Export failure and its consequences: evidence from Colombian exporters

Abstract

Exporters pay high fixed costs to enter foreign markets, yet the majority will not export beyond one year. What happens to these exporters after they fail abroad? For these firms, exporting likely resulted in heavy profit losses. Despite this, the trade literature largely ignores export failure and views exporting as a simple cost-benefit analysis based on foreign profits and trade costs. This rationale ignores the differential effect export failure may have on financially-constrained firms. This study develops a heterogeneous-firm model with financial constraints and marketing costs to show how export failure can have the following effects: (1) make the liquidity constraint more likely to bind, (2) force financially-constrained firms to limit marketing expenditure and, hence, decrease domestic sales, and (3) induce some firms to default. A Colombian dataset merging firm-level trade and financial data is built to test the propositions of the model. The author finds evidence that export failure has a differential impact on financially-constrained firms. After exporting, financially constrained unsuccessful exporters have a worse cash flow to total assets ratio, lower domestic revenue, slower domestic revenue growth, and a higher probability of going out of business. The findings are robust to comparisons with similar successful exporters and even non-exporters, and an instrumental variable approach.

Appendices

Appendix A Proofs and extensions

1.1 Credit-constrained firm threshold

1.2 Maximization problem for unconstrained firms

For financially unconstrained firms, Eq. (4) does not bind and firms can borrow as much as they desire. Substituting Eqs. (2), (3), and (5) into the maximization problem gives the problem for unconstrained unsuccessful exporters:

$$\begin{aligned} \max _{p_i,L_i} \ E \pi _i(\phi _i)=L_iA p_i^{1-\sigma }- \frac{L_iA\ p_i^{-\sigma } }{\phi _i} -f_x -f_d -L_i^\beta \end{aligned}$$

(8)

Firms set prices by maximizing Eq. (8) with respect to $p_i$. The profit-maximizing price is the following:

$$\begin{aligned} p_i^*=\frac{\sigma }{\sigma -1}\frac{1}{\phi _i}=\frac{\mu }{\phi _i} \end{aligned}$$

(9)

where $\mu =\frac{\sigma }{\sigma -1}$ is the firm’s constant markup above marginal cost. Notice that $L_i$ levels do not affect this decision.

The number of consumers a firm reaches, $L_i$, increases net revenue, $p_iq_i-\frac{q_i}{\phi _i}$, but also increases marginal marketing costs, $\beta L_i^{\beta -1}$, at an increasing rate. Profit-maximizing firms set the marginal cost of marketing equal to the marginal revenue of marketing. That is, by maximizing Eq. (8) with respect to $L_i$ and substituting in the profit-maximizing price (Eq. 9), I get the profit-maximizing marketing expenditure:

$$\begin{aligned} L_i^* =\left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{\beta -1}} \left( \frac{\mu }{\phi _i}\right) ^{\frac{1-\sigma }{\beta -1}} \end{aligned}$$

(10)

Since neither the fixed-exporting costs nor foreign revenue affects this decision, all financially unconstrained firms in the domestic market, regardless of their classification (non-exporter, unsuccessful exporter, and successful exporter), choose $L_i^*$. $L_i^*$ is increasing in productivity, $\frac{\partial L_i^*}{\partial \phi _i}>0$.

1.3 Constrained firm threshold

For all financially constrained firms, Eq. (4) binds when setting price and marketing levels equal to the profit-maximizing $p_i$ and $L_i$. For the firm at the constrained/unconstrained threshold, Eq. (4) binds and yet the firm still chooses $p_i^*$ and $L_i^*$. To find this firm, I substitute all of the constraints from the maximization problem and the profit-maximizing $p_i^*$ and $L_i^*$ into Eq. (4), and solve for $\phi _i$. For unsuccessful exporters, the constrained threshold firm, $\phi _C^{fail}$, is the following:

$$\begin{aligned} \phi _C^{fail} = \mu \left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{ f_x +f_d-(1-\lambda )f_e}{\lambda \beta -1} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

(11)

