The Effect of Interest Rates on Bank Risk-Taking: An Empirical Study
E. Mittendorp
Abstract
Many economists view the low interest-rate environment of the pre-financial crisis period as an element that triggered increased bank risk-taking in their search for higher returns. Briefly stated, the majority of economists suggest that a low interest-rate environment reduces bank margins and informational asymmetries. As a reaction to this, banks relax their lending standards, which inevitably leads to an increase in the ratio of risky assets to total assets in their portfolios and an increase in the ratio of non-performing loans to total loans. A recent article by Delis & Kouretas (2011) presents strong empirical evidence that, in the 2001-2008 time period, the low interest rate environment has substantially increased bank risk-taking among Eurozone banks. Due to a number of factors, e.g. the introduction of the Basel II guidelines by the Basel Committee on Banking and Supervision, the introduction of the Dodd-Frank Wall Street Reform and Consumer Protection Act by the United States Government and the major shift of public opinion against excessive risk-taking by banks, bank bonuses, and banks in general, these results may not hold anymore or significantly differ in the U.S. This paper researches the effect of interest rates on bank risk-taking of U.S. banks and finds that the results are less pronounced and more ambiguous than Delis & Kouretas’ (2011) results. On the one hand, my results show that there is a positive, but economically negligible, relationship between interest rates and the ratio of risky assets to total assets. On the other hand, there is a clear and distinct negative relationship between interest rates and the ratio of non-performing loans to total consumer loans. There is clear evidence that U.S. banks react differently to a low interest-rate environment than Eurozone banks and adjust their risk-taking accordingly. Estimation of the results with different types of interest rates, different bank risk-taking proxies and different time periods did not alter the results significantly.
Keywords: Interest Rates, Monetary Policy, Bank Risk-Taking JEL Classification: C33, E43, E52, G21
Date: 14th of January 2016
Studentnumber: 1883089
1. Literature review
Since the financial crisis of 2007 banks have been under intense scrutiny by the public, governments, and national and international regulators. The majority places the blame of the financial crisis on excessive bank risk-taking due to the low-interest rate environment of the early to the mid 2000s. It is believed that, due to the fairly long period of low-interest rates prior to 2007, banks experienced a decrease in their bank margins and informational asymmetries. Banks responded by relaxing their lending standards, which inevitably led to an increase in the ratio of risky assets to total assets in their portfolios and an increase in the percentage of defaults of their loans and the severity of these defaults. According to this general consensus, this increased bank risk-taking behavior ultimately led to the collapse of Lehman Brothers in 2008 and the subsequent meltdown of the entire financial system.
emitted by a central bank about a likely rise or fall in interest rates and its perception regarding the macroeconomic environment are responsible for inducing banks to change their risk-taking behavior. They present evidence for the link between monetary policies, central bank communication and bank risk-taking behavior and their findings reveal that central bank communication influences the behavior of banks once their risk perceptions are affected.
One of the core tasks of banks is the so-called maturity transformation, the transformation of short-term deposits into long-short-term loans. This entails a possible risk in the case of a bank run, when depositors come to the bank in large numbers at the same time to claim their money, and their money is not readily available and will probably only be there after quite some time. The profitability of maturity transformation is dependent on the level of the short-term and long-term interest rates. The profitability increases as the difference between the short-term and the long-term interest rates increases, in other words when the slope of the yield curve steepens. Alessandri & Nelson (2012) researched whether bank profitability varies with interest rates by presenting a model of a monopolistically competitive bank subject to repricing frictions and test the predictions of the model using a panel dataset on UK banks. They found that high interest rates are associated with large interest income margins and that the slope of the yield curve matters for a banks’ interest income. Level and slope affect a banks’ interest income and trading income in the opposite direction, which is consistent with banks hedging interest rate risk through derivatives. Although even after accounting for these interest rate hedging strategies, large banks appeared to retain a residual exposure to UK interest rates and they stated that higher rates have an unambiguously positive effect on bank profits in the long run. Dell’Ariccia, Laeven & Marquez (2014) investigated whether a low interest rate environment leads to greater bank risk-taking. They showed that, when banks are able to adjust their own capital structures, reductions in real interest rates lead to greater leverage and higher risk for any downward sloping loan demand function. However, if their capital structure is fixed, the effect depends on the degree of leverage a bank has. Following a decrease in interest rates, well capitalized banks may increase risk-taking, while highly levered banks may decrease risk-taking if loan demand is linear or concave. They concluded that three forces – interest-rate pass-through, risk shifting, and leverage – determine how changes in interest rate conditions affect a bank’s risk-taking.
