1. Introduction

In Post-Keynesian economic thought money is endogenously determined by economic activity in a modern economy: "loans create deposits" and "deposits generate reserves." New money is created by lending and is destroyed when loans are paid back. Banks act not as intermediaries bound by reserves that lend deposits; rather, they are central economic actors that create money in the forms of loans (Werner, 2016). Thus, an understanding of the drivers and dynamics of lending behavior is central to an understanding of the financial business cycle.

Central bankers have long recognized that banks create money. The Central Bank of Canada governor, Towers (1939), observed that "[e]ach and every time a bank makes a loan, new bank credit is created -new deposits -brand new money." The New York Federal Reserve Vice President, Holmes (1969), recognized the Fed's operational constraints on the money supply: "In the real world, banks extend credit, creating deposits in the process, and look for the reserve later." McLeay et al. (2014) of the Bank of England clarified misconceptions concerning money creation a modern economy thusly^*: "banks do not act simply as intermediaries, lending out deposits that savers place with them, and nor do they 'multiply up' central bank money to create new loans and deposits."

^*For an empirical demonstration of money creation by a commercial bank from loan creation to money transfer see Werner(2014, 2016).

This perspective is also central to the Financial Instability hypothesis (Minsky, 1977, 2008) in which Minsky integrated Keynes' observation concerning the social psychology of bankers (Keynes, 1931)

"[a] 'sound banker, alas! is not one who foresees danger and avoids it, but one who, when he is ruined, is ruined in a conventional way along with his fellows, so that no one can really blame him."

with Keynes' view of the importance of cognitive and social psychology as a drivers of fluctuations in the financial and real economy (Keynes, 1937):

"We assume that the present is a much more serviceable guide to the future than a candid examination of past experience would show it to have been hitherto.... We assume that the existing state of opinion as expressed in prices and the character of existing output is based on a correct summing up of future prospects, ... Knowing that our own individual judgement is worthless, we endeavor to fall back on the judgement of the rest of the world which is perhaps better informed. That is, we endeavor to conform with the behavior of the majority or the average.... Now a practical theory of the future based on these three principles has certain marked characteristics. In particular, being based on so flimsy a foundation, it is subject to sudden and violent changes."

Lenders interact within a social structure that has norms for group members' common behaviors and network mechanisms controlling the flow of information. They rely on other lenders to justify their economic actions and this gives rise to the phenomenon of "social embeddedness" in banking (Granovetter, 2005).

In this paper we provide further evidence of the importance of social psychology in the generation of the financial business cycle in a capitalist economy by modeling the evolution of lending in terms of psychological and economic drivers that matter to bankers. Our analysis employs the opinion-formation model introduced by Weidlich (1972) and later elaborated by Weidlich and Hagg (1983) with which the social psychology of economic agents can be included in the dynamics of economic incentives.^† Our analysis develops earlier work on the sociodynamics of lending (Hawkins, 2011) through the use of simulation developed by Lux(1997, 2009a, b) and recently applied to the problem of lending opinion formation by Ghonghadze and Lux(2012, 2016). The work of Ghonghadze and Lux (2016) is of particular interest as it demonstrates that a rich set of lending-opinion data – the Federal Reserve's Senior Loan Officer Opinion Survey on Bank Lending Practices (SLOOS) – can be successfully incorporated into the opinion-formation model. Our interest is in extending this work beyond the United States to economies where lending-opinion data sets may be less complete. The results of Ghonghadze and Lux (2016) suggests that machine-learning approaches may be of use in identifying the subset of lending-opinion data that is key to lending-opinion formation and a goal of our paper is to demonstrate that this is so.

^†See also Weidlich (2000) and Helbing (2010).

To this end after an introduction of the opinion-formation model in Section 2 we begin our analysis in Section 3.1 with a demonstration that the U.S. lending study of Ghonghadze and Lux (2016) can be reproduced, both to validate their (and our) work with this data set and to motivate the use of random forests – a machine-learning approach to variable reduction – for this problem. We examine the use of random forests on the U.S. lending data set and then apply it to lending surveys provided by the European Central Bank, and the Bank of Japan in Sections 3.2 and 3.3, respectively. We close with a reflection on the results, both expected and unexpected, of our study in Section 4.

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2. The Opinion-Formation Model

The competitiveness of a loan product is determined by the credit spread – the difference between the interest rate of a loan product and the bank's cost of funds – that a bank charges. Setting the level of the spread is a key task of banking and the factors that bear on this key decision are the drivers of the opinion-formation model. As in Ghonghadze and Lux (2016) we consider a collection of $2N$ bankers facing this question at a point in time $t$. Of these, $n^{+}_{t}$ are positively disposed to lend and $n^{-}_{t}$ are against lending at that time; by construction $n^{+}_{t} + n^{-}_{t} = 2N$. This state of opinion can be represented by the difference:

$2n_{t} = n^{+}_{t} - n^{-}_{t}$

(1)

where $n_t \in [-N, N ]$. When $n_{t} = N$, all bankers choose to lend, and when $n_{t} = -N$ all choose not to. The lending-opinion index, or the average lending sentiment, at time $t$ can be written as the normalized difference of opinion:

$x_{t}: = \frac{n_{t}}{N} = \frac{ n^{+}_{t} - n^{-}_{t} }{2N}.$

(2)

which, as noted by Ghonghadze and Lux (2016), is precisely how empirical diffusion indices are calculated.

