ESCOLA de P ´
OS-GRADUAC
¸ ˜
AO em ECONOMIA
Fernanda Corrˆ
ea Fernandes
Essays on Macroeconomics and
Banking
Rio de Janeiro 2016
Essays on Macroeconomics and
Banking
Tese para obten¸c˜ao do grau de Doutor apresentada `a Escola de P´os-Gradua¸c˜ao em Economia
´
Area de concentra¸c˜ao: Economia Banc´aria e Dinˆamicae Desenvolvimento
Orientador: Felipe Saraiva Iachan
Rio de Janeiro 2016
Ficha catalográfica elaborada pela Biblioteca Mario Henrique Simonsen/FGV
Fernandes, Fernanda Corrêa
Essays on macroeconomics and banking / Fernanda Corrêa Fernandes. - 2017. 72 f.
Tese (doutorado) - Fundação Getulio Vargas, Escola de Pós-Graduação em Economia.
Orientador: Felipe Saraiva Iachan. Inclui bibliografia.
1. Bancos. 2. Risco financeiro. 3. Contágio financeiro. 4. Finanças. I. Iachan, Felipe Saraiva. II. Fundação Getulio Vargas. Escola de Pós-Graduação em Economia. III.Título.
Em primeiro lugar, o agradecimento a Deus pela sua ajuda bem presente e certamente necess´aria em todos os momentos.
Em seguida, `a minha m˜ae, cujo carinho e dedica¸c˜ao foram essenciais durante toda minha vida acadˆemica.
Ao meu orientador, Felipe Iachan, pelos ensinamentos e paciˆencia ao longo de todos esses anos.
Ao Bruno Mendon¸ca e a Luciene Torres, pelo companheirismo incans´avel nessa grande jor-nada.
Essa tese ´e composta por dois cap´ıtulos. No primeiro, desenvolvo um modelo para quantificar o papel da heterogeneidade setorial, em rela¸c˜ao ao acesso a cr´edito, na determina¸c˜ao dos efeitos da integra¸c˜ao financeira. Fric¸c˜oes financeiras geram m´a-aloca¸c˜ao de recursos, resultando em baixa produtividade e produto por trabalhador em economias emergentes. Dada a existˆencia de heterogeneidade setorial no acesso a cr´edito, essas fri¸c˜oes apresentam efeitos desproporcionais em vari´aveis setorias, assim como na taxa de cˆambio. Esses elementos s˜ao capazes de explicar regularidades do desenvolvimento, como o elevado pre¸co relativo dos bens comercializ´aveis e a baixa produtividade relativa desse setor nos pa´ıses em desenvolvimento. Adicionalmente, mostro que a integra¸c˜ao dom´estica e externa apresentam diferentes impactos na economia. Enquanto a primeira ´e vital para reduzir a m´a-aloca¸c˜ao de recursos, a segunda ´e crucial para reduzir a taxa de juros dom´estica e estimular um maior engajamento dos agentes na economia real. Quantifico esses resultados e mostro que a integra¸c˜ao financeira apresenta efeitos n˜ao triviais na produti-vidade agregada/setorial, na acumula¸c˜ao de capital e no produto por trabalhador dos pa´ıses. No segundo cap´ıtulo, por sua vez, analiso a propaga¸c˜ao de choques por uma rede financeira, identificando a rela¸c˜ao entre a heterogeneidade das institui¸c˜oes financeiras e a resiliˆencia do sistema. Os bancos s˜ao diferenciados de acordo com seu tamanho e grau de centralidade na rede, de modo a formar uma rede n´ucleo-periferia similar `as empiricamente observadas. Em rela¸c˜ao aos efeitos de choques inesperados, mostro que as conex˜oes funcionam como meio de propaga¸c˜ao de perdas e provo a possibilidade de cont´agio em equil´ıbrio. Em contraste com a vis˜ao intuitiva, mostro que ´e necess´aria uma lacuna entre o tamanho do banco n´ucleo e perif´erico para que o primeiro alcance a relevˆancia sistˆemica esperada. Nesse caso, a presen¸ca de bancos n´ucleo ´e crucial para a propaga¸c˜ao de choques que os atinjam diretamente, assim como para a prote¸c˜ao do sistema contra choques perif´ericos. As implica¸c˜oes de pol´ıtica s˜ao claras nesse caso. A autoridade monet´aria n˜ao precisa resgatar bancos perif´ericos para evitar o cont´agio. Por fim, analiso a resiliˆencia relativa de algumas redes financeiras. Mostro que a rede n´ucleo-periferia ´e mais resiliente do que a rede circular. Como a ´ultima ´e utilizada recorrentemente, o risco de cont´agio pode estar superestimado na literatura.
Palavras-chave: fric¸c˜oes financeiras, desenvolvimento financeiro, rede financeira, cont´agio, risco sistˆemico.
This thesis is composed by two chapters. In the first one, I develop a framework to quantify the role of sectoral heterogeneity, with regard to credit access, in explaining the effects of financial integration. Financial frictions generate a misallocation of resources, implying a low total factor productivity and output per worker in emerging economies. Given the existence of sectoral het-erogeneity in credit access, these frictions also have disproportionate effects on sectoral variables, as well as on exchange rate. These elements are able to explain some development regularities, as the higher relative price of tradable goods and the relative unproductive tradable goods sector in poor countries. Moreover, I show that domestic and external financial integration have differ-ent impacts on the economy. While the former is vital to reduce the misallocation of resources, the last is crucial to reduce the domestic interest rate and stimulate a deeper engagement of entrepreneurs in real activity. I quantify these results and show that financial integration has nontrivial effects on aggregate/sector-level productivity, capital accumulation and output per worker. In the second chapter, in turn, I analyse the propagation of shocks throughout a fi-nancial network, identifying the relation between heterogeneity of institutions and the resilience of the system. I distinguish banks according to their size and degree of centrality in order to form a core-periphery network, similar to those empirically observed. Regarding the effects of unexpected shocks, I argue that connections work as a way of propagation of losses and prove the possibility of contagion in equilibrium. Unlike the intuitive perception, I point out that a gap between the size of central and peripheral agents is required for the former to achieve the expected systemic relevance. When it occurs, the presence of core banks is crucial for easing the propagation of direct losses, as well as for protecting the system against peripheral shocks. The policy implications are clear in such cases. Monetary authorities do not need to rescue peripheral banks in order to avoid contagion. I conclude by analysing the relative resilience of some networks. I show that the core-periphery network is more resilient than the circular one. Since the last is mostly used, the contagion risk might be overestimated in literature.
Keywords: financial frictions, financial development, financial network, contagion, systemic risk.
1.1 Os efeitos de equil´ıbrio geral de mudan¸cas na integra¸c˜ao externa . . . 26
1.2 Os efeitos de equil´ıbrio geral de mudan¸cas na integra¸c˜ao dom´estica . . . 28
1.3 Os efeitos de equil´ıbrio geral de mudan¸cas no desenvolvimento financeiro . . . 30
1.4 Os efeitos de equil´ıbrio geral de mudan¸cas no desenvolvimento financeiro (αN =
αT = 0, 3) . . . 32
2.1 Rede n´ucleo-periferia - menores exposi¸c˜oes compat´ıveis com a aloca¸c˜ao ´otima . . 39
1.1 Calibra¸c˜ao . . . 25
1 Integra¸c˜ao Financeira e o Papel da Heterogeneidade Setorial 11
1.1 Introdu¸c˜ao. . . 11
1.2 Ambiente Econˆomico . . . 14
1.3 Equil´ıbrio . . . 17
1.3.1 Problema dos Agentes . . . 18
1.4 An´alise Quantitativa . . . 24
1.4.1 Calibra¸c˜ao . . . 24
1.4.2 Simula¸c˜oes . . . 25
1.5 Robustez . . . 31
1.6 Conclus˜ao . . . 31
2 Cont´agio na Rede N´ucleo-Periferia com Bancos Heterogˆeneos 34 2.1 Ambiente Econˆomico . . . 36
2.2 Divis˜ao de Risco ´Otima e Dep´ositos Interbanc´arios . . . 37
2.3 Fragilidade . . . 40
2.3.1 Defini¸c˜ao de Equil´ıbrio em Continua¸c˜ao . . . 40
2.3.2 Consumidores . . . 40
2.3.3 Bancos: Ordem de Liquida¸c˜ao e Falˆencia . . . 40
2.3.4 Mecanismos de Cont´agio. . . 41
2.4 Heterogeneidade e Cont´agio . . . 42
2.5 Cont´agio em Equil´ıbrio. . . 45
2.6 Resiliˆencia . . . 47
2.7 Robustez . . . 49
2.8 Conclus˜ao . . . 50
Referˆencias Bibliogr´africas 55
Apˆendice A Integra¸c˜ao Financeira e o Papel da Heterogeneidade Setorial 56
Financial Integration and The Role
of Sectoral Heterogeneity
1.1
Introduction
The importance of business environment to economic development has been extensively dis-cussed in the literature. There is evidence that financial frictions generate a missallocation of resources, being responsible to partially explain the lower output per worker in emerging econo-mies. Collateral constraints are a kind of financial friction that usually arise in these countries1.
