Norwegian Bank Losses and the Macroeconomy: An Econometric Study.

Norwegian Bank Losses and the

Macroeconomy: An Econometric Study.

Elias Magan

Thesis submitted for the degree of

Master in Economic Theory and Econometrics 30 credits

Department of Economics

Faculty of Social Sciences

UNIVERSITY OF OSLO

Norwegian Bank Losses and the

Macroeconomy: An Econometric Study.

Elias Magan

© 2020 Elias Magan

Norwegian Bank Losses and the Macroeconomy: An Econometric Study.

http://www.duo.uio.no/

Printed: Reprosentralen, University of Oslo

Abstract

Banks have a central role in the financial system as credit intermediaries and payment service providers. History has shown that the banks’ financial position fluctuates with the macroeconomy. Moreover, a development that can destabilize the banking industry is a risk to financial stability in Norway. This thesis aims at understanding how macroeco- nomics variables affect banks’ losses on loans, using time series data of Norwegian banks’

losses and relevant macroeconomic variables over the sample 1990 Q1 – 2018 Q4.

By estimating using an autoregressive distributed lag model, it is found that annual GDP growth, nominal interest rate, unemployment, and household interest rate expense in terms of disposable income had a significant effect on loan loss. The empirical analysis focuses on the robustness of the model. In particular, by transforming unemployment and interest rate expense by a logistic function to test for the implication of loan losses being low until the variables reach a threshold value. The results are compared with those of a transformed loss variable that accounts for the increase of the domestic debt level. It is controlled for large outliers and the implication of excluding unemployment from the regression. Moreover, recursive estimation shows that the coefficients are stable over the sample period. The results are also robust with respect to using instrumental variable estimation instead of OLS.

Preface

This thesis represents the end of my studies at the Department of Economics, University of Oslo. I am grateful for the experiences and knowledge the last five years as a student has given me.

I would like to thank Ragnar Nymoen for his excellent supervision. Insightful suggestions and comments have been invaluable, as well as engaging discussions of economic topics. It has been an honor to learn from such a knowledgeable researcher.

I want to thank my fellow students for the uplifting environment. I am also grateful for the support of my family and friends.

Any errors are solely my responsibility.

Oslo, May 2020 Elias Magan

Contents

1 Introduction 1

2 Background 2

2.1 The role of banks and banking theory . . . 2

2.2 Banking in Norway . . . 3

2.3 Bank losses and financial stability . . . 4

3 Previous studies 7 4 The data set 11 4.1 Loan loss . . . 11

4.2 Explanatory variables . . . 12

5 Methodology 18 5.1 Stationarity and non-stationarity . . . 18

5.1.1 Order of integration . . . 20

5.2 Autoregressive Distributed Lag Models . . . 21

5.3 Diagnostic Tests . . . 22

6 Modeling Results 24 6.1 Stationarity and unit root test . . . 24

6.1.1 Statistical properties of the loss variable . . . 25

6.1.2 ADF test results for all variables . . . 28

6.2 Autoregressive Distributed Lag Model . . . 29

6.3 Robustness of the model . . . 31

6.3.1 Non-linear functional form . . . 31

6.3.2 Are the coefficients robust with respect to outliers? . . . 34

6.3.3 Loss as a percentage of total public debt . . . 36

6.3.4 Robustness of coefficients when excluding unemployment . . . 37

6.3.5 Stability of estimated parameters . . . 38

6.4 Robustness with respect to estimation method . . . 40

7 Conclusion 43

A Appendix A: Data Appendix 49

B Appendix B: Supplements to chapter 6. 51

List of Figures

1 Loan Loss in Mill NOK, Source: Data Appendix . . . 5

2 Loan Loss as percentage of total debt; 1990Q1-2018Q4 . . . 11

3 Loan debt public, non-financial firms and households; 1990Q1-2018Q4 . . . 13

4 Nominal interest rate and interest rate on outstanding loans; 1990Q1-2018Q4 13 5 Real Estate Price index; 1990Q1-2018Q4 . . . 14

6 Gross Domestic Product; 1990Q1-2018Q4 . . . 14

7 Unemployment; 1990Q1-2018Q4 . . . 15

8 Consumer Price Index; 1990Q1-2018Q4 . . . 15

9 Disposable income, billion NOK; 1990Q1-2018Q4 . . . 16

10 Interest expense in million NOK and interest expense as a percentage of disposable income; 1990Q1-2018Q4 . . . 16

11 Recursive least squares graphical constancy statistics 1995Q1-2018q4 . . . 40

B1 Nonlinear funtional form encompassing test model 1 vs. model 2 . . . 51

B2 Nonlinear funtional form encompassing test model 1 vs. model 3 . . . 51

B3 Nonlinear funtional form encompassing test model 2 vs. model 3 . . . 52

List of Tables

1 Some charecteristics of previous studies . . . 9 2 ADF-tests LOSS and ∆LOSS . . . 26 3 ADF-test loss and ∆loss (loss as percentage of total domestic debt) . . . . 27 4 Results from the Augmented Dickey-Fuller test . . . 28 5 Regression results using OLS: Model equation (6.3) 1990q2-2018q4 . . . . 29 6 Regression results using OLS: Nonlinear functional form 1990q2-2018q4 . . 32 7 Encompassing test statistics: 1991(2) - 2018(4) . . . 33 8 Regression results using OLS: Including dummies 1990q2-2018q4 . . . 34 9 Regression results using OLS: loss as percentage of total public debt 1990q2-

2018q4 . . . 36 10 Regression results using OLS: Exluding unemployment 1990q2-2018q4 . . . 38 11 Instability test for model equation (6.5), 1991q2-2018q4 . . . 39 12 Estimated results using 2SLS. 1990q2-2018q4 . . . 42

1 Introduction

Banks are an intrinsic part of the economy. Both households and firms have a relation with a bank, and banks provide a large proportion of loans to both groups. Historical periods of economic upturn and downturn have shown that bank’s financial position fluctuates with the macroeconomy. Conversely, if the banking sector experiences a significant negative shock, this can have an impact on the whole economy (Haare et al., 2015).