One also assumes there to be a lending-configuration dependent individual lender transition probability per unit time representing the change from being willing to lend to being unwilling to lend which we write as $p_{+-}(n)$; and similarly for the transition from being unwilling to lend to being willing to lend $p_{-+}(n)$. Finally, if one considers the simplest case where the lending configuration changes by the change of lending opinion of only a single lender per unit time, the equation of motion for the probability that the lending community is in configuration $n$ at time $t$, $p(n; t)$, is given by the master equation

$\begin{align} \frac{\partial p(n;t)}{\partial t} & = \big [ w_{\downarrow} (n+1) p(n+1;t) - w_{\downarrow} (n) p(n;t) \big ] \nonumber \\ & + \big [ w_{\uparrow} (n-1)p(n-1;t) - w_{\uparrow} (n)p(n;t) \big ] \end{align}$

(3)

where $w_{\uparrow}(n) = (N -n)p_{+-} (n)$ and $w_{\downarrow}(n) = (N + n)p_{-+}(n)$. The terms in the first set of brackets on the right-hand side of Eq. (3) indicate the change to $p(n; t)$ resulting from a single lender moving from the position of being willing to lend to being unwilling to lend $w_{\downarrow}(n)$: the first term in this bracket describes the increase in configuration probability due to transitions from the configuration with one more net lender while the second term describes the decrease in configuration probability from transitions to the configuration with one less net lender. Similarly, terms in the second set of brackets on the right-hand side of Eq. (3) indicate the change to $p(n; t)$ that result from a single lender moving from the position of being unwilling to lend to being willing to lend $w_{\uparrow}(n)$: the first term in this bracket describes the increase in configuration probability due to transitions from that with one less net lender while the second term describes the decrease in configuration probability from transitions to that with one more net lender.

This master equation description of probability dynamics is, for our purposes, more conveniently handled using the related FokkerPlanck equation

$\frac{\partial P(x;t)}{\partial t} =- \frac{\partial}{\partial x} \big [ K(x)P(x;t) \big ] + \frac{1}{2N} \frac{\partial^2}{\partial x^2} \big [ Q(x)P(x;t) \big ]$

(4)

which describes the evolution of the probability of the lending sentiment $P (x; t) = Np(Nx; t)$, and where $K (x) = \left (w_{\uparrow}(n) -w_{\downarrow}(n) \right) /N$ is the drift coefficient and $Q (x) = \left (w_{\uparrow}(n) + w_{\downarrow}(n) \right) /N$ is the diffusion coefficient.^‡

^‡The term $K(x)$ represents a force that acts on opinion formation which, given the dependence on $\alpha_1$ through Eqs. (5) – (7) links this force to the opinion of others, has a social component. This force implies the existence of a potential $V(x)$ where $K(x) = -\partial_x V(x)$ which likewise has a social component (Helbing, 2010). The social component of the force represents psychic tension which a banker will seek to eliminate by behavior that moves them to a minimum of the social field $V(x)$. At the minimum psychic tension vanishes; eliminated in this case by conforming to lending opinion of others.

One can link this model to the view of bank decision making advanced by Keynes (1931) and (Minsky, 1977, 2008) by summarizing that view as follows: (ⅰ) banks make their decisions in part by relying on their own independent observations and analysis, but (ⅱ) bankers are willing to adapt to the peers opinion once it becomes the majority, and that (ⅲ) bankers' preference and their willingness to adapt may vary over time. This summary can be incorporated into the opinion-formation model by writing the transition probabilities as^§

^§See Weidlich and Haag (1983), Lux(1997, 2009a, b) and Ghonghadze and Lux (2016).

$w_{\uparrow}(x) = \frac{n^{-}}{2N}\nu \exp(U(\cdot)) = (1-x)\nu\exp(U(\cdot))$

(5)

$w_{\downarrow}(x) = \frac{n^{+}}{2N}\nu \exp(-U(\cdot)) =(1+x)\nu\exp(-U(\cdot))$

(6)

and

$U(x_{t}, Z_{t};\theta) = \alpha_{0} +\alpha_{1}x_{t} + \sum\limits_{i=2}^{M}\beta_{i}Z_{i} \label{U}$

(7)

where $n^{+}/2N$ and $n^{-}/2N$ measure the attitude towards lending, $\nu$ is the speed with which lending opinion changes, $\alpha_{0}$ measures the individual component of lending decisions, $\alpha_{1}$ measures the influence on lending decision of other lenders, the $Z_i$ are relevant economic data such as GDP and unemployment that affect lending decisions and which bear on the lending decision with weight $\beta_i, i=1, \ldots, M$, and $\theta = \left \{ \nu, {\boldsymbol \alpha}, \boldsymbol \beta \right \}$ denotes the collection of coefficients to be estimated.

Our simulation implementation follows that of Ghonghadze and Lux (2016) by writing the drift and diffusion terms as

$K(x_{t}, Z_{t};\theta) = 2 \nu \cosh(U(x_{t}, Z_{t};\theta))(\tanh(U(x_{t}, Z_{t};\theta))-x_{t})$

(8)

and

$Q(x_{t}, Z_{t};\theta) = 2 \nu \cosh(U(x_{t}, Z_{t};\theta))(1-x_{t}\tanh(U(x_{t}, Z_{t};\theta)))/N$

(9)

and numerically evaluating the stochastic differential equation

$dx_{t} = K(x_{t}, Z_{t};\theta)dt + \sqrt{Q(x_{t}, Z_{t};\theta)}dW_{t}$

(10)

associated with our Fokker-Planck equation where $W_{t}$ is the standard Wiener process.

