# Liquidity matters when measuring bank output

Raphaël Chiappini, Bertrand Groslambert, Olivier Bruno

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Raphaël Chiappini, Bertrand Groslambert, Olivier Bruno. Liquidity matters when measuring bank output. 2022. hal-03896568

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Distributed under a Creative Commons Attribution 4.0 International License
Liquidity matters when
measuring bank output

Raphaël CHIAPPINI

Univ. Bordeaux, CNRS, BSE, UMR 6060, F-33600 Pessac, France

Bertrand GROSLAMBERT

Université Côte d'Azur, SKEMA Business School

Olivier BRUNO

Université Côte d'Azur, CNRS, GREDEG, SKEMA Business School
Abstract

We develop a new method for calculating bank output that addresses the flaws of the current approach of the System of National Accounts. We implement a simple model-free method that removes the “pure” credit risk premium from the production of banks while keeping the liquidity provision as part of the total bank output. Using both local projections and autoregressive distributed lag models, we show that our method produces bank output estimates that are consistent with the evolution of the economic activity and that remain always positive including during periods of financial stress. This method satisfies the four conditions set by the Inter-Secretariat Working Group on National Accounts. Furthermore, our method reveals that the banking output of the eurozone is overestimated by approximately 40 percent over the period 2003-2017.

**Keywords:** bank output, liquidity premium, risk premium, ARDL, local projections.

**JEL:** E01, E44.

**To cite this paper:** CHIAPPINI, Raphaël, GROSLAMBERT, Bertrand and BRUNO, Olivier (2022), Liquidity matters when measuring bank output, Bordeaux Economics Working Papers, BxWP2022-20

https://ideas.repec.org/p/grt/bdxewp/2022-20.html

<figure><img src="image_2.png" /></figure>
# Liquidity matters when measuring bank output

Raphaël Chiappini*

Bertrand Groslambert†

Olivier Bruno‡

## Abstract

We develop a new method for calculating bank output that addresses the flaws of the current approach of the System of National Accounts. We implement a simple model-free method that removes the “pure” credit risk premium from the production of banks while keeping the liquidity provision as part of the total bank output. Using both local projections and autoregressive distributed lag models, we show that our method produces bank output estimates that are consistent with the evolution of the economic activity and that remain always positive including during periods of financial stress. This method satisfies the four conditions set by the Inter-Secretariat Working Group on National Accounts. Furthermore, our method reveals that the banking output of the eurozone is overestimated by approximately 40 percent over the period 2003-2017.

**Keywords:** bank output, liquidity premium, risk premium, ARDL, local projections

**JEL Classification:** E01, E44

<footnote>*Univ. Bordeaux, CNRS, BSE, UMR 6060, F-33600, Pessac, E-mail: raphael.chiappini@ubordeaux.fr.</footnote>

<footnote>†Université Côte d'Azur, SKEMA Business School, 60 rue Dostoïevski, 06902 Sophia Antipolis, France, E-mail: bertrand.groslambert@skema.edu.</footnote>

<footnote>‡Université Côte d'Azur, CNRS, GREDEG, SKEMA Business School, 250 rue Albert Einstein, 06560 Valbonne Sophia-Antipolis, France, E-mail: bruno@gredeg.cnrs.fr.</footnote>
# 1 Introduction

The financial sector has a central place in both developing and developed economies. The share of finance in Gross Domestic Product (GDP) has experienced a continuous growth over the past 60 years as depicted in Philippon and Reshef (2013). For instance, the share of the financial sector in the United States' GDP has risen from less than 4% in 1970 to around 7% in 2005. A similar trend can be observed for the United Kingdom (4% to 7,5%), Canada (4% to 6%) and Japan (5% to 6%). In the European Union, the increase is less pronounced, as we can observe an increase of 3 percentage points for Belgium, 1,5 percentage points for Germany and only 1 percentage point for France during the same period. Among the financial sector, the role of financial intermediaries is important in promoting economic growth (Rajan and Zingales, 1998). Indeed, they pool funds, produce information, transfer resources and share risks which directly benefits to both lenders and borrowers (Philippon, 2015). These services are compensated as they create value added.

Nevertheless, measuring this valued added remains a huge challenge (Sakuma, 2013; Hagino and Sonoda, 2010). Indeed, the remuneration for these financial intermediation services are not directly charged to the customers. Instead, they come from the spread between interest rates receivable on financial assets and interest rates payable on financial liabilities. They are known in national accounting under the acronym FISIM (financial intermediation services indirectly measured). The problem revolves around the estimation of the reference rate used to estimate the spreads on loans and deposits. During the financial crisis, the production of FISIM as measured by the method of the 2008 System of National Accounts (SNA) grew substantially (Akritidis and Francis, 2017). For instance, the banking value added estimated by the 2008 SNA has increased by 21% in Germany and 63% in France between 2007 and 2010¹. This estimation has been considered implausible by most national accountants (Davies, 2010), and made this issue even more acute. Since then, an intense debate has flourished to provide a more accurate method to estimate bank output (Zieschang, 2016). With no clear consensus emerging, the Task Force of the Inter-Secretariat Working Group on National Accounts (ISWGNA, 2013, p. 5) recommended

<footnote n="1">¹According to Eurostat data.</footnote>
that: “research continues in this area [...] to develop methods and data that can support estimation in the future”.

On one side of the debate, scholars such as Diewert et al. (2012), Diewert (2014), Zieschang (2016) and Fixler and Zieschang (2019) favour a reference rate specific to each bank and based on the bank's cost of capital. Using this type of reference rates implies that the value added of banks contains some elements of risk remuneration. However, critics of this approach contend that compensation for assuming credit default risk should not be part of the banks' value added. On the other side, Wang et al. (2010), Basu et al. (2011) and Colangelo and Inklaar (2012) advocate using a series of reference rates specific to the risk and maturity of each type of deposit and loan instruments. This alternative approach has the merit of removing the credit risk-related remuneration from the banking output but has the disadvantage of eliminating all liquidity-related services from the SNA account, which goes against the consensus reached by the community (ISWGNA, 2013). Borrowing from both sides of the debate, we introduce a new method that excludes the compensation for bearing credit risk in the spirit of Wang et al. (2010) and Colangelo and Inklaar (2012), but also includes the liquidity transformation services as advocated by Fixler and Zieschang (2019) and recommended by the United Nations Statistics Division (2014).

