Download Does consumer credit support domestic growth or imports?

Does consumer credit support domestic growth or imports? Evidence from
France
Jérôme Coffinet1, Geoffrey Devost, Chourouk Ghorbel-Karker and Christophe Jadeau
Abstract
Consumer credit plays a crucial role in macroeconomics, as it supports household expenses.
This is especially true when, in bad times, household income decelerates or even decreases:
hence, consumer credit may constitute a substitute to income in order to foster households’
expenses.
Nevertheless, the aggregate effect on domestic growth also depends on the structure of
expenses: when imports play an important role in the economy, consumer credit may
conversely boost imports rather than domestic growth.
This paper seeks to evaluate the aggregate effect of consumer credit shocks both on imports
and domestic growth. Thus, we estimate a vector error correction model on French quarterly
data over the 1993-2015 period.
We find that the impact of consumer credit shocks is particularly strong on imports, both on
the short and on the long-term, and even stronger than on GDP. Despite structural breaks in
1993 and 2007, our results are robust to various specifications.
1
Banque de France, Directorate General Statistics. [email protected] . The views expressed in
the paper are the sole responsibility of the authors and do not necessarily represent those of the Banque de
France.
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1. Introduction
Since the outbreak of the economic and financial crisis, many measures have been introduced
in order not only to ensure financial stability, but also to foster a sustainable economic
growth, compatible with sounder fundamentals in households’ indebtedness. For instance, in
France, the regulation of consumer credit has undergone deep changes, particularly with the
so-called “Lagarde law” implemented in July 1, 2010, whose major objectives are to improve
consumers’ protection and prevent over-indebtedness. As a result, the law generated
significant changes in the consumer credit market, the most important of which allowing
reduced informational frictions, a better informed consumers’ choice and a decrease in
incentives for credit agencies to refer clients to revolving loans. A Committee chaired by the
Governor of the Banque de France has been responsible for monitoring the effectiveness of
these measures between 2012 and 2014, which has resulted in a reduced use of revolving
credit in favor of more traditional consumer credit. Nonetheless,
the consumer credit
supporting the domestic economy or rather benefiting the economy of trading partners
through increased imports remains an open issue.
Indeed, if the impact of consumer credit on output growth is clearly positive in the short run
in a closed economy (through the increase of consumption), its effect is more uncertain in an
open economy: when, for instance, a household decides to subscribe a credit to finance the
purchase of a vehicle, this may result in the import a foreign car rather than in the making of a
domestic one. This is particularly true in very open countries.
Very few studies have examined this issue specifically. Rather, the literature addresses
separately different aspects of it, which justifies our approach.
Indeed, until the 1970-80's, the assumption of complete markets and the theory of market
efficiency allowed to consider credit as a completely substitutable asset to other financial
assets without any specific impact on the macroeconomy.
From the 80's, the emergence of the information economy and contract theory (Akerlof,
1970;Stiglitz and Weiss, 1981) helped highlight the specific characteristics of credit. In this
literature, credit is often limited to credit to companies. It was then recognized that credit had
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a short-term negative effect on aggregate demand when restrictive monetary policy was
conducted, consistently with the "credit view of the monetary transmission" (Blinder and
Stiglitz, 1983; Bernanke and Blinder, 1988; Bernanke and Gertler, 1989; Kiyotaki and Moore,
1997).
The recent financial crisis also contributed to foster research on credit rationing (Gertler and
Kiyotaki, 2010 ; Kremp and Sevestre, 2013) and other frictions. Nevertheless, this strand of
the literature is still focused on credit to companies. Finally, while the literature on the
relationship between the economic cycle and credit is rich, the long-term impact of credit on
growth has been little explored and generally seen as an aspect of financial deepening.
Therefore most of this literature is concentrated in development economics (Greenwood and
Jovanovic 1990, Galor and Zeira 1993). The main message of this literature is that the
development of the credit market improves risk diversification, consumption smoothing and
thus human capital accumulation (Acemoglu 2008).
