2. 1
Contents
1. INTRODUCTION .....................................................................................................1
2. Theoretical aspects.....................................................................................................1
Table 1: Herfindahl- Hirshman Index computed for the relevant period.................2
Table 2: Post Vs. Pre: Comparison with British Banker’s association data up to
2002............................................................................................................................2
A brief overview of the Rose Panzar Statistic:...........................................................3
3. Data and Methods ......................................................................................................4
Table 3a. Interpreting the Panzar-Rose H-statistic...................................................4
Table 3b. Interpreting the Panzar-Rose H-statistic (contd.) .....................................5
4. RESULTS ..................................................................................................................5
Equation for Competitive Equilibrium (Results of regression eqn. 1).......................5
Equation for Equilibrium (Results of regression eqn. 2)...........................................7
5. Conclusion and Further Ideas ....................................................................................8
Code for Computing the Herfindahl–Hirschman Indices:.........................................9
Code for computing Competitive Equilibrium ..........................................................9
Bibliography ..................................................................................................................9
1. INTRODUCTION
Competition in the Banking sector has far reaching consequences over other sectors,
whose survival is crucial on loans. It is easy to see in case of variance on returns, and
low covariance among firms, competing for sector, a monopoly in business financing
leads to monopolistic pricing in various sectors, eg. Telecom Industry Auctions （
How (Not) to Run Auctions:the European 3G Telecom Auctions，2002）.
As a consequence the evolution of competitive structure in the retail banking sector
gains more substance, although it is interesting to motivate the study in its own merit,
considering interest rates as prices. To do the analysis, following （Competitive
conditions among the major British banks，2007）, Rosse–Panzar methodology is
explored on both Gross Earnings and Core Earnings of aggregated Bank Data in UK.
Finally we also compare results from the classical “concentration ratio” approach:
Herfindahl–Hirschman Indices.
Another reason to carry out this study is to evaluate the post-crisis evolution of the
banking sector since 2007.
2. Theoretical aspects
The U.S. Department of Justice considers a market with a Herfindahl Hirshman
Indices of less than 1,000 to be a competitive marketplace; a result of 1,000-1,800 to
be a moderately concentrated marketplace; and a result of 1,800 or greater to be a
highly concentrated marketplace. The Table below shows the Herfindahl-Hirshman
Indices computed for each year.
3. 2
Table 1: Herfindahl- Hirshman Index computed for the relevant period.
Year
Herfindahl–
Hirschman
Indices
2007 2191
2008 2172
2009 2121
2010 2077
2011 2049
2012 2064
2013 2042
This motivates the discussion into banking as a highly concentrated market.
Nevertheless, a few acquisitions and sell outs have been carried out, attributed to the
economic slump, namely, disinvestments of Lloyds Banking Group Plc and The
Royal Bank of Scotland Group Plc have happened in late 2012-2013, and can be
reflected in falling indices. The code used to generate the table in Eviews can be
found in Appendix A.
（Conduct in a banking duopoly，1994）; （Financial Dependence, Banking Sector
Competition,and Economic Growth，2005）find conduct that is much more
competitive than the market structure, by concentration ratio like HHI would suggest,
and much more market power than the market structure would suggest, respectively,
implying that HHI can poorly reflect market power. This holds in the current, post-
crisis evaluation, and demands a more thorough model based finding.
To present a more scientific introspection, however the Roze-Panzar methodology is
adapted. Both the procedure suffer from a serious lacuna namely, aggregation of
different product markets. Housing societies are treated “same as banks”. Some
products are more competitive than others. Following （How do UK financial
institutions really price their products? Journal of Banking & Finance，2001）, Net
Interest Income as a good proxy for market share, although banks do price their
products differently, and if the product mix varies, market share is poorly aggregated
by Net Interest Income. Cournot type behaviour was evident in the credit card market
as interest rate setting was sensitive to the number of suppliers, while mortgage rate
seemed more competitive. Non-Interest Income however displayed Price
Discrimination, and hence is exclude from our analysis.
Table 2: Post Vs. Pre: Comparison with British Banker’s association data up to
2002
Year/measure HHI
1986 1428.470
1991 1423.817
1996 1051.831
2002 1249.696
In the UK, it is widely believed that the Banking crisis had similar effects that the
collapse of Lehman Brothers had on the US banking sector. Faced with negative
market assessments and a crisis of confidence among peer institutions, many banks
4. 3
depend strongly on central bank funding. Amidst major financial restructuring of the
retail banking industry, new empirical industrial organization which assesses
deviations between observed and marginal cost pricing, without explicitly using any
market structure indictor, but includes a Bank Specific variable becomes imperative.
We thus motivate our study with two aspects, higher conventional indices, as a result
of crisis (The fact that some bigger institutions survived, simply because they were
“too big to fail”), and decreasing equity value of banking institution, staggering
revenue and low Revenue Growth.