2. Data and methodology
This present paper builds upon the methodology employed in Delis & Kouretas (2011) and investigates the effect of interest rates on the level of bank risk-taking by using a panel regression model with a risk variable, r of bank i at time t, that is a function of the interest-rate variable, ir, a set of bank-specific control variables, b of bank i at time t, and a set of macroeconomic and structural control variables, c at time t, which are common to all banks in any particular year. The general empirical model to be estimated is of the following order:
rit = α + β1irit + β2bit + β3ct + uit (1)
Table 1
Descriptive statistics.
Variable Mean Standard deviation Minimum Maximum
Risky assets 0.939 0.062 0.117 1
Adjusted risky assets 0.942 0.062 0.117 1
Non-performing loans 0.015 0.024 0 0.498
Capitalization 0.108 0.038 -0.006 0.961
Profitability 0.011 0.011 -0.260 0.469
Size 11.868 1.308 7.676 21.453
Efficiency 1.340 0.510 -1.792 62.325
Off-balance sheet items 0.144 0.942 0 128.385
Economic growth 1.948 1.640 -2.775 4.092 Inflation 2.035 0.669 0.759 3.217 Importance of banks 219.878 16.337 190.962 243.859 Concentration 42.192 2.774 39.416 47.109 Short-term rate 1.827 1.926 0.031 5.988 Long-term rate 3.818 1.114 1.802 6.029 Central-bank rate 2.010 2.052 0.089 6.235
Bank-level lending rate 0.096 0.209 0 21.791
This table reports summary statistics for the variable used in the empirical analysis. The variables are as follows: risk assets is the ratio of risk assets to total assets, adjusted risk assets is the ratio of adjusted risk assets to total assets, non-performing loans is the ratio of non-performing loans to total loans, capitalization is the ratio of equity capital to total assets, profitability is the ratio of profits before tax to total assets, size is the natural logarithm of total assets, efficiency is the ratio of total revenue to total expenses, off-balance sheet items is the ratio of off-balance sheet items to total assets, economic growth is annual GDP growth, inflation is annual CPI inflation, importance of banks is the domestic credit provided by the banking sector as a share of GDP, concentration is the 3-bank concentration ratio, short-term rate is the annual average of the 3-month interbank rate, long-term rate is the annual average of the 10-year US government yield, central-bank rate is the annual average of monthly average federal funds rate, and bank-level lending rate is the ratio of interest income to total customer loans.
Table 2
Correlation Matrix.
Capitalization Lagged profitability
2.1 Bank risk-taking
I will proxy the risk-taking behavior of banks using a ratio of risky assets to total assets, an alternative ratio of risky assets to total assets, and a ratio of non-performing loans to total loans. The ratio of risky assets to total assets is a proxy for the riskiness of bank portfolios at any point in time. The risky assets of a bank include all the bank’s assets except cash, government securities, which are valued at market value, and balances due from other banks. This means that all the assets of a bank subject to changes in value due to market conditions or changes in the quality of credit are qualified as risky assets. An increase in the ratio of risky assets to total assets corresponds to a riskier portfolio position of a bank and an increase in bank risk-taking behavior. In my dataset the risky assets variable has a mean value of 0.940, with a lower average value of 0.894 in 2012 and a higher average value of 0.964 in 2007. However, one could put forward the argument that, looking at how some governments struggled with their public finances, and their interest and debt repayments in recent years, government securities should also be qualified as a risky asset. Next to the aforementioned risky asset measure of Delis & Kouretas (2011), I will use an alternative qualification for the term risky assets. For this alternative measure of risky assets, the risky assets of a bank include all the bank’s assets except cash and balances due from other banks. So for this alternative measure, government securities are qualified as risky assets instead of riskless assets. In my dataset the adjusted risky assets variable has a mean of value of 0.942, with a lower average value of 0.894 in 2012 and a higher value of 0.968 in 2007. The pattern of average annual values of these risky assets ratio variables is in line with the 2007 financial crisis. The average annual values of risky assets and adjusted risky assets slowly increase up to and including 2007, which is the height financial crisis, and then sharply decrease and stabilize in the subsequent years at a lower level than the pre-financial crisis level.
number of consumers defaulted on their loans, while the higher pre-financial crisis level shows the aftermath of the 2007 financial crisis and the fact that a greater amount of consumers had troubles repaying their loans.
