 0.1. A consensus has emerged that innovation has a significant effect on productivity at the level of the firm, industry and country, whether measured by R&D spending, patenting, or innovation counts. (Cameron, p. 21) Social rate of return (70 to about 100 percent) to business enterprise R&D is far above the private rate of return (10 to 15 percent) (e.g., Hall, 1996; Jones and Williams, 1998). 4
Introduction (3) Aggregate R&D intensities in OECD economies 6 Business enterprise expenditure on R&D (BERD) in 2001 as a percentage of value added in industry 5 4 3 2 1 0 Mexico (1999) Turkey (2000) Greece (1999) Poland New Zealand (1999) Portugal Hungary Slovak Republic Spain Italy Australia (2000) Czech Republic Ireland Norway Canada Netherlands Austria (1998) United Kingdom France Belgium (2000) Denmark (1999) Germany Iceland Korea United States Switzerland (2000) Japan Finland Sweden in % There is substantial variation in aggregate (private) R&D intensities. How can this variation be explained? Potential determinants of R&D spending: [i] human capital; [ii] intellectual property rights; [iii] product market competition; [iv] sectoral structure; [v] public policies (e.g. R&D subsidies). 5
Introduction (4) Romer s analysis rests on three premises (1) Economic growth is driven by technological progress as well as capital accumulation; (2) Technological progress results from deliberate actions taken by private agents who respond to market incentives; (3) Technological knowledge is a non rivalrous input. 6
The challenge of modeling technological change The final output technology may be expressed as Y=F(A,K,L), where F(.) is C² with F(.)/ X>0 and ²F(.)/ X²<0 for all X {A, K, L}. Usual assumption: output technology exhibits CRS in private inputs K and L. Neoclassical theory relies on perfect competition: all factors are rewarded according to their MP. This implies that output is exactly exhausted F K := F(.)/ K denotes the marginal product of capital etc. Any theory which rests on perfect competition, CRS, and premise (2) runs into a fundamental problem Those agents who produce technical change are assumed to react to market incentives and must hence be rewarded. Since output is, however, completely used up by paying wages to labor and rental prices to capital owners, nothing is left to reward researchers. 7
The structure of the model (1) Three sectors (production side) Final-output sector (perfect competition) Machine sector (monopolistic competition) R&D sector (perfect competition) Households Supply labor inelastically Split income into consumption and saving according to KRR Lend financial capital to x-firms (production and blueprints) 8
The structure of the model (2) machine sector R&D sector L households final output sector C households 9
The structure of the model (3) Households The economy is populated by a continuum of mass one of identical households. Each household is endowed with L units of labor services per unit of time, which are inelastically supplied to the market. Households choose C(t) so as to maximize Optimal consumption obeys the well-known Keynes Ramsey rule (KRR) 10
The structure of the model (4) Final output sector ( Y sector ) Firms produce a homogenous good Y (used for consumption or investment). The Y-market is perfectly competitive. The technology is given by i [0,,A]: machine type index A: number of machine types x(i): number of machines of type i Since x(i)=x i in symmetric equilibrium, the above stated technology can be expressed as Y=L Y 1 α Ax α. Using K:=Ax ( total number of machines ) one may write This is a CD-technology with labor augmenting technical change. Increasing A and holding K=Ax constant (by reducing x when A is increased) boosts the productivity of labor. Hence, this technology captures the basic idea that division of labor and specialization makes production more efficient (A. Smith). 11
The structure of the model (4a) Machine index: discrete Machine index: continuous Assumption: Consider three economies Total amount of machines Ax i =R is always the same. However, Y is higher, the higher is A! The above formulation captures increasing returns to specialization. 12
The structure of the model (5) Machine sector ( x sector ) Producers in this sector manufacture differentiated capital goods x(i), labeled "producer durables" or "machines". Production technology: x(i)=k(i) It takes one unit of raw capital to produce one unit of any x(i). The marginal cost of any x therefore equals the interest rate r. As a technical and legal prerequisite for production, firms must at first purchase a blueprint (design). The x-market is hence monopolistically competitive (large number of monopolists producing goods which are imperfect substitutes). It is assumed that x producers rent their machines to Y producers by charging a rental price p x. 13
The structure of the model (6) The R&D sector Firms in the R&D sector search for blueprints ( designs ), which are the technical prerequisite to produce new types of machines. The market for blueprints is perfectly competitive. The R&D technology is given by Notice that the productivity of researchers L A increases with technological knowledge measured by A; see premise (iii) above. There is a double knife edge restriction implicit in this formulation: The partial elasticities of A and L A in the production of A are both equal to unity. 14
The structure of the model (7): General equilibrium A general equilibrium in this economy consist of time paths for the quantities {L Y (t), L A (t), {x(i)} i=0a, A(t), K(t), Y(t), a(t), C(t)} t=0 and the prices {w Y (t), w RD (t), r(t), p A (t), {p(i)} i=0a } t=0 such that Final goods producers, intermediate goods producers, and R&D firms maximize profits at each t [0,..., ]. Households maximize intertemporal welfare. The no-arbitrage-condition holds: p A /p A +π/p A =r. The capital market clears, i.e. a(t)l=k(t)+p A (t)a(t) with K(t)= 0A x(i)di at each t [0,..., ]. The labor market clears, i.e. L S (t)=l D (t) at each t [0,..., ]. The goods markets clear, i.e. x S (i)=x D (i) for all i [0,...,A] and Y(t)=I(t)+C(t) at each t [0,..., ]. 15