There are existing studies on Norwegian data, however not with the same modeling strategy used in this study and for different sample periods. Existing studies also use other definitions of the left-hand side variable in the models. The section of previous studies includes a discussion of the differences and why this study focuses on banks’ losses. Loan loss and related variables reported by banks are affected by financial reporting and by accounting rules and practice, which is not a central part of the study.

The next chapter consists of a background of the Norwegian banking sector and macroeconomic environment for the sample period of the years 1990-2018, followed by a presentation of previous studies. This paper focuses on Norway. However, to motivate the choice of relevant explanatory variables, as well as suitable modeling framework, com- ments on studies from other countries are included.

Chapter 4 is a presentation of the data, data sources, and the properties of the data.

Most of the data is collected from Statistics Norway and is publicly available. The follow- ing chapters present the theoretical methodology used, followed by modeling results and the conclusion. The empirical modeling has been used as implemented in the computer program PcGive 14, and as documented in Doornik and Hendry (2013).

2 Background

2.1 The role of banks and banking theory

Banks have been part of the economy for a long time, and especially in times of relative stability their role may be overlooked. One can even pose an existential question about why banks exist and about what their role is.

The fundamental issue is that a two-way transaction, of a good and means of payment, involves direct reflection of the characteristics of the agents. A financial transaction, like a loan, is valued on the perceived characteristics of the individual issuing the promise. An individual borrows with an obligation to repay. The individuals’ ability to repay depends on several factors, including honesty and willingness, but also many economic factors outside the borrower’s control.

A lender faces various information costs. A search cost related to potential borrowers, obtaining information and negotiating a contract. They face an adverse selection problem due to the asymmetry in information. The lender is unable to observe the characteristics of the borrowers. The lender can, in most cases, not control the behavior of the borrower, which leads to a moral hazard problem (Lewis, 1992).

A bank tries to solve or mitigate these problems for an individual lender, investor, or household. They provide depositors with liquidity insurance.(Diamond and Dybvig, 1983). Households face shocks to their income and consumption over time. When banks issue demand deposits, banks provide risk-sharing among households. This risk-sharing makes for the improvement of the competitive market.

Banks offer monitoring services to investors, which eliminates the duplication of mon- itoring costs (Diamond, 1984). This elimination is perhaps one of the main reasons why banks exist. Firms are assumed to have more information about their investments and the future of their projects than an investor would. The investor could get more information, but only after paying the monitoring cost, which is considerable. The bank takes this

cost, saving the cost for the investor and offers lending to the firm at a lower cost than direct lending would.

The model by Diamond and Rajan (2001) takes into account that both investors and borrowers care about liquidity. Investors and depositors are unsure when they consider to sell their financial assets and to take out their deposits, and borrowers or firms want to be able to raise funding in the future. As a financial intermediary a bank can solve the problem. In contrast to direct lending, depositors’ assets remain liquid, and it offers firms the security that their funding will not prematurely be collected.

2.2 Banking in Norway

Norwegian banks are, in general, classified as either a commercial bank or a savings bank. A commercial bank, in contrast to a savings bank, is founded as a limited liability company. Savings banks are traditionally organized as a self-owned foundation. The savings banks are expected, but not legally obligated, to support the local community with reliably banking services, and to support local activity (Norges Bank, 2019).

There has been a significant decrease in the number of savings banks in Norway. From around 600 in 1960 to under 100 today (Sparebankforeningen, 2019).

Alliances within the savings bank industry formed in the 1990s. As one of the largest groups, SpareBank 1-Group, was established in 1996. The Eika-Group was established in 1997. The main goal of these alliances was to offer some standard products, while the banking services were carried out in the individual banks themselves.

The entry of foreign banks to the Norwegian market in 1985 resulted in several mergers and acquisitions. The market share of Norwegian commercial banks fell significantly. By the end of 2018, there were 21 Norwegian commercial banks.

The largest bank in Norway today is DNB. The cooperation was formed by several merg- ers, including Bergen Bank, Den Norske Creditbank, which formed DNB. Later, a merger between DNB and Postbanken, then Gjensidige Nor (Norges Bank, 2019).

Deposits in Norwegian banks are guaranteed for up to NOK 2 million per depositor per member bank, where there are 130 member banks as of August 2019. In the case where a bank is no longer able to provide depositors with their assets, the Norwegian Banks Guarantee Fund reimburses the guaranteed deposits (The Norwegian Banks Guarantee Fund, 2020).

2.3 Bank losses and financial stability

A financial system with fluctuations, but without crisis, can be characterized as having financial stability. Periods before a downturn has often been characterized by rising prices in investment objects and real estate, lending growth to both households and firms have also been high. This growth might make firms and households vulnerable to financial stress.

As discussed above, banks transform short term deposits to long term loans, offering liquidity insurance. Banks are closely interlinked, meaning that a problem in one bank may spread to others. Financial distress spreads through payment and settlement systems.

Insolvency of a bank has, in general, large implications because it may affect other banks as well. Resulting in a negative effect for firms, households, and financial markets. Because of risk, banks are in general regulated more than other firms (Gjedrums, 1999).

When lending money to a borrower, the bank calculates a borrower’s ability to repay the loan, as well as the impact of increased interest rates. A borrower would, in general, not borrow money if they expect not to be able to pay it back. This makes bank losses challenging to predict.

High household debt relative to income leaves a low net disposable income, making them more sensitive to shocks. High relative debt in isolation decreases the household’s flexibil- ity because a larger part of the income goes to interest payments. There are several ways this can affect the banks. Firstly, if the household is no longer able to repay the debt because of the high cost. This cost may be due to the rising debt level, higher interest rates, or loss in income. This effect can be increased if there is a decrease in real estate

prices due to a decrease in household equity. That makes it harder to refinance existing debt or increase the debt with real estate as collateral. These effects are direct from households to the loss in banks.

Households may also decrease their consumption and investing in compensating for the higher debt cost. This may lead to more bankruptcies of companies and more considerable loss in banks. This is an indirect effect or a demand channel. Thirdly lower demand for housing may lead to housing prices to fall, and bank losses may arise in loans to develop- ers and similar real estate companies. This is also an indirect effect or a housing-channel (Kragh-Sørensen and Solheim, 2014b).