The impact of illiquidity on the price of bonds and on credit spread is well documented. For example, using several alternative liquidity measures proposed in the literature, Friewald et al. (2012) found that liquidity proxies account for approximately 14 percent of the explained time-series variation of the yield spread changes over time for individual bonds. These results, which Bao et al. (2011) confirm, underline that in times of financial stress, liquidity effects are the dominant driver of credit spread and take over the credit risk component. On the contrary, quantitative easing measures have reduced the liquidity premia and indirectly credit risk after the financial crisis as depicted by Wong et al. (2019) for the U.K. However, these liquidity effects on the value of credit spread do not reflect the fundamental level of credit risk. They are due to financial market microstructure or to portfolio reallocation during period of stress.
In this paper, we propose a new way to measure bank output based on a simple model-free method that removes the “pure” credit risk premium from the production of banks while keeping the liquidity provision as part of the total bank output. We use the spread between the yields of Kreditanstalt für Wiederaufbau (KfW) government-guaranteed agency bonds and German government bonds to estimate the liquidity premium over the term structure in the euro area. Then, we compute the adjusted liquidity-free reference rate for each maturity, and we use this new reference rate to estimate banking output of the eurozone during the period 2003-2017. We assess the performance of our method using the four criteria established by the ISWGNA (2013) (p. 20, §49) for producing reasonable reference rates and sensible FISIM:

1. Strong connection to underlying economic conditions as measured by volatility.

2. No sustained periods of negative FISIM.

3. Sensible changes in FISIM near economic turning points.

4. Data is observable.

We compare the new method with (1) the current 2008 SNA and (2) the full risk premia-excluded method (based on Colangelo and Inklaar (2012)'s method) and find that it is the only one that satisfies all four ISWGNA criteria. Indeed, using both local projections (LP) and autoregressive distributed lag (ARDL) models, we show that our method and the full risk premia-excluded method fulfil the first and third criteria, contrary to the current 2008 SNA method. On the second criteria, only our method and the current 2008 SNA method do not generate sustained periods of negative FISIM. Finally, regarding the fourth criteria, we show that we can find data to replicate the new method at the international level in Japan, the United Kingdom and the United States.

The main contribution of this paper is to provide a method that remains within the framework of the 2008 SNA, and that produces coherent and stable banking output even during periods of financial stress, including during times of volatile movements in reference rates and when liquidity markets are dysfunctional. The method eliminates the
occurrence of negative outputs and generates reliable output estimates. It improves the consistency of the current 2008 SNA, without requiring any drastic change in its architecture. Furthermore, the method relies on an opportunity cost approach to funds following the ISWGNA recommendations. It allows keeping the term premium and the remuneration linked to liquidity services and satisfies the four ISWGNA criteria. Putting the new method to work, we also show that the banking output estimate in the eurozone, over the period 2003-2017, is, on average, 46 percent lower than the current method predicts and 22 percent higher than the approach that adjusts for default risk premium only states. Therefore, this research adds to the literature on the measurement of the financial intermediation services starting with Fixler (1993) and Fixler and Zieschang (1999) and followed by Basu et al. (2011) and Inklaar and Wang (2013). This study also relates to the stream of research examining the size and efficiency of the banking industry including Greenwood and Scharfstein (2013), Philippon (2015) and Bazot (2018).

The remainder of the paper is organized as follows: Section 2 presents the database and the new method we propose to estimate bank output. Section 3 describes our main results, and Section 4 concludes.

## 2 Data and Methodology

The current 2008 SNA method uses a single reference rate, $r_f$, which is determined according national circumstances, usually an interbank rate. Then, it computes the total indirectly measured banking output (FISIM) as the sum between the FISIM on deposits and the FISIM on loans. FISIM on deposits are calculated as the difference between the reference rate, $r_f$, and the rate actually paid to depositors, $r_D$, multiplied by the amount of deposits. FISIM on loans are given by the difference between the rate paid to banks by borrowers, $r_L$, and the reference rate, $r_f$, multiplied by the amounts of loans.

$$FISIM = (r_f - r_D) \times Deposits + (r_L - r_f) \times Loans \quad (1)$$
We basically follow the same approach as the 2008 SNA except that we chose different reference rates in lieu of a single $r_f$. We use the data provided by the ECB Statistical Data Warehouse for series on loans and deposits.<fnref n="2" /> Interest rates on market debt security come from the ECB database, Bloomberg and Markit iBoxx. Our dataset covers the period 2003-2017 and includes the 2008-2009 subprime crisis and 2010-2013 European sovereign debt crisis periods, when liquidity dried up dramatically on the bonds market. In our analysis, we focus on the two most important institutional sectors—namely, non-financial corporations (S11) and households and non-profit institutions serving households (NPISH) (S14 and S15). These represent approximately 80 percent of the total outstanding amounts.

## 2.1 Deposits

ISWGNA (2013) concluded that liquidity transformation services are part of the banking output, and it found that the current method for computing FISIM on deposits is correct and does not require any changes. Consequently, we follow the 2008 SNA and keep a single reference rate that reflects the average of short-term interbank lending rates (Euribor). To determine the FISIM on deposits, we need the outstanding amounts and outstanding amount rates for each of the sectors, categories and maturities of deposits as described in Table 1.

## 2.2 Loans - Credit Risk

Considering risk-bearing as a non-productive activity, we aim to remove any risk remuneration from the banking output. In a first step, we calculate a series of reference rates, including the risk of default and any term premium in the spirit of Wang et al. (2010), Basu et al. (2011) and Colangelo and Inklaar (2012). We do so for each institutional sector, each type of loan and each maturity. Using the European Central Bank (ECB) database enables us to categorize the statistical series presented in Table 2. For each type of loan, we need the quantity and the price of the financial intermediation services.

<footnote n="2">²See http://sdw.ecb.europa.eu/.</footnote>
The quantity of financial intermediation generated by banks over the duration of loans depends on the nature of the financial services provided. Some services, such as screening, are performed only once at the initiation of the deal; other services occur regularly until termination of the contract. This suggests using the outstanding amounts of loans and deposits rather than the amounts of new business as a measure of quantity of loans. We retain the former approach, which also corresponds to the 2008 SNA method.

The price of the financial intermediation services is represented by the margins on loans, which corresponds to the spreads between some reference rates and the actual interest rates on loans. For the actual interest rate, it is necessary to choose between “new business” rates and “outstanding amount” rates. Because the spread between the reference rate and the actual interest rate applies to the stock of loans in the relevant instrument category, the SNA proposes using the outstanding amount rates. We follow this recommendation.

