ï»¿ WPS6094
Policy Research Working Paper 6094
Why Donâ€™t Banks Lend to Egyptâ€™s Private Sector?
Santiago Herrera
Christophe Hurlin
Chahir Zaki
The World Bank
Middle East and North Africa Region
Economic Policy, Poverty and Gender
June 2012
Policy Research Working Paper 6094
Abstract
Bank credit to Egyptâ€™s private sector decreased over trough of the global crisis, capital flowed back into Egypt
the last decade, despite a recapitalized banking system and deposit growth stopped being a drag on the supply
and high rates of economic growth. Recent macro- side, but bank credit to the government continued to
economic turmoil has reinforced the trend. This paper drive the decrease in the private sectorâ€™s credit supply.
explains the decrease based on credit supply and demand Beginning in the final quarter of 2010, capital flows
considerations by 1) presenting stylized facts regarding reversed in tandem with global capital markets, and in
the evolution of the banksâ€™ sources and fund use in January 2011 the popular uprising that ousted President
2005 to 2011, noting two different cycles of external Hosni Mubarak added an Egypt-specific shock that
capital flows, and 2) estimating private credit supply accentuated the outflow. Lending capacity dragged again,
and demand equations using quarterly data from 1998 accounting for 10 percent of the estimated fall in private
to 2011. The system of simultaneous equations is credit. Credit to the government continued to drain
estimated both assuming continuous market clearing resources, accounting for 70â€“80 percent of the estimated
and allowing for transitory price rigidity entailing market total decline. Reduced economic activity contributed
disequilibrium. The main results are robust to the market around 15 percent of the total fall in credit. The relative
clearing assumption. During the global financial crisis, a importance of these factors contrasts with that of the
significant capital outflow stalled bank deposit growth, preceding capital inflow period, when credit to the
which in turn affected the private sectorâ€™s credit supply. government accounted for 54 percent of the estimated
At the same time, the banking sector increased credit to fall, while demand factors accounted for a similar
the government. Both factors reduced the private sectorâ€™s percentage.
credit supply during the period under study. After the
This paper is a product of the Economic Policy, Poverty and Gender, Middle East and North Africa Region. It is part of
a larger effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org.
The author may be contacted at sherrera@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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Produced by the Research Support Team
Why Donâ€™t Banks Lend to Egyptâ€™s Private Sector?1
Santiago Herrera2 Christophe Hurlin3 Chahir Zaki4
Keywords: Private credit, Egypt, Supply and Demand System, Disequilibrium model.
J.E.L Classification : D50, E42, C32, P00
1
This paper is a product of the MNSED Unit, MNSPR Department/Network, sector Borad: EPOL. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at
http://econ.worldbank.org. The author may be contacted at sherrera@worldbank.org. The authors thank Adolfo
Barajas for detailed comments on a previous draft of the paper. The paper is individually authored, and does not
necessarily represent the views neither of The World Bank nor of its Executive Directors.
2
Santiago Herrera, Lead Economist, World Bank, Cairo, Egypt. Email: sherrera@worldbank.org
3
Christophe Hurlin, Orleans University, Orleans, France. christophe.hurlin@univ-orleans.fr
4
Chahir Zaki, Assistant Professor, Cairo University, Cairo, Egypt. Email: chahir.zaki@feps.edu.eg
2
1. Introduction
Since 2000, banking credit to the private sector has declined in real terms and as a share
of Egyptâ€™s GDP. During the past decade the banking system witnessed recapitalization of public
banks and two different cycles of external capital flows. Capital flowed in until mid-2008 when
the global financial crisis erupted, and flowed out until mid-2009. As global risk appetite
recovered, capital flowed back in until the last quarter of 2010, when global capital markets
tightened again and the January 2011 uprising accentuated the capital outflow.
Aside from the capital flowsâ€™ stop-go cycles, public finance deficits and financing needs
created an expansion-contraction-expansion cycle that affected bank credit to the private
sector. Output fluctuations with episodes of high growth as well as output contractions affected
the private sectorâ€™s demand for credit. This paper describes how these factors interact to
produce a decline in credit to the private sector.
The paper first examines the stylized facts of bank credit to the private sector in an
international context, benchmarking the expected amount of private sector credit for a country
with Egyptâ€™s characteristics (using FINSTAT, a benchmarking tool developed by the World Bank).
It also explores the evolution of banking sector sources and uses, based on its aggregate
balance sheet and similar exercises performed for Latin America and the MENA regions (Barajas
et al., 2002; 2010).
The central objective of the paper is to estimate credit supply and demand equations in
line with the abundant empirical literature on the topic. Some studies examine the issue
assuming that prices are flexible enough to clear the market by equalizing supply and demand.
Others assume that prices are not perfectly flexible and estimate demand and supply equations
using the short-side rule (i.e. that observed credit quantities can occur on the demand or supply
schedules, whichever is smallest, at a given interest rate). Assuming an excess supply or
demand at a given point, the researcher infers the likelihood of the observed quantity being on
the supply or demand regimes. Empirical studies based on aggregate time series data and
applied to business loans include Laffont and Garcia (1977) for the Canadian market, Sealey
(1979) and King (1986) for the US market. Pazarbasioglu (1997) and Kim (1999) investigate
whether there was a credit crunch, respectively in Finland following the banking crisis of 1991-
92, in Korea following the financial crisis in December 1997. In Latin America, Catao (1997) and
Braun and Levy-Yeyati (2000) assessed credit contraction for Argentina, Berrospide and Dorich
(2001) for Peru, Carrasquilla, Galindo and Vasquez (2000) and Barajas, Lopez and Oliveros
(2001) for Colombia, Barajas and Steiner (2002) for Colombia, Peru and Mexico, and Hurlin and
Kierzenkowski (2007) for Poland.
3
The rest of the paper is organized as follows. Section Two describes some stylized facts
for the credit market in Egypt and compares the case with peer countries. It also discusses the
evolution of the banking sectorâ€™s main sources and uses of funds. Section Three describes the
methodology of credit demand and supply estimation and presents the data sources. Section
Four reports and interprets the empirical results within the macroeconomic context. Section
Five concludes.
2. Stylized Facts
2.1 Private Credit in Egypt in an International Context
In comparing Egypt to other countries, two trends emerge. First, while
private credit to GDP declined continuously since 2000 in Egypt, it increased in Morocco,
Tunisia, India and Turkey (see Figure 1). Second, in 2009, Egypt was performing below the
MENA countriesâ€™ average (40 percent), the middle income countries average (41.6 percent) and
its peer group average (49.9 percent) (see Figure 2 and Table 1).
Figure 1: Private Credit/GDP (percent) in Selected Peer Economies
Source: Finstat (2011)
4
Figure 2: Private Credit/GDP (percent) - Regional Comparison
Source: Finstat (2011)
Table 1: Private Credit/GDP (percent) Regional Comparison
S01IFS0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Egypt, Arab Rep. 52.0 54.9 54.7 53.9 54.0 51.2 49.3 45.5 42.8 36.2
MENA Average 37.7 38.0 37.0 36.1 36.3 37.1 38.1 39.5 39.5 40.3
MENA Median 34.4 28.4 26.2 25.6 27.7 28.2 30.9 34.3 31.2 33.8
LMC Average 29.5 29.2 29.1 29.7 31.1 33.5 35.0 38.1 39.9 41.6
LMC Median 27.1 23.9 21.1 24.4 25.5 27.3 29.1 30.3 32.2 33.6
HIC OECD Median 81.1 92.8 94.4 97.7 98.4 102.2 104.1 105.0 108.2 111.5
Peer Group Average 42.6 40.3 41.1 40.8 41.6 42.8 43.9 45.7 48.5 49.9
Expected median 19.0 19.2 19.4 21.1 22.8 23.8 25.7 28.3 31.1 31.6
Number of countries used for the regional and income group benchmarks (not the OECD benchmark)
S03FSI0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Regional benchmarks 11 11 11 11 11 11 11 11 11 11
Income group benchmarks 47 47 48 48 48 48 48 48 48 47
Source: Finstat (2011)
Having examined the international context for evolution of private credit in Egypt and
expected levels based on this sample of countries, we turn now to the domestic context.
5
2.2 Sources and Uses of Funds of the Banking Sector
Total bank credit as a share of GDP has been falling since 2006, except in 2011, when
credit to the government jumped by six percentage points of GDP (see Table 2).5 The banking
sectorâ€™s claims on the government (Figure 3) and on the business sector (Figure 4) show
divergent trends.
