N° 101 Juillet 2018
A simple financial accelerator in a Auteurs: Ferdy ADAM (STATEC) et Christian standard macro-econometric model GLOCKER (Wifo) *
Abstract
Nowadays quite common in DSGE models, the linkages between the real and the financial sectors are usually absent in traditional macro-econometric models, used
for forecasting and policy analysis. This work introduces a so called «financial
accelerator» into a standard estimated macro-model, called Modux, representing the Luxembourgish economy. These linkages have been introduced both for
machinery and equipment investment and residential investment. The present
paper aims at bringing both extensions together in a recently re-estimated version
of Modux. Model simulations show that the inclusion of the financial accelerator replicates the stylized facts of the literature (cycle amplification) and might also
help to better design standard real demand multipliers. The financial accelerator
also proves to be a useful tool to improve the forecasting performance of a general
macro-econometric model, the more so in times of financial stress.
Keywords: macroeconometric modelling, financial accelerator, public spending
multipliers, financial crises
JEL Codes: E17; E51; E63; G01
* The authors wish to thank above all the members of STATEC’s forecasting and modelling Division CMP for valuable comments, as well as Profs. M. Marcellino and L. Fontagné and some anonymous participants at Ecomod 2018 conference.
Les articles publiés dans la série "Économie et statistiques" n'engagent que leurs auteurs. Ils ne reflètent pas forcément les vues du STATEC et n'engagent en rien sa responsabilité.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
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Introduction
Standard macroeconomic models usually assume perfect capital markets where there is no role for interactions between real and financial factors. The Global Financial Crisis of 2007–2009 however highlighted the extent to which fluctuations in asset prices, credit and capital flows can have dramatic impacts on the financial position of households, corporations and sovereign alike, and therefore on the real economy. The aim of this paper is to summarize how such interactions work through in a standard estimated macro-econometric model Modux, representing the Luxembourgish economy (see Adam 2004 and 2007).
The theoretical foundations for the incorporation of these relations have been developed over the past three decades. Bernanke and Gertler (1989) is an early study in this respect. Kiyotaki and Moore (1997) provide another approach to adding financial interactions in a model of the macroeconomy.
It this literature, three possible channels of interactions between the financial and the real sides are distinguished:
• From the real economy to the financial markets: recessions impact the lending/borrowing behaviour of banks (mostly in terms of risk taking); • Amplification (by financial frictions): when financial frictions (i.e. imperfections) are prevalent, financial markets do not work smoothly, and the magnitude of the feedback loop between the real sector and the financial sector gains importance; • Financial shocks (which impact the real economy): because of disruptions in financial markets, fewer funds can be channelled from lenders to borrowers, and the real economy is impacted.
Those channels have been integrated into Modux, the macro econometric model of STATEC, by means of simple relations, however derived from theory, and based on econometric analysis. Corresponding work has been published in two STATEC Working papers (Glocker 2016 and 2017): Glocker (2016) estimates a financial accelerator mechanism for machinery and capital investment whereas Glocker (2017) does the same for housing investment. The aim of this paper is to bring both extensions together and to present model simulations in order to illustrate the importance of the (new) transmissions channels between the real economy and the financial sector. For this purpose, shock simulations are undertaken and compared with and without “financial accelerator”.
Main results are as follows: - whole model simulations with financial accelerator (scenario analysis) remain meaningful, i.e. the model stabilises, however over a short period only (5 years); - comparisons of results with and without financial accelerator confirm stylized facts found in related research, i.e. - amplification (shocks with financial accelerator are magnified); - oscillation (shocks with financial accelerator present more pronounced cycles); - one additional finding is that classic public demand multipliers with financial accelerator also increase, in line with a vast literature on the importance of Keynesian multipliers in times of financial stress (see for ex. Corsetti et al., 2012); - the forecast performance of the financial accelerator model seems to beat the standard model in terms of dispersion and accuracy in about 75% of the variables tested. In the remainder of the paper, we will first present the literature review and the theoretical relations that have been estimated, followed by the summarized econometric results. Details are in the appendix. In a final part we will exhibit shock simulations both with and without financial accelerator, in order to emphasize the role and the importance of the latter in the workings of the macro model, before summing up the work done on forecasting properties.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
3 1. Literature review
1.1 Theoretical aspects1
The financial accelerator (or credit multiplier) explicitly interconnects financial markets and the real economy in an environment which is characterized by incomplete capital markets. An important result from the literature on the credit channel is that under the presence of information asymmetries, firms are likely to finance investment projects using internal funds (for instance retained earnings) rather than drawing on external finance. Put differently, external finance is more costly than internal finance. This difference is called the external finance premium, which is essentially a mark-up over the price of internal finance. This premium arises due to various frictions, as for instance, external lenders cannot perfectly observe nor control the risks that a project inherits under which a bank supplies funds to borrowers. Hence lenders require a compensation for the expected agency costs.
The key innovation in financial accelerator models is that they embed the problem of information asymmetries in a standard macroeconomic model. The key variable in these models is the net worth of borrowers, which is accumulated by means of retained earnings. Shocks to net worth relative to total finance requirements generate endogenous changes in agency costs and in the finance premium for external funds which are charged above risk-free rates. In this set-up, any structural shock is likely to be amplified relative to a model set-up where the financial accelerator extension is omitted.
Over the past three decades, rigorous analytical models have investigated the linkages between financial markets and the real economy. There is also a well-established series of publications in macroeconomics concerning the incorporation of financial market frictions (i.e. market imperfections) in standard macroeconomic models. Bernanke and Gertler (1989) is an early study in this respect. Kiyotaki and Moore (1997) provide another approach to adding financial frictions in a general equilibrium model of the macro economy.
Standard macroeconomic models, though, usually embed the Modigliani-Miller assumption about perfect capital markets. Hence there is no theoretical role for modelling the interactions between real and financial factors. The Global Financial Crisis of 2008–09 highlighted the extent to which fluctuations in asset prices, credit and capital flows can have a dramatic impact on the financial position of households, corporations and sovereign alike and by this, violating the Modigliani-Miller assumption. In this context, the crisis has brought back in mind the importance surrounding macro-financial linkages; however, it is yet only another incident highlighting the importance of real and financial linkages.
It is convenient to distinguish three possible channels linking financial flows and real economic activity:
• From the real economy to the financial markets: If this were the only linkage between real and financial flows, the explicit modelling of the financial sector would be of limited relevance for understanding movements in real economic activities.
• Amplification: This hypothesis states that financial frictions exacerbate a recession, however, they are not considered as the cause of the recession. In this context, something wrong happens in the real sector in the first place. This could be caused by exogenous shocks to productivity, the terms-of-trade, monetary aggregates, interest rates, preferences, etc. These structural innovations would trigger a macroeconomic contraction even in the absence of financial market frictions. When financial frictions are prevalent, however, i.e. financial markets do not work smoothly, the magnitude of the contraction becomes more pronounced. Therefore, financial frictions amplify the macroeconomic impact of the exogenous changes.
1 For an excellent and recent review of the literature: Claessens & Kose (2018): “Frontiers of macrofinancial linkages”.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
4 • Financial shocks: A third hypothesis is that the initial disruption arises in the financial sector of the economy. There are no initial changes in the nonfinancial sector. Because of the disruption in financial markets, fewer funds can be channelled from lenders to borrowers. As a result of the credit tightening, borrowers cut on spending and hiring, and this generates a recession. In other words, this channel considers financial markets as the main source of shocks. This has received less attention in the academic literature (with the exception of the work of Hyman Philip Minski (1992)), though recently, more studies started to explore this possibility.
Most of the literature in macro-finance has focused on the second channel, that is, on the amplification mechanism generated by financial market frictions. It is for this reason that macro-financial linkages are generally considered as a mechanism that establishes a two-way interaction between the real economy and the financial sector; this is in line with the amplification hypothesis. Shocks arising in the real economy can be propagated through financial markets, thereby amplifying business cycles. Conversely, financial markets can be the source of shocks, which, in turn, can lead to more pronounced real economic fluctuations.
Bernanke and Gertler (1989), Carlstrom and Fuerst (1997), Kiyotaki and Moore (1997) and Bernanke et al. (1999) focus on amplification mechanisms, collectively known as “the financial accelerator”, which operates through the demand side of financial transactions. These contributions show how accelerator effects arise when small shocks, real or financial, are propagated and amplified across the real economy as they lead to changes in the access to finance. Early work in this area focuses purely on the demand side of credit and ignores credit supply frictions originating on the supply side.
The crisis, however, made it clear that incorporating financial frictions without explicitly modelling financial intermediaries meant that the models were unable to generate the adverse feedback loops between the financial system and the real economy that had been a prominent characteristic of the crisis. Against this background, more recent theoretical and empirical research has illustrated the importance of amplification channels operating on the supply side. In this context, Gerali et al. (2010) represent one of the first attempts to introduce a banking sector into a quantitative DSGE model of the euro area with financial frictions. They find that the banking sector not only exacerbates the propagation of supply shocks, but also that shocks originating there can explain the bulk of the decline in euro area GDP in 2008. In addition, the destruction of bank capital has severe implications for investment and economic activity.
