Keywords: Private information, long-term financial contracts, exporter dynamics, international trade, financial intermediation
Empirical studies of firms and industries reveal that most exports are produced by a small number of very large firms. In the United States, for example, less than 5 percent of all firms exported some of their production in 2010. More than 97 percent of these exporters were small- and medium-sized firms (500 employees or less), which accounted for about 34 percent of total exports.4 In contrast to large exporters, there is substantial year-to-year transition in and out of export markets for smaller firms. New exporters are typically small relative to the average exporter and frequently stop exporting after one year, while continuing exporters are more likely to expand rapidly in export markets (Bernard & Jensen (2004)).
Does access to credit affect a firm's decision to export? How does the nature of the credit relationship between banks and firms shape the growth of new exporters? Small- and medium-sized firms tend to be more reliant on external financing, which is mostly debt as equity is typically owned by proprietors. There is substantial empirical evidence that the financial conditions faced by small and young firms play an important role in shaping their growth, which is widely interpreted as indirect evidence of frictional financial markets.5 Hysteresis in export markets suggests the presence of a fixed cost of entry (e.g., Das et al. (2007), Paravisini et al. (2011)), thereby suggesting that participation in international trade requires greater access to financing. This in turn could imply that the export decisions of small and medium-sized firms to export is sensitive to the availability of credit. Minetti & Zhu (2011) find evidence supporting this hypothesis by showing that the probability of exporting and the intensity of export is significantly lower for credit rationed firms in Italy.6
Economic theory posits that small and young firms are generally more opaque to external scrutiny. This opaqueness creates an informational asymmetry between lenders and entrepreneurs leading to adverse selection and moral hazard problems. As a result, competitive banks may choose to either ration the supply of credit to young and small firms instead of increasing the price of credit to clear the market (e.g., Stiglitz & Weiss (1981)), or to reduce the private information through repeated interaction and monitoring of firms (e.g., Diamond (1984,1991), Rajan (1992), and Allen & Gale (1999)). Clementi & Hopenhayn (2006) show that long-term financial contracts that are constrained efficient under private information can help account for some of the empirical regularities on firm dynamics - firm entry and exit, and the mean and variance of firm growth. Economic theory is, however, relatively uninformative regarding how private information and long-term credit relationships may affect firms' export decisions and shape their growth in international markets. We propose to fill this gap by studying a general equilibrium multi-country model economy in which entrepreneurs and lenders enter into multi-period credit relationships that are constrained efficient under informational asymmetry.
In the model, entrepreneurs are born with a blueprint to start a long-lived firm. A firm requires an initial fixed investment to start, and working capital to pay for factor input and the trade cost before production takes place. New entrepreneurs do not have wealth to start a firm, and must seek financing from competitive financial intermediaries. Financial frictions arise because financial intermediaries cannot directly observe the revenue generated by the firms they are financing, and must instead rely on reports from creditor entrepreneurs. Financial intermediaries mitigate the moral hazard by offering new entrepreneurs a long-term financing contract designed to induce truthful reporting. The financial arrangement in our model is closely related to that in Clementi & Hopenhayn (2006), and a financing constraint emerges as an outcome of the optimal contract.
In equilibrium, new firms operate below their efficient level, and the financing constraint is relaxed as the entrepreneur's claim to future cash-flows increases. Firms that are able to service their debt for a sufficiently long time may borrow enough to pay the trade costs and expand into international markets. New exporters are less financially constrained than domestic firms, but their growth continues to depend on their performance each period until they become fully unconstrained. Financial intermediaries actively engage in maturity and risk transformation in a competitive financial market using workers' and entrepreneurs' short-term deposits to fund a portfolio of long-term risky projects.
Consistent with empirical regularities on firms dynamics (e.g, Cooley & Quadrini (2001)), the model implies that older and larger firms have lower average and more stable growth rates, and are more likely to survive; and that smaller and younger firms pay fewer dividends, borrow and invest more, and that the investment of small firms is more sensitive to cash flows, even after controlling for their future profitability. Consistent with with empirical studies on exporters (e.g., Eaton et al. (2007) and Ruhl & Willis (2008)), the model implies that new exporters account only for a small share of total exports, and that a large fraction of new exporters does not continue to export in the following year. Furthermore, continuing exporters are less likely to exit export markets as the number of years exporting increases, have larger and more stable sales, and generally reach their efficient size in a few years.
