Non-Equilibrium Industry Dynamics with
Knowledge-Based Competition: An
Agent-Based Computational Model
Myong-Hun Chang
Department of Economics
Cleveland State University
2007 International Conference of the System Dynamics Society
Boston, Massachusetts
July 29 – August 2, 2007
Empirical Regularities in Industrial
Dynamics
• Gort and Klepper (Economic Journal, 1982)
– Shake-outs
• No. of Producers initially rises, then declines sharply,
eventually converging to a stable level
– Industry Outputs
• Increasing at a decreasing rate over the course of the
industrial development
– Market Price
• Monotonically declining at a decreasing rate
• Further Empirical Evidences
• Klepper and Simons (Industrial and Corporate
Change, 1997)
• Klepper and Simons (Strategic Management Journal,
2000)
• Klepper and Simons (Journal of Political Economy,
2000)
• Klepper (RAND Journal of Economics, 2002)
• Theoretical Models
– Klepper and Graddy (RAND Journal of
Economics, 1990)
– Jovanovic and MacDonald (Journal of Political
Economy, 1994)
– Common Properties
• Potential entrants: Heterogeneous costs
• Firm-level learning through one-time innovation or
imperfect imitation upon entry  persistent cost
heterogeneity
• Market competition  Exits  Shakeouts
• Firms maximize discounted expected profits
My Objective
• To propose a computational model which
is:
– Capable of generating all of the empirical
regularities for a wide range of parameter
configurations
– Rich enough to allow comparative dynamics
analysis: examine the impacts various
parameters have on the resulting industry
dynamics
• How do industry-specific factors (parameter
configurations) affect the regularities?
Inter-Industry Differences Affecting
the Evolutionary Process
• Klepper and Graddy (1990)
“… there are important differences across industries in the factors
that condition the evolutionary process. More fundamentally, it
suggests that there are exogenous factors that differ across
industries that affect the pace and severity of the evolutionary
process.”
• Dunne, Roberts, and Samuelson (RJE, 1988)
“… we find substantial and persistent differences in entry and exit
rates across industries. Entry and exit rates at a point in time are
also highly correlated across industries so that industries with
higher than average entry rates tend to also have higher than
average exit rates. Together these suggest that industry-specific
factors play an important role in determining entry and exit
patterns.”
• Industry-specific factors considered in this
paper
– Size of the Market Demand
– Level of the Fixed Cost
– Availability of Potential Entrants
– Initial Wealth Levels of the Firms
– Industry-specific Search Propensity
– Complexity of the Technology Space
The Model
• Production Process (Technology) as a Complex
System of Activities
– N distinct activities for a production process
– For each activity, there is a finite set of methods
• 2 methods for simplicity – {0, 1}
– Space of all possible production technologies = {0, 1}N
– A particular choice of technology is a binary vector of
length N
• x = (x1, …, xN), where xi= 0 or 1.
– Distance between two such vectors
• Hamming distance: D(x, y) = ∑Ni=1|xi – yi|
• Production Efficiency for a particular choice
of a technology, x: e(x)  fitness
– Simple average of the efficiency contributions
that the N individual activities make
– Production efficiency of a given technology is
influenced by the exact way in which the
methods chosen for various activities fit
together.
– For each activity, there are K (< N) other
activities that influence the contribution of a
given activity to the overall efficiency of the
firm’s production system.
– Let vj(xj, x1j, …, xKj) be the contribution of activity
j to a firm’s production efficiency.
