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The Effect of Income Inequality on Debt
Delinquencies
Name: Evan Troelstra Student number: 10107320
Email: e_troelstra@hotmail.com
Supervisor: Dr. M. Pradhan Second reader: Dr. N. Leefmans
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Table of Contents
Introduction ... 4
1. Literature Review ... 6
1.1. Overview of Iacoviello (2008) ... 6
1.2. Additional Supporting Literature ... 13
2. Outline of the Model ... 20
2.1. Environment ... 20
2.2. Patient Agents ... 22
2.3. Impatient Agents ... 23
3. Data, Calibration and Simulation ... 28
4. Results and Discussion ... 32
5. Conclusion ... 39
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Introduction
In the wake of the recent financial downturn income inequality has resurfaced as a prominent topic of discussion. In light of this one may wonder whether or not had the discussion taken place earlier if some of the effects of the financial crisis could have been mitigated, or perhaps even avoided
altogether. The role of debt in the most recent financial crisis has been well established, for instance papers such as Brunnermeier (2008) give a central role to debt in explaining how the crisis came about, however there is much less discussion on what the role of income inequality may have been.
One paper that does look at the role of income inequality in causing household debt is Iacoviello (2008). In Iacoviello (2008) it is pointed out that in the long run household debt is closely mirrored by income inequality and on the shorter term timescale household debt is related to economic growth. Using these two observations as motivation Iacoviello constructs a DSGE model that is able to explain the rise of household debt as a result of income inequality increases.
In this paper the aim will be to take Iacoviello’s model one step further by examining whether household delinquency can be explained as a result of income inequality. By doing so hopefully some credence could be given to the argument that perhaps the rise of income inequality should be
considered a root cause of the most recent financial downturn, as loan delinquency was considered to be a trigger of crisis. More specifically this paper seeks to answer the question: can one construct a quantitative model to explain delinquencies as a result of income inequality increases, thusly explaining how income distribution shocks can cause delinquencies?
A notable feature of Iacoviello’s paper was the use of an idiosyncratic framework in which the consumption, debt, and asset positions of each agent in the economy is individually determined and then aggregated. Using an idiosyncratic framework allows for a greater degree of realism in the model as it can allow for delinquency as a result of coordination problems even though at an aggregate level
5 the market clears. Consider the case when there are only two groups in a two-period model economy. If one group lends to another group in the first period, and income and consumption does not change in the second, then there will necessarily be default even though at an aggregate level the credit market clears. Without an idiosyncratic framework this sort of phenomena would be not be observed.
This paper seeks to extend Iacoviello (2008) by adding the aspect of loan delinquencies to the presented idiosyncratic framework, thereby justifying income inequality as a direct contributing cause of economic instability. To do this some of the assumptions made in Iacoviello (2008) will be relaxed, plus some features will be added. Specifically, delinquency needs to be defined for the model, and then incorporated to the framework presented in Iacoviello (2008). The element of delinquency will be introduced by placing a minimum consumption constraint on the agents of the economy.
Adding delinquency adds a degree of realism to the Iacoviello framework. Delinquency is an important indicator that is often considered alongside debt levels as it is often a factor in credit events. This improves the Iacoviello model in that besides showing how income inequality increases results increased debt, it also shows how debt delinquency rates are connected to changes in output. The extended model thus is able to show a mechanism in which income inequality increases debt, thereby causing changes in output to be associated with greater volumes of debt becoming delinquent at higher levels of income inequality. This increases the chance that credit events can occur. From this mechanism the increase in income inequality leading up to both the Great Depression and the more recent major financial crisis of 2007 can be interpreted as being directly responsible in creating the conditions that allowed systematic vulnerabilities to grow until they reached critical levels resulting in the crises.
Understanding this link is important because if correct it would imply that allowing income inequality to increase unchecked leads to structural decreases in the stability of the financial system, and consequently the economy as whole.
6 The thesis will proceed as follows. Section 1 will provide a literature review, in which a detailed overview of the model presented in Iacoviello (2008) will be given, as well as arguments from supporting literature justifying the addition of delinquency. Section 2 will present the extended model that includes loan delinquencies. In Section 3 the calibration and simulation of the model will be discussed. Then in Section 4 the results will be presented and discussed. The thesis will be concluded in Section 5.
1. Literature Review
The primary focus of this thesis will be to extend the framework provided in Iacoviello (2008) by adding the aspect of loan delinquency to it. To this end the literature review will proceed as follows. First, a detailed overview of Iacoviello (2008) will be presented, adding a few points from more recent literature. Then a rationale for the addition of delinquency to the model will be provided.
1.1.
Overview of Iacoviello (2008)
In Iacoviello (2008) an idiosyncratic model is developed in order to study the effect of income inequality on debt in the time period 1963-2003. This paper was motivated by two empirical facts concerning household debt. The first was that household debt trends moved closely in tandem with income inequality trends in the given time period, namely that from 1963 until 1980 both remained fairly constant and that from 1980 until 2003 both measures increased rather dramatically. The second empirical fact that motivated Iacoviello (2008) was that in the given time period it was found that the cycles of household debt and economic activity were quite closely synchronized. So more specifically Iacoviello (2008) sought to create a model to explain those observations.
The model that Iacoviello developed used a non-linear system of equations to determine the debt, housing, and consumption positions of each agent in the economy. This was done by means of solving a utility optimization problem for each individual, and then reconciling these with aggregate
7 equations that ensured the market would clear. Income inequality was inputted into the system as an exogenous variable and was determined from data. The data points were used to calculate distributions that were used to determine each year’s income and income shocks. Log-normal distributions were then sampled and normalized so that the goods market would clear. This was used to determine the income positions of agents in the economy. As well loan to value ratios that determined borrowing were set exogenously as well. The remaining variable, consumption, debt and housing were determined endogenously by the model.
It was noted in Iacoviello (2008) that up until that point there had not been any studies that had attempted to connect both micro and macro elements together in order to explain the behavior of households. Raskin (2013) also notes that typically most models simply look at representative
households and do not look differences across agents. There are some papers cited by Iacoviello (2008) that do look heterogeneous agents, namely Krusell and Smith (1998) which was used as a basis for Iacoviello’s model; however it is not a standard approach. As mentioned in the introduction though these models have the advantage that they are able to account for nuances that may be paved over by aggregated macro models.
Even though there are a multitude of explanations for the rise of household debt, for instance reduced cost of financial leveraging, smaller business cycle fluctuations, financial innovation, and changes in the regulatory environment, Iacoviello (2008) argued that these explanations provided an incomplete picture as the need to access credit was influenced by both aggregate and idiosyncratic considerations.
The reasoning provided in Iacoviello (2008) to justify the idiosyncratic framework, which also applies to the approach used in this thesis is as follows. At the aggregated macroeconomic level it is argued that in the long-run economic growth is accompanied with financial development which allows
8 for more efficient allocation of funds between those with surplus funds and those that have profitable use for them, accounting for the trend increase. The cyclical component is accounted for by the pro-cyclical nature of borrowers’ balance sheets, which causes credit to be correlated with economic activity.
On the micro cross-sectional level Iacoviello argues the following connection of income inequality and debt. He posits the situation in which permanent income does not change while the individual income becomes more volatile over time. In this case borrowing will increase as individuals smooth their consumption which is determined primarily by permanent income. In other words, assuming the credit market clears so that the sum of positive and negative debt positions equals zero, the sum of negative positions, hence debt, will increase as more individuals borrow to reduce the difference between their permanent income which affects consumption, and their temporary individual income.
