LOW INTEREST RATES AND BANK RISK-TAKING IN THE U.S.: AN EMPIRICAL STUDY

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Master’s thesis MSc. Finance

LOW INTEREST RATES AND BANK RISK-TAKING IN THE U.S.: AN EMPIRICAL STUDY

Abstract:

In this thesis I investigate the relationship between low interest rates and bank risk-taking. I make use of data of 4,818 U.S. banks from 2003 to 2016, a short- and long-term interest rate, and demonstrate that, after adjusting for fixed bank- and time effects, low interest rates do not result in banks’ increasing their risk-taking. This result is in contrast to the existing literature.

Keywords: Interest Rates, Bank risk-taking, Risk-level score, Risk assets, Panel data, Bank effects, Time effects.

University of Groningen

Faculty of Economics and Business

Rick T. R. Last (s2203219)

Supervisor: prof. dr. R.E. Wessels

Groningen, July 2017

10406 words

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1. Introduction

Banks play a role in the transportation of risk (Chen and Lin, 2016). They issue riskless and liquid deposits on one side of the balance sheet, and finance more risky and illiquid assets on the other side of the balance sheet. For these risky and illiquid assets banks receive a return. In general, the higher the risk, the higher the return. This is called the risk-return trade- off of banks. Banks make a decision with respect to this risk-return trade-off. Banks with a larger risk appetite are willing to accept more risk in order to achieve higher returns. Interest rates can influence banks’ behavior with respect to this risk-return trade of. If interest rates are low, expected rates of returns are low as well. This threatens bank returns, and thus bank profitability. Rajan (2006) argues for the existence of a so-called search for yield effect. This effect means that if interest rates are low, banks are induced to increase risk by investing in more risky assets, in an attempt to maintain a high rate of return. This is one of the ways the risk-taking channel of monetary policy, introduced by Borio and Zu (2012) operates in. The risk-taking channel of monetary policy is about the link between monetary policy and the perception and pricing of risk (Borio and Zu, 2012), and is discussed in more detail in section 2.

The purpose of this thesis is to empirically investigate whether such a search-for-yield effect actually exists by examining whether low interest rates have in fact induced banks to take more risk. Bank risk-taking will be measured in two ways. Firstly, the risk-level score (in banking literature known as the z-score) will be used. This measures the probability of insolvency and is frequently used in the literature on bank risk-taking (see e.g. Laeven and Levine, 2009). The second measure for bank risk-taking is the ratio of risky assets to total assets as used in a study of Drakos, Kouretas, and Tsoumas (2016). The majority of literature emphasizes the effect of low short-term interest rates on bank risk-taking (Maddaloni and Peydró, 2011). However, there is an indication that low long-term interest rates drives bank risk-taking as well (Aramonte, Lee, and Stebunovs, 2015). Therefore the effect of both low short- and long-term interest rates on bank risk-taking will be investigated.

The data for this thesis comes from a data set of 4,818 U.S. banks for collected via Orbis

Bank Focus. Data from 2003 to 2016 is analyzed. In this period interest rates have fluctuated

strongly. The effective federal funds rate peaked at 5.41% in February 2007 and bottomed

with 0.04% in December 2011. The yield on ten year U.S. treasury bonds peaked at 5.26% in

June 2007 and bottomed with 1.47% in July 2012. In figure 1 a graphical impression of both

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interest rates over time is demonstrated. The fluctuations in interest rates in this period makes this period extremely appropriate to analyze.

The main findings of this study are in contrast to the existing literature. After controlling for fixed bank- and time effect, the data provides no evidence for a significant relationship between low interest rates and bank risk-taking, in any of the analyzed periods. The remainder of this thesis is organized as follows. Section 2 discusses the theoretical background. Section 3 describes various methods to measure bank risk- taking. Section 4 describes the data. In section 5 hypotheses are developed. Section 6 provides the statistical model. In Section 7 the results are presented. Finally, section 8 concludes and discusses.

2. Literature review

Bank risk-taking and low interest rates have been the subject of several studies in the literature, sometimes in a more broader framework about monetary policy. Some researchers attempt to demonstrate a relationship in theoretical models, other authors try to provide empirical evidence. In the following section different findings with regards to bank risk-taking and monetary policy will be elucidated. Of course, monetary policy consists not only of interest rate policy, but according to Belke (2013), the short-term interest rate is the key variable for monetary policy.

Dell’Ariccia, Laeven, and Marquez (2014) develop a model in which banks can engage in costly monitoring to reduce the credit risk in their loan portfolios. They find a difference

Figure 1. Plot of the effective federal funds rate (EFFR) and the yield on 10 year U.S. treasury bonds (U.S. 10 Y) over the 2003-2016 period in percentages (%).

0,00

1,00

2,00

3,00

4,00

5,00

6,00 20032004200520062007200820092010201120122013201420152016

% Date

U.S. 10 Y EFFR

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between banks that can change their capital structure and banks that have a fixed capital structure. Banks are confronted with a fixed capital structure if they optimally would choose a level of capital below the regulatory minimum. In this case they are forced to maintain the minimum level of equity, which makes their capital structure practically fixed for at least the near future. When banks have the ability to adjust their capital structure a lower interest rate results in increasing leverage and lowering monitoring. Bank leverage is a key factor driving bank risk-taking can be seen as a function of a bank’s capital structure (Dell’Ariccia, Laeven, and Suarez, 2017). With banks that have a fixed capital structure this link between interest rates and bank risk-taking is less evident. Highly levered banks with a fixed capital structure will decrease their risk-taking when interest rates are falling. These highly levered banks are already faced with capital constraints and other minimum requirements and hence have less opportunity to increase risk. However, well capitalized banks with a fixed capital structure, will increase risk when interest rates are falling by decreasing monitoring (Dell’Ariccia et al., 2014). In contrast to highly levered banks, these well capitalized banks have the opportunity to increase risk. A decrease in monitoring can be a sign of higher risk taking since shareholders are less able to oversee management decisions, and it gives also rise to a classical agency problem. Managers have an opportunity to increase risk-taking since losses are borne by shareholders in the first place.