The limited enforcement of contracts implies that entrepreneurs can default on intertemporal promises, turning the pleading of collateral a necessary condition for accessing financing. No-netheless, as shown by Liberti and Main (2010) and La Porta et al (1998), financial development improves enforcement processes and reduces information asymmetry, easing collateral require-ments2. The lack of financial development, in turn, results in an higher need for collateral, making producers more financially constrained and adversely affecting capital accumulation, as well as firms’ production.
Although firms face credit constraints, collateral requirements are asymmetric between sec-tors. According to Tornell and Westermann (2003)3, most producers of tradable goods have access to international capital markets, while nontradable goods firms are in general bank-dependent and face tighter borrowing constraints. Likewise, The Global Development Finance (The World Bank, 2004) argues that participation in international trade can help firms enjoy an easier access to external financing. Since traded goods serve as collateral, tradable goods producers have a natural advantage over nontradable goods firms in credit access. Furthermore, the commercial relationship with international institutions provides information about firm’s creditworthiness and makes foreign creditors more willing to extend credit to participants of international trade.
Given this asymmetry, financial development affects sectors disproportionately and might have impacts on sectorial capital allocation, relative sectoral total factor productivity and GDP composition. Once the real exchange rate is the relative price of tradable and nontradable goods, it should also be expected disproportionate effects on prices as a result of enforcement improvements. Having this in mind, we develop a framework to quantify the role of sectoral
1Evidences can be found in the enterprise survey of World Bank Group. Several indicators regarding credit
sources, loan requirements and access to financial services are reported.
2See also Hanedara et al (2014).
3The authors use data from the World Business Economic Survey (2001) and run distinct probit regressions
where the dependent variables are: the degree of financing as an obstacle to running the business and the degree of collateral as a barrier to obtain finance. The crucial independent variable is a dummy that is equal to one for non-tradable firms and zero, otherwise. Even after controlling for some factors, they find a significant positive parameter on the dummy that indicates the result mentioned above.
heterogeneity in explaining the aggregate consequences of financial development. Our analysis is focused on small open economies in order to check emerging markets response to financial progress. Since those countries have weaker institutions, it is crucial to study this issue in such cases.
We show that sectoral heterogeneity and financial frictions have a critical role in generating some empirical regularities in economic development. While financial frictions are able to explain the empirical relation between financial development and output per capita across countries, the presence of sectoral heterogeneity in credit access is crucial to explain the large difference in relative prices, sectorial capital accumulation and sector-level productivity between rich and poor economies. Moreover, we discover that the nature of financial development is essential to determine its economic effects. Since firms face collateral constraints in domestic and foreign credit markets, improvements in enforcement conditions might occur in these two points of view. Hence, financial development cannot be summarized in a single condition. It is formed by a mix of external and domestic financial integration of a country and the nature of the improvement must be take into account when analysing its impacts. This point is specially important given the empirical evidences of sectoral asymmetry in the access to foreign credit markets.
In our setting, we consider the existence of tradable and nontradable goods sector, formed by a continuum of heterogeneous entrepreneurs with regard to their productivity. These agents have access to domestic credit markets, where risk-free bonds may be traded. Since they are heterogeneous, borrowing might be interesting for some entrepreneurs, while lending might make sense for others. Furthermore, there is an international credit market where debt can be contracted at an exogenous interest rate. Although entrepreneurs have access to credit markets, they cannot contract any amount of debt. Once borrowers are able to divert funds, they have a limited amount of borrowing at both domestic and foreign markets. We assume that firms can only secure their loans using part of their capital stock. Given the limited enforcement environment and the risk-free bonds assumption, it implies that lenders only extend credit when the loan is totally secured by borrower’s plegdeable assets. Since both collateral value and interest payments depend on prices, the credit constraints are endogenous in our setting, as in Kiyotaki and Moore (1997).
We also assume that there is a difference in the ability of domestic and foreign creditors to collect collateral. In line with Caballero and Krishnamurthy (2001), the collateral that can be pledged by foreign investors is only a fraction of the amount collected by the domestic creditors in case of default. Following the empirical evidences of sectoral heterogeneity in credit access, we also consider that the tradable goods sector has an easier access to foreign credit markets. It means that foreign creditors is less able to collect collateral of nontradable goods producers and, then, the external dependence of this sector is limited.
Based on this environment, we find that sectoral heterogeneity and financial frictions are key elements in explaining the rich consequences of financial development. Once the improve-ments in enforcement conditions increase the entrepreneurial access to credit market, it allows a better allocation of resources between projects. Note that the credit suppliers are the least productive agents of the economy who choose not to run their projects. When there is a lack of financial development, the resources cannot flow freely from the less productive agents to the more productive ones. Then, productive projects cannot run at full capacity and the remaining resources go to unproductive firms. It is clearly an inefficient allocation and it is the reason why improvements in financial development result in a boost of total factor productivity and output per capita. Since the total factor productivity is endogenous in our model, we capture and quantify the gap between the TFP and output per worker of developed and developing countries.
We calibrate our model using data from Argentina. Considering a 5% of raise in both measures of financial development, we show that the country experiences an increase of 5.7% in
its real output per worker and 3.0% in its TFP. Our results are consistent with a wide empirical literature on the subject. For example, King and Levine (1993) and Beck et al (2000) find that financial development is positively correlated to output per capita across countries, as well as to aggregate credit measures. In addition, Hall and Jones (1999) shows that the total factor productivity has substantial role in generating differences in countries’ income.
In addition, we also find that the sectoral heterogeneity is responsible for explaining the disproportionate effects of financial development on different sectors. We show that financial development tends to favor tradable goods producers. It happens because two main reasons: their higher capital intensity and easier access to foreign credit markets. Regarding the last, we have argued that there are empirical evidences that tradable goods firms rely relatively more on foreign debt. Thus, this sector is specially favored by improvements in external integration. Their leverage ratio raises as a consequence of such changes, while the effects on nontradable goods producers are only secondary through prices movements. It enables the tradable goods sector to increase its capital accumulation, which in turn is reflected on total sectoral output. The higher capital intensity also plays an important role. Since tradable goods sector tends to be more capital intensive, the gain generated by the better allocation of resources is amplified and it is possible to observe a relative increase in its total factor productivity. These two points imply a relative scarcity of nontradable goods, causing an exchange appreciation.
The sectoral results are also quantified in our work. Again, supposing an increase of 5% in both measures of financial development, we show that the TFP of tradable goods sector raises 3.4%, while it is only verified an increase of 2.6% in the TFP of nontradable goods sector. Regarding the capital accumulation, we also observe a disproportionate effect. More specifically, there is an expansion of 9.6% and 8.3% in the capital stock of tradable and nontradable goods sectors, respectively. These movements are reflected in the real exchange rate, which appreciates 3.1%. Our results are supported by empirical evidences. For example, Hsieh and Klenow (2007) show that the tradable goods sector is particularly unproductive in less developed economies4. Ballassa (1964) and Samuelson (1964) in turn document that the relative price of tradable goods is higher in poor countries.
