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Volume 11 Issue 4, October-December 2023 

ISSN: 2836-9416 

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BASEL III REGULATIONS AND THEIR INFLUENCE ON 
BANKING OPERATIONS: A STUDY OF LOAN QUANTITY AND 

INTEREST RATES 
 
 

Dr. Dimitrios Gavalas and Professor Maria Kritikou 
University of Aegean, Business School, Dept. of Shipping, Trade &Transport, Chios, Greece. 

 
Abstract: In the aftermath of the 2008 financial crisis, a pressing need for financial sector regulation 
and supervision reform became evident. This reform effort was initiated by the G20, with key 
organizations like the Financial Stability Board and the Basel Committee on Banking Supervision 
(BCBS) taking the lead. Their goal was to enact a comprehensive agenda of regulatory changes to 
enhance the resilience of the banking sector, enabling it to better withstand financial and economic 
stressors while minimizing adverse effects on the real economy. 
These reform measures, introduced over a two-year period starting in 2009, comprised several 
critical components. The initial installment, known as Basel II, included strengthening trading book 
capital requirements, imposing higher capital requirements for re-securitization products held in 
both the banking and trading books, and providing enhanced guidance on Pillar II, which focuses on 
the supervisory review process. Subsequently, in late 2010, the BCBS released Basel III, outlining 
further reforms. These measures aimed at refining regulatory capital definitions, introducing a 
leverage ratio as a risk-based capital requirement safeguard, establishing capital buffers, enhancing 
risk coverage by improving the methodology for measuring counterparty credit risk, and 
implementing rigorous liquidity measurement standards. 
These regulatory reforms mark significant progress in bolstering the financial sector's resilience and 
risk management capabilities. This study delves into their implications, effectiveness, and broader 
impacts on the global financial landscape. 
Keywords: financial regulation, Basel III, banking sector, risk management, financial stability. 
  
1. Introduction   
Towards the end of 2008, it became clear that weaknesses in financial sector regulation and 
supervision had significantly contributed to the crisis.   
The efforts to reform the financial sector regulation began under the aegis of G20, and both the 
Financial Stability Board and the Basel Committee on Banking Supervision (BCBS) embarked on an 
ambitious agenda for regulatory reforms (FSI, 2010). During the next two years a number of initiatives 
were taken by the BCBS with the objective of improving the banking sector’s ability to absorb shocks 
arising from financial and economic stress and to reduce the risk of spill-over from the financial sector 
to the real economy.    
The first installment of these measures announced in July 2009 (Basel II) included strengthening of 
the trading book capital requirements, higher capital requirements for re-securitization products held 
in both the banking book and trading book and strengthening of guidance on Pillar II (supervisory 

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review process). In late 2010 the BCBS issued the Basel III document enumerating measures focused 
on improvements in the definition of regulatory capital, introduction of a leverage ratio as a backstop 
for risk-based capital requirement, capital buffers, enhancement of risk coverage through 
improvements in the methodology to measure counterparty credit risk and liquidity measurement 
standards (Hakura&Cosimano, 2011).   
The reforms focus firstly on the micro-prudential (bank-level) regulations which will help raise the 
resilience of individual banking institutions during periods of stress; secondly, on macro-prudential 
regulations involving system-wide risks that can build up across the banking sector as well as the 
procyclical amplification of these risks over time (BIS, 2010b). The new regulations tighten the 
definition of bank capital and require that banks hold a larger amount of capital for a given amount of 
assets and expand the coverage of bank assets. The purpose of this paper is to estimate whether and to 
what extent these higher capital requirements will lead to higher loan rates and slower credit growth.   
This paper aims to broaden and deepen the understanding of the likely impact of the new capital 
requirements on bank lending and volume of lending, introduced under the Basel III framework rates. 
Complementing the studies mentioned above, the contribution of this paper is twofold concerning the 
understanding and testing of the impact of the new regulations on the banks.    
Firstly, the paper derives empirically testable relations from a structural model of the capital channel 
of monetary policy developed by Chami and Cosimano (2010). In doing so it follows Barajas et al. 
(2010) analysis of large bank holding companies in the United States. In this model, loan demand 
shocks are transmitted to the credit supply via the regulatory capital constraint. In particular, a bank’s 
decision to hold capital is modeled as a call option on the optimal future loans issued by the bank. This 
option value of the bank’s capital increases when the expected level of loans and the amount of capital 
required by the regulator increase. The bank’s choice of capital influences its loan rate since the 
marginal cost of loans is a weighted average of the marginal cost of deposits and equity. Consequently, 
the loan rate raises with an increase in required capital as long as the marginal cost of equity exceeds 
the marginal cost of deposits.    
Another contribution of this paper is that it considers two different groupings of banks: (i) commercial 
banks in advanced European economies that experienced a banking crisis between 2007 and 2010; and 
(ii) commercial banks in advanced  
European economies that did not experience a banking crisis between 2007 and 2010. It would have 
been preferable to extend the time range but there was a lack of appropriate data for the next two years 
(2011 and 2012).   
The empirical estimation of our data relies on a Generalized Method of Moment (GMM) estimation 
procedure which captures the banks’ simultaneous decisions on how much capital to hold, at what level 
to set the loan rate and the size of their loan portfolio (Gropp&Heider, 2010; Miller et al., 2010; Hall, 
2005). In line with Cosimano and Hakura (2011) the first stage regression for banks’ holdings of capital 
is specified in terms of previous-period changes in capital, interest expenses (interest payables) and 
non-interest expenses (figure 1). The hypothesis is that there is a negative and convex relationship 
between a bank’s capital and each of these factors. In particular, an increase in the future marginal cost 
of loans results in the bank issuing fewer loans so that the need for equity fades. The loan rate is the 
dependent variable in the second stage regression and is specified in terms of the optimal bank capital 

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predicted by the first stage regression as well as interest and non-interest expenses and the level of 
economic activity.   
  
  
  
  
  
  
Figure 1: The Generalized Method of Moment (GMM) Estimation Procedure  

The key findings of the paper are as follows. First, a 1 percent increase in the equity-to-asset ratio is 
associated with a 0.05 percent average increase in the loan rate for banks in countries that experienced 
a banking crisis during 2007-2010. For banks in countries that did not experience a banking crisis 
during 2007-2010 it is associated with a 0.02 percent average increase. Secondly, assuming a 1.3 
percentage point increase in the equity-to-asset ratio to meet the Basel III regulations, the country-
bycountry estimations imply a reduction in the volume of loans by an average 4.97 percent in the long 
run for the banks in countries that experienced a crisis and by 18.67 percent for the banks in countries 
that did not experience a crisis. The wide variance in the results reflects cross-country differences in 
the elasticity of loan demand with respect to loan interest rate and bank’s net cost of raising equity. The 
authors’ model shows that the estimated elasticity of loan demand ranges from -1.00 percent for Ireland 
to -6.59 percent for Denmark. An upper bound on the net cost of raising equity (i.e. the return on equity 
relative to the marginal cost of deposits) is estimated to range from 0.01 basis points in Sweden to 20 
basis points in Ireland.  
The remainder of the paper is organized as follows. Section 2 refers to related literature. Section 3 
presents some descriptive statistics for the two groupings of banks examined in the paper. Section 3 
describes the structural model for banks’ optimal holding of capital and presents the specification of 
the empirical tests for bank capital, lending rates and loans. The core principals of the GMM estimator 