In a survey of literature on interest rates and bank risk-taking, Borio and Zhu (2012) introduce the so called risk-taking channel of monetary policy. This channel describes the relationship between bank risk-taking and low interest rates. Borio and Zhu (2012), pp 242.

define this as “the impact of changes in policy rates on either risk perceptions or risk-

tolerance and hence of the degree of risk in the portfolios, on the pricing of assets, and on the

price and non-price terms of the extension funding”. The first way in which this risk-taking

channel of monetary policy operates is that lower interest rates affect valuations, incomes,

profits, and cash flows. A lower interest rate implies a lower discount factor. With a lower

discount factor future cash flows have a higher value. This can result in banks changing their

risk perceptions and increasing their risk tolerance. Besides this the procyclical behavior of

certain variables can widen risk tolerances as well. According to Borio and Zhu (2012) risk

measures tend to shift procyclically because measured risk tends to decline during expansions

and tends to increase during contractions. One example of this is that volatilities decline in

rising markets, this releases risk-budgets and instigates position-taking which can be seen as

increased risk-taking (Borio and Zhu, 2012).

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However, it is important to emphasize the effect of a low discount factor. A low discount factor increases the value of future cashflows and hence the value of assets. This can result in an increase in banks’ willingness to provide credits as the present value of assets increases, and is, in this case, not a result of reduced risk aversion. This might not be a very strong effect, but it works in the same direction as the effect of increased bank risk-taking as a result of a lower interest rate. It is difficult to place one statement above the other, but it is this last effect which is under investigation in this thesis.

The second way in which the risk-taking channel operates is, according to Borio and Zhu (2012), the so called ‘search for yield’ effect. This effect is the subject of more recent literature (see e.g. Rajan, 2006). If interest rates are low, the gap between interest rates and target rate-of-returns increases. Firms have less interest in decreasing their target rates of return with when interest rates are falling. Especially pension funds, insurance companies, and banks often have nominal long-term liabilities with fixed interest rates on their balance sheets. This makes it undesirable to lower rate of returns because these companies have to match the level or return they promised to their counterparties. In an attempt to achieve these desired returns the companies are searching for higher yield, which is associated with higher risk. In a study of Geršl, Jakubík, Kowalczyk, Ongena, and Peydró (2012) this search for yield effect is supported with empirical evidence. They investigate, with data consisting of more than two hundred thousand loan-period observations from roughly 2003 to 2009 of banks in the Czech Republic, whether low interest rates encourage banks to increase lending to borrowers with a more riskier past and whether low interest rates encourage banks to extend new loans that default more soon. They conclude that in both cases it is true and claim that low interest rates increases banks’ tolerance for risk. Banks that want to maintain their rates of return, reach out to riskier investments or borrowers. Because of this they are able to ask a higher rate of return in times of monetary expansion (Geršl et al., 2012). This search for yield effect is also the subject of a study of Rajan (2006). In this study the author argues that low interest rates can be a source of procyclical risk in financial markets. Rajan (2016), also emphasizes the effect of long-term liabilities with fixed interest rates. If interest rates decrease, riskless assets become less attractive and there might be no other alternative than searching for riskier investments because otherwise they would default on their commitments.

Thus, in order to maintain a constant average rate of return, banks have the tendency to invest in riskier assets by shifting into riskier market segments such as real estate, private equity, hedge funds, or developing-country stocks and bonds (Buch, Eickmeier, and Prieto, 2013;

Gambacorta et al., 2010; Rajan, 2006). On the contrary, if interest rates are high, Rajan (2006)

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reasons that financial companies can become more conservative. It can lead to reallocation from riskier assets towards more safe assets. A higher risk-free rate also raises the hurdle rate for investments. This can result in cutting projects that are associated with low returns or high risk (Dell’Ariccia et al., 2016).

Continued low short-term interest rates, i.e. a steep term structure of interest rates, imply a high net interest margin for banks. The interest income banks collect on their long-term assets, for example mortgages, is relatively high compared to the interest expense on their short-term liabilities, for example saving accounts. According to Adrian and Shin (2010) this increases banks’ risk-taking capacity. Buch et al. (2013) use a dataset consisting of quarterly data of new issued loans made from 1997 to 2008 in the U.S. This data is collected via the Survey of Terms of Business Lending. This survey examines the terms of all commercial- and industrial loans the participating banks made. In this way, each loan of each bank is assigned a risk rating. Buch et al. (2013) found that if interest rates are ‘too-low-for-too-long’, small- and foreign banks participate in additional risk taking. With interest being too-low-for-too- long the authors mean the period from 2003 to 2005.

Delis and Kouretas (2011) suggest a theory in which they state that low-interest rates drive bank margins and informational asymmetries down. Banks react by softening their lending standards. The consequence of this is a higher level of risky loans in their portfolio. In addition to this theory Delis and Kouretas (2011) find empirical evidence for a strong relationship between low interest-rates and bank risk taking. They made use of an unbalanced panel dataset with accounting data over the 2001-2008 period of commercial banks, cooperative banks, and saving banks in Europe. They argue that that an environment with low interest rates increases the amount of risky assets in a bank’s portfolio. This is in line with the earlier mentioned study of for example Rajan (2006). In a similar study limited to only Eastern European banks, Drakos et al. (2016) find the same results with accounting data of the 1997-2011 period.

In a study of Ioannidou, Ongena, and Peydró (2015) the risk-taking channel of monetary

policy in Bolivia is investigated. They do this by examining the way in which changes in the

short-term interest rate affect the quality of new loans. They analyze a dataset consisting of

detailed monthly information about outstanding loans of all Bolivian banks from 1999 to

2003 and find that a lower monetary policy rate increases the risk appetite of banks. This

increased risk appetite results in banks granting riskier loans to borrowers with bad credit

scores. These riskier loans are naturally more likely to default. The results of this study are

supported by related studies of Jiménez, Ongena, Peydró, and Saurina (2014) and

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Dell’Ariccia et al. (2017). The former study investigates the relationship between short-term interest rates and bank risk-taking in Spain. By analyzing a dataset of detailed monthly loan information of almost all loans granted by all banks from 2002 to 2008 they find that a lower overnight interest rate causes banks to take more risk in their lending. They argue that loans are granted to more risky firms and the loans themselves are larger in volume as well. This will eventually result in higher credit risk for the bank. The authors further argue that lower long-term interest rates or other key macro-economic variables do not induce banks to increase their credit risk (Jiménez et al. 2014). In the study of Dell’Ariccia et al. (2017) the relationship between the short-term interest rate and the riskiness of new loans is investigated as well. In this study the same data is used as in the earlier mentioned study of Buch et al.

