Business Conditions and Exit Risks Across Countries

Abstract

The risk of market exit that business firms face is significant and differs widely across countries. This paper explores the links between countries’ business conditions and the exit risk at the country level. We set up a general equilibrium model which allows us to derive sharp predictions concerning how key factors which shape a country’s business and trade environment impact on the exit risk of firms which operate in these environments. The model is able to explain the negative correlation between countries’ average labor productivity and the perceived risks of exit borne out in the facts and its predictions accord with evidence on country differences in business conditions.

Appendices

Appendices

1.1 Appendix A-The Comparative Statics of the Exit Rates

Mature firm concept. Take the derivative of $E{{\left[ {\delta {{{\left( \phi \right)}}^{-1 }}\left| {\phi > {\phi^{*}}} \right.} \right]}^{-1 }}=\left[ {1-G\left( {{\phi^{*}}} \right)} \right]{{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi } \right]}^{-1 }}$ with respect to ϕ ^*. This yields $\frac{{dE{{{\left[ {\delta {{{\left( \phi \right)}}^{-1 }}\left| {\phi > {\phi^{*}}} \right.} \right]}}^{-1 }}}}{{d{\phi^{*}}}}=g\left( {{\phi^{*}}} \right){{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\frac{{g\left( \phi \right)}}{{\delta \left( \phi \right)}}} d\phi } \right]}^{-1 }}\left[ {\frac{{1-G\left( {{\phi^{*}}} \right)}}{{\delta \left( {{\phi^{*}}} \right)}}{{{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\frac{{g\left( \phi \right)}}{{\delta \left( \phi \right)}}} d\phi } \right]}}^{-1 }}-1} \right]<0$.

We find that ${{{dE{{{\left[ {\delta {{{\left( \phi \right)}}^{-1 }}\left| {\phi > {\phi^{*}}} \right.} \right]}}^{-1 }}}} \left/ {{d{\phi^{*}}}} \right.} > 0$ iff ${{{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta \left( {{\phi^{*}}} \right)\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi } \right]}} \left/ {{\int\nolimits_{{{\phi^{*}}}}^{\infty } {g\left( \phi \right)} d\phi }} \right.} > 1$, which holds true for any density g(ϕ) as δ(ϕ ^*) > δ(ϕ)

The failing start-up concept. Substituting $E{{\left[ {\delta {{{\left( \phi \right)}}^{-1 }}\left| {\phi > {\phi^{*}}} \right.} \right]}^{-1 }}=\left[ {1-G\left( {{\phi^{*}}} \right)} \right]{{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi } \right]}^{-1 }}$ into the risk of start up failure yields $G\left( {{{\phi }^{*}}} \right){{M}_{e}}/M = G\left( {{{\phi }^{*}}} \right)/\int_{{{{\phi }^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{{ - 1}}}g\left( \phi \right)} d\phi$ which is increasing in ϕ ^* (as G(ϕ ^*) rises whereas $\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi$ decreases in ϕ ^* as $\delta {{\left( \phi \right)}^{-1 }}g\left( \phi \right)>0$).

The overall exit rate. We use $E{{\left[ {\delta {{{\left( \phi \right)}}^{-1 }}\left| {\phi > {\phi^{*}}} \right.} \right]}^{-1 }}=\left[ {1-G\left( {{\phi^{*}}} \right)} \right]{{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi } \right]}^{-1 }}$ in the overall exit rate to get ${{{{M_e}}} \left/ {M} \right.}={{\left[ {\int\nolimits_{{{\phi^{*}}}}^{\infty } {\delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi } \right]}^{-1 }}$ which increases in ϕ ^*as $\delta {{\left( \phi \right)}^{-1 }}g\left( \phi \right)>0$.