For each type of loan, a corresponding reference rate is selected from the same systematic risk and maturity profiles. Then we need to find a corresponding bond index for which systematic risk is as close as possible to each type of bonds. For non-financial corporations, we use the iBoxx € non-financials. This index comprises 1000 firms and is split by maturities 1 to 3 years, 3 to 5 years, 5 to 7 years, 7 to 10 years and more than 10 years. For households and NPISH, there are no such comparable bond indices, because they do not raise money directly from the markets. However, we can estimate their risk by assessing the covered bond rates. The latter are issued by financial institutions and backed by mortgage loans to pay interests on the covered bonds. The interests paid by households are passed on to the covered bond investors. The iBoxx € Covered tracks the evolution of this market. It comprises approximately 700 bonds split along the maturities 1 to 3 years, 3 to 5 years, 5 to 7 years, 7 to 10 years and more than 10 years. We retain this index for measuring the households and NPISH systematic risk. This gives us for each type of loan *i* of maturity *t* a market reference rate $r_{it}^M$ based on the yields
on market securities with the same systematic risk. In opposition to the single reference rate currently used in the 2008 SNA, this rate reflects the credit default risk and allows removing the remuneration related to the credit risk premium from the banking output, as recommended by the Task Force of the ISWGNA (2013, p. 22, §60).

$$r_{it}^{M} = \begin{cases} Corporate bond index_{it} & \text{if non-financial corporations} \\ Covered bond index_{it} & \text{if households NPISH} \end{cases}$$

## 2.3 Loans - Liquidity Risk

In a second step, we estimate the liquidity risk premium, which we subtract from the reference rates $r_{it}^M$ calculated previously. The liquidity risk reflects the potential difficulty that may be encountered when buying or selling an asset due to the deterioration of trading conditions. This risk has been studied by Brunnermeier (2009) and Acharya and Skeie (2011), and its importance was highlighted during the financial crisis (Gianfelice et al., 2015). The ISWGNA (2013) concluded that the liquidity transformation services should be part of the banking output therefore, the reference rate must be free of any liquidity risk and we need to adjust the market reference rate by removing the liquidity premium. To do so, in the spirit of Amihud and Mendelson (1991) and Warga (1992), we follow the literature that decomposes yields into liquidity and credit risk and computes the liquidity premium as the spread between bonds with the same credit quality but with different liquidity.

We implement a model-free measure of market liquidity, directly calculated from asset prices, and borrow the methodology from Longstaff (2004). Longstaff extracts the yield differential between U.S. Treasury bonds and same maturity bonds issued by RefCorp (Resolution Funding Corporation), which is a U.S. government agency, guaranteed by the U.S. Treasury. Ejsing et al. (2015) and Schwarz (2019) adopted a similar approach for the euro area, and this is the path that we follow. More specifically, we examine the yields of highly liquid German government bonds and some less liquid German government-guaranteed agency bonds, namely the KfW agency bonds. KfW bonds are fully and
explicitly guaranteed by the government and have the same credit risk as the German government bonds, they also have the same tax treatment.

Schestag et al. (2016) evaluated a comprehensive list of measures of liquidity and found that most of them perform well. Monfort and Renne (2014) proposed an alternative method to that of Longstaff (2004), which does not directly consider the German government bonds but subtracts German CDS from maturity-matched German bonds to neutralize any credit risk premium. However, taking into account the ISWGNA (2013)'s concern about the feasibility of new methods, we prefer the simplicity of the Longstaff (2004) model-free approach, which relies only on the assumptions that both issuers share exactly the same credit risk. We recover daily prices from Bloomberg from January 1st, 2003 to Dec 31st, 2017. We select fixed annual coupon, euro-denominated, bullet KfW bonds comparable to the German government bonds. Our dataset consists of 124 KfW bonds maturing between 2003 and 2037 and 204 German government bonds maturing between 2003 and 2048. Table 3 provides the summary statistics of the dataset.

From these baskets, we create generic historical series of 1-year up to 15-year maturity. As the maturities do not match perfectly, we need to interpolate the yield curves, and we use the Svensson (1994) method for recovering monthly yield curves of each issuer. Then we subtract the yields on KfW bonds from the yields on German government bonds with corresponding maturities and find the liquidity premium for each maturity t ranging from 1 year to 15 years.

$$ \textit{Liquidity premium}_t = \textit{Yield Agency}_t - \textit{Yield government}_t \quad (2) $$

Next, we compute the adjusted liquidity-free reference rate:

$$ r_{it}^{M*} = r_{it}^{M} - \textit{Liquidity Premium}_t \quad (3) $$

We calculate the liquidity premium as the spread between bond yields of the same
credit quality but of different liquidity.

Schwarz (2019) and Monfort and Renne (2014) established the existence of a common-
ality in market liquidity in the cross-section of countries, implying that the KfW liquidity
premium carries European-wide liquidity-pricing effects. For example, Figure 1 shows the
liquidity premium extracted from the 6-year German government bonds and the 6-year
KfW bonds. Until the second quarter of 2007, the liquidity premium is less than 0.1
percent. Then, it gradually increases and reaches a maximum of almost 1 percent at the
height of the subprime crisis in the fourth quarter of 2008. It recedes rapidly until the
first quarter of 2010 and then increases again rapidly with the onset of the euro crisis.
It reaches a second peak at 0.84 percent in the fourth quarter of 2011 corresponding
to the most acute time of the euro crisis. Then, after the arrival of Mario Draghi as
head of the European Central Bank and the resulting change in its policy, the liquidity
premium decreases almost continuously and reaches a pre-crisis level from mid-2014 to
mid-2015. From that date, it rises again but remains well below the level reached during
the subprime and euro crisis, and fluctuates around 0.2 percent. In Figure 2, we take the
spread between the 6-year French and German government bonds as a crude measure of
the financial crisis intensity, and find a strong correlation between the evolution of the
liquidity premium and the crisis intensity. Our measure of liquidity premium reflects the
flight to quality that occurs in times of crisis when investors prefer to hold highly liquid
securities and widen the spread between assets of same credit quality.

## 2.4 *Empirical methods to investigate the link between FISIM and macroeconomic conditions*

To test the relevance of the different methods with regard to the first and third ISWGNA
criteria, we adopt two different tests.
**On the short run.** First, we investigate the short-run relationship between estimated FISIM and economic cycle of the euro area, proxied by its Gross Domestic Product (GDP) or the Economic Sentiment Index (ESI) of the area. For that, we rely on the general method proposed by Jordà (2005) and Jordà (2009) to estimate impulse response functions (IRF) from local projections. Indeed, this method is robust to the misspecification representation of the data generating process (DGP), which is not represented by a VAR. This method does not impose any underlying dynamics on the variables in the system, contrary to VAR models. In its basic form, local projection consists of a sequence of regressions of the endogenous variable shifted several steps ahead. As a result, the approach consists in estimating the following equation:

$$ \Delta_h Y_{t+h} = \beta^h EC_t + \epsilon_t^h \quad (4) $$

where $\Delta_h Y_{t+h} = Y_{t+h} - Y_{t-1}$ and corresponds to the log change in the FISIM estimated from base quarter $t$ up to quarter $t+h$, using the different methods<fnref n="3" />, and $EC_t$ is the measure of the euro area economic cycle (euro area GDP or euro area ESI) at time $t$. Each step of the accumulated IRF is obtained from a different equation and directly corresponds to the estimates of $\beta^h$.