Had this firm not tried to export, it would not have the export loan, and would be in better financial health. This can be seen by comparing this firm to a similar non-exporting firm. The constrained threshold firm for the non-exporters is the same, except $f_x=0$. Thus, I can also think of the threshold firm $\phi _C^{dom}$ as the threshold firm for all exporters before trying to enter the foreign market:

$$\begin{aligned} \phi _C^{dom} = \mu \left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{f_d-(1-\lambda )f_e }{\lambda \beta -1} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

(12)

Successful exporters have to pay the fixed export costs, just like the unsuccessful exporters, but now have two revenue sources. While all successful exporters sell abroad, not all will export at the profit maximizing $p_i^*$ and $L_i^*$. The constrained threshold firm for successful exporters depends on the size of the foreign market, foreign prices, and the other trade costs. If the successful exporter enters a foreign market similar to that of the home market, $Y_h=Y_f=Y$, with a price level equal to that of the domestic level times the iceberg trade costs, $P_f=P_h\cdot \tau _{if}=P$, then $A_f=A_h\cdot \tau _{if}^{\sigma -1}$ and the threshold firm for successful exporters, $\phi _C^{succ}$, becomes:

$$\begin{aligned} \phi _C^{succ} = \mu \left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{f_x+f_d-(1-\lambda )f_e}{2(\lambda \beta -1)} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

(13)

For the general case where the firm does not export to a market similar to that of the home market, see Appendix A.6.a.²⁴

1.4 Proof of proposition 1

Proof for the first statement: Essentially, the cutoff for non-exporters is the cutoff before a firm attempts to export, irrespective of export success. Thus, to prove the first part of the proposition, I compare the constrained threshold for successful and unsuccessful exporters, individually, with that of the non-exporter threshold.

To prove that the threshold for unsuccessful exporters is higher after the export attempt ($\phi _C^{dom}<\phi _C^{fail}$), Eq.  (11) must be bigger than Eq. (12). This holds as long as $f_x>0$. Notice also that the threshold increases with exporting fixed costs ($\frac{\partial \phi _C}{\partial f_x}>0$). The sign of the derivative is positive because $\frac{1-\beta }{\beta (1-\sigma )}>0$; since $\beta >1$ is required for an interior marketing solution and $\sigma >1$ is required for an interior pricing solution; and I assume fixed costs are greater than the collateral times the financial friction ($f_d >(1-\lambda )f_e$) and $\lambda \beta >1$.

To prove that the threshold for successful exporters is higher after exporting ($\phi _C^{dom}<\phi _C^{succ}$), Eq. (13) must be larger than Eq. (12). This holds as long as $f_d-f_x< (1-\lambda )f_e$. This statement is true since $(1-\lambda )f_e>0$ and $f_x>f_d$. Thus, some successful exporters that were not previously financially constrained might become constrained.

Proof for the second statement: For the second statement, I compare the thresholds between successful exporters (Eq. 13) and unsuccessful exporters (Eq. 11). Comparing the two thresholds, $\phi _C^{succ}<\phi _C^{fail}$ if

$$\begin{aligned} \frac{1}{2} \left( f_x+f_d-(1-\lambda )f_e \right) <\left( f_x +f_d -(1-\lambda )f_e \right) \end{aligned}$$

This holds because $(1-\lambda )f_e <f_x+f_d$. While both types of firms are worse off in terms of domestic revenue, the difference between successful and unsuccessful financially constrained exporters is that the successful ones are not solely dependent on the domestic market for their revenue.

1.5 Credit-constrained firm marketing decision

For financially constrained firms, choosing the profit-maximizing $p_i$ and $L_i$ results in Eq. (4) binding. These firms are unable to get their desired financing and reduce their need for financing by lowering their marketing costs, which results in fewer consumers. The marginal revenue from reaching more consumers is constant while the marginal costs will be increasing. Furthermore, reaching more consumers, higher $L_i$, requires more financing, $\frac{\partial F(L_I)}{\partial L_i}=\beta L_i^{\beta -1}$, which increases the repayment necessary to meet creditors’ demands, $\frac{\partial B_i}{\partial L_i}=\frac{\beta L_i^{\beta -1}}{\lambda }$. These two equations only equal when there are no financial frictions ($\lambda =1$). An unconstrained risk-neutral firm discounts the repayment by $\lambda$. A financially constrained firm is unable to discount because of the liquidity constraint, and sets $L_i$ below $L_i^*$. Since deviation from optimum $L_i$ lowers profits, the firm deviates as little as possible to ensure that the creditors break even. The second-best $L_i$ for unsuccessful exporters is determined by setting Eq.  (4) to equality and substituting in Eqs. (2), (3), (5) and (9). I get the following equation:

$$\begin{aligned} \frac{L_iA}{\sigma }\left( \frac{\mu }{\phi _i}\right) ^{1-\sigma } -\frac{L_i^\beta }{\lambda } = \frac{ f_x+f_d -(1-\lambda )f_e}{\lambda } \end{aligned}$$

