Relationship Networks in Banking Around a Sovereign Default and Currency Crisis

Abstract

We study how banks’ exposure to a sovereign crisis gets transmitted onto the corporate sector. To do so, we use data on the universe of banks and firms in Argentina during the crisis of 2001. We build a model characterized by matching frictions in which firms establish (long-term) relationships with banks that are subject to balance sheet disruptions. Credit relationships with banks more exposed to the crisis suffer the most. However, this relationship-level effect overstates the true cost of the crisis since profitable firms (e.g., exporters after a devaluation) might find it optimal to switch lenders, reducing the negative impact on overall credit and activity. Using linked bank-firm and firm-level data, we find evidence largely consistent with our theory.

Appendices

Appendix 1: Theoretical Model

In this section we present a model characterized by search and matching frictions in which firms (borrowers) have established long-term relationships with their lenders. Using our model, we derive testable implications that shed light on how the state of the banking network affects credit supply and real activity and we use these implications as a guide to design the empirical specification of the next sections.

1.1 Appendix 1.1: Environment

Banks and firms are assumed to be distributed on islands. There are a total of $(I+1)$ islands: a total of I peripheral island and a central one. Islands are labeled from 0 to I, where the island labeled 0 is the central island. There are a total of B banks per island (including the central island) and F firms on islands 1 through I (note that there are no firms on the central island). The relationships between firms and banks in the peripheral islands are interpreted as existing relationships that do not require costly setup costs. The central island is meant to represent a market where new firm-bank relationships are established after incurring in a cost.

Each period, a fraction $\alpha _i$ of all firms on the ith island receive an investment opportunity. Investment opportunities, or projects, need to be financed by banks in order to produce. Each financed project produces y units of output that is split between the firm and the bank financing the project. Per project, the firm receives $(y-r_i)$, and the bank receives $r_i$, where $r_i$ can be interpreted as the interest rate on the $i_{th}$ island. Firms remain in the market for only one period.

Each bank on the ith island receives $v_i$ units of available credit to be offered in the ith market. Once banks and firms meet, they split the surplus of the match after bargaining, with the bank’s bargaining power given by $\phi$.

Banks and firms find each other using a constant-returns-to-scale matching function:

$$\begin{aligned} M = m \left( F \alpha _i \right) ^{\gamma } \left( B \nu _i \right) ^{1-\gamma }. \end{aligned}$$

(5)

Given this matching technology, market tightness is indicated by $\theta _i=\frac{Bv_i}{F\alpha _i}$. The probability of an investment opportunity to be financed is then given by $q(\theta _i) = \frac{M}{F \alpha _i} = m \left( \frac{Bv_i}{F\alpha _i} \right) ^{1-\gamma }$, and the probability of a unit of available bank credit being matched to a firm is $p(\theta _i) = \frac{M}{B v_i}$. While firms can transfer investment projects from their ith island to the central island by paying a switching cost z, unmatched credit vacancies cannot be moved.

Total output is then measured by the total number of projects successfully financed $q(\theta _i) F \alpha _i$.

The timing is as follows: First, the vectors $\alpha$ and v containing the information on $\alpha _i$ and $v_i$ for all islands are observed, and peripheral island markets open for all islands 1 through I. Then, the central market opens and firms can decide to take their unmatched projects to the central island by paying the cost z.

1.2 Appendix 1.2: Equilibrium

On the central island, matched firms and banks bargain over the match surplus without any outside option:

$$\begin{aligned}&\max _{r_0} (y-r_0)^{1-\phi } r_0^{\phi } \\&\quad r_0 = \phi y \end{aligned}$$

This determines the interest rate on the central island, which is given by $r_0 = \phi y$. The equilibrium on the central island affects the outside option for firms in the peripheral islands and the matching surplus to be split between banks and firms in the peripheral islands.

The outside option of a firm on the peripheral island is given by

$$\begin{aligned} U_i=\max (0,q(\theta _0)(1-\phi )y-z). \end{aligned}$$

(6)

Notice that $U_i$ is independent of island i conditions, so it can be labeled as U. The matching surplus in the ith island is then:

$$\begin{aligned} S=y-U. \end{aligned}$$

(7)

This is so because banks in the peripheral islands cannot transfer their credit vacancies to the central island. This fact determines that their outside option is effectively zero. Again, the surplus of a match on the peripheral island is not affected by the island conditions; therefore we label it as S.

The banks in the peripheral islands receive $\phi S$, which is constant across all peripheral islands. This is because, independent of the island’s conditions, they all share the same outside option for firms given by the transition to the central island U.

In particular, banks in all peripheral islands receive

$$\begin{aligned} r_i=\phi (y-\max (0,q(\theta _0)(1-\phi )y-z)). \end{aligned}$$

(8)

After the first sub-period finishes, there are a fraction $(1-q(\theta _i))$ of projects that could not find a bank on the ith island. Then, the firm must decide to pay the transition cost to the central island or scrap the project. At this point, the firm will transition to the central island market as long as $z<q(\theta _0)(y(1-\phi ))$, where $\theta _0$ is the market tightness on the central island and determines the probability of successfully finding financing for the project.