(2013), but in this study the sample period is from 1997 to 2011. They conclude that low short-term interest rates increase the riskiness of new loans and hence bank risk-taking increases as well.

In studies of Maddaloni and Peydró (2011) and Maddaloni, Peydró, and Scopel (2008) the relationship between interest rates and banks’ lending standards is investigated. In both studies they use answers from bank lending surveys. In the U.S. this is the Senior Loan Officer Opinion Survey on Bank Lending Practices and for the Euro area this is the Bank Lending Survey. Both surveys are conducted quarterly among senior loan officers. In the former study the U.S., from 1991 to 2008 and the Euro area, from 2003 to 2008, is under investigation, the latter study is limited to the Euro area, from 2003 to 2008, only. With the answers from the survey in both studies the authors create the net percentage of banks that tighten their lending standards. If this is a negative value it implies that most banks loosened their lending standards. A loosening of lending standards is associated with higher bank risk- taking because it results in a higher proportion of lower quality loans in banks’ loan portfolios and this makes banks’ portfolios more risky. Both studies conclude that a low short-term interest rate results in banks softening their lending standards and hence in higher bank risk- taking. Maddaloni and Peydró (2011) argue that this was a key factor leading to the financial crisis around 2007. The authors also find that short-term rates are more important in explaining bank risk-taking than long-term interest rates or other macro-economic variables.

However, in a study of Aramonte et al. (2015) the authors do find evidence for a

relationship between long-term interest rates and bank risk-taking. In this study they

investigate the risk-taking behavior of banks and nonbanks lenders by measuring the riskiness

of syndicated loan portfolios in an environment of current low long-term interest rates and

expected future low long-term interest rates. They use confidential supervisory data of every

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quarter from 2009 to 2014 in the U.S. This consists of detailed syndicated loan data, including probabilities of default for every given loan, from 18 banks which are the most active in the syndicated loan business. The probability of default is the variable they eventually use in the analysis. They find that the riskiness of these portfolios increases when long-term rates are expected to stay low for some time.

3. Measuring bank risk-taking

One of the most important decisions in this thesis is to determine the way in which bank risk-taking is measured. In the literature there are several methods applied to measure bank risk-taking. Some researchers employ lending standards as risk measure (see e.g. Dell’Ariccia and Marquez, 2006; Maddaloni et al., 2011, Ioannidou et al., 2015, Jiménez et al., 2014). If lending standards are weakened this is associated with higher bank risk since less creditworthy consumers and/or business are provided with a loan more soon. This implies higher risk for the bank. Another measure of bank risk is total risk and is used by Adhikari and Agrawal (2016). They define total risk as the standard deviation of a bank’s daily stock returns during a fiscal year. Also Laeven and Levin (2009) use the volatility of equity returns as risk measure. The disadvantage of this measure is though that only listed banks with available market data can be included in the analysis. Another risk measure used by Adhikari and Agrawal (2016) is tail risk, which is the expected-shortfall measure introduced by Acharya, Pedersen, Philippon, and Richardson (2010). A different measure for bank risk- taking is used by Ashraf, Zheng and Arshad (2016) and is the volatility of net interest income.

Delis and Kouretas (2011) use the ratio of risky assets to total assets and the ratio of non- performing loans to total loans. The ratio of risky assets to total assets is also used in the study of Drakos et al. (2016). In both studies risky assets are defined as all assets except cash, government securities, and balances from other banks or central banks. It can also be described as all assets subject to change in value as a result of changing market conditions.

An increase of the ratio of risky assets to total assets ratio implies a more risky portfolio of the bank and hence higher bank risk-taking. The ratio of non-performing loans to total loans represents the quality of a bank assets and can be used as a proxy for credit risk (Delis and Kouretas, 2011).

A risk measure which have been employed extensively in recent literature on bank risk-

taking is the risk-level score. In the literature also known as the z-score (see e.g. Adhikari et

al. 2016; Ashraf et al. 2016; Drakos et al. 2016; Laeven and Levine, 2009; Houston, Lin, and

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Ma, 2010). To avoid confusion with the well-known z-score in statistics and Altman’s z-score (a statistical technique that predicts default probabilities of publicly traded manufacturing companies), this measure is labelled risk-level score as of now in this thesis. The risk-level score reflects a bank’s probability of insolvency and is calculated by the sum of the return on assets (ROA) and the capital asset ratio (CAR) divided by the standard deviation of asset returns (𝜎

_𝑅𝑂𝐴

).

There can be referred to insolvency when the level of equity (E) and profits (π) summed is smaller than zero (E+π < 0). The probability of insolvency happening, prob. (E+π) < 0, can be measured by the distance between the mean of (E+π ) to where (E+π) < 0. This distance can be standardized by dividing (E+π) by the standard deviation of (E+π). Given the distribution of (E+π), this distance can then be translated into a probability. If assets are defined as A, ROA is defined as π/A, and CAR is defined as E/A, the probability of insolvency can be expressed as prob.(ROA<-CAR). With normally distributed profits the inverse of the probability of insolvency equals (ROA+CAR)/ 𝜎

_𝑅𝑂𝐴

). This inverse of the probability of insolvency is defined as the risk-level score (Laeven and Levine, 2009). The risk-level score stands for the number of standard deviations that the returns on assets have to drop for a bank to become insolvent. A higher risk-level score indicates that the bank is stable and further away from insolvency and implies less bank risk-taking. The distribution of the risk-level score is highly skewed and therefore in several studies, including this thesis, the natural logarithm of the risk-level score is used as final risk measure (see e.g. Laeven and Levine, 2009; Houston et al., 2010). From now one, the natural logarithm of the risk-level score is meant by the phrase risk-level score.

In a study of Lepetit and Strobel (2015) the authors argue that the risk-level score is an adequate measure for bank risk-taking. They investigate the ranges of different risk measures and demonstrate that the range of the risk-level score lies on the (-∞,∞) interval. This means that all numbers are real and therefore it is well applicable for statistical techniques. Lepetit and Strobel (2015) conclude that the risk-level score is an appropriate risk measure to use in regression analysis as dependent variable.