  

  

  

  

  

  

  

  

  

  

  

  

  

  

First stage  
Regression   

Second   stage  
Regression   

Holdings of capital   

Loan rate   

Δ  ( Capital )   

Δ  ( ) Interest expenses   

Δ  Non ( - interest  expenses)   

Optimal bank capital   

Level of economic activity   

Interest expenses   

Non - interest expenses   

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are presented in section 4. Section 5 reports the results. Finally, the conclusion is presented in section 
6.  
2. Related Literature  
There are several studies which have handled the effects of capital requirements upon banking 
performance.  To begin with some of them seek the degree on which capital requirement levels affect 
the profitability of commercial banks. For example, Rojas-Suarez (2002) argued that capital standards 
are not found to strengthen banks in emerging countries when Chiuri et al. (2002) found that the 
enforcement of capital requirements is found to reduce the supply of finance; to help prevent negative 
macroeconomic effects, capital requirements should be phased in gradually. The worst impact is 
usually felt when capital requirements are implemented in the aftermath of a crisis. In response to the 
deposit insurance post crisis, Demirguc-Kunt and Kane (2002) challenge the rationale of encouraging 
countries to adopt explicit deposit insurance without first addressing supervisory and institutional 
financial weaknesses. ‘Weak’ countries that adopt explicit deposit insurance usually find that the 
economic conditions subsequently suffer because private sector monitoring is replaced with poor-
quality government monitoring (Cullet al., 2002; Laeven, 2002).  
Several studies in this category offer a descriptive debate over arbitrary balance of regulation (e.g. Di 
Noia& Di Giorgio, 1999; De Bondt&Prast, 2000 inter alia). Ferri et al. (2001) argue that the linking of 
bank capital requirements to private sector ratings would prove undesirable for non-high-income 
countries. Corporate and bank ratings in low-income countries are not updated as often or as 
extensively as high-income countries. Accordingly, banks in lower-income countries with improved 
asset quality would be disadvantaged.   
Analysis of explicit or implicit deposit insurance is a familiar regulatory theme in regard to risk-shifting 
within an economy. 
Explicit deposit insurance occurs when a government guarantees the safety of bank deposits. The level 
of coverage may vary between different types of depositors and banks to avoid bank runs but not 
without moral hazard issues to contend (Laeven, 2002). Implicit deposit insurance entails uninsured 
deposits. The expectation of government bailout of the depositor is extremely high in Eastern Europe 
and Latin America and moderately high in Asia and Africa (Hovakimian et al., 2003). It is 
recommended that banking supervision should be assigned to an agency formally separated from the 
central bank because the inflation rate is higher and more volatile in countries where the central bank 
acts as a monopolist regulator. Not all countries can afford deposit insurance, especially those with 
weak banks and regulators (Di Noia& Di Giorgio, 1999).  
Moreover, one part of literature argues that there are significant macroeconomic benefits from raising 
bank equity. Higher capital requirements lower leverage and the risk of bank bankruptcies (e.g. Admati 
et al., 2010). Another part of literature points out that there could be a significant cost of implementing 
a regime with higher capital requirements (i.e. BIS, 2010a). Higher capital requirements will increase 
banks’ marginal cost of loans if the marginal cost of capital is greater than the marginal cost of deposits, 
i.e. if there is a net cost of raising capital. In that case, a higher cost of equity financing relative to debt 
financing would lead banks to raise the price of their lending and could slow loan growth and hold back 
the economic recovery (Angelini et al., 2011).  

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Other studies have examined the impact of higher capital requirements on bank lending rates and the 
volume of lending. Kashyap et al. (2010) calibrate key parameters of the United States’ banking system 
to identify the impact of an increase in the equity-to-asset ratio. They find an upper bound of 6 basis 
points for the increase in U.S. banks’ lending spreads following an increase in the capital-to-asset ratio 
in line with that required under Basel III. BIS (2010a) estimates a significantly higher increase in the 
lending spread on the order of between 12.2 and 15.5 basis points, based on simulations with 38 
macroeconomic models maintained by the central banks of advanced economies. Angelini et al. (2011) 
reports similar findings. Similarly with the help of aggregate banking data Slovik and Cournede (2011) 
use accounting relations to find that lending spreads could be expected to increase by about 15 basis 
points.  
Several papers have analyzed the impact of monetary policy on banks with capital constraints ending 
in differing conclusions. Whether monetary policy affects bank lending or not depends on the 
assumption that bank loans are financed by reservable deposits or on the imperfect elasticity of the 
supply of non-reservable deposits. For example, Labadie (1995) using an overlapping generations 
framework shows that the addition of capital constraints on banks has no real effect. This result hinges 
on the assumption that banks can costlessly raise equity or external funds. On the other hand Kopecky 
and VanHoose (2004a, 2004b) following deterministic models assume an increasing marginal cost of 
equity in a competitive banking industry with capital constraints binding in the short term; monetary 
policy in their framework has real effects. Thakor (1996) uses an asymmetric information model of bank 
lending but maintains the assumption of costly external funds. He shows that monetary policy impacts 
bank lending. 
Furthermore, Bolton and Freixas (2006) provide an asymmetric information explanation for the high 
cost of external funds for banks. In a general equilibrium model they demonstrate how an open market 
sale of securities decreases the net interest margin for the bank which shifts lending away from firms 
with poor projects. On the other hand, firms with positive net present value projects as well as banks 
shift away from bonds since they are crowded out by government bonds. However, with the total capital 
constraint always binding, the total amount of lending does not change. Finally, Van den Heuvel (2002) 
using a dynamic model of banking analyses the role of bank capital channel in the transmission of 
monetary policy. He shows simulations in which the resulting interest rate mismatch implies that 
monetary policy affects the supply of loans through its impact on the value of bank capital.  
3. Data and Descriptive Statistics  
Annual data regarding commercial banks for a number of advanced European countries are obtained 
from the Bankscope database for the 2003-2010 period. Two different groupings of banks are 
examined. The first grouping includes the commercial banks in a group of European economies that 
experienced a banking crisis between 2007 and 2010. The second grouping includes the commercial 
banks in a group of European economies that did not experience a banking crisis between 2007 and 
2010.   
The sample consisted of advanced European economies where the amount of available information was 
sufficient for performing all necessary calculations.  
How may one define a banking crisis? The IMF (1998) defines a banking crisis as a situation in which 
bank runs and widespread failures induce banks to suspend the convertibility of their liabilities or 