The reasoning just given was used to motivate the central question of the paper: how do the shocks to aggregate income and to its distribution affect the behavior of credit flows? The model that Iacoviello (2008) uses to address this question was a simplified version of the stochastic growth model presented in Krusell and Smith (1998) which he modified to account for individual heterogeneity.
The environment of the model used in Iacoviello (2008) is as follows. Firstly, time is assumed to be discrete. The economy is comprised of infinitely lived heterogeneous agents. The agents differ in their incomes, discount rates and access to credit.
An initial income endowment is given by randomly sampling a log-normal distribution that has been calibrated from data, and thus is an exogenous variable of the model. This initial endowment then has bearing on how financial and real assets are accumulated. For each individual income is made up of
9 three components; an individual-specific fixed effect, a varying aggregate component, and a time-varying individual component.
The population is then divided into two groups. One group consists of ‘patient agents’ who are not credit constrained (credit limits never are binding), and can trade one-period consumption loans unhindered. The other group consists of ‘impatient agents’ who are credit constrained and are required to use collateral to obtain financing. In this framework all loans are assumed to be repaid, so that no default occurs. Each group has its own discount rate, with the patient agent’s discount rate being assumed to be equal to or less than the impatient agent’s discount rate.
The model itself can be summarized as follows. For the patient agents Iacoviello (2008) uses the following lifetime utility equation of consumption and housing:
max 𝐸𝐸0� 𝛽𝛽𝑡𝑡(log 𝑐𝑐𝑖𝑖𝑡𝑡+ log ℎ𝑖𝑖𝑡𝑡 ∞
𝑡𝑡=0
)
where 𝑖𝑖 = {1,2,3, … , 𝑛𝑛}, n being the number of patient agents in the economy, where c is consumption and h is the amount housing that individual i has. The wealth constraint is given by:
𝑐𝑐𝑖𝑖𝑡𝑡 + ℎ𝑖𝑖𝑡𝑡− (1 − 𝛿𝛿)ℎ𝑖𝑖𝑡𝑡+ 𝑅𝑅𝑡𝑡−1𝑏𝑏𝑖𝑖𝑡𝑡−1 = 𝑦𝑦𝑖𝑖𝑡𝑡+ 𝑏𝑏𝑖𝑖𝑡𝑡− ∅(𝑏𝑏𝑖𝑖𝑡𝑡− 𝑏𝑏𝑖𝑖)2
For the flow of wealth constraint 𝑏𝑏𝑖𝑖 denotes the debt of agent i, R is the gross interest rate, and
𝑦𝑦𝑖𝑖 is household income of individual i.
Each agent has the following Euler equations consumption and housing respectively:
1 𝑐𝑐𝑖𝑖𝑡𝑡− 2∅(𝑏𝑏𝑖𝑖𝑡𝑡− 𝑏𝑏𝑖𝑖) = 𝐸𝐸𝑡𝑡( 𝛽𝛽 𝑐𝑐𝑖𝑖𝑡𝑡+1𝑅𝑅𝑡𝑡) 1 𝑐𝑐𝑖𝑖𝑡𝑡 = 𝑗𝑗 ℎ𝑖𝑖𝑡𝑡+ 𝛽𝛽( 1 − 𝛿𝛿 𝑐𝑐𝑖𝑖𝑡𝑡+1)
10 For impatient agents the set of equations is modified slightly to include a collateral constraint, as well the discount rate is different. The utility equation maximized is:
max 𝐸𝐸0� 𝛾𝛾𝑡𝑡(log 𝑐𝑐𝑖𝑖𝑡𝑡+ log ℎ𝑖𝑖𝑡𝑡 ∞
𝑡𝑡=0
)
where 𝑖𝑖 = {𝑛𝑛 + 1, 𝑛𝑛 + 2, … , 𝑁𝑁}. The budget constraint is as follows:
𝑐𝑐𝑖𝑖𝑡𝑡 + ℎ𝑖𝑖𝑡𝑡− (1 − 𝛿𝛿)ℎ𝑖𝑖𝑡𝑡−1+ 𝑅𝑅𝑡𝑡−1𝑏𝑏𝑖𝑖𝑡𝑡−1= 𝑦𝑦𝑖𝑖𝑡𝑡+ 𝑏𝑏𝑖𝑖𝑡𝑡
The collateral constraint, the main distinguishing between patient and impatient, is as follows:
𝑏𝑏𝑖𝑖𝑡𝑡 ≤ 𝑚𝑚𝑡𝑡ℎ𝑖𝑖𝑡𝑡
Where 𝑚𝑚𝑡𝑡 is the loan to value ratio, which is an exogenous variable calibrated from data. For the
impatient agents Iacoviello (2008) provides the following Euler equations:
1 𝑐𝑐𝑖𝑖𝑡𝑡 = 𝐸𝐸𝑡𝑡� 𝛾𝛾 𝑐𝑐𝑖𝑖𝑡𝑡+1𝑅𝑅𝑡𝑡� + 𝜆𝜆𝑖𝑖𝑡𝑡 1 𝑐𝑐𝑖𝑖𝑡𝑡 = 𝑗𝑗 ℎ𝑖𝑖𝑡𝑡+ 𝛾𝛾𝐸𝐸𝑡𝑡� 1 − 𝛿𝛿 𝑐𝑐𝑖𝑖𝑡𝑡+1� + 𝑚𝑚𝑡𝑡𝜆𝜆𝑖𝑖𝑡𝑡
Note the Lagrange multiplier will be strictly positive given that 𝛾𝛾 < 𝛽𝛽, this implies that the patient agents’ behavior will determine the interest rate.
The economy can then be seen to consist of a set of stationary stochastic processes for the endogenous variables {ℎ𝑡𝑡, 𝑐𝑐𝑡𝑡, 𝑏𝑏𝑡𝑡, 𝑅𝑅𝑡𝑡}𝑡𝑡=0∞ , where ℎ𝑡𝑡= {ℎ1𝑡𝑡, … , ℎ𝑁𝑁𝑡𝑡}, 𝑐𝑐𝑡𝑡 = {𝑐𝑐1𝑡𝑡, … , 𝑐𝑐𝑁𝑁𝑡𝑡}, and 𝑏𝑏𝑡𝑡 =
{𝑏𝑏1𝑡𝑡, … , 𝑏𝑏𝑁𝑁𝑡𝑡} . These vectors satisfy the above constraints and Euler equations, as well as the following
11 �(𝑐𝑐𝑖𝑖𝑡𝑡+ (ℎ𝑖𝑖𝑡𝑡− (1 − 𝛿𝛿)ℎ𝑖𝑖𝑡𝑡−1) 𝑁𝑁 𝑖𝑖=1 ) + � ∅(𝑏𝑏𝑖𝑖𝑡𝑡− 𝑏𝑏𝑖𝑖)2 𝑛𝑛 𝑖𝑖=1 = � 𝑦𝑦𝑖𝑖𝑡𝑡 ≡ 𝑌𝑌𝑡𝑡 𝑁𝑁 𝑖𝑖=1
For the market clearing condition given above 𝑦𝑦𝑡𝑡 = {𝑦𝑦1𝑡𝑡, … , 𝑦𝑦𝑁𝑁𝑡𝑡}, and 𝑚𝑚𝑡𝑡 along with the initial
conditions {ℎ𝑡𝑡−1, 𝑏𝑏𝑡𝑡−1, 𝑅𝑅𝑡𝑡−1} are determined from data. The individual specific initial values are filled
using log-normal distributions, that distribution will be used in this thesis as well. This yields 4𝑁𝑁 + 3 equations, where 𝑁𝑁 is the number of agents in the economy. Iacoviello (2008) found that using N>500 did not add anything to the results.