Empirical application with this model requires estimating the parameters $\theta$. Ghonghadze and Lux (2012) solved Eq. (4) using the Crank-Nicolson method together with the log Maximum Likelihood on the solution $P(x; t)$ to estimate $\theta$. This method, while rigorous, is computationally expensive. Ghonghadze and Lux (2016) later introduced the use of the more efficient Quasi Maximum Likelihood Estimate (QLME) method where $P$ is approximated as a conditional normal distribution and:

$E(x_{t+1}| x_{t}) = x_{t} + K(x_{t}, Z_{t};\theta)\Delta t$

(11)

$Var(x_{t+1}| x_{t}) = Q(x_{t}, Z_{t};\theta)\Delta t.$

(12)

Given $T$ observations $\{ x_{1}, \cdots, x_{T} \}$, $\theta$ is estimated by maximizing the log-likelihood function

$L = \sum\limits_{t=1}^{T-1} \ln(N(x_{t+1}|x_{t}, Z_{t};\theta)),$

(13)

where $N(x_{t+1}|x_{t}, Z_{t}; \theta)$ is normal density with mean $E(x_{t+1}| x_{t})$ and variance $Var(x_{t+1}| x_{t})$. We solve $L$ numerically using the Newton Conjugate Gradient method in Scipy's Generic likelihood model.

In applications of this model one often encounters references to different versions of the model based on the number of terms on the right-hand side of Eq. (7) that are retained; calibration with all $Z_i=0$ being a "model" and those with differing numbers of $Z_i$ being referred to as other "models" (see, for example, Ghonghadze and Lux (2016) and references therein). Operationally our references in this manner later in this paper are to the opinion-formation model, Eqs. (8)–(13), with similarly different expressions of Eq. (7).

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3. Credit Dynamics

Our datasets of interest are central bank lending surveys. The Federal Reserve (Fed), the European Central Bank (ECB), and the Bank of Japan (BOJ) all publish quarterly surveys of their bank's lending practices.^¶ The Fed survey is the oldest, dating back to 1990. Japan followed suit a decade later and the European survey launched in 2003 with details on each country within the Union. All surveys ask banks whether they change credit standards and spreads for firms and households, and why they change their lending policies.

^¶The Bank of England also began publishing a survey after the beginning of the Great Recession. Unfortunately, their survey data is weighted by the level of importance, and is therefore incompatible with our model assumption. Since the raw data is not yet available the application of our approach to British banking sentiment cannot proceed at this time.

We begin our study with an examination of the Fed survey. Working with the Fed data allows us to validate our approach against the earlier work of Ghonghadze and Lux (2016) and to provide context for our introduction of a machine-learning technique (random forests) into the variable selection process. We then extend this analysis to the surveys of the ECB and the BOJ.

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3.1. Credit Dynamics in the United States

The Fed's Senior Loan Officer Opinion Survey on Bank Lending Practices (SLOOS) is conducted at the beginning of each calendar quarter, covering up to 60 large domestic commercial banks and up to 24 large foreign banks. All have asset greater than ＄3 billion or at most 5% of commercial and industrial loans to total assets. We focus on question 2(d) of the survey which concerns the credit spread on commercial and industrial loans for middle and large firms:

2. For applications for C & I loans or credit lines – other than those to be used to finance mergers and acquisitions – from large and middle-market firms and from small firms that your bank currently is willing to approve, how have the terms of those loans changed over the past three months? (emphasis added) (d) Spread of loan rates over your bank's cost of funds (wider spreads = tightened, narrower spread = eased)

Five options are available: tightened considerably, tightened somewhat, remained basically unchanged, eased somewhat, and eased considerably. On average around 70 banks answer this question. From the responses to this question a diffusion index (DI) can be constructed as the the net percent of banks that eased less those that tightened, and the results of such a construction are shown in Fig. 1.^‖ The dynamic range and speed of change of the DICS in the U.S. is striking and reveals, interestingly, that banks collectively tighten credit well before the last two recessions and that they loosen credit quickly once a recession has ended.

^‖In the Fed's report, this diffusion index is the net percentage of banks that tightened less those that eased.

The survey gives a series of factors for banks to choose if they changed lending policies in the past quarter. The following six factors have been consistently reported since 1999:

If your bank has tightened or eased its credit standards or its terms for C & I loans or credit lines over the past three months, how important have been the following possible reasons for the change? (Please respond to either A, B, or both as appropriate and rate each possible reason using the following scale: 1 = not important, 2 = somewhat important, 3 = very important)

(a) Deterioration (improvement) in current or expected capital position.

(b) Less (more) favorable or more (less) uncertain economic outlook.

(c) Worsening (improvement) of industry-specific problems.^**

^**The surveys before 2001 Q3 split this reason into 2 parts: competition from nonbank lenders and other banks. We take the average of their value.

(d) Less (more) aggressive competition from others.

(e) Reduced (increased) risk tolerance for risk.

(f) Decreased (increased) liquidity in the secondary market for these loans.

The data associated with these questions are only available in the pdf version of the Fed reports. Thus to calculate an associated sentiment concerning lending we extracted the data from the reports for the period 1999–2017 and recalculated the mean for each reason.^†† The means of these reasons – potential drivers of lending sentiment and the DICS from Fig. 1 – are shown together in Fig. 2. Beginning with the top-left panel we see that negative values about uncertainty correlates well with the DICS; positive values less so. The opposite is seen concerning competition in the upper-right panel where a positive view shows the greatest dynamic range. A bank's capital position is remarkably uncorrelated with the DICS as shown in the left-hand middle panel, although negative industry-specific issues correlate strongly with the the DICS. The panels in the bottom row of Fig 2 show that negative risk tolerance and liquidity have greater correlation with DICS than do their positive counterparts.