Finally, we argue that financial development should not be summarized in a single condition, as commonly studied in the literature. It is reflected on the enforcement conditions between domestic lenders and borrowers, but also between foreign and domestic agents. We show that improvements in these two measures have different roles in the economy. The domestic inte-gration is vital to reduce the misalocation in poor countries and to boost their total factor productivity. The external integration, however, is crucial to reduce the domestic interest rate and increase the extensive margin of firms, allowing a deeper involvement of entrepreneurs in real production. One should note that these two measures tend to follow a joint path and, then, these effects tend to happen simultaneously. If it is the case, we argue that the effect of domestic integration tends to stand out. If it is not, we contribute to the literature by showing the exact impact of domestic and external integration separately.
Our paper is related to a vast literature of financial frictions and economic development5.
Our microeconomic environment is based on Homolstrom and Tirole (1997). We follow the authors’ notion that firms might divert funds without necessarily paying their debts and face credit constraints due to the monitoring problem. Following Cabballero and Krishnamurthy (2001) and Frazao (2014), we consider the existence of heterogeneity in the ability of domestic and foreign creditors to collect collateral and introduce credit market segregation in our model. In addition, we have a close relation to macroeconomic models which argue that limited
commit-4Buera, Kaboski and Shin (2011) construct measures of sector-level TFP for manufacturing and services
value-add for 18 OECD countries and find that relative TFP of manufacturing to services is positively correlated with output per worker.
ment environment contributes to missallocation of resources in the presence of entrepreneurial heterogeneity, as Kiyotaki and Moore (1997). Our work also presents important similarities to Buera and Moll (2015) with regard to productivity heterogeneity and endogenous total factor productivity. This paper takes together financial frictions and individuals heterogeneity, in order to study the mapping from a credit crunch to aggregate wedges.
Regarding the literature of financial development, our work is most closely related to Buera, Kaboski and Shin (2011). This paper studies the role of scale heterogeneity between industries in explaining the effects of financial development. They consider sector specific fixed cost that leads to differences in the scale of production across sectors and firms’ ability to overcome credit constraints with internal funds. They show that sectors with larger scale are disproportionately vulnerable to financial frictions and that it explains the asymmetric effects of financial deve-lopment. The link between our paper and theirs is the empirical evidence that tradable goods sector tends to be formed by large scale firms. However, it is worth noting that they do not consider the existence of foreign credit market6. It means that their paper does not capture
and neither quantify the role of sectoral heterogeneity, with regard to foreign credit access, in generating the regularities of financial development. Since this is the main goal of our work, we depart from them in a nontrivial manner. In addition, given the absence of foreign credit market, the authors summarize financial development in an one-dimensional parameter, which is equivalent to domestic financial integration in our paper. Nevertheless, we discover that there is a crucial difference between the effects of external and domestic financial integration on the economy and, hence, it should be take into account when analysing the consequences of financial development.
Moll (2014) also studies the effects of financial frictions on the accumulation of capital and wealth of countries. It analyses both steady states and transition dynamics and concludes that the persistence of idiosyncratic productivity shocks determines the size of steady-state productivity losses, as well as the speed of transitions. Although our environment is based on some similar elements, we depart from this paper by focusing on the effects of financial frictions on sectoral level, as well as by considering the role of enforcement conditions between domestic and foreign agents.
The paper is organized as follows. Section 2 presents the environment. In section 3, theo-retical results are presented and the equilibrium is characterized. In section 4, we calibrate the model and present the quantitative results. Robustness test and conclusion follow in section 5 and 6.
1.2
Environment
Consider a small open economy model with tradable and nontradable sectors, formed by three group of individuals: tradable producers, nontradable producers and workers. Each sector is composed by a continuum of entrepreneurs with unitary measure7. Tradable producers are indexed by i ∈ [0, 1], while nontradable producers are indexed by j ∈ [0, 1]. Besides sectoral heterogeneity, entrepreneurs can also differ within a sector. They are heterogeneous in their productivity (zit, zjt), capital stock holdings (kit, kjt), domestic debt (dit, djt) and international
debt (d∗it, d∗jt). We assume that their productivity is a stochastic variable, drawn from a distri-bution ψ(z) at each period. In order to simplify the analysis, this variable is assumed to be i.i.d across time and entrepreneurs. Regarding preferences, the utility function is given as follows:
6In their framework, individuals have access to financial intermediaries who are responsible to allow the flow
of resources between domestic agents.
E0 ∞ X t=0 βtu(Cıt) u(C) = C1−η 1 − η ı ∈ {i, j}, (1.1)
with E(·) being the expectation operator, β the discount factor and σ the coefficient of relative risk aversion. In addition, the consumption basket, Cıt, is given by an Armington-type CES
aggregator between tradable (cT
ıt) and nontradable goods (cNıt).
Cıt= [ω(cTıt) σ−1 σ + (1 − ω)(cN ıt) σ−1 σ ] σ σ−1
In each period t, entrepreneurs of sector s can access a production technology, which uses capital stock and labor as inputs.
yı= (zıtkıt)αs(lı)1−αs αs∈ (0, 1),
In addition, there is an investment technology that entrepreneurs of both sectors can use to transform tradable goods into investment goods. This function assumes the linear form below, where δ is the depreciation rate and xıt is the individual investment at period t.
kıt+1= xıt+ (1 − δ)kıt
In our setting, there is also a competitive labor market in which entrepreneurs can hire workers paying the wage wt. Since workers are homogeneous and there is an unit mass of
them, we consider a representative worker. Preferences are the same as for entrepreneurs and, therefore, workers do not face a trade-off between leisure and consumption. In what follows CwtT and CN
wtrepresent the representative worker’s consumption of tradable goods and of nontradable
goods, respectively.
We assume further the existence of a domestic and an international credit market where risk-free bonds are traded only by entrepreneurs8. Domestic and foreign bonds differ in two
main features: their denomination and interest rates. While foreign bonds pay the exogenous interest rate (r∗) and are denominated in terms of tradable goods, domestic bonds pay the domestic interest rate (r) in units of nontradable goods. Define dıt and d∗ıt as the stock of debt
contracted by entrepreneur ı from domestic and foreign agents, respectively. Then, normalizing the price of tradable goods to 1 and defining pt as the price of nontradable goods, we have the
following budget constraints.
Entrepreneurs of Tradable Good Sector:
cTit+ ptcNit + kit+1 = yit− wlit+ (1 − δ)kit+ ptdit+1+ d∗it+1− pt(1 + rt)dit− (1 + r∗)d∗it, (1.2)
Entrepreneurs of Nontradable Good Sector:
cTjt+ ptcNjt + kjt+1= ptyjt− wljt+ (1 − δ)kjt+ ptdjt+1+ d∗jt+1− pt(1 + rt)djt− (1 + r∗)d∗jt,
(1.3) Entrepreneurs also face credit constraints. The existence of limited commitment in our envi-ronment implies that their liabilities must be backed up with their plegdeable assets. Similarly to Holmstrom and Tirole (1997), we assume that entrepreneurs can run away with their profits from production and with a fraction 1 − θ of their capital stock. Then, domestic creditors only accept entrepreneurs’ foreign bonds and a fraction θ of their capital stock as a collateral. In contrast, foreign creditors have a lower ability to collect debtors’ assets. Moreover, domestic bonds are not viewed as collateral for foreign loans, in contrast to what happens with foreign bonds at domestic credit markets. More specifically, the credit constraints are given by:
Entrepreneurs of Tradable Good Sector:
(1 + r∗)d∗it+1≤ θ∗kit+1 (1.4)
pt+1(1 + rt+1)dit+1≤ θkit+1− (1 + r∗)d∗it+1, (1.5)
Entrepreneurs of Nontradable Good Sector:
(1 + r∗)d∗jt+1≤ 0 (1.6)
pt+1(1 + rt+1)djt+1≤ θkjt+1− (1 + r∗)d∗jt+1, (1.7)
where θ∗ ∈ (0, θ) and θ ∈ (0, 1).