1.2 Appendix B-The Link Between the Productivity Cutoffs in the Open Economy

• (i) We depart from the ratios of the ZCPCs ${r_i}\left( {\phi_i^{*}} \right)=\sigma {w_i}{f_i}$ and ${r_{xi }}\left( {\phi_{xi}^{*}} \right)=\sigma\,{w_i}\,{f_{xi }}$, where ${r_i}(\phi_i^{*})$ and ${r_{xi }}\left( {\phi_{xi}^{*}} \right)$ are home (export) market profits of firms from country i and follow the procedure in Demidova (2008) and get $\phi_{xi}^{*}={{\left( {{{{{w_i}}} \left/ {{{w_j}}} \right.}} \right)}^{{\sigma /\left( {\sigma -1} \right)}}}{t_i}\phi_j^{*}$ where ${t_i}\equiv {\tau_{ij }}{{\left( {{f_{xi }}/{f_j}} \right)}^{{1/\left( {\sigma -1} \right)}}}$.

• (ii) We assume that only firms that serve the domestic market can export, i.e. $\phi_{xi}^{*} > \phi_i^{*}$. This holds true if ${\tau_{ij }}{{\left( {{f_{xi }}/{f_i}} \right)}^{{1/\left( {\sigma -1} \right)}}}\left( {{P_i}/{P_j}} \right){{\left( {{L_i}/{L_j}} \right)}^{{1/\left( {\sigma -1} \right)}}} > 1$. With ${P_i}={{\left( {\beta {L_i}/\sigma {f_i}} \right)}^{{1/\left( {1-\sigma } \right)}}}w_i^{{\sigma /\left( {\sigma -1} \right)}}{{\left( {\rho \phi_i^{*}} \right)}^{-1 }}$ this becomes ${f_{xi }}/{f_j} > \tau_{ij}^{{1-\sigma }}{{\left( {{w_j}/{w_i}} \right)}^{\sigma }}{{\left( {\phi_i^{*}/\phi_j^{*}} \right)}^{{\sigma -1}}}$ (The price index follows from ${P_i}=M_{ti}^{{1/\left( {1-\sigma } \right)}}p\left( {{{{\widetilde{\phi}}}_{ti }}} \right)$ where ${M_{ti }}\equiv {M_i}+{M_{xj }}$ is the mass of all (domestic and foreign) firms selling their products in i and ${{\widetilde{\phi}}_{ti }}\equiv {{\left[ {\left( {{1 \left/ {{{M_{ti }}}} \right.}} \right)\left\{ {\int\nolimits_{{\phi_i^{*}}}^{\infty } {{\phi^{{\sigma -1}}}{M_i}\left( \phi \right)d\phi } +{{{\left( {{{{{w_j}}} \left/ {{{w_i}}} \right.}} \right)}}^{{1-\sigma }}}{{{\left( {{\tau_{ji }}} \right)}}^{{1-\sigma }}}\int\nolimits_{{\phi_{xj}^{*}}}^{\infty } {{\phi^{{\sigma -1}}}{M_{xj }}\left( \phi \right)d\phi } } \right\}} \right]}^{{{1 \left/ {{\left( {\sigma -1} \right)}} \right.}}}}$ a measure of their average productivity. Consumer in i spend ${M_{ti }}\,{r_i}\left( {{{{\widetilde{\phi}}}_{ti }}} \right)=\beta {L_i}$ on heterogeneous goods. With ${r_i}\left( {{{{\widetilde{\phi}}}_{ti }}} \right)={{\left( {{{{\widetilde{\phi}}}_{ti }}/\phi_i^{*}} \right)}^{{\sigma -1}}}{r_i}\left( {\phi_i^{*}} \right)$ and ${r_i}\left( {\phi_i^{*}} \right)=\sigma\,{w_i}\,{f_i}$ we get ${M_{ti }}=\beta {L_i}{{\left( {{{{\widetilde{\phi}}}_{ti }}/\phi_i^{*}} \right)}^{{1-\sigma }}}/\sigma\,{w_i}{f_i}$).