Other contributions involving financial institutions and markets are Brunnermeier and Pedersen (2009), Adrian and Shin (2008) and Geanakoplos (2008) to name a few. New models that include both demand and supply types of macro-financial linkages (Brunnermeier and Sannikov (2014), Gertler and Kiyotaki (2011), Williamson (2012) and Dávila and Korinek (2017)) have been developed.
Most of the research in this area has focused on extending dynamic stochastic general equilibrium (DSGE) models by means of financial frictions in order to introduce macrofinancial linkages. The recent critique towards DSGE models, though, has induced researches to also consider models other than of a DSGE nature for incorporating financial frictions. These models are primarily large-scale macroeconometric models, like Modux, which are again increasingly used in policy making institutions (Blanchard 2017). Bårdsen et al. (2006) and Bårdsen and Nymoen (2009) are some interesting contributions in this area. The flexibility of this kind of models, in conjunction with the fact that most of their parameters are estimated rather than calibrated, renders them attractive for simulations beyond their traditional scope. In this respect, Hammersland and Jacobsen (2008) and Hammersland and Træe (2014) utilized them in order to assess the implications of an asset boom in general and a strong and steady increase in housing prices in particular. Even though these models’ theoretic foundations are less stringent than those of DSGE models, they rely heavily on mechanisms commonly considered within the DSGE literature. One of them is the classical financial accelerator mechanism as popularized by Bernanke et al. (1999).
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
5 1.2 The financial accelerator in other estimated macro models
There do not seem to exist many papers which tackle issues like the one described here. A small non- representative survey among research or policy institutions from Belgium, France and the Netherlands revealed that none of them seemed to have similarly functioning mechanisms/models.
One reference in the literature is Hammersland & Træe (2014). They describe a macroeconomic framework, first completed in 2007, which focuses on financial frictions and was initially tailored to the needs of Norway’s central bank financial stability wing. It was later put to use as a stress testing device and has also been frequently used to illustrate the relative importance of different transmission channels. In contrast to highly stylized model representations frequently used for illustrating the working of the financial accelerator mechanism, the model adopted by the Norwegian central bank integrates such a feature in a fully-fledged macro-econometric structural model framework, similar to Modux.
According to the authors, a forecast comparison undertaken between that model and an alternative macro- econometric model without a financial block suggests that financial feedback mechanisms – in addition to enhancing the practical relevance of a model by incorporating a mechanism of high real-world authenticity – may improve the forecasting properties of theory informed macro-econometric models in general.
The model is an estimated equilibrium-correction model with backward-looking rational expectations and a credit channel for monetary policy. It is based on quarterly data and features, a.o. a reduced form equation for GDP. The model has been designed and estimated using classical estimation methods and not imposing a priori restrictions (distributional or otherwise). The role of the financial block is primarily to take account of the co-movements and pro-cyclicality of credit, asset prices and real economic activity that typically characterize a financial accelerator. As such, it is mainly used for constructing risk scenarios related to low- probability events.
Hammersland & Træe (2014) simulate 5 shocks in total: a rise in the money market interest rate; a shock to the price level; a shock to wages; a shock to productivity; a drop in consumer confidence. Of these, only the shock on interest rates is comparable with what has been done with Modux, but Hammersland & Træe (2014) have simulated a temporary shock, whereas we have simulated a permanent one. Still, comparisons on a qualitative basis are valid. Indeed, all the important variables like GDP, prices, credit, employment move in the same direction, in both models. Comparison is even more difficult as Modux is a yearly model, whereas Hammersland & Træe (2014) are working in a quarterly set-up.
Concerning forecast performance (see section 5. of this paper), a comparison undertaken between their model and an alternative macroeconometric model without a financial block suggests that financial feedback mechanisms may improve the respective properties “of theory informed macroeconomtric models in general”. All in all, their results, both concerning simulations and forecasts, do not jeopardize the ones we found.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
6 2. The financial accelerator in Modux
This part exposes the theoretical relations (in a summarized way) representing the financial accelerator in our standard estimated macro model as they are derived from Glocker (2016, 2017), which constitute the foundation for this research. Detailed tables can be found in the appendix.
Capital stock = f [volume drivers (+); real credit (+), real user cost (-)] (1)
The capital stock is modelled separating machinery and equipment investment (including non-residential buildings) and housing investment. Investment, as it enters GDP from the expenditure side, equals the first difference of capital spending, plus depreciation. Capital demand depends on a volume driver (either the level of real private (non-banking) value added or total population) and credit supply, expressed in real terms, i.e. deflated by investment prices. In the housing investment equation, the user cost of capital, which is a function of the credit rate, plays as well (negative coefficient). In the light of the financial accelerator, all things equal, higher credit entails more capital spending (higher investment). The user cost, which directly depends on the market lending rate for housing credits, is also present in the standard specification, as are of course the volume drivers.
Credit = f [capital stock (+); price (+); credit rate or risk premium (-)] (2)
Credit supply primarily depends on the demand for physical capital: higher investment entails more credits, the only source of financing in this model being external finance. Higher prices, ceteris paribus, also imply more credit volume, this is especially interesting in the case of housing booms and busts… The measure for the cost of credits differs: for machinery and equipment credits, it’s the risk premium (credit rate less the 3 month money market rate) whereas for the housing credits, it’s the credit rate itself that was retained. A higher credit rate has a direct impact via the user cost of capital but it also plays indirectly, and this illustrates to some extent the financial accelerator mechanism, as it lowers credit demand, which then exerts a downward pressure on capital demand, etc…
With these two rather simple functions, it’s already possible to emphasize the intertwined relations between capital and credit, and to understand how the financial accelerator works through the three following channels, as stated before:
- real activity which causes movements in financial flows (credit); - amplification (of the cycle): higher credit higher investment; - transmission of financial shocks to the real side (i.e. from interest rates) higher credit, …;.
Let’s now move to the next step, the explanation of the lending or credit rate:
Credit rate = f [3 mmm rate (+); leverage (+)] (3)
The credit rate that borrowers have to pay to the lenders (banks) depends on the 3 month money market rate and the leverage. The latter – an identity – is defined as follows:
Leverage = credit / (capital * price) (4)
Capital * price is the nominal value of physical capital, which is a proxy for collateral. The higher the credits with respect to the value of collateral, the higher the risk (of not being reimbursed) taken by the lenders (the banks), the higher the rate they charge. A fall in the value of collateral, through lower prices (cf. “boom to bust”), or less investment, also makes credit more expensive.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
7 Risk premium = credit rate – 3 mmm rate (5)
The risk premium is the difference between the effective cost of credit and the short term interest rate:
As inspired by Glocker (2016, 2017), the risk premium is an identity, i.e. the difference between the endogenous credit rate and the exogenous 3 month money market rate, which itself depends on the Central bank lending rate or on the financial markets. In the later developments that have been integrated into Modux, the risk premium has been made endogenous whereas the credit rate simply presents a “markup” on the risk free 3 month interbank rate.
In the next section, these relations are presented in more detail i.e. with their numerical specifications that have been retained in Modux for the purpose of the simulations that are presented later, and more generally, for the purpose of day-to-day forecasting as it is one of STATEC's mission. Econometric results can be found in the appendix.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
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3. Estimated equations
The estimated equations relating to the financial accelerator mechanism as they are retained in the macro model and as they were used to simulate the shocks differ slightly from the ones presented in Glocker (2016, 2017) as they are referred to in the previous section. Main reasons are data revisions, longer estimation periods and some improvements in specification. One notable difference is that the credit rate is not any more modelled directly as an error correction equation (which lead to counter intuitive simulation results) but that instead the risk premium is modelled endogenously, in a simple level equation. The credit rate is then the mark-up of the risk premium on the risk free money market rate. All in all, the specifications are now a bit more parsimonious, without jeopardizing the financial accelerator mechanism as put forward in Glocker (2016, 2017). Detailed econometric estimation results are in the appendix. It should be signalled that equations have not been estimated as simultaneous systems of interdependent relations but with the means of simple OLS estimations, one by one, due to short sample length. This section compares results between the financial accelerator for machinery and equipment investment and housing investment, emphasizing long run elasticities, while mostly skipping econometrics.
a. Capital demand
In a modelling setup which is derived from a standard CES production function, capital demand depends on real output, usually with unit elasticity, and negatively on some measure of capital or credit cost, like the Jörgensen-type user cost of capital that is integrated in Modux. As put forward in Glocker (2016), this specification, even if it is econometrically valid, fails to explain accurately the large dip in capital spending during the 2008/2009 bust.
In our financial accelerator set-up, this core specification (real value added as a volume driver and some price of capital) is maintained, at least for machinery and equipment investment, but it is augmented with a measure of the stock of credit. As the distribution of the residuals shows (see appendix), this specification does take into account the fall in capital spending during the financial crisis, if not perfectly, surely better than in the standard case.