However, Büyükkarabacak and Krause (2009) underline that it is crucial to distinguish private
household credit from private business credit in order to study the impact of private credit on
GDP. Using data from 9 developing and transition countries, they find that, while private
business credit is not correlated with net exports, private household credit is negatively and
significantly correlated with net exports. Moreover, they find that a higher proportion of
business credit supports net exports: in order to reduce the foreign trade deficit, business
credit should be favored over household credit. Thus, only in the case of transition economies,
Buyukkarabacak and Krause highlight a relationship between household credit and imports,
but without distinguishing credit for house purchase and consumer credit. Yet, if housing
credit accounts for a wide majority of outstanding household credit, consumer credit is more
likely to impact the trade balance. Hence, using a Schumpeterian framework, Sassi (2014)
proposes a more precise decomposition of credit and studies jointly the effects of consumer
credit market and investment credit market on economic growth, reaching similar results to
those of Büyükkarabacak and Krause (2009).
In addition, while a range of theoretical papers explain the link between consumption and
income, little research is dedicated to the links between aggregate consumption and consumer
credit. In particular, in permanent income and life cycle papers (Friedman, 1957, Hall 1978,
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Flavin 1981, Modigliani 1986, Campbell and Mankiw 1990), credit demand only reacts in a
“passive” way to income shocks.
An important contribution is however Ludvigson (1999) which shows both that the rationing
of credit decreases contemporary consumption and that current consumption may be affected
by the anticipation of future rationing. Empirically, he shows that credit (namely credit
including revolving credit) has a positive and significant effect on consumption growth,
regardless of the effect of income. Consumption is found “excessively sensitive” to credit, in
contrast with predictions based on the life cycle hypothesis.
Finally, the connection between credit and imports has also received very little attention. In
the very specific context on Turkey during the 2008 crisis, Özülke (2011) studies the effect of
consumer credit on the current account balance, and finds that the recovery in consumption is
concomitant with the increase in consumer credit outstanding. Özülke emphasizes a strong
link between the increase in consumer credit and the increase in the trade deficit, which had
already been found in developing and developed countries by Demirgüç-Kunt and
Detragiache (1998) before 2008 crisis.
There is however a significant literature on the link between growth and imports. Hooper,
Johnson and Marquez (2000) show for example that an increase of 1% of GDP in the U.S.
leads to an increase of 2% of the expenditure for imports. The idea that imports stimulate
growth in the short run is developed by Humpage (2000), who shows that imports or more
generally international trade promotes the specialization or the transfer of technology, leading
to an improvement of global well-being.
In addition, private consumption structurally plays a key role in the French economy. While it
accounts for only 56% of GDP, which is below US (69%), Japan (61%), and close to
Germany (55%), in order to dampen current difficulties of growth resumption, one major
issue regarding the implementation of economic policies aimed to stimulate the consumption
of households and to limit the use of fiscal policies. Although consumer credit is not used so
massively in France as in the United States, for example (outstanding credit amounts in
France to 146 billion euros, which represents 14% of the French GDP; in the United States, it
amounts to 3 106 billion dollars, or 20% of the U.S. GDP), this remains an important means
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of consumption smoothing. It is therefore interesting to look at how the consumption of
households reacts to shocks on consumer credit.
The rest of the paper is organized as follows. Section 1 describes the data used and presents
some descriptive statistics. Section 2 details the error correction model selected. The main
results are exposed and commented in section 3. Finally,
section 4 summarizes and
concludes.
2. Data description
The database incorporates the stock of consumer credit over the period 1993Q1-2013Q3
which is the main variable to be studied. The interest rate of consumer credit is also available,
as well as the households debt or savings ratios. For each time series, 83 points are available.
Hence, this database allows including consumer credit, macroeconomic variables of the
business cycle, and interest rates.
Chart 1.1 (in annex) represents macroeconomic time series (in logarithms). One can
immediately notice that the series have an upward trend over the period which strongly
supports the non-stationarity of these time series. An important question will be whether this
non-stationarity is deterministic, stochastic, or more probably a combination of both.