**On the long-run.** In a second step, we run a cointegration analysis to test the long-term relationship between the computed FISIM and the economic cycle (first criterion) but also the adjustment speed towards this equilibrium relationship in the short run (third criterion). For this purpose, we employ the ARDL bounds testing procedure developed by Pesaran and Shin (1998) and Pesaran et al. (2001). We prefer this method to standard cointegration tests such as those of Johansen (1991) or Engle and Granger (1987) for several reasons.

<footnote n="3">³The three methods are: the current method developed by the 2008 SNA, the method adjusted for the credit risk premium, and the method adjusted for both credit risk and liquidity premium. As the method adjusted for the risk premium provides negative FISIM, we compute the logarithm of this variable using the following transformation: $ln(Y_t - Min(Y_t) + 1)$.</footnote>
First, one important feature of the bound testing procedure proposed by Pesaran et al. (2001) is that it can be applied to a set of regressors that are a mixture of I(0) and I(1) variables. However, Cheung and Lai (1993) put forth evidence that standard unit root tests suffer from size distortion and low power in the case of small samples, as is the case in our analysis. Second, the bound testing procedure is robust in case of small samples whereas others could be biased in this case. Finally, as Narayan (2005) suggests, the method provides robust t-statistics and, thus, unbiased long-term estimates even if one or more regressors are potentially endogenous.

Following Pesaran et al. (2001), we estimate the conditional error correction model presented in Equation 5 to obtain the bound tests:

$$ \Delta Y_t = \mu + \delta Y_{t-1} + \sum_{i=1}^{k} \gamma_i \Delta Y_{t-i} + \theta EC_{t-1} + \sum_{j=1}^{l} \tau_j \Delta EC_{t-j} + \epsilon_t, \quad (5) $$

where $Y_t$ is the logarithm of FISIM estimated using the different methods proposed herein at time t. $EC_t$ is the measure of the euro area economic cycle (euro area GDP or euro area ESI) at time t. $k$ and $l$ are the lags of the ARDL model selected according to the Schwartz information criterion and $\epsilon_t$ are the errors of the model assumed to be independent and identically distributed.

The bound test, testing the null hypothesis of no cointegration, developed by Pesaran et al. (2001) is based on an F-test statistics, as follows:

$$ H_0 : \delta = \theta = 0 \quad (6) $$

Pesaran et al. (2001) provided two sets of critical values for their bound test. The first set is computed assuming that all variables in the ARDL model are stationary. For the second set, all variables of the ARDL model are supposed to be I(1). These two sets of critical values provide bounds for all regressors. The decision procedure is as follows: if the F-statistic is lower than the lower bound, the null hypothesis cannot be rejected and
there is no long-term relationship between the two studied variables. The reverse is true if the F-statistic is higher than the upper bound. However, the test is inconclusive if the F-statistic falls between the two bounds. In this case, standard unit root tests have to be computed.

# 3 Results

## 3.1 *Estimated FISIM*

We compute FISIM under respectively (1) the current regulation, (2) the default risk adjusted, and (3) the default and liquidity risk adjusted for the eurozone. Table 4 presents these results split by sector and averaged over the period 2003-2017. As expected, FISIM adjusted for default risk and FISIM adjusted for default and liquidity risk are much lower than those obtained by the current method, especially from 2008 to 2015, which is consistent with the economic intuition. The method we propose (column 3) reduces the banking output estimate of the eurozone by a significant 46 percent compared with the current regulation (column 1). This reduction is more pronounced for the non-financial corporation sector with 52 percent than for the household sector with 42 percent. Our method generates on average 22 percent more than the approach that adjusts for default risk premium only (column 2).<fnref n="4" /> Figure 5 shows the quarterly production of FISIM under these different approaches.

The difference between the banking output under the current regulation and the risk-adjusted methods varies over time. It was at its maximum during the subprime crisis and the euro crisis. The current method leads to paradoxical results because FISIM dramatically increased during the financial crisis of 2008 and the eurozone crisis of 2012. Thereafter FISIM initiated a declining trend with low volatility. Conversely, the risk-adjusted methods resulted in a sharp decline of the banking output in the first quarter of 2009, and again at the end of 2010 and the beginning of 2011. Since then, they have

<footnote n="4">⁴Colangelo and Inklaar (2012) use a slightly different method that adjusts for both default risk and term premium. The results adjusted for default risk premium (column 2) are in line with theirs.</footnote>
gradually recovered and have been fluctuating at the pre-crisis levels since 2014. At first glance, the risk-adjusted methods present a picture more consistent with the evolution of the business cycle.

Then, we examine separately the FISIM on loans and the FISIM on deposits. We find that except in 2011, the FISIM on deposits have been negative every quarter since 2009 (Figure 4). This result is related to the emergence of negative interest margins on deposits when the reference rate falls below the interest rates on deposits (see Figures A.1 and A.2 in the Appendix). This confirms the view of Ravets (2011) and Groslambert et al. (2016), who found that negative output on deposits is not only due to the near-zero interest rate policy but also explained by the changing behavior of banks towards deposits. Deposits have become an important liquidity resource for banks, and consequently, banks are ready to pay for them.

For FISIM on loans (Figure 5), we find roughly the same patterns as for total FISIM. The current method exhibits a threefold increase in banking output at the time of the crisis and then stabilize around 300 billion euros per quarter. Because the growth rate of the outstanding amount of loans has been flat since 2009, these variations are mostly explained by the evolution of the interest rate margin. This huge increase was caused by the plummeting of the 2008 SNA reference rate due to an accommodating monetary policy by the ECB from 2008 (see Figures A.3 to A.6 in the Appendix). Both alternative methods show a very different evolution of the banking output. They dropped during the subprime crisis and again during the eurozone crisis but then recovered dramatically from a low in the first quarter of 2011 until 2014. Since then, they have fluctuated around 200 billion euros at about 25 percent less than the current method.
## 3.2 Performance of the different methods

In this section, we compare the respective merits of each method by using the four criteria established by the ISWGNA (2013) for producing reasonable reference rates and sensible FISIM estimates which are described in the 1.

### 3.2.1 Connection with underlying economic conditions and sensible changes near turning points

**Short run analysis.** First, we test the time series properties of our different variables using both the Augmented Dickey-Fuller (ADF) test and the stationarity test developed by Kwiatkowski et al. (1992). Table A.1. in the Appendix reports the results of the unit root tests. All variables seems to be I(0) or I(1). Figures 6 and 7 displays impulse responses of estimated FISIM to one standard deviation innovations of the explanatory variables (ESI or current GDP) in a 95% marginal confidence band using the LP method. Note that estimation of impluse response coefficients can lead to wider marginal error bands in case of serial correlation. The use of conditional error bands allows to remove the variability caused by serial correlation.