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which compels the government to intervene in the banking system on a large scale. To identify banking 
crises existing empirical studies (Kaminsky& Reinhart, 1999; Glick & Hutchison, 2001; Bordo et al., 
2001 inter alia) rely on the observation of certain events such as forced bank closures, mergers, runs 
on financial institutions and government emerging measures. For instance, DemirgucKunt and 
Detragiache (1998) identify an episode as a crisis when at least one of the following conditions holds: 
(i) the ratio of non-performing assets to total assets in the banking system exceeded 10%; (ii) the cost 
of the rescue operation was at least 2% of the GDP; (iii) banking sector problems resulted in a large-
scale nationalization of banks; (iv) extensive bank runs took place or emergency measures such as 
deposit freezes, prolonged bank holidays, or generalized deposit guarantees were enacted by the 
government in response to the crisis.  
According to Von Hagen and Ho (2007) such observation has several shortcomings. First, it tends to 
identify banking crises too late. For example, the cost of a bailout is available only after a crisis and with 
a time lag. Events such as the nationalization of banks and bank holidays are likely to occur only when 
a crisis has already spread to the whole economy. Governments may provide hidden support to banks 
at the early stages of a crisis for political reasons; that is early policy interventions may not be 
observable. Second, there are few objective standards for deciding whether a given policy intervention 
is ‘large’. Third, the timing of crisis periods on this basis is difficult because the exact date of policy 
interventions is often uncertain or unclear (Caprio&Klingebiel, 1996). Fourth, such a method identifies 
crises only when they are severe enough to trigger market events. Crises successfully contained by 
prompt corrective policies are neglected.    
The index of money market pressure (IMP), developed by Von Hagen and Ho (2007) has been used in 
order to identify banking crises. They define the reservesto-bank deposits ratio γ as the ratio of total 
reserves held by the banking system to total non-bank deposits in the banking sector.   
In a period of high tension in the money market this ratio increases either because the central bank 
makes additional reserves available to the banking system or because depositors withdraw their funds 
from the banks. Actually, the IMP denotes the weighted average of changes in the ratio of reserves to 
bank deposits and changes in the short-term real interest rate (the real interest rate on short term 
loans), (figure 2).    
Figure 2: Ways of Reaction for the Central Bank, in Case of Increase in the  

 
The weights are the sample standard deviations of the two components. Thus, the index is defined as:   

t r t 
IMPt     

Demand  for  Reserves   

  

  

  

  

  

  

  

Increase in demand for  
reserves    

Central  
Bank   

Short - term i nterest  
rate    

Supply of bank reserves    

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r           (1) 
where∆γ is the change in total bank reserves relative to non-bank deposits, ∆r is the change in the short 
term real interest rate and σ refers to the standard deviation of each variable. Table 1 reports the year 
and quarter in which IMP meets two criteria: (i) it exceeds the 98.5 percentile, 97 percentile, and 95 
percentile of the sample distribution of IMP for each advanced economy; and (ii) there is an increase 
in IMP by at least five percent from the previous period. The first condition assures that only 
exceptional events are identified as crises. However, since every empirical distribution must have a 98.5 
percentile, the second condition is used to allow for the possibility that countries had no banking crisis 
during the sample period. Note that relaxing the first condition and using a lower percentile raises the 
risk of calling too many episodes crises, while tightening it increases the risk of missing true crises.   
Table 1 identifies banking crises in European economies using the IMP. Based on this index, Austria, 
Belgium, Germany, Greece, Netherlands, Sweden, Spain, Italy, and the United Kingdom are identified 
as having experienced a banking crisis between 2007 and 2010 when the cutoff is the 98.5 percentile 
(shown in faded color).  
Table 1: Banking Crises in European Economies Identified Using the Von Hagen and Ho 
(2007) Index of Money Market Pressure.  
  
    Thresholds    
Country  98.5%  97%  95%  
Austria  2008q4  1994q4,2008q4  1994q4,1995q4,1999q3,2008q4  
Belgium  2006q4,2008q3  2005q4,2006q4,2008q3  1997q4,2005q4,2006q4,2008q3  
Czech 
Republic  

1997q2,1997q4  1997q2,1997q4,2008q4  1994q1,1997q2,1997q4,2008q4  

Denmark  1993q1,1993q3  1993q1,1993q3,2000q3  1993q1,1993q3,2000q3,2008q3  
Finland  1992q3,1999q4  1992q3,1999q4,2008q3  1992q3,1999q4,2000q3,2008q3  
France  1992q3,1993q3  1992q3,1993q3  1992q3,1993q3,2008q3  
Germany  2008q3  1997q4,2008q3  1997q4,2000q4,2008q3  
Greece  2008q4,2010q1  1993q1,2008q4,2010q1  1993q1,1998q3,2008q4,2010q1  
Ireland  1992q3  1992q3  1992q3,2008q3,2009q1  
Italy  1992q3,2008q4  1992q3,2000q2,2008q4  1992q3,1999q4,2000q2,2008q4  
Netherlands  2008q3  2003q3,2008q3  2001q3,2003q3,2008q3,2009q3  
Portugal  1992q3,1994q2  1992q3,1994q2,2008q3  1992q3,1994q2,2007q3,2008q3  
Spain  1992q4,2008q3  1992q4,2007q3,2008q3  1992q4,1995q2,2007q3,2008q3  
Sweden  2008q4  2008q4  2008q4,2009q3  
United Kingdom  2008q3,2009q2  1993q3,2008q3,2009q2  1993q3,2007q3,2008q3,2009q2  
Note: Each column reports the year and the quarter in which the Von Hagen and Ho   
(2007) index of money market pressure (IMP) meets two criteria: (i) it exceeds the 98.5 percentile, 97 
percentile, and 95 percentile of the sample distribution of IMP for each advanced economy in the 
sample; and (ii) the increase in IMP from the previous period is by at least five percent (see text for 
explanation). Faded countries represent advance European economies identified as having experienced 
a banking crisis between 2007 and 2010.  

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A possible objection against this method might be that modern banking crises are asset-side rather 
liability-side crises. An example is that a banking crisis caused primarily by a collapse in real estates’ 
prices (e.g. USA in 2007 or China in 2013) or a wave of corporate bankruptcies. But if the demand for 
reserves increases when the quality of bank assets deteriorates, such a dichotomy is irrelevant for the 
purposes of this study. A second objection is that this method is not applicable to environments where 
interest rates are controlled by the central bank.  
Tightening the second condition increases the risk of missing true crisis episodes. In the empirical 
work, using a 10% minimum increase would exclude some well-known crisis episodes in the data.  
But the IMP has the advantage that its quality does not depend on the flexibility of interest rates as long 
as the central bank’s interest rate management relies on market measures to control the interest rate. 
A third objection might be that using the IMP, one can identify the beginning but not the end of a 
banking crisis. This is true, but after studying the more relevant literature it seems that there is no 
consensus on what kind of criteria one should use to declare that a crisis is over. Such issue is 
recommended for further research. 
Later on, in tables 2-3 bank profitability is examined and represented by the return on equity (ROE). It 
seems that this measurement was markedly affected by the 2007-2010 financial crisis for each grouping 
of banks. Further insight into the changes in the banks’ profitability can be obtained from the equation 
expressing the ROE as the product of the equity multiplier  (A/E) and the return on assets (ROA). The 
ROA can be decomposed using methodology of Koch and MacDonald (2007) as follows:  
A A   NIM NII NIE SG PLL TAX       (2)  
ROE E ROA E         

 
A A A A A A   

, where E is equity; A is total assets; NIM is the net interest margin calculated as the difference between 
interest income (II) and interest expense (IE); NII is non– interest income; SG is security gains (or 
losses); NIE is non–interest expense; PLL is provisions for loan losses, and TAX is the taxes paid.  
Table 2 shows the degree of banks’ profitability - as measured by the ROE - in European economies 
that registered a financial crisis between 2007 and 2010.These banks only registered a negative ROE 
in 2009 (shown in faded color). The decline in these banks profitability is largely attributable to the 
decline in (NII+SG-TAX)/A stemming from losses on securities (a small percentage of the decline can 
also be attributed to NII because of the decline in off-balance sheet assets; it is presumed that taxes did 
not change appreciably over this period and the 0.4 percentage point increase in the loan loss provision 
ratio that are amplified by the sharp increase in the equity multiplier between 2007 and 2010.   
The equity multiplier for this group of banks increases substantially in 2009. Furthermore, the 
noninterest expense ratio declined by almost one percentage point between 2007 and 2010. 
 
