Renting versus Buying: System Dynamics Approach to Housing
SiniSa Sovilj
University of Zagreb,
HR-10000 Zagreb, CROATIA
sinisa.sovilj@ieee.org
Marina Tkalec
Institute of Economics, Zagreb
HR-10000 Zagreb, CROATIA
mtkalec@eizg.hr
Paper to be presented at the 32nd International Conference of the System Dynamics
Society, Delft, Netherlands, July 20 — July 24, 2014
Abstract
This paper studies a widespread and important life dilemma of renting and buying a home.
We adopt a system dynamics approach to housing research and clarify the benefits of
hankk deli;
system dynamics and double-entry in the determinants of buying and
renting a home decision. We included all important inflows and outflows of money and
accumulation dynamics of assets, liabilities and equity for both dilemma choices. The
model is general in the sense that one can use data from any market, but in this paper the
parameters are estimated using Croatian historical data. We consider two policy
scenarios; one in which there are tax deductions on interest payments, and the other
without the tax policy measure. Our results suggest that the renting scenario is optimal in
comparison to the buying scenario when there are no tax deductions on interest payments.
This suggests that tax deductions should be introduced in case the government wants to
stimulate the real estate market and the construction sector, or abandoned if the
government perceives a housing bubble is being supported by a certain tax policy.
Keywords: equity flow, home ownership, home renting, system dynamics
Introduction
Buying or renting a home is a widespread personal dilemma and one of the most difficult
and most important ones, as it usually represents the largest life investment for most
people. In its core, the dilemma boils down to a choice between renting a home and renting
money from a financial institution in order to buy a home. Due to its large scale in financial
terms and far-reaching consequences from the dilemma holder’s view, it deserves the
attention of the dilemma holder in the first place, but also the attention of the public policy
maker, and the academia [1, 2].
A thirty-year period prior to the stock market collapse of 2007 that was coupled with
substantial increase in house prices, buying a house was considered a good investment.
Although the estimates for the US show that nominal house prices increased on average by
3 percent, while the rise in real prices, adjusted for inflation, was just a bit above zero [2,
3], housing was indeed a good investment because it was usually leveraged to a great
degree. For example, a house price increase of only three percent and a mortgage with a 20
percent down payment brings a 15 percent increase in homeowner’s equity. In bad times
however, leverage turns against the holder. A 20 percent down payment coupled with a 20
percent price decline, wipes out all of the buyer’s equity [3]. Therefore, taking up a
mortgage to buy a house at the peak of the housing cycle, in 2006 or in 2007, usually meant
that the mortgage owners were soon confronted with falling values of their collateral that
was driving down their net worth, seriously threatening their ability to service the
mortgage. This most recent housing bubble and its burst showed the “good” and the “bad”
side of buying a house and manifested just how severe a mortgage can become if taken at
the wrong time. Now, more than ever, it seems that housing decisions should be done with
great care, taking into consideration all available factors.
This paper uses the system dynamics and double-entry bookkeeping approach in order to
model all available determinants of buying and renting a house. We included all important
inflows and outflows of money and accumulation dynamics of assets, liabilities and equity
for both dilemma choices. The conclusions we made are based on the dynamics of the
equity flow and the stock accumulation in different scenarios. Our results offer an analysis
of both strategies and provide straightforward advice on the choice of housing strategy.
The key parameters of the model are: housing appreciation rate (measured by prices),
mortgage fixed interest rate, interest rate on saving deposits or return on investment if the
saving deposit is invested, property tax rate, and deductibility of the mortgage interest. To
estimate the parameters we use historical data available for the Croatian real estate market.
However, as the modeling approach is general, the data can be from any market and
especially from the US real estate market which has the longest historical data series.
Most people confronted with the dilemma, naively compare monthly annuity payments
with monthly rent payments, and make their decisions based on this simple comparison.
However, this way they ignore the fact that a part of the monthly annuity payment goes to
the principal (inflow to equity) which is similar to saving, while the interest portion of the
payment is deductible and in some degree can offset the interest expense on home
mortgage. Moreover, simply comparing the housing and the stock market ignores the fact
that housing pays something as a dividend because one can live in it without paying rent. In
order to make the comparison credible, living in a house should pay an “occupancy
dividend” of around seven percent [3].