Figure: Staggering Prices in economy.
A brief overview of the Rose Panzar Statistic:
First, at the bank level, profit is maximized where marginal revenue is equal to
marginal cost:
Rl
i is the marginal revenue function, Cl
i is marginal cost function, yi is the output of
bank i, 𝜅 is the number of banks, 𝜐𝑖 and qi consist of exogenous variables having
bank-specific impact revenue and cost functions, fi is a vector of bank i’s factor
input prices.
The second equation is an implication of the model is that the zero profit constraint
holds at the industry level:
From this we can interpret the H statistic as responsiveness of revenue to factor
prices:
Roze and Panzar, in （Structure, conduct and comparative statistics，1982） have
shown how we can categorise the market based on H, and this is shown in the next
section vide Tables 3a and 3b.
5. 4
3. Data and Methods
Data has been fetched from Bank Scope and consists of 11 Banks surviving in the
economy from 2007 to 2013.
We have 73 observations, because of disinvestments in the relevant period as well, so
the panel of ours is an unbalanced panel.
The Rose-Panzar Model is an obvious candidate as it suffers from less anti-
competitive bias in small samples, when the economy is in transitional disequilibrium.
As a break from previous Structural Equation Models it has fewer restrictions, and is
therefore robust to small sample bias, and helps analysing changing conditions and
policy to precision. To accommodate heterogeneity across the banks, an error-
component model, with Bank- and time-specific fixed effects is used. Finally,
following （Competitive conditions among the major British banks，2007）, it can
be argued that the economy is recovering, so Growth in GDP is covered as a
component as well. In the following equation, REV stands for ratio of bank (interest)
revenue to total assets; PL denotes personnel expenses to employees (unit price of
labour); PK denotes other expenses to fixed assets (proxy for unit price of capital); PF
denotes ratio of annual interest expenses to total loanable funds (unit price of funds),
RISKASS denotes the ratio of provisions to total assets, and ROA is the Return on
assets.
--------- (1)
Subscript i denotes ith Bank and t denotes year, in accordance with standard Panel
symbols. 𝜇 denotes the unobservable bank-specific fixed effect and 𝜐 denotes IID
random error, tested on Gaussian assumptions. It is not required to break the time-
sample for test of distinct trends, or for structural breaks, as done in （Competitive
conditions among the major British banks，2007） which underlie methods in
addressing the problem of simultaneity between real GDP and Growth term, mainly
because the conditions of post recovery is quite rigid, and real GDP (not nominal gdp)
would be hardly affected in this case.
The statistic of interest is the H statistic:
Table 3a. Interpreting the Panzar-Rose H-statistic
Parameter Region Competitive Environment Test
H 0
- Monopoly or conjectural variations short-term oligopoly.
- Each bank operates independently as under monopoly
profit maximizing conditions.
- H is a decreasing function of the perceived demand
elasticity.
0 H 1
- Monopolistic competition
- Free entry (Chamberlinian) equilibrium excess capacity.
- H is an increasing function of the perceived demand
elasticity.
6. 5
H 1
- Perfect competition, or natural monopoly in a perfect
contestable market, or sales maximizing firm subject to
break even constraint.
- Free entry equilibrium with full (efficient) capacity
utilization.
The equilibrium condition is modelled as:
Where 𝜂 denotes the bank specific individual effect. Again equilibrium H is:
----------(2)
Table 3b. Interpreting the Panzar-Rose H-statistic (contd.)
Parameter Region Market Equilibrium Test
H = 0 - Equilibrium
H 0 (truncated) - Disequilibrium
It is summative that if the sample is not in the long-run equilibrium, H<0 in the first
regression no longer establishes monopolistic market conditions, but remains true that
H>0 disproves monopoly or conjectural variation short-run oligopoly.
4. RESULTS
Equation for Competitive Equilibrium (Results of regression eqn. 1)
Dependent Variable: @LOG(REV)
Method: Panel Least Squares
Date: 01/02/15 Time: 22:08
Sample: 2007 2013
Periods included: 7
Cross-sections included: 11
Total panel (unbalanced) observations: 65
Variable Coefficient Std. Error t-Statistic Prob.