1.3 Appendix C: The Equilibrium Condition in the Open Economy

The free entry condition (FEC) states that the value of entry is zero in equilibrium, ${v^E}\equiv E\left[ {\sum\nolimits_{t=0}^{\infty } {{{{\left( {1-\delta \left( \phi \right)} \right)}}^t}\pi \left( \phi \right)} } \right]-w\,{f_e}=E\left[ {\pi \left( \phi \right)/\delta \left( \phi \right)} \right]-w\,{f_e}=0$. Under international trade, the FEC for country i is as stated in section 4. As ${\pi_i}\left( \phi \right)={r_i}\left( \phi \right)/\sigma - > {w_i}{f_i}$, the expected profits become $E\left[ {\left. {{{{{\pi_i}\left( \phi \right)}} \left/ {{\delta \left( \phi \right)}} \right.}} \right|\phi >\phi_i^{*}} \right]={{{E\left[ {\left. {{{{{r_i}\left( \phi \right)}} \left/ {{\delta \left( \phi \right)}} \right.}} \right|\phi >\phi_i^{*}} \right]}} \left/ {\sigma } \right.}-{w_i}{f_i}E\left[ {\left. {\delta {{{\left( \phi \right)}}^{-1 }}} \right|\phi >\phi_i^{*}} \right]$. We use $r\left( \phi \right)={{\left( {\phi /{\phi}^{\prime}} \right)}^{{\sigma -1}}}r\left( {\phi^{\prime}} \right)$ where $\phi_i^{{\prime \sigma -1}}\equiv E\left[ {\left. {{{{{\phi^{{\sigma -1}}}}} \left/ {{\delta \left( \phi \right)}} \right.}} \right|\phi >\phi_i^{*}} \right]$ to write the expected profits as ${\pi_i}\left( {\phi_i^{\prime }} \right)-{w_i}{f_i}\left( {E\left[ {\left. {\delta {{{\left( \phi \right)}}^{-1 }}} \right|\phi >\phi_i^{*}} \right]-1} \right)$. $E\left[ {\left. {{{{{\pi_{xi }}\left( \phi \right)}} \left/ {{\delta \left( \phi \right)}} \right.}} \right|\phi >\phi_{xi}^{*}} \right]={\pi_{xi }}\left( {{{{\phi^{\prime}}}_{xi }}} \right)-{w_i}{f_{xi }}\left( {E\left[ {\left. {\delta {{{\left( \phi \right)}}^{-1 }}} \right|\phi >\phi_{xi}^{*}} \right]-1} \right)$ follows by analogy. The zero cutoff profit conditions (ZCPCs) are defined by ${r_i}\left( {\phi_i^{*}} \right)=\sigma\,{w_i}{f_i}$ and ${r_{xi }}\left( {\phi_{xi}^{*}} \right)=\sigma\,{w_i}{f_{xi }}$. Using $r\left( {\phi \prime } \right)={{\left( {\phi \prime /{\phi^{*}}} \right)}^{{\sigma -1}}}r\left( {{\phi^{*}}} \right)$, we get ${\pi_i}\left( {\phi_i^{\prime }} \right)=\left[ {{{{\left( {{{{\phi_i^{\prime }}} \left/ {{\phi_i^{*}}} \right.}} \right)}}^{{\sigma -1}}}-1} \right]{w_i}{f_i}$ (domestic ZCPC) and ${\pi_{xi }}\left( {\phi_{xi}^{\prime }} \right)=\left[ {{{{\left( {{{{\phi_{xi}^{\prime }}} \left/ {{\phi_{xi}^{*}}} \right.}} \right)}}^{{\sigma -1}}}-1} \right]{w_i}{f_{xi }}$ (export ZCPC). Plug the ZCPCs into the FEC, substitute $\phi _{i}^{{\prime \sigma - 1}} \equiv E\left[ {\left. {{{\phi }^{{\sigma - 1}}}/\delta \left( \phi \right)} \right|\phi > \phi _{i}^{*}} \right] = \int_{{\phi _{i}^{*}}}^{\infty } {{{\phi }^{{\sigma - 1}}}\cdot \delta {{{\left( \phi \right)}}^{{ - 1}}}g\left( \phi \right)} d\phi /\left[ {1 - G\left( {\phi _{i}^{*}} \right)} \right]$ and use $\phi_{xi}^{*}={{\left( {{{{{w_i}}} \left/ {{{w_j}}} \right.}} \right)}^{{\sigma /\left( {\sigma -1} \right)}}}{t_i}\phi_j^{*}$ to derive Eq. (2). The limits of j(ϕ ^*) are $\mathop{\lim}\limits_{{\phi^{*}\to \infty }}j\left( {\phi^{*}} \right)=0$ and $\mathop{\lim}\limits_{{{\phi^{*}}\to 1}}j\left( {{\phi^{*}}} \right)=E\left[ {\left( {{\phi^{{\sigma -1}}}-1} \right)\cdot \delta {{{\left( \phi \right)}}^{-1 }}} \right]>0$, the slope is ${{{dj\left( {{\phi^{*}}} \right)}} \left/ {{d{\phi^{*}}}} \right.}=-\left( {\sigma -1} \right){{{\phi {\prime^{{\sigma -1}}}\left[ {1-G\left( {{\phi^{*}}} \right)} \right]}} \left/ {{{\phi^{{*\sigma }}}}} \right.} < 0$.