Because of the provided adequacy of the risk-level score and the fact that this measure is suited for regression analysis it is used as a measure of bank risk-taking in this study.

However, because in this study bank risk-taking is also investigated over time and not solely

cross-sectional a time varying risk-level score for every bank is necessary. Various methods

for constructing this time varying risk-level score are available. For the CAR there is not much

discussion and the value of each individual period is used the most often. However, for the

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value of ROA there are several possibilities. The value of each individual period for ROA can be used, or a mean value of ROA can be calculated (over a rolling window or over the full period). The standard deviation of ROA can be calculated over a rolling time window or can be calculated over the full period.

In this thesis the standard deviation of ROA is calculated over the full period being investigated. A a mean value of ROA will not be used, instead the value of each individual period will be used. This is preferred above using a mean value since banks’ risk profiles can change over time. Using a mean value would result in a risk-level score which is too stable and this is not considered to capture bank risk-taking adequately. Also for the CAR the value of each individual period is used. This is line with studies of Beck and Laeven (2006) and Hesse and Čihák (2007).

To summarize, for each bank i, the standard deviation of the ROA is calculated over the full period being investigated, T. This will be combined with the values of ROA and CAR for each individual year t. The result is a risk-level score for each bank, i, for each year, t. Finally, the natural logarithm is taken to obtain the final risk measure:

𝑟𝑖𝑠𝑘 − 𝑙𝑒𝑣𝑒𝑙 𝑠𝑐𝑜𝑟𝑒

_𝑖𝑡

= ln (

^𝑅𝑂𝐴^𝑖𝑡^{+ 𝐶𝐴𝑅}^𝑖𝑡

𝜎_{𝑅𝑂𝐴,𝑇𝑖}

) (1)

Because of the logarithmic function the expression in brackets has to be positive. This requirement is not satisfied for the data of two banks. For these banks it is not possible to calculate a risk-level score in any year and therefore these banks are excluded from the analysis. Besides this is the requirement not satisfied for a total of sixteen individual risk-level scores. This is not a problem since 16 missing values are negligible compared to the total number of 67,452 observations, and there is no pattern in the missing values. This explains why the number of observations of the risk-level score is smaller than the number of observations of the other variables (summary statistics are reported in table 2). Furthermore, it is important to remember that a higher value of the risk-level score implies a more stable bank and less bank risk-taking.

An advantage of using the risk-level score is that it can be computed by using accounting data only. This implies that non-listed banks can also be analyzed. At the same time this can be a limitation. The risk-level score is only as good and reliable as the underlying accounting framework. If the accounting input is incorrect, the risk-level score will be incorrect as well.

A concept as this is known as garbage in, garbage out (GIGO). But, because the owner of the

bank data database applies around two hundred quality controls to ensure the validity of the

data, the presence of GIGO is not expected. Either way, the literature about the adequacy of

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the risk-level score and the fact that these kind of measures are in emerging use in the literature provides the required confidence about the appropriateness of the risk-level score.

Notwithstanding the appropriateness of the risk-level score, an alternative risk measure will is used for robustness checks. This alternative measure will be used to make the analysis more robust. The alternative measure included will follow the studies of Delis and Kouretas (2011) and Drakos et al. (2016) and is the ratio of risky assets to total assets, denoted as risk assets. Risk assets capture the current risk-taking behavior of banks. The difference with the risk-level score is that the latter is affected by a bank’s past investment choices, it is not solely a measure of current risk-taking behavior, but also of accumulated risk of the past (Drakos et al., 2016). Risk assets are defined for each bank i, in each year t. An increase risk assets implies a more risky portfolio of the bank and therefore higher risk-taking.

4. Data and variables

To investigate whether low interest rates result in more bank risk-taking and to test the hypotheses, which will be introduced section 5, two interest rates and annual bank data of 4,818 U.S. banks is analyzed. The included banks are commercial, cooperative, or savings banks. U.S. banks are chosen because more historical data is available for banks in this region. Annual data is of better usage because not every bank discloses quarterly data.

Using quarterly data would imply reducing the number of banks enormously. Besides this is the investigated period of sufficient length to ensure the quantity of annual data. According to Ashcraft (2006) and Gambacorta (2005), annual data is sufficient to analyze the impact of monetary policy rates. The data used in this study are compiled from the following sources:

1) Annual bank data are collected via Orbis Bank Focus (the successor of the widely used Bankscope), owned by Bureau van Dijk. This a worldwide database and comprises detailed information of annual reports, information providers, and regulatory sources of more than 40 thousand financial institutions. To avoid double counting data is used from consolidated accounts, and only if those are not available from unconsolidated accounts. Banks with available data for each variable for every year, from 2003 to 2016, are included in the sample.

2) Short-and long-term interest rates are obtained via a website of the Federal Reserve

¹

. 3) Macro-economic data are collected via the website of the Worldbank

².

The annual

GDP growth rate of 2016 is at this moment not yet available at Worldbank. To avoid

1 https://apps.newyorkfed.org/markets/autorates/fed%20funds and https://fred.stlouisfed.org/series/DGS10.

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having to reduce the period being investigated with one year, the annual GDP growth rate of 2016 is collected via the U.S. Bureau of Economic Analyses

³

.

With this data a data set of 4,818 banks, consisting of annual year-end data with a total of 67,452 observations, is build. The sample may be affected by survivorship bias. Only banks that have survived the financial crisis are included. However, this will only make the analysis more prudent since the dataset will consists of relative stable banks. A potential relationship between interest rates and bank risk-taking will not be overestimated. It is safe to say that possible survivorship bias will not result in detecting a relationship that otherwise would not be detected.

Table 1

Definitions and sources of variables.

4.1 Interest rates

Two interest rates are used in this thesis, one short-term rate and one long-term rate. This in order to identify the potential different effects of both rates on bank risk-taking. The short- term rate which is used is the Effective Federal Funds Rate (EFFR). This is a weighted average of rates that borrowing banks pay to lending banks to borrow overnight funds. The long term rate which is used is the yield on a ten year U.S. treasury bond. Following prior studies (see e.g. Delis and Kouretas, 2011; Drakos et al., 2016), for both rates an annual average rate based on monthly rates is calculated and is used in the analysis.