This paper contributes to the theoretical literature exploring the dynamics of firm export decisions. Research in this direction has modeled firm export dynamics as the outcome of learning as in Eaton et al. (2012), investment in risky R&D as in Atkeson & Burstein (2010), persistent idiosyncratic shocks to productivity (e.g., Ruhl & Willis (2008), Arkolakis (2011) and Alessandria & Choi (2011), and Kohn et al. (2011)).7 A key difference is that selection into export markets does not depend on a firm's (expected) productivity (e.g., Melitz (2003)), which is constant in our model. Rather, selection into export market depends on a firm's present value of expected discounted cash flow, whose evolution is governed by the financial contract and its performance. Furthermore, our general equilibrium framework proposes a novel link between industry dynamics, the balance sheets of lenders, and aggregate conditions, thereby relating financial intermediation to international trade.
The rest of the paper is organized as follows: Section 2 presents the model and Section 3 describes the financial arrangement between investors and entrepreneurs and derives the properties of the optimal contract. Section 4 defines the general equilibrium, and section 5.1 analyzes the model numerically. Concluding comments are contained in Section 6; proofs of propositions and derivations are relegated to the Appendix.
Workers are born without wealth, survive into the next period with exogenous probability , and are instantly replaced by new ones when deceased. Workers discount the future at rate and are endowed with one unit of time each period, which they allocate between labor and leisure. Labor is paid at wage , and workers use their income to either buy the numéraire consumption good , or to purchase contingent claims at price that pay units of consumption in the next period if the agent is alive, and zero otherwise. Agents do not value bequests, and will thus place all their savings in these claims. Workers assess their consumption-leisure decision according to
New entrepreneurs are born with a blueprint to produce an intermediate good . Entrepreneurs, like workers, are born without wealth, survive into the next period with probability , and are instantly replaced upon death. Entrepreneurs are risk-neutral, and discount the future at the rate .9 We assume entrepreneurs do not make labor-leisure decisions, and instead devote a fixed fraction of their time to supervise their firm. Entrepreneurs assess their consumption decision according to
Financial intermediaries are risk-neutral and discounts the future at the same rate as entrepreneurs. They raise short-term deposits from workers via the annuity market, and can offer long-term financing to the entrepreneurs. The assumptions on worker characteristics imply stationary demographics of workers so that annuities can be offered without risk. Deposits from workers and entreprenuers in period are used to fund entrepreneurs' risky projects in period . Repayments from entrepreneurs to the intermediary are used to repay the deposits with interest. Perfect competition and constant returns to scale in financial intermediation implies that we can focus on a representative financial intermediary.
The final good is assembled by a large number of firms using domestically produced and imported intermediate goods and a constant elasticity of substitution aggregator. Intermediate goods are imperfect substitutes, and final good producers maximize their profit
Producing an intermediate good requires an initial investment that is sunk, and per period working resources to hire labor and to be used as capital. The -th firm produces the -th good according to a neo-classical production function , where is capital input and is labor input. We assume that the capital used in production is fully depreciated at the end of the period. An entrepreneur wishing to export must pay a fixed export cost before production begins, and chooses the quantity and of goods to sell domestically and abroad, respectively.10 It follows that the allocation of period working resources must satisfy:
The -th firm is a monopolist for its differentiated product, and takes the inverse demand function for its product - price as a function of quantity - as given. Project returns of all firms are subject to a sequence of independent and identically distributed idiosyncratic revenue shocks , where . Firm status is indexed by , where and indicate that a firm sells to the domestic market only, or to both the domestic and export market, respectively. The maximum revenue a firm can generate with resources is:11
Revenues are only observed by entrepreneurs, so lenders can only learn about the firm's performance and the realizations of the revenue shocks through entrepreneurs' reports, . We denote the history of reports up to period by . A contract is a set of decision rules . Conditional on surviving, a firm is either liquidated, , in which case the entrepreneur receives and the financial intermediary receives , where is the salvage value, or it remains in operation. If a firm is kept in operation, the contract specifies whether or not the firm exports, , and the size of the loan, . After production takes place and revenues are realized, an entrepreneur makes a repayment to the financial intermediary conditional on his ex-post report . Figure 1 summarizes the timing of events within one period.
A reporting strategy for an entrepreneur is a sequence of reports , where is the true history of realizations of revenue shocks. After every history , the pair implies an expected discounted cash flow and for the entrepreneur and the financial intermediary, respectively. A feasible and incentive compatible contract is optimal if it maximizes for every possible . Following Clementi & Hopenhayn (2006), we refer to and as equity and debt, respectively, so that the joint surplus is the value of the firm.