^††Responses were weighted by the scale of importance (0, 1, 2) as well as their fraction of the total number of banks responding. The reasons contributing to tighten lending policies are set to be negative. If a reason has value 0, it means either (ⅰ) no bank eased or tightened lending or (ⅱ) all banks think the reason is not important. If 2 (-2), all banks consider it is very important; 1 (-1) means banks think it is somewhat important. Values in between mean some banks eased and/or tightened lending and have mixed opinions.

There is also an interesting asymmetry in the two largest potential drivers of the DICS change. When banks tighten lending uncertainty is the main driving force, but uncersainty has almost no effect in easing credit. By contrast, competition is the main driving force when banks ease lending. Such repeated asymmetric response during business cycles provide an empirical support for the assumptions of the opinion-formation model. Banks formulate their economic outlook, but they are also impacted by their peers' decisions. When they are not sure about their customers' creditworthiness they tighten lending. But once their peers "control the Street" (competition increases) the state of the economy – and, by implication, the customer – becomes less important in driving credit expansion and lending decisions. Curiously, lending decisions found to be much less dependent on capital positions and loan liquidity. Finally we note that lending decision are less dependent on capital position and loan liquidity. The former is consistent with the post-Kenyesian interpretation of endogenous money and the fact that at least some problems with capital structure can be remedied through short-term borrowing from the central bank of other commercial banks. The latter suggests a lack of existential dependence for most banks on loan trading.

The high rate of change – both positive and negative – of the DICS and associated drivers (e.g., uncertainty and competition) during the 2008 Great Recession suggest that opinion changed in a manner known as a phase transition; a phenomena that can be simulated using the opinion-formation model (Weidlich and Haag, 1983). This has important implications for systemic risk management since the onset of a phase transition is less about the event that caused it (which has historically been the focus of risk management) and more about the state of the system (economy) at the point when the phase transition occurs.

Next we turn to the opinion-formation model and some of the specifications examined by Ghonghadze and Lux (2016). When there are no exogenous effects $Z_i$ and banks only look to their peers for guidance on lending the dynamics driver $U$ can be written

$U(x_{t}, Z_{t}; \theta) = \alpha_{0} +\alpha_{1}x_{t}$

(14)

where $\theta = \left \{ \nu, \alpha_{0}, \alpha_{1} \right \}$ or

$U(x_{t}, Z_{t}; \theta) = \alpha_{0} +\alpha_{1} x_{t}^{+} + \alpha_{2} x_{t}^{-}$

(15)

where

$\begin{align} \theta = \left \{ \nu, \alpha_{0}, \alpha_1, \alpha_2 \right \} \;, \quad x_{t}^{+} & = \begin{cases} x_{t}& \text{$x_{t}>0$ } \\ 0 & \text{$x_{t}\leq0$} \end{cases} \;, \quad \text{and} \quad x_{t}^{-} = \begin{cases} x_{t}& \text{ $x_{t} \leq 0$} \\ 0 & \text{$x_{t}>0$} \end{cases} \end{align}$

(16)

Ghonghadze and Lux (2016) refer to the specification given by Eq. (14) as "Model 1" and that given by Eq. (15) as "Model 2" and we shall do so as well. Model 1 assumes that contemporaneous lending opinion is the sole driver and that positive and negative values of lending sentiment have the same weight. Model 2 relaxes the assumption of identical weight by allowing for a difference in how positive and negative values of lending sentiment impact the lending decision.

To ensure that our approach was consistent with that of Ghonghadze and Lux (2016) we estimated these specifications, the results of which are shown in Table 1. Model 1 indicates the current lending opinion, $\alpha_1$, has significant impact and the opinion turn-over rate, $\nu$, suggests banks change their credit opinions quickly. Model 2 yields coefficients for positive ($\alpha_1$) and negative ($\alpha_1$) lending opinion that are slightly different, but they overlap within two-standard-deviation region. Comparing Models 1 and 2 on an information basis one would prefer Model 2 slightly as the Akaike Information Criterion (AIC) and Bayesian Information Criterion(BIC) for this model are somewhat better than those of Model 1.

A simulation of the DICS using Model 2 is shown in Fig. 3. The predicted values follow the actual data well. In this simulation the simulation the credit spread variables ($x_{t+}, x_{t-}$) in Eq. (15) are updated using the survey data rather than the simulated values. This level of agreement between the simulated and observed DICS suggests that the current opinion index of credit spread has strong predictive power concerning the credit dynamics for the next quarter.

Examining the stability of the Model 2 coefficients yielded two interesting results. First, the coefficients are stable over time, meaning banks are constantly looking at each other, and splitting the diffusion index may not be able to capture banks' asymmetric reaction to their peers. Second, the model estimation becomes stable after 60 data points. The model is also time independent once it is conditioned on the current quarter because the coefficients vary little after the data is randomly shuffled. These results and the conjuncture that only the current opinions have a much stronger impact on lending decisions suggest that most existing machine-learning algorithms are worth considering in the analysis of this diffusion index.

While the simulation results based on the current value(s) of the DICS are promising, the assumption that a banker would solely focus on current data is rather strong. This assumption was relaxed by Ghonghadze and Lux (2016) in their Model 3 where Eq. (15) is extended to include the past quarter's credit spread:

$U(x_{t}, Z_{t};\theta) = \alpha_{0} +\alpha_{1}x_{t}^{+} + \alpha_{2}x_{t}^{-} + \alpha_{3}x_{t-1}^{+} + \alpha_{4}x_{t-1}^{-} ,$

(17)

where

$\begin{align} \theta = \{ \alpha_{0}, \alpha_{1}, \alpha_{2} \} \;, \qquad x_s^{+} & = \begin{cases} x_s & x_s >0 \\ 0 & x_s \leq 0 \end{cases} \qquad x_S^{-} = \begin{cases} x_s & x_s \leq 0 \\ 0 & x_s>0 \end{cases} \end{align}$

(18)

The estimated coefficients for this model are shown in Table 2 where we see that the sum of coefficients for both positive and negative credit spread are close to those of Eq. (15). This suggests that banks' decision strongly rely on the lending opinion of the current period. Statistically, however there are issues with Model 3 that might recommend against it. Specifically, it is worse in terms of BIC and the coefficients of current and past DICS coefficients have conflicting signs; an indication of over-fitting.