LOSS

1990 1995 2000 2005 2010 2015 2020

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

MILL NOK

LOSS

Figure 1: Loan Loss in Mill NOK, Source: Data Appendix

Regarding bank losses and the modeling of Norwegian bank losses, the figure shows aggregated losses in Norwegian banks, from the first quarter in 1990 to the fourth quarter of 2018. We can identify the 1990-1992 Norwegian Banking Crisis in the data.

Real interest rates had been small or negative in the period leading up to the crisis, making for large loan demand. Higher demand for goods and services in Norway than the rest of Europe lead to a deficit in the trade balance, giving higher prices and wage growth.

Policymakers tightened the fiscal policy. A combination of unbalance in the market and the economic tightening lead to lower growth. Moving onward, there was an increase in the number of bankruptcies, and banks experiences as much as 4,5% loss of total loans to

firms. The banking sector experienced large deficits, decreasing their equity (Haare et al., 2015).

Following the timeline, losses decreased after the banking crisis. Several measures were taken, both by banks and through regulatory changes, to prevent similar events from happening in the future. A slowdown in the global economic environment in 2001-2002 had an impact on losses in this period. The effects were short-lived, and the Norwegian economy recovered quickly (Benedictow, 2005).

The 2008 Financial crisis had a global impact, including Norway. There was a lower expectation for future growth, leading to a significant decrease in demand and produc- tion. The figure shows an increase in loan losses in this period. Fiscal policy turned expansionary, and the financial conditions gradually improved by the end of 2009 (Haare et al., 2015).

3 Previous studies

The purpose of this chapter is to present previous studies of bank losses in Norway and other countries. The findings from these studies are used to help decide the framework used in the econometric modeling, in particular the set of relevant explanatory variables.

In regards to modeling, there is no universal baseline used in this research. The stud- ies presented below uses macroeconomic explanatory variables, bank-specific explanatory variables, or a combination. Since this chapter aims to present empirical research on this topic, it presents studies done on bank losses and non-performing loans, since they are closely related. Table 3.1 presents some characteristics of previous studies. There is a description of the different left-hand side variables at the end of the chapter, which might be useful in understanding the variable choice.

Hol (2001) is a research paper discussing how macroeconomic variables might explain losses, using loss data from Fokus Bank. Hol used time-series data from 1991-1999 and developed both an autoregressive distributed lag model and an error correction model.

The statistically significant variables were GDP, change in an Industrial Production Index, change of losses lagged, change of money supply M1 and interest rates on loans. Both models explained about 70% of the variation of losses. The research covers the period of the Norwegian Banking Crisis and offers essential insight into the topic.

Hess et al. (2008) is a study on Australasian banks’ credit losses, with data from 1980- 2005. This study is an interesting time frame because it leads up to the financial crisis of 2008. They found that GDP growth, unemployment rate, real estate prices, and the stock market had a statistically significant effect on credit loss. Banks with strong loan growth experienced higher credit losses, with a lag of 2-3 years.

With a focus on loan growth and future loan loss, Kvisgaard and Vale (2018) looked into whether lending growth leads to higher loan loss in Norway. Large bank losses often occur after a period of high lending growth at an aggregate level. The study tests this at an individual bank level. The data period is 1995-2016, where it has been an increase in

the level of unsecured debt in Norway. Unlike the results of Hess et al. (2008), the results show that the economic effects are not statistically significant. However, as is pointed out in there study, there were no significant disruptions in the Norwegian banking sector, and it is difficult to capture the pure effect of high unsecured lending growth.

In regards to the Norwegian banks, Berge and Boye (2007) investegated which macroe- conomic variables that contribute to banks’ non-performing loans and high-risk loans for the period leading up to the financial crisis. This study was part of the Norwegian central bank research into the credit-market. They separated the estimates for private and com- mercial loans. In line with intuition, they found that disposable income, real estate prices, unemployment rate, and interest rate had the strongest effect on the private side. They also found that the non-performing loans and loans with a high probability of default were at an all-time low. They observed an increase in these loans on the commercial side in 2002-2003 that reversed from 2004.

A similar study was done by Qwader (2019) on Jordanian banks. Focusing purely on how macroeconomic variables might impact non-performing loans (NPL) in Jordanian banks. Qwader developed an autoregressive distributed-lagged model and concluded that there is a significantly long and short term relationship between NPL, GDP, interest rates, and external grants. On the other hand, Qwader concluded that there is no impact on the long or short run of the rate of unemployment, which is contrary to most other studies.

Looking at studies that used both macroeconomic explanatory variables and bank- specific, Louzis et al. (2012) published a study where they looked into determinants of non-performing loans in Greece. They tested the hypothesis that rising sovereign debt leads to an increase in NPL. The hypothesis was based on Reinhard and Rogoff (2010) that found statistical evidence that the banking crisis most often precedes or coincides with a sovereign debt crisis. Louzis, Voldis, and Metaxas found strong evidence in favor of this hypothesis for Greece. This hypothesis was not included in the other studies presented.

The study done by Kjosevski et al. (2019) is an example of a study that uses both

bank-specific and macroeconomic variables in explaining non-performing loans. The study looks at Macedonia, with the time frame of 2003Q4 to 2014Q4. Similar to the other studies, they developed an autoregressive distributed lagged model. The bank-specific determinants where the banks’ profitability and growth in loans. The results regarding macroeconomics are in line with other studies, but they also found that the exchange rate has a positive and statistically significant impact on the level of NPL.

Considering studies of Norwegian banks, the paper by Hol (2001) serves as an impor- tant reference point, due to the research question and approach. The paper was written in hindsight of the Norwegian banking crisis. This is where this research differ, focusing on a more recent sample period. Kvisgaard and Vale (2018) had a similar sample period, but tried to answer a specific research question on lending growth and loan loss.Berge and Boye (2007) had a broader approach, where they included a higher number of macroeco- nomic variables. However, the sample ended before the 2008 financial crisis, excluding an essential economic event.