For individual specific income Iacoviello (2008) uses the following equation:
𝑦𝑦𝑖𝑖𝑡𝑡 = 𝑓𝑓𝑖𝑖𝑎𝑎𝑡𝑡𝑧𝑧𝑖𝑖𝑡𝑡
Where 𝑓𝑓𝑖𝑖 is the individual specific fixed effect, 𝑎𝑎𝑡𝑡 is the aggregate component, and 𝑧𝑧𝑖𝑖𝑡𝑡 is the
idiosyncratic component. This then gives the following for the autoregressive equations, both of which are set to equal zero in the initial steady state:
𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎 𝑡𝑡 = 𝜌𝜌𝑎𝑎 𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑡𝑡−1+ 𝑒𝑒𝑎𝑎𝑡𝑡 , 𝑒𝑒𝑎𝑎 ~ 𝑁𝑁(0, 𝑘𝑘) 𝑙𝑙𝑙𝑙𝑙𝑙𝑧𝑧𝑖𝑖𝑡𝑡 = 𝜌𝜌𝑧𝑧 𝑙𝑙𝑙𝑙𝑙𝑙 𝑧𝑧𝑖𝑖𝑡𝑡−1+ 𝑒𝑒𝑖𝑖𝑡𝑡 , 𝑒𝑒𝑖𝑖𝑡𝑡 ~ 𝑁𝑁(−𝑥𝑥𝑡𝑡, 𝑣𝑣𝑡𝑡2) 𝑥𝑥𝑡𝑡 =(𝑣𝑣𝑡𝑡 2− 𝜌𝜌 𝑧𝑧(1 − 𝜌𝜌𝑧𝑧) ∑𝑡𝑡−1𝑖𝑖=𝑜𝑜𝜌𝜌𝑧𝑧2(𝑡𝑡−1−𝑖𝑖)𝑣𝑣𝑖𝑖2) 2 𝑣𝑣𝑡𝑡2 = 𝑣𝑣𝑎𝑎𝑣𝑣(log 𝑦𝑦𝑡𝑡) − 𝜌𝜌𝑧𝑧2𝑣𝑣𝑎𝑎𝑣𝑣(log 𝑦𝑦𝑡𝑡−1) − (1 − 𝜌𝜌𝑧𝑧2)𝑠𝑠2
Finally, we have the equation for the loan to value ration as follows:
𝑚𝑚𝑡𝑡 = (1 − 𝜌𝜌𝑚𝑚)𝑚𝑚𝑠𝑠𝑠𝑠+ 𝜌𝜌𝑚𝑚𝑚𝑚𝑡𝑡−1+ 𝑒𝑒𝑚𝑚𝑡𝑡 , 𝑒𝑒𝑚𝑚𝑡𝑡 ~ 𝑁𝑁(0, 𝜎𝜎𝑚𝑚2)
The values of parameters used in Iacoviello (2008) which will also be used in this thesis are summarized in the following table:
12 Table 1: Parameter Values
Parameter Interpretation Value
𝛾𝛾 Discount factor, impatient agents 0.865
𝛽𝛽 Discount factor, patient factor 0.965
𝑗𝑗 Weight on housing in utility function 0.117
𝛿𝛿 Housing depreciation rate 0.04
𝑚𝑚 Loan-to-value ratio 0.729
𝑛𝑛/𝑁𝑁 Fraction of patient agents 0.65
∅ Bond adjustment costs 0.0001
𝜌𝜌𝑧𝑧 Auto-correlation coefficient of individual
income 0.75
With the exception of the bond adjustment cost these parameters were assembled from an assortment of literature, and were determined either by empirical studies or observations, for further details see Iacoviello (2008).
In summary initial steady states for endogenous variables are determined by using data on aggregate observations to generate log-normal distributions for the population. Exogenous variables are determined in a similar manner for the entire time period in question, with the difference that the income process coefficients are determined by generating trend and cyclical component using a bandpass filter. The system of equations is then used to generate time series for the endogenous variables, most relevantly the debt position.
The model was found to be robust in variation of some of the parameters, as well as the model was cross referenced with a transitional dynamics version of the model which mitigated the issue that linearization would pose due to potentially binding constraints.
The main findings of Iacoviello (2008) were that the empirical observations mentioned could be explained in terms of the framework just provided. More specifically it was found that the model was able to approximate the debt to income ratio in the 1963-2003, that it could roughly capture the cyclical nature of debt, and furthermore that it could replicate the results of Krueger and Perri (2006) in which
13 income inequality increases were greater than consumption inequality increases. It should be noted that a more recent study by Aguiar and Bils (2011) found that income inequality increases have been
accompanied by proportional increases in income inequality. However Aguiar and Bils (2011) did not consider data for the top five percent of income earners, thus for this thesis the contention of Krueger and Perri (2006) will be assumed to hold. Finally Iacoviello (2008) found that in the model provided debt increased as a result of income inequality increases.
1.2.
Additional Supporting Literature
In this thesis the primary aim will be to extend the model developed in Iacoviello to include delinquency. As well the model will be updated to include more recent data that takes into account the most recent financial crisis. Therefore this thesis will seek to examine the effect of income inequality of delinquency in the time period 1991-2012.
Given the results found in Iacoviello (2008) in which debt increases were tied to income increases as well as the debt cycle and the economic activity cycle being correlated it stands to reason that Iacoviello’s framework could be extended to include debt delinquency.
The mechanism is fairly straight forward. If debt increases going into the peak of the business cycle there could momentum in the lending market that causes debt to increase past the peak of economic activity. As economic activity declines there would be an increasing debt to income ratio that would make it more difficult to repay debts which would cause increased delinquency coupled with falling consumption. This along with an overall increase in debt resulting from income inequality would cause the magnitude of the delinquency to be amplified.
Once this delinquency reached a certain threshold it could trigger a crisis as outlined in as banks cut lending due to unprecedented delinquency which could then lead to the fire sale of assets causing a
14 loss spiral as outlined in Brunnermeier (2009). High delinquency rates could then cause a prolonged recession as banks faced unknown conditions, which would hinder lending to smaller lenders with lower credit ratings thereby causing debt to decrease. In the process this reduces total consumption due to the lower marginal propensity to consume of higher income individuals (Kruger & Perri, 2006). This would lead to a protracted period of lower economic activity due to inefficient credit allocation as outlined by Bernanke (1983). Thus the increase of income inequality over the past several decades could then be viewed as a direct cause of the most recent financial downturn in the United States, as well as a contributing factor to the prolonged period of low economic activity following the downturn.
A survey of literature on economic stability found that to date there has not been a direct connection of income inequality increases to major financial downturn, although the anecdotal evidence of there being large income inequality increases preceding both the Great Depression and the more recent financial crisis of 2008 suggests quite strongly that there may be a connection. In the literature the only study found that connected income inequality to economic instability was Allesina & Perotti (1996) which examined a political channel in which it was found that income inequality lead to social unrest which increased the likelihood thereby increasing uncertainty of property rights in turn
decreasing investment and consequently decreasing growth as well. Other papers examining economic instability tended to focus on debt and asset prices, for instance Brunnermeier (2008) and Han & Lee (2012) or the effects of aggregate investment, such as Pindyck (1993).
