A Theory of Growth Cycles

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A Theory of Growth Cycles

• Michele Boldrin (Minnesota)
• Jesus Fernandez Villaverde (Penn)

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Basic Motivations

• Factor shares are not constant
• Factor shares are strongly cyclical
• Dont believe in exogenous TFP stories

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Goals

• Account for the cyclicality of factor shares
• Modeling growth and cycles
• Without appealing to exogenous TFP
• Consistency with traditional facts

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Capital share

• Oscillates very substantially
• 5-6 points of GNP in the aggregate
• more in the corporate sector
• Movements not due to changes in sectorial
  composition
• Very regular cyclical pattern

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Net Operating Surplus in Three Expansions
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Corporate Profits
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Ingredient 1

• For given technology, factor proportions are
  fixed.

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• If you want some substitutability, use CES

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Ingredient 2

• Technological change is factor saving

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• In fact, it is mostly labor saving

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Ingredient 3

• Technological change is discrete and costly

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Ingredient 4

• Labor gets paid its opportunity cost, i.e.

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Related Literature

• Karl Marx, Das Kapital
• John Hicks, Theory of Wages
• Samuelson-Kennedy-Weizsacker 1960s
• Mario Tronti, Operai e Capitale
• Richard Goodwin, Prey-Predator Model
• Boldrin-Horvath and Gomme-Greenwood (1995)
• Blanchard (1997) and Caballero-Hammour (1998)
• Ambler-Cardia (1998) Boldrin-Levine (2001),Young
  (2004, 2005), Hansen-Prescott (2005)

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Basic Model

• Representative agent
• Sequence of aggregate fixed coefficients
  technologies
• Innovation requires only output, not labor
• Neither aggregate uncertainty nor idiosyncratic
  risk at firms level

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Preferences

• Representative agent with standard expected
  utility preferences

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Technology (1)

• Set of active technologies

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Technology (2)

• Accumulation, innovation and resources constraint

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Technology (3)

• Productive Capacity and Potential Employment

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Equilibrium implications

• In each period there is a marginal technology,
  i.e. the worst technology which does not get
  scrapped
• Labor is allocated to technologies in order of
  decreasing productivity
• Only the best available technology is
  accumulated, at least under certainty
• Rate of return on is not equalized across
  js

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First Order Conditions (1)

• Determining Employment in period t

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First Order Conditions (2)

• Return from investing in best available
  technology

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First Order Conditions (3)

• Return from adopting a new technology

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Accumulate or innovate?
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Do it with prices (1)

• Implications of zero profits

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Do it with prices (2)

• When the marginal technology is scrapped the
  price of its machines drop to zero. This implies
  the following law of motion for the wage rate

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Do it with prices (3)
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The movie to come

• At bottom of recession labor is cheap and old
  capacity is being replaced with new one
• As the latter accumulates, labor shifts from
  marginal to inframarginal technologies, and labor
  productivity increases.
• Because labor demand is low, wage is low and
  profits rise
• As capacity accumulates, employment and wages
  increase, profits max out and decrease till it is
  worth introducing a new technology and scrapping
  lots of old plants. That starts a new recession.