• Random draw from [0, 100] according to uniform
distribution
– Overall efficiency of the firm is:
• e(x) = (1/N) ∑Ni=1vi(xi, x1i, …, xKi)
– Efficiency landscape defined on Euclidean
space with each activity of a firm being
represented by a dimension of the space and
the final dimension indicating the efficiency of
the firm
– Firm’s innovation/imitation activities  Search
over the efficiency landscape
• Efficiency landscape
– Rugged if K > 0: Multiple local optima
– Impact of N and K
Demand and Cost
• Demand
– P(Q) = a – Q
• Cost
– C(qi) = fi + ci(xi)·qi
– ci(xi) = 100 – e(xi)
– C(qi) = f + [100 – e(xi)]qi
• m-firm Cournot oligopoly with asymmetric
costs
m
– = [1/(m+1)](a + ∑ cj)
– qi* = P* - ci
– Π(qi*) = (qi*)2 – f
P*
– ci ≤ ck  qi* ≥ qk*  Π(qi*) ≥ Π(qk*)
Dynamic Structure
• Beginning of Period-t
– St-1: set of surviving firms from t-1 (S0=Ø)
• Some active and some inactive
– xit-1: survivor i’s technology from t-1 ( cit-1)
– wit-1: firm i’s current wealth carried from t-1
– Rt: set of potential entrants with xkt ( ckt)
Four Stages
• Stage 1: Entry decisions by potential
entrants
• Stage 2: Innovation/imitation decisions by
surviving incumbents
• Stage 3: Output decisions and market
competition
• Stage 4: Exit decisions
Entry (Stage 1)
Surviving incumbents from t-1
(with xit-1 and wit-1)
Pool of potential entrants
(with xkt and $b)
Enter iff as efficient as the
least efficient active
incumbent
Search by Incumbents (Stage 2)
α: probability of
search
(exogenous)
βit: probability of
innovation
(endogenous)
1-βit: probability
of imitation
xit
Competition (Stage 3)
Cournot equilibrium with
asymmetric costs
Πit
Exits (Stage 4)
wit = wit-1 + Πit
Stay in, iff wit ≥ d
Exit, otherwise
d: threshold
wealth level
Design of Computational
Experiments
• Parameters
– N: no. of activities
– K: degree of complexity
– r: No. of potential entrants per period
– f: fixed cost
– a: market size
– b: start-up budget for a new entrant
– d: threshold wealth balance for exit
– α: probability of search
• Outputs to examine
– no. of operating firms in t
– no. of actual entrants in t
– no. of exits in t
– equilibrium market price in t
– equilibrium industry output in t
– industry concentration (HHI) in t
– distribution of firms’ marginal costs in t
– distribution of firm outputs in t
– distribution of technologies (xit for all i)
Baseline
•
•
•
•
•
•
•
•
•
N = 16
K=2
r = 10
f = 20
a = 200
b = 100
d = 0.0
α = 1.0
T = 4,000 periods
U.S. automobile tire industry
• Gort & Klepper (1982)
• Jovanovic & MacDonald (1994)
Computational Results
Entry, Exit, and Shakeout
Price, Output, and
Concentration
Distribution of Marginal Costs and
Firm Outputs
Number of Distinct Technologies
Degree of Technological Diversity
(no. distinct technologies/no. of firms)
Comparative Dynamics
Results
• Turnover is higher (aggregate numbers of
entry and exit over time are
simultaneously greater) when:
– market demand is larger
– potential entrants pool is larger
– start-up fund is smaller
– firms have a lower propensity to search
• No. of surviving incumbents is higher in the
long run when:
– market demand is larger
– fixed cost is lower
– pool of potential entrants is larger
– production process entails a smaller number of
component activities
• Degree of technological diversity is higher in
the long run when:
– market demand is smaller
– fixed cost is higher
– potential entrants pool is smaller
– start-fund is smaller
– firms have weaker propensity to search
– production process entails a greater number of
component activities
– there is a greater degree of interdependence
among component activities
Conclusion
• Production process as a system of interdependent activities
• Firm as an adaptive entity whose survival
depends on its ability to discover ways to
perform various activities with greater
efficiency than its rivals
• Selection pressure applied on the
population of firms through the entry of
new firms and the competition among the
incumbent firms
• Empirical regularities re-generated
• Examined how the regularities are affected
by various industry-specific factors
– market attributes
– search propensities
– nature of the technological space