Note that we assume an asymmetry in the extent in which foreign credit markets value the plegdeability of the capital stock of different goods producers. Since there is empirical evidence that tradable producers have more access to international credit markets9, we assume
that foreign creditors have more information about them and a greater ability to collect their assets. In order to simplify the analysis and make the role of credit asymmetry more clear, we assume that no assets of nontradable producers can be used as a collateral for foreign loans. For this reason, the right-hand side of (3) is zero. In other words, it means that nontradable producers are not able to raise foreign debt.
It is worth noting that θ might be interpreted as the degree of domestic financial integra-tion of the economy. It represents the strength of legal instituintegra-tions enforcing contracts between domestic agents. Since more developed economies tend to have better institutions, this para-meter is higher in such cases. Conversely, one should expect lower degree of collateralization in emerging markets.
Furthermore, the difference between θ and θ∗ must also be highlighted in this perspective. In general the literature studies the impact of financial development on GDP, considering that the degree of enforceability of contracts is the same regardless the origin of counterparts10.
9See Tornell and Westermann (2003) and The Global Development Finance (The World Bank, 2004). 10It means θ = θ∗
A strict consequence of this assumption in settings similar to ours is the absence of credit market segregation. In these cases, the domestic interest rate equals the international interest rate in equilibrium. The empirical evidences, however, do not support the consequence of this assumption. Differences between interest rates are commonly seen in credit markets. Moreover, it is crucial to take this differential into account. Once there are strong evidences of asymmetric collateral requirements between tradable and nontradable goods sectors, it might have important effects on both aggregate and sectoral variables. With this in mind, we assume that foreign creditors do not have the same ability to enforce domestic contracts as their domestic peers. Additionally, θ∗ might be understood as the strength of legal institutions enforcing contracts between domestic and foreign agents. In a different manner, it represents the external financial integration of the economy.
Finally, note that firms might be interested in contract debt in order to boost their pro-duction next period. Since entrepreneurs have private knowledge of zit+1 at the end of period
t, they know it when decide whether to contract domestic/foreign debt and to rent capital, kit+1. Therefore, the decision to borrow at period t depends on the productivity of period
t + 1 due to our timing assumption. Once entrepreneurs are heterogeneous in their productivity, there is an interesting role for domestic credit market in our setting and we eliminate uninsured idiosyncratic investment risk.
1.3
Equilibrium
The equilibrium in this economy is defined as sequences of prices {pt, rt, wt}∞t=0and quantities
such that, taking the sequence of prices and r∗ as given, (i) entrepreneurs of tradable goods sector maximize (1) subject to (2), (4), (5) and the positivity constraints; (ii) entrepreneurs of nontradable goods sector maximize (1) subject to (3), (6), (7) and the positivity constraints; (iii) the representative worker maximizes (1) subject to his budget constraint, and (iv) all markets clear at all periods t:
Z cTitϕi+ Z cTjtϕj+ CwtT + Z kit+1ϕi+ Z kjt+1ϕj− (1 − δ) Z kitϕi+ Z kjtϕj = Z yitTϕi− (1 + r∗) Z d∗itϕi+ Z d∗jtϕj + Z d∗it+1ϕi+ Z d∗jt+1ϕj Z cNitϕi+ Z cNjtϕj+ CwtN = Z yNjtϕj Z litϕi+ Z ljtϕj = 1 Z ditϕi+ Z djtϕj = 0
1.3.1 Entrepreneurs Problem
In order to solve the model, it is important to note that some entrepreneurs’ decisions do not have intertemporal effects. In Lemma 1, we prove this point and split the problem into three subproblems, where one of them is the intertemporal problem.
Lemma 1: The problem of entrepreneurs, that is, to choose stochastic processes {cTit, cNit, lit,
kit+1, dit+1, d∗it+1}∞t=0to maximize (1) subject to (2),(4),(5) in the case of tradable goods producers
and to choose {cT
jt, cNjt, ljt, kjt+1, djt+1, d∗jt+1}∞t=0to maximize (1) subject to (3),(6),(7) in the case
of nontradable goods producers, can be broken into the following three subproblems. Entrepreneurs of Tradable Goods Sector
i) Consumption Basket Problem: Allocate the period t consumption expenditure among different goods. max cT ıt,cNıt [ωcTıt σ−1 σ + (1 − ω)cN ıt σ−1 σ ]σ−1σ s.t. cTıt+ ptcNıt = PtCıt where Pt≡ [ωσ+ (1 − ω)σp1−σt ] 1
1−σ is the price index of the economy.
ii) Profit Maximization Problem: Choose optimal labor demand as a function of capital stock.
max
lit
(zitkit)αsl1−αit s − wtlit
iii) Intertemporal Problem: Allocate total wealth among consumption expenditure and savings.
max
Cit,kit+1,dit+1,d∗it+1
E ∞ X t=0 βtu(Cit) s.t.
PtCit+ kit+1= ηTtzitkit+ (1 − δ)kit+ ptdit+1+ d∗it+1− pt(1 + rt)dit− (1 + r∗)d∗it
(1 + r∗)d∗it+1 ≤ θ∗kit+1
where tradable producers’ profit is a function of optimal capital stock, derived in the profit maximization problem.
The subproblems of entrepreneurs of nontradable goods sector follow a similar structure and are shown in the appendix.
Since the optimal share of tradable goods and nontradable goods in the consumption basket and the optimal labor demand can be determined by solving static problems in each period, we can work with a reduced intertemporal problem. In this problem, entrepreneurs choose the total amount to save and the composition of their savings among domestic bonds, foreign bonds and capital stock. That said, it is convenient to write entrepreneurs’ intertemporal problem in a recursive form. In the case of entrepreneur i, the problem can be written recursively as follows.
VtT(k, d, d∗, z−1, z) = max C,d′,d∗′,k′ u(C) + βE[Vt+1T (k′, d′, d∗′, z, z′)] (1.8) s.t PtCi+ ki′ = ηtTz−1iki+ (1 − δ)ki+ ptdi′+ d∗i′− pt(1 + rt)di− (1 + r∗)d∗i (4), (5), k′ ≥ 0
There are a couple of things that should be noted here. First, the time structure of the model implies that, at time t, entrepreneur i knows zit and zit+1, which are represented in the
recursive problem as z−1and z. Second, the recursive problem can be simplified by reducing the
number of state variables. Note that, since both bonds and capital can be converted one-to-one into final goods, what matters for entrepreneur’s decisions is his net-worth.
Besides reducing the number of state variables, we can simplify the problem further. Given the time structure of the model, one can prove that the recursive problem can be broken into two. The amount of consumption and total savings are set in the “optimal savings problem”. In turn, the agent decides the proportion of his savings that should be allocated in each asset in a problem apart, called the “optimal portfolio problem”. To see all these points, define mit
and ait as the net-worth and total savings of entrepreneur i of tradable goods sector1112.
mTit≡ ηTtzitkit+ (1 − δ)kit− pt(1 + rt)dit− (1 + r∗)d∗it
aTit≡ kit− pt−1dit− d∗it
11Simirlaly, define m
jtand ajtas the net-worth and savings of entrepreneur j of nontradable goods sector. I.e,
mjt≡U p
1 α
t ηtzjtkjt+ (1 − δ)kjt− pt(1 + rt)djt− (1 + r∗)d∗jt and aNjt≡ kjt− pt−1djt− d∗jt.