Table 2: Credit as Share of GDP
credit of banking sector in local currency ( as % of GDP)
2006 2007 2008 2009 2010 2011
total credit 0.789 0.662 0.568 0.623 0.596 0.631
gov 0.387 0.309 0.249 0.325 0.322 0.382
pub bus 0.043 0.025 0.022 0.023 0.018 0.018
priv bus 0.278 0.254 0.219 0.200 0.182 0.161
household 0.081 0.074 0.078 0.076 0.075 0.070
Source: Central Bank of Egypt (CBE) monthly reports
Figure 3: Real Claims on Government vs. Private Sector
Source: The Central Bank of Egypt
Note: Real figures of claims on government and private sector were obtained by deflating nominal figures
by the CPI index
5
This section and the remainder of the paper uses Central Bank of Egypt (CBE) data on credit aggregates. Section I
used the FINSTATS database for all variables to ensure comparability across countries.
6
To explain private sector lending we will examine the sources and uses of banking funds
during this period using the methodology of an existing study of bank credit contraction in Latin
America (IMF Staff papers Barajas-Steiner, 2002), to facilitate comparison.
Figure 4: Growth Rates of Claims on Gov. and Private Sector
Source: Central Bank of Egypt
The banking sectorâ€™s fund sources are deposits (Dt); net foreign liabilities (NFLt), and
bank capital (Kt). Uses include lending to the private sector (CPSt), lending to the government
(GOVt), changing its net credit position with the CBE (CBt), and cash holdings or other assets
(OTHt). Hence, credit to private sector can be defined as follows:
CPSt = Dt + NFLt + Kt - GOVt - CBt - OTHt
Private sector credit growth (and change) can be decomposed into changes in these
other balance sheet items that either contribute to or offset the decline:
âˆ†CPSt/CPSt-1 = âˆ†Dt/CPSt-1 + âˆ†NFLt/CPSt-1 + âˆ†Kt/CPSt-1 - âˆ†GOVt /CPSt-1 - âˆ†CBt/CPSt-1 - âˆ†OTHt/CPSt-1
Table 3 shows the changes in sources and uses of funds for the period 2005 to 2011.
Real deposits are the main force behind the changes, exhibiting high growth rates during the
boom years of 2007 and 2008, a time when real net foreign liabilities were falling. The 2009
data reflects the impact of the global crisis (data corresponds to fiscal years, ending in June),
when the banking sectorâ€™s net foreign liabilities increased, compensating the decrease in the
deposits as a source of funding. The general trend in the uses of funds shows that the real
7
credit position with the CBE was the main alternative use of funds until 2009 when real credit
to the government began taking over as the main use of banking sector funds.
In 2011, against a background of political unrest, real credit to the private sector
decreased by 8.5 percent, as a result of contraction of sources by 17 percent and of alternative
uses by 8.5 percent. The banking sectorâ€™s adjustment to capital outflow consisted of
compensating the contraction of net foreign liabilities with a reduction in the net credit position
with the CBE by a similar magnitude.
Table 3: Change in sources and uses of funds of the banking sector
(for fiscal years ending in June) as a ratio to real credit to the private sector
2005 2006 2007 2008 2009 2010 2011
Change in credit to the private sector -0.044 0.009 -0.015 0.017 -0.078 -0.029 -0.085
Change in sources 0.062 0.035 -0.026 0.116 -0.038 0.024 -0.170
Change in deposits 0.066 0.086 0.115 0.047 -0.171 -0.031 -0.044
Local currency 0.055 0.098 0.023 0.083 -0.072 0.030 -0.048
Foreign currency -0.002 -0.013 0.030 -0.028 -0.053 -0.054 -0.020
Other 0.013 0.000 0.061 -0.008 -0.045 -0.008 0.024
Change in foreign liabilities -0.010 -0.072 -0.121 0.046 0.146 0.060 -0.077
Change in capital 0.006 0.022 -0.019 0.023 -0.014 -0.005 -0.049
Change in alternative uses 0.106 0.026 -0.010 0.100 0.040 0.052 -0.085
Change in credit government 0.065 0.050 -0.108 0.013 0.210 0.072 0.044
Change in net credit to CBE 0.026 -0.020 0.066 0.074 -0.142 -0.025 -0.144
Change in other assets & cash 0.015 -0.004 0.033 0.013 -0.028 0.006 0.014
Source: Central Bank of Egypt
Note: Real figures of all aggregates were obtained by deflating nominal figures by the CPI index from CAPMAS.
During the capital inflow period 2006 to 2008, the Egyptian banking sector did not fund
credit operations expanding its net foreign liabilities. In fact, during the capital inflow years the
banking sectorâ€™s liabilities with the rest of the world became instead a contractive factor. In
2009, when capital flowed out in response to the global crisis, banks used their external
liabilities as a funding source, playing a counter-cyclical role. Only in 2011, during the capital
outflow related to the January uprising, were the net foreign liabilities pro-cyclical.
The role of Egyptâ€™s central bank (CBE) helps explain this puzzling behavior. During the
capital inflow period, the CBE intervened to prevent the domestic currencyâ€™s appreciation.
CBEâ€™s foreign currency assets increased from USD 23 billion in June 2006 to USD 48 billion in
June 2008. To compensate for this expansion, the banks had to increase their net credit
8
position with the CBE, especially in 2007 and 2008. During the capital outflow periods 2009 and
2011, the banking sector reduced its net credit position with the CBE.
Table 4 â€“ Change in CBE foreign currency assets (in Billion US$)
Int. Res. Change
& For. in CBE Current Capital
Assets1 IR & FA2 Account3 Account4
Mar 17.6 2.6 1.0 1.6
Jun 19.2 1.6 0.1 1.5
2005
Sept 22.0 2.8 0.2 2.6
Dec 23.4 1.4 0.8 0.6
Mar 23.7 0.3 0.9 -0.6
Jun 23.2 -0.5 -0.1 -0.4
2006
Sept 25.9 2.7 1.3 1.4
Dec 32.0 6.1 0.4 5.7
Mar 36.4 4.4 1.1 3.3
Jun 38.5 2.1 -0.6 2.7
2007
Sept 38.9 0.4 -0.1 0.5
Dec 43.2 4.3 -0.2 4.5
Mar 47.5 4.3 0.7 3.6
Jun 48.5 1.0 0.5 0.5
2008
Sept 41.9 -6.6 -1.0 -5.6
Dec 34.9 -7.0 -1.5 -5.5
Mar 32.1 -2.8 -0.9 -1.9
Jun 31.7 -0.4 -1.0 0.6
2009
Sept 35.6 3.9 -0.5 4.4
Dec 36.0 0.4 -0.8 1.2
Mar 39.3 3.3 -1.3 4.6
Jun 40.7 1.4 -1.7 3.1
2010
Sept 45.7 5.0 -0.8 5.8
Dec 43.5 -2.2 -0.6 -1.6
Mar 30.5 -13.0 -1.0 -12.0
Jun 26.5 -4.0 -0.4 -3.6
2011
Sept 24.5 -2.0 -2.2 0.2
Dec 18.5 -6.0 -1.8 -4.2
Source: Authorsâ€™ calculations based on CBE monthly reports.
Notes: 1. International reserves + foreign assets of the CBE.
2. Change in (1)
3. Current account from the CBE monthly reports
4. (2) â€“ (3)
9
Table 3 also shows a significant expansion of credit to government in FY2009 (30
percent), accompanied by a change in the banking sectorâ€™s net credit position with the CBE.
This may reflect a countercyclical monetary policy by the CBE who provided liquidity to the
banking system to accommodate the governmentâ€™s higher demand for credit.
Figures 5 and 6 show the evolution of bank deposits. Until 2008 they grew at a
significantly higher rate than the uses of funds. As of mid-2008 they stagnated and growth rates
in Figure 6 show a close synchronicity with capital flows.
Figure 5 Real Deposits in Local and Foreign Currency (in constant EGP)
Source: Central Bank of Egypt
10
Figure 6: Real Deposits in Local and Foreign Currency (growth rates in percent)
Source: Central Bank of Egypt
From the demand for credit side, two factors typically affect credit expansion and/or
contraction, i.e. the level of economic activity and the availability of alternative funding
sources. Egyptâ€™s economic activity measured by the real industrial production index was clearly
expanding, especially in the period 2002-2008, but then began contracting (see Figure 7).6
Figure 7: Real Industrial Production
Source: CAPMAS. Note: Real industrial production obtained by deflating nominal figures by the CPI index.
6
Quarterly GDP data is only available starting in 2002, while the industrial production index is available since 1998.
The larger degrees of freedom for the econometric estimation explains the choice of this variable.