Figures 6 reveals that a positive shock on euro area GDP has a significant negative im- pact on FISIM estimated using the current method, which seems counterintuitive. When FISIM are computed using the full risk premia-excluded method and the credit risk premia only-excluded method, results are different. Indeed, Figure 6 shows that a one standard deviation innovations of euro area entails an increase of FISIM. FISIM estimated using the full risk premia-excluded method increase by 0.28 percentage points, while FISIM computed using the credit risk premia only-excluded method increase by 0.6 percentage points two quarters following the shock. These results put forth the evidence that FISIM computed using the current method seems to be disconnected from macroeconomic con- ditions on the short-run, while FISIM estimated using the two other methods are not. Figure 7 confirms this conclusion by using the ESI rather than the euro area GDP to proxy for macroeconomic conditions.
**Long run analysis.** The Schwartz information criterion is used to select the optimal number of lags for the estimation of the ARDL models. We also correct standard errors for autocorrelation and heteroscedasticity using the Newey-West transformation. Table 5 summarizes results of the bound tests and presents the long-term relationship between the estimated FISIM and the eurozone's GDP, as long as the error correction term is based on the estimation of the ARDL models. Table 5 also displays autocorrelation and heteroscedasticity tests to check the accuracy of estimations. Note that ARDL models are estimated without an intercept and a trend, as both intercept and trend are not significant at the 5 percent level.

Column (1) of Table 5 depicts the current method for the computation of FISIM, column (2) provides the results for the full risk premia-excluded method and column (3) presents the results for the credit risk premia only-excluded method. The results indicate that the null hypothesis of no cointegration between FISIM estimated by the current SNA method and the euro's area current GDP cannot be rejected at the 5 percent level. Therefore, the current method fails to satisfy the requirements provided by the ISWGNA. By contrast, FISIM adjusted for credit risk and liquidity premia and for credit risk premium only are related to eurozone's economic cycle, as the null hypothesis of no cointegration with the eurozone's GDP is rejected at the 1 percent level. Consequently, the first criterion proposed by the ISWGNA (2013) is only fulfilled by these two methods.

Then, we evaluate the third criterion proposed by the ISWGNA, which means that FISIM exhibits sensible changes near economic turning points, using the adjustment speed estimated in the error correction model. The results in Table 5 show that the coefficient associated with the error correction term is significant at the 1 percent level only in the last two estimations. This indicates that deviations from the long-term relationship are eliminated more quickly in the case of the method adjusted for default risk premium only and in the case of the method adjusted for both default risk and liquidity premium. Therefore, the volatility of FISIM from factors not connected with the economic cycle
is much lower with the latter two methods. As a consequence, the method adjusted for default risk premium only and the method adjusted for both default risk and liquidity premium are more in line with the third criterion proposed by the ISWGNA (2013), contrary to the current method. Note that we observe a strong difference between the adjustment speed estimated for the method adjusted for the default risk only and the one estimated for the method adjusted for both risk and liquidity premia. At first glance, we could conclude that the method adjusted for the default risk only produces better results because the adjustment speed towards long-term equilibrium is higher. However, we find that the discrepancy in adjustment speed between the two methods is only linked to the logarithmic transformation applied to the method adjusted for default risk, as it entails negative values.<fnref n="5" /> Indeed, if we apply the same transformation to the method adjusted for both liquidity and default risk premia, we obtain a similar coefficient for the adjustment speed as shown in Table A.2. of the Appendix.

To test the robustness of our results, we also conduct the ARDL cointegration testing procedure of Pesaran et al. (2001) on the ESI of this area. Table 6 reports the results and confirms our previous conclusions

In summary, our results provide evidence that the method adjusted for the default risk premium and the method adjusted for both the default risk and liquidity premia outperform the current method in terms of the first and third criteria proposed by the ISWGNA (2013). They are more connected with the economic cycle and minimize the part of volatility due to factors not related to this economic cycle. It is important to note that our results are robust to the use of another method to measure the liquidity premium. Indeed, if we rely on the spread between the iBoxx euro non-financial corporate bond index and its subset, the iBoxx euro liquid non-financial corporate bond index, we obtain very similar results, as shown in Table A.3. of the Appendix.

<footnote n="5">⁵See footnote 4 for a presentation of the applied transformation.</footnote>
### 3.2.2 No sustained periods of negative FISIM

The ISWGNA debated the notion of negative FISIM and their theoretical meaning (Ahmad, 2012) and concluded that negative FISIM was not conceptually possible and recommended that any method for computing FISIM should not produce sustained periods of negative FISIM. Table 7 gives the number of occurrences of negative quarterly FISIM in the period 2003-2017. The current regulation method does not generate any quarter of total negative FISIM (column 1). Conversely, the method adjusted for the default risk premium generates three quarters of negative total output in the first half of 2009 and the first quarter of 2011. This comes from the overestimation of the reference rate during a period of financial stress, which dramatically decreases the FISIM on loans. The method generates five quarters of negative FISIM on loans in the last quarter of 2008, the two first quarters of 2009 and in the first two quarters of 2011 (column 2). The method adjusting for default risk and liquidity premium corrects this flaw and does not generate any negative quarterly output, contrary to the default risk only method.

The current regulation method and the method adjusted for risk and liquidity premia comply with the second criteria of the ISWGNA. This is not the case for the method adjusted for default risk premium only. This raises issues of consistency of this method during periods of financial stress because it is difficult to explain a sustained negative output on loans.

### 3.2.3 Observable data

Compared with the current regulation, the new proposed methods require additional data to compute the default risk premium and the liquidity risk premium. For the default risk, it is necessary to find a non-financial corporate bond index and a covered bond index. These types of data are easily accessible through third party vendors such as Markit Iboxx, Bank of America Merrill Lynch or Bloomberg Barclays. For the liquidity risk, one needs to have both liquid and non-liquid credit riskless bond issuers with a sufficient number of bonds in all maturity segments. In the eurozone, KfW bonds are good candidates (Monfort
and Renne, 2014; Schwarz, 2019). For the United States, one can use RefCorp bonds as shown by Longstaff (2004). Hattori (2019) developed a similar approach with Japanese government-guaranteed bonds. In the United Kingdom, one can use the bonds issued by the Network Rail Infrastructure Finance PLC, which benefits from the British government guarantee in full and carries the same credit ratings as the UK sovereign. Thus, we can estimate the liquidity risk premium across a large number of countries directly from asset prices without relying on a specific model. Consequently, we can conclude that data are observable, and the method we propose to correct for credit risk and liquidity premium can be easily implemented in the countries that have a large banking sector.