(14)

For the before-exporting decision, set $f_x=0$. This is also the $L_i$ chosen by non-exporters. Thus, non-exporters choose $L_i$ based on the following equation:

$$\begin{aligned} \frac{L_iA}{\sigma }\left( \frac{\mu }{\phi _i}\right) ^{1-\sigma } -\frac{L_i^\beta }{\lambda } = \frac{f_d -(1-\lambda )f_e}{\lambda } \end{aligned}$$

(15)

For financially constrained successful exporters, the firm’s choice of $L_i$ depends on the foreign market and the trade costs. So, a previously financially constrained firm can become more constrained, less constrained or, even, unconstrained. The outcome depends on the net revenue from the foreign market. As before, if a firm enters a similar sized market ($Y_h=Y_f=Y$) with a foreign price level equal to that of the domestic price times the iceberg trade costs ($P_f=P_h\cdot \tau _{if}=P$), then $A_h=A_f=A$ and the successful exporter chooses the following $L_i$ in both markets:

$$\begin{aligned} \frac{L_iA}{\sigma }\left( \frac{\mu }{\phi _i}\right) ^{1-\sigma } -\frac{L_i^\beta }{\lambda } = \frac{f_x+f_d -(1-\lambda )f_e}{2\lambda } \end{aligned}$$

(16)

Below I show that there is a lower-bound for $L_i$, prove that $L_i$ is increasing with productivity ($\frac{\partial L_i}{\partial \phi _i}>0$), and link $L_i$ to domestic revenue.

1.6 Lower threshold for $L_i$

While I cannot solve for $L_i$, I know $L_i$ is between the profit-maximizing $L_i$ (Eq. 10) and the $L_i$ that maximizes the left-hand side of Eqs. (14) to (16). Notice that maximizing the left-hand side of Eqs. (14) to (16) with respect to $L_i$ is just like maximizing expected profits with respect to $L_i$ in the unconstrained case, except that the marketing costs are divided by $\lambda$.²⁵ There is no incentive to lower $L_i$ beyond the value that maximizes the left-hand side of the above equation because beyond that point the discounted marginal repayment cost of marketing, $\beta L_i^{\beta -1}$, is lower than the marginal revenue of marketing, $p_i q_i - \frac{q_i}{\phi _i}$; and the firm would be better off increasing $L_i$.

The $L_i$ maximizing the left-hand side of Eq.  (14) to (16) is given by the following equations:

$$\begin{aligned} L_i^C =\lambda ^{\frac{1}{{\beta -1}}}\left( \frac{A}{\sigma \beta } \right) ^{\frac{1}{{\beta -1}}} \left( \frac{\mu }{\phi _i}\right) ^{\frac{1-\sigma }{{\beta -1}}} \end{aligned}$$

(17)

From Eq. (10) and (17), I can see that $L_i^C =\lambda ^{\frac{1}{{\beta -1}}}L_i^*$. Since $\lambda <1$ and $\beta >1$, then $\lambda ^{\frac{1}{{\beta -1}}}<1$ and $L_i^C <L_i^*$. Thus, as in Manova (2013), financially constrained firms choose either an $L_i$ that lies between these two values or one of these two values.