2.2 Interest rates
This paper examines the relationship between the level of interest rates and the level of bank risk-taking. To examine this, I estimate regressions with various interest rates, more specifically a short-term interest rate, a long-short-term interest rate, a central-bank rate and a bank-level lending rate. Data for the short-term interest rate, the long-term interest rate and the central-bank interest rate are obtained from Thomson Reuters Datastream and concerns annual averages of these specific interest rates. More specifically, the short-term interest rate is the annual average of the 3-month interbank rate, the long-term interest rate is the annual average of the 10-year US government bond yield and the central-bank interest rate is the annual average of the monthly Federal Reserve Funds Rate. The summary statistic of these interest rate variables are reported in Table 1. Using various interest rate variables allows me to capture different aspects of the impact of interest rates and monetary policy changes on bank risk-taking, and check for the robustness of the results of my estimations. The average values of these interest rate variables have been declining from 2000 up to 2003, started climbing from 2004 up to 2007 and have been declining since. The sharp decline in the short-term interest rate and central-bank interest rate and the less sharp decline of the long-term interest in the 2000-2003 and 2008-2014 period can be attributed to the adverse economic situation in the USA and the related efforts of the Federal Reserve to pursue an expansionary monetary policy and increase economic growth.
relationship is clearly negative and shows that a lower interest rate leads to a higher ratio of non-performing loans to total loans and thus to a higher level of bank risk-taking. These figures are the first evidence that the effect of interest rates on bank risk-taking for U.S. banks is more profound on the level of non-performing loans than on the amount of risk assets.
Figure 2. Bank-level lending rate and bank risk-taking. This figure shows the non-parametric regression between bank risk-taking, measured by the ratio of non-performing loans to total loans, and the bank-level lending rate, measured by the ratio of interest income to total customer loans. This figure reports all values of the bank-level lending rate up to 0.25. This regression line reflects the clear negative relationship between bank risk-taking and the bank-level lending rate.
2.3 Control variables
Several control variables will also be included into my estimations. New risk management techniques introduced into the banking sector in the 1990s and 2000s and new highly sophisticated technologies allowed, and still allow, banks to increase the level of risk assets as a share of their total assets and thereby raise their overall profitability. There has to be controlled for these new risk management techniques and technological changes, because otherwise an increase in the ratio of risky assets to total assets of a bank does not necessarily reflect an increase in bank risk-taking behavior but could reflect more new risk management techniques and more sophisticated risk-related technology available to banks. Next to this, I will control for cross-country differences using country dummy variables. Besides these technology and cross-country control variables, I will include several bank- and country-level controls to avoid the omitted-variables bias.
are expected to tradeoff higher levels of equity capital for risky assets, this relationship clearly being endogenous. In turn, the impact of profitability on bank risk-taking is quite ambiguous. On the one hand, a higher level of risky assets may be associated with higher profits and these higher levels of profits may be used to issue new loans in the subsequent period. On the other hand, too many risky assets may lead to non-performing loans and lower profitability that will eventually lead to fewer risky assets in the following period. To this end, profitability will be treated as an endogenous variable and, because profitability in this period affects the amount of risky assets and non-performing loans in the following period, will enter the estimated equations lagged once. In addition, bank size, efficiency, and the size of non-traditional banking activities a bank performs could also be important elements in shaping bank risk-taking behavior. In all estimated equations I control for the size of a bank using the natural logarithm of their real total assets. Since banks at any given point in time should be are aware of their size, this could influence their risk-taking behavior, and therefore I do not consider this variable as endogenous, but rather as predetermined (Athanasoglou et al. (2008)). Technologically efficient banks may be more capable in managing their risks; however, higher bank risk-taking may also explain technological efficiency levels if they are responsible for the level of bank income. Clearly, efficiency, measured by the ratio of total revenue to total expenses, will also enter the estimated equations as an endogenous variable. Another bank-level control variable is the size of non-traditional banking activities, which increased sharply over the last decade. I control for these activities using the ratio of off-balance sheet items to total bank assets. The effect of the off-balance sheet items ratio is also ambiguous. On the one hand, a higher level of bank risk-taking might be caused by an increased non-traditional banking activities. On the other hand, a low level of bank risk-taking might lead to an increase of non-traditional banking activities. Because this relationship is endogenous, it will enter the estimated equations as an endogenous variable.