The specifications differ slightly between capital spending on machinery and equipment and housing. For both there is a volume driver (real value added of the private non-financial sector in the first case, total population in the second) but whereas the elasticity on real value added is constrained to equal one, respecting some theoretical priors, in the case of housing capital demand, it is freely estimated, at 0.8.
The user cost of capital still works in the case of machinery & equipment capital spending (elasticity = -0.3), but in the case of housing capital demand, it comes no longer as a significant variable. There it has been replaced by credit, which obviously still depends on financial conditions (cf. below). So the latter play indirectly on capital spending in the case of housing (through credit), but directly in the case of machinery & equipment (through the user cost which includes the credit rate).
Credit, which is expressed in real terms, acts positively on capital spending, but with a low elasticity: a 1% higher stock of credits implies a rise of capital demand of about 0.1% (a bit less in the case of housing). As we will shortly see, credit, on the other hand depends on capital spending, which then establishes the first dynamic feedback loop between the real side of the economy and the financial side.
Both equations have a lagged dependent term in the short run (first differenced) which reflects the slow moving feature of capital spending. It has to be recalled that capital spending, or better the capital stock, accumulates past investment expenditures over several years, so there is a natural inertia in the series,
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
9 which is more of a statistical feature than an economic one, but reveals itself in the dynamics and also has an impact on forecast and simulation analysis.
The short run part of capital spending in the case of machinery & equipment investment includes total investment in planes and satellites. This makes sense, as capital is first differenced, which can then be directly related to investment spending. Investment in satellites and planes is quite important in Luxembourg, amounting to between 10 and 25% of total investment in machinery and equipment. Even if there might be some endogeneity issues, the inclusion of the term in the capital equation highly improves the fit and the values of the elasticities.
In both cases, the error correction term is about -0.3, which denotes a reasonable speed of adjustment.
Table 1: Capital demand
Machinery and equipment Residential
Short run Long run Short run Long run
Elasticities, if not stated otherwise 1 Lagged dependent 0.38 (1.52) N/A 0.57 (6.37) N/A Volume driver: private non-financial real value added 0.14 (1.91) (1) Volume driver: total population 0.86 (6.45) (0.79) Real user cost of capital - (-0.3) - - Real credit - (0.1) 0.02 (2.66) (0.08) 2 Investment in planes and satellites 0.0061 (1.52) -
Error correction term -0.33 (-2.19) -0.32 (-5.80) Constant -0.25 (-1.90) -0.68 (-5.78) Dummies (short run) 2016 2005, 2007
Estimation period 2000-2016 1995-2016 Adj. R^2 / ser. corr. LM test (propab.) 0.42 0.99 0.88 0.40
Source: Author's calculations
1 N/A means "not applicable" i.e. not tested because meaningless; "-" means tested but not significant and therefore not retained; empty cells stand for different prior specification for each model. T-statistics between parenthesis; constrained parameters (from separated long run estimations) between parenthesis. 2 Included in EUR (unit: billions), as it can take negative values (disinvestment); the investment in satellites and planes relates to 2 companies, often following an investment plan which is not necessarily linked to the general stance of the economy; not included this variable leads to different coefficients and a less well specified equation. The estimated coefficient means that 1 bn of investment in that area increases the total capital stock of machinery and equipment devices by 0.6% in the short run. b. Credit
The credit variables, as they have been constructed, relate to long term investment decisions. Obviously, treasury credits for non-financial firms, consumption credits for households or bank-to-bank loans have not been retained. Credit supply depends on investment decisions. Since the modelling of capital demand derives from the CES specification, we had to take the total stock of credits too (instead of flows i.e. new credits).
So in our set-up, credit supply depends on capital demand. The elasticities are about 2 (2.2 for credits to non-financial firms and 1.8 for housing credit). Their values above 1 translate higher volatility for credit, and also higher average growth.
Credits are also driven by prices, with a close-to-one elasticity in the long run. Whereas credits to non- financial firms have been deflated with the investment price, in the case of house prices, total transaction prices have been used, including sales of existing homes. The latter is justified as credits for housing are not only a function of investment i.e. new constructions, but also of purchases of existing housing stock (which however is excluded from investment in the national accounts data).
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
10 In both cases, it is not the interest rate that influences the demand for credit, but the risk premium, i.e. the mark-up on the risk-free three month money market rate. A higher risk premium induces a lower demand for credit. This is a semi-elasticity, as the risk premium can also become negative (at least in the case of shock simulations). The coefficient is higher in the long run in the case of non-financial firms, than for households, denoting a higher reactivity to credit market conditions. This might be related to the fact that over the estimation period, the housing market remained very dynamic in Luxembourg, despite the financial crisis and its consequences with the value of collateral persistently on the rise, which has to a large extend reduced the risk taken by banks.
The error correction terms indicate a moderate path towards the long-run equilibrium (-0.2 to -0.3).
Table 2: Credit
Credits to non financial firms Housing credit
Short run Long run Short run Long run
Elasticities, if not stated otherwise 1
2 Price level (1) (1) 0.39 (2.67) (0.86) 3 Capital stock (real) 0.26 (0.15) (2.2) 0.11 (2.33) (1.8) 4 Risk premium -0.1 (-3.24) -0.75 - (-0.1)
Error correction term -0.30 (-7.24) -0.20 (-3.08) Constant 0.62 (5.78) 0.73 (3.36) Dummies (short run) - 2000
Estimation period 2000-2016 2000-2016 Adj. R^2 / ser. corr. LM test (propab.) 0.77 0.36 0.78 0.17
Source: author's calculations
1 N/A means "not applicable" i.e. not tested because meaningless; "-" means tested but not significant and therefore not retained; empty cells stand for different prior specification for each model. T-statistics between parenthesis; constrained parameters (from separated long run estimations) between parenthesis. 2 Investment price (machinery and equipment) and house prices (sales prices, old and new).
3 Machinery and equipment, in the case of non financial firms; NB: first difference of log(residential investment) in the short run part of the housing capital demand equation.
4 Credit rate - risk free 3 month money market rate; not expressed in logs, as it can take negative values. Semi-elasticity as the risk premium can take negative values.
Figure 1: Risk premia Figure 2: Measures of leverage
2.5 50 45 2 40 35 1.5 30
% 25 1 20 15 Percentage points 0.5 10 5 0 0 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 1999 2000 2001 2002 2003 2004 2010 2011 2012 2013 2014 2015 2016 2005 2006 2007 2008 2009 Risk premium on housing credits Leverage, housing credits Risk premium on investment credits to non-financial firms Leverage, credits to non-financial corporations
Source: STATEC, BCL Source: STATEC, BCL
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
11 c. Risk premia
The risk premium is the difference between the credit or lending rate charged to the borrowers (firms and households) and the risk free three month money market rate.
The risk premia have been falling sharply prior to the financial crisis, and rose thereafter to levels not seen in the decade before. Whereas they have come down somewhat for companies, banks increased their margins on housing credits, at least until 2016, to some extent perhaps in order to remain profitable, in an environment of low interest rates and a continuously dynamic market in Luxembourg.
According to the literature, risk premia depend on the business stance, on a kind of risk measure confronting credit and collateral and on the spread (yield curve). For sake of simplicity, and also to avoid some counter- intuitive effects, the risk premia have been estimated as simple level equations, ignoring to some extent their short run dynamics. Contrary to the literature, where these relations are often calibrated, ours is – at least partially – estimated.
For the measure of the business cycle we use the output gap, which comes up with a negative coefficient: a better economy lowers the probability of default of the borrower and hence incites the banks to charge less for credit. In the case of credits to non-financial firms, it is calibrated, whereas it is econometrically estimated in the case of credits for housing. In the latter case, a one percentage point increase in the gap lowers the risk premium by about 10 basis points. For non-financial firms, the effect is about half. The coefficient on the gap has been calibrated to a value in accordance with the other parameters, some of them estimated.
The risk measure is proxied by an indicator of leverage. The simplest way of staying in accordance with the macro model (i.e. not introducing new series that would then have to be endogenized or forecasted) was to divide the stock of credit (risk factor for the banks) by the value of the collateral, i.e. the nominal capital stock. Volume capital stock has to that effect been multiplied by a price (investment or transaction prices).
One can see that leverage seems to be generally trending upwards, with a possible break however after the crisis. Whereas it seems more to stabilize for housing credit, it has decreased rather sharply for firms, and picked up again around 2014/2015, altogether in accordance with the business cycle. Hence there seems to be some kind of positive correlation between the respective measures for leverage and for the risk premium: for the households, the leverage has remained high, and the risk premium hardly decreased or even increased. For the companies, there was a sharp drop in leverage, which went hand in hand with a decreased risk premium.
However, despite this apparent co-movement, the coefficients on the leverage could not be estimated together with the spread and the output gap in one equation (note that we have only about a dozen observations). Estimations however undertaken with the leverage as sole explanatory variable worked well (as shows the graphical analysis), and gave a valuable starting point for the calibration of the coefficients. The results indicate that a 1 percentage point increase in the leverage raises the risk premium for mortgage loans by 5 basis points. The effect is about half for investment in machinery and equipment.