1.7 Proof that constrained $L_i$ is increasing in $\phi _i$

The equations for the constrained $L_i$ choice for all firms are identical on the left hand side: $\frac{L_iA}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma }-\frac{L_i^\beta }{\lambda }$ (see Eq. 14 for the unsuccessful exporter choice, Eq. 15 for the domestic producer choice, and Eq. 16 for the successful exporter choice). The right hand side differs, but it does not vary by productivity or marketing choice. To prove that the constrained $L_i$ choice is increasing in $\phi _i$ I take the total derivative of each of the equations and set them equal to zero. In all cases I get the following:

$$\begin{aligned} \frac{dL_{i}}{d\phi } =\frac{(\sigma -1)\phi ^{\sigma -2}\frac{L_{i}A}{\sigma }\left( \mu \right) ^{1-\sigma }}{\frac{\beta L_{i}^{\beta -1}}{\lambda } - \frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma } }>0 \end{aligned}$$

This is positive since $\sigma >1$, and $\frac{\beta L_{i}^{\beta -1}}{\lambda } >\frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma }$, that is, for financially unconstrained firms, marginal revenue from marketing is less than the marginal cost from marketing. Notice that $\frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma }$ is the marginal revenue of marketing and $\frac{\beta L_{i}^{\beta -1}}{\lambda }$ is the marginal cost of borrowing for marketing costs. All firms are risk neutral, and all unconstrained firms choose the $L_i$ that sets the discounted marginal cost, $\beta L_{i}^{\beta -1}$, equal to the marginal revenue of marketing, $\frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma }$. The discounted marginal cost is below the marginal cost of borrowing for marketing, $\frac{\beta L_{i}^{\beta -1}}{\lambda }$. Financially constrained firms would like to do the same, but doing so makes their liquidity constraint bind. As they decrease $L_i$, their marginal cost of borrowing for marketing decreases, but it is still above their marginal revenue. Deviating from the profit maximizing $L_i$ also means lower expected profits, so the firms deviate as little as possible.

As mentioned above, there is no point in lowering $L_i$ below $L_i^C$, and hence no point in lowering marginal costs below that which equates marginal revenue to marginal cost of borrowing for marketing. So the least productive firm to produce has to set marginal cost of borrowing for marketing equal to marginal revenue of marketing. All firms set marginal cost of borrowing for marketing greater than or equal to the marginal revenue $\left( \frac{\beta L_{i}^{\beta -1}}{\lambda } \ge \frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma } \right)$ and only unconstrained firms set the discounted marginal cost of marketing equal to marginal revenue of marketing $\left( \beta L_{i}^{\beta -1}=\frac{A}{\sigma }\left( \frac{\mu }{\phi }\right) ^{1-\sigma } \right)$.

1.8 Domestic revenues before and after exporting

Domestic revenue ($v_i$) for all firms is $p_iq_i=L_iA \left( \frac{\mu }{\phi _i}\right) ^{1-\sigma }$. This is because $L_i$ does not affect the pricing decision and all firms, whether financially constrained or not, set $p_i$ equal to $p_i^*$. $L_i$, as shown above, does depend on a firm’s productivity draw and on whether or not the firm is financially constrained. To get the domestic revenue for financially unconstrained firms, substitute in the profit-maximizing $L_i$ ($L_i^*$ from Eq. 10) into the domestic revenue equation to get the profit-maximizing domestic revenue:

$$\begin{aligned} v_i^*=A^\frac{\beta }{\beta -1}\left( \frac{1}{\sigma \beta }\right) ^{\frac{1}{\beta -1}} \left( \frac{\mu }{\phi _i}\right) ^{\frac{\beta (1-\sigma )}{\beta -1}} \end{aligned}$$

(18)

For financially constrained firms, $L_i$ is determined by Eqs.  (14), (15), and (16), depending on whether the firm is an unsuccessful exporter, a non-exporter, or a successful exporter, respectively. This $L_i$ for financially constrained firms in all cases, as mentioned above, is between the profit maximizing $L_i^*$ (Eq. 10) and $L_i^C$ (Eq. 17). Thus, total domestic revenues is between the total domestic revenues for financially unconstrained firms (Eq. 18) and the lower-bound domestic revenue for all firms. To get the lower-bound domestic revenues , substitute in the lower-bound $L_i$ ($L_i^C$ from Eq. 17) into the domestic revenue equation to get the lower-bound domestic revenue:

$$\begin{aligned} v_i^C=\lambda ^{\frac{1}{{\beta -1}}}A^\frac{\beta }{\beta -1}\left( \frac{1}{\sigma \beta }\right) ^{\frac{1}{\beta -1}} \left( \frac{\mu }{\phi _i}\right) ^{\frac{\beta (1-\sigma )}{\beta -1}} \end{aligned}$$

(19)

The lower bound in Eq. (19) does not depend on the classification of the firm (non-exporter, unsuccessful exporter, or successful exporter). It does, however, depend on the productivity draw. Notice that $v_i^C=\lambda ^{\frac{1}{\beta -1}}v_i$, so $v_i^C<v_i$ .

