The House Price Dynamics with Household Debt: The
Korean Case
Feb. 2013
Hyun Jeong Kim*, Jong Chil Son**, Myung-Soo Yie***
Disclaimer: This paper should not be reported as representing the views of the
Bank of Korea. The views expressed are those of the authors and do not
necessarily represent those of the Bank of Korea or the Bank of Korea's policy.
_________________________________
* Head in Macroeconomics Team, Economic Research Institute, the Bank of Korea, 39 Namdaemunno, Jung-gu,
Seoul, 100-794, Korea (Tel: 82-2-759-5428, E-mail: hynjkim@bok.or.kr)
** Senior Economist, Economic Research Institute, the Bank of Korea, 39 Namdaemunno, Jung-gu, Seoul, 100794, Korea, (Tel: 82-2-759-5424, E-mail: jcson@bok.or.kr)
*** Economist, Economic Research Institute, the Bank of Korea, 39 Namdaemunno, Jung-gu, Seoul, 100-794,
Korea, (Tel: 82-2-759-5411, E-mail: yie@bok.or.kr)
1
Abstract
This paper revisits long-run determinants of house prices and analyzes the house
price dynamics with the Korean data, while taking into account the close
relationships between house prices and household debt. We also attempt to forecast
trend house prices over the next five years. The result of cointegrating regressions
shows that the rise in house prices during the 2000s in Korea was strongly related
with the steep increase in household debt. And, as the estimated error correcting
process reveals, the adjustment in house prices has been made gradually, as it takes
about four years for the difference between actual and fundamental (long-run) house
prices to be reduced by half. Finally, the mid-run house price forecast shows that
house prices are not likely to rise as sharply as they did in the 2000s in near future,
when considering the long-term changes in the macro-financial environment.
Key words: House Prices, Household Debt, Cointegrating Regression, Error Correcting
Process, Forecast
JEL classification code: E44, C32, J10
2
Ⅰ. Introduction
Over the last decade, Korea has witnessed distinct and simultaneous rises in house prices
and household debt. In Korea, house prices1 increased by an annual average of 7.3% during
the 2001-2011 period nationwide, with those in the Seoul metropolitan area by 9.3%. In the
meantime, the level of household debt stood at 1,036 trillion won as of the end of 2011,
having marked a rapid increase by more than three times the 2000 debt level of 329 trillion
won. Household debt to disposable income ratio registered at 1.6 at end-2011, which is even
higher than the corresponding figure of 1.3 in the United States when the economy was hit by
the sub-prime mortgage crisis. As in other advanced countries, household indebtedness in
Korea has been heightened due mainly to an increase in mortgage loans, with mortgage
lending by commercial banks having increased by an annual average of 12.6% during 200420112.
A number of researchers (Debelle, 2004; Dynan and Kohn, 2007) have pointed out that
house prices and household debt are closely related. This is because, in an imperfect credit
market, real assets, as collaterals for bank loans, play the role of financial accelerator3 in that
changes in real asset prices interact with changes in household borrowing, consumption and
construction investment.
In Korea, house prices seem to have recently entered into an adjustment phase along
with the deterioration of household income flows since the 2008 global financial crisis,
although the adjustment is not universal, but especially prominent in the metropolitan area.
1
2
3
Hereafter, house prices in Korea refer to the nominal nationwide price index compiled on a monthly basis by Kookmin
Bank.
Mortgage lending accounted for 67% of total household lending by commercial banks as of the end of 2011.
According to Aoki et al. (2004), the financial accelerator theory of Bernanke et al. (1999) can be directly applied to the
household sector.
3
Fast demographic changes facing the Korean economy also seem to contribute to such
adjustment by lowering expectation of asset price inflation in the future. In fact, the working
age population is expected to begin decreasing from 2017 and the 35- to 59 year-old age
cohort accounting for a majority of total demand for housing assets has already started to
decrease from 2012, due mainly to Korea’s low fertility rate and aging population. Such
changes in macroeconomic environment are likely to affect the future path of house prices
and household debt. Furthermore, if the extent of house price correction is substantial, it may
have a significantly negative impact on household debt sustainability, giving rise to
macroeconomic and financial instability.
For the major economies, the literature that analyzes the determinants of house prices
and the interaction between house prices and household debt has been growing (Gerlach and
Peng, 2005; Antipa and Lecat, 2009; and Gimeno and Martinez-Carrascal, 2010). Research
on emerging markets including Korea, however, is limited and, therefore, very little is known
about the linkages between long- and short-run dynamics of house prices and the degree of
household indebtedness. On the other hand, the importance of the relevant information about
the house prices, such as the degree of deviations of historical prices from their long-run
values and their speed of adjustment to the equilibrium, has been increasing for policy
makers as well as researchers after the 2008 financial crisis. In this vein, this paper aims to
fill the gaps in the literature and further address the issues in the Korean context where
household indebtedness has been particularly steeply increasing in a rather short space of
time, over a decade. We attempt to investigate the dynamics of house prices in Korea, while
incorporating their relationship with household debt, using stock-flow and error correction
models, and forecast trend or equilibrium house prices in near future.
4
Main findings of this paper regarding the factors affecting house prices in the long-run
and house price dynamics in the short run are overall consistent with those in the literature.