 
 
 
 
 

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Table 2: Banking Indicators for European Economies that had a Banking  
Crisis in 2007-2010  
  

  2007   2008   2009   2010   

Equity-asset ratio           
Mean   14.2   13.5   11.2   10.9   
Median   8.7   7.9   8.1   8.2   
Std. Dev.   17.1   17.4   12.8   12.6   
No. of Obs.   
  
Total capital ratio   

892   
  
  

929   
  
  

497   
  
  

484   
  
  

Mean   18.1   14.8   14.9   14.8   
Median   12.2   12.4   12.9   12.8   
Std. Dev.   29.1   9.7   8.3   8.2   
No. of Obs.   
  
Tier 1 capital ratio   

364   
  
  

461   
  
  

101   
  
  

95   
  
  

Mean   15.7   12.4   12.4   12.4   
Median   9.6   10.6   10.8   10.6   
Std. Dev.   30.7   9.5   7.5   7.3   
No. of Obs.   
  
Return on average equity (ROE)   

344   
  
  

424   
  
  

317   
  
  

296   
  
  

Mean   9.8   3.4   -0.5   0.3   
Median   8.2   4.4   4.1   3.9   
Std. Dev.   17.5   28.3   24.1   23.8   
No. of Obs.   
  
Decomposition of bank profitability   

911   
  
  

937   
  
  

492   
  
  

488   
  
  

Equity multiplier (A/E)   7.2   7.4   8.5   8.1   
Net interest margin (NIM /A )   3.2   2.6   3.1   2.9   
Interest expense to total assets (IE/A)   3.3   2.6   1.7   1.5   
Noninterest expenses (NIE /A )   5.2   5.1   4.0   3.8   
Loan loss provisions (PLL/A )   0.4   0.5   0.9   0.7   
Noninterest income plus 
securities gains,  net of taxes (NII 
+ SG - TAX )/A   
  

4.1   
  
  

3.4   
  
  

2.1   
  
  

1.8   
  
  

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Off-balance sheet items to total assets   

Mean   21.4   18.3   19.3   18.5   
Median   6.5   5.1   9.1   8.8   
Std. Dev.   61.6   55.3   36.8   32.3   
No. of Obs.   701   744   426   389   

  
Similar results are reported in table 3 for the banks in European countries that did not experience a 
financial crisis with the exception of the decline in ROE being larger for this group of banks (shown in 
faded color) due to their larger equity multiplier.  
Table 3: Banking Indicators for European Economies that did not have a  
Banking Crisis in 2007-2010  
  

  2007   2008   2009   2010   

Equity-asset ratio           
Mean   8.7   7.6   7.3   7.1   
Median   6.3   5.6   5.4   5.1   
Std. Dev.   8.8   8.3   8.9   8.2   
No. of Obs.   
  
Total capital ratio   

333   
  
  

333   
  
  

224   
  
  

218   
  
  

Mean   13.9   13.5   14.1   13.8   
Median   11.2   10.9   12.1   11.7   
Std. Dev.   18.6   16.8   16.9   16.7   
No. of Obs.   
  
Tier 1 capital ratio   

231   
  
  

242   
  
  

264   
  
  

255   
  
  

Mean   11.1   10.9   11.5   11.1   
Median   8.5   9.2   9.5   9.3   
Std. Dev.   18.8   17.3   17.4   17.3   
No. of Obs.   
  
Return on average equity 
(ROE)   

221   
  
  

239   
  
  

203   
  
  

188   
  
  

Mean   8.9   2.7   -5.1   3.4   
Median   8.6   4.5   1.3   1.1   
Std. Dev.   18.6   30.5   38.4   37.8   
No. of Obs.   
  

351   
  
  

351   
  
  

256   
  
  

222   
  
  

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Decomposition of bank 
profitability   

Equity multiplier (A/E)   11.1   12.1   12.8   12.1   
Net interest margin (NIM /A )   2.3   2.3   2.0   1.9   
Interest expense to total 
assets (IE/A)   

2.1   2.2   1.0   1.0   

Noninterest expenses (NIE /A 
)   

2.2   2.2   2.6   2.5   

Loan loss provisions (PLL/A)   0.1   0.2   0.6   0.3   
Noninterest income plus securities 
gains,  1.4  net of taxes (NII + SG - 
TAX )/A   
    
Off-balance sheet items to total 
assets     

1.3   
  
  

1.3   
  
  

1.3   
  
  

Mean  20.1   17.8   13.1   13.1   
Median  8.3   6.2   2.6   2.2   
Std. Dev.  38.1   32.2   31.4   31.2   
No. of Obs.  337   337   227   211   

In summary, the information derived from table 2 and table 3 suggests that the financial crisis had a 
significant negative impact on bank profitability including banks in countries that did not experience a 
crisis. The decline was directly associated mostly with capital losses on marketable securities. As a 
consequence banks experienced a significant deterioration in their equity-to-asset ratios.  
4. Specification of Empirical Results   
Following Greene (2012), Cosimano and Hakura (2011) and Chami and Cosimano (2010), the level of 
capital held by banks depends on the banks’ anticipation of their optimal loans in the future. Capital is 
seen as a call option in which the strike price is the difference between the expected optimal loans and 
the amount of loans supported by the capital. The capital limits the amount of loans since a fraction of 
the total loans must be held as capital. If the optimal amount of loans during the next period exceeds 
this limit, then the bank would suffer a lost opportunity which is measured by the shadow price on the 
capital constraint (Greene, 2012). In this case the total capital has a positive option value and the bank 
will tend to hold more capital than required in order to gain flexibility to increase its supply of loans in 
the future. If on the other hand there is a low demand for loans in the future such that the shock to 
demand is below the critical level, the total capital serves no purpose resulting in zero payoffs.   
Thereinafter, banks with more capital will have a higher strike price since their loan capacity is greater. 
As a result, an increase in capital leads to a decrease in the demand for future capital, K’. An increase 
in the marginal cost of loans leads an impending forecast of a higher marginal cost by the bank since 
such changes tend to persist into the future. Consequently, a bank anticipates a decrease in their 
optimal future loans and will in turn reduce their holding of capital at present. Similarly - as stated in 
Cosimano and Hakura (2011) - an increase in marginal revenue related to stronger economic activity 
will lead to an increase in optimal loans so that the optimal capital goes up. 