Table 1: Some charecteristics of previous studies

Study Country Sample Data Type LHS-variable

Hol (2001) Norway 1991-1999 Macroeconomic LL

Hess et al. (2008) Australia&

New Zealand 1980-2005 Macroeconomic CLE

Kvisgaard and Vale (2018) Norway 1995-2016 Bank Specific/

Microeconomic LL&LLP&DL Berge and Boye (2007) Norway 1993-2005 Macroeconomic NPL

Qwader (2019) Jordan 2001-2017 Macroeconomic NPL

- LL: Loan Loss

- CLE: Credit Loss Experienced

- NPL: Non-performing loans

- DL: Defaulted Loans

- LLP: Loan Loss Provision

The studies presented above have different left-hand side variables. A short explana- tion might be useful, and is presented in the frame below:

Defenitions of Loan-Loss Concepts:

Non-Performing Loan: In general, a loan is defined as non-performing if no payments have made the last 90 days. Some banks might sell the loan claim to a debt collection service at this point. A non-performing loan might become performing if payments are made. This distinction can make the data on non- performing loans have considerable noise within the overall trends.

Defaulted loans: in the period before December 2009 loans were reported as defaulted with the same definition as non-performing loans. In the period from January 2009- December 2017, it was changed to 30 days. Later to be changed back to 90 days in January 2018.

Loan Loss Provisions: Regulatory rules and lending principles require banks to put aside a proportion of outstanding loans. This practice is to account for uncollected loans or loan payments. Loans that are considered as having a high default risk or that are non-performing makes for higher loan loss provisions that can be on individual loans or a group of loans. If a sector experiences a significant downturn, the bank might consider the probability of default to be higher and increase loan loss provisions for the group of loans to this sector. The measure of loan loss provisions is subject to the individual banks’ risk calculation and does not directly reflect the real loss.

Credit Loss Experience: is a collective term, mostly used as a synonym for loan loss provisions.

Loan loss: is the sum of net loan loss provisions and unexpected loan losses in that period (not previously accounted for). Within one accounting period, the bank calculated loan loss provisions for that period and adjusts for any changes for numbers reported in previous periods. Then adds any unexpected loan loss.

The sum should represent the actual loss.

4 The data set

This chapter includes a presentation of the data set used in the research. The first section motivates the use of a transformed loss variable, followed by a presentation of relevant macroeconomic variables.

4.1 Loan loss

The time series of loan losses in Norwegian banks and the connection to financial stability were presented in chapter 2. As discussed previously, banks will naturally have some losses due to the risk of firms and households not being able to handle the debt burden.

In figure 3, the total debt level in Norway has increased over the sample period. It is reasonable to assume that banks’ losses in Million NOK will increase when the debt level has increased significantly over time. However, when comparing losses over time, this might not be a fair representation.

To be able to consider the effect of the increased debt-level, a new loss variable is constructed by dividing loan loss by the total domestic debt level. The new variable, denoted loss, shows the percentage of loan loss relative to the public debt level.

loss

1990 1995 2000 2005 2010 2015 2020

0.0 0.5 1.0 1.5 2.0

%

loss

Figure 2: Loan Loss as percentage of total debt; 1990Q1-2018Q4

Although the new loss variable shows some of the same characteristics as the one previously presented, the Norwegian Banking Crisis stands out, due to the losses being large and the debt level low. A discussion of some time series characteristics of the two different loss variables is included in the next chapter.

Several considerations were made when it comes to transforming this variable. A transformation by taking the natural logarithm is not possible due to some negative values.

However, even with only positive values taking the natural logarithm is not necessarily the best transformation. Because:

lim

x→0⁺log(x) = −∞

x→+∞lim log(x) = +∞

Most values of the loss variable are close to zero. When taking the natural logarithm, this will give large negative numbers, giving it a high relative value. When banks experi- ence larges losses, like in the early 1990s, this will have a lower relative value because of the slope of the logarithmic function. Concluding that it is best to model the loss variable as is, not transformed by taking the natural logarithm.

4.2 Explanatory variables

In order to be able to compare the results in this thesis with the results obtained by previous researchers, a data set that includes the most important explanatory variables in the studies reviewed above was constructed. Most of the variables were collected from Statistics Norway. The exceptions are the nominal interest rate, a property price index and household interest rate expense. These variables have been were collected from The Norwegian Central Bank, Macrobond and the database Norwegian Aggregate Model.

The sample period is the 1. quarter of 1990 to the 4. quarter of 2018. All observations are quarterly. Some variables were converted from monthly to quarterly. See the data appendix for a detailed description of each variable.

ILGP ILGF

ILGH

1990 1995 2000 2005 2010 2015 2020

250 500 750 1000 1250 1500 1750 2000 2250 2500

BILL NOK

ILGP ILGF

ILGH

Figure 3: Loan debt public, non-financial firms and households; 1990Q1-2018Q4

Domestic loan debt has increased significantly over the sample period. The figure shows the total domestic loan debt to the public, non-financial firms and households.

Interest rates on loans have decreased (figure 4.3), making it less expensive to borrow.

NOMR IRL

1990 1995 2000 2005 2010 2015 2020

2 4 6 8 10 12 14

%

NOMR IRL

Figure 4: Nominal interest rate and interest rate on outstanding loans; 1990Q1-2018Q4

The two lines represent the nominal interest rate (NOMR) and the average interest rate on outstanding loans in banks (IRL). Banks set their interest rate according to the central banks’ nominal interest rate. We can see that there is a lag from where the nominal interest rate changes to when the interest on loans changes.

REPI

1990 1995 2000 2005 2010 2015 2020

50 75 100 125 150 175

200 REPI

Figure 5: Real Estate Price index; 1990Q1-2018Q4

Figure 5 shows property prices over the period. There is a strong upward trend, with a slight decrease in 1990-1993 and 2007-2008. Looking at the two previous figures, the interest rates on loans have fallen, making it less expensive to borrow. The debt level has increased, making real estate prices increase accordingly.

GDP

1990 1995 2000 2005 2010 2015 2020

200 300 400 500 600 700

BILL NOK

GDP

Figure 6: Gross Domestic Product; 1990Q1-2018Q4

Figure 6 shows the Gross Domestic Product (GDP) for mainland Norway in million NOK, which includes the total market value of all goods and services produced. GDP has a clear upward trend.