On the other hand, the chart shows a possible cointegrating relationship between some series.
Indeed, the curves illustrate a similar average growth and a relatively constant gap. This is
particularly true for imports and exports, which are very often cointegrated variables. Finally,
we can notice that the recent economic crisis has not had the same effect on all these
variables. If outstanding credit2, or consumption, appears to have been relatively little
affected, imports and GDP seem to have suffered a severe negative shock and no longer
follow the same trend. During the various stages of the modeling, we will endeavor to take
into account of this break.
2
The reports of the Usury reform Monitoring Committee show that the negative effect of the economic crisis
on consumer credit outstanding has been limited thanks to the reforms within the credit to the consumer
market
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Graphical representations of the interest rates series appear in Chart 1.2. Here again,
especially for the Euribor 3-month rate and the consumer credit rate, the series seem nonstationary since they both exhibit a downward trend. The effect of the financial crisis is
highly visible, with a marked decrease in the short-term rate, resulting from the monetary
policy reaction. Finally, the short-term rate and the consumer credit rate appear to be strongly
correlated and possibly cointegrated. This result is not surprising, knowing that credit rate
depends on the refinancing cost of banks on the markets, which is even closely linked to
money market rates.
a. Choice of variables
The choice of variables is based on economic theory and the existing literature. Chart 1.3
provides a simplified representation of the expected interactions between key variables. When
credit is more expensive for consumers, the demand for credit decreases. Conversely, the
increase in outstanding credit, meaning rising demand for credit, creates upward price (here
the rates), all things equal also, in particular, if the supply of credit does not evolve. On the
other hand, an increase in the stock implies, by definition, an increase in consumption.
Similarly, according to economic theory, an increase in the disposable income of the
households leads to a rise in consumption in a smaller proportion, so overall demand in the
country. From a Keynesian perspective, with production being determined by demand in the
short run, consumers can contribute positively to growth if it is geared towards a domestic
demand rather than to external demand. In the latter case, the increase in consumption, due to
outstanding credit and/or income, will have a positive effect on the level of imports. If the
local supply does not meet this demand, this can lead to an increase in imports.
b. Stationarity
To investigate the stationarity of the series, two types of tests were performed. Firstly, unitroot tests were conducted on all the variables: ADF, ERS, DFGLS. The so-called second
generation tests have been widely preferred to standard unit root tests like the Phillips-Perron
test. Second generation tests are in fact better able to detect non-stationarity in the presence of
small samples. Secondly, the stationarity KPSS test was performed to check the adequacy of
the results.
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Table 1.1 summarizes the results of the tests. Annex B also provides the detailed study of
stationarity for outstanding series.
The results show that credit outstanding in level is non-stationary. The origin of the nonstationarity appears to come from an upward trend. As expected, macroeconomic variables
such as GDP, consumption and imports are not stationary. The same conclusion applies to the
sets of credit rates. Inflation meanwhile appears stationary.
Hence, tests are conducted after differentiation of all the series. The results for credit do not
all converge. If, for the ERS and ADF tests, the transform series is stationary, other tests
reject the stationarity hypothesis. Thus, this series will be regarded as I(1) later in the study. If
it turns out that the series is in fact I(2), a number of phenomena should appear in the VECM,
and will lead to revise this assumption. A similar approach was adopted for the series of the
short rate, for which tests also give mixed results. This strategy is also motivated by the fact
that the choice of 10% critical values allows to opt for the stationarity of these series in first
differences. All of the other series are identified as I(1) by the different tests. Those results are
consistent with the literature on this subject.
To summarize, this study indicates that the whole series are I(1), except the inflation rate
which is I(0).
c. Correlations
Now, the analysis focuses on the joint movements of variables. To this end, the use of
correlation matrices seemed relevant. First, a static correlation matrix allows to study the
contemporary relationship between the variables. Then, the introduction of dynamics in the
correlation matrix is useful for determining if the correlation between variables follows a
certain movement. We will also have a first look at the relevance of causality between the
variables.