1.9 Proof of proposition 2

Proof for the first statement: Essentially, $L_i$ for non-exporters is the $L_i$ for successful and unsuccessful exporters before these firms attempted to export. Thus, to prove the first part of the proposition, I simply compare the $L_i$ choice for successful and unsuccessful exporters, individually, with that of non-exporters. As mentioned earlier, $L_i$ is decreasing between the profit-maximizing $L_i^*$ and $L^C_i$, so $\frac{\partial LHS_i}{\partial L_i}<0$ in Eqs. (14), (15), and (16). Since $\frac{\partial LHS_i}{\partial L_i}<0$, to prove that the $L_i$ for constrained unsuccessful exporters is lower after exporting ($L^{dom}>L^{fail}$), I have to show that the right-hand side of Eq. (14) is higher than that of Eq.  (15), that is $f_d -(1-\lambda )f_e < f_x +f_d -(1-\lambda )f_e$. Since $0<f_x$, then $L^{dom}>L^{fail}$. Alternatively, I can also note that $\frac{\partial L_i}{\partial f_x}<0$. I can show that $\frac{\partial RHS_i}{\partial f_x}>0$, and thus $\frac{\partial L_i}{\partial f_x}<0$. Taking the derivative of the right hand side with respect to $f_x$, I get $\frac{\partial RHS_i}{\partial f_x} = \frac{1}{\lambda }>0$, and $\frac{\partial L_i}{\partial f_x}<0$.

For a constrained successful exporter, whether the firm reaches more or less domestic consumers, ($L^{dom}>L^{succ}$) depends on whether or not the new market loosens or tightens the financial constraint. If the export market is similar to the home market, then it is likely that entering the new market tightens the constraint and the firm reaches fewer domestic consumers. To prove this I compare Eqs. (15) and (16). $L^{dom}>L^{succ}$ when

$$\begin{aligned} f_d -(1-\lambda )f_e < \frac{1}{2}\left( f_x +f_d -(1-\lambda )f_e \right) \end{aligned}$$

That is, when $f_d -f_x<(1-\lambda )f_e$. This must be the case since $f_d<f_x$ and $0<(1-\lambda )f_e$.

Proof for the second statement: I can prove that the constrained $L_i$ is less for unsuccessful than for successful exporters ($L^{fail}<L^{succ}$) from Eqs. (14) and (16). In those equations, successful exporters are better off as long as $\frac{1}{2} \left( f_x+f_d-(1-\lambda )f_e \right) <\left( f_x +f_d -(1-\lambda )f_e \right)$. This is the case, as already shown in Appendix A.2.

1.10 Firm production threshold

Some potentially profitable firms will stop producing as a result of export failure. Firms with productivity below $\phi ^0_i$ do not produce because, even if they give all profits to the creditor, the creditor still does not break even. The cutoff is defined by the constrained firm, $\phi ^0_i$, whose $L_i$ choice equals $L^C_i$. That is, the firm producing at the lower-bound $L_i$. As mentioned above, there is no incentive to set $L_i$ below this level.

To identify the firm producing at the threshold, substitute Eq.  (17) into Eq. (14). Solving for $\phi _0$ gives the firm producing at the production threshold for unsuccessful exporters:

$$\begin{aligned} \phi _0^{fail} = \mu \left( \frac{A\lambda }{\sigma }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{ f_x+f_d -(1-\lambda )f_e}{\beta -1} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

(20)

The threshold for non-exporters is also the threshold for all firms before they enter the export market. Set $f_x=0$ to get the non-exporting firm producing at the production threshold:

$$\begin{aligned} \phi _0^{dom} = \mu \left( \frac{A\lambda }{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{f_d-(1-\lambda )f_e}{\beta -1} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

(21)

Firms know the potential consequences of entering the export market. No firm exports if export success would force it to default.