First, we estimate how far actual house prices deviate from their long-run (equilibrium)
values, especially for house price boom periods. Long-run house prices are defined as the
values determined by fundamental factors, including permanent incomes, user costs and
demographic structures. We also measure the extent of difference between actual house
prices and the long-run (equilibrium) values and found that it narrows to a substantial degree,
if we include household debt in the set of fundamental factors, as a proxy for financial market
developments. The estimation result of the error correction model shows that adjustment in
house prices is made gradually, as it takes about four years for the difference between
historical and long-run house prices to narrow by half. This result is generally consistent with
the literature, which repeatedly reports the persistency in house price dynamism across
countries. Finally, we conduct forecasts of the long-run trend of house prices based upon
alternative scenarios regarding household debt, under which household debt to income ratio
is assumed to keep rising, stay at its current level, or decline. The forecast indicates that the
long-run (equilibrium) nominal house price is expected to increase at a slightly slower pace
than the 3% (steady state) inflation at the most over the next 5 years, implying a house price
decline in real term.
The rest of this paper proceeds as follows. Chapter Ⅱ provides an overview of
previous studies on the determinants of house prices, including those explicitly taking
household debt into account. Chapter Ⅲ gives the basic information about the data and
reports the empirical findings aforementioned—results of cointegrating regression, the shortrun dynamics of house prices, and the forecast of trend house prices. Chapter Ⅳ summarizes
5
with some policy implications.
Ⅱ. Literature survey
Debelle (2004) and Dynan and Kohn (2007) point out that over the last two decades
household debt based on mortgages in particular has increased greatly in major developed
countries, and that this is due mainly to changes in tax codes4, demographic structures, relaxed
financial regulation, low interest rates and asset price increases. A number of studies indicate that
house prices can play the role of financial accelerator that propagates shocks through the entire
economy, since people borrow money on the collateral of their houses (Kiyotaki and Moore, 1997;
Aoki et. Al, 2004; Iacoviello, 2005; Iacoviello and Minetti, 2007).
There is no dispute among researchers about the fact that household debt and house
prices are closely related with each other. Using error correction models, a number of
empirical analyses have been conducted on the relationship between these two factors.
Oikarinen (2009), Gimeno and Martinez-Carrascal (2010), in their analyses of the house
prices in Finland and Spain, show that house prices and house-related lending are
interdependent. Gerlach and Peng (2005) maintain that a rise in real estate prices led to an
increase in bank credits in analyzing real estate market causality in Hong Kong. In Korea, Kim
and Kim (2009) find that the effect of household debt on house prices has increased since the
currency crisis, through use of a vector error correction model. Jeong (2006) argues that asset
prices and liquidity affect each other positively (+) in both the long as well as short terms.
Meanwhile, there are a number of studies that analyze the house price determinants on
4
According to Debelle (2004), since the U.S. tax reform in 1986 which repealed all tax reductions on lending rates except
mortgage interest rates, mortgage loans have increased. Also, similar tax benefits to mortgage loans have caused increases
in household debt and house prices in the U.K., the Netherlands, Finland, Norway, and Sweden.
6
the supply and demand sides in the house market, taking into account household debt and
borrowing constraints. Favilukis et al. (2010) argue that the more efficiently the house
financing market is operating, the less risk premium the market will have, which will lead to an
increase in house demand, and a consequent rise in house prices. Muellbauer and Murphy
(1997), Meen (2002), McCarthy and Peach (2002), and Antipa and Lecat (2009) contend that
real disposable income, interest rates, demographic change, the housing finance system and
lax borrowing conditions play major parts in deciding house prices. In particular, McCarthy
and Peach (2002) conclude that the house price increase in the U.S. in the early 2000s was
caused by fundamental determinants such as increases in household income and decreases in
mortgage rates. Antipa and Lecat (2009) do an estimation to see which factors affect house
prices in France and Spain, using an error correction model. Their results show house prices in
the countries to be about 20% overvalued compared with their level explainable by
fundamental determinants, but that the extent of overvaluation is reduced when the eased
borrowing conditions are considered.
Glaeser et al. (2008) and Mian and Sufi (2009) put emphasis on supply factors in the
housing and lending markets, respectively. Glaeser et al. (2008) establish a bubble model of
house prices and show that more supply elasticity in the housing market can lead to a smaller
scope of increase and less persistence in house prices. Mian and Sufi (2009) use data from the
United States to show that the less the elasticity of housing supply in a region, the faster
house prices increase increased before the global financial crisis. They also show that the
higher the ratio of sub-prime lending in a region, the steeper the increase in credit there.
Studies on the factors determining house prices in Korea conducted by Kang and Um
(2004) and Lee and Song (2007). Lee and Song (2007) analyze long-run models based on
7
housing market supply and demand, similarly to this study, and show that historical house
prices were lower than long-run house prices explainable by fundamental determinants. The
caveat of these papers is that when they estimated their house price determinants, they did not
consider other important factors such as investment in house construction and demographic
change. Kang and Um (2004) conducted an empirical analysis of house prices in Seoul using
a stock-flow model, and showed that lending conditions can affect the formation of proper
house prices.
This paper analyzes the long-run equilibrium house prices by estimating a house price
determinant function considering various fundamental factors such as house stock, the user
cost of house ownership, demographic change and household debt. We also investigate the
short-run dynamics of house prices using an error correction model, as well as predicting the
long-term trend of fundamental house prices, in the hope of shedding some lights on the
future path of current house prices.
