Gibrat's legacy
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  • 1. Gibrat's Legacy
    J Sutton
    Journal of Economic Literature
  • 2. Organization
    Gibrat’s Law
    Early Literature on Growth
    Current Literature on Growth
    Size Distribution Reconsidered: Bounds Approach
    Turbulence in the Measures
    Decline and Exit of firms
    Summary
    Critique
  • 3. Gibrat’s law
    1930 – The proportional Effect.
    “Growth is proportional to increase in size”
    X axis – Log of growth
    Y axis – (z)
    - R(z) = 1/pG (e /Z) dz
  • 4. Gibrat’s law(contd).
    The equation
    Log xt = log x0+e0+e1+….
    xt–Growth at a given time.
    Since then,
    game theoretic (stochastic models/maximizing models) have been used to explain growth
    Hjalmarsson(1974), Jovanovic(1982),Selten(1983)
  • 5. Early Literature
    1950 – 1970 – Gibrat’s law + assumptions
    1970’s – Herbert Simon (GL + stochastic growth)
    two key constraints [growth a opportunity]
    Gibrat's Law: the probability that the next opportunity is taken up by any particular active firm is proportional to the current size of the firm.
    Entry: the probability that the next opportunity is taken up by a new entrant is constant over time
  • 6. Early Literature
    Standard deviations of growth grew slightly less proportionally compared to employee growth.
    Growth a size was a good first approximation
    Mansfield introduced the constraint of firm Survival
  • 7. The New Literature
    Problems handled were of heteroscedasticity, stochasticisty
    Program introduced stochastic elements to conventional maximizing models, corrections for sample bias
    Studies attempted at the following:
    (a) the probability of survival of a firm, conditional on its age, size, and other characteristics, and
    (b) the probability distribution describing the firm's growth rate conditional on survival, and its dependency on age, size, and other characteristics
  • 8. The New Literature(effects)
    The studies of Evans and of Dunne,Roberts, and Samuelson both permit an investigation of age as well as size effects.
    Size and Growth
    the probability of survival increases with firm (or plant) size.
    the proportional rate of growth of a firm (or plant) conditional on survival is decreasing in size.
    The Life Cycle
    For any given size of firm (or plant), the proportional rate
    of growth is smaller according as the firm (or plant) is older
  • 9. The New Literature(shakeout)
    Shakeout - number of producers tends first to rise to a peak, and later falls to some lower level.
    Jovanovicand Glenn MacDonald – Learning Model
  • 10. The New Literature(Simon Model)
    Constraint 1 - The probability that the next market opportunity is filled by any currently active firm is nondecreasing in the size of that firm.
    Constraint 2 - A constant rate of entry for New firms into the industry(sub markets).
  • 11. The New Literature
    Lower Bound
  • 12. Turbulence
    Reasons
    underlying fluctuations in the pattern of demand across product varieties or plant locations
    the displacement of existing technologies (modes of production) by alternatives
    the displacement of existing products by new and superior substitutes.
    State based stochastic models [ Ariel Pakes]
    Ericson-Pakes model
    equilibrium is characterized as the stationary state of a stochastic process, in which the fortunes of individual firms rise and fall over time.
    Numerical simulations reported to date has been on a small number of firms (fewer than ten)
  • 13. Decline and Exit of firms
    Is the process of industrial decline associated with any systematic changes in market structure?
    No proof of size effects (of small vs. large firms)
    Homogeneous goods with particular cost structure -(Leuberman 1990)
    Capacity can’t be reduced irreversibly – (Deily -1991)
    Disappeared firms (bankruptcy, voluntary liquidation and merger)- (Martha Schary 1991) – possible to reject a simple profitable model
  • 14. Summary
    Literature focuses on small number of statistical irregularities
    Focus has been to improve existing models and add explanative factors to various phenomenon.
    Bringing strategic interactions into models of firms
    Constraining the model within bounds(maxima or minima) – Bounds approach
  • 15. Critique
    Good Summary of Literature on Research in Growth of Firms.
    Provides for Alternative avenues for exploration
    Two Takeaways
    Further research needed to arrive at a general framework explaining Growths of industries (firms) and Markets.
    Phenomenon such as
    industry turbulence,
    Exits / declines need further examination