Using the method of Abreu et al. (1990), the optimal contract can be written recursively by using as a state variable and by defining and as promised continuation values. It follows that equity must satisfy the following accounting identity:
Panel (a) of Figure 2 plots the optimal value of the firm, , and the value to the intermediary, , as a function of equity, . A firm faces a binding borrowing constraint whenever its equity is below , where is the unconstrained level of resources. That is, is the level of resources that solves the static profit maximization of the firm such that . New firms start at , so that expected profits of the intermediary cover the cost of the initial investment . Smaller firms take on more debt than larger firms, and firms with equity less than cannot borrow enough to pay the trade costs.
Firms' access to credit and growth are determined by the evolution of their capital structure. Using constraints (8), (9) and (10), and solving for next period's equity conditional on the revenue report yields the following law of motion for equity:
Figure 3 plots the decision rules for loans, repayments, and dividends as a function of equity. Due to risk-neutrality, joint surplus is maximized when equity grows fastest, so dividends to the entrepreneur are optimally zero until the firm can no longer grow faster by postponing dividends, which is when . This implies that it is optimal for the financial intermediary to set the entrepreneur's repayments to for whenever as it allows for the fastest accumulation of equity toward the unconstrained level. Furthermore, the optimization problem takes place on the convex set , which implies whenever . From constraints (8) and (9):
Panel (c) of Figure 3 plots the investment rate conditional on receiving a high and low revenue shock as a function of equity. Investment by constrained firms is always positive after receiving a high shock, and always negative after recieving a low shock for constrained firms. The investment of small firm, and therefore cashflow, is also more sensitive to revenue shocks than that of larger firms. Furhermore, there is a large increase in investment once the firm becomes an exporter, with subsequent very high possible disinvestment should the firm receive a low shock and exit export markets.
Perfect competition in the financial sector implies that annuities are priced at the workers' survival rate .17 The assumptions on worker characteristics ensure that there exists a stationary demographic with constant aggregate deposits and labor supply. Let and be the deposits and hours worked of a -period old worker. Setting the mass of workers to one, it follows that aggregate deposits by workers each period are given by
Perfect competition in the financial sector also implies that financial intermediaries break even on new contracts with entrepreneurs, or that
in equilibrium. As discussed in the previous section, firm equity evolves according to the conditional continuation values specified in the contract,
and , and the sequence of revenue shocks. Let
be the state space for firm equity so that
be the Borel algebra generated by
, and the measure defined over
. Proposition 4 follows:
Proposition 4There exists a unique stationary distribution of firms that is ergodic.
The intermediary uses the capital it has accumulated through entreprenuers' repayment, , and workers' deposits, , to finance the initial set-up cost and the wage and capital expenditures of all firms before production takes place. It follows that the capital market clears when
Furthermore, the intermediary's budget must be balanced each period. That is, the intermediary's receipts from entrepreneurs plus the scrap value from liquidating poorly performing firms and the return on their own equity must be large enough to finance the cost of borrowing funds on the capital market. A stationary distribution of firms implies that in equilibrium, and it follows that:
Labor market clearing requires that the labor supply from workers is equal to the demand for labor by firms, so that:
Proposition 4.3 There exists a worldwide stationary equilibrium.
The contract needs to be solved numerically.23 Once the value of the firm and the decision rule for loan size are known, the remaining decision rules can be expressed in closed form as functions of . Given the initial firm size and the law of motion for , we can simulate the life-cycle of a large number of firms to estimate the stationary distribution of firms.24
Let the instantaneous utility function for the workers be .25 We simplify the analysis by considering the case of symmetric countries and a constant returns to scale Cobb-Douglas production technology for intermediate goods: , with . The final good is produced according to a constant elasticity of substituion (CES) production function with constant returns to scale.