1.4 Appendix D: Comparative Statics of the Equilibrium

We apply Cramer’s rule to Eq. (2). By Leibniz’ rule we get ${{{\partial H}} \left/ {{\partial \phi_H^{*}}} \right.} < 0$, ${{{\partial H}} \left/ {{\partial \phi_F^{*}}} \right.} < 0$, ${{{\partial F}} \left/ {{\partial \phi_H^{*}}} \right.} < 0$, and ${{{\partial F}} \left/ {{\partial \phi_F^{*}}} \right.} < 0$. The determinant of the matrix of derivatives of Eq. (2) is positive, as $\phi {\prime^{{\sigma -1}}}\left[ {1-G\left( {{\phi^{*}}} \right)} \right]=\int\nolimits_{{{\phi^{*}}}}^{\infty } {{\phi^{{\sigma -1}}}\cdot \delta {{{\left( \phi \right)}}^{-1 }}g\left( \phi \right)} d\phi$ decreases in ϕ ^* and $\phi_{xi}^{*} > \phi_i^{*}$.

Unilateral trade integration. We get $- {{{\partial H}} \left/ {{\partial {f_{xH }}}} \right.} > 0$, $- {{{\partial F}} \left/ {{\partial {f_{xF }}}} \right.} > 0$, $- {{{\partial F}} \left/ {{\partial {t_F}}} \right.} > 0$, $- {{{\partial H}} \left/ {{\partial {t_H}}} \right.} > 0$, and ${{{\partial H}} \left/ {{\partial {t_F}}} \right.}={{{\partial H}} \left/ {{\partial {f_{xF }}}} \right.}={{{\partial F}} \left/ {{\partial {t_H}}} \right.}={{{\partial F}} \left/ {{\partial {f_{xH }}}} \right.}=0$. It follows that $- {{{\partial \phi_i^{*}}} \left/ {{\partial {t_i}}} \right.} > 0$, $- {{{\partial \phi_i^{*}}} \left/ {{\partial {t_j}}} \right.} < 0$, ${{{\partial \phi_i^{*}}} \left/ {{\partial {f_{xi }}}} \right.} < 0$ and ${{{\partial \phi_i^{*}}} \left/ {{\partial {f_{xj }}}} \right.} > 0$.