1.11 Proof of proposition 3

Proof for the first statement: Essentially, the production cutoff for non-exporters is the production cutoff for successful and unsuccessful exporters before the firms attempt to export. To prove the first statement, I compare successful and unsuccessful exporters, individually, with non-exporters.

To prove that the production threshold for unsuccessful exporters is higher after exporting ($\phi _0^{dom}<\phi _0^{fail}$), I have to show that $f_d -(1-\lambda )f_e <\left( f_x +f_d -(1-\lambda )f_e\right)$. This holds as long as $f_x >0$. Alternatively, I can prove that $\frac{\partial \phi _0}{\partial f_x}>0$ or that the following is greater than zero:

$$\begin{aligned} \frac{\partial \phi _0^{fail}}{\partial f_x}= \mu \left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \frac{1-\beta }{\beta (1-\sigma )} \lambda ^\frac{\beta }{1-\beta } \frac{ 1}{\beta -1} \left( \lambda ^\frac{\beta }{1-\beta } \frac{ 1}{\beta -1} \left( f_x +f_d -(1-\lambda )f_e \right) \right) ^{\frac{1-\beta }{\beta (1-\sigma )}-1} >0 \end{aligned}$$

This sign is positive because (1) $\frac{1-\beta }{\beta (1-\sigma )}>0$ since $\beta ,\sigma >1$, (2) $f_x +f_d >(1-\lambda )f_e$ since $f_x>f_d>f_e$, and (3) $\frac{1}{\beta -1}>0$ since $\beta >1$.

Proof for the second statement: Since firms export only if they expect to be better off, no firms export if they would be worse off conditional of surviving abroad. Since the production threshold for unsuccessful exporters is higher after exporting than before, it means the production threshold is also higher for unsuccessful than successful exporters ($\phi _0^{succ}<\phi _0^{fail}$).

1.11.1 General case: successful exporters

Unconstrained threshold for successful exporters: For the firms that export to foreign market f (successful exporters), I get the following financial constraint:

$$\begin{aligned} p_{ih} q_{ih}-\frac{q_{ih}}{\phi _i}+p_{if} q_{if} - \frac{\tau _{if} q_{if}}{\phi _i} \ge B_i \end{aligned}$$

For a financially constrained firm, this equation binds when setting the price and marketing levels equal to the profit-maximizing $p_{ih}^*$, $p_{if}^*$, $L_{ih}^*$ and $L_{if}^*$. To get the threshold for constrained/unconstrained firms, I bind the equation above and substitute in the firm’s profit-maximizing prices and marketing level. Substituting in the demand equation, the marketing function, profit-maximizing prices and the modified creditors’ constraint (which needs to include the new loans for marketing in all countries) into the liquidity constraint for successful exporters, gives the following threshold:

$$\begin{aligned} \frac{L_{ih}^*A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{*\beta }}{\lambda } + \frac{L_{if}^*A_f}{\sigma }\left( \frac{\mu \tau _{if}}{ \phi }\right) ^{1-\sigma } -\frac{L_{if}^{*\beta }}{\lambda } = \frac{f_x + f_d -(1-\lambda )f_e}{\lambda } \end{aligned}$$

Substituting in $L_{ih}^*$ from Eq. (10) and the profit-maximizing $L_{if}^*$, gives the following condition:

$$\begin{aligned} \left( \frac{A_h}{\beta \sigma }\right) ^\frac{\beta }{\beta -1} \left( \frac{\mu }{ \phi }\right) ^\frac{\beta (1-\sigma )}{\beta -1} + \left( \frac{A_f}{\beta \sigma }\right) ^\frac{\beta }{\beta -1} \left( \frac{\mu \tau _{if}}{ \phi }\right) ^\frac{\beta (1-\sigma )}{\beta -1} = \frac{f_x + f_d -(1-\lambda )f_e}{\beta \lambda -1} \end{aligned}$$

Simplifying:

$$\begin{aligned} \phi _C^{succ} = \mu \left( \frac{1}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{f_x + f_d -(1-\lambda )f_e}{\lambda \beta -1} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}}\left( A^\frac{\beta }{\beta -1}_h + A^\frac{\beta }{\beta -1}_f\left( \tau _{if}\right) ^\frac{\beta (1-\sigma )}{\beta -1}\right) ^{-\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

Note that I assume that either the firm uses domestic labor for foreign marketing or that the foreign market wages are the same as those of the domestic market. I also assume that there are no additional trade costs in marketing.