Besides tangible variables, there are also many intangible ones. For example, in case the
landlord decides to raise the rent or if he decides to sell the property, the renters are in
distress. Not negligible is also the fact that in some countries, owning a house is often
regarded as a sign of success [4]. On the other hand, the renting a home offers the
flexibility and the alternative when the housing market is overpriced [1]. The recent study
[5] has shown that the high levels of home ownership are strongly linked to subsequent
rises in unemployment because labor mobility becomes reduced.
The buying vs. renting dilemma is obviously complex, implying that a complex analysis
should be applied in order to study it. We therefore take the system dynamics approach
because it seems to be the right tool for simulating and optimizing the choice between
renting and buying a home.
The rest of the paper is organized as follows. The following section displays the
methodology employed in detail. The third section presents results, while in the last section
we discuss the results and conclude the paper.
Stylized Facts
In this moment, 92% of households in Croatia are owners of their apartment or house. The
average apartments’ area is around 74.4 m2, with the average nominal price 1309 EUR/m2
in 2013 gives the initial home price set to 100.000 EUR.
Historical data series for the home price index are available at [6, 7] are shown in Figure 1,
covering the period of last 15 year (from 1998 to 2013).
Home Price Index
200
180
160
0 18 36 54 72 90 108 126 144 162 180
‘Time (Month)
Nominal Home Price Index :#
Real Home Price Index : #
Figure 1. Historical Home Price Index for last 180 months (15 years).
Mortgage Interest Rate Deposits Interest Rate
cane lL,
a oeaa
eos i iN Nina
inn
1 1
os 0s
2 i
as as
5 “s
a oT) oe es 30101612180
Tine (Mont) ime (ont)
Interest Rate: Non terest Rate on D
I Mortgage Ire Rate: # Real
‘CPI: * “cPrse
Figure 2. Mortgage and Deposits Interest Rates in last 180 months (15 years).
Figure 2 shows mortgage interest rates (with historical annual mean 7.06% and median
6.49%) and interest rate on deposits (with historical annual mean 5.41% and median
4.84%) which both give a bank spread premium of 1.65% annually.
Methodology
We set the tax rate for buying a house (property sales tax) at 5 percent. As property tax has
not yet been introduced in Croatia, we use the expected rate that is assumed to be around
0.15 percent of the house value paid annually. We have examined the effect of both of these
taxation scenarios on the buying versus renting dilemma.
We set the initial house price at 100,000 euros allowing both appreciation and depreciation
of the house value, as defined by the annual appreciation/depreciation rate.
We design two versions of the model: (1) the renting model shown in Figure 3 and (2) the
buying model shown in Figure 4. Both models are inspired by the work of the colleague,
professor Kaoru Yamaguchi [8], who has applied double-entry bookkeeping principles in
his modeling methodology. Bookkeeping principles make models more organized, and they
increase visualization quality, understanding, and motivation for research.
As shown in Figure 3, the renting model has only one liability stock which accumulates
renting expenses equal to a monthly rent. On the asset side, the renter has an initial saving
deposit (the principle), which is enlarged periodically by depositing new monthly savings.
These savings inflows depend on disposable income, renting expenses, and the marginal
propensity to consume. The renter also receives interest on saving that is included in the
amount of saving. Conservatively, we use the average bank passive interest rate on deposits
as the investment interest rate on saving deposits. Alternatively, the average return on
investments in securities or stocks can be used as well. We differentiate between the
interest and the principle in order to detect the exact contribution of savings, and the exact
contribution of interest in the appreciation of the renter’s asset.
We define the equity stock as a difference between assets and liabilities. Therefore the “Net
Worth of Equity” stock is defined as the accumulation of the difference between equity
inflows (saving and interest) and equity outflows (renting expenses), where initial equity is
equal to initial saving deposits. We were mostly interested in the dynamics of “Net Worth
of Equity” stock and the “Equity Inflow/Outflow Balance” flow. Obviously, positive and
maximal performance of both of these two variables is preferable. From these flows and
stocks we can derive some investment measures, such as return on assets (ROA) and
present value (PV) of future equity cash flows.
lest Interest — Ret [per month
Rate
Renting Expenses
Tnterest on Saving
Deposit
PER YEAR
Saving (Renting)
Disposable Net) Inia Saving
Income (Renting) Deposit
Mangal Basie
Propensity to Consumption o
Gross focome Consume
ipa eor™ Income Tx Rate
ay
=o)“ Eguty infow
(Renting)
|
}
Equity Ouow
(Renting)
quiy Info Outlow
Bobnce (Retig)
Figure 3. The renting model.