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In view of this and following Barajas et al. (2010), the relation for the banks’ choice of capital is specified 
as:   
  
K 0 1 2 K Δ K 3 4 K rD 5 6 K CL CD

7   log(A)   (3)  

 

 
A  A  A  A   A  
Here, K is total current capital, Κ’ is future capital, A is total assets, rD is the interest rate on deposits, 
CL is the non-interest marginal factor cost of loans and CD is the  non-  K  interest 
marginal factor cost of deposits. Call options 1 2 0  
are generally A decreasing and convex in the strike price (Kolb  
&Overdahl, 2010). As a result it is expected that  such that α1<0, α2>0. Similarly, it is expected that 
α3<0, α4>0, α5<0 and    
α6>0. Consequently, a decrease in past capital which lowers the strike price should lead to a significant 
increase in total current capital. This impact should be smaller when the bank has more initial capital 
consistent with the convex property of call options (Hull, 2012). In addition, a decrease in interest and 
non-interest expenses should lead to an increase in bank capital at a decreasing rate.    
Banks are assumed to have some monopoly power so that they choose the interest rate on loans (rL) 
such that the marginal revenue of loans equals to its marginal cost (Claessens&Laeven, 2004). The 
marginal cost consists of the interest rate on deposits A D K (rD) and the non-interest marginal cost of 
loans and r deposits A respectively CLand CD. The marginal cost of loans also depends on the risk 
adjusted rate of return on capital (RAROC)  (see figure 3).     
Figure 3: Relationship of Marginal Revenue and Cost of Loans  

 
Thus, following Cosimano and Hakura (2011) total marginal cost (MC) is given by  
MC D rD CD CL A DrK    (4) 

 
A   

  

  

  

  

  

  

  

  

  

  

Marginal cost of loans   N on - interest marginal cost  
of loans   

Interest rate on  deposits   

N on - interest marginal cost  
of  deposits   

Marginal  
revenue of  
loans   

Interest  
rate on  
loans   

R isk adjusted rate of return  
on capital   

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Here rK is the return on equity (ROE), A is total assets and D is deposits so that bank capital is K’ = A - 
D. As a result the marginal cost raises with an increase in bank capital only if rK>(rD+ CD). Moreover 
the marginal revenue of loans depends on economic activity M as it impacts the demand for loans. 
Following Fase (1995) the optimal loan rate is given by:  
  
rL b0 b1rD b2 CL CD b3 K b4 log A b5 M 1    (5) A 

  
An increase in the deposit rate, the non-interest cost of deposits and the provision for loan losses would 
lead to an increase in the loan rate since the  
K marginal cost of loans would increase. The marginal cost also increases with an A increase in 
RAROC. This effect is measured by the optimal capital asset ratio   
as given in Equation 5 above. An increase in the demand for loans would raise  
both marginal revenue and the loan rate. This effect is captured by the level of economic activity (M) as 
measured by real GDP and the inflation rate. Finally, 1 denotes the estimation error.   
With monopoly power the demand for loans (L) depends on the optimal loan rate of the bank as 
determined in (5) above and the level of economic activity (M). As a result the demand for loans (L) can 
be modeled as: 
L c0 c1 rL c2 M 2         
, where ci, (i=0,1,2) are parameters to be estimated. It is expected that an increase in the loan rate would 
reduce the demand for loans and hence loans issued by the bank. On the other hand an increase in 
economic activity is expected to raise the demand for loans. Note thatc1and c2capture the long-run 
responses of loans to changes in loan rates and the level of economic activity.   
Hull (2012) argues that banks simultaneously choose the optimal amount of capital to hold, the loan 
rate, and the quantity of loans. Because of this simultaneity a GMM estimation procedure is properly 
used.   
In the first stage (figure 4) the capital regression is estimated to determine the bank’s optimal (or 
projected) level of capital (equation 3). The change in the capitalto-asset ratio, the interest expense 
ratio, the non-interest expense ratio and the nonperforming loans-to-total assets ratio as well as the 
interaction of each of these variables with the previous period capital-to-asset ratio are assumed to be 
instruments for the optimal capital ratio.   
  

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The predicted demand for capital is then used in the second-stage regression (equation 5) for the bank’s 
loan rate (figure 5).   
Figure 5: Second stage in the Generalized Method of Moment Procedure  
  

   
The GMM estimations are conducted following Greene (2012) and Zeileis (2004) using the Bartlett 
kernel function (analyzed in the following section) thereby yielding heteroskedasticity - 
autocorrelation-consistent (HAC) standard errors (using Matlab R2011b software). Lastly the 
regression for the demand for loans (equation 6) is estimated using the loan rates predicted by the 
GMM estimations as an explanatory variable (figure 6).   
Figure 6: Regression for the Demand for Loans  

   
The estimations for the two grouping of banks are conducted using data for the 2003 
to 2010 period. The estimations are conducted on a country-by-country basis. The number of banks 
included in every assessment depends on the degree of concentration of the banking system in each 
country and the availability/accessibility of the data in the Bankscope database.   
5. Heteroskedasticity and Autocorrelation Consistent (HAC) Standard Errors   
Following Laszlo (1999) the following equation shows how the asymptotic covariance matrix of the 
GMM estimator could be derived in the presence of conditional heteroskedasticity:  
  

n 

 
  

where ˆ is the diagonal matrix of squared residuals uˆi2from ~ , the consistent but not necessarily 
efficient first-step GMM estimator. The resulting estimateSˆcan be used to conduct consistent inference 

Demand for 
loans  

Sˆ 1n i 1 uˆi2Zi Zi   
1n ˆ   

      (7)  

Figure 4: First stage in the Generalized Met hod of Moment procedure   

  

  

  

  

  

  

  

  

  

Optimal  
level of  
capital 

  

Interest  
expense   

Capital - to - asset   

Non - interest  
expense   

First  
stage  
GMM    

Capit 
al    

Non - performing  
loans - to - total assets   

P revious  
period  

capital - to - 
asset   

Loan rate   Second stage GMM    
Optimallevel of  

capital   

Simple regression    
Loan  
rate   

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48 | P a g e  

 j 

for the first-step estimator or it can be used to obtain and conduct inference for the efficient GMM 
estimator.  
The estimator is now further extended to handle the case of non-independent  
errors in a time series context. The notation is correspondingly  

gt g s 0,t s 
changed so that observations are indexed by t and s rather than i. In the presence of serial correlation . 
In order to derive consistent estimates of S, j gtgt j is defined as the auto-covariance matrix 
for lag j. The long-run covariance matrix can be then written  

 
S AVar g 0 j j         (8)  
j 1   
, which may be seen as a generalization of equation (7) with 0 gig i and j 

gtgt j , j 1, 2,   
is defined as the product ofZt andut , the auto-covariance matrices may be  
expressed as  

j utut jZt Zt j .ut ˆ j andut j are then replaced by consistent residuals from first-stage 
estimation to compute the sample auto-covariance matrices defined as   

ˆ 1 n j   gˆtgˆt j 1 n j Zt uˆtuˆt jZt j      
 (9) j 

 
 

n   t 1 n t 1  
There is no existence of an infinite number of sample autocovariances to insert into the infinite sum in 
equation (8). Furthermore, it is not possible to simply insert all the autocovariances from 1 through n 
because this would imply that the  
gˆ i is going off to infinity with the sample number of sample orthogonality conditions size which 
precludes obtaining a consistent estimate of S. The autocovariances must converge to zero 
asymptotically as n increases. One way to handle this in would be for the summation to be truncated at 
a specified lag q. Thus the S matrix can be estimated by 
Sˆ ˆ0 q1 k qjn ˆj ˆ j     (10) j  

  
ut and u t j are replaced by consistent estimates from first-stage , where 
estimation. The kernel function,  j 

 
kqn   q n defined as the  
applies appropriate weights to the terms of the summation with 
bandwidth of the kernel possibly as a function of n (Hayashi, 2000). In many kernels consistency is 
obtained by having the weight Sˆ fall to zero after a certain number 1 of lags. One important and 
frequently used approach to this problem is  

qn that of Newey and West (1987) which generates using the Bartlett kernel function and a 
user-specified value of q. For the Bartlett kernel    