If the firm enters a similar size market ($Y_h=Y_f=Y$) with a price level equal to that of the domestic level times the iceberg trade costs ($P_f=P_h\cdot \tau _{if}$), then $A_f=A_h\cdot \tau _{if}^{\sigma -1}$ and the above equation simplifies to:

$$\begin{aligned} \phi _C^{succ} = \mu \left( \frac{A}{\sigma \beta }\right) ^{\frac{1}{ (1-\sigma )}} \left( \frac{f_x+f_d-(1-\lambda )f_e}{2(\lambda \beta -1)} \right) ^{\frac{1-\beta }{\beta (1-\sigma )}} \end{aligned}$$

Credit-constrained marketing decision for successful exporters: A successful exporter must decide how much to charge for its product and how much to spend on marketing at home and abroad. The product prices are not affected by the liquidity constraint, and the firm always charges the profit maximizing prices in each market. Substituting these prices into the expected profit equation and the modified credit budget constraint into the maximization problem, gives the following:

$$\begin{aligned} Max \ E\pi _i(p_i,L_i;\phi _i)=\frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -L_{ih}^\beta + \frac{L_{if}A_f}{\sigma }\left( \frac{\mu \tau _{if}}{ \phi }\right) ^{1-\sigma } -L_{if}^\beta -f_x -f_d \end{aligned}$$

Subject to the binding financing constraint:

$$\begin{aligned} \frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{\beta }}{\lambda } + \frac{L_{if}A_f}{\sigma }\left( \frac{\mu \tau _{if}}{ \phi }\right) ^{1-\sigma } -\frac{L_{if}^{\beta }}{\lambda }\ge \left( \frac{f_x +f_d -(1-\lambda )f_e }{\lambda } \right) \end{aligned}$$

Using $\varepsilon$ as the multiplier, I get:

$$\begin{aligned} \frac{\partial \pi _i}{\partial L_{ih}}:&\ \ \frac{\sigma \beta L_{ih}^{\beta -1}}{A_h\left( \frac{\mu }{ \phi _i}\right) ^{1-\sigma }}=\frac{1+\varepsilon }{1+\frac{\varepsilon }{\lambda }}\\ \frac{\partial \pi _i}{\partial L_{if}}:&\ \ \frac{\sigma \beta L_{if}^{\beta -1}}{A_f\left( \frac{\mu \tau _{if}}{ \phi _i}\right) ^{1-\sigma }}=\frac{1+\varepsilon }{1+\frac{\varepsilon }{\lambda }}\\ \frac{\partial \pi _i}{\partial \varepsilon }:&\ \ \frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{\beta }}{\lambda } + \frac{L_{if}A_f}{\sigma }\left( \frac{\mu \tau _{if}}{ \phi }\right) ^{1-\sigma } -\frac{L_{if}^{\beta }}{\lambda }= \frac{f_x +f_d -(1-\lambda )f_e }{\lambda } \end{aligned}$$

This means that $L_{if}=\left( \frac{A_f}{A_h}\right) ^\frac{1}{\beta -1}\left( \tau _{if}\right) ^\frac{1-\sigma }{\beta -1}L_{ih}$. Substituting $L_{if}$ out of the financial constraint:

$$\begin{aligned} \left( \frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{\beta }}{\lambda }\right) \left( 1 + \left( \frac{A_f}{A_h}\right) ^\frac{\beta }{\beta -1}\left( \tau _{if} \right) ^\frac{\beta (1-\sigma )}{\beta -1} \right) =\frac{f_x +f_d -(1-\lambda )f_e }{\lambda } \end{aligned}$$