A period in the model is 1 year. We begin by fixing five parameters: The worker death rate is chosen so that the average life of workers is 50 years. The iceberg cost of exporting is set to 40 percent, which is in line with previous studies such as Anderson & van Wincoop (2004). The probability of a high revenue shock is 0.5, which produces investment volatility roughly in line with studies of firm such as Cooper & Haltiwanger (2006); and the salvage value is set to 80 percent of the set-up cost . We set the elasticity of substitution between intermediates to , which is consistent with Broda & Weinstein (2006).26
Given the above, the six remaining parameters are jointly chosen to match the following six moments:27 a labor income share of 60 percent, an average working time of 35 percent, an interest rate of 4 percent, an exit and entry rate of 6.3 percent (in line with Lee & Mukoyama (2008)), a share of exporters of 27 percent in line with Bernard et al. (2007), and we require that new firms start at a size that is 15 percent of the unconstrained firm size.28 Table 1 summarizes the calibration. After solving the model, we simulate the life of firms from which we compute the statistics reported in Table 2 and the figures discussed in the next sub-section.
Table 2 shows that, in the aggregate, the consumption-to-output and investment-to-output ratios are roughly in line with data, which principally follows from targeting the labor income share and labor hours. The export-to-output ratio is 8.7 percent, which is in line with the US over the last four decades.29
Our results on firm dynamics are consistent with the empirical regularities reported in Cooley & Quadrini (2001) and similar to those in Clementi & Hopenhayn (2006). Panel (a) of Figure 4 shows that the hazard rate of exit first increases for new firms and then decreases with firm age. On average, 1.2 percent of all firms are liquidated every period, which accounts for about 20 percent of all exiting firms. Panels (b) and (c) of Figure 4 plots the mean and standard deviation for firms of a given age, respectively, and show that younger firms experience a faster albeit more volatile growth than older ones.30
Comparing exporters to domestic firms, Table 2 shows that the average exporter is four times larger (in terms of labor and capital) than the average domestic firm. On one hand, the contract requires that the entrepreneur have sufficient stake into the firm (by accumulating equity) to obtain a loan that is sufficiently large to pay the export costs and generate the additional revenue. On the other hand, the financial position of a firm improves and its access to credit increases after it begins exporting (Figure 5). Thus, while less financially constrained firms are able to export, the financial health of exporters is substantially higher than that of domestic firms because of their activities. This observation highlights the great difficulty of disentangling these two effects in the data.
Let us begin our discussion of exporter dynamics with an example. Figure 6 plots the life-cycle of three firms taken from our sample of simulated firms. It takes 13 years for Firm 1 to accumulate enough equity to beginning exporting, but it exits export markets after its first year. Firm 1 gains access again to export markets at age 15, from which time it continues to grow until it reaches its efficient size at age 21 and finally exits at age 25. Firm 2 reaches the export lottery region after 12 years but initially fails to secure funding to export. Firm 2 successfully become an exporter 2 years later and continue to export until it exits at age 17. Firm 3 is the least successful of our three firms, and was never able to grow nearly large enough to export, and was liquidated by the bank at age 23.31
The long-term financial contract plays an important role in shaping both the extensive as well as the intensive margin of trade. New exporters face a high probability of exit from export markets during their first year. Panel (a) of Figure 6 plots the hazard rate of exit from export markets. A third of new exporters exit after their first year. Continuing exporters become less likely to exit as their export spells increase, until they only face the exogenous exit rate of 5 percent. To see this, note that new exporters start out with equity that is close to the export lottery region, so that a low shock leads to exit from export markets if the firm loses the lottery. But since firms grow on average, older exporters, who have more equity, are further away from the export lottery region; and unconstrained exporters only cease to export when the entrepreneur dies.
Young exporters grow faster than established ones, but their growth is more volatile. Panels (b) and (c) of of Figure 6 plot the mean and standard deviation of investment of exporter conditional on the length of their export spell. The average growth rate of a two year old exporter is 1.2 percent, and is close to 0 after ten years. The standard deviation of investment, however, is about five times higher for a two year old exporter than a ten year old one.
Few firms start exporting every year, and continuing exporters expand rapidly. Panel (a) of Figure 7 shows that new exporters start with about two thirds of the resources used by an unconstrained firm, and operate close to their unconstrained size (95 percent) after exporting for five years (on average).
New exporters are small, and most exports are produced by very large firms. Only 3.3 percent of domestic firms start exporting every period, and this cohort accounts for about 9 percent of all exporters (panel (b) of Figure 7). Exporters that have been exporting for up to five years account only for approximately 25 percent of all exports (panel (c) of Figure 7). Therefore, the model predicts that the bulk of all exports is produced by established firms that have been exporting for five years or more.