11
The availability of alternative funding sources for firms (captured by the evolution of the
stock market index, EGX 30) expanded significantly in the boom period 2004 to 2008. During
the 2008 global crisis it fell precipitously, recovering again during the renewed capital inflow,
and falling again in the recent macroeconomic turmoil (Figure 8).
Figure 8: Stock Market Index - EGX30
Source: The Egyptian Stock Market.
3 Methodology
Given the stylized facts regarding credit demand and supply determinants, we can verify
the statistical validity of expected relationships and quantify the impact of different factors.
Following Laffont and Garcia (1977) and others, this section estimates aggregate
demand and supply functions of bank credit to Egyptâ€™s private sector using two assumptions: an
equilibrium approach and a disequilibrium one. The first assumes that prices are flexible and
clear the market continuously, and estimates the system of simultaneous equations using
traditional methods. The second method relaxes the market clearing assumption, allowing for
transitory excess supply or demand situations, and estimates the system of equations using the
Maddala and Nelson (1974) disequilibrium technique.
12
3.1 Equilibrium Hypothesis
In the specification of the supply and demand functions, the identification of the model
requires that one or more variables included in one function be excluded from the other.
Following Barajas and Steiner (2002), our identification variables in the demand equation
capture the macroeconomic environment that affects credit demand: real industrial production
(RIP) and the stock market index (EGX30). The former reflects the business environment and
has a positive effect on credit demand; the latter represents an alternative form of financing for
Egyptian firms, and should therefore have a negative impact on credit demand. Real lending
rate (RLEN) is added to determine the impact of credit prices on credit demand.
The variables introduced in the supply function measure the banksâ€™ ability to supply
loanable funds. We constructed an exogenous â€œlending capacityâ€? (LEND.CAP.) variable which
consists of real total deposits minus banksâ€™ real reserves. The higher the total deposits, the
more the bank will supply credit. By contrast, the higher the reserves, the lower the available
loanable funds. Therefore, we expect a positive effect of the lending capacity variable on credit
to private sector.
To capture the trade-off that banks face when lending to the government, we
introduced the real T-bill rates (RTBILL) in the supply function. This variable is mostly exogenous
to the banking system but affect banksâ€™ willingness to lend to the government. The higher the
T-bill rates, the more funds banks provide to government and hence the less they can lend to
private firms. Therefore, it has a negative impact on credit supply to the private sector. Finally,
lending rates (RLEN) were introduced to determine the impact of credit prices on credit supply7.
Our dependent variable is real credit to the private sector (RCRPV).
The system of equations is:
Supply function:
ln(RCRPV)t=Î²0 + Î²1 (RLEN)t + Î²2 ln(RTBILL)t + Î²3ln(LEND.CAP)t-1 + Ñ”t (1)
Demand function:
ln(RCRPV)t =Î±0 + Î±1 (RLEN)t + Î±2 ln(RIP)t-1 + Î±3 ln(EGX30)t-1 + Îµt (2)
with Ñ”t and Îµt the respective disturbance terms.
7
Real rates were computed using the Fisherâ€™s relation (1+i) = (1+r)(1+Ï€) where i is the nominal rate, r the real rate and Ï€ the
inflation rate. Therefore, r = (1+i)/(1+Ï€) â€“ 1.
13
We ran the regression using different techniques. First, using a seemingly unrelated
regression, we estimated the supply and demand system assuming that the disturbances across
equations are contemporaneously correlated (Zellner, 1962). Next, we ran it using a
multivariate regression. Finally, we used OLS and 2SLS regressions.
3.2 Disequilibrium Hypothesis
Since Fair and Jaffee (1972) extensive literature has adressed the econometric problems
associated with estimating demand and supply schedules in disequilibrium markets. The main
approach consists in using maximum likelihood ( ML ) methods. In a seminal paper, Maddala
and Nelson (1974) derived the general likelihood function for different disequilibrium models
and proposed the appropriate ML estimating procedures.
Their model is as follows:
dt = x1,t ï?¢1 ï€« ï?¥1,t
'
(3)
st = x'2,t ï?¢ 2 ï€« ï?¥ 2,t (4)
qt = min ï€¨dt , st ï€© (5)
where dt denotes the unobservable quantity demanded during period t;
st the unobservable quantity supplied during period t;
'
ï€¨
(1) (1) (1)
ï€©'
x1,t = x1,t x2,t ...xK ,t is a vector of K1 explanatory variables that influence dt;
1
= ï€¨x ï€© is a vector of K
'
x'2,t (2) (2)
1,t 2,t
(2)
x ...xK ,t 2, explanatory variables that influence st;
2
Î²1 and Î²2 are respectively (K1,1) and (K2,1) vectors of parameters.
We assume that dt and st are unobservable at date t, whereas x1,t and x2,t are
observable. The variable qt denotes the actual quantity observed at time t. The equation (5) is
the crucial disequilibrium hypothesis, which allows for the possibility that the price of the
exchanged good is not perfectly flexible and rationing occurs.
More generally, equation (5) indicates that any disequilibrium that occurs (i.e. any
divergence between the quantity supplied and demanded) results from an incomplete price
adjustment. Therefore, on the basis of voluntary exchange the â€˜short sideâ€™ of the market
prevails. With equation (5), the model indicates the probabilities of each observation belonging
to either supplied or demanded quantities.
14
Next, we present the modelâ€™s theoretical underpinnings. In a first version, following
Maddala and Nelson (1974), we assume that both residuals Îµ1,t and Îµ2,t are stationary
processes, independently and normally distributed with variance Ïƒ21 and Ïƒ22 respectively.
Under these regularity assumptions, the transformed variable Îµ 1,t - Îµ2,t is normally distributed
with a variance equal to Ïƒ2 = Ïƒ21+Ïƒ22.
Hence, the reduced variable (Îµ1,t - Îµ2,t)/Ïƒ follows a N(0,1). The probability that the
observation qt belongs to the demand regime, denoted Ï€t(d), can then be computed as the
corresponding N(0,1) fractile:
x2
ï€
= Pï€¨Dt < St ï€© = ï?†ï€¨ht ï€© =
ï€¨d ï€© 1 ht
ï?°t
2ï?° ïƒ²ï€ï‚¥
e 2
dx (6)
ï€¨ ï€©
where ht = x'2,t ï?¢ 2 ï€ x1,t ï?¢1 /ï?³ , and ï?†ï€¨x ï€© denotes the cumulative distribution function of the
'
N(0,1). Symmetrically, the probability of obtaining the supply regime, denoted Ï€ t(s), is defined
by Pï€¨St < Dt ï€© = 1 ï€ ï?†ï€¨ht ï€© 8
3.3 Data
The quarterly dataset from 1998 to 2011 was compiled from different sources. Data
regarding credit to private sector came from the banking survey published in CBEâ€™s monthly
report. Total deposits, banksâ€™ reserves with the CBE (that were used to construct the lending
capacity) and bank lending rates also come from the same source. Industrial production comes
from the Central Agency for Public Mobilization and Statistics (CAPMAS) deflated by the CPI;
and the stock market index (EGX30) as reported by the Egyptian Stock Market. EGX 30 Index is
a market capitalization-weighted index. Finally, lending rates were taken from CBE reports
while T-Bill rates were gathered from Ministry of Finance reports9.
All nominal variables were deflated by the consumer price index. To partially control for
endogeneity bias, the models use the lagged values for industrial production, bank deposits,
bank reserves and the stock market index.
8
For further details, see appendix 1-4
9
To check whether our series are stationary or not, we ran the Augmented Dickey-Fuller test and found they all suffer from a
unit root problem. After taking the first difference and running the ADF, we found our variables stationary. Finally, we
conducted the Johansenâ€™s test to determine whether our series are co-integrated or not. We found that they form a co-
integrated vector, allowing us to estimate the model in levels.
15
4 Empirical Results
4.1 Results of the Equilibrium Hypothesis
Table 5 presents the regression results using different techniques, all of which yield
similar results. In the demand equation, real industrial production has the expected positive
sign while the stock market index has a negative impact on the demand for credit, reflecting its
role as a substitute for bank credit. The real lending rate turns out with an unexpected positive
sign and statistically significant coefficient.
Table 5: Demand and Supply of Private Credit (Equilibrium Estimation)
SURE MVREG
Ln(Claim. Priv.) Ln(Claim. Priv.)
Supply Demand Supply Demand
Real Lending Rate 1.721*** 0.892*** 1.721*** 0.892***
(0.327) (0.212) (0.343) (0.222)
Real T-bill Rate -0.958*** -0.958***
(0.335) (0.351)
Ln(Lagged Lending Cap.) 0.198*** 0.198***
(0.0584) (0.0612)
Ln(Lagged Industrial Prod.) 0.249*** 0.249***
(0.0523) (0.0548)
Ln(Lagged EGX 30) -0.0397*** -0.0397***
(0.0121) (0.0126)
Constant 6.165*** 6.566*** 6.165*** 6.566***
(0.497) (0.285) (0.521) (0.299)
Observations 45 45 45 45
R-squared 0.458 0.491 0.458 0.491
OLS 2SLS
Ln(Claim. Priv.) Ln(Claim. Priv.)