Ⅲ. Empirical analysis
This section evaluates the sustainability of current house prices by quantitative analysis of
the long- and short-term relationships between house prices and household debt using long- and
short-term house price estimation. Forecasting is also done on the long-term fundamental house
price trend for one decade ahead.
1. Model and data
8
The fundamental analytical framework is based on a stock-flow model5, as is frequently
used in housing market analysis. In this model, demand for housing is determined, as shown
in equation (1), by exogenous variables (e.g. the population factor n), real permanent income
(y), real house prices (hp) and the user cost of house ownership (uc), and given a constant
housing supply amount over a certain period of time, the housing market achieves
equilibrium through equation (1). This paper explores the effect of eased borrowing
constraints on house prices by adding a household debt to income ratio variable (hl).
D (n, y, hp, uc) = S
(1)
In the meantime, new house supply (𝛥𝑆) is assumed to be provided gradually, in
consideration of the depreciation rate (δ), real house prices (hp), and housing construction
costs (cc):
ΔS = C (ℎ𝑝, 𝑐𝑐) − 𝛿𝑆
(2)
In consideration of equations (1) and (2), the long-run house price equation can be expressed
as equation (3), which is also used in McCarthy and Peach (2002) and Antipa and Lecat
(2009):
ℎ𝑝𝑡 = 𝛼0 + 𝛼1 𝑠𝑡 + 𝛼2 𝑦𝑡 + 𝛼3 𝑛𝑡 + 𝛼4 𝑢𝑐𝑡 + 𝜖𝑡
(3)
where ℎ𝑝𝑡 denotes real house prices, 𝑠𝑡 the house capital stock, 𝑦𝑡 real permanent income,
𝑛𝑡 the economically active population, 𝑢𝑐𝑡 the user cost of house ownership, and 𝜖𝑡 the
5
Please see DiPasquale and Wheaton (1994) for a more specific discussion.
9
error term, with all variables other than the user cost of house ownership (𝑢𝑐𝑡 ) being level
variables in logarithms. The long-run house price equation can be estimated by a
simultaneous equation with supply and demand functions. However, this paper estimates a
long-run demand equation which considers house capital stock (𝑠𝑡 ), a variable representing
the supply side.6 Among the explanatory variables, increases in the house capital stock (𝑠𝑡 )
and the user cost of house ownership (𝑢𝑐𝑡 ) are likely to lead to declines in house prices,
whereas increases in real permanent income (𝑦𝑡 ) and economically active population (𝑛𝑡 ) are
expected to push house prices up. The user cost of house ownership (𝑢𝑐𝑡 ) is determined by
the borrowing interest rate, the tax burden, and the expected capital gains from changes in
house prices in the future, as in Poterba (1984) (equation (4)):
𝑦
ℎ𝑝
𝑢𝑐𝑡 = ℎ𝑝𝑡 [(1 − τ𝑡 )(𝑖𝑡 + 𝜏𝑡𝑝 ) + 𝛿 − 𝐸𝜋𝑡+1
]
(4)
𝑦
where, 𝜏𝑡 denotes the average income tax rate, 𝑖 the borrowing rate, 𝜏𝑡𝑝 the average property
ℎ𝑝
tax rate δ the house price depreciation rate, and 𝐸𝜋𝑡+1
means the expected rate of house
price increase.
The following method is used to estimate the long-run house price equation shown in
equation (3). First, a cointegration test is carried out to see whether cointegration
relationships exist among the variables 7 . Given the cointegration relationships found, a
Granger causality test is then executed to check causality among the variables. If endogenous
variables exist among the explanatory variables, the equation is estimated by a 2SLS method
6
7
This is based on the identification problem. That is, that at a given point in time we can only observe the equilibrium
information from realized data of house prices, which restricts us to be able to only identify either the demand or supply
curve. If the supply side of the housing market is more unstable than the demand side, due to government policy, the
estimated equation is more likely to be the demand curve. This paper accordingly estimates the house price equation based
on the demand side.
Please see Engle and Granger (1987) for a more detailed discussion.
10
using lagged variables as instruments. We in addition, use FMOLS (Fully Modified OLS)
and CCR (Canonical Cointegrating Regression)8 to deal with endogeneity issues among the
variables, as a robustness check of the model.
In reality, current house prices can differ from their long-run trend. Estimation is hence made
on a short-run adjustment equation incorporating the error correcting process. This analysis
enables us to estimate the extent of herd behavior in the house market and the speed of
adjustment to equilibrium. The short-run adjustment equation can be expressed as equation (5):
∗ )
Δℎ𝑝𝑡 = 𝛼0 + 𝛼1 (ℎ𝑝𝑡−1 − ℎ𝑝𝑡−1
+ ∑4𝑖=1 𝛼1+𝑖 Δℎ𝑝𝑡+𝑖 + 𝛼6 Δ𝑦𝑡 + 𝛼7 Δdt𝑖𝑡 + 𝜂𝑡
(5)
∗
where ℎ𝑝𝑡−1 − ℎ𝑝𝑡−1
denotes the error term of previous quarter in long-run house price
equation. Equation (5) includes four lagged variables of house prices representing their autoregressive characteristic. Since all of the variables are considered stationary, the short-run
adjustment equation is estimated using the OLS method with Newey-West standard errors. In the
short-run, the rate of real income growth (Δ𝑦𝑡 ) and the differenced series of the household debtto-income ratio (Δ𝑑𝑡𝑖𝑡 ) are used as further explanatory variables.
