Survival of the Fittest: Natural Selection Revisited*

Transcription

1 Survival of the Fittest: Natural Selection Revisited* ABSTRACT The evidence shows firms relocating across industries or product lines are empirically relevant in industry dynamics, constituting one-third of entry Yet, existing theories of industry dynamics focus exclusively on new entrants and assume that though firms may be fundamentally different, their exit payoff is exogenously fixed and identical; and the endowments accumulated by a firm when active cannot be transferred to other firms or industries when exiting We relax these assumptions by modeling two forms of exit: a firm may shut down by selling its assets to earn their salvage value, or reallocate its assets at a cost to enter another industry or product line We investigate the ensuing industry dynamics, and demonstrate they are consistent with existing empirical evidence on entry and exit Calibrating the model suggests firms transferring across industries account for slightly less than one-half of exit JEL Codes: D92, L11, L25 Keywords: firm survival, entry and exit, industry dynamics Jose M Plehn-Dujowich Department of Economics University at Buffalo (SUNY) 435 Fronczak Hall Buffalo, NY 1426 jplehn@buffaloedu *I would like to thank Serguey Braguinsky and Michael Gort for helpful comments, and Dunli Li for research assistance

2 1 INTRODUCTION Firms relocating across industries or product lines are empirically relevant in industry dynamics: transferring firms account for one-third of entry; two-thirds of surviving firms alter their product mix every five years; and firms previously active (in another industry) are the most successful type of entrant in terms of subsequent market share and survival rate [Dunne, Roberts, and Samuelson (1988), Bernard, Redding, and Schott (25)] Yet, existing theories of industry dynamics focus exclusively on new entrants and assume that when a firm exits, it shuts down to receive the same fixed, exogenous payoff [Jovanovic (1982), Hopenhayn (1992), Jovanovic and MacDonald (1994)] This implies that though firms may be fundamentally different, their exit payoff is identical; and the endowments accumulated by a firm while active cannot be transferred to other firms, industries, or product lines when exiting Exit is not synonymous with failure Firms exit in predominantly two distinct ways [Dunne, Klimek, and Roberts (25), Holmes and Schmitz (199, 1995), Agarwal and Gort (1996)]: when a firm ceases operating, its assets are sold at their salvage value; and when it exits a line of business, it may reallocate the assets and know-how of one plant towards another plant or line of business 1 As such, the value of exiting possibly depends on the firm s endowments and their alternative uses, rather than being fixed at an arbitrary level Hence, there are two types of entrants: firms not previously active in any industry, ie new entrants; and existing firms that relocate to a different industry 2 This paper investigates the industry dynamics that ensue from incorporating both forms of entry and exit, in a manner that is consistent with the empirical evidence There is a continuum of business units or plants (called firms ), each run by a manager of heterogeneous skill While active, firms augment their stock of (physical, human, and organizational) capital The return on capital is a function of the firm s managerial skill and the industry s permanent state of demand/productivity These two are complements in that a skilled firm more ably takes advantage of favorable economic conditions There are two types of firms, specialized and adaptive A specialized firm accumulates industry-specific capital, thus it can only be active in one particular industry Upon learning the state of its industry, a specialized firm decides 1 There is a third form of exit via acquisition or merger, but we do not consider this possibility Jovanovic and Rousseau (22) model the incentive to merge, and Schary (1991) studies empirically the tendency of firms to exit via merger, voluntary liquidation, or bankruptcy in the cotton textile industry 2 There is a third form of entry via diversification, but we do not consider this possibility 1

3 whether to remain active in the industry or shut down, which entails selling the firm s accumulated capital to receive its (exogenou scrap value An adaptive firm can transfer from one industry to another, while losing the portion of its capital stock that is industry-specific Upon learning the state of its industry, an adaptive firm decides whether to remain active in the industry, shut down (to sell its capital for scrap), or transfer to another industry Not all firms that exit do so because they are inefficient, and not all firms that enter are new In equilibrium, there are two classes of adaptive firms depending on their skill Highskill adaptive firms never shut down: if the state of their industry is below a threshold, they transfer to another industry hoping for better economic conditions; otherwise, they remain active in the industry A high-skill adaptive firm benefits more from a favorable state, but by the same token it incurs a greater opportunity cost from being active in an industry with an unfavorable state If the industry is experiencing an economic downturn, high-skill adaptive firms are prompted to search for a more lucrative industry to complement their high ability Low-skill adaptive firms and specialized firms never transfer across industries: if the state of their industry is below a threshold, they shut down; otherwise, they remain active in the industry For a low-skill adaptive firm to remain active, the state of its industry must be sufficiently high to overcome the firm s low return on capital If the industry is in a downturn, low-skill adaptive firms cannot justify losing a portion of their capital when transferring to another industry, and instead sell their assets to earn their scrap value Specialized firms remain active in the industry if their skill is sufficiently high to outweigh the payoff of shutting down Adaptive and specialized firms of high skill populate industries experiencing a boom, while adaptive and specialized firms of low skill shut down from them Specialized firms of high skill populate industries experiencing a bust, while adaptive and specialized firms of low skill shut down from them and adaptive firms of high skill transfer out of them The more skilled is an adaptive firm, the more likely it is to transfer than shut down Transfers only occur out of industries in distress, while efficient firms with highly specialized capital remain active in such industries Because firms cannot observe the state of an industry prior to entry, all industries exhibit firms transferring into them We show our findings are consistent with empirical evidence on entry and exit by new entrants versus firms relocating, the characteristics of firms transferring versus shutting down, and the relationship between firm size and survival 2

