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Gibrat's legacy

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Gibrat's legacy

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