A higher leverage raises the risk premium, which then lowers credit and investment or capital demand. The net effect on the leverage depends on the overall reaction of capital and credit, and hence also on the type of shock. But as long as the decrease in capital is stronger than the one in credit (i.e. the leverage continues to increase), the negative feedback loop continues to work. This is the second transmission channel of the financial accelerator. Remember that the first one was between capital and credit.
Finally the spread, or the orientation of the yield curve, measured here as the difference between the long term government bond rate in the eurozone and the short term three months risk-free money market rate is
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
12 the single most important determinant, as regards estimation results, since it clearly shows up significantly with a reasonable parameter. Hence, a 10 basis points increase in the spread results in the transmission of 3 basis points hike to the risk premium. Additionally, the risk premium on housing credit depends on the short term rate: an increase in the short term rate of 10 basis points, independently on the spread, increases the risk premium by 1 basis point.
Table 3: Risk premia
Credits to non financial firms Risk premia on2: housing credit Spread (govt. bonds - 3 month money market rate) 0.29 0.28 3 month money market rate - 0.13 Output gap -0.055 -0.10 Leverage (credits / nominal capital stock) 0.005 0.0025 Constant -0.25 -0.68 Dummies (short run) 2016 2005, 2007 Estimation period 1999-2016 1995-2016
Source: Author's calculations
1 N/A means "not applicable" i.e. not tested because meaningless; "-" means tested but not significant and therefore not retained. 2 As variables are not expressed in logs, the coefficients are not elasticities
d. Summing up: variable names, estimated long run parts and identities
CAPBMEQ_R: Capital demand, machinery and equipment CAPBRES_R: Capital demand, residential investment CREDNFC: credits to non financial firms (stocks) CREDRESMEN: mortgage credits (stocks) IMEQCAL: investment in planes and satellites IRES_R: investments, residential buildings (new constructions) LEVMEN: leverage ratio, mortgage credits LEVNFC: leverage, credits to non financial firms P_IMEQ: investment prices, machinery and equipment P_IMMOLU: house prices (transactions, old and new) P_IRES: price deflator, residential investment (new constructions) P_VABPRVO: value added prices, non financial, private POPTOT: total resident population PUCMEQNFC: user cost of capital, machinery and equipment RISKMEN: risk premium on interest rates for credits for residential investment (mortgages) RISKNFC: risk premium on interest rates for credits to non financial firms RISKNFC: risk premium on interest rates for credits to non financial firms R_RETMEQ_R: depreciation rate, machinery and equipment TICTEUR: 3 month interest rates, eurozone TIHYP: interest rate on mortgage loans TINFC: interest rate on loans to non financial corporations VABPRVO_R: value added (vol.) non banking, private
LOG(CAPBMEQ_R) = LOG(VABPRVO_R) - 0.3*LOG(PUCMEQNFC/P_VABPRVO) + 0.1*LOG(CREDNFC/P_IMEQ) LOG(CAPBRES_R) = 0.79*LOG(POPTOT) + 0.08*LOG(CREDRESMEN/P_IRES) LOG(CREDNFC/P_IMEQ) = 2.2*LOG(CAPBMEQ_R) - 0.75*RISKNFC LOG(CREDRESMEN) = 1.8*LOG(CAPBRES_R) + 0.86*LOG(P_IMMOLU) - 0.1*RISKMEN RISKNFC = 0.005*LEVNFC - 0.055*OG + 0.29*(TILTEUR-TICTEUR) RISKMEN = 0.0025*LEVMEN - 0.10*OG + 0.28*(TILTEUR-TICTEUR) + 0.13*TICTEUR PUCMEQNFC = P_IMEQ*(TINFC/100 + R_RETMEQ_R/100 - DLOG(P_IMEQ))/(1 – R_IMRWPMPRVO/100) TINFC = TICTEUR + RISKNFC TIHYP = TICTEUR + RISKMEN LEVMEN = CREDRESMEN / (CAPBRES_R * P_IMMOLU) LEVNFC = CREDNFC / ( CAPBMEQ_R * P_IMEQ)
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
13 Figure 3: Main relations simplified
Capital / Credit investment
Leverage
Output gap / real Risk premia economy
Source: authors
4. Simulation results
In this section, we are going to present some shock simulations that have been applied to a baseline (medium term forecast until 2022) in order to evaluate the functioning of the model with and without financial accelerator. All shocks are maintained, i.e. permanent level shifts. The last one is done with the financial accelerator augmented model only, all others being carried out in a comparative approach, i.e. with and without financial accelerator:
Fiscal multiplier shocks (increase of 1% of GDP due to public investment and intermediate consumption); Increase in eurozone GDP (+0.5%); Increase in the short term interest rate (100 basis points); Increase in the risk premium (50 basis points). a. Fiscal multiplier shocks
We show how the public spending multipliers are affected by the presence of a financial accelerator. We concentrate on the financial transmission channels that are implemented in Modux which transit through the risk premium and the credit channel. We ignore all other economic linkages, like traditional multiplier effects.
The Keynesian multipliers with financial accelerator tend to be higher in the initial phase than those "without" but they are decreasing faster and become even negative towards the end of the simulation period. We are going to try to explain why this is so by analysing the mechanisms that are in place, with their linkages and feedback loops.
It is also noteworthy that the multipliers "with financial accelerator" tend to be higher than 1 in the short run, which is an interesting feature for a small open economy, where one usually expects small multipliers, lower than 1, or even close to 0. However, there is a whole set of papers that tried to show that public spending multipliers trend to depend on the position in the cycle and also seem to be higher (and higher than one) in times of the financial stress.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
14 Figures 4 – 7: Fiscal multiplier shocks
1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 % % 0.2 0.2 0.0 0.0 -0.2 -0.4 -0.2 -0.6 -0.4 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Public investment multiplier, without financial accelerator Intermediate consumption multiplier, without financial accelerator Public investment multiplier, with financial accelerator Intermediate consumption multiplier, with financial accelerator
6.0 1.6
4.0 1.4 1.2 2.0 1.0 0.0 0.8 -2.0 % 0.6 Basis points -4.0 0.4 -6.0 0.2
-8.0 0.0 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impact on the risk premium Impact on machinery and capital equipment, without financial Contribution from the output gap accelerator Impact on machinery and capital equipment, with financial Contribution from the leverage accelerator
Source: author's calculations
This finding can be related to the literature on the cycle-dependence of fiscal spending multipliers although in Modux, multipliers are stable over time i.e. they just depend on whether or not financial linkages are included (hence model-dependent). For example, Corsetti et al. (2012) write: “We […] find output and consumption multipliers to be unusually high during times of financial crisis”.
Note also that there is not much difference between the multiplier from investment spending and the one from intermediate consumption, so we will concentrate on the former to develop the economic reasoning underpinning the results.
The risk premium decreases, because the output gap (OG) increases, due to the favourable shock on activity (higher public spending). Due to a generally lower perceived risk of fall-outs, banks accept a lower mark-up on the price of the funds that they lend out in terms of credits to non-financial corporations which lowers the market interest rate and the user cost of capital. This involves higher investment, which in turn raises the leverage (credits / nominal capital stock), which pushes up the risk premium after some time (see contribution from leverage in fig. 4-7), to a point where it's higher than in the baseline. At this point, the opposite effect happens, namely, capital demand and investment fall, dragging the economy down.
This cyclical feature is typical for a financial accelerator: it emphasizes the fluctuations of the economy: pushes it higher, when it's already booming, and lowers it in phases of depression or deceleration. All the simulations shown in this paper work like that. It's nice and interesting that such sophisticated and
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
15 important results can be obtained in a consistent manner with quite a simple extension of the model and by only introducing a few additional variables.
Towards the end of the simulation period, a closing of the output-gap adds to pushing the risk premium beyond the levels in the baseline. What was a stimulus to the economy now becomes a drag, quite importantly so…
As stated before, the financial accelerator, the way it is implemented in Modux, features two self-reinforcing feedback loops:
- A first one which passes through the risk premium: a better economic outcome lowers the risk premium which raises investment, which improves the economic situation, which lowers the risk premium, etc... up to a point where the negative forces start dominating; the higher leverage raises the risk premium which slows investment and pulls GDP back down to the baseline levels, or even below;
- A second one which passes through the credit channel: higher credit entails higher capital demand which causes higher credit, etc...
Note that both channels overlap, because higher capital demand has an impact on GDP, which pushes the output-gap down, aso.
So these 2 feedback loops taken together explain that in the case of a simulation of a 1% of GDP increase of public investment, capital spending on machinery and investment is up to 1 percentage point higher than in the normal case. The impact on investment is magnified a lot (since investment, in a simplified way, is the first difference of capital spending; fluctuations in investment are always much higher than on the capital stock, which accumulates past investment expenditures).
Hence, private investment first increases then decreases (is lower than in the baseline). The impact is much higher on machinery and equipment investment than on residential capital expenditure. Actually, investment in machinery and equipment is simulated to decrease by 60% at the end of the period. In a historic perspective, these (in absolute value) high growth rates are not uncommon for this very volatile series of the luxembourgish economy and should not be interpreted as poor or hazardous simulation results.