Supply Demand Supply Demand
Real Lending Rate 2.509*** 0.788*** 2.509*** 0.788***
(0.391) (0.235) (0.391) (0.235)
Real T-bill Rate -1.892*** -1.892***
(0.431) (0.431)
Ln(Lagged Lending Cap.) 0.241*** 0.241***
(0.0658) (0.0658)
Ln(Lagged Industrial Prod.) 0.378*** 0.378***
(0.0622) (0.0622)
Ln(Lagged EGX 30) -0.0785*** -0.0785***
(0.0155) (0.0155)
Constant 5.776*** 6.044*** 5.776*** 6.044***
(0.560) (0.328) (0.560) (0.328)
Observations 45 45 45 45
R-squared 0.517 0.560 0.517 0.560
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
16
Concerning the supply function, we found lending capacity to be positively and
statistically significant related to credit supply. The trade-off between government and private
sector seems to be an important factor in explaining Egyptâ€™s credit contraction. The more the
banks provide loans to the government, the less they can lend to private firms. Consequently,
the coefficient associated to the real T-bill interest rate is negative and statistically significant.
Finally, in a supply function we expect a positive impact of credit prices on credit quantities. The
real lending rate in fact has a positive and statistically significant impact on credit supply at 1
percent.
4.2 Results of the Disequilibrium Hypothesis
Table 6 summarizes the results using the disequilibrium model, with the same
specifications as in the previous section. We use the two-step OLS parameters of the previous
section as the initial values for the maximization process (see appendix for more details).
We checked the resultsâ€™ robustness using various initial conditions for the algorithm of
ML maximization and various methods to optimize the ML (i.e. by finding the zero of the
gradient; by minimizing with or without condition on the parameter; with a
numerical/analytical gradient, etc.). The results (available upon request) show that the ML
estimated parameters are robust to these changes.
Figure 9 shows each regimeâ€™s estimated probabilities for the best model in terms of the
log-likelihood statistics and information criteria. It is conventional to assume an excess of
supply (respectively demand) when the estimated probability of the supply regime (respectively
demand) is higher than 0.5.
These estimated probabilities of supply and demand regimes clearly indicate that the
probabilities of regimes are often larger than 0.8 or less than 0.2. We can identify two main
periods: for 2001-2003, there was excess demand of credit that progressively decreased and
switched to an excess of supply situation until 2011. After the global crisis (in 2008) both the
demand and supply of credit to the private sector diminished, and while the fall in the supply is
estimated to be greater, the excess supply still persists.
17
Table 6: Demand and Supply of Private Credit (Disequilibrium estimation)
Equations Estimates
Supply equation
Constant 6.6444***
(7.2737)
Real lending rate 2.7062***
(4.5826)
Real T-bill rates -2.1912***
(-3.8632)
Ln(Lagged lending capacity) 0.1387*
(1.2887)
Variance of residuals 0.0564***
(48.308)
Demand equation
Constant 4.7733***
(9.5659)
Real lending rate 0.7455
(1.1246)
Ln(Lagged real industrial production) 0.6378***
(9.7747)
Ln(Lagged stock market index) -0.1127***
(-8.4481)
Variance of residuals 0.0066***
(187.20)
Log-likelihood -84.0863
Adjusted RÂ² 0.4750
Frequency of supply regimes (FS) 22.22%
Frequency of demand regimes (FD) 77.78%
AkaÃ¯ke Information criteria -252.41
Schwarz Information Criteria -234.34
Notes: 1) Asymptotic t-statistics are in parentheses.
2) FD (FS) denotes the frequency of demand (supply) regimes given that a period or regime
occurs when the corresponding probability is higher than 0.5.
18
Figure 9: Unconditional Probability of the Regime S or D
1
0.9
0.8
0.7
0.6
Probability of supply regime
0.5
Probability of demand regime
0.4
0.3
0.2
0.1
0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Source: Constructed by the authors.
The disequilibrium econometrics approach based on the short-side rule is consistent
with the theory of equilibrium credit rationing derived from asymmetric information models.
Because of moral hazard and adverse selection problems, an excess demand in the loan market
may exist, since a rise in the loan interest rate can reduce the banksâ€™ expected return.
If each bank attracts only the least profitable customers, each may have an excess
supply of loanable funds, but none will accept to reduce its interest rate. Consequently, there
may be an excess credit supply in the banking sector, without a fall in the interest rate to clear
the loan market. This excess of supply can be observed in Figure 10, illustrating the estimated
demand and supply for the private sectorâ€™s real claims.
19
Figure 10: Estimated Demand and Supply
8.2
Supply equation
8.15 Demand equation
8.1
8.05
8
7.95
7.9
7.85
7.8
7.75
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Source: Constructed by the authors.
Figure 11: Adjustment on quantities
8
7.95
7.9
7.85
7.8
Historical quantities
Fitted quantities
7.75
7.7
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Source: Constructed by the authors.
20
4.3 Decomposing the Predicted Changes in Credit
The models presented in Tables 5 and 6 allow us to determine the relative importance
of demand and supply factors in the evolution of credit to the private sector during five sub-
periods. These are categorized based on external capital flows: inflow periods (July 2001-June
2004, July 2004-June 2008, July 2009-September 2010) or outflow periods (July 2008-June
2009, and October 2010-June 2011).
Predicted change is calculated by multiplying the coefficients obtained in the previous
section by the change in the explanatory variable throughout a given sub-period. Changes
brought about as a result of adjustments in interest rates show a movement along supply and
demand curves. By contrast, changes in the other explanatory variables show the predicted
shifts in the curves.
Tables 7 and 8 present the results for different sub-periods using the equilibrium and
disequilibrium models respectively. The two models yield similar results even when the
absolute numbers differ. The disequilibrium model offers more volatile predictions, given the
greater elasticity of the credit supply to changes in the real T-bill rates (2.19 in the
disequilibrium model versus 1.89 in the equilibrium model) and the larger elasticity of the
demand for credit to changes in alternative funding sources (-.11 in the disequilibrium model
versus -.08 in the equilibrium one).
General trends persist despite the differences. Until 2008, lending capacity growth is the
single most important credit supply factor, whereas after 2009 it is credit to the government
(captured by the real T-bill rate). From the demand perspective, both the level of activity and
the alternative funding sources switch dominant roles.
During the period July 2004 to June 2008, from the demand side, the availability of
substitute funding sources was partially dampened by the positive impact of economic
expansion. From the bank credit supply side, moderate growth in credit to the government
compensated the equally moderate lending capacity.
During the global crisis (July 2008 to June 2009) a significant capital outflow led to a
negative impact of lending capacity, which in turn affected the private sectorâ€™s credit supply.
Additionally, the banking sector gave credit to the government. Both made the supply effect
dominant during the period. From the demand side, the contraction of economic activity
21
mitigated credit demand but the lack of alternative funding sources led to higher demand for
credit from the banking sector.
After the June 2009 trough of the global crisis, capital flowed back into the country.
Lending capacity growth stopped being a drag on the supply side, and availability of alternative
funding sources released pressure from the demand side (Tables 7 and 8). Now credit to the
government was behind the fall in credit to the private sector.
From the last quarter of 2010 (October) capital started flowing out of Egypt, in tandem
with global capital markets, and the January 2011 uprising added an Egypt-specific shock that
accentuated the outflow. Capacity of lending declines dragged again and credit to the
government continued to drain resources. During this period, credit to the government
accounts for between 70 and 80 percent of the predicted total decline in credit, and the fall in
deposits accounts for almost 10 percent of the predicted fall in private credit. The slowdown in
economic activity accounts for about 15 percent of the predicted total fall in credit.
Table 9 summarizes these findings by presenting 1) how supply is higher or lower than
demand shifts for each period 2) whether the shifts are in the same direction or operate in
opposite ways, and 3) the main determinant of supply and demand shifts.