As shown in Table 1, quarterly data for the 1991Q1-2011Q4 period are used, while the
time series plots for the major variables are displayed in Appendix 1. This paper introduces
‘real house capital stock’ variable which has not yet been dealt with in the previous Korean
literature. The data is total capital stock for residential buildings, as calculated by Cho and
Lee (2009) who estimate annual data with a perpetual inventory method that compiles the
capital stock by deducting the amounts of waste and depreciation after accumulation of
investment in the previous period. We use interpolation to calculate quarterly data based on
8
In general, the OLS estimator can be inefficient and biased when unit roots exist in both the dependent and the explanatory
variables. The FMOLS and CCR methods are designed to deal with this problem. Please see Phillips and Hansen (1990),
and Park (1992) for more detailed discussions.
11
the annual house stock data.
Table 1: Data
Variable
Explanation (ln denotes natural logarithms)
ℎ𝑝𝑡 : Real house price
ln (house price1)/GDP deflator)
𝑠𝑡 : Real house capital stock
𝑦𝑡 : Real income
𝑛𝑡 : Economically active population3)
𝑢𝑐𝑡 : User cost of house ownership
𝑑𝑡𝑖𝑡 : Debt- to-income ratio
ln (real house capital stock)
ln (real gross national income2))
ln (economically active population after
seasonal adjustment)
Estimated based on equation (4) (refer to Table 2)
Household debt in flow of funds/quarterly nominal GNI
Note: 1) This is the nationwide nominal house prices and standardization is applied such that the house price of the fourth
quarter of 2005 is 100 in line with the GDP deflator.
2) Real disposable income of the household sector can be more appropriate, but quarterly frequency data are
unavailable. The national income also generally shows trends quite close to disposable income of the household
sector by and large.
3) The number of households can be more appropriate; however, quarterly frequency data are unavailable.
Data: Kookmin Bank, Cho and Lee (2009), KOSIS of Statistics Korea, and ECOS of the Bank of Korea.
Instead of the commonly used interest rate, this paper also incorporate the user cost of
house ownership (𝑢𝑐𝑡 ) as an explanatory variable. The user cost of house ownership (𝑢𝑐𝑡 )
comprehensively considers the average income tax rate, average property tax rate, housing
depreciation rate, expected rate of house price increase in the near future and borrowing
interest rate. In Table 2, the expected rate of house price increase is estimated, following
McCarthy and Peach (2002), by the moving averages of the previous three years’ rates of
house price increase. The assumption is that each economic agent forms an adaptive
expectation based on house prices in the last three years9. In the meantime, the rate of
depreciation of the real house capital stock is 4.8%, as in Cho and Lee (2009), assuming
simple amortization by 1.2% each quarter. The rates of comprehensive income tax and
property tax are calculated based on the amounts of these taxes paid relative to taxable
income for the year concerned, on a nationwide basis.
9
Although a forward-looking rational agent who tries to decide whether or not to buy a house can be more realistic, in the
sense that he or she can consider all available information such as upcoming business conditions, housing market tax
reform, etc., this paper only considers adaptive expectations due to the lack of data reflecting rational expectations.
12
Table 2: Data used for calculation of the user cost of house ownership
Variables
𝑦
𝜏𝑡 : Average rate of comprehensive income tax1)
𝑝
𝜏𝑡 : Average rate of property tax1)
δ: Rate of depreciation rate of real housing
capital stock
𝑖: CD (certificate of deposit) rate
ℎ𝑝
𝐸π𝑡+1 : Expected rate of house price increase in
future
Explanations
Amount of tax / taxable income
Taxation on buildings/taxable property income, (aggregate
real estate tax also considered since 2005)
Applying an annual rate of 4.8% (quarterly rate 1.2%)
Mortgage lending rates usually vary in direct relationship
with CD rates.
Using moving averages of 3 years' rates of house price
increase; year-on-year basis
Note: 1) Those are effective (not marginal) tax rates calculated based on the annual tax statistics. Quarterly data is generated
by interpolation on the annual data using the cubic function.
Data: National Tax Service, Ministry of Public Administration and Security『Annual Local Tax Statistics Report』, Cho
and Lee (2009), and Kookmin Bank
Table 3 shows the results of unit root tests based on the Augmented Dickey-Fuller method,
revealing that every level variable has a unit root but every first differenced one is a
stationary time series.
Table 3: Unit root test1)
Null hypothesis (𝐻0 ): time series have unit roots
Variables
Levels
Constant term
Constant term + trend
0.4689
0.5156
ℎ𝑝𝑡
0.2532
0.6530
𝑠𝑡
0.4808
0.2059
𝑦𝑡
0.0857
0.1881
𝑛𝑡
0.6689
0.3213
𝑢𝑐𝑡
0.9501
0.5161
𝑑𝑡𝑖𝑡
First differences
Excluding
0.0005
0.0305
0.0000
0.0002
0.0000
0.0000
Note: 1) Numerical values are p-values for the null hypotheses.