# 4 Conclusion

Following the recommendation of the group of experts on FISIM (ISWGNA, 2013), we aimed to develop a method for calculating banking output that excludes the credit risk premium. Our approach differs from Colangelo and Inklaar (2012)'s as it removes the liquidity risk premium that may greatly affect the evolution of interest rates in times of financial crisis. The method that we propose corrects the problems raised by both the current SNA method and by the full risk premia-excluded method. First, our method generates less volatile banking output than that obtained with the alternative methods. Our results are more in accordance with the changes in the economic cycle between 2003 and 2017. Second, while taking into account the credit risk, our method does not lead to negative banking output, even during periods of financial stress. This indicates that the liquidity premium plays a major role in the rise of credit spread during the subprime and the eurozone crises, when the two other methods led to diverging results. Third, the method proposed herein relies on data available for most developed economies and therefore can be applicable for Japan, the United Kingdom, and the United States. Finally, we show that the current SNA method overestimates banking output, while the full risk premia-excluded method underestimates it. Not only is measuring precisely financial intermediation services important for national accounting, but it is also a sensitive question for the research on the productivity of the banking industry (Philippon, 2015) and the
study of possible rent-seeking activity (Greenwood and Scharfstein, 2013; Zingales, 2015).
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# Appendix
List of Figures

<table><tr><td>1</td><td>Liquidity premium KfW 6-year</td><td>28</td></tr><tr><td>2</td><td>Financial crisis intensity and liquidity premium</td><td>29</td></tr><tr><td>3</td><td>Quarterly FISIM under various methods</td><td>30</td></tr><tr><td>4</td><td>FISIM on deposits (million euros).</td><td>31</td></tr><tr><td>5</td><td>FISIM on loans (million euros).</td><td>32</td></tr><tr><td>6</td><td>FISIM local projection responses to a positive current GDP shock</td><td>33</td></tr><tr><td>7</td><td>FISIM local projection responses to a positive ESI shock</td><td>34</td></tr></table>
<figure><img src="image_3.png" /><figcaption>Figure 1: Liquidity premium KfW 6-year</figcaption></figure>

This figure shows the 6-year German government and KfW bond yields and the resulting liquidity premium.
<figure><img src="image_4.png" /><figcaption>Figure 2: Financial crisis intensity and liquidity premium</figcaption></figure>

This figure shows the evolution of the financial crisis intensity measured by the spread between the 6-year French government bond yields and the 6-year German government bond yields and the evolution of the liquidity premium (6-year).
<figure><img src="image_5.png" /><figcaption>Figure 3: Quarterly FISIM under various methods</figcaption></figure>

This figure shows the quarterly production of FISIM under the current regulation (2008 SNA), the default risk adjusted method as suggested in ISWGNA (2013) and the method that adjusts for both default risk and liquidity premium. All figures are in million euros.
<figure><img src="image_6.png" /><figcaption>Figure 4: FISIM on deposits (million euros).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 5: FISIM on loans (million euros).</figcaption></figure>
Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISIM (current method) to current GDP
(Joint: 0.039 Cumulative: 0.356)

<figure><img src="image_8.png" /></figure>

Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISIM (Liquidity and default risk adj.) to current GDP
(Joint: 0.557 Cumulative: 0.636)

<figure><img src="image_9.png" /></figure>

Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISIM (Risk default adj. only) to current GDP
(Joint: 0.014 Cumulative: 0.328)

<figure><img src="image_10.png" /></figure>

Figure 6: FISIM local projection responses to a positive current GDP shock
Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISM (current regulation) to ESI
(Joint: 0.295 Cumulative: 0.487)

<figure><img src="image_11.png" /></figure>

Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISIM (Liquidity and risk adjusted) to ESI
(Joint: 0.594 Cumulative: 0.900)

<figure><img src="image_12.png" /></figure>

Response to Cholesky One S.D. Innovations 95.0% Conditional confidence bands

Response of FISIM (default risk only) to ESI
(Joint: 0.044 Cumulative: 0.324)

<figure><img src="image_13.png" /></figure>

Figure 7: FISIM local projection responses to a positive ESI shock
<figure><img src="image_14.png" /><figcaption>Figure A.1: Interest rate on household deposits and reference rate</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure A.2: Interest rate on non-financial corporation deposits and reference rate</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure A.3: Interest rate on mortgage loans and reference rate</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure A.5: Interest rate on consumer loans and reference rate</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Figure A.5: Interest rate on other loans to households and reference rate</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Figure A.6: Interest rate on loans to non-financial corporations and reference rate</figcaption></figure>
List of Tables