4 Transfers across industries are widespread, and if firms have the option of relocating, they do so in great numbers We calibrate the model to find that 6719% of industries have (high-skill adaptive) firms transferring out to other industries; 7768% of new adaptive firms that enter an industry, and subsequently learn the industry is experiencing a bust, transfer out to other industries (while the remaining 2232% shut down); and, averaging over all industries in the economy, transfers account for 4463% of all firms exiting Overall, then, the evidence shows one-third of entry is due to transfers, and our model suggests one-half of exit is accounted for by firms relocating across industries, thus transfers constitute an integral component of both entry and exit, and should thereby be incorporated in theories of industry dynamics The paper is organized as follows We review existing evidence on relocation and product switching (Section 2), present the model (Section 3), derive the industry dynamics (Section 4), correlate our findings with the evidence (Section 5), calibrate the model (Section 6), and conclude (Section 7) 2 EVIDENCE ON RELOCATION AND PRODUCT SWITCHING Dunne, Roberts, and Samuelson (1988) show that firms relocating across industries are empirically relevant in industry dynamics, constituting slightly over one-third of entry 3 The authors examine patterns of firm entry and exit in the 4-digit US manufacturing industries over the period (divided into four periods according to the census years 1963, 1967, 1972, 1977, and 1982) Firm-level production in each 4-digit industry is constructed by aggregating over all plants owned by a firm A firm is defined as a producer in a 4-digit industry, thus multi-product producers are counted as a firm in each 4-digit industry in which they are active 4 Entrants are disaggregated into new firms not previously active in any 4-digit industry (labeled new entrants ), existing firms that diversify into a different 4-digit industry by opening new production facilities (labeled diversifying firm, and existing firms that enter a different 4-digit industry by altering the mix of outputs they produce in existing plants (labeled transferring firm Table 1 summarizes the patterns of firm entry over the four sample periods 3 Dunne, Roberts, and Samuelson (1989) obtain similar results to those discussed here in twenty-six 4-digit US chemical industries over the period using census data 4 Other studies using census data assign the entirety of a plant s output to the 4-digit industry that accounts for the largest proportion of the value of the plant s output, thus each plant is treated as producing a single 4-digit product If relative levels of the outputs produced in the plant change, then a plant may spuriously be observed to exit a 4- digit industry and enter another 3

5 , , , and according to whether the firm is a new entrant, a diversifying firm, or a transferring firm Averaging over all sample periods, transfers account for 361% of all entrants and 3559% of the market share held by all entrants Table 2 disaggregates the exit variables by type of firm entry On average, firms that entered the industry as transfers account for 355% of all firms exiting and have a collective market share of 3537% amongst all firms exiting Bernard, Redding, and Schott (25) document the extent to which US manufacturing firms add and drop products (defined as 5-digit industrie across five-year census intervals over the period Plant-level data was aggregated up to the firm level A product addition represents: (a) the acquisition of a plant that is producing a product new to the firm 5 ; (b) a product innovation, ie the creation of a new good at a plant classified in an existing 5-digit industry; or (c) starting production of an existing good that is new to the firm The average US manufacturing firm produces 23 products at the beginning of a five-year census interval, and subsequently adds 11 products and drops 11 products 68% of surviving firms alter their product mix every five years, 12% by dropping products, 11% by adding products, and 45% by both adding and dropping products An average of 93% of all manufacturing output is produced by firms that change their product mix across census years Net product switching is responsible for ten times more aggregate manufacturing output growth than net entry Product switching changes a firm s mix of industries 69% of firms that change products alter their mix of 4-digit industries in doing so and 31% alter their mix of 2-digit industries Averaging over all firms that add products, 58% add products in 4-digit industries new to the firm, and 21% add products in 2-digit industries new to the firm Averaging over all products that are added, 53% are in 4-digit industries new to the firm, and 16% are in 2-digit industries new to the firm 26% of current output originates from 4-digit industries new to the firm, while 23% of current output is in 4-digit industries the firm will abandon in five years We infer that firms relocating across industries or product lines are quantitatively important in terms of both entry and exit, yet have been ignored theoretically Current models of industry dynamics assume that all entrants are new firms and all exit entails shutting down, whereas we recognize there is another form of entry and exit, the implications of which we investigate in this paper Because the evidence shows a significant proportion of firms enter by 5 Product additions through acquisitions account for less than 1% of all product switches 4

6 having transferred from other industries, we question whether all firms that exit do so because they are inefficient 3 THE MODEL There is a continuum of plants or business units, called firms, each run independently by a manager of heterogeneous skill s [, ) drawn from the distribution H There is a collection of industries or product lines that reside within the same technological area, eg a 2- digit sector These product lines (eg 4-digit industrie are sufficiently different that each has its own independent permanent state of demand/productivity Since all industries reside in the same technological sector, industries have identical characteristics and draw their state A [, ) from the same distribution F With this structure, there is heterogeneity across industries, and heterogeneity across firms within each industry Let K denote the stock of physical, human, and organizational capital of a firm A firm with skill s is endowed with an AK production technology: when active in an industry with the state of demand/productivity A, the firm s profits are sak Managerial skill and the state are complements: the more skilled is a firm s manager, the more ably the firm can take advantage of favorable economic conditions is Firms accumulate capital while active The exogenous scrap (or salvage) value of capital q < 1 Capital is not specific to the firm, thus its scrap value is independent of managerial skill A firm with skill s and capital stock K active in an industry with state A incurs the cost C( I / K; A, per unit of investment I In the spirit of the Q theory of investment, the marginal cost of investing is decreasing in the capital stock and increasing in the magnitude of the investment Because capital earns a higher return in an industry with a favorable state, the (marginal) cost of investing is increasing in the state of the industry A 6 Due to capital-skill complementarity, it is more costly for skilled firms to adapt capital to firm-specific requirements, thus C( I / K; A, is also increasing in skill s The stock of capital evolves according to K = ( 1 δ ) K + I, where < δ < 1 is the rate of depreciation The firm discounts the future according to the discount factor < β < 1 6 This would arise in a general equilibrium model since in a competitive capital market the marginal cost of capital equals its (average) marginal product, which in turn is a function of the state of the industry 5