As for debt delinquency there are not any comprehensive studies linking income inequality and debt delinquency. The most straight forward explanation of debt delinquency is that it is linked to unemployment (Agarwal & Liu, 2003). Thus as people become unemployed they are unable to meet their debt obligations. This however is not an all-encompassing explanation though as it does not explain how consumer debt delinquency can increase during times of increasing economic activity and
15 employment, which was observed in the period 1995-2001 (Agarwal & Liu, 2003). Thus other
explanations are needed.
Composition effects also play a role in determining debt delinquency (Gross & Soulels 2002, Danis & Cross 2008). As debt is issued the more credit worthy borrowers obtain financing before less credit worthy customers, thus as more debt is issued the quality of the borrower pool decreases. For instance, Danis and Cross (2008) found that the rate of debt delinquency for sub-prime mortgages was approximately five times higher than it was the regular mortgage market, and that the sub-prime mortgage market had significantly increased in size. Thus as the total amount of debt grew the delinquency rates increased.
Besides composition effects another explanation is that as financial markets developed the costs associated with delinquency and bankruptcy declined. Thus the lower costs of delinquency and
bankruptcy compared to the cost of maintaining the loan in good status fell, causing delinquencies to increase (DeVaney and Lytton 1995, Gross and Soulels 2002, Agarwal and Liu 2003). At the same time though one would expect the accuracy of loan issuance to improve, contributing to a declining trend in debt delinquency.
In Figure 1 the consumer debt delinquency rates from 1991 until 2013, with the recessions highlighted in grey are shown. The most prominent feature of this graph is that each recession is followed by a period of declining debt deduction rates. Although the data set is somewhat limited it appears that debt delinquency is strongly counter-cyclical to economic activity. In the long-run there seems to be a trend of decreasing delinquency rates. Thus the observation of Agarwal & Liu (2003) that delinquency was found to increase with economic activity was correct; however it only described the upward section of a debt delinquency cycle.
16 From these explanations of debt delinquency one can draw approximate parallels between the behavior of debt and debt delinquency, namely that like debt, debt delinquency will have both trend and cyclical components across time. The trend component for delinquency rates is somewhat different than for debt in that it has a zero lower bound. Over time it stands to reason as financial markets develop average delinquency should continue to approach zero as banks improve their lending practice, however informational asymmetries along with structural decreases in the borrowers’ cost of
delinquency will prevent delinquency rates from being zero.
Meanwhile, the debt delinquency cycle, which is of primary significance for this thesis, can be seen to be fundamentally determined by real business cycle, driven by fluctuations in the income and wealth of borrowers caused by changes in employment status and asset returns. Herein lays the role for income inequality. When an economic downturn hits the debt delinquency rates will be to a large extent determined by the financial cushion of the individuals compromising the economy this in turn is
determined by the income inequality (Raskin, 2013). Of secondary significance will be the compositional effects. This ties back to Bernanke (1983), in which after downturn lenders will seek out the most stable credit worthy borrowers, then as economic activity increases lending will increase to other borrowers which will lead to a lagged increase in delinquency rates.
Given these parallels between debt behavior and the observations of debt delinquency, the framework provided in Iacoviello (2008) is suitable for looking at the effect of income inequality on debt delinquency as it provides a means to keep track of all the individual debt positions, as well as the debt delinquency positions which will be added for this thesis. The debt delinquency positions can be
aggregated to generate a measure of delinquency that can be compared to observed data. Since income inequality is of central significance in determining the debt/wealth positions in Iacoviello (2008) it should by extension explain debt delinquency rates as well.
17 Figure 1: Debt Delinquency 1991-2012
To examine this consider the following two-period model in which there is a finite number of individuals. To begin assume that total output is fixed for each period and that the growth rate of total output is known. Assume that individual consumption is a function of income and that the marginal propensity to consume is lower at lower income levels. This implies that there will need to be lending and borrowing to clear the goods market, and that below a certain income level individuals will borrow, and that above a certain income individuals will lend. This situation is outlined in the following figure:
18 Figure 2: Diagram Illustrating First Period Borrowing and Lending
Assume then that the lending is based on the expected earnings of the individual in the second period, and that this is expected to be the same as the first period. Since the model has two-periods money is only lent in the first period and subsequently repaid in the second period. Thus in the second period consumption of each individual will be equal to their income plus loan repayments.
Next impose a minimum consumption constraint in the second period. This minimum
consumption can be seen as a poverty line below which individuals will simply forgo repaying their loans in order to make necessary purchases. The minimum consumption threshold is also assumed not to be known when the loans are made. This situation is shown in the following diagram:
Individuals n Am ou nt Income Consumption N borrowing lending
Period 1
19 Figure 3: Diagram Illustrating Second Period Borrowing and Lending
As shown in the diagram all individuals with income less than individual m will enter delinquency as their expected consumption is below their actual consumption. In this simplified framework the amount of delinquency is determined by four factors; the income inequality level, the initial amount of lending, the interest rates charged on loans and the minimum consumption level.
An income inequality increase will make the income curve more concave. This shifts the intersection of the expected consumption curve rightwards, thereby increasing delinquency. Here delinquency can be seen as the sum of the differences between minimum consumption and expected consumption such that expected consumption is less than the minimum consumption. It is simple to show that ceteris paribus increasing the minimum consumption level will shift the intersection
rightwards which will have the same effect. Increasing the interest rate and initial loan amounts will also increase delinquency as it lowers the expected period-two consumption of all individuals who borrowed in period-one. Individuals n Am ou nt
Income + Loan Repayment Consumption
N delinquency
cmin
20 Using this simplified framework it is possible to explain the most recent crises. A combination of increased debt holdings by lower income individuals along with increased income inequality pushed a large segment of society towards their minimum consumption threshold. This was justified as increasing lending kept income steady. Then once an income shock hit the segment of society with low incomes and high debt entered delinquency en-masse as they were simultaneously pushed past their minimum consumption thresholds. This in turn triggered uncertainty which reduced lending and in turn output.
2. Outline of the Model
2.1.
Environment
The model that will be used in this seeks to maintain as many aspects of the model presented in Iacoviello (2008) as possible, while adding the dimension of debt delinquency. To that end as in
Iacoviello (2008) the economy will consist of a large number of infinitely lived agents. These agents will be separated into two groups as before, patient agents and impatient agents that differ in their discount rates and how they are able to interact with the credit market. All agents will differ in their income, which is determined initially by a stochastic endowment. Income can be used to accumulate financial and housing assets over time. Agents will be indexed by 𝑖𝑖.
The credit market is where this model will differ fundamentally from Iacoviello (2008). Instead of one period loans being paid with probability one each period agents will in certain cases be allowed to become delinquent on their debts. Debt delinquency will be introduced by adding a consumption constraint on the credit constrained agents. This consumption constraint intends to add an aspect of imperfect foresight into the credit market in which the impatient agents under estimate the amount of consumption they require. In the model this will be represented by the ‘optimal’ amount of
21 consumption being below a certain threshold. This can be seen as representing a poverty line which is required to maintain a certain standard of living that individuals misjudge.
So how is delinquency different from being allowed to take on more debt? In both cases there is an increase of debt for the individual in question. Delinquent debt is simply a category of debt that should have been repaid but was not due to insufficient resources. Implicit in this is that delinquency does not necessarily increase with debt since it is subject to the minimum consumption condition. In the original framework debt was given in the form of one period loans, increases in debt were
accommodated by issuing new loans of greater amounts. The extension made in this thesis allowed debt to exist for more than one period in the event that there weren’t sufficient funds to repay the debt. In other words a portion of the previous periods’ debt was allowed to remain unpaid, which was then classified as delinquent debt.