There is widespread empirical evidence that financial fictions play an important role in shaping the growth of small and young firms. There is also growing empirical evidence that the export decisions of firms are sensitive to the availability of credit. This paper investigates how private information and long-term credit relationships may affect firms' export decisions and shape their growth in international markets. We propose and analyze a general equilibrium multi-country model economy in which entrepreneurs and lenders enter into multi-period credit relationships subject to an informational asymmetry.
We show that the model is consistent with empirical regularities on firms dynamics from the industrial organization literature, and with the models proposed to account for them. Furthermore, in line with recent empirical studies on firm export dynamics, our model predicts that new exporters account only for a small share of total exports, and that a large fraction of new exporters does not continue to export in the following year. Continuing exporters, are less likely to exit export markets as the export spell increases; moreover, continuing exporters experience faster and more volatile growth, and generally reach their efficient size in a few years.
The first-order condition for the maximization of equation (4) with respect to variety yields
Let us redefine the inverse demand functions as and similarly , where
The workers problem can be written recursively as
To show this condition holds, we start from the zero profit condition for final goods producers and invoke the market clearing condition for intermediate goods (Equation (23)):
Proposition E.1 There exists a point such that for all , and for all .
Proof It is optimal to reach the unconstrained value in the shortest time possible because the joint surplus is maximized there and both the entrepreneur and the financial intermediary are risk-neutral and share the same discount factor. Hence, repayments should be set equal to revenues as long as . This follows the argument set forth in Clementi & Hopenhayn (2006). Let us thus rewrite the value of a firm with a given export status as
When the equity of a domestic firm goes to zero, its value goes to : the first constraint, together with the fact that continuation values have to be non-negative, forces continuation values to go to zero, as equity approaches zero. It follows that the spread between and goes to zero, so has to go to zero to maintain incentive compatibility. Therefore, the optimal resource advancement of a domestic firm will approach zero and thus its value will go to the discounted scrap value. In the case of an exporting firm, the logic is very similar, except that the resource advancement approaches the fixed cost of exporting , which cannot be seized by the entrepreneur. The value of an exporting firm with equity zero will hence be the discounted scrap value minus the cost of paying the export cost, . As both firm value functions are increasing and concave, and strictly so for , the fact that and implies a unique crossing.
Proposition E.2 The function contains an interval on which it is not concave. This implies together with risk neutrality that it is optimal to use an export lottery.
Proof As shown in the previous proposition, there exists a unique equity value where the two value functions cross. For any given , the slope of the exporting firm's value function is steeper than the slope of the non-exporting firm, i.e. . This follows from the fact that the same is true for the underlying revenue functions. Therefore, by continuity of the value functions, . This implies that the function is not concave on some interval . Since the marginal profit of an extra unit of resources goes to infinity as approaches zero, , and as the slope of the exporting value function is zero at the unconstrained level, .
Proof of Proposition 3.1 As outlined above, is increasing and concave for , so any convex combination of the two functions and is too. Since and for some (otherwise it would not pay to finance firms at all), and by assumption, . We know that , so by concavity of the functions , it follows that . Finally, because , it has to be that .
The first point follows immediately from the fact that the expected value of the liquidation lottery is equal to the equity with which an entrepreneur enters it, thus pinning down the probabilities of liquidation and survival. To prove the second point, we have to show that . From the above, it follows that the interval is non-empty. By definition, , which implies together with concavity that . This means that no company with finds it profitable to export, and all companies with do. A company with equity is offered a lottery with expected value equal to the equity the entrepreneur had before. The probabilities of getting and are determined thereby. An entrepreneur wins the lottery with probability , receiving and thus exporting; with probability , he gets and will hence not export.
Concerning the third point, it is clear that is linear in the two lottery regions. When , the value of the firm does not change anymore, so it will stay constant at . The functions are strictly increasing as long as , since is strictly increasing in that region. Therefore the firm value function is strictly increasing for all .
Proof of Proposition 3.2 Partition the domain of the contract in five parts . From the above when and when .33 When , the firm is unconstrained and there is no need to provide any incentives to report the truth (as all revenues will go to the entrepreneur), and hence , so . Whenever or , the firm enters a lottery and will either end up with or , with the expected value of the lottery being exactly equal to the promised value or . The expected next period equity for each of these is and , so that . Similarly, when , the lottery for liquidation yields the expected payoff , and the expected equity for next period is then just .
In the stationary steady state, given interest rate and wage , perfect competition in the financial market implies financial intermediaries earn zero-profit on a new contract. This implies new entrepreneurs receive an initial equity , for which the lender earns just enough to break even. The initial equity is endogenous in the general equilibrium.