2 http://databank.worldbank.org/data/reports.aspx?source=2&series=NY.GDP.DEFL.KD.ZG&country=.

3 https://www.bea.gov/national/index.htm#gdp.

Variable Definition Source

Risk-level score

Risk assets

Capitalization Ratio of equity to total assets.

Lagged profitability Ratio of profits before tax to total assets. Included with a time lag of one.

Efficiency Ratio of operating expense to operating revenue.

Size Natural logarithm of total assets Bank loans Ratio of bank loans to total assets.

Inflation Annual U.S. inflation rate.

GDP growth Annual U.S. GDP growth rate

Short rate Annual average of montly Effective Federal Funds rates.

Long rate Annual average of montly rates on a ten year U.S. treasury bond.

Natural logarithm of the sum of the return on assets (ROA) and the capital asset ratio (CAR), divided by the standard deviation of the return on assets. The standard deviation of ROA is calculated over the full period being investigated.

Ratio of risky assets to total assets. Risky assets are defined as all assets except cash, government securities, and balances from other banks or central banks.

Orbis Bank Focus and calculations

Worldbank

Federal Reserve and calculations

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4.2 Control variables

Since there are several other variables which can influence risk-taking behavior, control variables are needed to extract the effects of these other variables. The control variables included in the risk-equations for the risk-level score and risk assets are similar to the control variables used in other studies (e.g. Delis and Kouretas, 2011; Demirgüç-Kunt, Detragiache, and Tressel, 2008; Drakos et al., 2016; Laeven and Levin, 2009). The first group of control variables included are bank characteristics. Bank characteristics are included because these can affect a bank’s financial strength. The first bank characteristic is capitalization. A bank’s capitalization is measured by the ratio of equity to total assets. A higher level of equity can imply a higher level of risky assets and hence higher risk because shareholders demand an equity return. The second bank characteristic is profitability and is measured by the ratio of profits before tax to total assets. This control variable is included with a time lag of one. A higher level of risky assets results in higher profits in good times, and these higher profits can be used to create new loans in the next period. If the level of risk is too high it can cause problematic loans and lower profitability. As a result this might induce banks to reduce the level of risky assets in the next period (Delis and Kouretas, 2011). The third bank characteristic is efficiency. Bank efficiency is measured by the ratio of operating expense to operating revenue. A higher value of this ratio indicates a less efficient bank. A less efficient bank could have less expertise and mediocre risk management, which can result in higher, perhaps without being aware, risk-taking (Drakos et al., 2016). Other included control variables are bank size, measured by the natural logarithm of total assets, and the ratio of bank loans to total assets, denoted as bank loans. A higher level of bank loans is expected to affect bank risk-taking positively. The second group of control variables consists of macro- economic variables. These are included to control for different macro-economic circumstances. The first one is the annual inflation rate. Inflation is expected to affect bank risk-taking negatively. Higher inflation means increased uncertainty and this can reduce risk- taking incentives (Delis and Kouretas, 2011). Further included is the annual GDP growth rate.

A higher GDP growth rate implies better macroeconomic conditions and this could cause banks to increase their lending in search for a higher rate of return (Delis and Kouretas, 2011).

A positive correlation between GDP growth and bank risk-taking is expected.

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14 Table 2

Summary statistics.

This table reports summary statistics of all variables. The sample consists of annual bank data of U.S. banks, interest rates (short- and long-term), and other macro-economic variables for the 2003-2016 period. Risk-level score is the natural logarithm of the sum of the return on assets year in t and the capital asset ratio in year t, divided by the volatility of the return on assets, calculated over the period from 2003 to 2016, and is a measure of bank risk-taking. Risk assets is the ratio of risky assets to total asset (risky assets are all assets except cash, government securities, and balances from other banks or central banks), and is a second measure of bank risk-taking. Capitalization is the ratio of equity to total assets. Lagged profitability is the ratio of profits before tax to total assets of the previous year. Efficiency is the ratio of operating expense to operating revenue. Size is the natural logarithm of total assets. Bank loans is the ratio of bank loans to total assets. Inflation is the annual inflation rate in the U.S. GDP growth is the annual GDP growth rate in the U.S. Short-rate is the annualized average of monthly rates of the effective federal funds rate. Long-rate is the annualized average of monthly rates on a ten years U.S.

treasury bond. The mean, standard deviation, minimum, and maximum of inflation, GDP growth, delta short-rate, and delta long-rate are in percentages.

Table 1 displays the variables employed in the analysis, together with the definitions and sources. Summary statistics of all variables are reported in table 2. In table 3 the correlations of all covariates are presented. The correlation between the short rate and the long rate is somewhat high, but this is not a problem since these variables are treated separately. Notable is the reported correlation between the risk-level score and risk assets. It is negative, meaning that a low risk-level score is associated with a higher level of risk assets. This is logical, since they both indicate high bank risk-taking. But, the correlation coefficient is not indicating a very strong relationship between the two variables, it rather is a weak relationship. According to Drakos et al. (2006) the relationship between the two is not as straightforward as one might think. A lower risk-level score could be related to a higher level of risk assets if these risk assets are associated with lower a lower level of equity because of an increased bank’s risk appetite, or if the volatility of ROA has increased because of a more risky investment strategy.

On the other hand, a higher level of risk assets could also be related to a higher risk-level score if the bank has a better risk management and advanced monitoring in place (Drakos et al., 2016).

Observations M ean Standard deviation M inimum M aximum

Risk-level score 67,436 3.770 0.864 -3.944 6.681

Risk assets 67,452 0.747 0.154 0.002 1.000

Capitalization 67,452 11.535 7.670 0.809 100.000

Lagged Profitability 67,452 0.012 0.024 -1.658 0.937

Efficiency 67,452 0.690 0.770 -82.403 150.219

Size 67,452 12.064 1.380 7.407 21.457

Bank loans 67,452 60.850 16.597 0.000 99.240

Inflation 67,452 2.088 1.180 -0.356 3.839

GDP growth 67,452 1.851 1.584 -2.776 3.786

Short-rate 67,452 1.352 1.728 0.089 5.026

Long-rate 67,452 3.250 1.011 1.745 4.795

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15 Table 3

Correlation Matrix.