Figures 8 – 9: Fiscal multiplier shocks (continued)
3.5 20 10 3.0 0 2.5 -10 -20 2.0 -30
% 1.5 % -40 1.0 -50 -60 0.5 -70 0.0 -80 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impact on credit to non financial corporations Impact on total investment Impact on machinery and equipment investment Impact on machinery and capital equipment, with financial accelerator Impact on residential investment
Source: author's calculations
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
16 b. Eurozone activity shock
We simulate the impact of a permanent increase of 0.5% of Eurozone GDP. This triggers an impact of more or less double that - i.e. 1% - in the short run on domestic GDP, before it quickly reverts to a lower value. We might see here two stylized facts of the Luxembourgish (LU) economy (that can be shown easily on past observed data): it tends to amplify the euro-zone (EZ) cycle and it tends to exhibit higher volatility.
The amplification of the cycle (elasticity between EZ GDP and LU GDP greater than 1) comes from the short term elasticity between EZ GDP and the stock market index which is close to 8 (elasticity based on econometric estimations). The stock market clearly fluctuates more than real activity, especially in the short run. This feeds then back into exports of financial services that have a high weight in the Luxembourgish economy, and hence boosts GDP.
The volatility seems to come from a financial accelerator effect (at least as Modux is now designed) so we are mainly interested in the differences with/without financial multiplier. As a matter of fact, the similarities with the fiscal multiplier shocks are striking, i.e., amplification in the beginning, then faster down turn in the medium term (see graphs) but correspond to the literature. The risk premium is the leading driver of the differences.
Figures 10 – 13: Impact of a permanent increase of eurozone GDP by 0.5%
1.4 4.5 1.2 4 1.0 3.5 0.8 3 0.6 2.5 % % 0.4 2 0.2 1.5 0.0 1 -0.2 0.5 -0.4 0 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impact on domestic GDP, without financial accelerator Impulse: permament increase of EZ GDP by 0.5%
Impact on domestic GDP, with financial accelerator Consecutive reaction of Eurostoxx
6.0 2.0 4.0 2.0 1.5 0.0 -2.0 1.0 -4.0
-6.0 % Basis points -8.0 0.5 -10.0 -12.0 0.0 -14.0 2017 2018 2019 2020 2021 2022 -0.5 2017 2018 2019 2020 2021 2022 Impact on the risk premium, non financial corporations Impact on the leverage, non financial corporations Impact on the risk premium, mortgage credits to households Impact on the leverage, households Impact on the output gap
Source: author's calculations
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
17 The risk premium actually decreases in the beginning, due to the more positive output gap. The progressive fading away of the initial impulse and the rise of the leverage annihilate the favourable impact on the risk premium, up to a point where it is actually reverted. The fall in the risk premium, as before, raises investment, and therefore growth, amplifying the positive impulse from Eurozone activity.
As with the fiscal expansion, in a first stage, the output gap becomes positive, which lowers the risk premium and more generally the cost of credit, whereas leverage rises. In the second phase, the progressive closing of the output gap, together with the increased leverage, bring the risk premium back to its original value, respectively above it.
Credit and capital stock are linked by a mutual dependence, which is one illustration of the financial accelerator. Econometric results however show that credit to non-financial corporations, which is used to invest in machinery and equipment, is more sensitive to financial variables, as can be verified in figure 14. Indeed, whereas for credits to households (financing residential investment), the coefficients on the capital stock and the risk premium are respectively 1.8 and 0.1, they are 2.2 and 0.75 for the equation explaining capital spending on machinery and equipment. Economically, this could be interpreted by recalling that the housing market in Luxembourg is in a long-lasting upward trend due to high inflow of migrations, and that financial conditions seem to play less in the decision making process of banks and borrowers. This could also be linked to rather strict conditions in terms of individual guarantees that borrowers have to present if they aim at investing in housing, swiping somehow away concerns on the macro side. In other words, it is not as big a risk lending to households for buying homes, as it is giving loans to companies to expand their production facilities.
Now, the crucial point is that capital and labour act as substitutes in the production function. Hence, since capital reacts slowly but investment is affected already by the slow-down of capital, labour is more affected (in the case of the financial accelerator). In other words, in the normal set-up of the model, without financial accelerator, the reactions of employment and capital are about of the same order of magnitude, whereas with a financial accelerator, employment decreases proportionately more. This can also be seen on unemployment, which is actually higher, towards the end, in the case of the financial accelerator. To some extent, it contributes to amplify the cycle, as it has quite important feedback loops on economic activity (it impacts private consumption and foreign labour supply, for example).
Figures 14 – 15: Impact of a permanent increase of Eurozone GDP by 0.5% (continued)
4.0 0.8 3.5 0.6 3.0 0.4 2.5 0.2 % % 2.0 0.0
1.5 -0.2
1.0 -0.4
0.5 -0.6
0.0 -0.8 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impact on credit to non financial corporations Impacts "with" - "without" financial accelerator on: Impact on credit to households (mortgages) Domestic GDP Employment Impact on total capital stock Capital stock Unemployment rate
Source: author's calculations
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
18 c. Increase in the short term interest rate
Here we are simulating a 1 percentage point or 100 basis points maintained increase in the 3 month money- market interest rate. We will present comparative simulations, with and without financial accelerator.
To understand the way these shocks play through, one has first to examine the way the interest rates are affected, with and without financial accelerator (figure 16).
In case of investment in machinery and equipment, without financial accelerator, the user cost of capital depends on the long term interest rate in the euro zone. However the latter is not dependent on the cycle, so the increase in the rates consecutive to the shock, that depresses investment and activity, does not have a retro-impact, hence no amplification of the shock (no feed-back loops). In the financial accelerator set-up, the user cost depends on the market rate, i.e. the effective cost of credit. The latter depends on the risk premium that co-moves with the cycle, hence feedback loops and amplification.
In the case of residential investment, the user cost depends in both cases on the mortgage interest rate. In the normal case, the latter is just a function of short and long rates (no feedback loops). But in the case of the financial accelerator, the latter is linked to the cycle and a measure of the leverage, hence feedback loops and amplification…
So we can see (fig. 16) that in the case of the financial accelerator, interest rates rise more than the initial impulse, at least for 2-3 years. In the end, they fall back however below the level of the impulse. This is due to the behavioural reaction of the risk premium that plays only in the case of the financial accelerator but that generates most of the effects that we will see on real variables. The risk premium is indeed impacted by the rise in the short term interest rate and it is therefore important to understand the underlying workings and pass-troughs:
• The risk premium decreases the very first year because the spread decreases. This is due to the way long term interest rates are modelled with a slow pass-through of the hike in short rates; • Later the risk premium increases, because of the negative output gap - depressed by lower investment - and the increased leverage. The impact on the mortgage premium is stronger because the output gap has a higher - absolute value - coefficient but also because there is a constant effect from the rise in the short term rate (see table 3 with far estimation results); • In the final phase, the risk premium decreases again, because the output gap becomes positive. This is due to the interplay of capital demand and investment, as we will see later.
The user cost of capital increases in the beginning, because the interest rates increase, as a consequence of the hike in the exogenous short term rate. Towards the end of the period, the user cost is then lower than in the baseline simulation, basically because the risk premia decrease, and the initial impulse of 1 percentage point on the short rates finds itself back with a lower-than-one impact on the commercial rates (charged on companies and households for the credits that they use to invest).
This initial increase in the user cost of capital lowers capital spending. This effect is more pronounced in the case of the financial accelerator than without, by about 2 percentage points (level impact, see fig. 20).
The fluctuations of investment (gross fixed capital formation) can largely outperform those of the capital stock (capital stock exhibits high inertia because it accumulates past investment). Hence the more pronounced reaction of investment (even if one has to be cautious in interpreting the order of magnitude rigorously) with a ratio of about 5-15 between the respective growth rates. When the (negative) impact on capital fades away, investment mechanically reacts by increasing. This effect is so big in the end that it has a positive impact on GDP, which then retro-impacts the risk premium through the output-gap.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
19 In graph 20, it is well visible how the financial accelerator impacts economic fluctuations, by amplifying them, and by making them more volatile.
The increase in interest rates decreases economic activity through the impact on the cost of capital and hence investment. Without the financial accelerator, GDP decreases by at most 0.3%, after 3-4 years. With the financial accelerator, the pass-through is faster – it hits a bottom 3 years after the shock - and about 5 times stronger at -1.5%. In case the financial accelerator is excluded, the monetary transmission channel works primarily via the traditional « interest rate channel », while if the financial accelerator is included, the monetary policy transmission channel involves both the «interest rate channel» as well as the «bank lending channel».