The long run growth rate The technology Y=(AL Y ) 1 α K α shows that, along the BGP, this model is equivalent to a neoclassical growth model with labor augmenting technical progress. This implies that the following relations must hold along the BGP: Y=K=C=A=g, where X:=X/X for all X {Y, K, C, A}. According to the R&D technology A=ηAL A the long run growth rate of A is Notice: L A =const. constitutes a steady state! The economically interesting question then concerns the determination of L A. This is the issue we consider at next. 16
The decentralized solution (1) Solu on strategy ( steady state) (1) Starting from the equilibrium condition w Y =w RD, we derive a relation r prod = f(g), which describes equilibrium on the production side of the economy. (2) The KRR r cons =σg+ρ describes equilibrium on the consumption side. (3) Simultaneous equilibrium on the production side and the consumption side, i.e. r prod =r cons, then allows the determination of r and g. 17
The decentralized solution (2) Equilibrium in the labor market We start with the equilibrium condition stating that w Y =w RD. Since the labor market is competitive, labor earns the respective value marginal product (notice that p Y =1) Recall: in symmetric equilibrium, the technology reads Y=L Y 1 α Ax α. How is the price of blueprints p A determined? 18
The decentralized solution (3) Price of a blueprint and equilibrium profits Noting that π and r are constant along a BGP, we may write Along the BGP both π and r are constant! Then p A = t π exp( r(τ t)dτ= π/r (alternatively: p A = 0 π exp( r t)dt= π/r). Profit of the typical x-producer is π=[p D (x) r]x, where p D (x) is the (inverse) demand function for machines Differentiate technology (*) w.r.t. any x. To determine equilibrium profits, we must note that the optimal supply price p S is a mark up (1/α) over marginal costs r (exercise!) From r=αp S, p D =p S =p x (equilibrium in x-market) and noting (**) we get 19
The decentralized solution (4) Equilibrium on the production side The equilibrium condition w Y =w RD can then be expressed as This immediately gives r=ηαl Y. Using L Y =L L A (labor market equilibrium) and L A =g/η (R&D technology) yields Recall that g is the steady state growth rate. This relation describes equilibrium on the production side of the economy. (Interpretation! Why is g and r negatively related?) 20
The decentralized solution (5) Labor market equilibrium I Points to notice: In this plot we vary only L Y holding the other variables (x, A, and r constant). Recall that L A =L L Y. L Y 21
The decentralized solution (6) Labor market equilibrium II The consequences of a wage subsidy can be seen from the FOC of the typical R&D firm (exercise: set up the FOC for max{p A A-(1 s A )w RD L A }!) L Y 22
The decentralized solution (7) The long run equilibrium growth rate Solving r=ηαl αg and r=σg+ρ for g gives g=(ηαl ρ)/(σ+α). Since growth cannot turn negative in this model, the complete solution for the long run growth rate is Long run growth obviously requires that the economy is large enough in the sense that ηαl>ρ ( critical threshold for labor). There is a scale effect since, provided that ηαl>ρ, larger economies (size being measured by L) do grow at a higher rate. (Economic intuition!) In the original Romer model there is human capital and unskilled labor such that both the threshold effect and the scale effect are associated with human capital instead of (unskilled) labor. 23
The decentralized solution (8) Illustration (s A =0) Exercise: draw this graph for, say, s A =0.2 instead of s A =0. What happens to g and r in steady state? Economic intuition! 24
Market imperfections and policy implications The social planner s solution is given by (see lecture notes) The decentralized growth rate is too low: g M <g S. Two market imperfections Intertemporal knowledge spill over effect (see R&D technology). This social benefit is not reflected in the market price p A =π/r. Typical machine producer realizes a monopoly profit (remember: this imperfection is necessary for market-based R&D). He cannot, however, appropriate the entire consumer surplus. Again, the market price of blueprints p A =π/r falls short of its social value. Both imperfections give rise to suboptimally low R&D investments. What are appropriate policy measures to correct for the market imperfections? 25
The Jones (1995) Model Jones critique The input into the R&D sector (at the level of the USA and at a global level) has risen in the past decades. The growth rate of TFP does not, however, increase over time. Hence, Jones (1995) has modified the Romer (1990) model to get rid of the scale effect implication. 26
The Jones (1995) Model The R&D technology and the steady state growth rate Jones (1995) assumes that the labor force grows at exponential growth rate n (as in the neoclassical model). The (aggregate) R&D technology has the following shape The steady state growth rate can be easily determined (only information about the R&D technology are required) 27
Notation and abbreviations Notation A 0<α<1 number of blueprints (=number of machine types) constant technology parameter w x(i) i [0,,A] Y wage rate number of machines of type i machine type index final output C consumption η>0 constant technology parameter C:=dC(t)/dt first derivative of C(t) w.r.t. time π operating profit of x-producer F K := F(.)/ K marginal product of capital ρ>0 time preference rate g M long-run growth rate (market economy) σ>0 constant parameter g S long-run growth rate (social planner s solution) Abbreviations K:=Ax L L A L Y p A p S, p D p x r an index of overall capital units of labor services per period of time amount labor devoted to R&D labor devoted to Y-production price of a blueprint supply price, demand price (for x-goods) equilibrium price of x-goods interest rate R&D BERD CRS KRR MP prod cons BGP research and development business enterprise expenditure on R&D constant returns to scale Keynes-Ramsey rule marginal product production side consumer side balanced growth path 28