Thus, the firm chooses the $L_{ih}$ that solves the following equation:

$$\begin{aligned} \frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{\beta }}{\lambda } =\left( 1 + \left( \frac{A_f}{A_h}\right) ^\frac{\beta }{\beta -1}\left( \tau _{if} \right) ^\frac{\beta (1-\sigma )}{\beta -1} \right) ^{-1}\frac{f_x +f_d -(1-\lambda )f_e }{\lambda } \end{aligned}$$

If the firm enters a similar sized market ($Y_h=Y_f=Y$) with a price level equal to that of the domestic level times the iceberg trade costs ($P_f=P_h\cdot \tau _{if}$), then the above equation simplifies to:

$$\begin{aligned} \frac{L_{ih}A_h}{\sigma }\left( \frac{\mu }{ \phi }\right) ^{1-\sigma } -\frac{L_{ih}^{\beta }}{\lambda } =\frac{f_x +f_d -(1-\lambda )f_e }{2\lambda } \end{aligned}$$

Firm production threshold for successful exporters: The firm production threshold for successful exporters does not change. All firms want to supply both markets and no firm would enter the export market if it knew that, conditional on surviving in the export market, it would have to exit the domestic market.

Appendix B The propensity score matching process

I match unsuccessful exporters to both successful exporters and non-exporters to control for pre-exporting observables, and also to create alternative control groups. In order to match these firms, I use nearest neighbor, propensity score matching (PSM); I perform 1-to-1 matching without replacement and impose a common support to find the match.²⁶

Since the ordering of the data might affect a firm’s match, I randomize the data before matching. To match the firms, I used the following variables: short-term labor, investment, and debt; long-term labor, investment, and debt; and inventory, property, domestic revenue, intangibles (intellectual property, patents, etc.), total assets, profits, and cash flow. Each of the variables is at the firm-year level and is transformed using an inverse hyperbolic sine transformation. I then regress these variables to predict the probability of firms being onetime exporters (ie. unsuccessful exporters), which gives me a propensity score value for all firms. I then modify these values to ensure that the match is within the same sector. I use these values to onetime exporters with successful exporters and non-exporters. With the matched sample, the only observable difference with unsuccessful exporters is either the firm’s exporting decision, in the case of non-exporters, or in the firm’s export success, in the case of successful exporters. Once I have a match, I can then replicate the baseline estimation procedure with two additional control groups.

There is some variation in matching onetime exporters with successful exporters and non-exporters. For non-exporters, I match them to an unsuccessful exporter based on the latter’s pre-exporting variables. Once matched, non-exporters are assign their “after-exporting” period based on the match; I force the match to be within the same start-up year and sector. The start-up year is based on when the firm first appeared in the SIREM dataset. The start-up sector is at the ISIC chapter level. Each non-exporter is assigned a pseudo exporting cohort and can be compared with unsuccessful exporters in the pre- and post-“exporting” periods. Since the before-exporting period length differs greatly by firm, I create an algorithm that uses as much of the data as possible to match firms. Thus, unsuccessful exporters with a lot of data in the pre-exporting period were matched with firms having at least as much data. For example, an unsuccessful exporter with five years of pre-exporting data would match with a non-exporting firm with at least 6 years of data. This process ensures that non-exporters do not exit the domestic market before the pseudo exporting year. I follow a similar procedure to match successful exporters with unsuccessful ones. However, I do not create an artificial after-exporting period for successful exporters as these firms already have an exporting cohort and I do not force the match to be within the same start up year.

Appendix C Tables

Table 6 Business Classifications and availability

Table 7 Financial data: average of firms operating in 2005

Table 8 Exit summary statistics: all firm types

Table 9 Probability of staying in business: probit estimates

Table 10 Matched Estimates: All Data

Table 11 Matched estimates: export failure and the probability of staying in business

Table 12 Probability of staying in business: matched probit estimates

Table 13 Revenue growth regressions: baseline and matched data

Table 14 Sector regressions: cash flow to total assets

Table 15 Sector regressions: log domestic revenue

Table 16 Other robustness checks: cash flow to total assets

Table 17 Other robustness checks: log domestic revenue

Table 18 SITC sector: code and name

Table 19 Financially constrained are the lowest 25% of firms

Table 20 Exit estimates: financial constrained is top 25% of firms

Table 21 Revenue growth regressions: instrumental variable approach