Following the previous results regarding the non-stationarity of the level variables, each
variable is considered in first-differences. The static correlation matrix (chart 1.4) allows to
easily visualize correlations between the series by using the color code indicating both the
meaning of the correlation (blue positively correlated, red negatively correlated) but also the
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intensity of the correlation (gradient combined with the volume of the circle). Non-significant
correlations to the 10% threshold are barred with a black cross.
In the light of this matrix, outstanding credit appears as correlated positively and significantly
with household consumption, GDP and imports. However, the correlation is stronger with
consumption (0.43) and GDP (0.45) than imports (0.29). On the other hand, they are
negatively correlated with the unemployment rate and inflation.
Household consumption follows the same pattern, with correlations more intense (0.53 with
GDP) and with imports (0.32). It is positively correlated with the confidence of households
(ICM) and negatively correlated with the saving index.
GDP, imports and exports as well as the GDP of the OECD countries are, as expected,
positively and strongly correlated. Furthermore, they are positively correlated with loan rates
and especially with the short term rate, as well as with domestic demand. On the other hand,
they are negatively correlated with the unemployment rate.
Finally, the ICM is negatively correlated with inflation. The rate of the consumer credit does
not appear to present a significant correlation with macroeconomic variables.
These correlations represent the overall correlation between the series based on the values
taken at the same date, i.e. contemporary correlations. An interesting approach would be to
study the correlations between lagged series.
The analysis is thus carried out within a dynamic correlation matrix approach4. The dynamic
correlations matrix is presented in Chart 1.5 that uses a color code similar to the previous
one5, with also a cross representing the non-significance of the correlation at the 10%
threshold. In addition, a lag of 0.25 represents a quarter, and as a consequence a lag of 1
represents a year.
The results show that the correlation is above all contemporary with household consumption
spending and GDP. On the other hand, the maximum correlation between imports and stocks
is at t-2. In other words, an increase in stocks is followed by an increase in imports two
4
f Boxes indicate the correlation between, for example, consumption on the date t and stocks on the dates t, t1, t-2...
5
However, the color scale is different.
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quarters later. The same observation can be made in relation with GDP and domestic demand.
In addition, there a a low but significant correlation with the short rate of lagged periods: a
rising stock leads to an increase in the borrowing rate.
Significant negative correlations are found with inflation, the CPI and the unemployment rate.
For inflation, the correlation is particularly present with lags: a decline in the stock follows an
increase of inflation in the previous quarters; it is same with the CPI. For the unemployment
rate,the previous lags are significant. Thus, a decline in the stock leads to the rise of
unemployment the following quarters and an increase in stocks leads to a decrease in
unemployment6.
The dynamics of household consumption correlations matrix is represented in Chart D14. It
shows that the (negative) correlation with the savings is inter alia contemporary, but that an
increase in consumption is preceded by an increase in savings in the previous quarter.
Similarly, the correlation with GDP is essentially contemporary, but still significant at +/- 2
quarters although less intense. Thus, an increase in consumption follows an increase in GDP,
but is also preceded by its increase. It is the same for outstanding credit. Finally, the same
remarks with the series of stocks can be made with inflation and the unemployment rate.
Descriptive analysis made to get a first intuition of the relevant variables to include in the
template. To have a first look at the short term relationships between variables, a Vector
Autoregressive (VAR) model analysis is detailed in the following section.
d. VAR analysis
This part goes somewhat further in the descriptive analysis using a vector autoregressive
model. It is probably not the best possible modeling since all of the dynamics of long term is
not taken into account. However, VAR modeling, because is simple and flexible. In addition,
this step also allows obtaining important information on the specification that will be used in
the cointegrated model.
6
This can be explained by an anticipation effect:for instance, individuals who leave unemployment can
anticipate their income will increase and thus take on consumer credit.
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This section presents the main results obtained. However, overall results, such as the choice of
the number of delays or tests on the residuals, are placed in Annex E.