This table reports correlation coefficients between all covariates. Risk-level score is the natural logarithm of the sum of the return on assets year t and the capital asset ratio year t, divided by the volatility of the return on assets, calculated over the period from 2003 to 2016, and is a measure of bank risk-taking. Risk assets is the ratio of risky assets to total asset (risky assets are defined as all assets except cash, government securities, and balances from other banks or central banks), and is a second measure of bank risk-taking. Capitalization is the ratio of equity to total assets. Lagged profitability is the ratio of profits before tax to total assets of the previous year. Efficiency is the ratio of operating expense to operating revenue. Size is the natural logarithm of total assets. Bank loans is the ratio of bank loans to total assets. Inflation is the annual inflation rate in the U.S. GDP growth is the annual GDP growth rate in the U.S. Short-rate is the annualized average of monthly rates of the effective federal funds rate. Long-rate is the annualized average of monthly rates on a ten years U.S. treasury bond. The mean, standard deviation, minimum, and maximum of inflation, GDP growth, delta short-rate, and delta long-rate are in percentages.

5. Hypotheses

Following the literature, banks react to low interest rates by increasing their exposure to risky assets. This is described by the risk-taking channel of monetary policy and the search for yield effect as discussed in the literature review. This bank risk-taking is measured in two ways. Firstly, the risk-level scores is used to measure bank risk-taking. If a bank participates in risk-taking by investing in more risky assets, the volatility of asset returns increases. This increased volatility is included in the denominator of the risk-level score as demonstrated in Eq. (1), and decreases the risk-level score. A lower risk-level score implies higher bank risk- taking and a higher probability of insolvency. Secondly, the increased exposure to risky assets in relation to total assets is captured by the risk measure risk assets. This is the ratio of risky assets to total assets. A higher level of risky assets also implies a higher risk profile of a bank and therefore higher bank risk-taking.

The relationship between interest rates and bank risk-taking is symmetric in such a way that in addition to the supposed relationship between low interest rates and high bank risk-

Risk-level score Risk assets Capitalization Lagged profitability Efficiency Size

Risk-level score 1

Risk assets -0.334 1

Capitalization 0.103 -0.247 1

Lagged profitability 0.057 -0.067 0.431 1

Efficiency -0.060 -0.016 -0.006 -0.072 1

Size -0.138 0.382 -0.176 -0.013 -0.045 1

Bank loans -0.292 0.763 -0.367 -0.129 -0.026 0.207

Inflation -0.007 0.005 -0.011 0.050 -0.021 -0.084

GDP growth 0.032 -0.063 0.004 0.026 -0.023 -0.040

Short-rate -0.016 0.030 -0.009 0.084 -0.022 -0.090

Long-rate -0.027 0.026 -0.021 0.064 -0.023 -0.138

Bank loans Inflation GDP growth Short-rate Long-rate

Bank loans 1

Inflation 0.028 1

GDP growth -0.031 0.371 1

Short-rate 0.086 0.596 0.195 1

Long-rate 0.076 0.567 0.150 0.812 1

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16

taking, high interest rates have the effect that banks can become more conservative with respect to risk-taking (Rajan, 2006). However, the emphasis in this thesis is to determine whether low interest rates increase bank risk-taking, and therefore the hypotheses are aimed at this.

The full period being investigated is from 2003 to 2016. Most of the related literature is on the relationship between low short-term interest rates and bank risk-taking (e.g. Adrian and Shin, 2010; Geršl et al., 2012; Ioannidou et al., 2015; Jiménez et al., 2014; Maddaloni and Peydró 2011, Maddaloni et al., 2008). However, since Aramonte et al. (2015) provided evidence that a low long-term interest rate drives risk taking as well, a long-term interest rate is included in the analysis. To analyze whether low interest rates increase bank risk-taking the following null hypotheses are developed:

H1: A low short-term interest rate does not increase bank risk-taking.

H2: A low long-term interest rate does not increases bank risk-taking.

Hypothesis H1 and H2 are tested against the alternative hypotheses that a low short- or long- term interest rates does increase bank risk-taking.

6. Model

Before developing the statistical model the variables themselves require extra attention. All variables, except for both the interest rates and the macro-economic control variables, change over time and between banks. It is likely that these variables contain fixed bank- and time effects. For example, it could be that banks have on average a higher level of risky assets in a certain year, not because of risk-taking incentives, but as a result of changing legislations. In this thesis the emphasis is solely on the impact of interest rates on bank risk-taking, and not in the impact of certain years or banks. Therefore it is necessary to transform these variables by adjusting for these potential fixed bank- and time effects. Not adjusting for these kind of fixed effects would imply assuming that banks’ behavior is fixed between banks and over years, and this is highly unlikely.

Assume the following where i is an index for banks and t is an index for time (in years).

𝑥

_𝑖𝑡

= 𝜇 + 𝛼

_𝑖

+ 𝛽

_𝑡

+ 𝜀

_𝑖𝑡

(2)

Where 𝑥

_𝑖𝑡

is any bank variable with a bank dimension i, and a time dimension t, and is the

value of this variable of bank i at time t. This variable is composed of an overall mean 𝜇, plus

a bank effect 𝛼

_𝑖

, a time effect 𝛽

_𝑡

, and a random component 𝜀

_𝑖𝑡

. This random component is

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17

what is important in this thesis since it is the value of the original variable without fixed bank- or time effects. The overall mean 𝜇 is estimated by:

𝜇̂ = 𝑥

_..

(3) and the is average of 𝑥 over both time and banks (a dot instead of an i or t in the subscript implies a fixed bank or time dimension respectively). The fixed bank effect 𝛼

_𝑖

is estimated by:

𝛼̂

_𝑖

= 𝑥

_𝑖.

− 𝑥

_..

(4) and is the difference between the bank mean of bank i and the overall mean. The fixed time effect 𝛽

_𝑡

is estimated by:

𝛽̂

_𝑡

= 𝑥

_.𝑡

− 𝑥

_..

(5) and is the difference between the time mean in year t and the overall mean. After collecting all terms and combining (2), (3), (4), and (5), the following equation is estimated:

𝑥

_𝑖𝑡

= 𝑥

_..