2. Empirical Analysis
2.1 Long-run house price equation
We conduct Johansen Cointegration and Granger causality tests on the variables before
estimating the long-run house price equation. As shown in Appendix 2, at a 5% level of
13
significance. There are three cointegration relationships among the variables. We also find that
real income (𝑦𝑡 ), the user cost of house ownership (𝑢𝑐𝑡 ) and the economically active
population (𝑛𝑡 ) appear to have exogeneity to the real house price (ℎ𝑝𝑡 ), whereas real house
capital stock (𝑠𝑡 ) appears to be an endogenous variable. The 2SLS estimation method is
therefore applied, using two lagged variables as instruments. FMOLS and CCR, which are
often used in cointegration regression analysis, are also applied for a robustness check:
Table 4: Long-run house price equation (1991-2011)
Constant
Real housing capital stock
Real income
User cost of house ownership
Economically active population
Adjusted R-square
Number of Obs.
Test of unit roots in error terms2)
2SLS
-54.334***
(9.555)
FMOLS
-63.176***
(15.541)
CCR
-63.003***
(15.805)
-1.950***
(0.173)
-2.211***
(0.278)
-2.218***
(0.274)
0.274
(0.417)
0.332
(0.681)
0.352
(0.717)
-0.899***
(0.201)
-0.923***
(0.319)
-0.928***
(0.298)
7.666***
(1.487)
8.822***
(2.415)
8.789***
(2.467)
0.666
82
0.020
0.679
83
0.010
0.678
83
0.010
Note: 1) Figures in parentheses are standard deviations, and ***, **, and * denote significance levels of
1%, 5% and 10%, respectively.
2) The p-values of the Augmented Dickey-Fuller test (excluding constant terms), on the null
hypothesis that a unit root exists in an error term are displayed.
As shown in Table 4, most of the results of long-run house price equation are in
accordance with the theoretical expectations. That is, increases in real house capital stock (𝑠𝑡 )
and the user cost of house ownership (𝑢𝑐𝑡 ) lead to decreases in real house prices (ℎ𝑝𝑡 ),
whereas increases in real income (𝑦𝑡 ) and the economically active population (𝑛𝑡 ) cause
house prices to rise. The real income (𝑦𝑡 ) variable, however, shows relatively low statistical
significance. In the meantime, the results of unit root tests on the error terms reject the null
14
hypothesis that they have unit roots at a 5% significance level, consistent with the Johansen
cointegration test results.
Next, we evaluate whether historical house prices are overvalued (or undervalued)
compared to their long-run trend based upon the estimation results presented above. As
shown in Figure 1 below, Korean house prices went through two rounds of steep increase in
the 2000s. The first round was from 2001 to 2003 and the second from 2006 to mid-2008,
right before the global financial crisis. During the first boom period, historical house prices
were still under the long-run house price trend reflecting economic fundamentals. This
implies that the rises in house prices in the first boom period can be interpreted as a process
of convergence to their long-run equilibrium level. As displayed in Figure 1, nominal house
prices were stagnant during the 1990s and then suddenly dropped after the 1997 Asian Crisis.
When we consider the relatively high inflation during that period, real house prices actually
underwent sizable negative growth. The rise in house prices during the first boom period can
therefore be interpreted as a counter reaction to over-deflation of house prices in the previous
decade. This is by and large consistent with Lee and Song (2007)’s findings of being unable
to observe any bubbles in house prices until 2005. In the second boom from 2006 to mid2008, however, historical house prices are conspicuously overvalued relative to the long-run
trend. There is a difference between the two prices of 6.3% on average10, a gap that has since
diminished as the rate of increase in historical house prices has slowed following the 2008
global financial crisis. In order to identify the factors other than economic fundamentals that,
account for the rise in house prices since 2006, we focus among many candidates on the role
of household debt. As discussed earlier, house prices and household debt might be closely
10
The patterns for the two house prices seen in the results of FMOLS and CCRs estimation are quite similar to those of our
2SLS estimations.
15
interconnected through mortgage lending and financial acceleration.
Figure 1: Historical and long-run house prices
Notes: 1) Nationwide nominal house price index, (4th quarter of 2005 = 100)
2) Long-run house prices are forecasts from the 2SLS estimation; similar results are obtained using the results of
estimation by FMOLS and CCR.
We accordingly estimate a long-run house price equation that includes the household
debt-to-income ratio11. After adding the household debt-to-income ratio variable (𝑑𝑡𝑖𝑡 ) to our
previous long-run house price equation12, we conduct Johansen cointegration and Granger
causality tests on it. The results show that three cointegration relations exist at the 5%
significance level, and that all variables with the exception of the real house capital stock (𝑠𝑡 )
appear to have exogeneity with respect to the real house price (ℎ𝑝𝑡 ).
The 2SLS estimation method is applied using two lagged variables of the housing capital
stock (𝑠𝑡 ) as instruments. The FMOLS and CCR cointegration regression methods are also
applied.
Table 5 shows the results of estimation for a long-run house prices incorporating
11
12
Favilukis et al. (2010) argue that financial development promoted by economic growth can be one of the fundamental
factors determining house prices, and that the household debt-to- income ratio can represent the degree of financial
development.
See Appendix 2 for a more detailed discussion.