UN1 UN3

UN2

1990 1995 2000 2005 2010 2015 2020

1 2 3 4 5 6

%

UN1 UN3

UN2

Figure 7: Unemployment; 1990Q1-2018Q4

Unemployment is the percentage of registered unemployed people, relative to the total workforce. The most commonly used is the age interval of 15-74 (UN1). However, the intervals 25-54 (UN2) and 55-74 (UN3) are reported. The number of bankruptcies (figure 4.7) and unemployment rate naturally has a similar path, especially the age group of 25-55. The unemployment rate for the age group of 55-74 decreased from 1990-2007 and has been more or less stable in the following years. This observation may indicate that the first age group has a larger effect on loan loss.

CPI

1990 1995 2000 2005 2010 2015 2020

60 70 80 90 100

110 CPI

Figure 8: Consumer Price Index; 1990Q1-2018Q4

Consumer Price Index (2015= 100) is a description of the development in consumer prices for goods and services purchased by households in Norway.

Thus it measures the underlying growth in consumer prices or inflation. In this analysis, the CPI is used to adjust variables from nominal to real values.

YDCD

1990 1995 2000 2005 2010 2015 2020

100 150 200 250 300 350 400

BILL NOK

YDCD

Figure 9: Disposable income, billion NOK; 1990Q1-2018Q4

Households’ disposable income (YDCD) measures the households’ income (wage, self- employment income etc.), taking into account net interest, dividends received and social contributions. The variable has a clear upward trend. There is a break in the graph, that is due to data from multiple sources being combined. However, the trend is dominant for the figure of interest rate expense as percentage of disposable income (RUYD) in figure 10.

RUH

1990 1995 2000 2005 2010 2015 2020

10000 20000 30000

MILL NOK%

RUH

RUYD

1990 1995 2000 2005 2010 2015 2020

10 15

20 RUYD

Figure 10: Interest expense in million NOK and interest expense as a percentage of disposable income; 1990Q1-2018Q4

The top figure shows interest expense on loans for households in million NOK. The interest expense is a product of two factors: the interest rate and total debt, presented in the previous figures. In isolation, low interest rate level indicates a low interest expense.

However, low interest rates contribute to high debt growth and total debt level. The net effect as we can see in the figure is that interest expense has increased in the sample period.

The bottom figure shows interest rate expense as a percentage of disposable income. This might be a more intuitive representation, with more information about the relative cost of debt to income over time. This parameter can be interpreted as a macro equivalent of the household’s debt burden. It is reasonable to assume that the number of households having trouble paying their debt will increase when this indicator increases.

5 Methodology

This section includes a presentation of the methodology used in the analysis. Firstly, the concept of stationarity, which is an essential concept in time series econometrics, followed by a short discussion of the order of integration. Subsection 5.2 includes a description of distributed lag models, which the rest of the analysis is based on. Lastly, a short description of the diagnostic tests reported for regressions in chapter 6.

5.1 Stationarity and non-stationarity

The consept of stationarity refers to the linear properties of the time series process. In particular expectation, variance and autocovariance. (Nymoen (2019), chapter 4.3) The stochastic time series process is defined by the stochastic difference equation where {Y_t;t= 0,±1,±2,±3, ...}:

Y_t=φ₀+φ₁Yt−1+φ₂Yt−2+...+φ_pYt−p+_{t t}∼ IID(0, σ²) ∀ t (5.1)

The notation _t∼ IID(0, σ²) is used to denote_t aswhite noise. Formally a process {_t;t= 0,±1,±2,±3, ...}is called white noise if: E(_t) = 0, V ar(_t) =E(²_t) = σ², and Cov(t, t−j) =γj = 0, for j 6= 0.

In equation 5.1, variable Y is weakly stationary if:

E(|Y_t|²)<∞ ∀t, E(Y_t) =µ ∀ t, and E[(Y_t−µ)(Yt−s−µ)] =γ_s ∀ t, s Brockwell and Davis (1991)

The first two moments must be finite and be constant over time. It is a necessary condition for the variable to be stationary. A variable that does not satisfy these conditions is non-stationary. The term covariance stationary is also common. In this thesis, I will use the term weakly stationary or simply stationary.

The concept of stationarity and the parallel to the mathematical properties of differ- ence equations can be illustrated by the first order autoregressive process AR(1), which is a speciall case of equation 5.1 :

Y_t=φ₀ +φ₁Yt−1+_{t t}∼ IID(0, σ²) ∀ t (5.2)

The solution of the difference equation can be expressed as:

Yt=φ0 t−1

X

j=0

λ^j₁+λ^t₁Y0 +

t−1

X

j=0

λ^j₁t−j (5.3)

Where λ₁ is the root of the characteristic equation λ₁ − φ₀ = 0. Looking at the definition ofweak stationarity above, the variance and autocovariance must be calculated.

The unconditional variance ofY_tcan be obtained from the stable solution ofY_t. The stable solution is based on |φ₁| < 1. The solution is:

Yt= φ₀ 1−φ₁ +

∞

X

i=0

φⁱ₁t−1 (5.4)

The unconditional expectation of 5.4 is:

E(Y_t) = φ0

1−φ₁ =µ (5.5)

Calculating the unconditional variance from 5.4, gives:

Var(Y_T) = σ²

1−φ²₁ (5.6)

The variance of Y_t calculated from the stable solution is independent of time, which is one of the necessary conditions defined above. Without going into to much detail, the conditional variance of Y_t given Y₀ is dependent on time t, showing that the variance is independent of time only for the case when the stability condition |φ₁| < 1 is satisfied.

Looking at the second condition regarding autocorrelation, it can be simplified by

subtracting µfrom 5.1. We end up with the expression of autocovariance:

E[(Yt−µ)(Yt−j −µ)] =φ1E[(Yt−1−µ)(Yt−j −µ)] (5.7)

Which can be expressed:

γ_j =φ₁γj−1

We can conclude that variance and autocovariance are independent of time, when the solution is calculated from the stable solutionY_t, ie. when|φ₁|< 1. The time series 5.2 is stationary exactly when the first-order difference equation has a globally asymptotically stable solution. This duality between the concepts of dynamic stability and stationarity can be generalized to higher order dynamics, see e.g. Nymoen (2019), Ch 3 and 4.