Our examination of Models 1-3 finds that the results of Ghonghadze and Lux (2016) can be reproduced with a different – albeit related – method for solving Eq. (10) and validates our implementation of their model. On a shared dataset our parameters agreed to at least 4 decimal points and our variances had at most a 7% difference; excellent agreement given our different methodologies.

Next we include exogenous variables. Candidate variables selected using the SLOOS reasons for changing lending policy, the work of (Ghonghadze and Lux, 2016), and empirical research on the ECB lending surveys (Köhler-Ulbrich et al., 2016; Altavilla et al., 2015) are shown in Table 3. The diffusion index of loan demand (DILD) was built from question 4A of the SLOOS which asks how the C & I loan demand from large and middle market size firms changed over the past quarter. Excessive Bond Premium (EBP) measures the investors' risk appetite in the corporate bond market, has been shown to be a statistically significant leading indicator for recessions and statistically significant for credit supply.^‡‡ In this paper we use the EBP to measure the aggregate risk preference. The NASDAQ is the well-known stock index and the VIX is the volatility index known also as the "fear index". The non-performing loan (NPL) rate measures the performance of bank loans. Loan defaults take time to be observed, so 3 year and 5 year average cumulative default rate are key indicators for S & P credit ratings (Hawkins, 2011). In addition, Bouwman and Malmendier (2015) find that a history of under-capitalization impacts a bank's risk preference, and in this analysis 1-6 years are statistically significant. Real GDP (RGDP) is lagged two quarters because of its release data (e.g., first quarter's GDP is only available by the end of second quarter). The mean responses from the Survey of Professional Forecasters (SPF) were used to approximate a banks' estimate for the future quarter.

^‡‡See Favara et al. (2016) & Gilchrist and Zakraj (2012), Favara et al. (2016), and Altavilla et al. (2015), respectively. This data is available on the FRED notes page. It assumes that the spread contains information on the expected default risk and independent risk preference. It is constructed by a simple unweighted average of credit spreads in corporate bonds from which one then subtracts each bonds' expected default risk implied in the spread through linear regression.

The survey also asks whether banks changed their credit spread in the past quarter, so we collected data with attention to the release data. We assume banks make decisions at the middle of each quarter and are able to access public data released near that time. They do not, however, have access to the data released near the end of the current quarter. Because banks have an asymmetric response to economic data as shown in Fig. 2, exogenous variables are de-meaned by their one-year exponential moving average (EMA), with positive and negative values considered separately.

To select relevant variables from this list we used the Boruta method; an algorithm that wraps the Random Forest classification algorithm (Breiman, 2001) and "iteratively removes the features which are proved by a statistical test to be less relevant than random probes" (Kursa and Rudnicki, 2010). The random-forest approach is an ensemble method that aggregates multiple decision trees. For a classification problem, a decision tree tries to split the data into groups based on input variables (or 'features'). For a regression problem, it takes the average of all points within a group.

Random forests combine independent decision trees and randomly choose the initial variable, decision boundaries, and variables used in each node when building trees. It makes decisions by the majority vote from the end nodes of each tree. Breiman (2001) demonstrated that the results generated with this method are unbiased and have low variance. In addition, the result always converges and its accuracy is usually immune from irrelevant variables. The robustness of the random forest approach was shown by Caruana and Niculescu-Mizil (2006) who compared multiple supervised-learning algorithms including support vector machines, neural nets, random forests, and logistic regression. While each method had an edge in one or two large datasets, random forests and neural nets were found to have the best overall performance across 11 large datasets. Kane et al. (2014) used the random forest method to predict outbreaks of H5N1 and found that it out-performed ARIMA. Khaidem et al. (2016) used random forests to predict trends in stock market and obtain 85% to 95% accuracy for one-month to three-month predictions.

An example of decision tree built using part of the dataset from Table 3 with one node and depth of two is shown in Fig. 4. Positive values in diffusion index of credit spread are labeled as 1 (to lend) and negative values are labeled as 0 (not to lend). The decision tree starts with the change of the non-performing loan rate as an initial split; the unemployment rate is then used to further partition the result.

The result of our random-forest variable selection is shown in Table 4. In this selection process we repeat the Boruta method 20 times with random sampling and count the number of times each variable is selected either as important or weak. The variables with "positive" or "negative" modifiers are those with values above or below their EMAs and provide different signals. Credit spread (DICS), loan demand (DILD), non-performing loans below mean (NPL negative), and excessive bond premium (EBP) are constantly selected as important. Unemployment rate below mean (Unemp negative) also ranks highly. Surprisingly, real GDP growth is not important; possibly because of its lags. We used the variables in the left column to calibrate the opinion-formation model because they have much higher importance scores.

The model coefficients of this calibration of Eq.(7) are shown in the upper portion of Table 5. The diffusion index of credit spread (DICS) has a very significant effect. The excessive bond premium (EBP) and unemployment above its one year EMA also has a significant impact on lending decisions.