16
household debt. The coefficient of the household debt-to-income ratio (𝑑𝑡𝑖𝑡 ) indicates that a
higher debt-to-income ratio pushes house prices up with statistical significance. The signs of
the coefficients of the other explanatory variables also correspond well to the theoretical
predictions. Depending upon the estimation method, however, the statistical significances
appear low when it comes to those of real income (𝑦𝑡 ), the user cost of house ownership (𝑢𝑐𝑡 )
and the economically active population (𝑛𝑡 ).
Table 5: Long-run house price equation with household debt (1991-2011)
Constant
Real housing capital stock
Real income
User cost of house ownership
Economically active population
Household debt-to-income ratio
Adjusted R-square
Number of Obs.
Unit root test for error terms2)
2SLS
-2.195
(5.598)
-1.251***
(0.093)
0.353*
(0.200)
-0.110
(0.108)
1.341
(0.813)
0.438***
(0.027)
0.923
82
0.001
FMOLS
-4.963
(9.315)
-1.223***
(0.154)
0.044
(0.334)
-0.139
(0.176)
1.949
(1.350)
0.459***
(0.046)
0.922
83
0.0003
CCR
-6.015
(9.630)
-1.232***
(0.154)
0.007
(0.351)
-0.138
(0.171)
2.112
(1.404)
0.458***
(0.045)
0.921
83
0.0003
Notes: 1) Figures in parentheses are the standard deviations, and ***, **, and * denote significance levels of 1%, 5%
and 10%, respectively.
2) The p-values of the Augmented Dickey-Fuller test (excluding constant terms) on null hypothesis such that a
unit root exists in an error term are displayed.
We again examine whether house prices are undervalued or overvalued compared with
their long-run trend. As shown in Figure 2, the overall fitness of the model is conspicuously
enhanced when the household debt-to-income ratio is incorporated. The degree of
overvaluation of historical nominal house prices during 2006 to mid-2008 is decreased, from
6.3% previously to 4.3%. The gap still unexplained by economic fundamentals and household
debt seems to be attributable to a combination of factors such as temporary excess demand
17
caused by expectations of additional house price increase, supply side factors that are not
sufficiently reflected in the equation, and institutional effects including the reform that took
place of the real estate tax system:
Figure 2: Historical and long-run house prices with household debt1)
Notes: 1) Nationwide nominal house price index, (4th quarter of 2005 = 100)
2) Long-run house prices are forecasts from the 2SLS estimation, and similar results are obtained when using the
estimation results by FMOLS and CCR.
2.2 Short-run house price adjustment equation
In the real housing market, there is now a gap between current and long-run house prices,
which it may take a certain amount of time to ease. We thus estimate a short-run house price
adjustment equation, including an error correcting process, as in equation (5). Analysis using
this equation enables us to identify the extent of herd behavior in the housing market, as well
as the speed of house price adjustment to a long-run equilibrium. Table 6 shows the results of
estimation via this equation, from which we can verify that historical house prices tend to
converge to their long-run trend, given that the coefficient of the previous quarter's error
correction term (historical house prices - long-run house prices) appears to have a negative
value (-) with statistical insignificance. This implies that the positive error correction term has
18
a trend of convergence to long-run house prices with relatively low power. In accordance
with Antipa and Lecat (2009), we estimate the speed of this convergence based on the size of
the error correction term (-0.037). The result shows that it takes about more than four years
for the gap between the two prices to narrow down by 50%.13
Table 6: Short-run house price adjustment equation (1991-2011)
Variables
Constant
Error correction term(-1)
Growth rate of real house prices (-1)
Growth rate of real house prices (-2)
Growth rate of real house prices (-3)
Growth rate of real house prices (-4)
(a)
-0.001
(0.003)
-0.037
(0.031)
1.394***
(0.142)
-0.536***
(0.181)
-0.034
(0.134)
0.055
(0.098)
(b)
-0.006
(0.004)
-0.036
(0.032)
1.333***
(0.110)
-0.516***
(0.161)
-0.054
(0.133)
0.130
(0.116)
0.148*
(0.086)
(c)
-0.009
(0.006)
-0.030
(0.032)
1.293***
(0.108)
-0.492***
(0.153)
-0.087
(0.130)
0.152
(0.116)
0.172*
(0.095)
0.027
(0.027)
0.882
0.886
0.886
76
76
76
Growth rate of real income
Change in household debt-to-income ratio
Adjusted R-square
Number of Obs.
Notes: 1) Estimation method is OLS with Newey-West standard errors.
2) ***, **, and * refer to significance levels of 1%, 5% and 10%, respectively.
When we look at the rates of house price increase, the first and second lagged variables of
them are positive and statistically significant, indicating that house prices tend to preserve
momentum, showing the persistence that is one of the stylized facts about house prices. In the
meantime, the coefficients of the other short-run variables correspond to the theoretical
predictions with statistical significance. The growth rate of real income has more significant
effects on the short-run changes in house prices, while the level variable has limited effects
13
(1–0.037)18 = 0.50. After 18 quarters (more than four years), the gap between the two prices narrows by 50%.
19
on long-run house prices. The change in the household debt-to-income ratio shows a limited
positive effect on the rate of house price increase, while the crucial effect seen in the long-run
perspective.
2.3 House price sustainability under alternative household debt scenarios
Lastly, we predict the paths of long-run house prices in the upcoming 5 years, based upon
three separate scenarios for developments related to household debt. This task requires longrun forecasts for four major macro variables – the real housing capital stock (𝑠𝑡 ), real income
(𝑦𝑡 ), the user cost of house ownership (𝑢𝑐𝑡 ), and the economically active population (𝑛𝑡 ). The
long-run forecasts for the period of 2013-2017 are from the Bank of Korea (2012) and
National Assembly Budget Office (2012), with the exception of that for the economically
active population.