Lemma 2: The dynamic program below is equivalent to (8). vtT(mT, z) = max aT ′ u mT − aT′ Pt ! + βEvTt+1(mTt+1(aT′, z)) mt+1(aT ′ , z′) = max k′,d′,d∗′ ηTt+1z′k′+ (1 − δ)k′− pt+1(1 + rt+1)d′− (1 + r∗)d∗ ′ s.t k′− ptd′− d∗ ′ = aT′ (4) (5) k′ ≥ 0
Since the intertemporal problem can be solved as a two-stage problem and the return of all assets is linear13, the optimal portfolio of savings is a corner solution. Moreover, there is a productivity threshold that defines whether capital is a good instrument to transfer wealth to next period. To attain these results, define the maximum leverage rate for entrepreneurs of tradable and nontradable goods sector at period t + 1 as:
ρTt+1≡ 1 − pt pt+1 (θ − θ∗) (1 + rt+1) − θ ∗ 1 + r∗ −1 , ρNt+1= 1 − pt pt+1 θ (1 + rt+1) −1
Lemma 3: The exchange rate-adjusted return on foreign bonds is the lower bound for domestic interest rate (rt ≥ (1 + r∗)pt−1pt − 1 ∀t) and there are productivity thresholds (˜zTt+1,
˜ zN
t+1) that define the behaviour of entrepreneurs. Let i and j be, respectively, an entrepreneur
of tradable goods sector and an entrepreneur of nontradable goods sector. Then, their optimal portfolio is given by:
kit+1= 0, if zit+1 < ˜zt+1T ; ρTt+1aTit+1, if zit+1 ≥ ˜zt+1T kjt+1= 0, if zjt+1< ˜zt+1N ; ρNt+1aNjt+1, if zjt+1≥ ˜zt+1N dit+1 = −aTit+1 pt , if zit+1 < ˜z T t+1; (θ−θ∗)ρT t+1aTit+1 pt+1(1+rt+1) , if zjt+1≥ ˜z T t+1. djt+1= −aNjt+1 pt , if zjt+1< ˜z N t+1; θρN t+1aNjt+1 pt+1(1+rt+1), if zit+1≥ ˜z N t+1.
13We have already proven in Lemma 1 that maximizing out over labor in the Profit Maximization Problem
leads a profit function that is linear in capital stock. It follows from the hypothesis of constant returns to scale production function.
d∗it+1= 0, if zit+1< ˜zt+1T ; θ∗ρT t+1aTit+1 (1+r∗) , if zit+1≥ ˜zt+1T . d∗jt+1= 0, if zit+1< ˜zt+1N ; 0, if zit+1≥ ˜zt+1N . where ˜zt+1T = (pt+1/pt)(1+rt+1)(1+r∗−θ∗)(1+r∗)−1−1+δ+θ∗ ηT t+1 and ˜z N t+1= (pt+1/pt)(1+rt+1)−1+δ p1/αt+1ηN t+1
Lemma 3 highlights key properties of the entrepreneurs’ behaviour. First of all, given the existence of a productivity threshold, the optimal choice of savings instruments relies only on entrepreneur’s productivity level next period. Additionally, the linearity of the problem im-plies that the optimal choice is at a corner. If the productivity is lower than the threshold, entrepreneurs choose to not hold capital stock. Otherwise, they take the maximal amount of debt allowed by credit constraints and obtain the largest quantity of capital goods. Clearly, the choice between domestic and foreign debt is determined by interest rates differential and credit constraints. We prove that the exchange rate-adjusted return on foreign bonds is the lower bound for the domestic interest rate in equilibrium14. Thus, if the productivity is higher than
the threshold, entrepreneurs of tradable goods sector take the maximal amount of foreign debt and use the remaining collateral to get domestic loans. In turn, entrepreneurs of nontradable goods sector take the maximal amount of domestic credit, once they cannot raise foreign debt. If instead the productivity is not high enough, we have the trivial solution: the full allocation of savings in domestic credit markets. Also, it is worth noting that agents take the total savings (at+1) as given when decide the amount to allocate in each asset.
Moreover, one should note that both productivity thresholds and leverage ratios rely on prices and collateral parameters. According to the last ones, we can see the direct effects of financial development on entrepreneurs’ choices. Since the nontradable goods sector does not have access to foreign credit markets, only improvements in domestic enforcement conditions affect this sector directly. Then, the effect of external financial development of an economy has asymmetric effects among sectors.
That being said, it is important to note that different nature of financial development has distinct effects on tradable goods sector. As intuitively expected, the leverage ratio of tradable goods producers increases as a result of improvements in both enforcement conditions. The productivity threshold, however, only responds to changes in the strength of legal institutions enforcing contracts between domestic and foreign agents15. Therefore, an increase in θ only affects directly the level of capital and debt of entrepreneurs, while raises in θ∗ also has straight consequences on their decision about being active or not. In other words, for a given vector of equilibrium prices, distinct natures of financial development has different effects on extensive and intensive margin of tradable goods sector.
In lemma 4, we prove that improvements in enforcement conditions between domestic and foreign agents have positive effects on the extensive and intensive margins of tradable goods producers16. Regarding the extensive margin, note that the productivity threshold of this sector is an increasing function of θ∗ in equilibrium. Thereby, an improvement in such enforcement condition leads a reduction of the productivity threshold and some entrepreneurs that would
14We show that domestic credit market does not clear when r
t<(1 + r∗)pt−1pt − 1, thus there is no equilibrium
in this case. See the Appendix.
15This asymmetry is once again due to the lower bound on domestic interest rate. In equilibrium, entrepreneurs
of tradable goods sector compare the net return of leverage capital per unit of net-worth to the return obtained in domestic credit market. Then, the threshold is determined and the effects of changes in collateral parameters on the net return of capital is totally offset by the opposite effect on the leverage ratio.
not operate their projects find interesting to run their businesses thereafter. In addition, the firms which were previously active experience an increase in their leverage ratio, as well as in their demand for capital and foreign debt. However, it is worth notable that the demand for domestic credit decreases. Since foreign loans are cheaper than the domestic ones, tradable goods producers prefer to take credit at international credit markets17. Intuitively, this results is clear and its proof follows in the appendix.
With regard to the effects of internal financial development on entrepreneurs’ choices, it follows directly from the definition of leverage ratio and optimal portfolio in Lemma 3 that it has positive impact on the intensive margin and credit demand of both sectors.
Lemma 4: For a given vector of equilibrium prices, improvements in enforcement conditions between domestic and foreign agents have positive effects on the intensive and extensive margin of tradable goods producers. In addition, it boosts their foreign debt, while reduce the domestic one.
Given these results, it would be interesting to analyse the impact of financial development on aggregate variables and prices. In order to simplify the entrepreneurs’s optimal savings problem and to attain some aggregate results analytically, we now impose the logarithmic utility case (η = 1). Given this assumption, Lemma 5 follows.
Lemma 5: Entrepreneurs’ total saving is a constant fraction of their previous net-worth.
aTit+1= βmTit
aNjt+1= βmNjt
Using the lemma above and the assumption of i.i.d distribution of productivities across time and entrepreneurs, we are able to characterize the equilibrium prices and the aggregate quantities of the economy. Then, proposition 1 follows.
Proposition 1: The aggregate production of tradable and nontradable goods are given by:
YtN = ZtN(KtN)α(LNt )1−α YtT = ZtT(KtT)α(LTt)1−α (1.9) where ZtN = R∞ ˜ zNt zψ(z)dz 1−Ψ(˜zN t ) α and ZtT = R∞ ˜ zTt zψ(z)dz 1−Ψ(˜zT t) α
are the actual TFP.
The aggregate consumption of each type of good follows below.
CtT = 1 + 1 − ω ω σ p1−σt −1 ((1 − β)(MtN+ MtT) + wt) (1.10) CtN = pt+ ω 1 − ω σ pσt −1 ((1 − β)(MtN + MtT) + wt) (1.11)
Furthermore, aggregate savings can be expressed as a function of prices and the total net-worth of both tradable and nontradable goods sectors.