Figure 4 presents the buying model. The liabilities in the model are the “Mortgage Loan”
and the “Interest on Mortgage Loan” that have to be paid to the mortgage provider. Again
we separate the flows of the “Principle Payment” and the “Interest Payment‘, because only
the interest is allowed to be recognized for tax deductions, and because the interest is
treated as equity outflow while the principle payment is treated as equity inflow (similar to
savings in the renter’s model).
The initial mortgage loan depends on the initial house price and on the amount of down
payment (that is 20 percent of the house price on average).
On the asset side we allow the house value to appreciate/depreciate depending on the
appreciation/depreciation rate. The system is very sensitive to this parameter, and for the
moment we have conservatively set the appreciation rate to 1.74% percent as our historical
data suggest. Later on, we plan to set the appreciation/depreciation rate to higher levels, as
one can usually notice in the short- and medium-run.
In the buying model, we also allow for saving, depending on the amount of disposable
income less taxes and expenses incurred as a consequence of buying a house (such as
property tax, maintenance costs, and mortgage payments). Tax deductions in the form of
income tax savings are included because the owner incurs tax deductible costs related to
property tax and mortgage interest payments.
Initial “Net Worth of Equity” is equal to “Initial Saving Deposit” reduced by the “Property
Sales Tax” that has to be paid in the moment of buying the house. The buying model is
obviously more complex, but from flows and stocks similar investment measures as return
on assets (ROA) and present value (PV) of future equity cash flow can be derived.
i ae H
Appreciation Rate
i
NS
Egy law
— puis)
Byuiy Ouffow 4g
Figure 4. The buying model.
Table 1 presents the list of all variables and their initial values used for estimating model
parameters.
Table 1. Model parameters’ names and default values.
Pz neter jue
Gross Income 16,800 EUR/year
Income Tax Rate 12% and 25% (income dependable)
Marginal Propensity to Consume 0.7
Basic Ci ptio 100 EUR/month
Initial Saving Deposit 20,000 EUR
Investment / Interest Rate on Deposit (annual) 5.41%
Rent 400 EUR/month
Discount Rate (=Cost of Capital) 71%
| Appreciation Rate 1.74%
Maximal Annual Tax Ded 1600 EUR/year
Mortgage Interest Rate (annual) 6.49%
Term (of mortgage) 30 year
Property Sales Tax Rate 5%
Property Tax Rate (annual) 0.15%
i Cost Rate (annual) 0.5%
Down Payment 20%
Initial House Price 100,000 EUR
Results
Figure 5 shows the results of simulation for the renting model (blue line, marked with “1””)
and the buying model (red line, marked with “2”) in the “Scenario A” without tax
deduction.
Equity Inflow/Outflow Net Worth of Equity
900 100,000
660 78,800
57,600
420 2
36,400
180
15,200
-60
-300 0 54 108 162 216 270 324
EU
FUR
0 54 «108-162-216 270-324 ‘Time (Month)
sini ej lac gle Monet) "Net Worth of Equity (Renting)" : #
ty Inow/Outfow Rene Rantingy #44 ggg i ="
"Exuity InfowiOutfow Balance (Buying): # 2——@ 2a aa "Net Worth of Equity (Buying)": # 2222
ROA ,
ia Present Value of Equity
30,000
6
23,940
o 2
5 17,880
5 2
a 5
7) a
11,820
6
5,760
-10
0 54 108162, 216-270 324 -300
Time (Month) 0 54 108-162-216 270-324
"ROA (Renting)" :# +++ +++ Time (Month)
"ROA (Buying)" :# —2—2—2—2—2—2—2— "PV (Renting)" :# —+— "PV (Buying)":# ——
Figure 5. Scenario (A), without tax deductions. Equity Inflow/Outflow Balance, Net
Worth of Equity, ROA and Present Value of Equity.