Our simulation of the opinion-formation model with the variables suggested by the random forest procedure is shown in Fig. 5. The first 5 observations are omitted because the DI loan demand is unavailable during that time. The simulation shares the same initial value with the actual data, but subsequent values in the dynamics driver $U$ are updated with calculated values. It captures the general trend of lending over the last two decades, but it fails at two significant moments near 1998 and 2007 for reasons that might lie in a spike in uncertainty seen in Fig. 2.

The first moment was the drop of the DI credit spread in Q3 1998 from 0.143 to -0.473. This is when Russia had its financial crisis, or "Russian Flu" (Kindleberger and O'Keefe, 2011). At this time Long-Term Capital Management (LTCM) was long Russian bonds and had business ties with many major banks; it went under as the Russian market crashed and banks waited for the Fed to clear market stress. Two quarters later the credit spread rebounded to -0.071. During this period, loan demand increased and unemployment rate continued to be lower its EMA and non-performing loan rates increased above its average, suggesting the Russian Flu was responsible for this drop in the DICS.

The second moment was the significant drop in the DICS in Q3 of 2007 from 0.321 to -0.346. This was a quarter after the bank run on Countrywide Financial; Northern Rock also had bank run on September 14th 2007 (Kindleberger and O'Keefe, 2011). It appears that banks might feel financial storms well before they are headlines.

To appreciate the effect of variable reduction provided by the random forest procedure, we compare the model with all variables. The results of the model estimation are shown in the lower portion of Table 5. The coefficients seem to have expected signs with the exception of corporate profit and the DICS and EBP remain significantly above zero. However, this model appears to be over-fit and has become sensitive noise; a situation made clear when we perform cross validation of simulations that compare the random-forest reduced variable set with the complete variable set shown in Fig. 6. In this analysis the forward 'prediction' used the first 70 points to estimate the model and then 'predicted' the actual diffusion index by with actual data (except the DI credit spread) for the exogenous variables. For the backward propagation, we use the last 70 points to build the model and then predicted the data (except the DI credit spread) 'backward'. The exact date of the switch was chosen to be near the financial crisis.

The reduced-variable model has relatively stable results for the forward 'prediction' shown in the upper left-hand panel of Fig. 6 as the economy moves out of recession, and while the backward propagation shown in the upper left-right panel of Fig. 6 is less accurate it still loosely follows the actual path. The unexpected 'Russian Flu' may have large impact here. When all variables are included the simulation becomes unstable. The forward prediction shown in the lower left-hand panel of Fig. 6 fits the data before 2008 well, but explodes near 2009. The backward propagation lower right-hand panel of Fig. 6 fits the data well to 2004, but the propagation to earlier times loses almost all predictive power.

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3.2. Credit Dynamics in the Euro Area

The European Central Bank quarterly bank lending survey was launched in 2003 with around 90 banks in all European areas and expanded in coverage to around 140 banks in 2016. Most are large banks, but specialized small banks are also included. The sample size for each country depends on its share of loan to private non-financial sector. The survey results are aggregated at the country level and compiled to Euro Area with weights on each country's loan share (Köhler-Ulbrich et al., 2016). The survey questions are similar to those of the U.S. SLOOS, covering lending to firms and households and factors changing lending policies. They are available in the ECB's Statistical Data Warehouse. We focus on the credit spread for average loans to firms:

3. Over the past three months, how have your bank's terms and conditions for new loans or credit lines to enterprises changed? Please rate the overall terms and conditions for this loan category and each factor using the following scale: 1. tightened considerably, 2. tightened somewhat, 3. remained basically unchanged, 4. eased somewhat, 5. eased considerably

(c) Your banks' loan margin (i.e. the spread over a relevant market reference rate) on average loans (wider spread = tightened, narrower spread = eased)

We chose the data series on average loans to all firms because it is the longest. Its diffusion index (DICS), constructed by the net percent of banks that eased minus banks that tightened credit spread weighted by each country's share of outstanding loans, is shown in Fig. 7; the grey bars being Euro Area recessions indicated by OECD Composite Leading Indicators. The Euro Area diffusion index behaves similarly to that of the U.S.: banks tighten lending immediately before recessions and ease credit quickly once the economy moves out of recession. An example of this is seen in the period from 2003 to 2007 when most European banks switched from tightening to easing, and in 2008 when the DICS spread dropped significantly.

The ECB survey also asks banks to rank factors that affect lending polices:

4. Over the past three months, how have the following factors affected your bank's credit terms and conditions as applied to new loans or credit lines to enterprises (as defined in the notes to question 3)? Please rate the contribution of the following factors to the tightening or easing of credit terms and conditions using the following scale: 1. contributed to tighten considerably, 2. contributed to tighten somewhat, 3. contributed basically unchanged, 4. contributed to eased somewhat, 5. contributed to eased

(a) Cost related to your bank's capital position

(b) Your bank's ability to access market financing

(c) Your bank's liquidity position

(d) Competition from other banks

(e) Competition from non-banks

(f) Competition from market financing

(g) General economic situation and outlook

(h) Industry or firm-specific outlook/borrowers' creditworthiness

(i) Risk related to the collateral demanded

These potential drivers of lending sentiment in the Euro Area are shown together with the DICS in Fig. 8. We see the same asymmetric effect on lending decisions as seen in US. When banks ease credit, competition – especially from other banks – is the main force as seen in the upper-left panel of Fig. 8. This explains the sharp increase in the DICS near 2005. The other reported factors shown in Fig. 8 have almost no impact on the upside. When banks tighten lending the general economic outlook tracks the DICS well as shown in the upper-right panel. Industrial problems and borrowers' creditworthiness seen in the lower panels of this Figure are also important in tightening credit but have almost no impact in easing. Surprisingly, the liquidity and capital positions, which are generally regarded as important in lending decisions, have far less importance as indicated in the middle panels of Fig. 8.