D∗t+1= DTt+1∗ = βMtT " θ∗ρT t+1 1 + r∗(1 − Ψ(˜z T t+1)) # (1.12) Kt+1= βMtNρNt+1(1 − Ψ(˜zt+1N )) + βMtTρTt+1(1 − Ψ(˜zt+1T )) (1.13)
In equilibrium, the exchange rate might satisfy:18
pt= 1 − ω ω CT t CN t σ1 (1.14)
Finally, the law-of-motion of the aggregate net-worth of both sectors are:
Mt+1N = p 1 α t+1ηt+1N Zt+1N 1 αKN t+1+ (1 − δ)Kt+1N − pt+1(1 + rt+1)Dt+1N (1.15) Mt+1T = ηTt+1Zt+1T 1 αKT t+1+ (1 − δ)Kt+1T − pt+1(1 + rt+1)Dt+1T − (1 + r∗)Dt+1∗ T (1.16)
In proposition 1, we prove some interesting points that should be highlighted here. First, the aggregate production function of both tradable and nontradable goods assumes a Cobb-Douglas function, where ZT
t and ZtN are the actual TFP of sectors. One might note, however, that they
differ from the “natural”productivities. Given the Law of Large Numbers, the sectors’s “na-tural”productivity is constant over time, even though individuals face productivity shocks and economic conditions may change19. In contrast, the actual TFP is a function of the productivity threshold. It means that the actual TFP of sectors is endogenous and might respond to changes in enforcement conditions.
Moreover, we prove that the aggregate consumption and savings depend on the aggregate net-worth of sectors20, as one can see in (10), (11), (12) and (13). Thus, it is not necessary
to know the wealth distribution across entrepreneurs to compute the equilibrium. This result is driven by the assumption of i.i.d distribution of individual productivity and simplifies the analysis. However, it can be relaxed if one judge appropriate.
Regarding the exchange rate, we prove that in equilibrium it is equal to the marginal rate of substitution of the tradable and nontradable goods. Once the exchange rate is the relative price of these goods, (14) follows from the entrepreneurs’ “consumption basket problem”. Finally, the prices of the economy and the aggregate variables define the law-of-motion of the aggregate net-worth of both sectors, as shown in (15) and (16).
18Since we are assuming homothetic preferences, the individual desired tradable over nontradable consumption
depends only on the relative price and not on wealth or total expenditure.
19The “natural”productivity is given by the mean of the distribution ψ. 20To see this point, note that the entrepreneur’s net-worth (m
it) is independent from his productivity (zit),
1.4
Quantitative Analysis
In this section, we describe the calibration of the model and compute some general equi-librium simulations in order to verify the impact of financial development on the aggregate variables and prices.
1.4.1 Calibration
Since we are working with a small open economy model and the lack of financial development is more exacerbated in emerging markets, our calibration uses data from Argentina: an example of developing country that has been studied in the literature. A period represents a year in our model. The log-utility case (η = 1) is maintained. The parameter α is calibrated for each sector separately due to the empirical evidences. We set it at 0.3 for nontradable goods sector and 0.4 for tradable goods sector. These values are usual and find support in Valentinyi and Herrendorf (2008)21. The depreciation rate and the world risk-free interest rate are calibrated at their standard values in the literature, that is, δ = 5% and r∗ = 2%. The intratemporal elasticity of substitution is estimated in the range between 0.40 and 0.83, according to Mendoza (2006), Gonzales-Rozada and Neumeyer (2003) and Stockman and Tesar (1995). Given the key role of this parameter in determining the exchange rate, we choose to be conservative and set it at the upper bound of its estimation. Since an higher elasticity implies a smaller change in the exchange rate as a result of a reduction in tradable goods consumption, this is the conservative choice.
The other parameters (β, ω, θ, θ∗) are set so that some key variables match their historical values of the data. The discount factor ultimately governs aggregate savings and, then, it is reasonable to set β so that the capital plus net foreign asset-to-GDP ratio in the model equals its historical average in Argentina. Using data from the World Penn Table (PWT) and the data set constructed by Lane and Milesi-Ferretti (2001)22, this ratio is approximately 1.97, which
yields a β of 0.903 in our model23.
In order to calibrate ω, we use data from the World Development Indicators which shows an average share of tradable goods in consumption of 32%. To achieve this value in our model, it is necessary to set ω at 0.31. This value is close to 0.32 used by Bianchi (2011) and not so different from other values used in the literature24.
Turning to the foreign collateral parameter, it is worth remembering that it represents the ability of international creditors to enforce contracts. It means that θ∗ is directly related to the
amount of foreign finance. Therefore, we calibrate this parameter so that the net foreign asset position to GDP ratio in our model matches its historical average. This calibration results in a value of θ∗= 0.3.
Finally, we use a different approach to calibrate the parameter of domestic credit constraint. According to the World Bank (2011), in its Entreprise Survey, and to Bebczuk (2011), 64% of firm’s capital is financed by its own funds on average in Argentina. Since we have already calibrated the foreign collateral parameter, we can use the level of total external finance, 36%, to calibrate θ. Using this approach, θ is set at 0.8. The whole calibration is summarized in table 1.
21This paper measures factor income shares at the sectoral level for the US economy. In the absence of sources
for Argentina, we set this parameter at the standard values which have supported for other economies.
22According to the PWT, the capital-to-GDP ratio is approximately 2.26. In turn, Lane and Milesi-Ferretti
(2001) reports a net-foreign-assets of -0,29.
23Values in the range of 0.90-0.91 are not uncommon in the literature for annual frequency. For example,
Bianchi (2011) reports β = 0, 91.
Tabela 1.1: Calibration
Value Target
International interest rate r = 2% Standard Value
Depreciation rate δ = 0.05 Standard Value
Output elasticity of capital αN = 0.3, αT = 0.4 Valentinyi and Herrendorf (2008)
Discount factor β = 0.903 Capital plus Net Foreign Asset/GDP = 1.97
Weight on tradables in CES ω = 0.31 Share of Tradable Consumption = 0.32
Elasticity of substitution σ = 0.83 Mendonza (2006)
International Credit Cofficient θ∗= 0.3 Net Foreign Assets to GDP ratio = -0.29
Domestic Credit Coefficient θ = 0.8 Share of Internal Finance = 0.64
1.4.2 Simulations
Using the previous calibration, we compute the steady-state of the model and do some exercises in order to analyse the impact of financial development on key sectoral variables, as well as on national aggregates and prices. Since there are two measures of financial development in our model, it is worth analysing the impact of each one separately. First, we assess the impact of an improvement in the enforcement conditions according to foreign creditors’ view. Considering all the remaining calibration unchanged, we compute the general equilibrium effects of changes in θ∗. The simulations follow in figure 1.
Given the sectoral asymmetry in the access to foreign credit market, increases in external financial integration lead to a structural change in the economy. Once the tradable goods sector tends to rely on foreign debt, the lack of external enforcement conditions is specially harmful to this sector. Hence, an improvement in external financial integration generates a reallocation of resources towards the production of tradable goods.
To understand this point, note that a positive change in θ∗raises the ability of tradable goods producers to collateralize their foreign debt. As a consequence, they are able to increase their capital stock, as well as their production. As proven in Lemma 4, their portfolio composition is also affected. While the foreign liabilities raise, there is a reduction of their domestic debt. In turn, this reduction results in a negative pressure on the domestic interest rate. For low values of θ, this is the effect that prevails in equilibrium at domestic credit market25.
The decrease in the interest rate affects the productivity threshold of nontradable goods producers, implying a raise in their capital stock as well. Although both sectors experience an higher capital accumulation, the movement is more pronounced for the tradable goods produ-cers26. Since this sector is directly affected by the increase in collateral parameter, its share in
total capital stock raises. In addition, there is also a reallocation of labor across sectors due to its close relation to capital stock in equilibrium. Thus, the improvement in external integration leads to a reallocation of resources across sectors, resulting in an increase of tradable goods share in total production.