7 is adaptive 7 Amongst firms of a given skill, the proportion λ is specialized, and the proportion 1 λ A specialized firm can only be active in a specific industry because its knowledge and expertise is limited to that field An adaptive firm can transfer from one industry to another (within the same 2-digit sector) because its managerial skill is adaptable, though relocating entails losing the portion < T < 1 of its capital stock 8 We may interpret T as the percentage of an adaptive firm s capital that is industry-specific With this interpretation, T is one hundred percent for specialized firms Prior to entry, the state of an industry is unobservable to both new entrants and transferring firms; and prior to first becoming active, skill is unobservable 9 Therefore, new firms are unaware of their skill and the industry s state prior to entry; and transferring firms already learned their skill, but are unaware of the state of the industry they are relocating to 31 The Firm s Problem Consider the problem of an adaptive firm that just entered an industry either as a new entrant or a transfer The timing within a period is the following A transfer learns the state of the industry and a new entrant learns its skill and the state of the industry by producing during the period 1 The firm then decides whether to remain active in the industry, shut down, or transfer to another industry the following period If the firm shuts down, it receives the payoff q per unit of capital Alternatively, the firm may exit to enter a different industry, while losing the portion T of its capital in the transfer The firm cannot observe another industry s state prior to entry, thus switching industries is equivalent to drawing a new state The problem of a specialized firm that just entered an industry (as a new entrant) is comparable The specialized firm first learns the state of the industry and its skill by producing during the period It then decides whether to remain active in the industry or shut down the next period to receive q per unit of capital 7 We assume λ is independent of managerial skill s to avoid making an assumption as to whether skilled firms are more or less likely to be specialized 8 We assume T is independent of managerial skill s to avoid making an assumption as to whether skilled firms have a comparative advantage at transferring across industries 9 These are similar assumptions to those in Barbarino and Jovanovic (24) that the market size of an industry is unknown prior to entry and Jovanovic (1982) that a firm s cost of production is unknown prior to entry 1 In other words, we may define one period in the model as the (average) amount of time it takes a firm to learn the state of the industry and, if it is a new entrant, its managerial ability 6

8 Let W ( A, K; denote the value function of an adaptive firm with skill s and capital stock K that is currently active in an industry with state A Industries solely differ on the basis of their realized state of demand/productivity that is drawn from the same distribution F It follows that, in equilibrium, the payoff of transferring to another industry is equal to the expected value (net of the transfer cost) of drawing a new state, The Bellman equation is given by E [ W ( A,(1 T) K ; ] (1) W ( A, K; = max sak C( I / K; s, A) I + β W ( A, K ;, subject to the law of motion I M K = ( 1 δ ) K + I An adaptive firm chooses between remaining active in the industry, shutting down, or transferring to another industry: (2) W M ( A, K ; = max{ W ( A, K ;, qk, E[ W ( A,(1 T ) K ; s]} x I / We exploit the fact that the firm s problem can be made proportional to capital Let K denote investment per unit of capital, and suppose the investment marginal cost function is C ( x; s, A) = csax / 2, where c is a constant parameter Let V ( A; denote the value of an adaptive firm with skill s per unit of capital in an industry with state A From (1), we have 2 (3) V ( A; = max sa csax / 2 + β (1 δ + x) V ( A; From (2), we have x (4) ( A; = max{ V ( A;, q,(1 T ) EV ( }, V M M where EV ( is the expected value of a firm with skill s per unit of capital The first-order condition (FOC) with respect to investment per unit of capital x yields the policy 1 (5) x( A; = ( csa) βv ( A; M Applying the investment policy to the Bellman equation, we find (6) V ( A; = sa + β (1 δ ) V ( A; + β (2csA) V ( A; Let V C ( A; M M denote the (continuation) value per unit of capital of remaining active in the industry Because the state of an industry is permanent, if the firm decides to stay active in the industry, it remains there forever, implying (7) V ( A; = sa + β (1 δ ) V ( A; + β (2csA) V ( A; C Solving this quadratic, we obtain the two roots C (8) ( A; = ( csa/ β ){1 β (1 δ ) ± [1 β (1 δ )] 2β / c} V C C 7