C 3.732273 3.122028 1.195464 0.2378
@LOG(PK) 0.201472 0.098942 2.036251 0.0473
@LOG(PF) -0.176428 0.064196 -2.748276 0.0084
@LOG(PL) 0.008421 0.116216 0.072462 0.9425
@LOG(RISKASS) 0.096573 0.063172 1.528736 0.1329
@LOG(TOTAL_ASSETS
) -0.475124 0.158060 -3.005982 0.0042
GROWTH 0.021890 0.017672 1.238688 0.2215
7. 6
Effects Specification
Cross-section fixed (dummy variables)
R-squared 0.806541 Mean dependent var -4.820703
Adjusted R-squared 0.742055 S.D. dependent var 0.498201
S.E. of regression 0.253028 Akaike info criterion 0.309254
Sum squared resid 3.073101 Schwarz criterion 0.877940
Log likelihood 6.949255 Hannan-Quinn criter. 0.533637
F-statistic 12.50720 Durbin-Watson stat 1.547120
Prob(F-statistic) 0.000000
Wald Test:
Equation: Untitled
Test Statistic Value df Probability
t-statistic 2.780360 48 0.0077
F-statistic 7.730403 (1, 48) 0.0077
Chi-square 7.730403 1 0.0054
Null Hypothesis: C(1)+C(2)+C(3)+C(4)=0
Null Hypothesis Summary:
Normalized Restriction (= 0) Value Std. Err.
C(1) + C(2) + C(3) + C(4) 3.765738 1.354406
Restrictions are linear in coefficients.
We can do a one tailed truncated F- test, manually as Eviews does not do a one tailed
test.
P(H>0)= 0.007733
We reject the Hypothesis that H>0 (and therefore H>1) finding strong evidence
in favour of Monopoly.
0
1
2
3
4
5
6
7
8
9
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Series: Standardized Residuals
Sample 2007 2013
Observations 65
Mean -1.71e-18
Median -0.021305
Maximum 0.568280
Minimum -0.568280
Std. Dev. 0.219128
Skewness 0.239797
Kurtosis 3.328333
Jarque-Bera 0.914910
Probability 0.632892
8. 7
We are unable to reject normality (by Jacque Bera Probability), which means we are
correct in our estimates. Adding a lagged growth term reduces the adjusted R squared,
and the residual fitted plot below does not show any distinct trend in error terms or
trend in volatility.
-3
-2
-1
0
1
2
3
BarclaysBankPlc-07
BarclaysBankPlc-09
BarclaysBankPlc-11
BarclaysBankPlc-13
BritanniaBuildingSociety-09
HBOSPlc-09
HBOSPlc-11
HBOSPlc-13
HSBCBankplc-08
HSBCBankplc-10
HSBCBankplc-12
LloydsBankingGroupPlc-07
LloydsBankingGroupPlc-09
LloydsBankingGroupPlc-11
LloydsBankingGroupPlc-13
ParagonGroupofCompaniesPlc-08
ParagonGroupofCompaniesPlc-10
ParagonGroupofCompaniesPlc-12
RoyalBankofScotlandGroupPlc(The)-07
RoyalBankofScotlandGroupPlc(The)-09
RoyalBankofScotlandGroupPlc(The)-11
RoyalBankofScotlandGroupPlc(The)-13
SchrodersPlc-09
SchrodersPlc-13
SkiptonBuildingSociety-10
SkiptonBuildingSociety-12
WestBromwichBuildingSociety-08
WestBromwichBuildingSociety-10
WestBromwichBuildingSociety-12
YorkshireBuildingSociety-07
YorkshireBuildingSociety-09
YorkshireBuildingSociety-11
YorkshireBuildingSociety-13
Standardized Residuals
While our model seems correctly specified tests for the H statistic is inconclusive, we
fail to reject the direction of H both ways.
Equation for Equilibrium (Results of regression eqn. 2)
Since Banks did incur negative returns on assets, we have, following （What Drives
Bank Competition? Some International Evidence，2004）, modified ROA to 1+ROA
to suit our equation. Since we are taking logarithms we cannot have negative values.
Dependent Variable: LOG(ROA)
Method: Panel Least Squares
Date: 01/02/15 Time: 23:43
Sample: 2007 2013
Periods included: 7
Cross-sections included: 11
Total panel (unbalanced) observations: 66
White cross-section standard errors & covariance (d.f. corrected)
WARNING: estimated coefficient covariance matrix is of reduced rank
Variable Coefficient Std. Error t-Statistic Prob.
@Log(C) 1.012886 0.000872 1161.358 0.0000
@Log(PF) -1.001433 0.046774 -21.40988 0.0000
@log(PL) -4.64E-06 1.41E-06 -3.282890 0.0019
@log(PK) -0.000305 0.000127 -2.405223 0.0200
9. 8
RISKASS -0.045588 0.146057 -0.312128 0.7563
TOTAL_ASSETS -4.92E-12 7.96E-13 -6.185780 0.0000
GROWTH 0.000181 0.000135 1.342578 0.1856
Effects Specification
Cross-section fixed (dummy variables)
R-squared 0.980416 Mean dependent var 0.990996
Adjusted R-squared 0.974021 S.D. dependent var 0.013891
S.E. of regression 0.002239 Akaike info criterion -9.148250
Sum squared resid 0.000246 Schwarz criterion -8.584248
Log likelihood 318.8923 Hannan-Quinn criter. -8.925386
F-statistic 153.3130 Durbin-Watson stat 1.535601
Prob(F-statistic) 0.000000
Wald Test:
Equation: Untitled
Test Statistic Value df Probability
t-statistic 0.240987 49
0.966307
F-statistic 0.058075 (1, 49)
0.966307
Chi-square 0.058075 1 0.9596
Null Hypothesis: C(1)+C(2)+C(3)+C(4)=0
Null Hypothesis Summary:
Normalized Restriction (= 0) Value Std. Err.