Table 7: Long-run forecasts for macroeconomic variables
(%)
Year
2012
2013
2014
2015
2016
2017
Growth rate of Growth rate of 35- Interest rate on 3Inflation
construction
to 59-year-old
year government
rate
2)
investment
population
bonds
Basis
: Real house
: Economically
: User cost of house
: Real income
capital stock active population
ownership
2.0
-0.9
-0.08
3.1
2.2
The Bank of
2.8
2.5
-0.28
3.3
2.5
Korea and
3.8
2.0
-0.32
3.5
2.8
National
3.9
1.5
-0.30
3.4
2.5
Assembly
3.4
2.0
-0.35
3.2
2.4
Budget Office1)
3.4
2.0
-0.48
3.2
2.4
Economic
growth rate
Note: 1) The Bank of Korea: Economic outlook for 2013; National Assembly Budget Office: Revised
economic prospect and fiscal analysis for the year 2012
2) Data from Statistics Korea
Table 7 illustrates the long-run forecasts for the different variables. First of all, the rate of
economic growth is assumed to hover at around 3.5% on average during 2013-2017. Next, the
20
rate of growth of the 35- to 59-year old population, from Statistics Korea data, is used as the basis
for predicting the economically active population since the age group between 35 and 59 can be
regarded as the core housing demand cohort in society. In the meantime, the average property
and income tax rates used in calculating the user cost of house ownership are assumed to
maintain their current values as of the 4th quarter of 2011. Capital gains from changes in
house prices are assumed to be the average value over 1991-2011 period (2.31%); in other
words, if long-run equilibrium inflation is around 2.5% then the rate of increase in real house
prices is near zero.
The three possible scenarios for the household debt-to-income ratio are as follow: i)
scenario 1 that the ratio will keep rising at the average speed during 2006 to 3rd quarter 2008,
which representing relatively usual economic situation right before the global financial crisis;
ii) scenario 2 that the ratio will stay at around average level (3.1614) from 2009 through 2011,
given that after having risen continuously in the 2000s, the ratio has stayed the same since the
global financial crisis in 2008; and iii) scenario 3 that the ratio will converge from 3.16 to its
average level during the 2006 to 3rd quarter 2008 (2.9), following deleveraging in the
household sector like that which occurred in major OECD countries including the U.S., the
UK, and Spain after the global financial crisis.
14
This value is the ratio of household lending in the flow of funds to quarterly nominal gross national income.
21
Figure 3: Forecasts of long-run house prices
Notes: 1) Nationwide nominal house price index, (4th quarter of 2005 = 100)
2) Forecasts are based on 2SLS estimation, and similar results are obtained when the results of estimation by FMOLS
and CCR are applied.
3) Scenario 1: household debt-to-income ratio will keep increasing at the average speed during 2006 to 3rd quarter
2008; scenario 2: the ratio will stay at average level from 2009 to 2011; scenario 3: the ratio will decrease from
current level to its average during the 2006 to 3rd quarter 2008.
Figure 3 shows the forecasts of fundamental house prices based upon these three scenarios
for household debt. First, if the household debt-to-income ratio rises at the similar speed during
2006 to 2008, the long-term trend of long-run house prices is expected to show gradual growth
a bit lower than the 3% inflation rate. This appears to be mainly caused by the decline in rate of
growth of the 35- to 59-year-old age group from 2012, despite a variety of reasons for house
prices to increase such as sound growth in real income, and a sizable fall in the rate of growth
in real housing capital stock. In the case where the household debt-to-income ratio maintains its
2009-2011 level, the long-term trend of long-run house prices is expected to stagnate around
2012 level. Finally in the case where the household debt-to-income ratio is gradually reduced to
its average level of the 2000s, the house price trend is expected to decrease at a slow pace. This
implies that a gradual shrinkage in household debt may lead to decline in house prices if there
are no significant changes in other long-run variables. Accordingly, given the low likelihood of
22
a rapid increase in the household debt-to-income ratio, the long-term trend of fundamental
house prices is expected to follow a path somewhere in between these three predictions.
As shown, the future long-term trend of fundamental house prices is expected to either
show gradual growth at below the 3% inflation rate, stay at a level similar to current house
prices or decrease at a slow pace depending on the household debt-to-income scenarios.
Given this prediction, house prices are unlikely to show a rapid increase, as they did in the
2000s. These expectations are based upon two major assumptions, however. The first is that
the current economic environments in the real economy and the financial markets will persist
without any additional shocks. The second is that the Korean economy will gradually
approach a long-term equilibrium state. Accordingly, we need to pay constant attention to the
possibility that house prices may respond sensitively to the institutional factors surrounding
the house market, such as the intensity and direction of changes in administrative policy
toward the housing market.
Ⅳ. Conclusion
Over the last 10 years, house prices and the size of household debt have displayed
simultaneous sizable increases. Amid the recent adjustment in house prices since the 2008
global financial crisis, concerns over the sustainability of house prices and household debt
have been growing and repeatedly revisited. This paper looks into the house price dynamics
that are in close relationships with household debt and forecasts the trend of long-run house
prices.