Figure 6 shows the results of simulation for the renting model (blue line, marked with “1”)
and the buying model (red line, marked with “2”) in the “Scenario B” with tax deduction
included.
Equity Inflow/Outflow Net Worth of Equity
1,000 100,000
740 80,000
60,000
480 “
% 2
EI Fo
40,000
220
20,000
-40
0 b
-300 0 54 108 162 216 270 324
0 34108-16226 270324 Time (Month)
spay tewceen nam ouarin es Set Wonb of gal (Reaigf = tee
“tapi Infow/Outtow Balince Duyingy :# 2——@—9 apg "Net Worth of Equity (Buying)" :# ——2—2—2—2—
ROA ,
‘0 Present Value of Equity
30,000
6
24,000
a 2
8 18,000
5 x
& |
2 Ey
12,000 wae
-6
6,000
-10
0 54 108162, .216 270324 0
Time (Month) 0 54 108-162-216 270-324
"ROA (Renting)" :— —-—+—+—+—+ ++ Time (Month)
"ROA (Buying)" :# —-2—2—2— 2222 "PV (Renting)" :# —+— "PV (Buying)":# ——
Figure 6. Scenario (B), with tax deductions. Equity Flow Balance, Net Worth of
Equity, ROA and Present Value of Equity.
Discussion & Conclusion
Scenario (A) in Figure 5 clearly shows that at the moment, as described by parameters in
Table 1, the renting scenario is optimal in comparison to the buying scenario. The equity
flow is negative for the first 10 years (or 120 months) but afterwards it becomes and stays
positive. The effective ROA bottoms out at around —9.6 percent and stays negative in the
first 10 years, but eventually it starts to increase as the capital invested from saving deposits
grows and converges towards a 4 percent annual return.
The renting scenario also allows higher savings due to a lower monthly cash outflow
(around 400 EUR a month), which eventually leads to higher saving after consumption. At
the end of the 30-year period, the equity from the initial 20,000 EUR accumulates to 91,238
EUR. The present value of equity future cash flows discounted by the average cost of
capital set at 7% is equal to 28,113 EUR.
In the buying scenario, the initial saving deposit is substantially decreased by the initial 5%
property sales tax. The cash outflow due to mortgage payments is higher (505.13 EUR),
and the equity flow is more negative and it takes 12.5 years (or 150 months) before it
becomes positive. The net worth of equity is negative for substantial time, and the initial
saving deposit invested as the part of equity is wiped out, and it takes 28 years (period
between 220-360 months) when the equity to become positive, due to a higher portion of
the principle payment at the mortgage term ending. After 30-years period, the net worth of
equity is equal to 60,090 EUR, significantly lower in comparison to 91,238 EUR from the
renting model. If we discount the future cash flow to equity with the discount rate of 7
percent, the present value of the future equity flow is only 11,713 EUR.
The reason for such discrepancy between the two scenarios for Croatia is in the tax
deduction which was abandoned in 2010. Before 2010, income tax deductions were
recognized for mortgage interest payments to the amount up to 1,600 EUR annually.
In Scenario (B) we model the market prior to 2010, therefore allowing the tax deduction.
From Figure 6 we can conclude that the dynamics of both models looks fairly similar and
the buying model accumulates slightly less equity at the amount of 89,076 EUR in
comparison with the 91,238 EUR accumulated in the renting model.
These results have interesting policy implications as they provide evidence of tax policy
effect on the housing market. In case the government wants to stimulate the real estate
market and the construction sector, it should allow for tax deductions on mortgage interest
or similar measures that make the buying strategy preferred when compared to the renting
strategy. On the other hand, if the government perceives a housing bubble is being
supported by a certain tax policy, it should reconsider its policy aims and adjust tax rates
and incentives accordingly.
For further research we would like to introduce the inflation rate and discuss real values
and nominal values when making housing investment decisions.
References
1. Khan, S., Finance and Capital Markets: Housing, in Videos on finance and
macroeconomics, S. Khan, Editor 2014, Khan Academy.
2 Shiller, R.J., Understanding Recent Trends in House Prices and Homeownership.
Housing, Housing Finance and Monetary Policy, 2008: p. 85-123
3: Conerly, B. Should You Buy A House Or Rent? The Economics Of Homeownership.