9 We rule out the larger root as follows To satisfy the transversality condition of the Bellman equation, the effective discount factor β ( 1 δ + x) must lie within the unit interval With the larger root, it is given by [1 β (1 δ )] 2β / c, which is clearly greater than one We infer the continuation value is equal to the smaller root: 2 (9) ( A; = csaω / β, V C where Ω 1 β (1 δ ) [1 β (1 δ )] 2 2 2β / c We assume the continuation value is real: (A1) 1 β (1 δ + 2 / c) An adaptive firm may remain active in the industry to receive V C ( A;, shut down to receive q, or transfer to another industry to receive ( 1 T ) EV ( We cannot compare the latter two options without knowing the expected value of the firm, but we cannot calculate the expected value of the firm without knowing its exit strategy As such, we begin by hypothesizing the firm never finds it optimal to shut down, and calculate its expected value under this presumption We then determine the conditions under which this exit strategy is optimal 32 Transferring Across Industries Consider an adaptive firm that never shuts down From (9), the (continuation) value of staying active in the industry is strictly increasing in the state of demand/productivity A Therefore, a (unique) threshold state  exists at which an adaptive firm with skill s is indifferent between remaining active in the industry versus transferring to another industry, which is defined by V C ( Aˆ; (1 T ) EV (, to yield: ˆ 1 2 (1) A = β (1 T )( csω) EV ( The adaptive firm relocates if the state of the industry is below the threshold  ; otherwise, it remains active in the industry The present value of transferring next period is 1 2 (11) ( A; = sa + β (1 δ )(1 T ) EV ( + (2csA) [ β (1 T ) EV ( ], V T while the present value of remaining active in the industry is V C ( A; The expected value of the firm thus satisfies Aˆ (12) EV ( = V ( A; df( A) + V ( A; df( A) T Aˆ C 8

10 Combining (1), (11), and (12), we obtain the following implicit equation for the threshold: Aˆ (13) Aˆ 2 2 /(1 T ) = [ β A /( cω) + β (1 δ ) Aˆ + ΩAˆ / 2] df( A) + AdF( A) In what follows, we treat  as a parameter when performing comparative statics, as it is solely a function of the fundamental parameters of the model We derived the expected value of the firm under the presumption that the firm never shuts down, which yields a payoff of q per unit of capital For this to be true, it must be the case that transferring to another industry yields a greater payoff, ie ( 1 T ) EV ( q The threshold state Â, given by (13), is independent of managerial skill, thus the expected value of the firm per Aˆ unit of capital EV ( 2 = csω[ β (1 T )] 1, is strictly increasing in skill It follows that we may define the cutoff ŝ as the unique skill level at which a firm is indifferent between transferring versus shutting down, ie ( 1 T ) EV (ˆ q, to obtain: 2 1 (14) sˆ = β q( cωaˆ) We conclude the following: LEMMA 1: An adaptive firm with skill s [ sˆ, ) (a high-skill adaptive firm) pursues the following trigger strategy: if the state of the industry is below the threshold Â, then it transfers to another industry; otherwise, it remains active in the industry Managerial skill and the state of demand/productivity of the industry are complements, thus adaptive firms run by managers with greater skill can take the most advantage of an industry experiencing favorable economic conditions, but by the same token such adaptive firms incur the highest (opportunity) cost when economic conditions are unfavorable The more skilled is an adaptive firm, the more it has to gain from finding an industry with a high state Being run by a manager with greater skill represents a tradeoff for an adaptive firm On the one hand, it increases the firm s return on capital, raising firm value, which diminishes the incentive to exit On the other hand, in equilibrium, raising firm value increases the expected payoff of transferring to another industry In our framework, the latter effect dominates: in an industry experiencing an economic downturn, adaptive firms with sufficiently high skill (ie exceeding ŝ ) are prompted to search for a more lucrative industry to complement their ability 9

11 33 Shutting Down Adaptive firms with skill s [, sˆ), termed low-skill adaptive firms, are not sufficiently skilled to engage in transfers, thus they choose between remaining active versus shutting down For an adaptive firm with skill s, the value of remaining active in an industry with state A, ie V C ( A;, which is given by (9), is strictly increasing in the state of the industry A, while the payoff of shutting down is fixed at q We infer that low-skill adaptive firms shut down if the state is sufficiently small, and remain active otherwise Define ~ A ( s ) as the threshold state at which an adaptive firm with skill s is indifferent between remaining active in the industry versus shutting down, ie ( A ~ ( ; q, to obtain: V C (15) ~ 2 1 A( = qβ ( csω) A specialized firm with skill s chooses between remaining active in the industry with state A, to earn V C ( A;, versus shutting down to receive the payoff q It follows that a specialized firm follows the same strategy as a low-skill adaptive firm We conclude the following: LEMMA 2: An adaptive firm with skill s [, sˆ ) (a low-skill adaptive firm) and a specialized firm pursue the following trigger strategy: if the state of the industry is below the threshold ~ A ( s ), then it shuts down; otherwise, it remains active in the industry A low-skill adaptive firm and a specialized firm face the tradeoff of remaining active in the industry versus shutting down to receive an exogenous payoff given by the scrap value of capital Because managerial skill and the state of the industry are complements, the more skilled is a low-skill adaptive firm or a specialized firm, the more stringent is its trigger strategy, ie the ~ threshold state A ( s ) is decreasing in s ~ The threshold A ( s ) is increasing in the scrap value of capital q because the greater is the exit payoff, the more favorable must be the state of the industry to justify remaining active in the industry As a result, the likelihood that a firm shuts down is smaller the greater is the firm s managerial skill and the smaller is the scrap value of capital 1