+ 𝑥

_𝑖.

− 𝑥

_..

+ 𝑥

_.𝑡

− 𝑥

_..

+ 𝜀

_𝑖𝑡

(6) Equation (6) can be rewritten as:

𝑥

_𝑖𝑡

− 𝑥

_𝑖.

− 𝑥

_.𝑗

+ 𝑥

_..

= 𝜀

_𝑖𝑡

(7) Where 𝜀

_𝑖𝑡

is the transformed value of the original variable 𝑥

_𝑖𝑡

, after it is adjusted for fixed time- and bank effects. Every value of the risk-level score, risk assets, capitalization, profitability, efficiency, size, and bank loans undergoes this transformation. Thus, for each value of these variables the overall mean is added, and the bank- and time mean are subtracted. The new variables are called the transformed variables. As of now there is only interest in these transformed values in this thesis since these are adjusted for fixed time- and bank effects. The transformed variables will be used in regression analysis, together with the interest rates and macro-economic control variables.

6.1 Regression equation

Panel regression analysis is suited to analyze the relationships between independent and dependent variables, and to infer about a causal relationship between, in this case, the short-or long term interest rates and the two measures of bank risk-taking. To test the developed hypotheses the following panel regression model is estimated:

𝑟

_𝑖𝑡

= 𝛼 + 𝛽

₁

𝑖𝑟

_𝑡

+ 𝛽

_𝑛

𝑏𝑐

_𝑖𝑡

+ 𝛽

_𝑛

𝑚𝑐

_𝑡

+ 𝑢

_𝑖𝑡

(8)

Where 𝑟

_𝑖𝑡

is a measure for bank risk-taking and is the transformed value of the risk-level

score or the transformed value of risk assets of bank i, at time t. This variable is dependent of

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18

𝑖𝑟

_𝑡

, the annual average of the short-or long term interest rate in year t and is a cross-sectional invariant variable. Other included explanatory variables are 𝑏𝑐

_𝑖𝑡

, which is a set of transformed values of bank level control variables of bank i at time t, and 𝑚𝑐

_𝑡

, which is a set of cross- sectional invariant macro-economic control variables at time t. This model is estimated by a pooled OLS method. But in contrary to a standard pooled OLS, fixed bank- and time effects are included, as described in section 6.

A Breusch-Pagan test for heteroskedasticity in linear regression models rejects the null hypothesis of homoscedasticity, the p-value of this test is 0.000. Therefore there is evidence for the presence of heteroskedasticity in the residuals. A test for serial correlation in the residuals rejects the null hypothesis of no serial correlation, the p-value of this test is 0.000.

Therefore there is evidence for the presence of serial correlation in the residuals (Drukker, 2003; Wooldridge, 2010). Using normal standard errors when the errors are heteroskedastic will still give unbiased coefficient estimates, but the standard errors could be incorrect. This makes that any inference made could be misleading and can subsequently result in type I or type II errors (whether this results in type I or type II errors depends on the form of heteroskedasticity but is beyond the scope of this thesis). If serial correlation is ignored the consequences are similar to the consequences of ignoring heteroskedasticity (Brooks, 2008).

Heteroskedastic and autocorrelation consistent (HAC) standard errors are used in every regression to handle both heteroskedasticity and serial correlation.

7. Results

Recall that the regressions are performed with the transformed values of the original bank- specific variables. Hence, if something is mentioned something about the risk-level score, risk assets, capitalization, lagged profitability, efficiency, or size, than there is referred to the transformed value of the particular variable. Besides this, recall that the dependent variables risk-level score and risk assets behave in a different direction. A lower value of risk-level score implies higher bank risk-taking whereas a high value of risk assets implies the same.

This is important to remember when interpreting regression results. For example, with the

risk-level score as dependent variable, a positive and significant coefficient of short-rate

would indicate that a low short-term interest rate is associated with higher bank risk-taking,

whereas with risk assets as dependent variable, a negative coefficient would indicate this

same relationship.

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19 Table 4

Relation between interest rates rate and bank risk-taking in the 2003-2016 period.

This table presents panel OLS regressions. The sample consists of 4818 U.S. banks with data for the 2003-2016 period.

In column 1 and 3 the dependent variable is the risk-level score. This is the natural logarithm of the sum of the return on assets in year t and the capital asset ratio in year t, divided by the volatility of the return on assets, calculated over the period from 2003 to 2016. In column 2 and 4 the dependent variable is risk assets. Risk assets is the ratio of risky assets to total assets (risky assets are defined as all assets except cash, government securities, and balances from other banks or central banks). Capitalization is the ratio of equity to total assets. Lagged profitability is the ratio of profits before tax to total assets, and is included with a time lag of one. Efficiency is the ratio of operating expense to operating revenue. Size is the natural logarithm of total assets. Bank loans is the ratio of bank loans to total assets. The values of all previous called variables are adjusted for fixed bank- and time effects before performing the regressions. Data of these variables are collected with Orbis Bank Focus. Inflation is the annual inflation rate, and GDP growth is the annual GDP growth rate. These two are collected via Worldbank. The most important independent variables are short-rate, in column 1 and 2, and long-rate, in column 3 and 4. Short-rate is the annualized average of monthly effective federal funds rates. Long-rate is the annualized average of monthly rates on a ten year U.S. treasury bond. Interest rates are collected via the Federal Reserve. All regressions are run with heteroskedastic and serial correlation robust standard errors. T-statistics are reported in brackets with ***, **, and, * indicating statistical significance at the 1%, 5%, and, 10% level, respectively.