Forbes, 2013.
4. Oh, D. and J.R. Burns. Estimating the Home-Purchase Cost of Seoul Citizens in
International System Dynamics Conference 2010. 2010. Seoul, Korea.
5. Blanchflower, D.G. and A.J. Oswald, Does High Home-Ownership Impair the
Labor Market? National Bureau of Economic Research Working Paper, 2013(No.
19079).
6. CBS. Croatian Bereau of Statistics - Croatian Economic Survey. 2013; Available
from: http://www.dzs.hr/default_e.htm.
7. CNB. Croatian Nationa Bank - Bulletin - Statistical Survey. Available from:
http://www.hnb.hr/eindex.htm.
8. Yamaguchi, K., Money and Macroeconomic Dynamics - Accounting System
Dynamics Approach. 2013: Japan Futures Research Center.
To analyze the theory we may consider four different levels of low-income targeting, each
representing one of the social insurance institutions: the encompassing, the corporatist, the
basic security and the targeted. The voluntary state-subsidized model is excluded from the
analysis because none of the 18 countries presented in Korpi and Palme’s paper belongs to
this category. In the simulation model, it is the parameter ‘Ratio to low income RL’ that is
changed between the four models of social insurance institutions. Put in order from the
highest to the lowest degree of low-income targeting the institutions are: the targeted, the
basic security, the encompassing and the corporatist. For simplicity, we translate these to four
values of ‘Ratio to low income RL’; 1.0, 0.8, 0.4 and 0.2. The values are portrayed in Table 1
together with short motivations based on the background. Note that this is a gross
simplification of the theory. We will simulate the model with these four parameter values.
Model of Social Relative degree ‘Ratio to Motivation
Insurance of Low Income low income
Institutions Targeting RL’
Targeted Very high 1.0(100%) Only citizens below the poverty line are
eligible (means test).
Basic Security High 0.8 (80%) Everyone insured by the same programs.
Enc i Low 0.4(40%) Eamings-related benefits.
Corporatist Very Low 0.2(20%) Social insurance programs reserved for
economically active population and
earnings-related.
Table 1: A summary of the values for the parameter ‘Ratio to low income RL’. ‘ivations based on the
3.2 Results
The results of the simulations of ‘Redistributive budget R’ are portrayed in Figure 11. The
targeted model, with the highest level of low-income targeting (in this simulation, all the
redistributive budget goes to ‘Transfers to low income TL’) results in the lowest redistributive
budget. The basic security model with the second highest level of poor people targeting also
leads to a low redistributive budget. Furthermore, the encompassing- and corporatist models
with lower levels of low-income targeting result in higher redistributive budgets. We may
accordingly argue that Figure 11 reproduces the reference modes of the models with high
levels of low-income targeting, i.e. both the targeted and the basic security models led to
16
comparably low redistributive budgets. Figure 11 also reproduces the reference modes of the
models with low levels of low-income targeting, i.e. both the corporatist and the
encompassing models led to comparably large redistributive budgets.
304
S DoS see eet.
o on
> .
2 25 4 ’
a 1;
B21
3 1 ‘
2 !,
3 " ——— 1: Targeted
Bis jy - .
3 i seeeee 0.8: Basic Security
£10 Bld === 0.4: Encompassing
S
3
2 — + 0.2: Corporatist
B54
2
@
oO
0 50
Time (Years)
Figure 11: The development of the Redistributive budget. Simulation based on the model formulation in Appendix 1
and the parameter values for ‘Ratio to low income RL’ presented in Table 1.
Now, let us consider the ‘Transfers to low income TL’ that we take as a proxy for equality
and poverty levels. The simulation results for ‘Transfers to low income TL’ are presented in
Figure 12. The targeted model leads to the lowest amount of transfers to the low income
earners. The basic security leads to the second lowest amount of transfers to the low income
earners. The encompassing leads to the largest amount of transfers to low income earners and
the corporatist to the second highest amount of transfers to low income earners. Furthermore,
Figure 12 reproduces the reference modes of the models with high levels of low-income
targeting, i.e. both the targeted and the basic security models led to comparably low transfers
to low income earners. The graph also reproduced the reference modes of the models with
low levels of low-income targeting, i.e. the both the corporatist and the encompassing models
led to comparably high transfers to low income eamers.