5.1.1 Order of integration

As discussed above, some variables are weakly stationary and are denoted X_t ∼ I(0).

Other variables can be made stationary by taking the difference. A variable Xt, that is an integrated time series and the first difference X_t is weakly stationary is said to be integrated of order one and denoted X_t ∼ I(1). Formally, looking at the first order difference equation:

Y_t=φ₀+φ₁Yt−1+_t (5.8)

Where _t is assumed to be white noise, with varianceσ², as noted above. The case where φ₁ = 1is as special case of the equation above, where the characteristic equation contains a single unit root, λ= 1. It can be made stationary by subtracting Yt−1 from both sides:

Y_t−Yt−1 =φ₀ +_t

Which results in:

∆Y_t=φ₀+_t

The exceptation and variance of ∆Y_t clearly does not depend on time t, when _t is white

noise, and is therefore stationary.

For some variables, we need to take the difference more than ones for it to become weakly stationary. In general, we use the notation X_t ∼ I(d), for a variable that is integrated of order d. One method for testing the order of integration is using the Dickey- Fuller test. Some theory and test results for the order of integration of the variables is presented in the next chapter.

5.2 Autoregressive Distributed Lag Models

A simple autoregressive distributed lag model, with only one explanatory variable and first order dynamics is expressed:

Y_t =φ₀+φ₁Yt−1+β₀X_t+β₁Xt−1+_t t = 1,2, ..., T (5.9) The conditional expectation of the error term, given the parameters is zero,

E(_t|X_t, Xt−1, Yt−1) = 0. Where the autoregressive part refers to φ₁Yt−1 and the distributed lag part β₀X_t+β₁Xt−1. Since the model includes only first order lag polynomials it is referred to as a ADL (1,1) model.

The OLS estimater of φ₀, φ₁, β₀ and β₁ are consistent if the error terms in the

regression are white noice. (Nymoen, 2019). Since, in practice, the order of dynamics is unknown a priori, the validity of the assumed absence of residual autocorrelation needs to be tested. The theory behind the test for residual autocorrelation will be explained in the next section, the results for the models are listed in chapter 6.

For the case of higher order dynamics the ADL(py, px) is expressed:

Y_t−φ₁Yt−1−...−φ_pyYt−p =φ₀+βX_t+β₁Xt−1+...+β_pxXt−p+_t (5.10)

The model can also be generalized by the inclusion of several explanatory variables and lag orders.

5.3 Diagnostic Tests

A short presentation of diagnostic tests is presented below. This will include some theory and how to interpret the test results. In chapter 6, the tests are performed and reported for each regression.

Residual autocorrelation

The test for residual autocorrelation is a Lagrange-multiplier test for r^th order residual autocorrelation. The term Lagrange-multiplier test is sometimes also used when testing for heteroscedasticity and should not be confused. The topic is largely developed by Godfrey (1978) and Harvey (1990).

The Lagrange-multiplier test is calculated by regressing the residuals on the regressors of the model and the lagged residuals from p to r:

u_t=

r

X

i=p

α_iut−i+_t where 0≤p≥r (5.11)

The test follows a χ²(r) distribution in large samples. The null hypothesises in that there is no autocorrelation.

Autoregressive Conditional Heteroscedasticity

The ARCH-test is used to determine if the variance of the errors _t is dependent on time. Is was developed by Engle (1982) and tests the null hypothesis of γ = 0 where:

E

u²_t|ut−1, ..., ut−r

=c0+

r

X

i=1

γiu²_t−i (5.12)

and γ = (γ₁, ..., γ_r). The auxiliary regression is calculated and the test takes the form of T R² and is therefor asymptotically distributed χ²(r) under the null-hypothesis.

Heteroscadasticity test

The test for heteroscedasticity is based on White (1980), and often referred to as a White-test. It uses a auxiliary regression on the regressors and their squares:

²_i =α₀+α₁X_i+α₂X_i², i= 1,2,3, ..., n, (5.13)

The null hypothesis is homoscedasticity, meaning that the coefficients are equal to zero.

The alternative is that the variance of _t depends on the regressors and their squares.

The conclusion is based on the usual F-test.

Normality test

The test was derived by Jarque and Bera (1987) and is based on the skewness (ˆκ²₃ =P ˆ³_i

σˆ³) and kurtosis (ˆκ²₄ =P ˆ⁴_i

σˆ⁴ −3) of the residuals estimated in the model.

The test statistic is derived from:

χ²_norm =χ²_skew+χ²_kurt.

where:

χ²_skew =nκˆ²₃

6 and χ²_kurt =nˆκ²₄ 24.

The null is normality of the errors _i. The normality test for disturbances is widely used, because of the statistical distribution of the OLS estimators. If we conclude that the normality assumption holds, the t-distribution and F-distribution is correctly used for testing significance of parameters. If the normality is rejected it can still be a good approximation when we have a large sample size.

In the empirical modeling below, the normality test, as well as the other tests mentioned above, has been used as they are implemented in the computer program PcGive 14, and as documented in Doornik and Hendry (2013).

6 Modeling Results

The existence of banks and the role of bank losses for financial stability was discussed in section 2, and some explanation for why macroeconomics affect banks. In this section, I investigate some statistical properties of the macro variables, concluding that most of the variables are I ∼ (1) variables. The main goal of this sections is to specify an empirical ADL model for bank losses. The specification process has considered variables that have been reported as significant in earlier studies and that seem relevant in light of theory and what we know about "good lending practice" in banks. The rest of the section is organized as an extensive analysis of the robustness of the estimated ADL-model.

6.1 Stationarity and unit root test

As a background to the empirical modeling, it is useful to present some descriptive statis- tics for the time series variables individually. As discussed previously, data is considered to be weakly stationery if the expectation and covariance are independent of time. The Dickey-Fuller unit root test is widely used in time series econometric. The Dickey-Fuller regression is as follows for the case with both an intercept and (deterministic) trend included:¹

∆Y_t =φ₀−π(1)Yt−1+δt+_{t t} ∼ N(0, σ²) (6.1) In order to test the hypothesis of a unit root in Y_t we test: H₀ : π(1) = 0. By comparing the t-value of π, which will be referred to as t-adf in the following, with the critical value from the appropriate Dickey-Fuller distribution, we can determine whether to reject the null hypothesis or not. In most statistical software, the correct critical values are reported. However, the paper by Ericsson and MacKinnon (1999) has further detail on the subject.