But then the risk premium is reverted, from being higher than in the baseline to being lower, basically because the leverage decreases (less capital relative to credit due to lower investment), but also because of the feedback loop between real and financial variables, working through the output gap, that becomes positive again.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
20 Figures 16 – 20: Impact of a 100 basis points increase in the money market rate
1.4 0.3 0.3 1.2 0.2 1.0 0.2 0.8 0.1 % % 0.1 0.6 0.0 0.4 -0.1 -0.1 0.2 -0.2 0.0 -0.2 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Short term interest rate (initial impulse) Government bond rate eurozone Impact on the risk premium, non financial corporations Mortgage rate (without fin. acc.) Mortgage rate (with fin. acc.) Impact on the risk premium, mortgage credits for households Credit rate, non financial corporations
25.0 50 20.0 40 15.0 30 20 10.0 % 10 5.0 % 0 0.0 -10 -5.0 -20 -10.0 -30 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impacts "with" - "without" financial accelerator on the user cost Impacts "with" - "without" financial accelerator on: of capital of: Machinery and equipment investment Gross fixed capital formation Gross capital stock Residential investment
4.0
3.0
2.0
1.0 % 0.0
-1.0
-2.0
-3.0 2017 2018 2019 2020 2021 2022 Impacts "with" - "without" financial accelerator on: Gross capital stock Real GDP Total employment Unemployment rate
Source: author's calculations
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
21 d. Independent shock on the risk premium (financial accelerator model only)
This shock can be brought in relation to the financial crisis, where risk premia were affected by general sentiments of fear and risk aversion (besides other spill-overs, cf. freezing of the interbank market, etc.). For the simulation, the risk premia on loans for machinery & equipment and residential investment are raised permanently by 50 basis points or 0.5 percentage point, which corresponds roughly to their natural volatility (standard deviation). This simulation can only be undertaken with the model comprising the financial accelerator, so there will be no comparative analysis.
The initial impact on the risk premia progressively fades away (fig. 21) but more slowly in the case of mortgage credits than in the case of credits to non-financial corporations. So there are two explanations to find:
- why the initial impulse (positive shock on the risk premium) slowly fades away; - why it is a slower movement in the case of credits to non-financial corporations.
The fading away is basically due to the leverage that diminishes, because investment recedes, due to the higher credit cost (exogenous increase in the risk premium that pushes the user cost higher). More on it hereafter…
The temporarily stronger impact on the premium on housing credits is due to the estimated coefficients that show a higher sensitivity to the output gap and a lower one to the leverage.
Figures 21 – 24: Impact of a 50 basis points increase in the risk premium
0.7 35.0
0.6 30.0
0.5 25.0
0.4 20.0 %
0.3 15.0 10.0 % points 0.2
0.1 5.0 0.0 0.0 2017 2018 2019 2020 2021 2022 2017 2018 2019 2020 2021 2022 Impact on the risk premia (%): Impact on the risk premia (% points): mortgage credits for households mortgage credits for households credits to non financial corporations credits to non financial corporations
0.15 2.5 0.10 2.0 0.05 1.5 0.00 1.0 -0.05 0.5 -0.10
% 0.0
% points -0.15 -0.20 -0.5 -0.25 -1.0 -0.30 -1.5 -0.35 -2.0 2017 2018 2019 2020 2021 2022 -2.5 Impact on the risk premia, contributions from: 2017 2018 2019 2020 2021 2022 output-gap, households Vol. GDP Total employment output-gap, non-fin. corporations leverage, households Capital stock (vol.) Unemployment rate leverage, non-fin. corp. Source: author's calculations
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
22 The endogenous reaction of the risk premium that explains the fading away of the exogenous impulse (graph 21 + 23) plays through the output-gap and the leverage. Whereas the impact from the gap is on the upside in the beginning (lower output gap ==> higher risk aversion ==> higher premium), lower credit demand implies a smaller leverage, which pulls the risk premium down. At a later stage, the output gap becomes higher again than in the baseline scenario, so both forces (gap, leverage) act in the same direction and pull the risk premium down over the simulation horizon.
On the other hand, the user cost of capital increases all over the period, due to the shock on the risk premium, but the effect is fading away (cf. endogenous reaction of the risk premium), as the economy recovers, and the output gap exceeds its initial level again. The user cost is impacting investment and capital demand that turn out to be lower, which then triggers a negative shock on the real side of the economy.
As with the other shocks that have been simulated, the financial accelerator mechanism implies a higher volatility, up to a point where initial negative effects are reverted and become positive. As before, it's due to the fact that the financial accelerator mechanism transits through the capital stock that affects investment, the latter largely amplifying the movements of the former, which then retro-impacts on GDP, the output- gap, etc...
One has to note that according to certain streams of the literature, the financial accelerator mechanism is not permanently at play, but only occasionally, in times of financial or economic stress most likely. On these occasions, one would see stronger transmissions, and stronger fluctuations, as in these examples, but not necessarily in normal or good economic times. So results that we have shown here are not to be taken as prima-facie evidence that standard models are miss-specified, but that the intertwined relation between the real and the financial side helps to better understand certain episodes of recent economic history. In principle, they should also help forecasters to be better prepared in the case of similar events in the future.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
23 5. Does the financial accelerator improve the forecast performance?
A last question which we want to answer relates to the overall forecasting performance of the model without respectively with the financial accelerator equations. Forecasts are for t+1 (one year ahead) and they shall be qualified as “full information” or “in-sample” as the model is not re-estimated over the respective past (but over the full period) and forecasts are hence in-sample. The more, exogenous variables are perfectly observed. To perform the forecast, the residuals of the estimated equations have been set to zero.
The model can be simulated over the period 2007-2016, hence there will be 10 observation points. The forecasted values are compared to the last available ones, which is different from what is generally done while examining forecast performance2. But since the focus does not so much lie on the overall forecasting performance of the model, but on the comparison “with”/”without” financial accelerator, these points can be ignored.
We calculate three measures of forecast accuracy/bias:
- the mean error (ME), which can be negative (overprediction) or positive (underprediction), and is an indicator of bias;
- the mean absolute error (MAE), which is based on the mean error, but avoids the compensation of negative and positive errors; the higher the MAE, the more inaccurate the forecast is or the more dispersion there is in the forecast; however, the MAE is known to be scale-dependent;
- the root of the mean error squared (RMSE), the most common measure of dispersion but also scale dependent, therefore, it might be useful to use another metric, which is…
- …the mean absolute scaled error (MASE); the latter divides the mean absolute forecast error by the mean of an absolute naïve forecast error; it hence corrects for the scale of the series (Hyndman and Koehler, 2006); the naïve forecast is simply the growth rate of the forecasted variable one period earlier; the mean absolute scaled error can be easily interpreted as values greater than one indicate that the naïve method performs better than the forecasts under consideration.
We try to answer two questions:
1. Does the crisis increase forecast uncertainty?
2. Does the financial accelerator decrease forecast uncertainty?
The first question is not directly related to the research question of the paper, namely the overall performance of a macro model with financial accelerator, but it is an interesting one and it can serve as reliability test of the model and also of the underlying data. The second then checks whether the financial accelerator indeed improves t+1 forecasts; it can be examined over the whole horizon resp. over the crisis period only.
Results are as follows (see tables 4,5 and 6, figures 25 and 26):
2 Usually, the comparison is with respect to the first estimate and not the last, as here.
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
24 - On the basis of the mean error3 and the mean absolute error, the crisis indeed renders forecasting less reliable for a majority of series, but this statement is not true for the mean absolute scaled error;
- It is indeed surprising that the mean absolute scaled error (MASE) does not suffer from the crisis (it actually improves in most cases during the financial crisis); we think this is due to the fact that the denominator, the mean absolute naïve error, increases due to the fact that in times of crises, volatility increases and the naïve method performs worse;
- Concerning the root mean squared error and the question whether it deteriorates during the financial crisis, results are mixed;
- Finally, the financial accelerator indeed improves the forecast accuracy, as can be seen from the fact that for a majority of series, namely 7 out of 12, the mean absolute error is lower; the same is true for the mean absolute scaled error, but the mean error does not seem to be affected;
- These results get even better for the crisis period (2008-2012), now also the mean error (which has been taken in absolute values) and the root mean squared error indicate a smaller bias; hence, the financial accelerator performs better in terms of forecast quality in 75% of the cases. These results hold also for a larger set of variables (results not reproduced here).