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k  
if j qn 1, 0 otherwise. These estimates are said to be HAC as they incorporate equation7 in 
computing.   
The Newey–West (Bartlett kernel function) specification is only one of many feasible HAC estimators 
of the covariance matrix. Andrews (1991) shows that in the class of positive semi-definite kernels the 
rate of convergence of Sˆ S depends on the choice of kernel and bandwidth. The Bartlett kernel’s 
performance is improved by those in a subset of this class including the Quadratic Spectral (QS) kernel. 
Most (but not all) of these kernels guarantee that the estimatedSˆ is positive, definite and therefore 
always invertible (Hall, 2005).  
Under conditional homoskedasticity the expression for the autocovariance matrix simplifies: 

j utut j tZt j utut j tZt j       (11)  
And the calculations of the corresponding kernel estimators also simplify (Hayashi, 2000). These 
estimators may perform better than their heteroskedastic/robust counterparts in finite samples.  
6. Cross-Country Estimation Results  
6.1Impact of Basel III on Banking Performance  
Table 4 reports the results of estimating equation (3) as the first stage in the GMM procedure on a 
country by country basis for the two groupings of banks. Due to the availability of data for countries 
that experienced a financial crisis between 2007 and 2010, results are reported for Germany, the United 
Kingdom, Greece and Sweden. On the other hand, France, Netherlands and Austria were excluded 
because of insufficient data. For the second grouping of banks in countries which did not experience a 
crisis, results are reported for Czech Republic, Denmark and Ireland. Even though the change in the 
equity-to-asset ratio has the predicted sign α1<0 for the U. K., Greece, Denmark and Ireland, it is 
statistically significant for only two countries (the U.K. and Denmark). The estimated coefficients on 
this variable for the other countries have the wrong sign and are statistically insignificant except for 
Sweden.   
The interaction term α2>0 has the correct sign for the U.K., Greece, Denmark, and Ireland; however 
only the U.K., Denmark and Ireland are statistically significant. The other countries have the wrong 
sign with Germany and Sweden being statistically significant. The results for the interest expense-to-
asset ratio are more consistent with the theory. All the countries that experienced a crisis have the 
correct signs α3<0 and α4>0 which are all statistically significant except Greece. Among the counties 
that did not experience a crisis, Denmark, Czech Republic, and Ireland had correctly signed and 
significant coefficients.  
Furthermore, the non-interest expense ratio has statistically significant and correct signs α5<0 and 
α6>0 for the U.K., Greece, Sweden, and Denmark. Nonperforming loans have significant and correct 
signs for none of the countries. The logarithm of total assets is only significant at the one percent level 
for the U.K. The coefficient on the logarithm of assets is negative for most of the countries implying 
that larger banks have smaller equity-to-asset ratios. Overall, the results are consistent with equation 
(3).   
The estimates for equation (5) for the two country groupings are provided in Table 5. Equity and 
interest expense ratios have the predicted signs and are statistically significant at the five percent level. 
The non-interest expense-to-asset ratio has the correct positive effect on the loan income of the banks 

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for all countries. They are statistically significant except for Denmark and Ireland. The results for 
nonperforming loans-to-assets are insignificant for most of the countries.    
Furthermore, table 6 reports the results of estimating the long run loan demand equation (6) for the 
country-by-country estimations. For most of the countries the loan rate has the expected negative 
impact on the loans issued by the bank. Given the mean predicted loan rate and loans for the banks in 
each respective country, the elasticity of loan demand with respect to the predicted loan rate in table 7 
is estimated to range from 1.00 percent in Ireland to 6.59 percent in Denmark. Consequently, the banks 
across most of these countries operate at loan levels associated with positive marginal revenue.   
Table 7: Impact of a 1.3 Percentage Point Increase in the Equity-Asset Ratio on Loans 
Based on Regressions for 2003–2010  
  

  
  

Impact on  
loan rate *   

Net Cost   Elasticity of   
of Raising Equity Loan 
Demand  
**   ***   

Percentage  
change in loans 
****   

Crisis 
countries   

        

Germany   0.13   0.11   -1.79   -7.11   
Sweden   0.04   0.01   -5.88   -3.64   
U.K.   0.06   0.04   -2.46   -4.16   
Average   
  
Other 
countries   

0.13   
  
  

0.16   
  
  

-3.37   
  
  

-4.97   
  
  

Denmark   0.23   0.17   -6.59   -31.11   
Ireland   0.21   0.20   -1.00   -6.23   
Average   0.22   0.18   -3.79   -18.67   
Source: Authors calculations  
* Based on estimates reported in table 5.  
** Impact on loan rate times the change in asset-to-equity ratio (equity multiplier). ***The elasticity of 
loan demand for each country banks is calculated by multiplying the estimated coefficient for the loan 
rate reported in table 6 by the average loan rate divided by average level of loans in the sample.  
**** This is calculated as the product of the percentage increase in the loan rate times the elasticity of 
loan demand with respect to changes in the loan rate.   
Table 8 summarizes the results when the estimations are conducted excluding the crisis period from 
the data. The average impact of the equity-to-asset ratio on the loan rate is slightly smaller when the 
crisis period is excluded for all countries. The elasticity of loan demand is on average lower in crisis 
countries and higher for noncrisis countries when the crisis period is excluded. This result might imply 
that the banks’ customers in crisis (non crisis) countries had a bigger (smaller) change in their demand 
for loans during the financial crisis. 

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Table 8: Impact of a 1.3 Percentage Point Increase in the Equity-Asset Ratio on Loans 
Based on Regressions for 2003–2007  
  

  
  

Impact on  
loan rate   

Net Cost  Elasticity of  Percentage   
of Raising Equity Loan Demand change in loans 
*** 
*   **   

Crisis countries           

Germany   0.11   0.09   -2.09   -7.63   
U.K.   0.02   0.02   -2.14   -2.16   
Average   
  
Other countries   

0.06   
  
  

0.05   
  
  

-2.11   
  
  

-4.89   
  
  