12 34 The Equilibrium Outcome Figure 1 illustrates the equilibrium in state-skill space An industry experiencing a boom is defined as one with a state A > Aˆ, and an industry experiencing a bust is defined as one with a state A Aˆ 11 Consider an industry with state A and define ~ ~ s ( A ) by A A( ~ s ( A )) : (16) ~ 2 1 s ( A) = qβ ( cωa) Note that s ˆ = ~ s ( Aˆ ) such that, by construction, in a boom, we have < sˆ, while in a bust, we have s ˆ < The following proposition describes the equilibrium outcome: PROPOSITION 1: Consider an industry with the state of demand/productivity A (a) Suppose the industry is in a boom ( A > Aˆ ) Adaptive and specialized firms with skill in the range [, ) shut down; and those in the range [, ) remain active in the industry (b) Suppose the industry is in a bust ( A Aˆ ) Adaptive firms with skill in the range [, sˆ) shut down; and those in the range [ sˆ, ) transfer to another industry Specialized firms with skill in the range [, ) shut down; and those in the range [, ) remain active in the industry In an industry experiencing a boom, adaptive firms parallel the behavior of specialized firms in a manner reminiscent of a traditional theory of industry dynamics: inefficient firms shut down, and efficient firms remain active in the industry For both types of firms, to remain active, their skill must be sufficiently great to exceed the salvage value of capital No (adaptive) firms transfer out of an industry in a boom, such that all exit entails shutting down: the economic condition of an industry in a boom is so favorable that, on average, other industries have inferior conditions, thus no adaptive firm has the incentive to lose the portion T of its capital stock to search for one of the (few) industries with a superior state In an industry experiencing a bust, inefficient adaptive and specialized firms shut down; efficient adaptive firms transfer to another industry; and efficient specialized firms remain active in the industry Firms with sufficiently high skill that are unable to relocate remain active in the industry, while firms with sufficiently high skill that are able to relocate do so The only 11 Calibrating the model below, we find that 6719% of industries are experiencing a bust, thus such a state is not synonymous with a recession 11

13 firms that remain active in industries experiencing a bust are efficient specialized firms Because managerial skill and the state of an industry are complements, efficient adaptive firms have much to gain from finding one of the (many) industries with a more favorable state, so they engage in a transfer Inefficient adaptive firms have less to gain from finding an industry with a more favorable state, so they cannot justify losing a portion of their capital in the transfer, and instead sell their capital to earn its scrap value Averaging across all firms in an industry, the greater is the state of demand/productivity, the greater is the proportion of firms that remain active in the industry Amongst all firms that exit, those transferring across industries are more skilled than those shutting down To see this, consider an industry with state A experiencing a bust Specialized firms with skill below ~ s ( A ) shut down; adaptive firms with skill below ŝ shut down; and adaptive firms with skill exceeding ŝ transfer to another industry The proportion λ of new entrants is specialized We infer the average skill of firms shutting down is λ sdh ( + (1 λ) sˆ sdh (, and the average skill of firms transferring is sˆ sdh ( We prove in Lemma A1 of the Appendix the latter is greater than the former, as claimed 35 The Cutoff Skill Level The cutoff skill level ŝ determines the proportion of high- versus low-skill adaptive firms An increase in s ˆ implies a rise in the proportion of low-skill adaptive firms, ie those that shut down if the state of their industry is sufficiently low; and a decline in the proportion of highskill adaptive firms, ie those that transfer to another industry if the state of their industry is sufficiently low From (14), we infer the following: LEMMA 3: The cutoff skill level ŝ is increasing in the salvage value of capital q, and decreasing in the threshold state  An increase in the scrap value of capital renders more attractive the option of shutting down, thus it has the dual effect of raising the likelihood that low-skill adaptive firms shut down 12

14 and incrementing the proportion of adaptive firms that follow the strategy of low-skill firms Therefore, the greater is the scrap value of capital, the more adaptive firms shut down overall; and because there are fewer high-skill adaptive firms resulting from the increase in the scrap value of capital, the number of firms that transfer from one industry to another declines Because managerial skill and the state of an industry are complements, adaptive firms in industries with favorable states apply lenient trigger strategies Consequently, the greater is the proportion of industries experiencing a bust, the greater is the proportion of adaptive firms within each industry following the trigger strategy of high-skill firms, ie the cutoff ŝ is decreasing in the threshold state  We infer that an increase in  has the dual effect of increasing the proportion of industries from which adaptive firms transfer out, and (via its effect on ŝ ) increasing the fraction of adaptive firms in each industry experiencing a bust that transfer out (instead of shutting down) 4 INDUSTRY DYNAMICS There is evidence from the universe of US manufacturing industries on the number of firms that transfer into industries, but not the number of firms that transfer out of industries, thus the contribution of transfers to entry is known, but the contribution of transfers to exit is unknown (other than for specific industrie We derive the industry dynamics to determine the factors influencing the rates of (both forms of) entry and exit; and calibrate our calculations in Section 6 so as to obtain a sense of the extent to which firms transfer out of industries We derive the number of firms transferring into an industry (sub-section 41); the total number of firms entering an industry (sub-section 42); the number of firms shutting down from an industry (sub-section 43); the number of firms transferring out of an industry (sub-section 44); and the total number of firms exiting from an industry (sub-section 45) Finally, we provide an overview of the results (sub-section 46) 41 The Number of Firms Transferring Into an Industry Let N( A, denote the number of firms with skill s that enter an industry with state A at the beginning of the period Let N S ( A, denote the number of specialized entrants, and N A ( A, the number of adaptive entrants, thus N( A, = N ( A, N ( A, At the beginning S + A 13