Thus delinquent debt arises as a result of minimum consumption constraints placed on the individuals. This implies that the nature of delinquent debt is different from regular debt increases in that a normal debt increase would result from an optimization decision to smooth consumption, whereas adding delinquent debt was a result of a the individual underestimating the amount of expenditures that they needed to make and then adjusting this amount upwards to the minimum consumption threshold by withholding debt repayment.
Adjusting the consumption upwards alters the dynamics of the model somewhat as debt and consumption levels are adjusted for other agents in the economy as well in order to ensure that the market clears. This has effects on the dynamics of the model as the income and debt distributions are changed. Consequently delinquent debt has a different effect than a normal increase in debt.
22 When ‘optimal’ consumption is found to be below the minimum consumption threshold the impatient agent will choose to consume the difference, financing the difference either by entering delinquency on previously held loans or by borrowing. The difference in consumption then will be proportionately deducted from the lenders of the delinquent loans. The delinquent loan will then be given priority before consumption until the delinquent loan is repaid, subject to the consumption constraint. This repayment will be treated as a windfall by the lenders who held delinquent debt.
Besides the income windfall above the minimum purchasing thresholds, delinquent debt was also repaid by preference. Within the Iacoviello (2008) framework this was accomplished by using the difference in the previous two periods’ debt to repay delinquent loans at the beginning of each period in the case that the debt position was reduced.
The income of the agents will be dealt with in the same way as in Iacoviello (2008), namely that income will be divided into three components; the individual specific fixed effect, an aggregated
component that changes with time, and individual specific effect that varies with time. Agents will differ in their initial income endowment, which was the source of income inequality in the model. This initial endowment will be based on income inequality observations, and be assigned by sampling a log-normal distribution.
2.2.
Patient Agents
For the patient agents the set of equations will be assumed to be identical to Iacoviello (2008). The rationale for this is that the patient agents will be assumed to be the responsible agents, who can accurately determine their consumption needs, thus will not need to withhold debt repayment to increase consumption.
23 Besides not entering delinquency themselves there was the additional assumption that the patient agents will be assumed to not expect delinquency on the loans they make. This can be interpreted as imperfect foresight on the part of lenders. Logically lenders wouldn’t make loans to an agent who is expected to become delinquent on a loan, thus this won’t be a consideration in the lenders utility optimization.
As a result of these assumptions the utility optimization problem, wealth constraint, and Euler equations will remain the same as the set of equations for the patient agents of Iacoviello (2008) outlined in the literature review.
2.3.
Impatient Agents
As was the case for the patient agents the set of equations describing the impatient agents will remain the same as they were in Iacoviello (2008). The addition of this thesis does not alter the actual non-linear system itself; it superimposes an algorithmic decision framework on top of it. This is a
fundamental difference from the majority of economic models in that it intends to introduce an element of realism to the DSGE framework by approximating behavior of agents that don’t properly form
expectations, and instead react to circumstances as they occur. Thus in this model agents will deal with extenuating circumstances in a rule based manner, and once these circumstances are dealt with the agents revert to making optimal decisions based on utility. The idiosyncratic framework is essential for this as the delinquents agents’ debt position can be tracked on an individualized basis.
As mentioned, delinquent debt is created when an individual’s income is at a level that debt repayment would require the individual to consume less than a minimum purchasing threshold. This delinquent debt will be pooled for each period and be assigned to the previous periods’ lenders in proportion to the amount of the originals loans, so for example if a lender in the previous period was
24 responsible for 5% of the loans they will also be allocated 5% of the delinquent debt. Delinquent debt pools will be repaid in chronological order. This will be done on a proportional basis, thus the individual that held 5% of the delinquent debt pool would also receive 5% of the total available funds available to repay delinquent debt.
To add delinquency to the model the following additions will be added to the framework presented in Iacoviello (2008). At the beginning of each period each agent’s income will be determined. If an agent has a debt that is delinquent that portion of the debt will be repaid with priority. Whether or not delinquent debt is repaid will depend on its position compared to a minimum income threshold below which individuals will not allocate any funds towards repaying delinquent debt.
If the delinquent debt payment is greater than the difference between the individual’s income and the minimum consumption threshold then the difference between the minimum consumption threshold and the individual’s income will be carried forward as delinquent debt. All agents that enter delinquency or who were already in delinquency will then automatically be assigned an income equal to the minimum consumption level.
If the agent’s income exceeds the minimum income threshold then difference will be used to repay the delinquent debt up to point where their disposable income equals the minimum income threshold. This leads to two categories of debt in the model, the delinquent debt that agents expected to be able to repay but couldn’t, and the ‘regular’ debt. Note that regular debt is treated similarly to Iacoviello (2008) in that it is issued as one-period loans, except that reductions in debt are counted towards delinquent debt repayment.
Once the delinquency and income positions have been updated at the beginning of the period consumption and borrowing can be determined. To do this first the debt positions are updated then consumption and housing is determined by solving the system of linear equations in a similar manner to
25 Iacoviello (2008). Here the delinquency debt repayment is processed prior to the optimal consumption decisions of the agents so that the windfall of delinquent debt repayment can be taken into account to determine the amount of ‘regular’ borrowing that will determine the next period’s debt.1
After the optimal consumption has been determined the new delinquent debt pool is calculated. To determine the new delinquent debt the consumption of agents whose optimal consumption level is below the minimum consumption threshold is increased to the minimum consumption threshold. This applies to the housing purchase amounts as well. These delinquency positions are then recorded individually for each agent so that they can be used in later periods to determine debt repayments as outlined above. It should be noted that it is required that this difference exceed the amount of borrowing in previous period.
If the previous period’s borrowing is not greater than the difference between the ‘optimal’ consumption and the minimum consumption the difference will be filled with current period borrowing so that those individuals with consumption less than minimum consumption are able to achieve the minimum consumption level, thus this amount will not be added to the delinquent debt pool.
If there are agents in the economy who have an ‘optimal’ consumption level below the minimum consumption level then the consumption of the other agents in the economy will have to be adjusted in order to maintain the goods market constraint. Firstly the consumption of agents with fund shortages will have to be increased to their optimal housing and consumption choice given the
threshold level. As this amount will be in part due to new delinquency and in part due to intratemporal increases in debt there will be two different stages of reducing the consumption of remaining agents in the economy in order to clear the market.
26 First the consumption of the holders of the previous period’s debt will have to be reduced. To do this first the new delinquent debt positions will be aggregated. Then, as described above, the consumption of the periods’ lenders will be reduced by the amount of the proportion of the new delinquent debt pool given to them.
Once the expenditure of the delinquent debt holders is reduced the consumption positions of the agents then needs to be checked again to see which agents fall below the minimum expenditure threshold. The difference between the minimum expenditure threshold and the available funds for expenditures will then be aggregated. This amount then will be proportionally deducted from the remaining agents in the economy.
Calculating delinquency in this way allowed for an individual’s debt position to increase without necessarily having to increase their delinquency, which is what was observed in reality.
The minimum consumption threshold will be defined to be a fraction of trend output. The minimum consumption threshold will be a constant term that is applicable to all agents in the economy. This fraction corresponds to the sum of the housing purchases and consumption.
In summary we have the following equations for delinquency component of the model.