7.1 Results full period

The empirical results of the full period regressions are presented in table 4. The results do not demonstrate a significant relationship between low interest rates and bank risk-taking. The coefficients of short-rate and long-rate are not significant at any level in all regressions with both the risk-level score or risk assets as dependent variable. Also the coefficients of inflation and GDP growth are not significant in all regressions. With respect to the bank-specific control variables the results are as follows. In the regressions with the risk-level score as

(1) (2) (3) (4)

Dependent variable Risk-level score Risk assets Risk-level score Risk assets

Capitalization 0.047*** 0.001* 0.047*** 0.001*

[28.696] [1.928] [28.696] [1.928]

Lagged Profitability 0.921*** -0.118*** 0.921*** -0.118***

[5.516] [-2.658] [5.516] [-2.657]

Efficiency -0.008** 0.000 -0.008** 0.000

[-2.199] [0.993] [-2.199] [0.993]

Size -0.017*** 0.009*** -0.017*** 0.009***

[-3.283] [4.845] [-3.283] [4.846]

Bank loans -0.008*** 0.007*** -0.008*** 0.007***

[-43.723] [106.119] [-43.727] [106.121]

Inflation -0.001 -0.000 -0.000 -0.000

[-1.046] [-0.052] [-0.721] [-0.035]

GDP growth 0.000 0.000 0.000 0.000

[1.115] [0.029] [1.099] [0.025]

Short-rate 0.000 -0.000

[0.573] [-0.046]

Long-rate 0.000 -0.000

[0.010] [-0.067]

Observations 67,436 67,452 67,436 67,452

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20

dependent variable the control variables are significant on the 1% level, except for efficiency which is only significant on the 5% level. Capitalization is positive, indicating that a higher capitalized bank is associated with lower bank risk-taking. Lagged profitability is positive, indicating that higher profitability in the previous year is associated with lower bank risk- taking. Size is negative, thus a higher level of total assets is associated with higher bank risk- taking. Efficiency is negative, indicating that a less efficient bank is associated with higher bank risk-taking. Finally, bank loans is negative, indicating that a higher proportion of bank loans is associated with higher bank risk-taking as well. With risk assets as dependent variable the sings and coefficients of the control variables are similar, except for efficiency, which is insignificant, and capitalization, whose sign is changed and is only significant on the 10% level. The sign of capitalization is positive in this case, indicating that a higher capitalized bank is associated with a higher proportion of risky assets. Because of the insignificant coefficients of short-rate and long rate, with both the dependent variables, null hypotheses H1 and H2 are not rejected. The data does not reveal a significant relation between low interest rates and bank risk-taking.

7.2 Differences in relationship low interest rates and bank risk-taking over time

The results in section 7.1 reveal that there is no relationship between low interest rates and

bank risk-taking in the full period. Figure 1 demonstrates that the short-term interest rate

fluctuated much strongly in the 2003-2008 period compared to the 2009-2016 period. After

2009 the short-term interest rate was relatively stable. Besides this, in the end of 2008 the

U.S. government introduced the Emergency Economic Stabilization Act, often called the is

bailout plan to stabilize the financial system in the U.S. It could be that this has prevented

banks from taking risk. This gives rise to the following question. Could the fact that no

relationship is found in the 2003-2016 period be caused because after 2009 banks were

prevented from taking risk, because of increased regulations, or because of the stable interest

rate (which can be seen as a regulation itself since the Federal Reserve determines target

rates)? It is possible that there is a significant relationship in the 2003-2008 period, but not in

the years thereafter, and that these effects cancel each other out so no effect is found in the

full period. To test whether this is the case, the 2003-2008 and 2009-2016 are analyzed

separately in the following paragraph. The same null hypotheses H1 and H2 are tested, but

then focused on the sub-periods. The standard deviation of ROA is in this case calculated over

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21

the corresponding periods. Also the fixed bank- and time effects, and the overall means of the bank-specific variables needed to

Table 5

transform the variables, are in this case calculated over these periods. The disadvantage from this split is that both periods could contain data that can be attributed to the period corresponding with the liquidity crisis. The advantage is that analyzing a 2003-2008 period makes it possible to compare results with other studies (e.g. Delis and Kouretas (2011), Jiménez et al. (2014), Maddaloni and Peydró (2011), and Maddaloni et al. (2008)) in which approximately the same period is investigated.

(1) (2) (3) (4)

Capitalization 0.036*** 0.002*** 0.036*** 0.002***

[18.476] [3.561] [18.476] [3.561]

Lagged Profitability 0.554** -0.065 0.554** -0.065

[2.290] [-1.340] [2.290] [-1.340]

Efficiency -0.004** 0.000 -0.004** 0.000

[-2.470] [0.185] [-2.469] [0.185]

Size -0.094*** 0.019*** -0.094*** 0.019***

[-10.440] [4.937] [-10.440] [4.937]

Bank loans -0.008*** 0.007*** -0.008*** 0.007***

[-24.191] [67.198] [-24.191] [67.198]

Inflation 0.000 -0.000 0.000 -0.000

[0.139] [-0.012] [0.292] [-0.015]

GDP growth 0.001 -0.000 0.001 -0.000

[1.516] [-0.007] [1.162] [-0.002]

Short-rate 0.000 -0.000

[0.823] [-0.013]

Long-rate 0.001 -0.000

[0.836] [-0.014]

Observations 28,901 28,908 28,901 28,908

(22)

22 Table 6

7.3 Results sub-periods

The empirical results of the regressions in the 2003-2008 period are presented in table 5.

The empirical results of the regressions in the 2009-2016 period are presented in table 6. Both periods demonstrate similar results. There is no evidence for a significant relationship between low short- or long-term interest rates and bank risk-taking in both the two periods.

The coefficients of short- and long-rate are insignificant in all regressions. Therefore null hypotheses H1 and H2 are not rejected for both the periods. The signs and significances of the

(1) (2) (3) (4)

Capitalization 0.058*** 0.001*** 0.058*** 0.001***

[22.759] [3.162] [22.755] [3.162]

Lagged Profitability 1.380*** -0.088* 1.380*** -0.088*

[6.349] [-1.817] [6.348] [-1.817]

Efficiency -0.065*** 0.001 -0.065*** 0.001

[-2.920] [0.572] [-2.920] [0.572]

Size -0.070*** -0.005** -0.070*** -0.005**

[-6.153] [-2.225] [-6.154] [-2.225]

Bank loans -0.009*** 0.007*** -0.009*** 0.007***

[-35.194] [97.521] [-35.198] [97.520]

Inflation -0.001 -0.000 -0.001 -0.000

[-0.997] [-0.047] [-0.868] [-0.040]

GDP growth 0.001 0.000 0.000 0.000

[1.115] [0.060] [0.631] [0.041]

Short-rate 0.002 0.000

[0.292] [0.007]

Long-rate -0.001 -0.000

[-0.859] [-0.039]

Observations 38,535 38,544 38,535 38,544