Denmark   0.19   0.13   -9.66   -39.23   
 
Source: Authors calculations  
* Impact on loan rate times the change in asset-to-equity ratio (equity multiplier). ** The elasticity 
of loan demand for each country banks is calculated by multiplying the estimated coefficient for the 
impact of the predicted loan rate from the secondstage GMM regression on loan demand by the 
average loan rate divided by average level of loans in the sample.  
*** This is calculated as the product of the percentage increase in the loan rate times the elasticity of 
loan demand with respect to changes in the loan rate.   
6.2 Comparing the Results with those of Other Studies  
To phase in the new regulations in a manner that is compatible with the global economic recovery, the 
Bank of International Settlements (BIS) and the Financial Stability Board (FSB) undertook studies to 
assess the macroeconomic effects of the transition to higher capital and liquidity requirements (Sinha, 
2012). In February 2010, a Macroeconomic Assessment Group (MAG) was set up by the BCBS (Basel 
Committee on Banking Supervision) and FSB which submitted an interim report in August 2010 (BIS, 
2010a) and a final report in December 2010 (BIS, 2010c). The MAG’s quantitative analysis was 
complemented by consultations with academics and experts in the private sector as well as with the 
IMF. The MAG applied common methodologies based on a set of scenariosfor shifts in capital and 
liquidity requirements over different transition periods.   
The MAG analysis proceeds on the basis that since it is more expensive for banks to fund assets with 
capital than with deposits or wholesale debt, banks facing stronger capital requirements will seek to 
use a combination of increasing retained earnings and issuing equity as well as reducing Risk Weighted 
Assets(RWAs), (Cornford, 2010). The approach will depend at least partially on the length of time over 
which capital needs to be increased. If the time span is shorter, banks are likely to emphasise equity 
issuance, shift in asset composition and reduced lending. In a longer implementation schedule banks 
will have more flexibility with regard to mechanisms and they may place more reliance on raising 
additional capital primarily through retained earnings which will substantially mitigate the impact on 
credit supply and eventually on aggregate activity. Based on evidence from past episodes the MAG 

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analysis assumes that banks will initially increase lending margins and reduce the quantity of new 
lending. Any increase in the cost and decline in the supply of bank loans could have a transitory impact 
on growth especially in sectors that rely heavily on bank credit. In the longer term, however, as banks 
become less risky both the cost and quantity of credit should recover, reversing the impact on 
consumption and investment.  
Based on the above intuition the MAG analysis was largely formulated on a two-step approach. The 
first step involves estimating the effect of higher capital targets on lending spreads and lending volumes 
using statistical relationships and accounting identities to predict how banks will adjust. The second 
step takes these forecast paths for lending spreads and volumes as inputs into standard macroeconomic 
forecasting models in use at central banks and regulatory agencies. These models are then used to 
estimate the effects of changes to lending spreads and bank lending standards on consumption, 
investment and other macroeconomic variables.   
In particular the 2009 Tier 1 ratio for Group 1 banks in the BIS study is 10.5 percent. It is interesting to 
note that this study’s 5.1 ROE is identical to the net equityto-risk weighted asset (CET1) ratio for their 
Group 1 banks (banks that have over three billion Euros of Tier 1 capital) while it is 11.1 percent before 
the changes in regulation (i.e. for the gross common equity tier 1 ratio) in the BIS study. This result 
suggests that the new equity to risk-weighted asset ratio is close to a pure equity-toasset ratio. The BIS 
estimates that under Basel III the equity to risk-weighted asset (CET1) ratio would fall to 5.7 percent 
from 11.1 percent for the gross CET1 ratio (pre-Basel III ratio) for Group 1 banks. Following Cosimano 
and Hakura (2011) it would be assumed that most of this decline is associated with tighter standards 
on bank equity with the removal of goodwill being the most important one. The rest of the decline arises 
from stricter rules on RWAs. The biggest contributors to this increase are adjustments for counterparty 
risk and the application of the capital definition.   
Table 7 reports calculations assuming capital shortfall of 1.3 percentage points under Basel III for the 
cross-country results. For the crisis countries a 1.3 percentage point increase in equity-asset ratio is 
estimated to have a more substantial impact on loans (5.07%). The impact of Basel III is largest in the 
non-crisis Denmark since it is estimated to have both a relatively high elasticity of loan demand with 
respect to changes in the loan rate and a high net cost of raising equity.   
If the crisis period is excluded from the estimation period (table 8) then the impact of Basel III in the 
crisis countries is slightly smaller following the lower elasticity of demand across these countries. On 
the other hand, the average elasticity of loan demand is larger for the non-crisis countries which 
dominate the decline in the cost of equity under the shorter time period.  
The results for the loan rates reported in column 1 in table 7 are broadly consistent with the findings 
from BIS (2010c) for the loan rate which showed that the mean lending rate (weighted by GDP) would 
increase (across 53 models) by 16.7 basis points over eight years and 15 basis points respectively. 
However the magnitude is significantly above the upper bound of 6 basis points calibrated in Kashyap 
et al. (2010).    
7.  Conclusions  
Basel III was developed in response to the deficiencies in financial regulation revealed by the late2000s 
financial crisis and the flaws spotted in Basel II as discussed in this paper. It is a global regulatory 
standard on bank capital adequacy, stress testing and market liquidity risk agreed upon by the members 

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of the Basel Committee on Banking Supervision in 2010-2011. This innovative framework strengthens 
bank capital requirements and introduces new regulatory requirements on bank liquidity and bank 
leverage. The change in the calculation of loan risk in Basel II for instance which some consider a causal 
factor in the credit bubble prior to the 2007-2008 collapse (in Basel II one of the principal factors of 
financial risk management was outsourced to companies that were not subject to supervision i.e. credit 
rating agencies). Ratings of creditworthiness and bonds, financial bundles and various other financial 
instruments were conducted by official agencies without supervision thus leading to AAA ratings on 
mortgage-backed securities, credit default swaps, and other instruments that proved in practice to be 
extremely bad credit risks. In Basel III a more formal scenario analysis is applied.  
This paper aims to broaden and deepen the understanding of the likely impact of the new capital 
requirements introduced under the Basel III framework on bank lending rates and volume of lending. 
The contribution of this paper is threefold concerning the understanding and testing of the impact of 
the new regulations on the banks. Firstly, the paper derives empirically testable relations from a 
structural model of the capital channel of monetary policy developed by Chami and Cosimano (2010). 
In doing so it follows Barajas et al. (2010) analysis of large bank holding companies in the United States. 
In this model loan demand shocks are transmitted to the credit supply via the regulatory capital 
constraint. In particular, a bank’s decision to hold capital is modeled as a call option on the optimal 
future loans issued by the bank. This option value of the bank’s capital increases when the expected 
level of loans and the amount of capital required by the regulator increase.   
The bank’s choice of capital influences its loan rate since the marginal cost of loans is a weighted average 
of the marginal cost of deposits and equity. Consequently the loan rate increases with an increase in 
required capital as long as the marginal cost of equity exceeds the marginal cost of deposits.  
On this basis, the paper’s results suggest that banks’ responses will vary considerably from one 
European economy to another reflecting cross-country variations in the tightness of capital constraints, 
banks’ net cost of raising equity, and elasticities of loan demand with respect to changes in loan rates. 
The country-bycountry estimations which include both large and small banks for which data is available 
in each country suggest that the net cost of raising equity by 1.3 percentage points ranges from 1 basis 
point in Sweden to 20 basis points in Ireland. Similarly the estimated elasticities of loan demand range 
from 1.0 percent in Ireland to 6.59 percent in Denmark. As a result the average impact of a 1.3 
percentage point increase in the equity-asset ratio on loan growth for the crisis countries is 5.07 
percent. This impact is significantly higher in the non-crisis countries such as Ireland and Denmark. 
The potential for a substantial impact of capital requirements makes it even more important for policy 
makers in these countries to identify exactly why the elasticity of loan demand or cost of equity is so 
high in these economies.  
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Table 4: GMM First-Stage Regressions for Holdings of Capital  
  

  
  
Note: The table shows the first stage GMM regression for the equity-asset ratio. Heteroskedasticity- 
and autocorrelation-consistent standard errors are shown in parentheses; significances of 1 (***), 5(**), 
and 10 (*) percent are indicated. 