Consider the sequence of equity levels from a single firm indefinitely replaced by a new one when it dies. It is clear is a sequence of random variables, and its evolution depends on the properties of the contracts and on the sequence of shocks - productivity, death, export, and liquidation. In what follows, we show that is a time-homogeneous Markov chain such that
Proposition F.1 (Stationary distribution) X is a time-homogeneous Markov chain on a general state space and is globally stable.
Equip the state space with a boundedly compact, separable, metrizable topology . Let be the measure space for the shocks. Let be any subset of . It follows for any and
For each , is a non-negative function on , and for each , is a probability measure on . Therefore, for any initial distribution , the stochastic process defined on is a time-homogeneous Markov chain. Let denote the corresponding Markov operator, and let denote the collection of firms distribution generated by for a given initial distribution.34
Write the stochastic kernel with the density representation so that for all . The Dobrushin coefficient of a stochastic kernel is defined by
Proposition F.2 (Existence of a stationary equilibrium) The unique and ergodic invariant distribution of is continuous in prices. The result follows if the conditions of (LeVan & Stachurski, 2007, Proposition 2) are satisfied and the proof is similar to the one in Verani (2011).
We investigate the effect of the elasticity of substitution between intermediate goods firms on firm dynamics and the aggregate by considering another world economy with . To help with the comparison, we calibrate the economy with to the same moments as the economy with . Table 3 summarizes the value of the parameters used for each economy.
|Worker's discount rate||0.959||0.959|
|Elasticity of leisure||2.300||2.304|
|Workers' death probability||0.02||0.02|
|Fixed export cost||0.033||0.012|
|Probability of high/low shock||0.5||0.5|
|Firm exogenous exit rate||0.047||0.05|
Table 4 reports the results for the two economies. Given the calibration, the wage rate, aggregate output, consumption and investment are roughly the same in the two model economies so that, from a macroeconomic point of view, the two world economies are comparable. However, a higher reduces the market power of intermediate goods producers at home and abroad. This translates into lower prices for all goods, with a comparatively greater decrease in the price of internationally traded goods. Furthermore, a decrease in firms' market power leads to a substantial reduction of the export share of aggregate output. A greater fraction of domestic firms begins exporting every period, and the hazard rate of exit for new exporters after one year is also higher. Last, a reduction in market power also increases the size differential between domestic and exporting firms, while the share of unconstrained firms becomes smaller.
|Targeted: Interest rate||0.040||0.040|
|Targeted: Hours worked||0.350||0.349|
|Targeted: Labor income share||0.597||0.602|
|Targeted: Entry/exit rate||0.066||0.063|
|Targeted: Relative size of entrants||0.158||0.153|
|Targeted: Share of exporters||0.273||0.269|
|Not targeted: Wage rate||0.493||0.501|
|Not targeted: Domestic goods price index||3.272||3.079|
|Not targeted: Imported goods price index||6.033||4.925|
|Not targeted: Output||0.289||0.291|
|Not targeted: Consumption/Output||0.796||0.792|
|Not targeted: Investment/Output||0.204||0.208|
|Not targeted: Export/Output||0.138||0.087|
|Not targeted: Entry rate in export market||0.028||0.033|
|Not targeted: Exit rate from export market after 1 year||0.256||0.320|
|Not targeted: New firm size relative to incumbents||0.321||0.335|
|Not targeted: Domestic firm size relative to exporters||0.269||0.242|
|Not targeted: Share of unconstrained firms||0.177||0.148|
The results for exports are driven by how the calibration for the economy with affects the fixed and variable trade costs, and . We keep the variable trade costs constant across the two economies, which implies that the ratio of exports to domestic sales decreases as market power decreases for each exporter.35 It follows that the fixed cost of exporting must be lower in an economy with a higher to keep the number exporters constant. This implies that the export lottery region is smaller making it easier for firms to enter and exit export markets.
Furthermore, unconstrained firms with lower market power use more resources and sell higher quantities of goods. Since large firms are always exporters, the relative size of exporters is also higher. A lower market power implies that firm profit is also lower, thereby reducing the speed of firm growth and leading to a smaller fraction of unconstrained firms.36 To see this, note that the incentive compatibility constraint binds for constrained firms, which implies that . It follows that smaller revenue implies that the spread between the continuation values is smaller too; and the number of steps needed to reach the unconstrained level is higher.