15 of every period, E new firms enter the (2-digit) sector within which all (4-digit) industries under consideration reside Moreover, each industry is subject to entry by firms transferring out of other industries New entrants learn the state of the industry and their skill upon entry, and transfers learn the state of the industry upon entry (and learned their skill upon first entering the sector) With probability f (A), a new entrant or transfer enters an industry with state A; with probability h(, a new entrant has the skill s; and the proportion λ of new entrants is specialized, so the number of specialized entrants equals (17) N S ( A, = λh( f ( A) E Let T I ( A, denote the number of (adaptive) firms with skill s that transfer into an industry with state A at the beginning of the period The proportion 1 λ of new entrants is adaptive The number of adaptive entrants equals the number of adaptive new entrants plus the number of (adaptive) firms transferring into the industry: (18) N ( A, = (1 λ ) h( f ( A) E T ( A, A + I In a steady state, the number of firms with skill s that transfer into an industry with state A at the beginning of the period equals the number of firms with skill s that transfer out of all other industries at the end of the previous period times the probability of drawing the state A No firms with skill below ŝ engage in a transfer, thus T I ( A, = if s sˆ Firms with skill exceeding ŝ transfer out of an industry if it is experiencing a bust, ie the state θ of the industry satisfies θ Â The number of adaptive entrants with skill s in an industry with state θ is N A ( θ, In an industry with state θ experiencing a bust, all the N A ( θ, firms with skill s > sˆ is transfer to another industry The probability that a transfer enters an industry with state A f (A), implying Aˆ (19) T ( A, = f ( A) N ( θ, dθ if s > sˆ I Using (18), we obtain the recursion Aˆ A (2) TI ( A, = f ( A) [(1 λ) h( f ( θ ) E + TI ( θ, ] dθ if s > sˆ 14

16 Define TI ( TI ( A, / f ( A), such that (2) becomes T ( = [(1 λ) h( E + T ( ] f ( θ ) dθ, 1 to obtain T I ( = [1 F( Aˆ)] (1 λ) h( F( Aˆ ) E, which yields the number of firms with skill s that transfer into an industry with state A: 1 (21) T I ( A, = [1 F( Aˆ)] (1 λ) h( F( Aˆ) f ( A) E if s > sˆ The total number of firms transferring into an industry with state A at the beginning of the I Aˆ I period equals T ( A) = I sˆ T ( A, ds Applying (21), we find I 1 (22) T I ( A) = [1 F( Aˆ)] [1 H (ˆ)](1 s λ) F( Aˆ) f ( A) E By noting that the cutoff skill level s ˆ, defined by (14), is increasing in q and decreasing in Â, we infer from (22): LEMMA 4: The number of firms transferring into an industry at the beginning of the period is decreasing in the salvage value of capital q, and increasing in the threshold state  and the proportion 1 λ of new entrants that is adaptive 42 The Total Number of Firms Entering an Industry Because no firms with skill below s ˆ engage in a transfer, the total number of firms with skill s sˆ that enter an industry with state A at the beginning of the period equals the number of new entrants: (23) N ( A, = h( f ( A) E if s sˆ The total number of firms with skill s > sˆ that enter an industry with state A equals the number of new entrants plus those transferring into the industry, Applying (21), we obtain 1 (24) N ( A, = [1 F( Aˆ)] [1 λf( Aˆ)] h( f ( A) E if s > sˆ N( A, = h( f ( A) E + T ( A, The total number of firms that enter an industry with state A at the beginning of the I period is N( A) = N( A, ds Applying (23) and (24), we obtain 15

17 1 (25) N ( A) = [1 F( Aˆ)] {1 F( Aˆ)[ λ + (1 λ) H (ˆ)]} s f ( A) E To summarize, the following firms enter an industry: adaptive and specialized new entrants and high-skill adaptive firms transferring into the industry We infer from (25) the following: LEMMA 5: The total number of firms entering an industry at the beginning of the period is decreasing in the salvage value of capital q, and increasing in the threshold state  and the proportion 1 λ of new entrants that is adaptive 43 The Number of Firms Transferring Out of an Industry No firms transfer out at the end of the period of an industry with state A experiencing a boom: T Boom ( A) = Let (A) denote the number of firms that transfer out of an industry T Bust with state A experiencing a bust In a bust, all adaptive entrants with skill exceeding ŝ transfer to another industry, thus T Bust ( A) = sˆ N A ( A, ds Applying (18) and (21), the number of firms that transfer out in a bust equals 1 (26) T Bust ( A) = [1 F( Aˆ)] [1 H ( sˆ)](1 λ) f ( A) E To summarize, all transfers and adaptive new entrants with skill exceeding ŝ that enter an industry, and subsequently learn it is experiencing a bust, transfer to another industry We infer from (26) the following: LEMMA 6: The number of firms transferring out at the end of the period of an industry experiencing a bust is decreasing in the salvage value of capital q, and increasing in the threshold state  and the proportion 1 λ of new entrants that is adaptive 44 The Number of Firms Shutting Down From an Industry Let D Boom (A) denote the number of firms that shut down at the end of the period from an industry with state A that is experiencing a boom (ie A > Aˆ ) In a boom, all entrants with skill below ~ s ( A ) shut down, yielding D ( A) = N( A, ds Because A > Aˆ, we have that Boom 16

18 < sˆ, implying the expression for N( A, given by (23) is applicable Therefore, the number of firms that shut down in a boom equals (27) D Boom ( A) = H ( ) f ( A) E Let (A) D Bust denote the number of firms that shut down at the end of the period from an industry with state A that is experiencing a bust (ie A Aˆ ) In a bust, all specialized entrants with skill below ~ s ( A ) shut down, and all adaptive entrants with skill below ŝ shut down: D Bust sˆ N S ( A, ds + ( A) = N ( A, ds From (17), we have N S ( A, = λh( f ( A) E No A firms that transferred in shut down (because, to be transfers, they had to have skill exceeding s ˆ ), thus all adaptive entrants that shut down are new firms: N A ( A, = (1 λ) h( f ( A) E Therefore, the number of firms that shut down in a bust equals (28) D Bust ( A) = [ λh ( ) + (1 λ) H (ˆ)] s f ( A) E We infer the following: LEMMA 7: The number of firms that shut down at the end of the period is increasing in the salvage value of capital q 12 The number of firms that shut down at the end of the period from an industry experiencing a bust is decreasing in the threshold state  and increasing in the proportion λ of new entrants that is specialized The Total Number of Firms Exiting an Industry Let X Boom (A) denote the total number of firms that exit at the end of the period an industry with state A experiencing a boom Because no firms transfer out of an industry in a boom, X Boom (A) equals D Boom (A), given by (27): (29) X Boom ( A) = H ( ) f ( A) E Specialized and adaptive new entrants with skill below ~ s ( A ) exit (by shutting down) in a boom The following firms remain active in a boom: all adaptive firms that transferred in; and specialized and adaptive new entrants with skill exceeding ~ s ( A ) 12 This holds irrespective of whether the industry is experiencing a boom or bust 13 The number of firms that shut down from an industry experiencing a boom is independent of  and λ 17