22
Table 7: Decomposition of Predicted Change in Real Credit (Equilibrium Hypothesis)
Supply
Coeff Growth Multiplication
Jul.01- Jul.04- Jul.08- Jul.09- Oct.10- Jul.01- Jul.04- Jul.08- Jul.09- Oct.10-
Jun.04 Jun.08 Jun.09 Sep.10 Jun.11 Jun.04 Jun.08 Jun.09 Sep.10 Jun.11
Real Lending rate 2.509 -1.5% -1.1% -4.1% 2.1% 0.6% -3.76% -2.66% -10.35% 5.18% 1.50%
Real Tbill rate -1.892 -1.3% -0.8% -4.2% 2.9% 3.6% 2.40% 1.43% 7.99% -5.56% -6.78%
Ln(Lend. Cap.) 0.241 11.5% 5.3% -5.9% -1.6% -2.6% 2.78% 1.27% -1.42% -0.39% -0.63%
1
Shifts in the curve 5.18% 2.70% 6.56% -5.95% -7.41%
2
Total changes in Supply 1.42% 0.04% -3.79% -0.78% -5.91%
Demand
Coeff Growth Multiplication
Jul.01- Jul.04- Jul.08- Jul.09- Oct.10- Jul.01- Jul.04- Jul.08- Jul.09- Oct.10-
Jun.04 Jun.08 Jun.09 Sep.10 Jun.11 Jun.04 Jun.08 Jun.09 Sep.10 Jun.11
Real Lending rate 0.788 -1.5% -1.1% -4.1% 2.1% 0.6% -1.18% -0.84% -3.25% 1.63% 0.47%
Ln(Industrial Prod.) 0.378 12.9% 10.1% -4.2% -7.0% -3.2% 4.86% 3.81% -1.60% -2.64% -1.21%
Ln(EGX 30) -0.079 21.5% 81.3% -40% 21.7% -7.5% -1.69% -6.38% 3.13% -1.71% 0.59%
3
Shifts in the curve 3.18% -2.57% 1.53% -4.35% -0.62%
4
Total changes in Demand 1.99% -3.41% -1.72% -2.72% -0.15%
5
Estimated Total shifts in Supply and Demand 8.35% 0.13% 8.10% -10.30% -8.03%
6
Estimated Total changes Private credit 3.41% -3.37% -5.51% -3.50% -6.06%
7
Observed Total changes Private credit 4.16% -0.29% -5.70% -6.13% -7.13%
Source: Constructed by the authors using the regressions results.
Notes:
1= change in real T-bill rates + change in lending capacity.
2= 1 + change in lending rate
3= change in industrial production and stock market index
4= 3+ change in lending rate + change in T-bill rate
5=1+3
6= 2+4
7= observed change in claims on private sector.
23
Table 8: Decomposition of Predicted Change in Real Credit (Disequilibrium Hypothesis)
Supply
Coeff Growth Multiplication
Jul.01- Jul.04- Jul.08- Jul.09- Oct.10- Jul.01- Jul.04- Jul.08- Jul.09- Oct.10-
Jun.04 Jun.08 Jun.09 Sep.10 Jun.11 Jun.04 Jun.08 Jun.09 Sep.10 Jun.11
Real Lending rate 2.706 -1.5% -1.1% -4.1% 2.1% 0.6% -4.06% -2.87% -11.16% 5.58% 1.62%
Real T-bill rate -2.191 -1.3% -0.8% -4.2% 2.9% 3.6% 2.78% 1.65% 9.25% -6.44% -7.85%
Ln(Lend. Cap.) 0.139 11.5% 5.3% -5.9% -1.6% -2.6% 1.60% 0.73% -0.82% -0.22% -0.36%
Shifts in the curve 4.38% 2.39% 8.43% -6.67% -8.22%
Total changes in Supply 0.32% -0.48% -2.74% -1.09% -6.60%
Demand
Coeff Growth Multiplication
Jul.01- Jul.04- Jul.08- Jul.09- Oct.10 Jul.01- Jul.04- Jul.08- Jul.09- Oct.10
Jun.04 Jun.08 Jun.09 Sep.10 Jun.11 Jun.04 Jun.08 Jun.09 Sep.10 Jun.11
Real Lending rate 0.746 -1.5% -1.1% -4.1% 2.1% 0.6% -1.12% -0.79% -3.08% 1.54% 0.45%
Ln(Industrial Prod.) 0.638 12.9% 10.1% -4.2% -7.0% -3.2% 8.21% 6.42% -2.70% -4.46% -2.04%
Ln(EGX 30) -0.113 21.5% 81.3% -39.9% 21.7% -7.5% -2.42% -9.16% 4.50% -2.45% 0.85%
Shifts in the curve 5.78% -2.74% 1.80% -6.91% -1.19%
Total changes in Demand 4.67% -3.53% -1.27% -5.37% -0.75%
Estimated Total shifts in Supply and Demand 10.2% -0.35% 10.23% -13.57% -9.41%
Estimated Total changes Private credit 4.98% -4.01% -4.01% -6.45% -7.34%
Observed Total changes Private credit 4.16% -0.29% -5.70% -6.13% -7.13%
Source: Constructed by the authors using the regressions results.
Notes:
1= change in real T-bill rates + change in lending capacity.
2= 1 + change in lending rate
3= change in industrial production and stock market index
4= 3+ change in lending rate + change in T-bill rate
5=1+3
6= 2+4
7= observed change in claims on private sector.
Table 9: Summary of the Decomposition Results
Equilibrium Disequilibrium
Shifts Direction Determinants Shifts Direction Determinants
Supply Demand Supply Demand
Jul.01-Jun.04 SD Same T-Bill rate Alternative Fin. S>D Same T-Bill rate Alternative Fin.
Jul.09-Sep.10 SD Same T-Bill rate. Industry S>D Same T-Bill rate Industry
5 Conclusions
The paper explained the credit contraction to the private sector based on the
banking sectorâ€™s sources and uses of funds, as well as estimating econometrically a
system of supply and demand for private credit. An analysis of the banking sectorâ€™s
sources and uses of funds reveals a close association of bank credit to the private sector
with external capital flows but mostly through the deposit growth rate, which was the
main determinant of the sources of funds. The banking sectorâ€™s net external liabilities
were countercyclical, i.e. they contracted during the capital inflow period and expanded
during the capital outflow. In this sense, the sector played a stabilizing role. Only during
the last cycle of capital outflow since the Revolution the net foreign liabilities have been
pro-cyclical. The banksâ€™ net credit position with the CBE fell during the capital outflow
episodes of 2009 and 2011 and increased during the capital inflow episodes, which may
be interpreted as an effective countercyclical monetary policy.
The system of simultaneous equations was estimated both assuming continuous
market clearing and allowing for transitory price rigidity entailing market disequilibrium.
The main results are robust to the market clearing assumption. Up to the global financial
crisis, the main elements driving bank credit were from the demand side, though in
opposing directions: vigorous industrial activity implied growing demand for bank credit,
but available alternative sources of financing implied lower demand for bank credit.
After the global financial crisis, the banking sectorâ€™s credit to the government played the
dominant role from the supply side, while subdued economic activity operated in the
same direction from the demand side.
Starting in the last quarter of 2010 capital flows reversed, in tandem with global
capital markets, and the events of January 2011 accentuated the outflow. The
slowdown in economic activity accounted for between 15 and 20 percent of the
predicted total fall in credit, while the expansion of the credit to the government
24
accounts for the remaining fall in the observed credit to the private sector. The relative
importance of these factors contrasts with that of the preceding capital inflow period
during which credit to the government accounted for about 50 percent of the estimated
fall, while demand factors accounted for a similar amount.
References
Barajas, A. E. Lopez and H. Oliveros (2001) â€œPorque en Colombia el credito al sector
privado es tan reducido?â€? Borradores de Economia No. 185. Banco de la Republica.
Barajas and Steiner (2002) â€œWhy donâ€™t they lend? Credit Stagnation in Latin
Americaâ€?, IMF Staff Papers. vol. 49. Special issue.
Barajas, A. R. Chami, R. Espinoza, and H. Hesse (2010) â€œRecent credit stagnation in
the MENA region: What to expect? What can be done?â€? IMF Working Paper
WP/10/219.
Berrospide, J. and J. Dorich (2001) â€œAspectos Microeconomicos de la Rresticcion
Crediticia en le Peru: 1997-2000â€?, Banco Central del Reserva del Peru, mimeo.
Braun, M. and E. Levy-Yeyati (2000) â€œThe Role of Banks in the Transmission of
Shocks: Mirco Evidence from Argentina 1996-1999â€?, Buenos Aires, Universidad
Torcuato Di Tella, mimeo.
Carrasquilla, A., A. Galindo and D. Vasquez (2000) â€œEl Gran Apreton Crediticio en
Colombia: una Interpretationâ€?, Coyuntura Economica, Vol. XXX, no. 1, pp. 107-115.
Catao, L. (1997) â€œBank Credit in Argentina in the Aftermath of the Mexican Crisis:
Supply or Demand Constrained?â€?, IMF Working Paper 97/32.