A five-variable model VAR(1) is estimated :
where et represents outstanding consumer credit, ct the consumption expenditure of
households, mt imports, gt the gross domestic product and rt the average rate of consumer
credit. Variables are expressed logarithms, except the average rate of appropriations.
The choice of modeling the first differences is due to non-stationarity of variables in levels.
Finally, control variables have been added: the household income delayed for a period wt-1, as
well as an indicator φ(Dt) to take account of the financial crisis. The order of the VAR was
determined by the common criteria for information. The results are not identical for all
criteria. We chose the VAR(1) which has the advantage of minimizing the number of
parameters to estimate taking into account the number of available observations.
The model can be rewritten in the following form:
The table 1.2 shows the results of the estimation. The analysis of the VAR model allows
highlighting several important elements.
First of all, outstanding credit has a significant impact on all endogenous variables. The
coefficients are significant at the 1% or 5% thresholds. One can therefore think, with a certain
degree of confidence, that consumer credit has an impact, at least in the short term, on
consumption, imports and GDP.
More specifically, the estimates show that outstanding credit has a positive impact on
household consumption, GDP and more surprisingly on imports. This first result supports the
idea that the consumer credit may not fully benefit French growth.
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On the other hand, in accordance with economic intuition, an increase in the rate of credit
weighs on stocks. In addition, household income has a positive impact on consumer credit,
household consumption as well as GDP. Finally, it appears that the crisis has not had a
significant impact on outstanding credit, while the effect on imports and growth is significant.
There again, these results are intuitive and consistent with economic theory.
If previous results have highlighted the positive impact of outstanding credit on the household
consumption, imports and GDP, the magnitude of these impacts has not yet been discussed.
Figure 1.6 shows the impulse response functions (IRFs) of a positive shock on the innovations
in credit7 .
The IRFs confirm the positive impact of outstanding credit on the macroeconomy.
Nevertheless, two important elements emerge immediately from the graphs. Firstly, a shock
on outstanding credit does not affect all variables with the same magnitude; secondly, these
variables do not show the same dynamics after the shock. Indeed, a shock on the credit has a
much more significant impact on imports than on GDP and consumption.
In addition, if the maximum effect of the shock on household consumption takes place in a
contemporary manner, another dynamic appears to govern imports. They are characterized by
a greater effect in t+1, but also by a greater persistence.
Quantitatively, in t, the impact of the shock on imports is 20% more important than the one on
consumption and, in t+1, the shock has a 4 times greater impact on imports. GDP, meanwhile,
presents an intermediate dynamics between these two trajectories.
In order to assess the results presented above, it is important to analyze residuals (see Annex
E). The results are relatively positive overall. First of all, residuals are mostly detected as
normal except for residuals of the consumption equation. No autocorrelation is detected,
except in t-4. Finally, the roots of the polynomial allow checking that the model is stable and
stationary.
7
VAR order affecting the interpretation of the results, outstanding credit was deliberately placed first, in order
to directly interpret the impact of a shock on this variable on other macroeconomic variables. The confidence
interval is calculated by bootstrapping, the confidence level was set at 80% and the number of simulations at
500. Higher numbers of simulations were tested in practice but withminimal impact.
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To improve the performance of the model and to enrich its economic interpretation, taking
into account the short and long term dynamics, a cointegrated vector error correction model
(VECM) is estimated and presented in the next section.
3. The Model
To estimate the VECM model, different steps have been undertaken. First, one should check
whether the series are integrated of the same-order. Then, using the information criteria, the
number of delays p of the model VAR(p) is determined. The next step is to identify the
number of cointegration relationships using the Johansen test (1988, 1991); it is followed by
the identification of the cointegrating relationships, i.e. the long term relationships between
variables. The last step is the estimation of the model by the method of maximum likelihood
and validation of the usual tests.