𝐷𝐷𝑖𝑖,𝑡𝑡 = � 𝑑𝑑𝑖𝑖,𝑡𝑡 𝑡𝑡 𝑡𝑡=0 𝑒𝑒𝑖𝑖,𝑡𝑡= 𝑐𝑐𝑖𝑖,𝑡𝑡+ ℎ𝑖𝑖,𝑡𝑡 𝑒𝑒𝑖𝑖,𝑡𝑡= ⎩ ⎨ ⎧𝑐𝑐𝑖𝑖,𝑡𝑡− 𝑐𝑐𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡+ ℎ𝑖𝑖,𝑡𝑡 𝑐𝑐− ℎ𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 , 𝑖𝑖𝑓𝑓 𝑐𝑐𝑖𝑖,𝑡𝑡> 𝑐𝑐𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 𝑎𝑎𝑛𝑛𝑑𝑑 ℎ𝑖𝑖,𝑡𝑡 > ℎ𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 𝑖𝑖,𝑡𝑡− 𝑐𝑐𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 , 𝑖𝑖𝑓𝑓 𝑐𝑐𝑖𝑖,𝑡𝑡> 𝑐𝑐𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 ℎ𝑖𝑖,𝑡𝑡 − ℎ𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 , 𝑖𝑖𝑓𝑓 ℎ𝑖𝑖,𝑡𝑡 > ℎ𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 0 , 𝑙𝑙𝑜𝑜ℎ𝑒𝑒𝑣𝑣𝑤𝑤𝑖𝑖𝑠𝑠𝑒𝑒
27 𝑝𝑝𝑖𝑖,𝑡𝑡= � 𝑦𝑦𝑖𝑖,𝑡𝑡− 𝑒𝑒𝑖𝑖,𝑡𝑡 , 𝑖𝑖𝑓𝑓 𝐷𝐷𝑖𝑖,𝑡𝑡−1 ≥ 𝑦𝑦𝑖𝑖,𝑡𝑡− 𝑦𝑦𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 𝐷𝐷𝑖𝑖,𝑡𝑡−1 , 𝑖𝑖𝑓𝑓 0 ≤ 𝐷𝐷𝑖𝑖,𝑡𝑡−1 < 𝑦𝑦𝑖𝑖,𝑡𝑡− 𝑦𝑦𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 0 , 𝑙𝑙𝑜𝑜ℎ𝑒𝑒𝑣𝑣𝑤𝑤𝑖𝑖𝑠𝑠𝑒𝑒 𝑦𝑦𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡 = 𝜃𝜃𝑦𝑦�𝑁𝑁𝑡𝑡
Above we have 𝐷𝐷𝑖𝑖,𝑡𝑡 as the total delinquent debt of individual i in time period t, 𝑑𝑑𝑖𝑖,𝑡𝑡 is the
delinquent debt added to individual i’s total delinquent debt in period t, and 𝑝𝑝𝑖𝑖,𝑡𝑡 is the delinquent debt
payment that individual i repays in period t.
For the minimum expenditure formula [add equation number] given by 𝑒𝑒𝑖𝑖,𝑡𝑡 we have 𝑦𝑦�𝑡𝑡 the
de-trended real income in period t and 𝜃𝜃 is the fraction of average total de-de-trended output that constitutes the poverty line. Note that the level of h and c are determined by the first order conditions. Rather than use an inflation adjustment a fraction of de-trended real output is used since inflation is connected to economic activity, as well income is already adjusted for inflation. The aim is to present the poverty line a relative position in society. Tying this to output reflects reality as in practice poverty is essentially related to the amount of total annual output an individual is able to obtain. Social and structural considerations will likely cause this fraction to be less volatile than economic growth, in essence it accounts for inertia of preferences. According to 2012 US census data the poverty line was equal 0.22 of the average income. This value was used initially and then calibrated.
Alternatively a constant annual growth rate can be applied. This could be interpreted as people’s expectations increasing each year regardless of economic activity due to a continuously increasing expectation of consumption. In other words people will always want more no matter what, and that minimum amount will be based on their previous requirements.
28 𝑐𝑐𝑖𝑖𝑡𝑡+ ℎ𝑖𝑖𝑡𝑡− (1 − 𝛿𝛿)ℎ𝑖𝑖𝑡𝑡−1+ 𝑅𝑅𝑡𝑡−1𝑏𝑏𝑖𝑖𝑡𝑡−1 = 𝑦𝑦𝑖𝑖𝑡𝑡− 𝑝𝑝𝑖𝑖,𝑡𝑡 + 𝑏𝑏𝑖𝑖𝑡𝑡
As mentioned the Euler equations remain unchanged. The final consideration is the new
delinquent debt which is determined once the system of equations for period t has been solved. For this we have the following equation:
𝑑𝑑𝑖𝑖,𝑡𝑡= � 𝑒𝑒𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡− 𝑒𝑒𝑖𝑖,𝑡𝑡 , 𝑖𝑖𝑓𝑓 𝑒𝑒𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡− 𝑒𝑒𝑖𝑖,𝑡𝑡 > 0 𝑎𝑎𝑛𝑛𝑑𝑑 𝑏𝑏𝑖𝑖,𝑡𝑡−1 > 𝑒𝑒𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡− 𝑒𝑒𝑖𝑖,𝑡𝑡 𝑏𝑏𝑖𝑖,𝑡𝑡−1 , 𝑖𝑖𝑓𝑓 𝑏𝑏𝑖𝑖,𝑡𝑡−1 < 𝑒𝑒𝑚𝑚𝑖𝑖𝑛𝑛,𝑡𝑡− 𝑒𝑒𝑖𝑖,𝑡𝑡 0, 𝑙𝑙𝑜𝑜ℎ𝑒𝑒𝑣𝑣𝑤𝑤𝑖𝑖𝑠𝑠𝑒𝑒 𝑋𝑋𝑡𝑡 = � 𝑑𝑑𝑖𝑖,𝑡𝑡 𝑁𝑁 𝑖𝑖=1 𝑋𝑋 = � 𝑋𝑋𝑡𝑡 𝑡𝑡 𝑖𝑖=0
The aggregated delinquency for period t is given by 𝑋𝑋𝑡𝑡, and the total delinquency is given by X.
Thus the time periods of the Iacoviello framework are essentially sub-divided into three parts. In the first delinquent debts are repaid, in the second the expenditure levels are determined, and in the final stage new delinquencies are determined. Once the delinquencies are determined the ratio of delinquent debt to total debt can be determined for each period and compared to the actual data in order to test the model.
3. Data, Calibration and Simulation
The data set used consisted of for the most part updated versions of the data sets used in Iacoviello (2008). Data treatment was identical as in Iacoviello (2008), with the exception of income
29 inequality data. For a full listing of the data sources used please refer to the appendix of Iacoviello (2008).
Data used for income inequality dealt with somewhat unconventionally. The income inequality measure used in Iacoviello (2008) was log-standard deviations of employed adult males between the age of 18-65 derived from Eckstein and Nagypal (2004), along with an extrapolated value for the 2003 data point. In this thesis it was not possible to use this data as the Eckstein and Nagypal (2004), paper was not updated for the time period 2003-2012. To get around this issue a function was derived from Gini coefficient data to create a close approximation of this data set used in Iacoviello (2008). The Gini index used is found in the ‘UNU-WIDER, ‘World Income Inequality Database (WIID3.0A)’, June 2014’ database. There was a very close fit for this function as the Gini coefficient and the inequality measure used in Iacoviello (2008) moved essentially in tandem with the Gini coefficient. This function was then used to generate a data set for the time period 1991-2012 that was used in the simulations.