Symmetric trade integration. By total differentiation of $\phi_H^{*}=\phi_H^{*}\left( {{t_H},{t_F}} \right)$ and setting $d{t_H}=d{t_F}=dt$ we have ${{{d\phi_H^{*}}} \left/ {dt } \right.}={{{\partial \phi_H^{*}}} \left/ {{\partial {t_H}}} \right.}+{{{\partial \phi_H^{*}}} \left/ {{\partial {t_F}}} \right.}$. It is easy to show that the productivity in H increases by symmetric trade integration, ${{{d\phi_H^{*}}} \left/ {dt } \right.} > 0$, whenever $\frac{{{{f}_{F}}{{W}^{\sigma }}}}{{{{f}_{{xF}}}}}\frac{{\phi _{H}^{{*\sigma - 1}}}}{{\phi _{F}^{{*\sigma - 1}}}}{{\phi }^{\prime }}_{F}^{{\sigma - 1}}\left[ {1 - {{G}_{F}}\left( {\phi _{F}^{*}} \right)} \right] - \frac{{{{t}_{H}}}}{{t_{F}^{\sigma }}}\phi _{{xF}}^{{\prime \sigma - 1}}\left[ {1 - {{G}_{F}}\left( {\phi _{{xF}}^{*}} \right)} \right] > 0$. This is the case whenever the countries have similar business conditions, which is reflected by similar cutoff productivities (i.e. $\phi_H^{*}\approx \phi_F^{*}$), or whenever H has a strong comparative advantage, i.e. $\phi_H^{*} > >\phi_F^{*}$ (from app. C it then follows that $\phi_{xF}^{*} > >\phi_F^{*}$; recall that ${{{d\phi {\prime^{{\sigma -1}}}\left[ {1-G\left( {{\phi^{*}}} \right)} \right]}} \left/ {d} \right.}{\phi^{*}} < 0$). If H has a strong comparative disadvantage so that $\phi_H^{*} < <\phi_F^{*}$, symmetric trade integration decreases H’s cutoff productivity, whereas the cutoff of F increases due to symmetry.

Changes in business conditions. We find $\partial \phi_i^{*}/\partial {f_{ei }} < 0$, ${{{\partial \phi_i^{*}}} \left/ {{\partial {f_{ej }}}} \right.} > 0$, ${{{\partial \phi_H^{*}}} \left/ {{\partial W}} \right.} > 0$ and ${{{\partial \phi_F^{*}}} \left/ {{\partial W}} \right.} < 0$ where $W\equiv {{{{w_F}}} \left/ {{{w_H}}} \right.}$. Concerning fixed labor investments, we have ${{{\partial \phi_H^{*}}} \left/ {{\partial {f_H}}} \right.} > 0$ if ${j_H}\left( {\phi_H^{*}} \right)\phi_F^{{\prime \sigma -1}}\left[ {1-{G_F}\left( {\phi_F^{*}} \right)} \right] > {{{{{{\left( {\phi_{xH}^{\prime}\phi_{xF}^{\prime }} \right)}}^{{\sigma -1}}}\left[ {1-{G_H}\left( {\phi_{xH}^{*}} \right)} \right]\left[ {1-{G_F}\left( {\phi_{xF}^{*}} \right)} \right]}} \left/ {{\left[ {\tau_{HF}^{{\sigma -1}}\tau_{FH}^{{\sigma -1}}\phi_H^{{*\sigma -1}}} \right]}} \right.}$. This is the case whenever trade costs are high (consider ${\tau_{HF }}={\tau_{FH }}=\tau \to \infty$). If trade costs are sufficiently small, then ${{{\partial \phi_H^{*}}} \left/ {{\partial {f_H}}} \right.} < 0$. Increases in f _F increase the domestic cutoff unambiguously, ${{{\partial \phi_H^{*}}} \left/ {{\partial {f_F}}} \right.} > 0$.

