Stochastic vs determinstic Flashcards
- Theory on the determinants of concentration reminds one somewhat of tower of Babel, nothing that could be labelled an integrated, universally accepted, theory of what determines the level of concentration in a given market.
- ‘hotch-potch’ of ideas
Davies et al (1988)
provides an example of a model with this implication, confirms the significance of the MES/Xc ratio: it alone determines concentration, albeit now in a non-linear way, using orderly sequential entry.
Worcester (1967
〖logS〗(i,t+1)-〖logS〗(i,t)=ϵ_t
ϵ_t is N(m,s^2)
Gibrat (1931)
Gibrat–> such information on the value of these parameter would be sufficient to summarise and compare concentration across industries
Hart (1975)
Gibrat process gives the ability to aggregate easily which is very useful
Aitchison and Brown (1957)
Variance of log firm size will increase over time. This is what …… refers to as a “spontaneous drift”. Implication is that in an industry of firms experiencing simple random growth of above sort will exhibit a pervasive tendency to increasing size inequalities and higher concentration over time.
Prais (1976)
Hart and Prais (1956) and Prais (1976) suggest a modification allowing for ‘regression to (or away from) the mean’. Admits the possibility that larger firms may tend to grow faster or slower than small forms, and involves reformulating the basic law as:
logZ_(i,t+1)=βlogZ_(i,t)+ϵ_( t)
suggest a more fundamental modification based explicitly based on economic theory, posits a technology which places both upper and lower bound on firm size, with constant returns between extremes in this case firm size will have an asymptotic four-parameter lognormal distribution.
Savings (1965)
1) A milder form of the law of proportionate effect which requires only that the expected growth of the aggregate size of all firms in a size class be independent of size. Only applies to firms in excess of some minimum MES this squares neatly with L-shaped cost curve.
2) Allow for new entry, with a constant probability that any increment in industry size will be satisfied by a new entrant.
Simon and Bonini’s (1958)
Important conclusion from Simon and Bonini’s model (1958)
1) The steady-state size distribution of the growth process is a Yule distribution which can be approximated in its upper tail by the pareto curve.
2) The Inequality parameter of the curve is determined uniquely by the probability of entry.
Davies and Lyons (1982) show that Pareto curve implies the following equation for the five-firm concentration ratio:
〖CR〗5=[MES/X]^((a-1 /a) ) [5a/a-1]^(a-1/a) (1-y)^(1/a)
working with US data for 1947-54 finds that the largest increase in CR occurred in the consumer durable and durable equipment industries. Argues this is compatible with stochastic models of concentration since it is precisely these types of industry in which one might expect substantial inter-firm variability in growth rates and thus in size inequalities.
Weiss (1963)
test Simon and Bonini’s (1958) model for a sample of 100 UK manufacturing industries and reported a very close fit R^2=0.9. Extraordinarily high fit confirms the usefulness of the model as starting point for empirical analysis
Davies and Lyon (1982)
Always problem in measuring MES proxy measures for MES are tautologically related to concentration. • It is virtually impossible to observe MES in an industry. Most have employed either the ‘survivor’ technique or simple statistical measures of typical plan/firm size as proxies for MES, usually plant size..
Davies (1980a) and Lyons (1980)
suggests a proxy for MES the ‘midpoint plant size’.
Weiss (1963)
employ time-series methodology for 30 UK industries between 1958-68. Report instances where increasing concentration derives:
Economies of scale
Contraction of the market
Forward integration
Government intervention
• Other industries in the sample provide examples leading to reductions in concentration
Market growth
Low entry barriers
High levels of concentration
• The last of these results suggest concentration is more likely to decline if concentration is already high.
• Mergers the reason in 14 out of 20 prime cause.
Hart and Clarke (1980)
Find a primary role for mergers
Weiss (1965) and Hannah & Kay (1977)
little to no evidence of relationship between size and growth using 147 large UK firms.
Geroski et al (2003)
Much of the literature reports a tendency for smaller firms to grow faster
(Dunne and Hughes 1994)
200,000 US manufacturing firms. Variability of growth rates decline with plant size
Dunne et al (1988)