The parameter values used in the trial run in this thesis were for the most part identical as they were in Iacoviello (2008). The main differences were that I for purposes of this thesis a lower number of agents were used, and the addition of a minimum consumption purchase constraint in order to allow for delinquencies.
Due to practical purposes of calculation time the number of agents used in this thesis was set to equal 50. In Iacoviello (2008) the non-linear system was solved a single time, where as in this thesis the system was solved for each period to determine the optimal consumption level given the changes in income caused by repaying delinquent debt. Hence the number of agents used was reduced in order to speed up calculation times. This did not drastically alter the results from test cases of 500 agents, as the desired characteristics could still be observed.
30 The other parameters that needed to be calibrated for this thesis were the minimum
consumption level and minimum housing levels which would require agents to take on additional debt, as well as the threshold of income which was required for agents to repay their delinquencies.
The minimum housing and consumption levels required determined the ease at which
individuals enter delinquency. This is because if these thresholds were higher individuals would be more likely to require additional borrowing, especially if they were at lower equilibrium income levels. On the other hand the minimum income level required before which delinquent debt was repaid will determine the persistence of delinquent debt, and thus have more of an influence on overall delinquency levels, as well as delinquency rate volatility.
The actual simulation of the model was carried out differently than Iacoviello (2008) since in each period the income, consumption, housing, and debt levels had to be altered to allow for
delinquencies. Exogenous factors were calculated in a similar manner as in Iacoviello (2008); the main difference was that the model put forward in this thesis iterated each period of the model put forth in Iacoviello (2008).
The simulation was performed as follows. First the model was run for the entire time period in a similar fashion to Iacoviello (2008). The purpose of this was three-fold. Firstly it was used to find the steady-states values of income that would be used for subsequent iterations. These steady-state values are also used for the initial values of the first simulation. Secondly it generated the exogenous shocks in a manner identical to Iacoviello (2008) for use in subsequent iterations. Finally, the first simulation of the model which used all time periods was used to generate data for the second period.
Once the initial simulation had been performed the initial delinquencies and delinquency repayments were calculated using the second period data in order to generate initial values that were used in further iterations of the model.
31 The delinquencies were calculated by comparing the minimum thresholds of consumption and housing of the constrained individuals to their actual consumption and housing positions. In the event that the actual position was lower than the threshold the consumption or housing position of that individual was adjusted upwards. This increase in consumption or housing was accompanied by a decrease of non-constrained lenders’ consumption or housing level, as well lenders increased the lending level to account for the increase of borrowing by individuals who took on delinquent debt.
As the individuals who increased their borrowing were the debt constrained individuals their delinquency can be interpreted as an increase of borrowing caused by the delinquent individuals receive the same amount of money they would have normally, and then ‘undoing’ the repayment of a part of their debt obligation from the previous period. In the original version of the model the entire loan would be repaid, and then an entire new loan would be made to cover the entirety of the purchase
requirement.
Once the initial delinquency levels of the individuals have been calculated the first round of delinquent debt repayment can take place. In this procedure the holder of delinquent debt was checked for surplus income above the minimum income threshold. If they had surplus income this amount was used to reduce the amount of delinquent debt they hold. As mentioned earlier the delinquent debt was repaid in chronological order on a proportional basis.
The debt delinquency repayment procedure was also the beginning of a three stage cycle that was repeated to generate the consumption, housing, income, and borrowing data for each period. It was followed by solving the actual model for optimal consumption and housing levels using the adjusted income levels using the data from the debt repayment procedure as the initial values for the given iteration. Once the model has been solved for the optimal values the new delinquencies for that given
32 period can be determined. This loop is repeated for each applicable period to generate the data set, including the delinquency rates of each period.
The following figure provides a diagram of the algorithm used:
Figure 4: Process diagram of the simulations
4. Results and Discussion
The algorithm outlined in section 3 was able to demonstrate the hypothesized behavior put forth in section 2 in which delinquency rates were expected to increase as a result of negative income shocks. From Figure 5, which shows the change in growth rate alongside the change in delinquency rates for a typical simulation, it can be seen that for the most part the slopes of each interval are of opposite sign. Thus a decrease in growth is associated with an increase in delinquency across most periods.
Solve for Steady States
Run complete
model with steady
states as initial
values.
Find
delinquencies
for period t = 1
Repay
delinquencies
Run iteration of
model
Find new
delinquencies
Repeat until data found for all time periods
33 Figure 5: Changes in debt and delinquency
With some lenience in interpretation it could also be argued that there is a trend of increase increasing delinquency rates that coincides with a trend of increasing income inequality. Looking at the trend lines for income variance shown in Figure 6 and the trend line for delinquency rates shown in Figure 7 it can be seen quite clearly that there are increasing trends for both. It should be noted though that the trend for debt delinquency increases was to a large extent determined by the calibration of the minimum consumption and housing thresholds. For instance, if there were no changes in the threshold values and they were initially set to quite low values delinquency rates would eventually reach zero. However as the aim of the thesis was to recreate this behavior this calibration was necessary to achieve the results of this thesis.
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15
Delta Growth and Delta Delinquency
Year C hange i n P er c ent age delta growth delta delinquency
34 Figure 6: Income variance of a typical simulation
Figure 7: Delinquency Rates
1990 1995 2000 2005 2010 2015 0.32 0.34 0.36 0.38 0.4 0.42 0.44 Income Variance Year V ar ianc e variance 1990 1995 2000 2005 2010 2015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Delinquency Rates Year P er cent D el inquenc y
35 Other possibilities for the delinquency trend would have been to base it on a more rigid
guideline such as the share of total income of the bottom decile. This would give a decreasing
delinquency rate over time as the growth of income of the lowest decile was than it was for the rest of the economy. This could be interpreted as an adaptive expectations view on the part of the lower class who expect their living standard to be based on the recent experiences. Alternatively this could be interpreted as a consequence of financial innovation through increased repayment enforcement ability which could put pressure on an individual’s ability to forgo loan repayment.
The trend of the data is somewhat ambiguous. Looking at Figure 1 it can be seen that there is an apparent spike of delinquency at the end of the early 90s recession, delinquency rates then fell into the mid-nineties. Following the decrease they increased for two years and then levelled off from the first quarter of 1997 until the recession in 2001, after the recession they fell approximately one percentage point in the lead up to the financial crisis. Before the crisis there was a turnaround in the movement of delinquency rates, they increased approximately two percentage points, peaking at the end of the recession. The overall trend for in the levels of delinquency rates is unclear.
The most significant feature of the data is a pattern in which there is a decline in delinquency rate after each recession. Preceding recessions there are either increasing delinquency rates, or
elevated levels of delinquency. Thus the cyclical pattern is fairly consistent, however there did not seem to be a clear trend in the levels of delinquency. This is fairly representative of the data generated by the simulations, although the simulations seemed to show a slight upward trend in overall level of
delinquency rates, however as mentioned there were several factors in determining this, some of which were not accounted for directly in the model.
The results of the simulation gave somewhat more volatile results than the data for the same time period; however the difference was not that great. In the data there is a 2% range in the consumer
36 loan delinquency rates, the simulations typically had a difference between maximum and minimum values of around 1.5%. This result though, given that the model exhibits higher growth volatility and does not take into account unemployment is surprisingly good at mimicking the behavior of delinquency rates on consumer loans.