17
14 |
2124
SG
& otc crcee: -
5 10 + 74
2
a 3 | J 1: Targeted
2 seeeee 0.8: Basic security
2 = + =0.4: Encompassing
<
£ === 0.2: Corporatist
Time (Years)
Figure 12: The development of transfers to low income. Simulation based on the model formulation in Appendix 1
and the parameter values for ‘Ratio to low income RL’ presented in Table 1.
Finally, let us consider the effects of different ‘Ratio to low income RL’ on ‘Transfers to low
income TL’, portrayed in Figure 13. The transfers are derived after 100 years of simulation.
The graph shows that with low ‘Ratio to low income RL’ (e.g. 0 to 0.2), the ‘Transfers to low
income TL’ are relatively low, and with high ‘Ratio to low income RL’ (e.g. 0.8 to 1), the
‘Transfers to low income TL’ are also low. However, in the middle of the range, between
around 0.3 and 0.7, the ‘Transfers to low income TL’ are relatively high.
Transfers to low income (USD per year)
b
o
1
i) 0.2 0.4 0.6 0.8
Ratio to low income
Figure 13: Structure-behavior graph of the Transfers to low income, as an effect of ratio to low income. Simulation
based on the model formulation in Appendix 1 and different parameter values for ‘Ratio to low income RL’.
18
4. Analysis and Discussion of Results
The system dynamics translation reproduces the reference modes, i.e. lower levels of low-
income targeting led to more redistribution and lower inequality and poverty, and higher
levels of low-income targeting led to less redistribution and higher inequality and poverty
levels based on the created simulation model.
Furthermore, the shape of the graph portrayed in Figure 13 suggests that there is a trade-off
between the size of the redistributive budget and the ratio to low income, as Korpi and Palme
(1998) suggest.
Figure 12 portrays that the corporatist model leads to lower levels of transfers to low income
eamers comparing to the encompassing model. This has to do with the fact that, although the
corporatist model leads to a great redistributive budget, the ratio of the redistributive budget
that is transferred to low income eamers is small. One may argue that the redistributive
budget of the corporatist model has less of a ‘redistributive effect’. Simultaneously, the
corporatist model leads to significantly higher transfers to low income comparing to the
targeted and basic security models, in line with Korpi and Palme’s (1998) reasoning that the
size of the redistributive budget is more critical than the ratio of the budget transferred to low
income.
However, we need not jump to conclusions based on the model behavior. The interpretations
of the theory e.g. with regards to the shapes of the table functions portrayed in Figure 7 and
Figure 9, may indicate that a reconstruction rather than translation of the theory has been
made. Also, as suggested in relation to the Bull’s Eye Diagram of Figure 10, more variables
may be modeled endogenously to better capture the dynamics in play. One simplification is
that the size of the economy is constant. Hence, there is no influence of the size of GDP on
‘Support for Redistribution’ and no influence of the ‘Redistributive budget’ on GDP
(assuming that GDP is the sum of ‘Redistributive budget R’ and ‘Rest of economy E’).
Moreover, there is no effect of GDP on the table functions of ‘Indicated support for
redistribution IS’ and ‘Desired redistributive budget DR’. Furthermore, the income
distribution, e.g. Gini is not modelled. Also, we should be careful in drawing conclusions
from the comparisons between the modeled behavior and the reference modes as the shapes of
the reference modes are very general.
19
5. Conclusions, Limitations and Future Work
This paper has studied Korpi and Palme’s (1998) paradox of redistribution through the
construction of a system dynamics model. The theory suggests that social insurance
institutions that target the poor and low-income eamers result in smaller redistributive budgets
and higher levels of poverty than social insurance institutions with lower levels of low-
income-targeting. The model was constructed following the steps of system dynamics
translations (Wheat, 2007). Moreover, the model was analyzed and compared to a simpler
static model in which the size of the redistributive budget did not change over time. The
structure was simulated with different values of low income targeting representing four types
of welfare state institutions. The resulting behavior supports Korpi and Palme’s (1998)
hypothesis. Thus, the model indicates that the paradox of redistribution is coherent when
translated into a system dynamics model.