This condition determines a threshold $\hat{\theta _0}=q^{-1}(z/(y(1-\phi )))=\frac{z}{\left[ m y(1-\phi )\right] }^{\frac{1}{1-\gamma }}$, above which all firms with unmatched projects at the peripheral island will transition to the central island. Intuitively, since the probability of finding a match is increasing in $\theta$, firms will pay the fixed cost only if, given the supply of credit in the central island, the demand for credit is such that the expected return (net of cost) is non-negative. If $\theta _0=\hat{\theta }_0$, then firms with unmatched projects are indifferent between transitioning to the central island and scrapping the project.

Let $\underline{\theta }_0=\frac{Bv_0}{F\sum _{i=1}^I\alpha _i(1-q(\theta _i))}$ denote the market tightness that would result if all unmatched firms transition to the central island (for a given $v_0$, $\{\alpha _i,v_i\}_{i=1}^{I}$). If $\underline{\theta }_0\ge \hat{\theta _0}$, all unmatched projects will in fact transition to the central island, and the central island market tightness equals

$$\begin{aligned} \theta _0=\underline{\theta }_0. \end{aligned}$$

(9)

If $\underline{\theta }_0<\hat{\theta }_0$, in equilibrium, not all unmatched firms will transition to the central island. Firms will transition until the equilibrium market tightness $\theta _0=\hat{\theta }_0$. Since $\underline{\theta }_0<\hat{\theta }_0$, it is possible to find the fraction of unmatched firms that will transition to the central island consistent with $\theta _0=\hat{\theta }_0$ by defining $\tau \in [0,1]$ such that

$$\begin{aligned} \frac{1}{\tau }\underline{\theta }_0=\hat{\theta }_0 \Leftrightarrow \tau = \frac{\underline{\theta }_0}{\hat{\theta }_0}. \end{aligned}$$

When $\theta _0=\hat{\theta _0}$ firms are indifferent between transitioning or not, so we assume that unmatched firms use a mixed strategy and transition to the central island with probability $\tau$.

1.3 Appendix 1.3: Shocks to Banks Exposed to Government Debt/Devaluation

It is assumed that in good times the vectors v and $\alpha$ are constant for all islands, generating a constant probability of financing for all projects across islands given by

$$\begin{aligned} q(\theta _i)+(1-q(\theta _i))\tau q(\theta _0)=q(Bv/F\alpha )+(1-q(Bv/F\alpha ))\tau q(\theta _0). \end{aligned}$$

(10)

In bad times, heterogeneous banks are subject to idiosyncratic shocks. A subset of islands receives loan vacancies that are lower than in good times. This lowers the probability of financing for all projects in all islands but in a heterogeneous way. This captures the idea that some banks are hit harder than others in some circumstances. In our case, it is banks that were exposed to government debt that cannot offer credit after the government defaults. The credit-availability shock represented by $v_i$ is meant to represent the supply of credit from banks after their asset position is affected by movements in the price of some of its components. In particular, if a bank holds government bonds that depreciate due to a default, it will have less available credit to offer to firms as a result.

For the islands where the stock of loan vacancies fell, there is a direct effect on the probability of financing $q(\theta _i)$ on their own island. The lower probability of financing on the peripheral island is not counteracted by the financing probability at the central island (which depends also on the probability of not finding financing on the peripheral island), because the term $(1-q(\theta _i))$ is multiplied by a number that is less than one given by $\tau q(\theta _0)$.

The phenomenon in the affected peripheral islands triggers a secondary effect on the central island that affects all projects in all islands. This additional flow of unmatched projects from the islands shocked with lower availability of credit causes $\theta _0$ or $\tau$ or both to fall, lowering the financing probability for all projects on the central island and lowering output.

1.4 Appendix 1.4: Testable Implications

Given the workings of the model and the availability of data, we can look at the following testable implications:

$$\begin{aligned} \frac{\partial q(\theta _i)}{\partial v_i}\ge 0 \end{aligned}$$

(11)

$$\begin{aligned} \frac{\partial \tau q(\theta _0)}{\partial v_i}\le 0. \end{aligned}$$

(12)

Equation (11) implies that the probability of finding financing from the perspective of the firm is increasing in the availability of funds $\nu _i$ for banks on the peripheral island (or initial island). In terms of empirical implementation, it would mean that after the devaluation, exporters whose long-term relationships with the banking system did not suffer as much after the sovereign default, should see their credit increase faster than their counterparts with relationships with banks where the availability of credit suffered as a result of the default.

Moreover, Eq. (12) states that new relationships on the central island and the availability of credit in the peripheral one should be negatively related to each other. That is, conditional on the availability of credit in the initial relationships, new relationships should start more often for those firms whose initial long-term bank relationships suffer the most with the default.