Different models have been tested. A visual approach has been adopted as a first step in order
to choose the most appropriate one, including the analysis of the IRFs and the chart of the
cointegrating relationship (which must be stationary). Then, after a screening of the models,
the analysis turned to the significance of the coefficients and the results of the different
models (residuals analysis...).
The model chosen is a five variable VECM(1), identical to those of the VAR model, including
a binary exogenous variable to take account of the economic crisis of 2007. In determining it,
a trend beak test9 shows a break in the series in the fourth quarter of 2007. The retained
specification is the one without quadratic trend in the variables in level and with a linear trend
in the cointegrating relationship. This modeling will be discussed further on in the report.
Finally, the considered period is 1995q1 - 2013q3, because there are signs that the currency
crisis of 1993 affects the model estimation.
The testing of the number of delays and the rank of cointegration tests are presented
respectively in tables 2.3 and 2.4. Firstly, the criteria for information select unanimously delay
9
The rupture test we use is the test supF; its peculiarity is to test and identify structural without a priori change
on the exact date.
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(at the 5% level). This would mean that short term dynamics is not involved in the equations
of the model VECM (p-1 in the equation). However, as this specification is not very
interesting, the selected model incorporates a short term dynamics, with the number of lags
set at p=2. This completes step 2 of the procedure.
Rank tests (test trace and the eigenvalue) indicate the number of cointegration equations
present in the template (step 3). However, the presence of an exogenous variable may distort
the critical values of the Johansen test, which should be handled with caution.
When including the exogenous variable, both tests provide the same result at the 5% level,
and indicate the presence of a single cointegrating relationship. To consolidate these results,
the tests were conducted without the exogenous variable. The first test reveals two equations
of cointegration while the second don’t. After analysis of different models with r=1 and r=2,
it is the first specification which has been retained.
Thus, the selected model is written as follows:
In the light of economic theory, several priori can be placed on the sign of the coefficients of
the cointegrating relationship. Indeed, we expect for example that outstanding credit depends
on long term consumption of households and on GDP. On the other hand, it is expected that
an increase in the average rate of appropriations is associated with a decrease in outstanding
credit through a decrease in the production of credit.
4. Results
This section presents the results of the estimation of the model selected in section 2 and the
analysis of the properties of generated waste. The limits of the approach of the model will be
showed in the following, as well as possible for additional research.
a. Estimation of the model
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The results of the estimation of the model are presented in table 3.5.
Coefficients Γ which represent short term causality are first considered. A first observation is
that few coefficients are significant. In particular, none of the coefficients, associated with
consumption or imports, is significant (at the 10% threshold). On the other hand, the stock of
credit has a positive impact significant at 10% on imports and negative on the credit rates.
Moreover, the credit rates have a significant negative effect at the 1% threshold on
outstanding amounts, similarly to the results obtained in the VAR. Therefore, an increase in
the rate of credit decreases the stock of credit because they become more expensive.
Finally, the crisis has had a significant and negative impact on consumption, imports and
GDP in accordance with what was expected. The effect is also significant but positive rates.
This can be explained by a desire for continued growth by an incentive to consumption.
As for the appropriations outstanding, it has not been impacted significantly during the crisis.
This result can be explained by changes in the regulatory framework of consumer credit that
have mitigated the negative impact of the crisis.
The table 3.6 provides the coefficients involved in the cointegrating relationship.
The relationship we obtain can be interpreted as meaning that consumption positively affects
appropriations outstanding, which conforms to intuition, since an increase in consumption
may require additional funding as the use of a consumer credit. We get the same result for
imports, although the ratio is much lower. Nevertheless, the economic interpretation is here
more difficult.
However, the coefficient whose magnitude is most important is GDP. Thus, growth positively
affects credit.
Finally, as expected, the rate negatively affects outstanding credit.
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The presence of a trend in the cointegrating relationship may be due to the crisis. As it is not
possible to include an indicator in the relationship, it is likely that the trend picks up part of
the regime change that occurred in the aftermath of the economic crisis.
This cointegration relationship is represented on the chart 3.7. Overall, this relationship seems
stationary until 2007 where a break in trend is visible.