<table><tr><td>1</td><td>Characteristics of deposits</td><td>42</td></tr><tr><td>2</td><td>Characteristics of loans</td><td>43</td></tr><tr><td>3</td><td>Summary statistics for KfW bonds and German government bonds</td><td>44</td></tr><tr><td>4</td><td>Imputed banking sector output (FISIM) in eurozone by sector, current regulation, and modified approaches (average January 2003–December 2017, million euros)</td><td>45</td></tr><tr><td>5</td><td>Results of bound tests with current eurozone's GDP (case no intercept)</td><td>46</td></tr><tr><td>6</td><td>Results of Bound tests for eurozone's ESI (Case no intercept)</td><td>47</td></tr><tr><td>7</td><td>Number of negative quarters of banking output on loans from Q1-2003 to Q4-2017</td><td>48</td></tr></table>
<table><caption>Table 1: Characteristics of deposits</caption><thead><tr><th colspan="3">Deposits</th></tr><tr><th>Sector</th><th>Category</th><th>Maturity</th></tr></thead><tbody><tr><td rowspan="3">Non-financial corporations (S11)</td><td>Overnight</td><td>-</td></tr><tr><td rowspan="2">With agreed maturity</td><td>Less than two years</td></tr><tr><td>More than two years</td></tr><tr><td rowspan="3">Households and NPISH (S14+S15)</td><td>Overnight</td><td>-</td></tr><tr><td rowspan="2">With agreed maturity</td><td>Less than two years</td></tr><tr><td>More than two years</td></tr><tr><td></td><td>Redeemable at notice</td><td>Less than three months</td></tr></tbody></table>
<table><caption>Table 2: Characteristics of loans</caption><thead><tr><th colspan="3">Loans</th></tr><tr><th>Sector</th><th>Category</th><th>Maturity</th></tr></thead><tbody><tr><td rowspan="3">Non-financial corporations (S11)</td><td rowspan="3">Loans</td><td>Less than 1 year</td></tr><tr><td>Between 1 and 5 years</td></tr><tr><td>More than 5 years</td></tr><tr><td rowspan="3">Households and NPISH (S14+S15)</td><td rowspan="3">Loans for house purchases</td><td>Less than 1 year</td></tr><tr><td>Between 1 and 5 years</td></tr><tr><td>Between 5 and 10 years</td></tr><tr><td></td><td></td><td>More than 10 years</td></tr><tr><td rowspan="3">Consumer credit</td><td rowspan="3"></td><td>Less than 1 year</td></tr><tr><td>Between 1 and 5 years</td></tr><tr><td>More than 5 years</td></tr><tr><td rowspan="3">Other loans</td><td rowspan="3"></td><td>Less than 1 year</td></tr><tr><td>Between 1 and 5 years</td></tr><tr><td>More than 5 years</td></tr></tbody></table>
<table><caption>Table 3: Summary statistics for KfW bonds and German government bonds</caption><thead><tr><th></th><th>KfW</th><th>German government bonds</th></tr></thead><tbody><tr><td>Number of bonds</td><td>124</td><td>204</td></tr><tr><td>Average time to maturity at issue date (in years)</td><td>6.28</td><td>7.45</td></tr><tr><td>Average coupon (in %)</td><td>2.08</td><td>2.69</td></tr><tr><td>Average issuing volume (in bn euros)</td><td>4.59</td><td>15.54</td></tr><tr><td>Total amount issued (in bn euros)</td><td>569</td><td>3170</td></tr></tbody></table>
<table><caption>Table 4: Imputed banking sector output (FISIM) in eurozone by sector, current regulation, and modified approaches (average January 2003–December 2017, million euros)</caption><thead><tr><th></th><th>(1)<br>Current<br>regulation 2008<br>SNA</th><th>(2)<br>Adjusted for<br>default risk<br>premium only</th><th>(3)<br>Adjusted for<br>default risk<br>premium and<br>liquidity<br>premium</th></tr></thead><tbody><tr><td>Total</td><td>234,251</td><td>103,36</td><td>125,911</td></tr><tr><td>Non-financial corporations</td><td>91,21</td><td>33,769</td><td>43,604</td></tr><tr><td>Households</td><td>143,04</td><td>69,591</td><td>82,308</td></tr></tbody></table>
<table><caption>Table 5: Results of bound tests with current eurozone's GDP (case no intercept)</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th></tr><tr><th></th><th>Current<br>regulation<br>2008 SNA</th><th>Adjusted for<br>default risk<br>premium<br>only</th><th>Adjusted for<br>default risk<br>premium<br>and liquidity<br>premium</th></tr></thead><tbody><tr><td>Model</td><td>ARDL (4,4)</td><td>ARDL (1,2)</td><td>ARDL (1,2)</td></tr><tr><td>Cointegrating vector</td><td>0.858***<br>(0.010)</td><td>0.720***<br>(0.020)</td><td>0.755***<br>(0.013)</td></tr><tr><td>ECT<sub>t-1</sub></td><td>-0.043<br>(0.026)</td><td>-0.969***<br>(0.154)</td><td>-0.461***<br>(0.098)</td></tr><tr><td>Diagnostic tests</td><td></td><td></td><td></td></tr><tr><td>QLB (1)</td><td>1.588</td><td>0.003</td><td>0.001</td></tr><tr><td>QLB (5)</td><td>4.063</td><td>1.944</td><td>0.987</td></tr><tr><td>QLB (10)</td><td>6.602</td><td>5.578</td><td>16.764*</td></tr><tr><td>ARCH-LM test</td><td>0.091</td><td>0.011</td><td>0.300</td></tr><tr><td>Bound tests</td><td></td><td></td><td></td></tr><tr><td>F-statistics</td><td>2.186</td><td>60.684</td><td>15.114</td></tr><tr><td>I(0) critical value (5%)</td><td>3.15</td><td>3.15</td><td>3.15</td></tr><tr><td>I(1) critical value (5%)</td><td>4.11</td><td>4.11</td><td>4.11</td></tr><tr><td>I(0) critical value (1%)</td><td>4.81</td><td>4.81</td><td>4.81</td></tr><tr><td>I(1) critical value (1%)</td><td>6.02</td><td>6.02</td><td>6.02</td></tr></tbody></table>

Note: Number in parentheses are standard errors. The model includes no intercept and no trend (Case I). Critical values for bound test come from Pesaran et al. (2001). ECTt-1 represents the coefficient associated with the adjustment speed in the error correction model. QLB represents the Ljung-Box statistic. ARCH-LM represents the ARCH-LM statistic to test for heteroscedasticity. Significance level: *** $p < 0.01$, ** $p < 0.05$, * $p < 0.1$.
<table><caption>Table 6: Results of Bound tests for eurozone's ESI (Case no intercept)</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th></tr><tr><th></th><th>Current<br>regulation<br>2008 SNA</th><th>Adjusted for<br>default risk<br>premium<br>only</th><th>Adjusted for<br>default risk<br>premium<br>and liquidity<br>premium</th></tr></thead><tbody><tr><td>Model</td><td>ARDL (4,1)</td><td>ARDL (1,2)</td><td>ARDL (1,2)</td></tr><tr><td>Cointegrating vector</td><td>2.679***<br>(0.033)</td><td>2.519***<br>(0.042)</td><td>2.526***<br>(0.029)</td></tr><tr><td>ECT<sub>t-1</sub></td><td>0.014<br>(0.013)</td><td>-0.924***<br>(0.214)</td><td>-0.458***<br>(0.107)</td></tr><tr><td>Diagnostic tests</td><td></td><td></td><td></td></tr><tr><td>QLB (1)</td><td>0.110</td><td>0.130</td><td>0.041</td></tr><tr><td>QLB (5)</td><td>4.355</td><td>6.686</td><td>1.286</td></tr><tr><td>QLB (10)</td><td>7.075</td><td>9.054</td><td>10.225</td></tr><tr><td>ARCH-LM test</td><td>0.417</td><td>6.141</td><td>0.195</td></tr><tr><td>Bound tests</td><td></td><td></td><td></td></tr><tr><td>F-statistics</td><td>0.923</td><td>29.037</td><td>8.165</td></tr><tr><td>I(0) critical value (5%)</td><td>3.15</td><td>3.15</td><td>3.15</td></tr><tr><td>I(1) critical value (5%)</td><td>4.11</td><td>4.11</td><td>4.11</td></tr><tr><td>I(0) critical value (1%)</td><td>4.81</td><td>4.81</td><td>4.81</td></tr><tr><td>I(1) critical value (1%)</td><td>6.02</td><td>6.02</td><td>6.02</td></tr></tbody></table>

Note: Number in parentheses are standard errors. The model includes no intercept and no trend (Case I). Critical values for bound test come from Pesaran et al. (2001). ECTt-1 represents the coefficient associated with the adjustment speed in the error correction model. QLB represents the Ljung-Box statistic. ARCH-LM represents the ARCH-LM statistic to test for heteroscedasticity. Significance level: *** $p < 0.01$, ** $p < 0.05$, * $p < 0.1$.
<table><caption>Table 7: Number of negative quarters of banking output on loans from Q1-2003 to Q4-2017</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th></tr><tr><th></th><th>Current<br>regulation<br>2008 SNA</th><th>Adjusted for<br>default risk<br>premium only</th><th>Adjusted for<br>default risk<br>premium and<br>liquidity<br>premium</th></tr></thead><tbody><tr><td>Total FISIM</td><td>0</td><td>3</td><td>0</td></tr><tr><td>FISIM on loans</td><td>0</td><td>5</td><td>0</td></tr><tr><td>FISIM on deposits*</td><td>32</td><td>32</td><td>32</td></tr></tbody></table>

