Non-Equilibrium Industry Dynamics with Knowledge-Based Competition: An Agent-Based Computational Model Myong-Hun Chang Cleveland State University

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 ► To pursue objective and coherent comparisons between industries which differ in their characteristics along the lines suggested by the parameter configurations considered in this paper

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 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 = (x 1, …, x N ), where x i = 0 or 1.  Distance between two such vectors ► Hamming distance: D(x, y) = ∑ N i=1 |x i – y i |

► 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.

K = 0: Activities independent of each other K = 1: K = 2: Higher K: Greater mutual interdependence

 Let v j (x j, x 1 j, …, x K j ) 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) ∑ N i=1 v i (x i, x 1 i, …, x K i )  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  P(Q) = a – Q ► Cost  C(q i ) = f i + c i (x i )·q i  c i (x i ) = 100 – e(x i )  C(q i ) = f + [100 – e(x i )]q i Demand and Cost

► m-firm Cournot oligopoly with asymmetric costs  P * = [1/(m+1)](a + ∑ m c j )  q i * = P * - c i  Π(q i * ) = (q i * ) 2 – f  c i ≤ c k  q i * ≥ q k *  Π(q i * ) ≥ Π(q k * )

Dynamic Structure ► Beginning of Period-t  S t-1 : set of surviving firms from t-1 (S 0 =Ø) ► Some active and some inactive  x i t-1 : survivor i’s technology from t-1 (  c i t-1 )  w i t-1 : firm i’s current wealth carried from t-1  R t : set of potential entrants with x k t (  c k t )

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) Pool of potential entrants (with x k t and $b) Surviving incumbents from t-1 (with x i t-1 and w i t-1 ) Enter iff as efficient as the least efficient active incumbent

Search by Incumbents (Stage 2) α: probability of search (exogenous) β i t : probability of innovation (endogenous) 1-β i t : probability of imitation xitxitxitxit

Competition (Stage 3) Cournot equilibrium with asymmetric costs ΠitΠitΠitΠit

Exits (Stage 4) w i t = w i t-1 + Π i t Stay in, iff w i t ≥ d Exit, otherwise d: threshold wealth level

Stage 1: Entry Decisions ► Each potential entrant, k, in R t has a technology, x k t, with an efficiency level of e(x k t ). ► Potential entrant, k, enters the industry if and only if e(x k t ) is at least as high as the efficiency level of the least efficient active incumbent from t-1. ► All entrants enter with a fixed “start-up budget” of $b (current wealth for the entrants)

Stage 2: Innovation/Imitation Decisions ► All surviving incumbents from t-1, S t-1, engage in innovation or imitation to search for an efficiency-enhancing technology. ► With probability, α, each incumbent gets one chance to search. With (1-α), the incumbent gets no opportunity to search. ► α: propensity to engage in exploration for improved technologies (common across all firms)

► If firm i gets to search in t, it chooses to “innovate” with probability β i t and “imitate” with probability 1-β i t. ► β i t : endogenous choice probability for pursuing innovation rather than imitation ► Innovation: Consider changing the method in one randomly chosen activity ► Imitation: Pick another firm j and consider copying the method employed by j in one randomly chosen activity  Choice of the target firm is stochastic with the probability based on a roulette wheel algorithm over firm profits from t-1.

► Adoption of a new technology  Adopt if and only if the efficiency of the proposed technology is greater than that of the current technology. ► Evolving β i t  Experience-weighted attraction learning (Camerer and Ho)  β i t goes up (down) if innovation (imitation) was successful.  A favorable experience through innovation (imitation) raises the probability that a firm will choose innovation (imitation) again in the future.

Stage 3: Output Decisions and Market Competition ► All surviving incumbents from t-1 and the new entrants from stage 2 of t have technologies with the corresponding efficiency levels and, hence, the marginal costs, c i t. ► Given the distribution of c i t ’s, find the Cournot equilibrium.  All active firms produce positive outputs.  All inactive firms produce zero output.

Stage 4: Exit Decisions ► Firm i’s wealth level in period t  w i t = w i t-1 + Π i t ► Exit decision rule  Stay in if and only if w i t ≥ d  Exit otherwise  d: threshold wealth level below which a firm must exit the market

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 (x i t 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 inter- dependent 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