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Table 5: GMM Second-Stage Regressions for Loan Rate  

Note: The table shows the second stage GMM regression for the loan rate. Heteroskedasticity- and 
autocorrelation-consistent standard errors are shown in parentheses; significances of 1 (***), 5(**), and 
10 (*) percent are indicated.  
Table 6: Loan Demand Equations  

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Note: Robust standard errors are shown in parentheses, and significances of 1 (***), 5 (**), and 10 (*) 
percent are indicated.  
  
Appendix  
  
The Generalized Method of Moments was introduced by Hansen, (1982). The equation to be estimated 
is, in matrix notation, y X uwith typical row yi Xi ui . The matrix of regressorsX is n × K, 
where n is the number of observations. Some of the regressors are endogenous, so that Xiui 

0. The set of regressors are being partitionedinto [X1 X2], with the K1regressorsX1 assumed under the 
null to be endogenous and the K2 (K − K1)  
remaining regressorsX2 assumed exogenous, giving yi X1X2 1 2 u .    
  
The set of instrumental variables is Z and is n × L. This is the full set of variables that are assumed to 
be exogenous, i.e. iui 0. The instruments are partitioned into [Z1 Z2], where the L1instruments 
Z1are excluded instruments and the remaining L2 (L−L1) instruments Z2 X2 are the included 
instruments/exogenous regressors (Baum, 2006):  
  
RegressorsX = [X1 X2] = [X1 Z2] = [Endogenous Exogenous]  
  
Instruments Z = [Z1 Z2] = [Excluded Included]  
  

  

  
  

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The order condition for identification of the equation is L  K implying there must be at least as many 
excluded instruments (L1) as there are endogenous regressors (K1) as Z2 is common to both lists. If L = 
K, the equation is exactly identified by the order condition; if L > K, the equation is over-identified. The 
order condition is necessary but not sufficient for identification.  
  
The assumption that the instruments Z are exogenous can be expressed as E(Ziui) = 0. In the case of 
linear GMM the L instruments give a set of L moments:gi iui  

i yi Xi , where gi is L × 1. The exogeneity of the instruments means that there are L moment 
conditions, or orthogonality conditions, that will be satisfied at the true value of : 

gi 0. Each of the L moment equations corresponds to a sample moment. For some given 
estimator ˆ , these L sample moments could be written asg ˆ n1 in 1   gi ˆ  
1 i n1 i yi i ˆ 1n uˆ.  

n 

 
  
The intuition behind GMM is to choose an estimator for that brings g ˆ as close  
to zero as possible. If the equation to be estimated is exactly identified, so that L = K, then there are as 
many equations (the L moment conditions) as unknowns: theK coefficients in ˆ .  
In this case it is possible to finda ˆ that solves g ˆ =0.  
  
If the equation is over-identified, however, so that L>K, then there are more  
equations than unknowns. In general it will not be possible to find a ˆ that will set all L sample moment 
conditions exactly to zero. In this case, an L × L weighting matrix W is used in order to construct a 
quadratic form in the moment conditions. This gives the GMM objective 
function:J ˆ ng ˆ Wg ˆ . A GMM estimator for is the ˆ that minimizesJ ˆ : 
 ˆGMM  arg min ˆ J ˆ ng ˆ Wg ˆ .  
  
In the linear case, deriving and solving the K first order conditions J ˆ 0 (treating ˆ 

 
W as a matrix of constants) yields the GMM estimator (The results of the minimization, and hence the 
GMM estimator, will be the same for weighting matrices that differ by a constant of proportionality).  
  
 ˆGMM X ZWZ X 1X ZWZ y       (a)  
  
The GMM estimator is consistent for any symmetric positive definite weighting matrix W, and thus 
there are as many GMM estimators as there are choices of weighting matrix W. Efficiency is not 
guaranteed for an arbitrary W, so the estimator defined in Equation (a) is referred as the possibly 
inefficient GMM estimator.   
  
The authors are particularly interested in efficient GMM estimators, namely GMM estimators with 
minimum asymptotic variance. Moreover, for any GMM estimator to be useful, inference should be 

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conducted and for that,estimates of the variance of the estimator are needed. Both require estimates of 
the covariance matrix of orthogonality conditions, a key concept in GMM estimation.  
  
Denoting by S the asymptotic covariance matrix of the moment conditions g:S  
AVar   g limn 1n uu where S is an L×L matrix and g = 1n 

u . That is, S is the  
variance of the limiting distribution of ng . The asymptotic distribution of the possibly inefficient 
GMMestimator can be writtenas follows. Let QXZ X i Z i . The asymptotic variance of the inefficient 
GMMestimator defined by an arbitrary weighting matrix W is given by:  
  
 V ˆGMM Q XZWQXZ 1 Q XZWSWQXZ 1 Q XZWQXZ 1    (b)  
  
Under standard assumptions the inefficient GMM estimator is “ n consistent”. That is, n 

ˆGMM N 0, V( ˆGMM)  , where denotes convergence in distribution.Strictly speaking, therefore, 
hypothesis tests should be performed on GMM, usingequation (b) for the variance-covariance matrix. 
Standard practice, however, is totransform the variancecovariance matrix (b) rather than the coefficient 
vector (a). This is done by normalizing 
 V ˆ 
GMM by 1/n, so that the variance-covariance matrixis in fact  
  

 V ˆGMM 1n Q XZWQXZ 1 QXZ WSWQXZ Q XZWQXZ 1  
 (c)  
  
The efficient GMM estimator (EGMM) makes use of an optimal weighting matrix W which minimizes 
the asymptotic variance of the estimator.   
This is achieved by choosing W = S−1. Substituting this into Equation (a) and Equation (c), the efficient 
GMM estimator is obtained:  
  
 ˆ EGMM X ZS 1Z X 1X ZS 1Z y       (d)  
  
with  asymptotic  variance V ˆEGMM Q XZS 1QXZ 1.  Similarly,  n 
 ˆEGMM N 0, V( ˆEGMM) . If an estimate of S exists, therefore, asymptotically correct inference 
for any GMM estimator could be conducted, efficient or inefficient. An estimate of S also makes the 
efficient GMM estimator a feasible estimator. In two-step feasible efficient GMM estimation an 
estimate of S is obtained in the first step and in the second step the estimator and its asymptotic variance 
is calculated using Equation (d).  
  
The first-step estimation of the matrix S requires the residuals of a consistent GMM  
~ 
estimator . Efficiency is not required in the first step of two-step GMM estimation, which simplifies 
the task considerably. But to obtain an estimate of S some further assumptions should be made. This is 

1 
n 

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illustrated using the case of independent but possibly heteroskedastic disturbances. If the errors are 
independent,  gi g j 0for i j, and so S AVar g  
 gigi  ui2Zi Zi .This matrix can be consistently estimated by an Eicker–Huber–White 
robust covariance estimator:  
  
Sˆ 1 i n1uˆi2Zi Zi n1 ˆ . n 

 
 

  
  
  

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