Fair R.C., Jaffee D.M. (1972) â€œMethods of Estimation for Markets in Disequilibriumâ€?,
Econometrica, 40, No. 3, May, pp. 497-514.
Hurlin, C. and R. Kierzenkowski (2007) â€œCredit market disequilibrium in Poland: Can
we find what we expect
25
Kim, H. (1999) â€œWas Credit Channel a Key Monetary Transmission Mechanism
Following the Recent Financial Crisis in the Republic of Korea?â€? World Bank Policy
Research Working Paper 2103.
Laffont J-J., Garcia R. (1977) â€œDisequilibrium Econometrics for Business Loans'',
Econometrica, 45, No. 5, July, pp. 1187-1204.
Laffont J-J., Monfort A. (1979) â€œDisequilibrium Econometrics in Dynamic Models'',
Journal of Econometrics, 11, No. 2-3, October-December, pp. 353-361.
Laroque G., Salanie B. (1995) â€œMacroeconometric Disequilibrium Models" , in
Handbook of Applied Econometrics, vol. 1, Blackwell, Mass., pp. 391-414.
Laroque G., Salanie B. (1997) â€œNormal Estimators for Cointegrating Relationships",
Economics Letters, 55, No. 2, August, pp. 185-189.
Maddala G.S., Nelson F.D. (1974) "Maximum Likelihood Methods for Models of
Markets in Disequilibrium", Econometrica, 42, No. 6, November, pp. 1013-1030.
Pazarabasioglu, C. (1997) â€œA Credit Crunch: Finland in the Aftermath of the Banking
Crisisâ€?, IMF Staff Papers, Vol. 44, No. 3, pp. 315-327.
Quandt R. (1988) The Econometrics of Disequilibrium, Blackwell.
Sealey, C (1979) â€œCredit Rationning in the Commercial Loan Market. Estimates of a
Structural Model under Conditions of Disequilibriumâ€?, Journal of Finance, Vol. 34,
pp. 689-702.
Zellner, (1962) â€œAn Efficient Method of Estimating Seemingly Unrelated Regressions
and Tests for Aggregation Bias,â€? Journal of the American Statistical Association, vol.
57, pp. 348â€“368.
26
Appendix 1: The log-likelihood function
Let ï?± denote the vector of structural parameters ï?± = ï€¨ï?¢1 ï?¢ 2 ï?³ 1ï?³ 2 ï€© . To compute
'
the marginal density, f Q ï€¨qt ï€© , of the observable variable qt , we consider the joint
t
density of d t and st , denoted g D ,S ï€¨dt , st ï€© . Given the definition of the disequilibrium,
t t
we know that:
f Q ï€¨qt ï€© = f Q ï€¨qt ï€© ï€« fQ S < D ï€¨qt ï€© (A.1)
t t Dt < St t t t
Next, we obtain the corresponding marginal density of qt on the two subsets (cf.
Appendix 2):
ï‚¥
fQ ï€¨qt ï€© = ïƒ²q =d g Dt ,St ï€¨dt , z ï€©dz (A.2)
t Dt < St t t
ï‚¥
fQ ï€¨qt ï€© = ïƒ²q = s g Dt ,St ï€¨z, st ï€©dz (A.3)
t St < Dt t t
Finally, we obtain the unconditional density function of Qt :
ï‚¥ ï‚¥
f Q ï€¨qt ï€© = f Q ï€¨qt ,ï?± ï€© = ïƒ² g D ,S ï€¨qt , z ï€©dz ï€« ïƒ² g D ,S ï€¨z, qt ï€©dz (A.4)
t t qt t t qt t t
Conditional to a structural parameters set ï?± and a sample of observable variables
qt , x1,t and x2,t observed on T periods, the log-likelihood function of the model is then
defined by:
ï?› ï??
T
Lï€¨ï?± ï€© = ïƒ¥ log f Q ï€¨qt ,ï?± ï€© (A.5)
t
t =1
If we assume that both residuals ï?¥ 1 and ï?¥ 2 are independent, the unconditional density
function of Qt can be expressed as follows:
1 ïƒ¦ x1,t ï?¢1 ï€ qt ïƒ¶ ïƒ¦ x'2,t ï?¢ 2 ï€ qt ïƒ¶
'
f Q ï€¨qt ï€© = ï?¦ïƒ§ ïƒ·ï?†ïƒ§ ïƒ·
t ï?³1 ïƒ§ ï?³1
ïƒ¨
ïƒ· ïƒ§
ïƒ¸ ïƒ¨ ï?³2 ïƒ·
ïƒ¸
ïƒ¦ x'2,t ï?¢ 2 ï€ qt ïƒ¶ ïƒ¦ x1,t ï?¢1 ï€ qt ïƒ¶
1
'
ï€« ï?¦ïƒ§ ïƒ§ ïƒ·ï?† ïƒ§ ïƒ· (A.6)
ï?³2 ïƒ¨ ï?³2 ïƒ· ïƒ§ ï?³1 ïƒ·
ïƒ¸ ïƒ¨ ïƒ¸
where Ï†(.) denotes the normal N(0,1) density function.
Appendix 2 provides the proof. In this case, the first and second order derivatives of
L(Î¸) can be computed analytically (Maddala and Nelson, 1974) or numerically. We can
use an iterative procedure such as the Newton-Raphson to obtain the ML estimates of
the structural parameters Î¸. Given the parametersâ€™ estimated values, we can assess the
27
probability that the observation qt belongs either to the demand or the supply regime,
ï€¨d ï€© ï€¨s ï€©
^ ^
ï?° t and ï?° t .
Appendix 2: Marginal densities of Qt in a stable disequilibrium model
Let g D ,S ï€¨dt , st ï€© denote the joint density of Dt and S t . We know that the
t t
corresponding marginal densities of the unobservable variables Dt and S t are defined
by:
ï‚¥ ï‚¥
f D ï€¨dt ï€© = ïƒ² g D ,S ï€¨dt , z ï€©dz f S ï€¨st ï€© = ïƒ² g D ,S ï€¨z, st ï€©dz
t ï€ï‚¥ t t t ï€ï‚¥ t t
(A.7)
We compute the marginal density of Qt on the two subset Qt = Dt , with Dt < St and
Qt = St , with St < Dt .
When Dt < St , for a given realization d t of Dt , the marginal density of Qt , is given by
the area defined by the joint density g D ,S ï€¨dt , z ï€© , for values z of S t superior to d t .
t t
Assuming that Dt < St , the marginal density of Qt is then given by:
ï‚¥
fQ ï€¨qt ï€© = ïƒ²q =d g Dt ,St ï€¨dt , z ï€©dz (A.8)
t Dt < St t t
Symmetrically, we obtain the marginal density of Qt when St < Dt .
