A R

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A RD Based Real Business Cycle Model

• Objectives
• Combine endogenous growth and Real Business
  Cycle (RBC) models.
• Focus on ties between RD innovation and
  financing
• Innovation shocks tie to business cyclein ways
  different from standard models
• Build a RBC model consistent with U.S data
• New Keynesian RBC model with staggered price
  adjustment

2

• Related Literature
• Prescott and Kydland(1982) neoclassical Solow
  model with exogenous technology shock
• Problems
• Cannot explain technology regress
• Contractionary effect in staggered price model
• RBC with Endogenous growth literature
• Howitt arrival of new general technological
  knowledge retards current growth
• Canton(2002) An i.i.d shock is introduced into
  the Luca-Uzawa models human capital accumulation
  equation
• Stadler(1990) with endogenous technical change,
  both real and money models yield very similar
  output processes. Learning-by-doing is the source
  of externality

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• Problems
• RD is countercyclical
• increasing return is an indispensable assumption
• steady state does not exist
• This paper tries to build up an alternative
  endogenous business cycle model
• Introduces 2 shocks in RD sector
• Random participation, e.g. change in outside
  opportunity
• Financial intermediation, e.g. unsatisfactory
  research progress, venture capitalist withdraw
  capital.

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General Equilibrium Mdel
Representative Consumer
Nt(z)
Ct
Kt-1(z)
Kt-1
Intermediate Sector
RD
Capital Producing sector
It
Yt(Z)
Final Good
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Consumption

• The representative household chooses to max
• Focs

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• Final Good Sector
• Dixit-Stiglitz(1977) CES production
• Optimal demand for intermediate good

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Intermediate Good Sector

• a continuum of monopolistically competitive firms
  owned by consumers, with compact support z
• Cobb-Douglas production
• Cost-minimization gives
• Where the markup is the inverse of real marginal
  cost
• Following the Calvos setup, the opportunity to
  adjust prices follows a Bernoulli distribution
• Define as the probability of keeping prices
  constant and the probability of
  changing prices

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• Firms choose price to maximize expected profit
• Capital Production

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• The zero profit condition gives
• RD Sector (Aghion and Howitt (1992))
• Each intermediate sector j is monopolized by the
  holder of a patent to the latest technology
  , produced by a continuum of research firms
• is cutting-edge technology in economy
  a template for all research firms.
• Any innovation raises by a constant factor
  of in the intermediate sector

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• At any point in time, there will be a
  distribution of productivity parameters across
  the sectors of the economy, with support
  , shifting rightward over time
• However, the long run distribution of relative
  productivity parameters will be
  stationary, see proposition 2.
• The research sector is portrayed as in the
  patent-race literature that has been surveyed by
  Tirole and Reignanum. A typical firm maximizes

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• FOC
• The value of is determined by the following
  asset equation
• is firm js final good input
• is the value of the firm
• is government subsidy to research

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Random Participation

• Rochet and Chone(1998) an adverse selection
  model with random reserved utility
• randomness can be change in outside opportunities
• it is assumed that the intermediate firms
  contract with two types of research firms such
  that an inefficient research agent has higher
  cost
• Pdf of participation

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• Incentive compatibility constraints
• first order necessary conditions are
• participation probability is randomized by
  assuming that follows a stationary first order
  Markov process
• This shock can be interpreted as if a Dutch
  Diseases-brighter prospect at an outside sector
  drags away resources for production and RD.

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Financial Intermediation

• assume that the risk neutral intermediate firms
  own the RD firms
• RD is financed by raising capital in the market
• King and Levine(1993) Letting f be the agency
  cost of identifying capable researcher
• be the probability of raising sufficient
  capital
• new arbitrage equation
• effective wage rate is increased by a factor of
  due to adverse selection

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• assume that follows a stationary markov process,
  perturbed by an i.i.d shock
• Reason
• investors are sensitive to RD news, for
  instance, new formula, new design and research
  progress. A negative shock can be unexpected
  delay of new invention, unsatisfactory research
  progress, termination of a project or competitors
  patent
• Investment was stimulated by waves of technology
  break-through news. A positive shock makes fund
  raising easier
• The capital accumulation equation can be
  rewritten as