off-balance sheet items and whether the bank has incentives to increase market discipline. Delis & Kouretas (2011) examine the relationship between the level of interest rates and the level of bank risk-taking behavior in a number of different countries that have adopted the euro as their currency. Since my paper examines this relationship in only one country and all banks are subject to the same national capital regulations, I do not control for these country-specific conditions. I do control however for the state of the macroeconomic environment using the annual rate of inflation and the GDP growth rate, and for financial structure with a ratio of domestic credit provided by banks to GDP (Männasoo and Mayes, 2009), which measures the importance of banks relative to the entire country’s economy. During more favorable macroeconomic conditions banks tend to increase their lending in their search for higher returns and therefore a positive relationship between GDP growth on the one hand and risky assets and non-performing loans on the other hand is expected. In addition, the share of credit provided by banks reflects the degree of the existence of alternative sources of finance for firms, for example funds gained from venture capitalists or from other alternative forms of financing, and also the degree of competition and development of the entire banking system (Larrain, 2006). Finally, I control for concentration in the banking sector using a 3-bank concentration ratio, which measures the market share of the three largest 3-banks in comparison to the entire industry. Boyd et al. (2006), among others, find that banks’ probability of failure is positively related with banking industry concentration, while other studies (e.g. Jimenez et al., 2007) suggest that problem loans and concentration are uncorrelated.
3. Econometric analysis and results
The estimation of Eq. (1) presents a number of challenges, the main two being the potential endogeneity of several bank-specific control variables, and the possible dynamic and persistent nature of bank risk-taking. Taking this into account, I start with a simple panel regression model with fixed effects. Following this simple panel regression model with fixed effects, I estimate a dynamic panel regression model that accounts for the dynamic and persistent nature of bank risk-taking behavior and the simultaneous endogenous nature of certain bank-specific characteristics.
3.1 Panel regression model with fixed effects
As mentioned in section 2, I put together a large balanced panel dataset which I will estimate using a panel data regression. There are three general approaches when using panel data analysis. Firstly, there is the approach of using independently pooled panels. The key assumption with this approach is that each entity within the panel dataset has no unique attributes and that are no universal effects across time. Secondly, there is the approach of using a fixed effects model. The key assumption with this approach is that each entity within the panel dataset does have unique attributes that are not the result of random variation and that do not vary across time. Thirdly, there is the approach of using a random effects model. The key assumption with this approach is that each entity within the panel dataset does have unique attributes but that they are the result of random variation, do not correlate with other individual regressors and are constant over time. For both the fixed effects and the random effects model, all entities have different intercepts that are constant over time. For the fixed effects model, this intercepts are entity-specific and does not vary over time, while under the random effects model, the intercepts for each entity are assumed to arise from a common intercept α, which is the same for all entities and constant over time, plus a random variable εi that varies
cross-entity but is constant over time.
fixed effects. Based on both the theoretical considerations and the empirical evidence, I will estimate Eq. (1) using a panel data model with fixed effects.