As just noted, the equation above includes both a constant and trend. It is custom to refer these parts of the model as the "deterministic augmentation." The reason being

1 ∆is used as a difference operator and−π(1)=(φ₁−1)

that in a specific special case, the regression is formulated with a constant and with no trend. When specifying Dickey-Fuller regression, it is of importance that the deterministic augmentation is specified in such a way that it is able to account for the trend behavior of the series, both under the null hypothesis and under the alternative hypothesis. (Nymoen (2019), chapter 9.7)

In the test conducted in the next subsection, I have had to test for unit-roots in regressions with higher-order dynamics. This is done by estimating the Augmented Dickey-Fuller regression (allowing dynamics of order p in Y_t):

∆Y_t=φ₀+

p−1

X

i=1

φ_i∆Yt−1+δt−π(1)Yt−1+_t (6.2) When testing the null-hypothesis H₀ : π(1) = 0, the critical values for the DF and ADF test are the same because both are asymptotic tests. A key point with stochastic augmentation is, as with other statistical testing, that the assumptions for the test to be valid are satisfied. If for example, the degree of stochastic augmentation is too low, the assumtion of white-noise error term in the ADF regression is violated, which undermines the reliability of the unit-root test.

6.1.1 Statistical properties of the loss variable

The table below shows The Augmented Dicky-Fuller test results for the variable LOSS reported in MILL NOK. The first column is the number of lagged differences. The second column reports the ADF test statistic, third column is the coefficient of y_t-1 . The next columns T-DY_lag and t-prob, gives the t-value of the longest lag (ofγss=1,2,3,4) and the according p-value of that lag. When choosing the correct lag length, the go to standard is to select the highest s with a significant last γ_s. As discussed above, the deterministic augmentation should be specified in such a way that it accounts for trend behavior, both under the null hypothesis and under the alternative hypothesis. Since the loss variable does not exhibit such trend behavior, the deterministic trend is not included in the ADF regressions.

Table 2: ADF-tests LOSS and ∆LOSS

LOSS: ADF tests (T = 110, Constant; 5% = -2.89, 1% = -3.49)

D-lag t-adf beta Y_1 t-DY_lag t-prob

4 -2.848 0.764 1.557 0.1224

3 -2.562 0.791 -1.649 0.1021

2 −3.058^∗ 0.756 -1.814 0.0724 1 −3.807^∗∗ 0.709 -1.118 0.2661 0 −4.618^∗∗ 0.676

∆LOSS: ADF tests (T = 110, Constant; 5% = -2.89, 1% = -3.49)

D-lag t-adf beta Y_1 t-DY_lag t-prob

4 −5.806^∗∗ -0.912 0.9143 0.3627 3 −6.240^∗∗ -0.756 -0.9511 0.3438 2 −9.241^∗∗ -0.934 2.318 0.0223 1 −10.70^∗∗ -0.585 2.848 0.0053 0 −13.43^∗∗ -0.250

∗∗ significant at 1%, ^∗ significant at 5%,

Table 2 shows the ADF test for LOSS. Using a 10% significance level, the correct lag length is 2. Comparing the according t-ADF to the critical value, we conclude that we can reject the null hypothesis of a unit root with a 5% significance level. This result indicates that loan losses are stationary.

The bottom part of table 2 shows the ADF-test for ∆LOSS. The rejection from the first ADF-test makes the test for the first difference less relevant, but for completeness, it is included. The ADF-test for ∆LOSS confirms the conclusion of loan losses being stationary, choosing two lags, rejecting the null hypothesis with a 1% significance level.

Table 3: ADF-test loss and ∆loss (loss as percentage of total domestic debt)

loss: ADF tests (T = 110, Constant; 5% = -2.89, 1% = -3.49)

D-lag t-adf beta Y_1 t-DY_lag t-prob

4 -2.613 0.826 0.712 0.4780

3 -2.560 0.830 -2.257 0.0261

2 −2.889^∗ 0.807 -3.447 0.0008 1 −3.742^∗∗ 0.741 -1.190 0.2367 0 −4.395^∗∗ 0.720

∆loss: ADF tests (T = 110, Constant; 5% = -2.89, 1% = -3.49)

D-lag t-adf beta Y_1 t-DY_lag t-prob

4 −5.869^∗∗ -1.085 0.3171 0.7518 3 −6.863^∗∗ -1.022 -0.4387 0.6618 2 −10.05^∗∗ -1.113 2.617 0.0102 1 −12.07^∗∗ -0.694 4.212 0.0001 0 −13.16^∗∗ -0.231

∗∗ significant at 1%, ^∗ significant at 5%,

Table 3 shows the results of the ADF test for the transformed variableloss and∆loss.

It is interesting to notice that we have a different conclusion about stationarity. We conclude by choosing three lags (p-value of 0,0261) and comparing the according t-adf with the critical value. We do not reject the null hypothesis of a unit root.

For the ADF test of ∆loss, we reject the null hypothesis with two lags at a 1% significance level. This indicates that the transformed loss variable is I(1).

However, the t-adf forloss is close to the critical value. Using a 10% significance level, the critical value is -2.5668, hence no rejection.² The conclusion influences the choice of model specification when modelling in section 6.2

2See Ericsson and MacKinnon (1999), page 304

6.1.2 ADF test results for all variables

The table shows the results from the Augmented Dickey-Fuller test for all variables defined in chapter 4.