C(1) + C(2) + C(3) + C(4) 0.011144 0.046242
Restrictions are linear in coefficients.
H0: H=0
HA: H<=0
Since F-statistic =0.966307
> .05, we fail to reject the null hypothesis, that H=0
In fact we can see at .05 and more significance levels, we can reject that H<=0
5. Conclusion and Further Ideas
Our findings in the Post-Crisis era concur with those in the pre-crisis era. We have
both stable equilibrium and strong monopoly tendencies, monopolistic or short run
oligopolistic pricing, concurring with the high observed HHI. A full-fledged study
should however, compare the pre and post crisis data using chow tests, and rolling
window methods. We also left out Non-Interest Operations of Banks. However, these
can be oligopolistic as well. A model cannot be completely justified unless potential
rival models are out ruled using GMM and similar methods. Finally the policy
extension. We all know Banking is monopolist. How this happens needs to be studied
into. Ideally Growth is a proxy for what we call a ‘signal’, which perhaps coordinates
this cartel like behaviour. Clearly implicit Hedging and other Bailout policies need to
be regulated, auditing firms concerns need to be looked into. Dwelving into all this,
10. 9
however goes beyond the current scope (and word limits).
Appendix A
Disclaimer:
1. Eviews 8.1 has been used. The author is not affiliated to Eviews, nor is it asserted
that he is doing the best use of the same, nor is he endorsing/ reccomending its use.
Eviews is a registered trademark of IHS Global Inc., 15 Inverness Way East,
Englewood, CO 80112, USA.
2. In the following code, Proxies and Data imputation has been toyed into. In real
world an array of data resources like Bloomberg could be used to intraplate this kind
of data using Classification methods. Although the bite is not strong, user discretion is
advised.
Code for Computing the Herfindahl–Hirschman Indices:
table(8,2) hhi
hhi(1,1)="Year"
hhi (1,2) = "Herfindahl–Hirschman Indices"
for !i = 1 to 7
!Y = @sum(net_interest_income)
genr sharehhi=((net_interest_income/!Y)*100)^2
smpl @first+!i-1 @first+!i-1
hhi(!i+1,1) = year(1+!i-1)
hhi(!i+1,2) = @sum(sharehhi)
next
Code for computing Competitive Equilibrium
genr
numemployee=@nan(number_of_employees,@nan(@nan(number_of_employees(-
1),number_of_employees(+3)),number_of_employees(+1)))
numemployee(1)=13490
genr pl = personnel_expenses/numemployee
genr REV = net_interest_income/total_assets
genr PK= OTHER_OPERATING_EXPENSES /FIXED_ASSETS
genr PF = TOTAL_INTEREST_EXPENSE /(TOTAL_ASSETS -FIXED_ASSETS -
LOAN_LOSS_PROVISIONS )
genr RISKASS = LOAN_LOSS_PROVISIONS /TOTAL_ASSETS
LS(CX=F) @LOG(Rev) @LOG(PF) @LOG(PL) @LOG(PK) @LOG( RISKASS
)@LOG(TOTAL_ASSETS) GROWTH
LS(CX=F) @LOG(ROA) @LOG(PF) @LOG(PL) @LOG(PK) @LOG( RISKASS
)@LOG(TOTAL_ASSETS) GROWTH
Bibliography
Competitive conditions among the major British banks． MatthewsKent,
MurindeVictor, ZhaoTianshu2007，Journal of Banking & Finance，Vol. 31，
pp.2025–2042．
11. 10
Conduct in a banking duopoly． Sherrill Shaffer; James Disalvos.l.，Journal of
Banking & Finance，1994．
Financial Dependence, Banking Sector Competition,and Economic Growth． Stijn
ClaessensLucLaevens.l.，World Bank Policy Research Working Paper 3481，2005
．
How (Not) to Run Auctions:the European 3G Telecom Auctions．
KlempererPaul2002，European Economic Review,．
How do UK financial institutions really price their products? Journal of Banking &
Finance． HeffernanS.A.,2001，Vol. 26．
Structure, conduct and comparative statistics． Panzar, J., Rosse, J.Paper No. 248.
，s.l.，Bell Laboratories Economic Discussion，1982．
What Drives Bank Competition? Some International Evidence． ClaessensStijn,
LaevenLucs.l.， Journal of Money, Credit and Banking, Blackwell Inc，2004．