Table 4: Error statistics from forecasts (t+1)
2007-2016 2008-2012
ME MAE MASE RMSE ME MAE MASE RMSE
Without financial accelerator
Real GDP -0.27 2.20 0.56 2.48 -0.47 2.45 0.45 2.75 Nominal GDP 0.40 2.16 0.48 2.45 -0.13 1.64 0.26 2.02 Real capital stock -0.04 0.41 1.10 0.49 0.24 0.39 0.91 0.40 Employment 0.07 0.78 0.88 1.00 0.14 1.14 0.88 1.29 Consumer prices -0.05 0.43 0.38 0.52 0.01 0.29 0.16 0.32 Average wage -0.07 0.56 0.84 0.66 0.08 0.62 1.11 0.69 Unemployed -1.09 6.41 0.59 7.44 -2.53 6.79 0.43 7.34 Public income -0.51 1.77 0.73 2.02 -0.70 2.32 0.65 2.34 Real capital stock, mach. & equip. 0.03 1.01 1.27 1.14 0.78 1.10 1.09 1.14 Real capital stock, housing -0.10 0.25 0.59 0.27 -0.19 0.19 0.44 0.21 Investment, mach. & equip. 0.22 13.51 0.78 15.58 10.32 14.99 0.67 15.55 Investment, housing -2.32 6.90 0.46 7.69 -4.61 4.61 0.25 5.17 With financial accelerator Real GDP -0.07 2.23 0.56 2.53 -0.52 2.58 0.47 2.94 Nominal GDP 0.63 2.24 0.50 2.50 -0.12 1.50 0.24 1.80 Real capital stock 0.06 0.30 0.81 0.34 0.14 0.32 0.74 0.35 Employment 0.17 0.81 0.91 1.02 0.12 1.16 0.89 1.32 Consumer prices -0.06 0.47 0.42 0.56 0.03 0.33 0.18 0.36 Average wage -0.09 0.55 0.82 0.64 0.10 0.56 1.00 0.62 Unemployed -1.51 6.41 0.60 7.59 -2.49 6.73 0.42 7.35 Public income -0.30 1.72 0.71 1.97 -0.58 2.20 0.62 2.21 Real capital stock, mach. & equip. 0.13 0.64 0.81 0.74 0.35 0.82 0.81 0.92 Real capital stock, housing 0.11 0.23 0.54 0.33 0.07 0.13 0.30 0.16 Investment, mach. & equip. 1.46 8.47 0.49 9.92 4.48 11.16 0.50 12.50 Investment, housing 3.10 6.82 0.45 9.77 1.66 3.43 0.18 4.21
Source: author's calculations ME: mean error; MAE: mean absolute error; MASE: mean absolute scaled error; RMSE: root mean squared error.
3 Note that for comparison matters, the mean error has been taken in absolute values.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
25 Table 5: The crisis increases the forecast uncertainty (= "TRUE")
Without financial accelerator With financial accelerator
ME MAE MASE RMSE ME MAE MASE RMSE
Real GDP TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE Nominal GDP FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Real capital stock TRUE FALSE FALSE FALSE TRUE TRUE FALSE TRUE Employment TRUE TRUE FALSE TRUE FALSE TRUE FALSE TRUE Consumer prices FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Average wage TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE Unemployed TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE Public income TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE Real capital stock, mach. & equip. TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE Real capital stock, housing TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Investment, mach. & equip. TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE Investment, housing TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
TOT ("TRUE") 10 7 1 4 7 8 2 6 %TOT 83 58 8 33 58 67 17 50
Source: author's calculations ME: mean error; MAE: mean absolute error; MASE: mean absolute scaled error; RMSE: root mean squared error.
Table 6: The financial accelerator increases forecast quality
2007-2016 2008-2012
ME MAE MASE RMSE ME MAE MASE RMSE
Real GDP TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Nominal GDP FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE Real capital stock FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Employment FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE Consumer prices FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Average wage FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE Unemployed FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE Public income TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Real capital stock, mach. & equip. FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Real capital stock, housing FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE Investment, mach. & equip. FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Investment, housing FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
TOT ("TRUE") 2 7 7 5 9 9 9 8 %TOT 17 58 58 42 75 75 75 67
Source: author's calculations ME: mean error; MAE: mean absolute error; MASE: mean absolute scaled error; RMSE: root mean squared error.
Figure 25: Real GDP, observations and forecasts Figure 26: Real GDP forecast errors
10.0 5.0 Underprediction 8.0 4.0 6.0 3.0 4.0 2.0 2.0 1.0 0.0 0.0 -2.0 -1.0 -4.0 -2.0 -6.0 -3.0 -8.0 -4.0 Overprediction -10.0 -5.0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2007 2010 2011 2012 2013 2014 2015 2016 2008 2009 Observed real GDP growth Forecast error with financial accelerator Forecast with financial accelerator Forecast without financial accelerator Forecast error without financial accelerator Source: author’s calculations Source: author’s calculations
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
26 6. Conclusions and further work
The purpose of this paper is to illustrate the workings of the financial accelerator in a simplified form in a standard macro-economic model. Hence, four comparative shocks have been simulated:
. Fiscal multiplier (with and without financial accelerator); External demand (with and without financial accelerator); Increase in the short term interest rate (with and without financial accelerator); Increase in the risk premium (with financial accelerator only).
The results of all shocks converge in the sense of the literature, namely amplification (shocks with financial accelerator are magnified) and stronger oscillation (shocks with financial accelerator tend to generate more pronounced cycles, i.e. stronger down- and upturns).
The main transmission channel is the risk premium which depends both on the real economy (through the output gap) and the financial side (through the leverage with divides credits by the nominal capital stock). Another channel passes through the “real capital demand – credit” nexus, where, according to our modelling, replicating research results, both variables exhibit statistically significant mutual dependence.
Even though the simulation period is short (five years with annual data), we find some evidence of shock correction or reversion, namely that the effect of a positive shock (economic expansion through favourable internal/external demand stimulus) results after some time in a negative impact (on domestic GDP). This does not happen in a model without a financial accelerator.
Model results can also be used to examine questions in relation to the housing market, as the new modelling introduces a measure for the leverage, adding to other variables already present, like interest rates or savings rate. This issue is highly important in Luxembourg in the context of ongoing discussions about housing shortages in times of strong economic and demographic expansion. More work on this issue and further comparison with other work (by the Central Bank for example) is warranted. The advantage of using Modux lies in the fact that labour supply is modelled in an endogenous manner and depends also on (endogenous) housing prices, among others. Hence, economic reasoning can be placed in a context of general instead of partial equilibrium.
It seems superfluous to affirm that in times of renewed financial and economic stress – to some extent risks seem to be building up again in major economies like the US and China – this version of Modux rather than the standard one without financial accelerator should be used. Indeed, up until now, short and medium term forecasts have been elaborated with the standard version, but simulations also show that the accuracy of the forecasts can be increased with the inclusion of the financial accelerator, even more so in times of financial stress, as has been tested over the period 2008-2012.
Current research at STATEC tries to replicate the annual real capital demand equation with quarterly data, hence overcoming short sample reserves on above presented econometric results. First results are promising and do not jeopardize the elasticities found in Glocker 2016 and 2017 or re-estimated in the context of this paper. That project also tries to include other sources of financing, i.e. own reserves, bonds or stock emissions.
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
27 7. References
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28 Geanakoplos, J. (1989). Arrow-Debreu model of general equilibrium. In General Equilibrium (pp. 43-61). Palgrave Macmillan, London.
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A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
29 8. Appendix
Figure GA1: Capital demand Figure GA4: Real economy drivers
80.0 700 30 70.0 600 25 60.0 500 50.0 20 400 40.0 15 30.0 300
Bn Bn of constantEUR 10 20.0 200
10.0 100 5 0.0 0 0 1977 1980 1983 1986 1989 1992 1995 1971 1974 1998 2001 2004 2007 2010 2013 2016 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015 1970 1973 1976 Capital demand, machinery and equipment Total population (1000, lhs) Capital demand, residential investment Value added, private non banking (bn constant EUR, rhs) Source: STATEC Source: STATEC
Figure GA2: Credits Figure GA5: Risk premia
30 000 3
25 000 2
20 000 2
Mio EUR Mio 15 000 1 10 000
5 000 1
0 0 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 1997 1999 2001 2003 2005 2007 2009 2011 2013 1993 1995 2015 Credits to non financial firms (stocks) Risk premium, credits to non financial corporations Mortgage credits Risk premium, mortgage credits
Source: BCL Source: STATEC, BCL
Figure GA3: Leverage Figure GA6: Interest rates
300 9 8 250 7 200 6 5 150 4 1994 = = 1994 100 100 3 2 50 1 0 0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Leverage, credts no non financial firms Interest rate, credits to non financial corporations Leverage, mortgage credits Mortgage rate
Source: STATEC, BCL Source: BCL
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
30 Figure GA7: Prices Figure GA9: Interest rates (eurozone)
1.2 16.0 14.0 1.1 12.0 1.0 10.0 8.0 0.9 6.0
0.8 4.0 2.0 0.7 0.0
0.6 -2.0 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 1990 1992 2016 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Short term interest rate, euro zone Price deflator, non financial, private value added Long term interest rate, euro zone Price deflator, machinery and equipment investment Source: STATEC Source: AMECO
Figure GA8: Prices (2)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Price deflator, residential investment (new buildings) Transaction price, residential buidings, old and new
Source: STATEC
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
31 Table TA1: Equation 1: capital demand, machinery and equipment
Variable Coefficient Std. Error t-Statistic Prob. DLOG(VABPRVO_R) 0.14 0.08 1.91 0.08 DLOG(CAPBMEQ_R(-1)) 0.38 0.25 1.52 0.16 IMEQCAL 0.0061 0.00 1.52 0.16 LOG(CAPBMEQ_R(-1))-LOG(VABPRVO_R(- 1))+0.3*LOG(PUCMEQNFC(-1)/P_VABPRVO(- 1))-0.1*LOG(CREDNFC(-1)/P_IMEQ(-1)) -0.33 0.15 -2.19 0.05 C -0.25 0.13 -1.90 0.08 D16 -0.03 0.01 -3.09 0.01
R-squared 0.60 Mean dependent var 0.045 Adjusted R-squared 0.42 S.D. dependent var 0.0080 S.E. of regression 0.0061 Akaike info criterion -7.100 Sum squared resid 0.0004 Schwarz criterion -6.806 Log likelihood 66.35 Hannan-Quinn criter. -7.071 F-statistic 3.30 Durbin-Watson stat 1.968 Prob(F-statistic) 0.046
Series names: CAPBMEQ_R: Capital demand, machinery and equipment VABPRVO_R: value added (vol.) non banking, private IMEQCAL: investment in planes and satellites PUCMEQNFC: user cost of capital, machinery and equipment P_VABPRVO: value added prices, non financial, private CREDNFC: credits to non financial firms (stocks) P_IMEQ: investment prices, machinery and equipment
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
32 Table TA2: Equation 2: capital demand, residential investment
Dependent Variable: DLOG(CAPBRES_R) Sample (adjusted): 1995 2016
Variable Coefficient Std. Error t-Statistic Prob.