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CalibrationParameters Specification

• the steady state value of labor, we set it to
  1/3, i.e., a third of total endowment of time.
• is 0.64
• gross interest rate equal to 1.01 per quarter
  (Prescott and Kydland 29) and 1.04 annually
• The depreciation rate 0.35
• coefficient of intertemporal substitution is
  0.5-0.9, meaning the representative household is
  slightly risk averse

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• Technology shock. interest rate policy surprise,
  random participation outside opportunity and
  financial intermediation shocks AR(1)
  coefficients are 0.95, 0.75, 0.75, 0.5
  respectively
• Gali, Gertler, and Lpez-Salido(2001), we set
  and equal to 1.5 and 0.5 respectively
• coefficient in Phillips relation is 0.014
• The steady state consumption-output ratio,
  investment-output ratio, government-output and
  RD-output ratios are set to 0.6, 0.15, 0.2 and
  0.05 respectively

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• The capital production function
• where can be interpreted as the adjustment
  cost coefficient
• The RD arrival
• The Poisson arrival rate exhibits diminishing
  return, which implies that invention becomes more
  difficult as the degree of complexity increases
  over time

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Results

• Typical perturbances include the famous Prescott
  and Kyland technology shocks (Prescott and Kyland
  (1982)), government expenditure surprises (King
  Plosser and Rebelo (1988)), money shocks (Gertler
  and Gali (1999)) and sunspot activity (Farmer and
  Guo (1994))
• the impulse response functions of traditional
  technology, government shocks are presented in
  figure 1.1 and figure 1.2
• One typical observation of this class of
  staggered price model is the countercyclical
  markup

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• The increase in derived demand drives up wages,
  marginal cost and thus depresses markup
• A Productivity shock reduces marginal cost and
  thus increase markup
• Figure 1.3 interest rate shock
• First, we want to deviate from the assumption of
  technology shock, in particular technology
  regress
• Second, interest rate shock can explain the
  variation in RD expenditure by affecting
  discounted profit of research project
• Technology shock impact on output, investment not
  make sense
• Countercyclical RD

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• Figure 1.1

22

• Figure 1.2

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• Figure 1.3

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• A positive interest shock depresses consumption
• it increases investment, as the representative
  household substitute consumption for investment.
• RD decreases because of lower discounted
  franchise profit but lower final good price
  increases it. The latter effect is larger.
• Notice that the order of volatility is
  investment, RD followed by output.

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• Figure 2.1 shows the impulse response of
  financial intermediation model with respect to an
  interest surprise
• Basically same as figure 1.3
• the model predicts that the variance of
  investment is larger than RD. Output has the
  least variation
• Impulse responses to a shock in financial
  intermediation is shown on figure 2.2
• we find different ordering of volatility RD
  followed by investment and then output

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• Figure 2.1

27

• Figure 2.2

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• Digression
• All of our models imply low output - labor hour
  correlation
• a hump-shaped output response can be generated by
  rewriting equation as
• For the random participation model, a shock in
  outside opportunity retards RD expenditure,
  output and investment as shown in figure 3.2
• Volatility order investment RD, output

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• The RD expenditure and capital both exhibits
  hump-shaped dynamic movement, since both current
  period and next period RD appear in the
  log-linearize equation
• random participation in RD sector alone-10 of
  GDP is capable of generating enough dynamic as
  most real business cycle models do
• the model in this paper does not require
  increasing returns, a steady state is guaranteed
  and it is consistent with most of the stylized
  facts.

30

• Figure 3.1

31

• Figure 3.2

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Second Moments Comparison

• Data
• 1953-2003 Chained-type real GDP and Gross
  Domestic Investment data from Bureau of Econonic
  Analysis
• National Science Foundation collects data for
  industry, government, university RD expenditure
• We choose to report the result for industry RD
  denominated in 2000 constant dollars
• Following RBC literature, we compute the logged
  series, demean them by Hodrick-Prescott filter,
  and finally compute variances and covariances by
  the residual series

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• The filtered data suggests that RD expenditure
  has highest variance, followed by investment and
  then output
• only the financial intermediation model is
  consistent with this stylized fact

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Table 1.1