Table 3
Interest rates and bank risk-taking: panel data model with fixed effects
I II III IV V VI Capitalization 0.096*** 0.111*** 0.096*** -0.008*** -0.014*** -0.008** (0.008) (0.008) (0.008) (0.003) (0.003) (0.003) Lagged profitability 0.454*** 0.414*** 0.451*** -0.574*** -0.559*** -0.572*** (0.019) (0.019) (0.019) (0.008) (0.008) (0.008) Bank size 0.011*** 0.015*** 0.011*** 0.002*** 0.000*** 0.002*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Efficiency 0.011*** 0.012*** 0.011*** -0.006*** -0.006*** -0.006*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Off-balance sheet items -0.000* -0.000* -0.000* 0.000 0.000 0.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Economic growth 0.001*** 0.000** 0.001*** -0.000*** -0.000 -0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Inflation 0.001*** 0.003*** 0.001*** -0.002*** -0.003*** -0.002*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Importance of banks -0.001*** -0.000*** -0.001*** 0.000*** 0.000*** 0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Concentration 0.005*** 0.003*** 0.005*** -0.000*** 0.000 -0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Short-term rate 0.002*** -0.001*** (0.000) (0.000) Long-term rate 0.012*** -0.005*** (0.000) (0.000) Central-bank rate 0.002*** -0.001*** (0.000) (0.000) Observations 74,067 74,067 74,067 74,067 74,067 74,067 R-squared 0.238 0.250 0.239 0.227 0.235 0.227 This table reports coefficients and standard errors (in parentheses). In regressions I-III the dependent variable is the ratio of risk assets to total assets and in regressions IV-VI the dependent variable is the ratio of non-performing loans to total loans. The explanatory variables are as follows: capitalization is the ratio of equity capital to total assets, lagged profitability is the ratio of profits before tax to total assets of the previous year, size is the natural logarithm of total assets, efficiency is the ratio of total revenue to total expenses, off-balance sheet items is the ratio of off-balance sheet items to total assets, economic growth is annual GDP growth, inflation is annual CPI inflation, importance of banks is the domestic credit provided by the banking sector as a share of GDP, concentration is the 3-bank concentration ratio, short-term rate is the annual average of the 3-month interbank rate, long-term rate is the annual average of the 10-year US government yield and central-bank rate is the annual average of monthly average federal funds rate. Observations is the total number of observations and r-squared shows the goodness of fit of the model. Note that this table does not contain the explanatory variable coefficients of the regressions with the adjusted risk assets as a dependent variable. These regressions have been done to estimate for robustness but the results do not significantly differ from the results of the regression with risk assets as the dependent variable. * Significant at the 1% level, ** Significant at the 5% level, and *** Significant at the 10% level.
loans to total loans. It can be seen that especially the long-term interest-rate variable has the largest effect on both risk-taking proxies in comparison to the other interest rate variables. These results suggest that U.S. banks react somewhat differently to a change in interest rates than European banks in countries that have adopted the euro. While a decrease in interest rates leads to a increase in risky assets and non-performing loans at European banks, it leads to a decrease in risky assets and an increase in non-performing loans at U.S. banks. For U.S. banks, the effect of increased bank risk-taking with respect to lowering interest rates is more pronounced in the total amount of non-performing loans than in the total amount of risky assets. Another interesting fact that can be seen from Table 3 is that a higher (lower) profitability in the current period leads to a higher (lower) amount of risky assets to total assets and to a lower (higher) amount of non-performing loans to total customer loans in the subsequent period. Banks that experience a lower profitability period in the current period will look for loans with a higher yield, and implicitly also a higher level of risk, which will eventually lead to a higher default percentage and thus a higher ratio of non-performing loans to total customer loans. However, although the interest rate variable coefficients are all significant, they are all close to zero and therefore display fairly little economic significance. While useful, these results should be interpreted with caution, as this simple panel regression model with fixed effects does not account for the possible dynamic and persistent nature of bank risk-taking behavior and the potential endogeneity of some of the bank-specific control variables. Therefore, in order to account for these issues, an improved and dynamic panel data methodology based on the generalized method of moments is discussed next.
3.2 Risk persistence and endogenous bank characteristics
certain capital requirements, such as the Basel capital requirements, or government regulations, such as the Dodd-Frank Wall Street Reform and Consumer Protection Act, may increase moral hazard or asymmetrical information issues and lead to inefficient and risky investments over a considerable period of time, leading to short-term deviations from its long-term bank risk-taking equilibrium. To conclude, if bank risk-taking is indeed persistent then a static model gives biased estimations and the preferred model is of a dynamic nature. In such a dynamic model, the coefficient on the lagged risk variable may be viewed upon as the speed of convergence to the long-term equilibrium of the dependent variable, in this case bank risk-taking. All these theoretical considerations lead to the estimation of the following adaptation of Eq. (1):
rit = α + (rit-1) + β1irit + β2bit + β3ct + uit (2)
does not break down in the presence of unit roots. Second, and most important in the setting of this paper, it accommodates the possible endogeneity between the dependent bank risk-taking variable and some of the bank-specific control variables by means of appropriate instruments. In particular, I treat as endogenous the bank-specific control variables capitalization, lagged profitability, efficiency, and off-balance sheet items. The theoretical reasoning why these bank-specific control variables should be treated as endogenous variables is mentioned in Section 2.3. Endogeneity of these bank-specific control variables means that they are correlated with the current period error term, uit, and with earlier shocks but uncorrelated with future period error terms, uit+1 to uit+n, and future shocks. These endogenous variables will then enter the equation by treating them identically as the dependent bank risk-taking variables. Next to this, the macroeconomic control variables will be treated as exogenous variables and the bank size variable will be treated as a predetermined variable. This means that that banks, in determining their level of bank risk-taking, are aware of the current macroeconomic environment as well as their size.