Another interesting result is its effects on the extensive margin of firms. Since the external financial integration tends to decrease the domestic interest rate, the productivity thresholds of both sector are negatively affected by an increase in θ∗. The result is a expansion of the
25Besides the effect mentioned above, there are several others. For example, the increase in extensive margin
leads to a reduction in credit supply and augments the demand, resulting in a positive pressure on interest rates. However, the net effect in equilibrium is the negative one. For high levels of θ∗
, however, the interest rate reaches its lower bound and further improvements in external enforcement conditions are not able to affect this price.
26For high levels of θ∗
, the nontradable goods sector experiences a marginal reduction of its capital stock as a result of trivial movements in the exchange rate and wages.
Figura 1.1: The general equilibrium effects of changes in external integration (θ∗) 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 0.65 0.66 0.67 0.68 0.69 0.70 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7
Exchange Rate and Interest Rate
θ= 0.8 Exchange Rate Interest Rate 39.6% 40.0% 40.4% 40.8% 41.2% 41.6% 42.0% 4.50 4.55 4.60 4.65 4.70 4.75 4.80 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 Production θ= 0.8 GDP
Tradable Goods Production/GDP
4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.10 5.20 5.30 5.40 5.50 5.60 5.70 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7
Sectoral Capital Stock
θ= 0.8
Nontradable Goods Sector Tradable Goods Sector
12.5 12.8 13.0 13.3 13.5 13.8 14.0 7.5 7.8 8.0 8.3 8.5 8.8 9.0 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7
Sectoral Capital Intensity
θ= 0.8
Nontradable Goods Sector Tradable Goods Sector
0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.60 0.61 0.62 0.63 0.64 0.65 0.66 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 Labor Allocation θ= 0.8
Nontradable Goods Sector Tradable Goods Sector
44% 45% 46% 47% 48% 49% 50% 9.5 9.8 10.0 10.3 10.5 10.8 11.0 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7
Total Capital Stock
θ= 0.8
Capital Stock
Capital of Tradable Goods Sector/Total Capital
0.0 0.5 1.0 1.5 2.0 2.5 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 Foreing Debt θ= 0.8 1.50 1.58 1.65 1.73 1.80 1.88 1.95 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 TFP θ= 0.8
Tradable Goods Sector Nontradable Goods Sector TFP 1.80 1.90 2.00 2.10 2.20 2.30 1.80 1.90 2.00 2.10 2.20 2.30 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 Productivity Threshold θ= 0.8
Nontradable Goods Sector Tradable Goods Sector
1.70 1.78 1.85 1.93 2.00 2.5 2.6 2.7 2.8 2.9 θ*=0.0 θ*=0.1 θ*=0 .2 θ*=0 .3 θ*=0 .4 θ*=0 .5 θ*=0 .6 θ*=0 .7 Sectoral Production θ* = 0.3 Nontradable Goods Sector Tradable Goods Sector
extensive margin of producers. It means that external financial integration is crucial to reduce the domestic interest rate and to allow a deeper engagement of entrepreneurs in real production. Since less productive entrepreneurs turn to be active, we also verify a decrease in the overall productivity of both sector. However, the net effect is positive for the economy once the lack of enforcement tends to limit productive projects and to increase the interest rate.
More straightforward results are also shown, as the increase in total production, foreign debt and wages27. Nonetheless, the main result is its role in the reduction of domestic interest rate
and its consequences for firms extensive margin. Additionally, its disproportionate effects on different sectors are worth notable, since result in a structural change in the economy.
Turning to the impacts of domestic financial integration, we follow the same approach used in the previous exercise. Considering all the remaining calibration unchanged, we determine the general equilibrium prices and quantities for different levels of θ, as follows in figure 2. Since the strengthening of internal enforcement conditions generates a better economic integration, it reduces the missallocation of resources. Note that it allows a better flow of resources from unproductive producers to productive ones. Then, positive changes in θ imply an increase in the aggregate capital stock, as well as in the aggregate production. Given the collateral accumulation, the country also experiences an expansion of its foreign debt.
Besides the effects on aggregate quantities, the increase in domestic integration leads to a key change in sectoral total factor productivity. Although the rise in collateral parameter tends to decrease both productivity thresholds, the response of the interest rate and wages is such that the negative effect is overcompensated. This result holds for both sectors, nevertheless there is a difference in their intensive. Since the tradable goods sector is more capital intensive, the reaction of its TFP is more exacerbated than the one verified for the nontradable goods sector28. It means that the former tends to be relatively unproductive in less developed countries, as supported by empirical evidences (Chang-Tai Hsieh and Peter Klenow 2007).
The movement in the exchange rate is closely related to the change in relative sectoral productivity. Since the tradable goods sector turns to be relatively more productive, there is an higher capital accumulation in this sector. This result implies an abundance of tradable goods in the economy. Once the exchange rate is the relative price of tradable and nontradable goods, we can observe an exchange appreciation as a result of improvements in domestic integration of a country. As one should note, this result also has empirical support. Balassa (1964) and Samuelson (1964) were the first to document the higher relative price of tradable goods in poor countries.
It is worth noting that the behavior of interest rate is crucial to determine the intensity of TFP reaction in our model for different levels of domestic integration. When the internal degree of collateralization is relatively low, the interest rate is constant. Given the weak demand for domestic credit, the interest rate equals the international one and small changes in θ do not put enough pressure on domestic credit markets. In this case, the raise of productivity thresholds is due to the increase in wages and is somewhat limited. In contrast, for high level of θ, the demand for domestic loans is already robust and the interest rate responds positively to improvements in domestic enforcement conditions. Then, there is a sharp increase in the productivity thresholds of both sectors. In this new equilibrium, the ability of entrepreneurs to collateralize their debt is higher, as well as the interest rate. It means that the resources are going to the productive
27Using the individual foreign credit constraints, one can show that there is a foreign credit constraint for the
aggregate economy which is similar to the individual ones. Moreover, this constraint is binding in equilibrium and the increase in aggregate foreign debt follows. In addition, following the pattern of the individual results, we also have a raise of aggregate production of both sectors.
28Note that the productivity threshold follow the same movement in different sectors and stay at a similar level.
It happens because the exchange appreciation tends to decrease the threshold of nontradable goods producers, avoiding a stronger increase in this variable.
Figura 1.2: The general equilibrium effects of changes in domestic integration (θ) 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 0.50 0.55 0.60 0.65 0.70 0.75 0.80 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1
Exchange Rate and Interest Rate
θ* = 0.3 Exchange Rate Interest Rate 38% 39% 40% 41% 42% 43% 44% 3.0 4.0 5.0 6.0 7.0 8.0 9.0 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1 Production θ*= 0.3 GDP
Tradable Goods Production/GDP
0.9 1.2 1.5 1.8 2.1 2.4 2.7 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1 TFP θ* = 0.3 TFP
TFP of Nontradable Goods Sector TFP of Tradable Goods Sector
45% 46% 47% 48% 49% 50% 51% 4.0 7.0 10.0 13.0 16.0 19.0 22.0 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1
Total Capital Stock
θ* = 0.3 Capital Stock
Capital of Tradable Goods Sector/Total Capital
2.3 3.6 4.9 6.2 7.5 8.8 10.1 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1
Sectoral Capital Stock
θ*= 0.3 Tradable Goods Sector Nontradable Goods Sector
4 8 12 16 20 24 28 4 6 8 10 12 14 16 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1
Sectoral Capital Intensity
θ* = 0.3 Nontradable Goods Sector Tradable Goods Sector
1.0 2.0 3.0 4.0 5.0 6.0 1.0 2.0 3.0 4.0 5.0 6.0 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1 Productivity Thrsehold θ*= 0.3 Nontradable Goods Sector Tradable Goods Sector
-1.8 -0.8 0.2 1.2 2.2 3.2 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1 Foreing Debt θ* = 0.3 2.0 2.2 2.4 2.6 2.8 3.0 1.8 2.6 3.3 4.1 4.8 5.6 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1
Wage and Price Index
θ* = 0.3 Wage Price Index 1.0 2.0 3.0 4.0 5.0 1.0 2.0 3.0 4.0 5.0 θ=0 .4 θ=0 .5 θ=0 .6 θ=0 .7 θ=0 .8 θ=0 .9 θ=1 Sectoral Production θ* = 0.3 Nontradable Goods Sector Tradable Goods Sector
firms, while the less productive ones are being expelled. This implies in a huge increase of total factor productivity, as show in figure 2.