Table 4: Results from the Augmented Dickey-Fuller test Variabel Constant Constant + Trend d-Lags t-ADF

LOSS 4 2¹ −3.058^∗

loss 4 3 −2.889^∗

LILGP 4 3 −2.077

LILGH 4 4 −2.532

LILGF 4 4 −2.827

IRL 4 1 −2.705

LREPI 4 4 −2.456

UN1 4 4 −2.682

UN2 4 4 −2.525

UN3 4 3 −1.390

NOMR 4 1 −2.630

LYDCD 4 3 −1.662

LRUH 4 4 −1.816

LRUYD 4 4 −3.725^∗∗

∆ LOSS 4 2 −9.241^∗∗

∆ loss 4 2 −10.05^∗∗

∆ LILGP 4 1 −3.463^∗

∆ LILGH 4 4 −2.532

∆ LILGP 4 1 −4.301^∗

∆ IRL 4 0 −6.381^∗∗

∆ LREPI 4 3 −3.865^∗∗

∆ UN1 4 3 −3.351^∗

∆ UN2 4 3 −3.797^∗∗

∆ UN3 4 2 −12.25^∗∗

∆ NORM 4 1 −6.134^∗∗

∆ LYDCD 4 4 −4.573^∗∗

∆ LRUH 4 4 −4225^∗∗

∆ LRUYD 4 3 −4225^∗

1Significant at 10% , * Significant at 5% (Dicky-Fuller Distirbution),

* Signingivcant at 1% (Dickey-Fuller Distribution)

The test indicates that most variables are I(1). The exception is the variable LRUYD (interest payment in percent of total debt) and LILGH (total household debt). Including four lags, we reject the null hypothesis of a unit root for LRUYD at a 1% level. This indicates that interest payment in terms of total domestic debt is I(0). Taking the second difference of total household debt and performing the same ADF-test, the results indicate that the variable is I(2). A new ADF-test after taking the second difference of total household debt, indicates that the variable is I(2).

6.2 Autoregressive Distributed Lag Model

In this first regression, the dependent variable is LOSS, which we recall is measured in million NOK. The explanatory variables are GDP growth, measured as one-year growth.

Households interest burden, nominal interest rate, and unemployment (15-74).

LOSS_t=θ₀+θ₁LOSSt−1+β₁D4LGDP_t+β₂D4LGDPt−1+β₃RU Y D_t+

β4RU Y Dt−1+β5U N1t+β6U N1t−1+β7N OM Rt+β8N OM Rt−1 +t (6.3)

Based on the previous studies presented in section 3, it is reasonable to expect that these variables are relevant also for my data set. The number of lags was determined by using PcGive dynamic lag structure analysis, which tests for the significance of each lag (up to 4 lags). We can use one lag, without loosing significant explanatory power, and without indication of large residual autocorrelation.The table bellow shows the regression output:

Table 5: Regression results using OLS: Model equation (6.3) 1990q2-2018q4

LOSS Coeff. Std.Error t-prob

Constant -298.4 602.8 0.622

LOSS_1 0.401^∗∗∗ 0.080 0.000

D4LGDP −14439^∗∗∗ 3596 0.000

D4LGDP_1 −9320^∗∗ 3691 0.013

RUYD 38198^∗∗∗ 13170 0.004

RUYD_1 -10317 12600 0.415

UN1 −651.4^∗∗∗ 196.1 0.001

UN1_1 619.3^∗∗∗ 183.7 0.001

NOMR 440.608^∗∗ 171.1 0.011

NOMR_1 −533.691^∗∗∗ 176.5 0.003

n = 111 no. of parameters = 10

R²= 0.689 log-likelihood = -897.316 AR 1-5 test: F(5,96) = 0.35194 ARCH 1-4 test: F(4,103) = 0.027822 Normality test: Chi^2(2) =29.036^∗∗

Hetero test: F(18,92) =3.116^∗∗

Hetero-X test: F(54,56) =7.563^∗∗

∗∗∗ significant at 1%, ^∗∗significant at 5%, ^∗ significant at 10%

The results show that all variables and lags are significant except for the lag of house- holds interest burden. GDP growth has a negative sign, which is in line with intuition.

With higher GDP growth, firms produce more and are less lightly to default on their loan obligations. Households interest burden (RUYD) is positive and significant. Banks experience higher loss when households interest payments in terms of disposable income increase. The lag of RUYD had a negative sign but is not significant. Unemployment has a somewhat surprising result. UN1 is significant and negative. It is expected that unem- ployment is correlated with GDP growth. However, the effect of unemployment might be captured by the other estimated coefficients. Subsection 6.3.4 will test the robustness of the estimated coefficients when unemployment is not included. The first lag of UN1 is significant and positive, which is more in line with intuition. Higher unemployment will lead to a higher loss in the next period. The nominal interest rate has a positive and significant effect, while the lag is negative and significant.

The test summary includes a battery of tests on the residuals. This includes tests for autocorrelation, autoregressive conditional heteroscadasticity, the normality of the distribution of the residuals and heteroscedasticity. As we can see in table 5, the normality test and the two tests for heteroscedasticity are significant. This result might be one source of uncertainty in the models. However, the test for lack of residual autocorrelation is insignificant, which is important for dynamic modeling. Considering the shape of the loss series, this is within what is excepted.

6.3 Robustness of the model

The ADL model is based on linearity in parameters. However, some explanatory vari- ables might not fit into this framework. Looking at figure 1 of LOSS, there are large outliers. This section goes into further detail addressing these problems, first by specify- ing a non-linear function form and then controlling for large outliers. Moreover, checking the robustness of the model.

6.3.1 Non-linear functional form

The intuition behind using a non-linear function form has an economic interpretation.

Using interest expense as a percentage of disposable income (RUYD) as an example, the cost of debt can increase some percent, and households are still able to make payments.

This is in particular because households can make changes to their consumption, which is also calculated by banks. However, if the increase is large enough and reaches a critical level, households may not be able to make loan payments. As an implication, loan losses might be low until interest expense reaches the critical level, then it rises sharply.

To test for this in the model, RUYD and UN1 (unemployment age 15-74) was transformed by using the logistic function:

N L(X) = 1

1 + exp (C∗(X - threshold value)) (6.4) (See for example Granger and Teräsvirta (1993))

The results of the transformation are two new variables, NLRUYD and NLUN1. The constant C and the threshold value are parameters of the non-linear function, which must be specified to separate the transformed variable from the untransformed. The constant used for NLRUYD is -70.0 and -1.5 for NLUN1. The threshold values were set to 11% for interest expense and 3.8% for unemployment. Some experimentation was done when determining the threshold values. The variables in question have values above the threshold, in particular after the Norwegian Banking Crisis, but also in the other periods where bank losses were at a high level.