In the end it was found that 1% annual increases on the minimum consumption and housing thresholds combined with a constant income requirement for the repayment gave the best results for delinquency rates.
Thus it was possible to imitate the delinquency observations to a large extent. Counter-cyclical behavior between output and growth was replicated, trends between income inequality and
delinquency levels were also replicated, as well as the magnitude of delinquency rate changes.
Given the results of the simulations it is reasonable to say that there was most likely a role of income inequality increases in triggering the most recent financial crisis through the fire-sale mechanism outlined in Brunnermeier (2009). The contribution of this thesis builds on the results of Iacoviello (2008) which showed how debt levels increased as a result of increases in income inequality. Not only were delinquency rates increasing, but debt levels overall were increasing. Consequently increases in delinquency rates when income inequality levels were higher resulted in much larger amounts of debt becoming delinquent.
Although in this model there are not asset sales to repay delinquent debt, in reality this would be the case. The fire-sale mechanism outlined in Brunnermeier (2008) would be sensitive to absolute amounts of asset sales, implying that increased income inequality will increase the likelihood of the fire sale events. This adds strength to the argument that income inequality increases were a significant factor in the most recent financial crisis, and likely the Great Depression as well.
37 Although the overall level of debt may increase the relative amount remains within a narrow range due to the accompanying increase in total debt. This implies that in this model that income inequality causes an increase in delinquency rates directly but due to the increasing level of total debt delinquency rates remained within a comparatively narrow range. In other words income inequality increases were interpreted through markets in terms of a more or less steady or falling delinquency rate which created a sense of lower risk even though the ‘debt constrained’ agents were taking on larger amounts of debt.
As a result there were larger amounts of debts which were more vulnerable to income shocks. Since the larger volumes of exposed debt were larger the impact on financial markets was amplified once the income shock occurred, leading to a severe downturn which had compounded effects on lending due segments of the lending markets relying on carryover financing practices. It is likely that the unprecedented increase in delinquency was due not only to a fall in income but to a drop in lending as well which created a feedback circle in which delinquency rates increased, a trend which reversed when income stabilized to the extent that they could compensate for the drop in lending. As well there was a large amount of default which lowered the delinquent debt levels adding to the reversal of the
delinquency trend following the recession.
The policy implication of this would be that improved macro-prudential supervision could reduce the severity of economic downturns through improved monitoring of exposed debt based on expected repayments that took into account minimum consumption levels, particularly on lower income individuals.
By reducing lending to individuals whose expected incomes were closer to the minimum consumption threshold the expected volume of delinquent debt caused by an income shock would be lower due the debt being held by individuals with more buffer in their income to maintain debt. There
38 would also be an added benefit of reducing housing price bubbles. By reducing the amount of lending to the lower income groups there is a reduction in the delusion of wealth. Lower income groups would have less funding to spend on housing resulting in lower returns to the housing markets. Lower returns to the housing market would put downward pressure on house prices and rental prices. All of these factors were issues in the most recent crisis and continue to be lingering problems.
The issue with this is of course is how the debt behavior would be altered, either the overall level of debt would be reduced or the lending market would be restricted to only wealthier individuals. In other words wealthier individuals would need to increase their borrowing and consumption. This would also create a problem as to whether or not interest rates would be lowered to wealthier
individuals thereby pushing them closer to their minimum consumption thresholds which in reality could be higher for individuals who have had historically higher income levels.
The implication of this then is that there should perhaps be restrictions placed on total lending levels based on the incomes of debt holders in combination with their expected incomes. From this estimates of debt delinquency levels based on income shocks could be created. This would give policy advisors an insight in the lending markets concerning what the impact of financial downturns would be. The results of this thesis shows that it would be reasonable to expect different consequences in
response to an income shock given different levels of debt and income inequality. Within the framework of this model the most severe downturns would be expected when there are high levels of debt in tandem with higher income inequality.
Actual data on the composition of the incomes of debt holders is difficult to find in reality. Anecdotally given that the lending standards were apparently low or lowered in the lead up to the recession one could reason that likely this was accompanied by an increase in lending to lower income individuals and hence increased the amount of debt that would likely become delinquent in the event of
39 an income shock. If this were the case for a given percent drop in output there would be an increased amount of delinquent debt. It would follow from this that if there were also a critical point at which the rate of asset sales resulting from delinquency triggered a spiral loss as outlined in Brunnermeier (2008) the chances of it being reached would be greater. In this case through the delinquency mechanism just outlined income inequality increases could be considered to be a direct contributing factor in triggering the financial crisis. To fully verify this however would require additional research to estimate the composition of the debt holders.
The performance of the model is evaluated on its ability to replicate a set of circumstances that are based on the behavior seen in reality. Specifically was the model able to show a counter-cyclical effect between output and delinquency rates, as well as explain an increasing trend for delinquency levels alongside increasing income inequality levels. The model was able to replicate these behaviors reasonably well thus the model performed reasonably well.
The patterns of the figures were not intended to replicate the data exactly. As in Iacoviello (2008) the figures shown were that of a typical simulation. Due to the way shocks were generated in the model there are not an exact consistent set of results to match the model. Instead the aim was to find a match in the behavior seen in the data, namely an inverse relationship between changes in output and changes in delinquency. In this regard the aim of the thesis was achieved.
5. Conclusion
In conclusion it was possible to generate a model to give a facsimile of the behavior of the debt delinquency between 1991 and 2012. The model presented in this thesis shows that there debt
delinquency can be introduced into the Iacoviello (2008) framework through the introduction of a minimum consumption threshold beyond which even though there was sufficient income for repayment
40 consumption took priority. The simulations resulted in debt delinquency behavior that was negatively correlated with the changes in growth.
More importantly for this thesis were the results of steady or slightly increasing delinquency rates despite increasing income inequality. One may have expected to see increasing delinquency rates since the total amount of delinquent debt was increasing. However increases in debt levels due to increased lending masked these increases in overall delinquency. This created a sense of normalcy in the delinquency rates which masked increases in the total volumes of delinquency rates. Thus when income shocks hit the economy faced unprecedented levels of delinquent debt from a normal or slightly above normal increase in delinquent debt, which magnified underlying problems in the debt markets by causing ‘overreactions’ based on unknown circumstances. So due to the increased level of debt held by agents whose total incomes were closer to their minimum consumption threshold the markets faced unseen levels of delinquent and defaulting debt. This contributed not only to the severity of the downturn via the spiral loss negative feedback mechanisms presented in Brunnermeier (2008) but also to the length of the recovery through reduction of lending to low-information borrowers’ due to an increase in uncertainty resulting from unprecedented volumes of delinquent debt, as outlined in Bernanke (1983).
The policy implications of the results are that more attention should be paid to the expected incomes of the recipients during the loan origination. By looking at the amount of debt vulnerable to income shocks the consequences of income shocks can be better anticipated which in turn could reduce the panic caused by problems in the financial markets. As well if the debt delinquency increase was seen in terms of structural terms, namely that the delinquencies were the result of the synchronized effects of an income shock, there could be a quicker return to an adjusted norm based on a sustainable level of
41 lending. This would improve the efficiency of credit allocation in the aftermath of crises reducing the amount of economic stagnation.
Further areas of research that would bolster the results of would include improving the model further to add debt default and to look at the effects of asset sales, specifically housing. In addition further research into the income composition of debt holders would also add to the results of this thesis and give a better indication of the usefulness of examining the expected incomes of debt holders. Looking at these areas may give further insights that could potentially be used to mitigate the effects of financial downturns.
42
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