However, the model is a very simplified representation of reality and there is a need for
caution when it comes to drawing conclusions from the results. The resulting model is a
theoretical representation of a theory in political economy. However, it clearly underlines the
importance of considering feedbacks and path dependency tendencies of political decision
making. As many variables remain excluded and exogenous, there is scope to develop a more
endogenous model. Such a model could preferably be compared with data of historical
behaviors of the mature welfare states.
As some interpretations of Korpi & Palme’s (1998) theory were made during the constructing
of the model, the model could benefit from expert reviews, not at least from the authors
Walter Korpi and Joakim Palme. Also other aspects of the feedbacks within social insurance
policies could be considered in further work. E.g. Korpi and Palme (2003) suggest that their
typology may be used to explain the resilience of the welfare states in times of austerity. Their
theories may also be extended to not only include elements of so called rational behavior of
the middle income eamers, but also solidarity with lower income earners.
Summing up, this modeling exercise indicates that system dynamics may play a vital role in
the current debate on inequality. The model presented may be further developed and
validated. This could give insights and contribute to the structural explanations to the
development of inequality.
20
References
Barlas, Y. (1996). Formal aspects of model validity and validation in system dynamics.
System Dynamics Review, 183-210.
Ford, A. (2009). Modeling the Environment. Washington DC: Island Press.
Forrester, J. W. (1969). Urban Dynamics. Cambridge: The M.L.T. Press.
Korpi, W., & Palme, J. (1998). The Paradox of Redistribution and Strategies of Equality:
Welfare State Institutions, Inequality and Poverty in the Western Countries. American
Sociological Review, 63(5), 661-687.
Korpi, W., & Palme, J. (August 2003). New Politics and Class Politics in the Context of
Austerity and Globalization: Welfare State Regress in 18 Countries, 1975-95.
American Political Science Review, 425-446.
Pierson, P. (1996). The New Politics of the Welfare State. World Politics, 143-179.
Piketty, T. (2013). Capital in the Twenty-First Century. Cambridge: Harvard University
Press.
Richardson, G. P. (2011). Reflections on the foundations of system dynamics. System
Dynamics Review, 219-243.
Stiglitz, J. E., (2013) The Price of Inequality: How Today’s Divided Society Endangers Our
Future. New Y ork: WW Norton & Company
Wheat, D. Conference Presenation (8 November 2007). Sachs’ Poverty Trap Theory: A
System Dynamics Translation. Congreso Latinoamericano de Dinamica de Sistemas.
Wilkinson, R. G., & Pickett, K. (2009). The Spirit Level: Why More Equal Societies Almost
Always Do Better. New Y ork: Allen Lane.
21
APPENDIX 1: MODEL VARIABLES AND EQUATIONS
The table shows brief definition of the model’s variables. The equations governing these
variables can be accessed with the STELLA/iThink model.
TABLE 2: MODEL VARIABLES AND EQUATIONS
Variables and equations
Units
t
R(t) = R(O) + I CR(s)ds;R(O) = IR=5
i)
The stock representing the redistributive budget, R, changes as the ‘change in
redistribution CR’ goes up or down. The initial size of the redistributive budget is
given by the ‘Initial redistributive budget IR’ which is set to 5 years.
US Dollars/year
t
E(t) = E(0) + —CR(s)ds; E(0) = IR = 100 — IR = 95
0
The stock representing the size of the rest of the economy, E, changes as the ‘change
in redistribution CR’ goes up or down. The redistributive budget, R, and the rest of
economy, E, together make up 100 US Dollars/year. Accordingly, the initial size of the
rest of economy is 100 less the redistributive budget R. It includes the far-reaching
assumption that the total size of the economy, i.e. R+E, is not affected by the size of
redistributions.
US Dollars/year
DR(t) —
cre) <PRO=RO
TCR
The change in redistribution, CR, is the rate at which the redistributive budget as part
of the rest of economy changes. It depends on the gap between the desired
redistributive budget, DR, and the redistributive budget, R, and the time for change in
redistribution, TCR, which is set to 2 years. It is assumed that it takes some time for a
new policy to be realized.