Before analyzing the magnitude of the impact on different variables, we have a look at the
values of the parameter (α) data in the table 3.5. This vector measures the magnitude of error
correction, i.e. the speed of adjustment of variables to deviations from the long-term
equilibrium.
The coefficient of adjustment of the equation of the stock is -0,054, meaning stocks need
more of 18 quarters to converge to the long-term relationship (1/0,054) after a shock.
It is now possible to explain the mechanism of transmission of a shock to credit from the
impulse-response functions. The analysis is here on the size of the impact on consumption,
imports and GDP rates.
The charts 3.8 represent the responses of the variables in the model following a shock to the
innovations of credit on the dynamics of the rates.
As in the case of the VAR approach and in accordance with the preceding analysis, the IRFs
confirm the positive impact of credit on the variables of interest. Again, the magnitude of
impact varies according to the variable of interest: the effect is more important on imports,
then GDP and consumption. Indeed, the impact on imports is 5 times more than the one on
consumption and 4 times more than the one on GDP.
However, following the shock, the dynamic is similar for all variables: the effect of the shock
is permanent, with a maximum effect in t+4.
With regard to the impact of a shock on stocks on the rate of credits, although the causation
may seem more intuitive in the opposite direction (if the rate decreases, outstanding
increases), the model approach neoclassical supply/demand allows a possible interpretation of
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the pattern of the IRF we obtain. Indeed, in the short term, if demand for credit increases,
there is a move on the demand curve that lowers the price, here the rate. If this increase in
demand is maintained in the long term, there is a shift of the demand curve for an unchanged
supply, which gives rise to a new equilibrium corresponding to higher than previous.
The different results of the VECM model confirm the first intuitions of descriptive statistics
and the VAR model. The VECM model clearly shows thatconsumer credit is involved in the
increase in imports in the long term. If consumer credit also plays its role in stimulating
consumption and GDP, this direct link is reduced via the recourse to imports.
The analysis of the residuals of the model in the next subsection will allow assessing the
quality of the results of the model VECM.
b. Residuals analysis
In this section, are analyzed the properties of the residuals of the VECM model presented in
the previous section. The aim here is to check if the residuals are normal and not
autocorrelated. This is an important step in the validation of the model. Indeed, if the residuals
do not respect the previous properties, this could for instance betray forgetting an important
variable in the model.
The first step in the analysis of residuals is to graphically examine their trajectory. Residuals
are therefore represented in chart 3.9. Graphical analysis seems to indicate that the residuals
have no particular dynamic. Residuals are quite strongly similar. In particular, it does not
display regularity in the trajectories, suggesting an oversight of variable or another problem of
model specification.
Nevertheless, in order to complete this first graphic analysis, a number of tests and Visual
diagnosis has been made. The results of these tests are presented in the following subsections.
i. Residuals normality
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First of all, is presented the analysis of normality of residuals, which relies on several
statistical tests. Test of normality of the residuals equation by equation succeeds a
multivariate normality test. The results of the various tests are synthesized in the tables below.
Table 3.7 shows the results of tests of the skewness coefficient. If residuals follow a normal
distribution then this coefficient should be close to 0. Note that in the equation of outstanding
credit and consumption this coefficient is greater than 0 in absolute value.
On the other hand, for the last three equations, the skewness coefficient is close to 0. The
rejection of the normality of the multivariate test comes here from the non-normality of the
residuals of the equation of consumption and, to a lesser extent, residuals of the equation of
outstanding credit.
The results of coefficient of flattening are presented in table 3.8. They are very similar to the
previous test. The only difference is that, here, the normality comes exclusively from
residuals of the consumption equation.
Finally, the Jarque-Bera test is presented in table 3.9. Here again the results are consistent
with what has been said previously. We reject the normality for residuals of the consumption
equation.