We applied the opinion-formation model to the Euro Area's diffusion index of credit spread, beginning with Models 1 and 2 from the U.S. analysis to examine potential asymmetry in the peer effect. The results shown in Table 6 are quite similar to those of the U.S., but from an information perspective (AIC and BIC) Model 1 outperforms Model 2, suggesting that separating this diffusion index by sign may not be an optimal choice. The simulation of Model 2 is shown in Fig. 9 where the DI credit spread in the dynamics driver $U$ is updated by actual data. The simulation misses the beginning of the Great Recession in 2007-8, but otherwise tracks the actual data well.

The candidate variables for the expanded opinion-formation model of the Euro Area shown in Table 7 were selected based on our experience with the U.S. data. In the Euro Area, the VIX, 'fear index', is replaced by the EURO STOXX 50 obtained from the Factset database. Forecast data for GDP, unemployment rate, and inflation rate was sourced from the ECB's SPF website. Corporate profit in the U.S. had little impact on lending decisions so it was excluded from the Euro data. The non-performing loan rate for the Euro Area is available, but it starts in Q2 2015 and is therefore not considered here. Excessive bond premium for the Euro Area is absent because bank level information is not publicly available.

The variable importance obtained from the Boruta method is shown in Table 8. In the absence of excessive bond premium and non-performing loan rates, the unemployment rate becomes an important variable. Real GDP, with two-period lags (because of the release date) and the forecast are less important. As before we chose variables in the left column because of their relevance.

The model estimation for selected variables in the upper portion of Table 9 gives consistent results and the variables have the expected signs. However, the unemployment rate may have less explanatory power because of the wide range of unemployment rates across Europe.

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3.3. Credit Dynamics in Japan

As we did for the U.S. data, we also compare the full variable estimation as a stability check. The full data estimation is shown in the lower portion of Table 9, and we also compare the forward prediction and backward propagation shown in Fig. 11. For the forward prediction shown in the left-hand panels of Fig. 11 we use the data before Q3 2013 to estimate the parameters and then update real data (except DI credit spread) to compute the prediction. For the backward propagation shown in the right-hand panels of Fig. 11 we use the data after Q3 2006 to build the model and use that date as the initial position. Then we backward update the data to compute the prediction. The forward prediction is relatively stable but the back propagation is very unstable. A potential explanation is the data length: the U.S. requires around 60 points to obtain stable parameters, but in these two simulations we only used 40 points for parameter estimation. The Euro Area data may be too short at this time to give a stable estimation for the extended model.

The structure and questions of the Bank of Japan (BOJ) lending survey are very similar to that of the United States. Credit spread data, however, is not available so we extracted the needed data from BOJ reports and calculated the DICS by taking the net percent difference of banks that eased less those that tightened. The resulting DICS for high-rating firms is shown in Fig. 12; the gray bars are OECD based recession period for Japan. The DICS of Japan differs significantly from those of the U.S. and the Euro Area in terms of its dynamic range. The DICS of Japan has a materially smaller dynamic range; particularly on the downside where its magnitude is less than 20% of those in the U.S. and the Euro Area.

The reasons for changing lending policy were extracted from Japanese-language survey reports. The BOJ only ask reasons for changing credit standards, but its credit standard DI has a very similar shape to the credit spread diffusion index so we use these data to approximate reasons for changing the credit spread.

If your bank has eased its credit standards for loans to firms over the past three months (as described in question 7), what were the important factors that led to the change? (Please rate each possible reason using the following scale: 3 = important, 2 = somewhat important, 1 = not important.

(a) An improvement (deterioration) in your bank's asset portfolio.

(b) A more (less) favorable or less (more) uncertain economic outlook.

(c) An improvement (worsening) in industry or firm specific problems.

(d) Competition from other banks.

(e) Competition from non-banks.

(f) Competition from capital markets.

(g) Risk tolerance.

These potential drivers of lending sentiment in Japan are shown together with the DICS in Fig. 13. The results are similar to those in the U.S. and the Euro Area. Competition from other banks has the strongest correlation with banks easing credit. Competition does not, however, appear to be a driver of credit tightening. For example, during the 2008 recession when most banks tightened credit the competition terms – whether from other banks, non-banks, or the capital markets – simply went to zero, not negative. Uncertainty has the second highest correlation with the DICS when credit is being eased. Lack of it drives lending during the boom from 2004 to 2007. During the financial crisis associated with the Great Recession in 2008 negative uncertainty also had a very strong effect. The asset portfolio of banks also had a negative impact during the Great Recession as loan repayment became less certain. The state of industry problems drives easing of credit but seems to have little impact on the downside. This may be due to a bank looking to others to ease while having ample evidence in the own non-performing loan book when times get tough to justify tightening.

Applying the opinion-formation model to Japan's DICS reveals that peer effects have a much less impact than in the U.S. and the Euro Area. In particular, as shown in Table 10, the coefficient for the DICS is negative; opposite that of the U.S. and Euro Area. The corresponding simulation shown in Fig. 14 does not track the observed DICS well. The simulation begins two-years later because business ad employment forecasts began in 2004.