With risky assets as proxy for bank risk-taking behavior, the impact of bank size is positive and significant, which most likely can be explained by the fact that larger banks have higher capital reserves and are more capable of sustaining losses. The impact of off-balance sheet items is not significant and does not add any understanding to this model. Bank capitalization is significant and positively related to the ratio of risky assets to total assets, which seems counterintuitive but could be explained by the significant difference in culture of U.S. banks compared to European banks or the fact that US banks have a different position in the U.S. economy than European banks in the European economy. The impact of lagged profitability is positive and significant, indicating that higher profits in the previous period significantly increase the amount of risk assets relatively to total assets in the current period. The effect of efficiency on risk assets to total assets is negative and significant, indicating that more efficient banks have on average lower amounts of risk assets to total assets. Regarding the macroeconomic variables, economic growth is positive and significant and higher economic growth leads to a higher amount of risky assets to total assets, while inflation is negative and significant and higher inflation leads to a lower amount of risky assets to total assets. In addition, a higher concentration of banks is positive and significant and leads to a higher amount of risky assets to total assets, while the importance of banks is very close to zero and therefore does not add any further understanding to the model.
model can be improved. Because this null hypothesis is rejected in my estimations and endogeneity is still present in the model, the results should be examined carefully.
Table 4
Interest rates and bank risk-taking: dynamic panel GMM estimator
I II III IV V VI
Lagged risk assets (t-1) 0.757*** 0.724*** 0.757*** (0.013) (0.014) (0.013) Lagged risk assets (t-2) 0.083*** 0.061*** 0.085***
(0.009) (0.009) (0.009)
Lagged non-performing loans (t-1) 0.792*** 0.787*** 0.792*** (0.015) (0.015) (0.015) Capitalization 0.111*** 0.133*** 0.115*** -0.023** -0.0186* -0.023** (0.026) (0.028) (0.026) (0.009) (0.009) (0.009) Lagged profitability 0.518*** 0.462*** 0.492*** -0.245*** -0.251*** -0.242*** (0.065) (0.062) (0.064) (0.032) (0.032) (0.032) Bank size 0.007*** 0.010*** 0.008*** -0.000*** -0.000 -0.000*** (0.001) (0.001) (0.000) (0.000) (0.000) (0.000) Efficiency -0.003** -0.003** -0.003** 0.001*** 0.001*** 0.001*** (0.001) (0.001) (0.001) (0.000) (0.000) (0.000) Off-balance sheet items 0.000 0.000 0.000 -0.000 -0.000 -0.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Economic growth 0.006*** 0.005*** 0.006*** -0.000*** -0.000*** -0.001*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Inflation -0.005*** -0.003*** -0.005*** -0.001*** -0.002*** -0.001*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Importance of banks -0.000*** -0.000*** -0.000*** -0.000*** -0.000*** -0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Concentration 0.002*** 0.001*** 0.001*** 0.000*** 0.000*** 0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Short-term rate 0.001*** -0.000*** (0.000) (0.000) Long-term rate 0.006*** -0.000*** (0.000) (0.000) Central-bank rate 0.001*** -0.000*** (0.000) (0.000) Observations 64,192 64,192 64,192 69,130 69,130 69,130 AR1 0.000 0.000 0.000 0.000 0.000 0.000 AR2 0.000 0.000 0.000 0.372 0.383 0.374 AR3 0.768 0.736 0.610 Hansen 0.000 0.000 0.000 0.000 0.000 0.000
4. Summary of findings and conclusion
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