The results, as the normality of the residuals, are therefore positive overall. Only one problem
remains with the consumption equation. The normality can be explained by the presence of an
extreme point. Indeed, examination of the QQ-plot (chart F.21) shows that the normality
comes from a strongly negative point at the beginning of sample.
ii. Autocorrelation of residuals
In this sub-section, the results related to the detection of the autocorrelation of the residuals. A
graphical diagnostic follows the analysis of the autocorrelogrammes and the statistical tests.
Chart 3.10 is the autocorrelogrammes of residuals of the different equations of the model
VECM. The results seem very satisfactory since almost all of the correlations remain within
the confidence interval given by the formula of Bartlett. However, note that some correlations
out of the confidence interval. It is for example the case for residuals of consumption to 5
delay equation or for residuals of the rate equation of delay 4 credits.
17
To complete the analysis of the autocorrelogrammes, the hanger test conducted. The results of
the test are presented in table 3.10.
Two statistic tests are reported in this table. The second statistic test adds a correction for
small samples.
Both tests deliver the same results. The hypothesis of non-autocorrelated residuals is accepted
for all considered delays10. It can be concluded with a degree of confidence that the residuals
are not autocorrelated.
To synthesize, the tailings are generally normal and are not autocorrelated. These results
validate the quality of the estimated model and its qualitative and quantitative implications.
Finally, the analysis of the roots of the polynomial, presented in chart F20 of the annex, shows
that the model is stable. Apart from the unit roots imposed by the VECM model, the roots are
inside the unit disk.
5. Conclusion
Our main objective was to analyze the impact of consumer credit on the macroeconomy in the
case of France. Specifically, we attempted to identify to what extent consumer credit supports
domestic growth, or rather contributes to increasing imports.
To address this issue we used multivariate times series models such as VAR and VECM. Our
main result is that consumer credit growth induces a significant increase in imports. We also
find a significant, but quantitatively less important, effect on consumption and GDP. These
results represent a first empirical evaluation of the link between consumer credit and the
external position of the France, putting in light a new channel explaining the trade deficit. In
light of the current macroeconomic environment but also of recent regulatory amendments to
the credit market, those results should allow stimulating debates among economists, but also
policy makers.
10
here up to 8 times and delays were considered
18
Our model has some limitations that could be overcome in future work. In particular, more
sophisticated methods could be used to endogenize structural breaks. To this end, a natural
extension of this study would be to use a Markov switching VECM (MS-VECM). In addition,
the use of this type of model would help identifying if shocks were able to alter the nature or
the intensity of the cointegrating relationships.
19
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22
Annexes
Chart 1.1
Chart 1.2
23
Chart 1.3 Expected interactions between macro-economic variables
Table 1.1 Unit root tests for interest series
24
Chart 1.4 Statistical correlations
Chart 1.5 Dynamic correlations of outstanding credit
25
Table 1.2 Model VAR(1) estimate
Chart 1.6 Impulse response function of VAR model
26
Table 3.5 Short-term dynamic coefficients
Table 3.6 Co-integration relation
Chart 3.7 Representation of VECM model co-integration relationship
27
Chart 3.8 IRFS of VECM model (Cholesky One S.D. Innovations)
Table 3.7 Skewness tests of VECM model residuals
Table 3.8 Kurtosis tests of VECM model residuals
28
Table 3.9 Jarque-Bera tests of VECM model residuals
Chart 3.9 Estimated residuals of VECM model
29
Chart 3.10 ACF of VECM residuals
Table 3.10 Portemanteau tests of VECM model residuals
30
C
Charts of differentiated series
Chart C.13 Charts of differentiated series
31
D
Dynamic correlations
Chart D.14 Dynamic correlations depending on consumption
32
E
the VAR model
E.1
Adjustment quality
Chart E.15 Observations and forecasts of VAR model
33
E.2.1 Graphical analysis
Chart E.16 Estimate residuals of VAR model
34
E.2.2 Normality of residuals
Table E.15 Jarque-Bera test on Var model residuals
Table E.16 Skewness tests on VAR model residuals
Table E.17 Kurtosis tests on VAR model residuals
35