Appendix 2: Data Appendix

We use data from the Central Bank of Argentina’s credit registry (called Central de Deudores). Our original sample expands from June 1999 to December 2005. While we use firm and bank-level information prior to the default and the devaluation, we focus the analysis on how credit and other variables evolved from June 2002 to December 2005. This sample contains 202,438 firms and 344,105 bank relationships (or loans). To construct our firm level sample, we apply the following filters

• 1. For each firm and period, we aggregate the loans (in real terms) with all banks. Call this variable “total debt.” For each firm, we compute the maximum value (over the time series) of total debt. To remove outliers we eliminate firms in the bottom 5% (very small firms) and top 2% of the distribution of maximum total debt.

• 2. We eliminate firms that report 12 or fewer observations.

• 3. We exclude government sector firms. We also exclude firms in the financial sector.

• 4. We eliminate lending relationship observations that are in the top or bottom 5% of the distribution of (quarterly) loan growth.

• 5. We eliminate lending relationships with less than 4 observations.

We are left with 97,279 firms and 159,312 lending relationships. Of these, there 33,333 firms with more than one lending relationship.³⁸

Table 10 provides summary statistics at the firm level.

Table 10 Summary statistics (firm level)

Table 11 shows the distribution of banking relationships for the firms in our sample (pre- and post-default/devaluation) as the fraction of firms and as the fraction of total loans.

Table 11 Distribution of banking relationships

Table 12 shows the distribution of the age of banking relationships for the firms in our sample (years 2003–2005). Relationships in the 21–25 months (year 2001), 46–50 months (year 2003), 61–65 months (year 2004) and 71–75 months (year 2005) bins correspond to firms with relationships that started at the beginning of our sample and operated continuously. Firms in the 1–5 months and 6–10 months bins are firms with banking relationships that started during the corresponding calendar year (there are some firms with new banking relationships in the 11–15 months bin). In the year 2004, we observe a large increase in the lower end of the age distribution and a significant decline in the fraction of relationships at the top end of the distribution.

Table 12 Distribution of age of banking relationships

Table 13 shows the sectoral allocation of credit by the banking sector in Argentina.

Table 13 Allocation of bank credit by sector

Appendix 3: Bank-Level Regressions: Robustness Checks

We use the following specification to study the correlation between the change in loans to the private non-financial sector ($\ell _{it}$) between period t and period $t-1$ for bank i (measured as a 3-month change) and a measure of exposure to government debt in 2001 prior to default ($\mathrm{E}_{i2001}$) and a measure of exposure to the devaluation via non-deposit foreign currency liabilities ($\mathrm{FC}_{i2001}$). We also include a set of bank-level controls ($X_{it}$) and month fixed effects ($\alpha _t$):

$$\begin{aligned} \Delta \ell _{it} = \alpha _t + \beta _1 \mathrm{E}_{i2001} + \beta _2 \mathrm{FC}_{i2001} + \beta _3 X_{it-1} + u_{it}. \end{aligned}$$

(13)

The controls at the bank level are intended to account for other variables that can impact the banks’ availability of loanable funds. As such the vector $X_{it-1}$ includes liquidity, leverage, the level of loans to the private non-financial sector, and profitability as measured by banks’ net income (Tables 14, 15).

Table 14 Bank-level effects of sovereign debt exposure

Table 15 Bank-level effects of sovereign debt and foreign currency exposure

Appendix 4: Relationship-Level Regressions: Robustness Checks

This section presents results from additional relationship-level regressions that we run following the specification in Eq. (3). The model of changes in credit from bank i to firm j in period t that we estimate is

$$\begin{aligned} \Delta \ell _{ijt} = \rho _{jt} + \beta _1 \mathrm{E}_{i2001} + \beta _2 \mathrm{FC}_{i2001} + \beta _3 R_{ijt-1} + \beta _4 X_{it-1} + e_{ijt}, \end{aligned}$$

where $\rho _jt$ are firm-time fixed effects, $\mathrm{E}_{i2001}$ and $\mathrm{FC}_{i2001}$ are defined as before and capture bank j exposure to the sovereign default and devaluation in 2001, $R_{ijt-1}$ are controls that capture the characteristic of the relationship between bank i and firm j (e.g., age of the relationship, concentration) and $X_{it-1}$ are standard bank-level characteristics such as bank size (measured by assets), liquidity, leverage, and profitability (Tables 16, 17).

Table 16 Relationship-level effects of sovereign debt exposure

Table 17 Relationship-level effects of sovereign debt and foreign currency exposure

Appendix 5: Firm-Level Regressions: Robustness Checks

This section presents results from additional firm-level regressions where we add firm characteristics as additional controls (Table 18) or we condition by the exporter status of the borrower (Tables 19, 20, 21, 22, 23).

Table 18 Firm-level effects of sovereign debt and foreign currency exposure

Table 19 Firm-Level effects of sovereign debt and foreign currency exposure (by export status)

Table 20 Firm-level effects of sovereign debt and foreign currency exposure (by export status), on impact in 2003

Table 21 Firm-level effects of sovereign debt and foreign currency exposure on probability of new relationships

Table 22 Firm-level effects of sovereign debt and foreign currency exposure on extensive margin of exports

Table 23 Firm-level effects of sovereign debt and foreign currency exposure on borrowers default