DLOG(CAPBRES_R(-1)) 0.57 0.09 6.37 0.00 DLOG(POPTOT) 0.86 0.13 6.45 0.00 DLOG(CREDRESMEN/P_IRES) 0.02 0.01 2.66 0.02 LOG(CAPBRES_R(-1))-0.79*LOG(POPTOT(-1))- 0.08*LOG(CREDRESMEN(-1)/P_IRES(-1)) -0.32 0.06 -5.80 0.00 D07-D05 0.01 0.00 4.64 0.00 C -0.68 0.12 -5.78 0.00
R-squared 0.91 Mean dependent var 0.020 Adjusted R-squared 0.88 S.D. dependent var 0.0054 S.E. of regression 0.0019 Akaike info criterion -9.465 Sum squared resid 0.0001 Schwarz criterion -9.167 Log likelihood 110.11 Hannan-Quinn criter. -9.394 F-statistic 30.54 Durbin-Watson stat 2.322 Prob(F-statistic) 0.000
Series names: CAPBRES_R: Capital demand, residential investment POPTOT: total resident population CREDRESMEN: mortgage credits (stocks) P_IRES: price deflator, residential investment (new constructions)
Table TA3: Equation 3: credit, non-financial corporations
Dependent Variable: DLOG(CREDNFC/P_IMEQ) Sample (adjusted): 2000 2016
Variable Coefficient Std. Error t-Statistic Prob.
DLOG(CAPBMEQ_R) 0.26 1.78 0.15 0.89 D(RISKNFC) -0.10 0.03 -3.24 0.01 LOG(CREDNFC(-1)/P_IMEQ(-1))- 2.2*LOG(CAPBMEQ_R(-1))+0.75*RISKNFC(-1) -0.30 0.04 -7.24 0.00 C 0.62 0.11 5.78 0.00
R-squared 0.81 Mean dependent var 0.079 Adjusted R-squared 0.766603 S.D. dependent var 0.11592 S.E. of regression 0.056 Akaike info criterion -2.725 Sum squared resid 0.041 Schwarz criterion -2.5285 Log likelihood 27.1585 Hannan-Quinn criter. -2.705 F-statistic 18.5175 Durbin-Watson stat 1.221 Prob(F-statistic) 0.000056
Series names: CREDNFC: credits to non financial firms (stocks) P_IMEQ: investment prices, machinery and equipment CAPBMEQ_R: Capital demand, machinery and equipment RISKNFC: risk premium on interest rates for credits to non financial firms
A simple financial accelerator in a standard macro-econometric model Economie et Statistiques Working papers du STATEC N° 101 juillet 2018
33 Table TA4: Equation 4: credit, residential investment
Dependent Variable: DLOG(CREDRESMEN) Sample: 2000 2016
Variable Coefficient Std. Error t-Statistic Prob.
DLOG(P_IMMOLU) 0.39 0.15 2.67 0.02 DLOG(IRES_R) 0.11 0.05 2.33 0.04 LOG(CREDRESMEN(-1))-1.8*LOG(CAPBRES_R(- 1))-0.86*LOG(P_IMMOLU(-1))+0.1*RISKMEN(- 1) -0.20 0.07 -3.08 0.01 C 0.73 0.22 3.36 0.01 D00 0.08 0.03 3.29 0.01
R-squared 0.84 Mean dependent var 0.10 Adjusted R-squared 0.78 S.D. dependent var 0.048 S.E. of regression 0.022 Akaike info criterion -4.53 Sum squared resid 0.0060 Schwarz criterion -4.28 Log likelihood 43.5 Hannan-Quinn criter. -4.51 F-statistic 15.5 Durbin-Watson stat 2.85 Prob(F-statistic) 0.00011
Series names: CREDRESMEN: mortgage credits (stocks) P_IMMOLU: house prices (transactions, old and new) IRES_R: investments, residential buildings (new constructions) CAPBRES_R: Capital demand, residential investment RISKMEN: risk premium on interest rates for credits for residential investment (mortgages)
Table TA5: Equation 5: risk premium, credits to non financial firms
Dependent Variable: RISKNFC-0.005*LEVNFC+0.055*OG Sample (adjusted): 1999 2016
Variable Coefficient Std. Error t-Statistic Prob.
TILTEUR-TICTEUR 0.29 0.04 6.54 0.00 C 0.15 0.08 1.91 0.08 D08-D15 -0.63 0.12 -5.15 0.00 D09-D14 -0.46 0.12 -3.90 0.00
R-squared 0.88 Mean dependent var 0.597 Adjusted R-squared 0.85 S.D. dependent var 0.44 S.E. of regression 0.17 Akaike info criterion -0.555 Sum squared resid 0.388 Schwarz criterion -0.36 Log likelihood 8.9946 Hannan-Quinn criter. -0.53 F-statistic 34.2 Durbin-Watson stat 1.19 Prob(F-statistic) 0.0000010
Series names: RISKNFC: risk premium on interest rates for credits to non financial firms LEVNFC: leverage, credits to non financial firms OG: output gap TILTEUR: long term govt bonds' interest rates, euro zone TICTEUR: 3 month interest rates, eurozone Dxx: dummy variables (1 for reference year, 0 elsewhere)
Economie et A simple financial accelerator in a standard macro-econometric model Statistiques Working papers du STATEC N° 101 juillet 2018
34 Table TA6: Equation 6: risk premium, credits for residential investment
Dependent Variable: RISKMEN-0.0025*LEVMEN Sample: 1995 2016
Variable Coefficient Std. Error t-Statistic Prob.
OG -0.10 0.04 -2.63 0.02 TILTEUR-TICTEUR 0.28 0.16 1.79 0.09 TICTEUR 0.13 0.05 2.52 0.02 C -0.25 0.37 -0.68 0.50 D16 1.17 0.41 2.88 0.01 D11-D15 -0.86 0.28 -3.12 0.007
R-squared 0.73 Mean dependent var 0.480 Adjusted R-squared 0.648 S.D. dependent var 0.58 S.E. of regression 0.3422 Akaike info criterion 0.92 Sum squared resid 1.87 Schwarz criterion 1.22 Log likelihood -4.12 Hannan-Quinn criter. 0.99 F-statistic 8.72 Durbin-Watson stat 1.33 Prob(F-statistic) 0.00038
Series names: RISKMEN: risk premium on interest rates for credits for residential investment (mortgages) LEVMEN: leverage ratio, mortgage credits OG: output gap TILTEUR: long term govt bonds' interest rates, euro zone TICTEUR: 3 month interest rates, eurozone Dxx: dummy variables (1 for reference year, 0 elsewhere)
Table TA7: Identities
TINFC = TICTEUR + RISKNFC
TINFC: interest rate on loans to non financial corporations TICTEUR: 3 month interest rates, eurozone RISKNFC: risk premium on interest rates for credits to non financial firms
TIHYP = TICTEUR + RISKMEN
TIHYP: interest rate on mortgage loans TICTEUR: 3 month interest rates, eurozone RISKMEN: risk premium on interest rates for credits for residential investment (mortgages)
LEVMEN = CREDRESMEN / (CAPBRES_R * P_IMMOLU)
LEVMEN: leverage ratio, mortgage credits CREDRESMEN: mortgage credits (stocks) CAPBRES_R: Capital demand, residential investment P_IMMOLU: house prices (transactions, old and new)
LEVNFC = CREDNFC / ( CAPBMEQ_R * P_IMEQ)
LEVNFC: leverage, credits to non financial firms CREDNFC: credits to non financial firms (stocks) CAPBMEQ_R: Capital demand, machinery and equipment P_IMEQ: investment prices, machinery and equipment
PUCMEQNFC = P_IMEQ*(TINFC/100 + R_RETMEQ_R/100 - DLOG(P_IMEQ))/(1 – R_IMRWPMPRVO/100)
PUCMEQNFC: user cost of capital, Jörgensen type P_IMEQ: machinery and equipment investment deflator R_RETMEQ_R: depreciation rate, machinery and equipment capital