ï‚¥
fQ ï€¨qt ï€© = ïƒ²q = s g Dt ,St ï€¨z, st ï€©dz (A.9)
t St < Dt t t
In general, we know that the marginal density of Qt is given by:
ï‚¥ ï‚¥
f Q ï€¨qt ï€© = ïƒ² g D ,S ï€¨qt , z ï€©dz ï€« ïƒ² g D , S ï€¨z, qt ï€©dz (A.10)
t qt t t qt t t
Let us assume that residuals ï?¥ 1 and ï?¥ 2 are independent ( ï?³ 12 = 0 ). In this case, the joint
density can be expressed as follows:
ïƒ¬ ïƒ¼
ïƒ¯ 1 ïƒ©ïƒ¦ d t ï€ x1,t ï?¢1 ïƒ¶ ïƒ¦ st ï€ x2,t ï?¢ 2 ïƒ¶ ïƒ¹ ïƒ¯
' 2 ' 2
g D , S ï€¨d t , st ï€©=
1
exp ïƒï€ ïƒªïƒ§ïƒ§
ïƒ· ï€«ïƒ§
ïƒ· ïƒ§ ï?³
ïƒ· ïƒºïƒ½
ïƒ· ïƒº (A.11)
t t 2ï?°ï?³ 1ï?³ 2 ïƒ¯ 2 ïƒªïƒ¨ ï?³1 ïƒ¸ ïƒ¨ ïƒ¸ ïƒ»ïƒ¯
ïƒ® ïƒ« 2
ïƒ¾
ïƒ© 1 ïƒ¦ d ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹
1 ïƒ© 1 ïƒ¦ s ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹
= exp ïƒªï€ ïƒ§ïƒ§
t 1,t 1
ïƒ· ïƒº ï‚´ exp ïƒªï€ ïƒ§ t
ïƒ· ïƒº ïƒ§
2,t 2
ïƒ· ïƒº
ïƒ· ïƒº
2ï?°ï?³ 1ï?³ 2 ïƒª 2ïƒ¨ ï?³1 ïƒ¸ ïƒ» ïƒª 2ïƒ¨ ï?³2 ïƒ¸ ïƒ»
ïƒ« ïƒ«
Now, consider the first member of the marginal density of Qt (equation A.4):
28
ïƒ¬ ïƒ© ïƒ¦ q ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹ ïƒ© 1 ïƒ¦ z ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹ ïƒ¼
ï‚¥ ïƒ¯ ïƒª 1 ïƒ§ t 1,t 1 ïƒ· ïƒº
ï‚¥ ïƒ¯
ïƒ²qt g Dt ,St ï€¨qt , z ï€©dz = 2ï?°ï?³ 1ï?³ 2 ïƒ²qt ïƒexp ïƒªï€ 2 ïƒ§ ï?³ 1 ïƒ· ïƒº ï‚´ exp ïƒªï€ 2 ïƒ§ ï?³ 2 ïƒ· ïƒº ïƒ½dz
1 2,t 2
ïƒª ïƒ¨ ïƒ§ ïƒ· ïƒº
ïƒ¯ ïƒ« ïƒ¨
ïƒ® ïƒ¸ ïƒ» ïƒ« ïƒ¸ ïƒ»ïƒ¯ïƒ¾
1 ïƒ© 1 ïƒ¦ q ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹ 1 ï‚¥
ïƒ© 1 ïƒ¦ z ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹
exp ïƒªï€ ïƒ§ t 1,t 1 ïƒ· ïƒº ï‚´ ïƒ²qt exp ïƒªï€ 2 ïƒ§ ï?³ 2 ïƒ· ïƒº dz
2,t 2
= ïƒ§ ïƒ· ïƒº ïƒ§ ïƒ· ïƒº
2ï?° ï?³ 1 ïƒª 2ïƒ¨ ï?³1 ïƒ¸ ïƒ» 2ï?° ï?³ 2 ïƒª ïƒ¨ ïƒ¸ ïƒ»
ïƒ« ïƒ«
In the first term of this expression, we recognize the value of the N ï€¨0,1ï€© density
ï€¨ ï€©
function at the particular point qt ï€ x1,t ï?¢1 /ï?³ 1. Indeed:
'
1 ïƒ© 1 ïƒ¦ q ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹ ïƒ¦ q ï€ x' ï?¢ ïƒ¶
exp ïƒªï€ ïƒ§ t 1,t 1 ïƒ· ïƒº = ï?¦ ïƒ§ t 1,t 1 ïƒ· (A.12)
2ï?° ïƒª 2ïƒ§ïƒ¨ ï?³1 ïƒ· ïƒº
ïƒ¸ ïƒ»
ïƒ§
ïƒ¨ ï?³1 ïƒ·
ïƒ¸
ïƒ«
where ï?¦ ï€¨.ï€© denotes the N ï€¨0,1ï€© density function. Since this function is symmetric the
first member of the marginal density of Qt can be expressed as:
ï‚¥ 1 ïƒ¦ x ï?¢ ï€q
'
ïƒ¶ ï‚¥
ïƒ© 1 ïƒ¦ z ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹
g D , S ï€¨qt , z ï€©dz = ï?¦ ïƒ§ 1,t 1 t
ïƒ²qt t t ïƒ·ï‚´ 1 ïƒ²qt exp ïƒªï€ 2 ïƒ§ ï?³ 2 ïƒ· ïƒº dz
2,t 2
(A.13)
ï?³1 ïƒ§ ï?³1
ïƒ¨
ïƒ·
ïƒ¸ 2ï?° ï?³ 2 ïƒª ïƒ¨ ïƒ§ ïƒ· ïƒº
ïƒ¸ ïƒ»
ïƒ«
The second term can be transformed in order to introduce the N ï€¨0,1ï€© cumulative
distribution function, denoted ï?†ï€¨.ï€© . Consider the following change in variable
~ ~
ï€¨ ï€©
z = z ï€ x'2,t ï?¢ 2 /ï?³ 2 , with dz = d z ï?³ 2 . Then, we have:
ïƒ¦ ~2ïƒ¶
ï‚¥
ïƒ© 1ïƒ¦zï€x ï?¢ ïƒ¶ ïƒ¹ ' 2
ï‚¥
ïƒ§ ïƒ· ~
1 1 ïƒ§ ï€ z ïƒ·d z ï?³ 2
exp ïƒªï€ ïƒ§
ïƒ²qt ïƒª 2 ïƒ§ ï?³ 2 ïƒ· ïƒº dz = ïƒ²ï‚² exp ïƒ§ 2 ïƒ·
2 2,t
(A.14)
2ï?° ï?³ 2 ïƒ· ïƒº 2ï?° ï?³ 2 qt
ïƒ« ïƒ¨ ïƒ¸ ïƒ» ïƒ§ ïƒ·
ïƒ¨ ïƒ¸
ïƒ¦ ~2ïƒ¶
ïƒ§ ïƒ·
1 ï‚¥ z ïƒ· ~
~ exp ïƒ§ ï€
= ïƒ² ïƒ§ 2 ïƒ·d z
2ï?° q t
ïƒ§ ïƒ·
ïƒ¨ ïƒ¸
~
with q t = ï€¨qt ï€ x'2,t ï?¢ 2 ï€©/ï?³ 2 . This integral can then be expressed as a function ï?†ï€¨.ï€©.
1 ïƒ© 1 ïƒ¦ z ï€ x' ï?¢ ïƒ¶ 2 ïƒ¹
ï‚¥ ïƒ¦~ ïƒ¶ ïƒ¦ ~ ïƒ¶
exp ïƒªï€ ïƒ§ ïƒ· ïƒº dz = 1 ï€ ï?†ïƒ§ q t ïƒ· = ï?†ïƒ§ ï€ q t ïƒ·
ïƒ² ïƒª 2ïƒ§ ï?³2 ïƒ· ïƒº
2,t 2
(A.15)
2ï?° ï?³ 2 qt ïƒ§ ïƒ· ïƒ§ ïƒ·
ïƒ« ïƒ¨ ïƒ¸ ïƒ» ïƒ¨ ïƒ¸ ïƒ¨ ïƒ¸
29
Finally, we obtain:
1 ïƒ¦ x1,t ï?¢1 ï€ qt ïƒ¶ ïƒ¦ x2,t ï?¢ 2 ï€ qt ïƒ¶
' '
ï‚¥
ïƒ²qt t t g D , S ï€¨qt , z ï€©dz =
ï?¦ïƒ§ ïƒ·ï?†ïƒ§ ïƒ· (A.16)
ï?³1 ïƒ§ ï?³1
ïƒ¨
ïƒ· ïƒ§
ïƒ¸ ïƒ¨ ï?³2 ïƒ·
ïƒ¸
Symmetrically, we can compute the second term of the marginal density of Qt
(equation A.10) as:
ï‚¥ ïƒ¦ x'2,t ï?¢ 2 ï€ qt ïƒ¶ ïƒ¦ x1,t ï?¢1 ï€ qt
'
ïƒ¶
g D , S ï€¨z, qt ï€©dz =
1
ïƒ²qt t t ï?³2 ïƒ¨ ï?³2
ïƒ·ï?†ïƒ§
ï?¦ïƒ§
ïƒ· ïƒ§
ïƒ§ ï?³1
ïƒ·
ïƒ· (A.17)
ïƒ¸ ïƒ¨ ïƒ¸
The marginal density of Qt is then defined by equation A.6:
1 ïƒ¦ x1,t ï?¢1 ï€ qt ïƒ¶ ïƒ¦ x'2,t ï?¢ 2 ï€ qt ïƒ¶
'
f Q ï€¨qt ï€© = ï?¦ ïƒ§
ïƒ§ ïƒ·ï?†ïƒ§
ïƒ· ïƒ§
ïƒ·
ïƒ·
t ï?³1 ïƒ¨ ï?³1 ïƒ¸ ïƒ¨ ï?³2 ïƒ¸
1 ïƒ¦ x'2,t ï?¢ 2 ï€ qt ïƒ¶ ïƒ¦ x1,t ï?¢1 ï€ qt
'
ïƒ¶
ï€« ï?¦ïƒ§
ïƒ§
ïƒ·ï?† ïƒ§
ïƒ· ïƒ§
ïƒ·
ïƒ·
ï?³2 ïƒ¨ ï?³2 ïƒ¸ ïƒ¨ ï?³1 ïƒ¸
Appendix 3: The choice of initial conditions in the ML optimization procedure
There are various methods to obtain the initial conditions on structural
parameters ï?± in the ML iteration. Here, we use a two-step OLS procedure. First, we
consider the linear regressions of the observation qt on the exogenous variables sets in
^ ^ ^
both functions: qt = xi' ,t ï?§ i ï€« ï? i ,t , with i = 1,2. Given the realizations of ï?§ 1 and ï?§ 2 , we
~ ^ ~ ^
compute a first approximation of demand and supply, as d t = x1,t ï?§ 1 and s t = x'2,t ï?§ 2 .