Technological potential. We model differences in technological potential by hazard rate stochastic dominance (HRSD) as in Demidova (2008). A productivity distribution G _a (ϕ) stochastically dominates a distribution G _b (ϕ) in terms of the hazard rate order, ${G_a}\left( \bullet \right){\succ_{hr }}{G_b}\left( \bullet \right)$, if ${g_a}\left( \phi \right)/\left[ {1-{G_a}\left( \phi \right)} \right] < {g_b}\left( \phi \right)/\left[ {1-{G_b}\left( \phi \right)} \right]$ holds true for any given productivity level ϕ. The merits of HRSD is that it allows us to compare the expectations of an increasing function above a given cutoff level, i.e. if y(x) is an increasing function, then ${E_H}\left[ {y(x)\left| {x>\phi } \right.} \right] > {E_F}\left[ {y(x)\left| {x>\phi } \right.} \right]$. To analyze the impact of a greater technological potential, rewrite ${j_a}\left( {{\phi^{*}}} \right)$ as follows ${j_a}\left( {{\phi^{*}}} \right)\equiv \int\nolimits_{{{\phi^{*}}}}^{\infty } {\left( {{\phi^{{\sigma -1}}}-1} \right)\cdot \delta \left( \phi \right){\;^{-1 }}\cdot {g_a}(\phi )} d\phi =\left[ {1-{G_a}\left( {{\phi^{*}}} \right)} \right]\cdot {E_a}\left[ {\left. {\left( {{\phi^{{\sigma -1}}}-1} \right)\cdot \delta \left( \phi \right){\;^{-1 }}} \right|\phi > {\phi^{*}}} \right]$. We get ${j_a}\left( {{\phi^{*}}} \right)-{j_b}\left( {{\phi^{*}}} \right)=\left[ {1-{G_a}\left( {{\phi^{*}}} \right)} \right]\cdot {E_a}\left[ {\left. {\left( {{\phi^{{\sigma -1}}}-1} \right)\delta {{{\left( \phi \right)}}^{-1 }}} \right|\phi > {\phi^{*}}} \right]-\left[ {1-{G_b}\left( {{\phi^{*}}} \right)} \right]\cdot {E_b}\left[ {\left. {\left( {{\phi^{{\sigma -1}}}-1} \right)\delta {{{\left( \phi \right)}}^{-1 }}} \right|\phi > {\phi^{*}}} \right]$. If ${G_a}\left( \bullet \right){\succ_{hr }}{G_b}\left( \bullet \right)$, then $\left[ {1-{G_a}\left( {{\phi^{*}}} \right)} \right]>\left[ {1-{G_b}\left( {{\phi^{*}}} \right)} \right]$ for any given productivity level ϕ ^*. As $e\equiv \left( {{\phi^{{\sigma -1}}}-1} \right)\cdot \delta \left( \phi \right){\;^{-1 }} > 0$ and de/dϕ, we have ${E_a}\left[ {\left. \bullet \right|\phi > {\phi^{*}}} \right] > {E_b}\left[ {\left. \bullet \right|\phi > {\phi^{*}}} \right]$ and ${j_a}\left( {{\phi^{*}}} \right) > {j_b}\left( {{\phi^{*}}} \right)$.

Consequently, if the technological potential of country H increases in the sense of HRSD, the value of the equilibrium condition $H\left( {\phi_H^{*},\phi_F^{*}} \right)$ increases in the short-run whereas the equilibrium condition $F\left( {\phi_H^{*},\phi_F^{*}} \right)$ remains unchanged. Consequently, $\phi_H^{*}$ increases and $\phi_F^{*}$ decreases.

Existence and uniqueness of the equilibrium. In equilibrium, both conditions in Eq. (2) have to be fulfilled. Furthermore, it must hold true that $\phi_i^{*} > 1$. As the domestic cutoff decreases with domestic disadvantages and foreign advantages, we assume that the countries must not be too different in aggregate (as a disadvantage with respect to factor can be compensated by an advantage with respect to another) to generate positive and meaningful cutoff productivities.