19 Let (A) X Bust denote the total number of firms that exit at the end of the period an industry with state A experiencing a bust, such that we have X ( A) = D ( A) T ( A) Applying (26) and (28), we obtain (3) X Bust A H ( ~ 1 ( ) = { λ s ( A)) + (1 λ)[1 F( Aˆ)] [1 H ( sˆ) F( Aˆ)]} f ( A) E Bust Bust + Bust The following firms exit an industry in a bust: specialized new entrants with skill below ~ s ( A ) shut down; adaptive new entrants with skill below ŝ shut down; adaptive new entrants with skill exceeding ŝ transfer out; and all adaptive firms that transferred in transfer out The following firms remain active in an industry in a bust: specialized new entrants with skill exceeding ~ s ( A ) We infer the following: LEMMA 8: The total number of firms that exit at the end of the period from an industry experiencing a bust is increasing in the threshold state  and the proportion 1 λ of new entrants that is adaptive The total number of firms that exit at the end of the period from an industry experiencing a boom is increasing in the salvage value of capital q Overview of the Results A fall in q reduces the payoff of shutting down, thus fewer (specialized and adaptive) firms shut down (Lemma 7) and more adaptive firms pursue the strategy of high-skill firms, ie ŝ falls (Lemma 3) As a result, more adaptive firms transfer out of an industry experiencing a bust (Lemma 6), which in equilibrium increases the number of firms transferring into each industry (Lemma 4) as well as the total number of firms entering each industry (Lemma 5) The greater is the proportion 1 λ of new entrants that is adaptive, the more firms transfer into an industry (Lemma 4), and the more firms transfer out of an industry in a bust (Lemma 6), thereby increasing the total number of firms entering an industry (Lemma 5) and the total number of firms exiting an industry in a bust (Lemma 8) The greater is the proportion λ of new entrants that is specialized, the more firms shut down from an industry in a bust (Lemma 7) The intuition is the following Consider an industry with state A experiencing a bust Specialized new entrants with skill below ~ s ( A ) shut 14 The total number of firms that exit from an industry in a boom is independent of  and λ The effect of q on the total number of firms that exit from an industry in a bust is ambiguous, for reasons explained below 18

20 down, and adaptive new entrants with skill below ŝ shut down Because the industry is in a bust, we have that > sˆ Therefore, the proportion H( ~ s ( A )) of specialized new entrants 15 that shut down is greater than the proportion H (sˆ) of adaptive new entrants that shut down It follows that the greater is the proportion shut down overall 16 λ of new entrants that is specialized, the more firms The greater is the proportion of industries experiencing a bust (ie the larger is  ), the more adaptive firms transfer out of industries (Lemma 6) and the fewer adaptive firms shut down from each industry experiencing a bust (Lemma 7), because an increase in  reduces ŝ ; in equilibrium, this raises the number of adaptive firms transferring into industries (Lemma 4) as well as the total number of firms entering each industry (Lemma 5) The total number of firms that exit an industry in a bust is increasing in the proportion 1 λ of new entrants that is adaptive (Lemma 8) The intuition is the following In an industry with state A experiencing a bust, all adaptive firms exit (low-skill adaptive firms shut down and high-skill adaptive firms transfer out), while specialized firms with skill below ~ s ( A ) shut down (and the remainder stay active in the industry) As a result, the greater is the proportion of firms that is adaptive, the greater is the rate of exit from an industry in a bust In an industry experiencing a boom, firms only exit by shutting down; and an increase in the salvage value of capital q raises the incentive to shut down, thus the total number of firms that exit an industry in a boom is increasing in q (Lemma 8) An increase in the salvage value of capital q has an ambiguous effect on the total number of firms that exit an industry in a bust To see this, we decompose firms exiting an industry in a bust into three cohorts First, all adaptive new entrants exit an industry in a bust (by shutting down or transferring), thus the size of this group is not sensitive to changes in q Second, specialized new entrants with skill below ~ s ( A ) shut down, thus the size of this group is increasing in q (Lemma 7) Third, all adaptive firms that transfer into an industry in a bust transfer out An increase in q reduces the proportion of adaptive firms that follow the strategy of high-skill firms, ie ŝ falls (Lemma 3), thus fewer firms transfer out of all other industries 15 No firms that transferred into an industry in a bust shut down from it because, to be transfers, their skill had to exceed ŝ 16 In an industry experiencing a boom, the same proportion H ( ~ s ( A )) of specialized and adaptive new entrants shuts down, thus the number of firms that shut down from an industry in a boom is independent of λ 19