'
^ ^
Even if we know that ï?§ 1 and ï?§ 2 , are not convergent estimators of ï?¢1 and ï?¢ 2 , we build
two subgroups of observations.
In the first subgroup, denoted by index d , we consider only the observations on
~ ~
Qt , X 1,t and X 2,t for which we have d t ï‚£ s t . In the second subgroup, we consider the
~ ~
observations for which we have s t ï‚£ d t . The second step of the procedure consists in
applying the OLS on both subgroups:
~ ~ ~ ~
ï€¨ ï€¨s
qtï€¨d ï€© = x1,dt ï€©' ï?¢ 1 ï€« ï? 1,t and qtï€¨s ï€© = x2,tï€©' ï?¢ 2 ï€« ï? 2,t (A.18)
30
~
Then, we use the OLS estimates ï?¢ i as starting values for ï?¢ i in the ML iteration. For
the parameters ï?³ 1 and ï?³ 2 , we adopt the following starting values:
~ 1
ni ~
ï?³i =
ni
ïƒ¥ ï? i, j
j =1
i = 1,2 (A.19)
where n1 denotes the size of the â€œdemandâ€? subgroup of observations for which we
~ ~
have d t ï‚£ s t , and n2 denotes the size of the corresponding â€œsupplyâ€? subgroup.1
Appendix 4: Test for Disequilibrium
Quandt (1988) proposed different approaches to test for disequilibrium. First, let us
rewrite the model to distinguish between the price variable pt (here the lending rate)
~ ~
and the other explanatory variables in each regime, denoted x 1,t and x 2,t (including the
constant).
'
~
d t = ï?¡ 1 pt ï€« x 1,t ï?¢1 ï€« ï?¥ 1t (A.20)
st = ï?¡ 2 pt ï€« x'2,t ï?¢ 2 ï€« ï?¥ 2t
(A.21)
qt = min ï€¨dt , st ï€© (A.22)
These tests are based on the reduced form from the equilibrium version of the model
given by:
ïƒ¦~ ïƒ¶
ïƒ¦ qt ïƒ¶ ïƒ§ ïƒ· ïƒ¦v ïƒ¶
ïƒ§ ïƒ· = ï€¨ll ï€ ï?¡ 2 ï?¢1 / ï€¨ï?¡ 1 ï€ ï?¡ 2 ï€©ï?¡ 1 ï?¢ 2 / ï€¨ï?¡ 1 ï€ ï?¡ 2 ï€© ï€ ï?¢1 / ï€¨ï?¡ 1 ï€ ï?¡ 2 ï€©ï?¢ 2 / ï€¨ï?¡ 1 ï€ ï?¡ 2 ï€©ï€©ïƒ§ x 1,t ïƒ· ï€« ïƒ§ 1t ïƒ·
ïƒ§p ïƒ· ïƒ§ ïƒ·
ïƒ¨ tïƒ¸ ~
ïƒ§ x ïƒ· ïƒ¨ v 2t ïƒ¸
ïƒ¨ 2,t ïƒ¸
(A.23)
Let
ï?¥ t = ï€¨ï?¥1t ï?¥ 2t ï€©' : N ï€¨0, ï?“ï€© and let ï?‡ denote the coefficients of the endogenous variables
vt = ï€¨v1t v2t ï€© : N ï€¨0, ï?—ï€© with ï?— = ï?·ij = ï?‡ ï?“ï?‡ .
' ï€1 ï€1
in the structural equation (A.20). Let
1
Monte Carlo simulations of the procedureâ€™s accuracy are available upon request.
31
Using the reduced form and the properties of vt , it can be shown that the equilibrium
quantity may be expressed as follows:
ï?· ïƒ¦ï?· ïƒ¶ ï?¢1 ~ ïƒ¦ ï?· ïƒ¶ ï?¢2 ~
qt = 12 pt ï€« ïƒ§ 12 ï€ ï?¡ 2 ïƒ·
ïƒ§ï?· ïƒ· ï€¨ï?¡ ï€ ï?¡ ï€© x 1,t ï€« ïƒ§ï?¡ 1 ï€ 12 ïƒ·
ïƒ§ x 2,t ï€« ï? t (A.24)
ï?· 22 ïƒ¨ 22 ïƒ¸ 1 2 ïƒ¨ ï?· 22 ïƒ· ï€¨ï?¡ 1 ï€ ï?¡ 2 ï€©
ïƒ¸
This equation is a hybrid between structural and reduced form equations and has the
following properties (1) all variables other than qt appear on the right hand side 2) its
error term is uncorrelated with any of the right hand variables and may be consistently
estimated by OLS 3) its coefficients are complicated but constant functions of the
original structural parameters.
If the disequilibrium model is appropriate, we can write :
qt = ï?¤ t dt ï€« ï€¨1 ï€ ï?¤ t ï€©st
(A.25)
where t
ï?¤ = 1 if dt < st and 0 otherwise. So, if the disequilibrium model is appropriate,
we have :
~ ~
qt = ï?›ï?¤ t ï?¡1 ï€« ï€¨1 ï€ ï?¤ t ï€©ï?¡ 2 ï?? pt ï€« ï?¤ t ï?¢1 x 1,t ï€« ï€¨1 ï€ ï?¤ t ï€©ï?¢ 2 x 2,t ï€« wt (A.26)
which is similar to A.24 except that the parameters are time varying. A simple test of the
disequilibrium assumption consists in testing the parametersâ€™ time stability in a
regression similar to equation A.24.
Quandt (1988) proposed to consider an equation of the general form:
~ ~
qt = ï?± 0 pt ï€« ï?±1 x 1,t ï€« ï?± 2 x 2,t ï€« ï?¥ t (A.27)
and to compute the simple recursive residuals. The cusum and cusum of squares test
can then be used to test the null hypothesis that the regression coefficient is constant,
i.e. the equilibrium hypothesis.
Figure 12 displays the cusum and cusum-square statistic and the confidence interval for
q
the null of equilibrium, based on the regression model (18) where t denotes the real
~
p
claims, t denotes the real lending rate, x 1,t includes the lagged real total deposits, the
lagged real banks deposit with the central bank and the lagged real net claims on
32
~
government, x 1,t includes the real T-bill rate, the lagged stock market index and the
lagged real industrial production.
The cusum of squares statistic is larger than the interval confidence since 2005, so the
parametersâ€™ null of constancy and hence the equilibrium assumption are rejected. The
cusum test gives a different result: the null of equilibrium is not rejected. But, this result
is not robust since the recursive estimates of the parameters (Figure 13) show that not
all the coeffcients are constant over time.
Figure 12: CUSUM Tests
1.6
1.2
0.8
0.4
0.0
-0.4
03 04 05 06 07 08 09 10 11
CUSUM of Squares 5% Significance
Source: Constructed by the authors.
20
10
0
-10
-20
03 04 05 06 07 08 09 10 11
CUSUM 5% Significance
33
Figure 13: Recursive Parameter Estimates
10 4
9
2
8
0
7
6
-2
5
-4
4
3 -6
04 05 06 07 08 09 10 11 04 05 06 07 08 09 10 11
Re c u rs i v e C(1 ) Es ti m a t e s Â± 2 S. E. Re c u rs i v e C(2 ) Es ti m a t e s Â± 2 S. E.
1 .0 0 .8
0 .5
0 .6
0 .0
0 .4
-0 . 5
-1 . 0
0 .2
-1 . 5
0 .0
-2 . 0
-2 . 5 -0 . 2
04 05 06 07 08 09 10 11 04 05 06 07 08 09 10 11
Re c u rs i v e C(3 ) Es ti m a t e s Â± 2 S. E. Re c u rs i v e C(4 ) Es ti m a t e s Â± 2 S. E.
0 .4 0 .0 5
0 .2 0 .0 0
0 .0 -0 . 0 5
-0 . 2 -0 . 1 0
-0 . 4 -0 . 1 5
-0 . 6 -0 . 2 0
04 05 06 07 08 09 10 11 04 05 06 07 08 09 10 11
Re c u rs i v e C(5 ) Es ti m a t e s Â± 2 S. E. Re c u rs i v e C(6 ) Es ti m a t e s Â± 2 S. E.
34