US
Dollars/year*2
TL(t) = R(t) X RL
Transfers to low income, TL, depends on the redistributive budget and the ratio of
the redistributive budget that is transferred to low income earners. The transfers to
low income is used as a proxy for determining poverty and inequality (i.e. the higher
the transfers to low income, TL, the lower the poverty and inequality). This is a far-
reaching assumption, but reasonable given the simplified representation of the
causal processes at play.
US Dollars/year
TM(t) = R(t) x 1— RL)
Transfers to middle income, TM, depends on the redistributive budget and the ratio
of the redistributive budget that is transferred to middle income earners. For
simplification, high income earners are not included in the model. They are assumed
not to affect the redistributive budget as they are assumed to always be against
expansions of the redistributive budget just as the low income earners are assumed
to always support expansions of the redistributive budget.
US Dollars/year
22
1S(t) = Graphical function (TM)
The indicated support for redistribution, IS, is determined through a graphical
function of the transfers to middle income. The graphical function is presented
below.
OF >”
8 © Indicated_support_for_redistribution_IS
M Graphical
rc
Indicated support Fe
c—
0 Transfers_to__middle_income_TM 100
Dimensionless
t
S(t) = S(0) + I CS(s)ds;S(0) = 1S(0)
i)
The stock support for redistribution, S, changes as the change in support, CS, goes up
or down. The initial support for redistribution is equal to the initial indicated support
for redistribution, IS. Together the stock opposition against redistribution, O, and the
support for redistribution, S, make up 1 or 100%, assuming each member of the
Dimensionless
(percentage)
middle classes is either supporting or opposing redistribution.
t
Dimensionless
O(t) =O(t) + I —CS(s)ds;0(0) = (1 —1S(0)) (percentage)
0
The stock opposition against redistribution, 0, changes as the change in support, CS,
goes up or down. The initial opposition against redistribution is one less the initial
support for redistribution, S (together the stock opposition against redistribution, 0,
and the support for redistribution, S, make up 1 or 100%, assuming each member of
the middle classes is either supporting or opposing redistribution).
IS(t) — S(t Percentage/Year
s(x) = SO=5O
TCS
The change in support, CS, is the rate at which the support for redistribution, S (and
accordingly the opposition against redistribution, 0) changes. It depends on the gap
between the indicated support for redistribution, IS, and the support for
redistribution, S, and the time for support change, TCS, which is set to 5 years. It is
assumed that it takes some time for the middle classes to change opinion.
23
DR(t) = Graphical function (S)
The desired redistributive budget, DR, is determined through a graphical function of
the support for redistribution, S. The graphical function is presented below.
EA © Desired redistrbutive_budget_DR #OG > *
Graphical
[100
Desired redistributiv
ce
0 Support_for_redistribution_S 1
Dimensionless
IR=5
The initial redistributive budget, IR, is set to 5 US Dollars per year. The assumption is
that the redistributive budget initially is 5 %. The two stocks (R and E) together make
up 100 which is a good number to depart from when comparing different models. It
can easy be changed for different countries.
Us Dollars/year
RL=0.8
The ratio to low income, RL, is set to 0,8 for the initial simulation but is, as explained
in the paper, changed according to the respective scenarios.
Dimensionless
TCS=5 Years
The time for support to change, TCS, is set to 5 years, assuming that it takes on
average 5 years for the change in transfers to the middle income to make their
attitude towards redistribution change.
TCR=2 Years
Time for change in redistribution, TCR, is set to 2 years. This is based on the
assumption that it takes on average 2 years for a policy change to be implemented.
24
APPENDIX 2: THE STELLA/ITHINK INTERFACE
The Paradox of
Redistribution:
A System Dynamics
Translation
ress nere tote the stor.
David Coliste
European Master Prosramme
in Sytem Dynamics, 2013-2015
Biel
predictive claims
Ratoto
low income RL Indicated supgor.
far radistiioion IS
—
Oppostion aganst
redistribution O Time
Tranctors to
Transfers to ‘middle income TM
Jow income Th
Redistributive
budget R
Change in Support for
regitrbuion S
raetnbution CR a
Tin or
ian meen ren
i Rest Desired redstouthe
budget OR
cf economy E
kama)
Iria radistibutive budget
25