Economic variables – selected based upon our experience with the U.S. and Euro Area – are shown in Table 11. The TANKAN, a short-term economic survey of enterprises beginning Q2 2004, was used as a proxy for banks' expectations. Part of the survey asks banks for their opinions on the future business and employment conditions. Their diffusion index (favorable minus unfavorable) is listed in the BOJ database. The VIX equivalent for Japan is the VXJ which follows the CBOE method for calculating the VIX. Non performing and bankruptcy loans are from Japan Financial Service Agency (FSA) which monitors bad loans among banks. It classifies three types of bad loans : (ⅰ) "bankrupt or de facto bankrupt" includes loans from borrowers who are legally bankrupt; (ⅱ) "doubtful loans" are from borrowers who are known in financial difficulties and are not expected to pay back principles and interest on time; (ⅲ)"special attention" loans are past due by more than 90 days (Kawashima and Nakabayashi, 2014). The data are reported by banks' self-assessment, but the FSA also publishes its inspection on major banks' bad loans. We group the non-performing loans by type (ⅱ) and (ⅲ) and choose bankruptcy by type (ⅰ) from major banks. The dataset is annual before 2004 and semi-annual after 2004, so we impute their missing quarterly data by cubic spline.

Our analysis of these variables using the Boruta method is shown in Table 12. Bankruptcy loans, both positive and negative, rank high in importance. Non-performing loans below their 1-year EMA (negative) also rank highly but the positive side does not, which raises the interesting question: are banks confident that their large-firm borrower will pay back loans even though they are in arrears? Banks' consensus on next quarter business matters, but their estimation on employment doesn't. Real GDP and unemployment are also not classified as important. We use variables on the left column of Table 12 because of their high importance scores.

The model estimation for these selected variables is given in the upper portion of Table 13 and shows that the coefficient for real GDP and for the VJX are both significant and have the expected sign. The inclusion of these extra variables, however, did not resolve the issue of the unexpected negative sign of the DICS.

The simulation using the variables selected by the random forest and Boruta method shown in Fig. 15 shows remarkable improvement over the simpler model shown in Fig. 14 and now tracks the observed DICS with the fidelity seen in the U.S. and the Euro Area. Extending the opinion-formation model for Japan to all variables as shown in the lower portion of Table 13 and we compare the predictive power of the multi-variable versions of the opinion-formation model for Japan in Fig. 16. For forward prediction shown in the left-hand column of panels, we use data before Q2 2014 to estimate model and update the real data (except DI credit spread). For the backward propagation show in the right-hand column of panels, of Fig. 16 we use Q4 2006 as the initial value and data afterward to estimate the model, then we backward update the real data (except DI credit spread); DI credit spread being updated by the calculated value. Including more variables via the Boruta method make the prediction better as shown in the upper panels of Fig. 16. Including all variables, however, does not as shown in the lower panels of Fig. 16.

Finally, to emphasize the importance of bad loans in lending decisions, we show the results of the extended opinion-formation model calibrated with and without bad loans in Fig. 17. The upper row of panels show the results for the Boruta-selected variables (left) and all variables (right) when bad loans are included in the calibration as discussed above. The lower row of panels show the same when bad loans are excluded from the calibration. When bad loans are included in the calibration the opinion-formation model performs well; whether using the Boruta-chosen variables or all the variables. When bad loans are not included the performance of the model degrades significantly, with the Great Recession underestimated and the credit-easing cycle of 2004-2007 either underestimated or missed completely.

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4. Discussion and Summary

In this paper we applied the opinion-formation model of Ghonghadze and Lux (2016) for the credit spread diffusion index (DICS) to the Euro Area and Japan and introduced the use of machine-learning techniques for variable selection. We validated our approach by comparing to the results of Ghonghadze and Lux (2016) for the U.S. as an important first step in our analysis. We find the banks react differently to economic factors for changing lending policies. Uncertainty and competition are two main factors that act differentially: the former in bad times and the latter in good times. Capital position and loan liquidity for banks in the U.S. and the Euro Area were found to have importance in the formation of lending decisions while in Japan we find that bad loans – those from firms in bankruptcy and non-performing loans – play a key role. In all regions the state of the stock market is found to be important in lending decisions.

The credit spread diffusion index displays momentum. Banks tighten the spread one or two quarters before economic downturn or unexpected event such as 'Russian Flu', and banks lend more if in the the past quarter they did so until uncertainty dominates the market; at which point liquidity decreases substantially. The success of the opinion-formation model in the DICS simulations supports the long-held notion that banks do consider their peers' lending opinions in addition to their own rational risk calculation when deciding whether to extend credit.

Interestingly, real GDP ranks very low in terms of importance. According to Okun's law, both unemployment and real GDP should have similar explanatory power. From a Post-Keynesian point of view, however, this finding is not unexpected. Loans are underwritten in nominal terms, so the price level matters. The substantial variation in economic situation across the Euro Area suggests that the promising results we found at the aggregate level here may extend to the country level as well.

The formal introduction of social psychology into the assessment of lending-opinion formation provides psychologically sound microfoundations for the understanding of the dynamics of the financial business cycle. This is critically important because suboptimal lending decisions driven largely by the actions of other banks remains remarkable robust as noted by John Mack of Morgan Stanley (Moore, 2009)

"I missed a piece of business. I can live with that, but as soon as I hung up the phone someone else put up 10 times leverage. We cannot control ourselves. You have to step in and control the Street."

to advances in economic risk measurement and management since Keynes' observations of banking social psychology in 1931. The opinion-formation model presented in this paper and in those we have cited shows promise as a framework for a coherent synthesis of psychology and economics as it pertains to the financial business cycle.

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Acknowledgement

We thank Professor Thomas Lux and Dr. Jaba Ghonghadze for helpful discussions concerning this work in general and for sharing a dataset that allowed us to confirm validation of our reproduction of their results in particular. We also thank Noah Golmant for helpful conversations on aspects of the simulation and data handling.

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Conflict of Interest

All authors declare no conflicts of interest in this paper.

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