Note: The FISIM on deposits are calculated in the same way as for the three methods.
<table><caption>Table A.1: Standard unit root tests</caption><thead><tr><th colspan="5">ADF</th></tr><tr><th></th><th colspan="2">Level</th><th colspan="2">First Diff.</th></tr><tr><th></th><th>Intercept</th><th>Intercept and trend</th><th>Intercept</th><th>Intercept and trend</th></tr></thead><tbody><tr><td>FISIM (current method)</td><td>-1.7700</td><td>-1.4621</td><td>-3.0447**</td><td>-3.1890*</td></tr><tr><td>FISIM (Default risk adj. only)</td><td>-5.4956***</td><td>-5.4560***</td><td>-11.0817***</td><td>-10.9855***</td></tr><tr><td>FISIM (Liquidity and Default risk adj.)</td><td>-3.4168**</td><td>-3.4110*</td><td>-8.6530***</td><td>-8.5803***</td></tr><tr><td>ESI</td><td>-2.3932</td><td>-2.4003</td><td>-4.8924***</td><td>-4.8749***</td></tr><tr><td>GDP</td><td>-1.1065</td><td>-2.7711</td><td>-3.2638**</td><td>-3.2597*</td></tr></tbody><thead><tr><th colspan="5">KPSS</th></tr><tr><th></th><th colspan="2">Level</th><th colspan="2">First Diff.</th></tr><tr><th></th><th>Intercept</th><th>Intercept and trend</th><th>Intercept</th><th>Intercept and trend</th></tr></thead><tbody><tr><td>FISIM (current method)</td><td>0.4664**</td><td>0.1711**</td><td>0.3207</td><td>0.0932</td></tr><tr><td>FISIM (Default risk adj. only)</td><td>0.1549</td><td>0.1547**</td><td>0.0908</td><td>0.0913</td></tr><tr><td>FISIM (Liquidity and Default risk adj.)</td><td>0.1578</td><td>0.1523**</td><td>0.1514</td><td>0.1391</td></tr><tr><td>ESI</td><td>0.1242</td><td>0.1170</td><td>0.0627</td><td>0.0523</td></tr><tr><td>GDP</td><td>0.9139***</td><td>0.1317*</td><td>0.1525</td><td>0.1217</td></tr></tbody></table>

Note: Lag length based on the Schwartz information criteria (SIC). Significance level: *** $p < 0.01$, ** $p < 0.05$, * $p < 0.1$.
<table><caption>Table A.2: Results of bound tests using transformation for FISIM (liquidity and risk adjusted)</caption><thead><tr><th></th><th>With current GDP</th><th>With ESI</th></tr></thead><tbody><tr><td>Model</td><td>ARDL (1,2)</td><td>ARDL (1,2)</td></tr><tr><td>Cointegrating vector</td><td>0.715***<br>(0.021)</td><td>2.474***<br>(0.046)</td></tr><tr><td>ECT<sub>t-1</sub></td><td>-0.920***<br>(0.145)</td><td>-0.934***<br>(0.198)</td></tr><tr><td>Diagnostic tests</td><td></td><td></td></tr><tr><td>QLB (1)</td><td>0.013</td><td>0.123</td></tr><tr><td>QLB (5)</td><td>0.920</td><td>5.184</td></tr><tr><td>QLB (10)</td><td>10.576</td><td>13.225</td></tr><tr><td>ARCH-LM test</td><td>0.000</td><td>0.053</td></tr><tr><td>Bound tests</td><td></td><td></td></tr><tr><td>F-statistics</td><td>47.403</td><td>28.027</td></tr><tr><td>I(0) critical value (5%)</td><td>3.15</td><td>3.15</td></tr><tr><td>I(1) critical value (5%)</td><td>4.11</td><td>4.11</td></tr><tr><td>I(0) critical value (1%)</td><td>4.81</td><td>4.81</td></tr><tr><td>I(1) critical value (1%)</td><td>6.02</td><td>6.02</td></tr></tbody></table>

Note: Number in parentheses are standard errors. The model includes no intercept and no trend (Case I). Critical values for bound test are taken from Pesaran et al. (2001). ECTt-1 represents the coefficient associated with the adjustment speed in the error correction model. QLB represents the Ljung-Box statistic. ARCH-LM represents the ARCH-LM statistic to test for heteroscedasticity. Significance level: *** $p < 0.01$, ** $p < 0.05$, * $p < 0.1$.
<table><caption>Table A.3: Results of bound tests using the iBoxx euro liquid non-financial corporate bond index to measure the liquidity premium</caption><thead><tr><th></th><th>With current GDP</th><th>With ESI</th></tr></thead><tbody><tr><td>Model</td><td>ARDL (1,2)</td><td>ARDL (1,0)</td></tr><tr><td>Cointegrating vector</td><td>0.755***<br>(0.014)</td><td>2.533***<br>(0.029)</td></tr><tr><td>ECT<sub>t-1</sub></td><td>-0.323***<br>(0.103)</td><td>-0.320***<br>(0.103)</td></tr><tr><td>Diagnostic tests</td><td></td><td></td></tr><tr><td>QLB (1)</td><td>0.534</td><td>0.641</td></tr><tr><td>QLB (5)</td><td>4.772</td><td>4.698</td></tr><tr><td>QLB (10)</td><td>18.032*</td><td>18.278*</td></tr><tr><td>ARCH-LM test</td><td>3.409*</td><td>7.425***</td></tr><tr><td>Bound tests</td><td></td><td></td></tr><tr><td>F-statistics</td><td>10.495</td><td>7.309</td></tr><tr><td>I(0) critical value (5%)</td><td>3.15</td><td>3.15</td></tr><tr><td>I(1) critical value (5%)</td><td>4.11</td><td>4.11</td></tr><tr><td>I(0) critical value (1%)</td><td>4.81</td><td>4.81</td></tr><tr><td>I(1) critical value (1%)</td><td>6.02</td><td>6.02</td></tr></tbody></table>

Note: Number in parentheses are standard errors. The model includes no intercept and no trend (Case I). Critical values for bound test are taken from Pesaran et al. (2001). ECTt-1 represents the coefficient associated with the adjustment speed in the error correction model. QLB represents the Ljung-Box statistic. ARCH-LM represents the ARCH-LM statistic to test for heteroscedasticity. Significance level: *** $p < 0.01$, ** $p < 0.05$, * $p < 0.1$.
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Ernest MIGUELEZ is the scientific coordinators of the Bordeaux Economics Working Papers. The layout and distribution are provided by Cyril MESMER.