21 (Lemma 6) In equilibrium, this leads to fewer firms transferring into an industry, implying fewer firms transfer out if the industry is experiencing a bust Overall, then, an increase in q raises the number of specialized firms that shut down, but reduces the number of adaptive firms that transfer out (that entered the industry by transferring in), such that the net effect is unclear 5 TESTING THE MODEL We demonstrate the model is consistent with existing empirical evidence on entry and exit by new entrants versus firms relocating across industries (sub-section 51), the characteristics of firms transferring versus shutting down (sub-section 52), and the relationship between firm size and survival (sub-section 53) 51 Entry and Exit by New versus Transferring Firms In Dunne, Roberts, and Samuelson (1988), there are three types of entrants: new firms; existing firms that diversify by opening new production facilities in a different industry (labeled diversifying firm 17 ; and existing firms that enter a different industry by altering the mix of outputs they produce in existing plants (labeled transferring firm The last type of entry represents a firm relocating across industries in the context of our model The evidence shows that, on average, upon entering and exiting, new entrants are smaller than transferring firms As shown in Table 1, relative to all existing producers, upon entering, transfers have an average relative size of 3485%, whereas for new entrants it is 2835% 18 As shown in Table 2, amongst all firms exiting, those that entered as transfers have an average size of 3277% relative to all existing producers, whereas those that entered as new firms have an average relative size of 2857% The model is consistent with the evidence on firm entry Within an industry, managerial skill determines firm size, as in Lucas (1978) Unaware of their skill prior to entry, new entrants are drawn from the skill distribution H On average, the skill of a new entrant is thus equal to the mean m of the distribution H The model predicts that firms transferring into an industry must be 17 We do not have a theory of the scope of the firm, so the empirical properties of diversifying firms are not relevant in testing the validity of our model s predictions 18 Diversifying firms are significantly larger than new entrants or transfers, having an average relative size of 871% This is not surprising given that scope and scale are highly correlated 2

22 sufficiently skilled to do so (in particular, having a skill level that exceeds the cutoff ŝ ), and hence are larger than new entrants The model is consistent with the evidence on firm exit, as it predicts the following New entrants are representative of the entire skill distribution H Amongst new entrants, the proportion λ is specialized and the proportion entrants, the proportion 1 λ is adaptive Amongst adaptive new H (sˆ) is low-skill and the proportion 1 H (ˆ is high-skill Consider an industry with the state of demand/productivity A No firms transfer out of an industry experiencing a boom, thus we suppose the industry is experiencing a bust, ie A Aˆ Amongst adaptive new entrants, those with skill below ŝ shut down, and those with skill exceeding ŝ transfer to another industry Hence, all adaptive new entrants exit at the end of the period, thus they have an average skill equal to the mean m of the distribution H Amongst specialized new entrants, those with skill below ~ s ( A ) shut down, and those with skill exceeding ~ s ( A ) stay active in the industry Hence, specialized new entrants that exit have an average skill of sdh ( We infer the average skill of new entrants that exit (by shutting down or transferring) an industry in a bust is λ sdh ( + (1 λ) m All firms that transferred into an industry in a bust at the beginning of the period transfer to another industry at the end of the period To be transfers, such firms had to have skill exceeding ŝ, thus their average skill is sˆ sdh ( We show in Lemma A2 of the Appendix that (31) sdh ( > λ sdh ( + (1 λ) m sˆ We infer that in an industry in a bust, the average skill of firms exiting that entered as transfers is greater than the average skill of firms exiting that entered as new entrants, thus they are larger 52 Transferring Out of an Industry versus Shutting Down Dunne, Klimek, and Roberts (25) study three food and four construction-related 4- digit manufacturing industries over five year census intervals covering the period

23 The authors estimate a multinomial logit with three outcomes: remain in operation in the industry; remain in operation but shift production to another industry (ie transfer); and shut down the plant Larger and more productive plants are more likely to transfer than shut down: a one standard deviation increase in plant size decreases the probability of closing the plant on average by 49% and decreases the probability of transferring by 74%; and a one standard deviation increase in plant relative productivity decreases the probability of closing the plant on average by 163% and decreases the probability of transferring by 28% The model is consistent with these findings Within an industry, managerial skill determines size and productivity In an industry with state A experiencing a bust, high-skill adaptive firms transfer to another industry, thus the average skill of firms transferring is sˆ sdh ( ; while low-skill adaptive firms and specialized firms with skill below ~ s ( A ) shut down, thus the average skill of firms shutting down is λ sdh ( + (1 λ) sˆ sdh ( We prove in Lemma A1 of the Appendix the former is greater than the latter, implying firms transferring out of an industry are larger and more productive than firms shutting down from that industry Dunne, Klimek, and Roberts also find that firms that transferred into an industry are much more likely to transfer out of the industry (as opposed to shutting down) than other entrants The model is consistent with this finding In an industry experiencing a boom, all firms that transferred into the industry remain active in the industry, and, in an industry experiencing a bust, all firms that transferred into the industry transfer out at the end of the period Therefore, averaging over all industries, the probability that a firm that transferred into an industry transfers out is equal to the probability that the industry is experiencing a bust, F(Aˆ) Consider new entrants Adaptive new entrants with skill below ~ s ( A ) shut down from an industry with state A in a boom; and, in an industry in a bust, adaptive new entrants with skill below ŝ shut down, while adaptive new entrants with skill exceeding ŝ transfer out Therefore, the probability that a new entrant transfers out of an industry is equal to the probability that the industry is experiencing a bust, times the probability that the new entrant is adaptive, times the probability that the adaptive new entrant has skill exceeding ŝ, ie ( 1 λ) F( Aˆ)[1 H (ˆ ], which is clearly smaller than F(Aˆ) 22