Therefore, improvements in the internal financial development have a wide effect on the economy. It has a key role of selection, expelling the less productive firms while allows the increase in capital stock and production of the more productive ones. The result is a relevant raise of TFP, aggregate capital stock and production. Analysing the prices, we only see the reflection of a more integrated economy and a different structure of production, with relative abundance of tradable goods.
Having analysed the impact of each nature of financial development, one might argue that it is reasonable to expect joint movements in these conditions. In order to contemplate this issue, we consider proportional increases in both collateral parameters and compute the new equilibrium, as show in figure 3. Due to the raise in firms ability to collateralize their loans, the economy experiences a boost in its GDP, aggregate capital stock and foreign debt. Since the capital accumulation is generated by increases in entrepreneurs’ debt, the interest rate also goes upwards29. Following a similar pattern, we can verify an higher wage in equilibrium.
Since the increase in the external and domestic financial integration have opposite effects on some sectoral variables and prices, it is interesting to note that the domestic financial integration is the dominant driver of sectoral movements. Turning to the first exercise, it is easy to see why the effects of external integration are offset. Note that, for high levels of θ∗, the interest rate is equal to its lower bound and further improvements in such enforcement conditions have no impact on this price. However, the change in domestic financial integration is amplified for high levels of θ. Once we are studying the effects of improvements in financial development in the neighborhood of the calibrated values, the effects of domestic financial integration prevail. For example, the response of sectoral TFP in this exercise is similar to the one observed in the case of changes in domestic financial integration exclusively, but it is partially offset by the effects of increases in external financial integration. The same pattern is verified for the exchange appreciation.
Then, we conclude that improvements in financial development generate structural changes in the economy. Since there is a difference between the ability of domestic and foreign creditors to collect collateral and there is also empirical evidence of asymmetric access to foreign credit market, the nature of improvements in financial development is crucial to determine the impact on sectoral variables and prices. To the best of our knowledge, the literature misses this point when disregard credit market segregation in the presence of asymmetric financing conditions across sectors.
As we have shown, improvements in enforcement conditions have important direct effects on the domestic interest rate and these movements play a critical role in endogenous unfolding. In the case of improvements in external enforcement conditions, we verify a decrease in the interest rate, which is followed by a rise in extensive margin of firms, a movement of capital stock towards the tradable goods production and an exchange depreciation. In contrast, increases in domestic collateral parameters lead to a raise in the domestic interest rate, resulting in a significant rise in the overall productivity and an exchange appreciation. Nevertheless, it is verified in both cases an increase in total production, capital accumulation and foreign debt, as empirically supported. Considering a general improvement in enforcement conditions, the effect of internal financial development prevails in equilibrium. As argued above, it has crucial implications for sectoral and aggregate variables that must be considered when analysing the economic effects of financial development. In order to quantify these movements, we calculate the impact of an increase of five percent in both collateral parameters. In this case, the real GDP of Argentina raises 5.7% and there is a real exchange appreciation of 3.1%. The movement in its total factor productivity
Figura 1.3: The general equilibrium effects of changes in financial development (θ and θ∗) 0% 1% 2% 3% 4% 5% 0.60 0.62 0.64 0.66 0.68 0.70 0% 5% 10% 15%
Exchange Rate and Interest Rate
Exchange Rate Interest Rate 1.7 1.9 2.1 2.3 2.5 2.7 1.8 2.3 2.8 3.3 3.8 4.3 0% 5% 10% 15%
Wage and Price Index
Wage Price Index 40.6% 40.7% 40.8% 40.9% 41.0% 4.40 4.80 5.20 5.60 6.00 0% 5% 10% 15% Production GDP Share of Tradable Goods Production 1.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 4.0 0% 5% 10% 15% Sectoral Production Nontradable Goods Sector
Tradable Goods Sector
12.0 14.0 16.0 18.0 20.0 8.5 9.5 10.5 11.5 12.5 0% 5% 10% 15%
Sectoral Capital Intensity
Nontradable Goods Sector Tradable Goods Sector
1.30 1.50 1.70 1.90 2.10 0% 5% 10% 15% TFP TFP
TFP of Nontradable Goods Sector TFP of Tradable Goods Sector
45.0% 46.0% 47.0% 48.0% 49.0% 50.0% 10.0 11.0 12.0 13.0 14.0 15.0 0% 5% 10% 15%
Total Capital Stock Capital Stock
Capital of Tradable Goods Sector/Total Capital
5.0 5.5 6.0 6.5 7.0 7.5 5.0 5.5 6.0 6.5 7.0 7.5 0% 5% 10% 15%
Sectoral Capital Stock Nontradable Goods Sector
Tradable Goods Sector
1.50 2.00 2.50 3.00 3.50 1.50 2.00 2.50 3.00 3.50 0% 5% 10% 15% Productivity Thrsehold
Nontradable Goods Sector Tradable Goods Sector
1.20 1.50 1.80 2.10 2.40 0% 5% 10% 15% Foreing Debt
is also notable. It increases 3.0%, being composed by a rise of 3.4% in the tradable goods sector and of 2.6% in the nontradable goods sector. This means that tradable goods sector tends to be relative unproductive in poor countries. Moreover, there is a disproportionate effect on the capital accumulation in this sector. We show that the capital stock of tradable goods sector rises 9.6%, while it is observed an increase of 8.3% in the other sector. These results show that there is a structural change in the economy as a result of improvements in financial development.
1.5
Robustness
In order to check if ours results are in fact generated by the sectoral heterogeneity in credit access, we do a robustness test by assuming homogeneity in sectoral capital share of income. Considering that the nontradable goods sector is so capital intensive as tradable goods sector, we determine the general equilibrium effects of financial development. With regard to aggregate variables, we show that our results are robust to this change. As one can see in figure 4, the output per worker increases, as well as the total capital stock and the total factor productivity. Supposing a raise of 5% in both measures of financial development, the real output per worker increases 6.53%, while the total factor productivity rises 4.0% and the capital stock expands 7.3%. Comparing with the case of heterogeneity in the capital share of income, the qualitative results are the same, however there is some difference in the magnitude of our quantitative results.
In sectoral level, most of results hold as well. There is an increase in the total productivity of both sectors and a relative raise in the capital accumulation of tradable goods producers. More specifically, we verify an increase of 8.52% in the capital stock of tradable goods sector and of 6.59% in the same variable of nontradable goods sector. Therefore, we still find that the tradable goods sector is favored by improvements in financial development. However, we do not observe a relative increase in the productivity of this sector. In this case, we find that both sectoral TFPs rise 4.1%, approximately. This result is not empirically supported and it might suggest that the share of capital income tend to differ across sectors. Regarding the behavior of prices, the interest rate also raises and the exchange rate appreciates almost 0.5%.
Then, we conclude that in fact the sectoral heterogeneity in foreign credit access plays an important role in explaining the regularities of financial development. Even if there is no difference in the share of income across sectors, the improvement in enforcement conditions is favorable to tradable goods sector.
1.6
Conclusion
This paper investigates the role of sectoral heterogeneity and financial frictions in explaining the disproportionate effects of financial development on different sectors. Our model relies on a rich microeconomic environment, where heterogeneous entrepreneurs face endogenous collateral constraints at both domestic and foreign credit markets. Given the existence of such financial friction, there is a missallocation of resources in the economy. Some entrepreneurs are not able to run productive projects, while less productive firms remain active. Since financial development improves enforcement processes and reduces information asymmetry, it allows a more efficient flow of resources across entrepreneurs. Hence, the total factor productivity, capital accumulation and output per worker raise as a result of financial development. Simulating an improvement of 5% in general enforcement conditions of Argentina, we show that the country experiences a boost of 5.7% in its real output per capita and that its TFP increases 3.0%.