The results of estimation generally confirm that household debt is one of the main factors
underlying the house price dynamics, consistent with the previous empirical findings in other
23
countries. More specifically, the results show that the increase in house prices during the first
boom period in the 2000s was actually a convergence to the long-run equilibrium level, while
during the second boom from 2006 to mid-2008, house prices were overvalued. The degree
of their over-valuation in the second boom period drops, however, from 6.3% to 4.3%, when
household debt is incorporated into the estimation.
Analysis by an error correction model meanwhile shows that adjustment takes place
gradually, as about four years are needed for the difference between historical and long-run
house prices to narrow by one-half. In addition, the process of short-run adjustment of house
prices is greatly affected by the persistence of house prices as well as short-fun fundamental
factors. Lastly, we forecast the trend of long-run house prices based upon three alternative
potential scenarios for household debt, one being that the household debt-to-income ratio will
rise at the similar pace of the periods before the global financial crisis, another that the
household debt-to-income ratio will stay where it is, and the other that it will be gradually
reduced back to its average of the periods before the crisis following deleveraging similar to
that seen in advanced countries. The forecasts indicate that long-run house prices over the
next 5 years can be expected to increase slightly, at a pace slower than the 3% inflation, stay
at a level around that of current house prices, or decrease gradually depending on the
household debt-to-income scenarios.
To sum up, when long-term changes in the macro-financial environment are considered,
house prices are unlikely to rise as sharply as they did in the 2000s. Specifically,
deleveraging pressures from the household debt burden and decelerating population growth
in the core housing demand age group are expected in the Korean economy of the near future.
Such expected changes in the trend of house prices can affect households' decisions on the
24
amounts of debt to hold. In turn, and as we can see from the 2007 sub-prime mortgage crisis
in the U.S., a potential steep change in household debt, either a sharp decline or a constant
rise, can heighten the potential systemic risks in the banking system. The government must
therefore devote enduring policy efforts to mitigating any possible steep changes in asset
values and to managing a proper level of the household debt-to- income ratio.
25
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27
Appendix 1: Time-series of the data
Real house prices
Real housing capital stock
.5
13.8
.4
13.6
.3
13.4
.2
13.2
.1
13.0
.0
12.8
-.1
12.6
-.2
12.4
-.3
12.2
92
94
96
98
00
02
04
06
08
10
12
92
94
Real income
96
98
00
02
04
06
08
10
12
Economically active population
12.5
10.15
12.4
10.10
12.3
10.05
12.2
12.1
10.00
12.0
9.95
11.9
9.90
11.8
9.85
11.7
9.80
11.6
92
94
96
98
00
02
04
06
08
10
92
12
User cost of housing ownership
94
96
98
00
02
04
06
08
10
12
Household debt to income ratio
3.6
.20
3.2
.15
2.8
.10
2.4
.05
2.0
.00
1.6
-.05
1.2
92
94
96
98
00
02
04
06
08
10
12
92
28
94
96
98
00
02
04
06
08
10
12
Growth rate of real house prices1)
Growth rate of real income1)
.15
.12
.10
.08
.05
.04
.00
.00
-.05
-.04
-.10
-.08
-.15
-.20
-.12
92
94
96
98
00
02
04
06
08
10
12
92
Change in household debt-to-income ratio2)
.6
.5
.4
.3
.2
.1
.0
-.1
-.2
92
94
96
98
00
02
04
06
08
10
12
Notes: 1) Yearly basis growth rates.
2) Simple differences.
29
94
96
98
00
02
04
06
08
10
12
Appendix 2: Johansen cointegration and Granger causality test results
1. Long-run house price equation without household debt
Cointegration test1)
Hypothesized
No. of CE(s)
None2)
Eigenvalue
Trace
Statistic
0.05
Critical Value
Prob.3)
0.342
100.047
69.819
0.000
At most 12)
0.297
66.086
47.856
0.000
2)
0.287
37.528
29.797
0.005
At most 3
0.091
10.107
15.495
0.273
At most 4
0.029
2.406
3.841
0.121
At most 2
Notes: 1) Trace test result indicates existence of three cointegrating relationships at a 5% significance level.
2) They illustrate rejection of the null hypothesis that there is no cointegrating relationship, at a 5% significance
level.
3) MacKinnon-Haug-Michelis (1999) p-values
2. Long-run house price equation with household debt
Cointegration test1)
Hypothesized
No. of CE(s)
None2)
Eigenvalue
Trace
Statistic
0.05
Critical Value
Prob.3)
0.461
146.744
95.754
0.000
At most 1
2)
0.384
96.692
69.819
0.000
At most 2
2)
0.301
57.385
47.856
0.005
At most 3
0.213
28.420
29.797
0.071
At most 4
0.078
9.005
15.495
0.365
At most 5
0.029
2.407
3.841
0.121
Notes: 1) Trace test result indicates existence of three cointegrating relationships at a 5% significance level.
2) They illustrate rejection of the null hypothesis that there is no cointegrating relationship, at a 5% significance
level.
3) MacKinnon-Haug-Michelis (1999) p-values
30
3. Granger causality test results
Granger causality test
Null Hypothesis
𝑠𝑡
⇏ ℎ𝑝𝑡
ℎ𝑝𝑡
𝑦𝑡
⇏
⇏
81
𝑠𝑡
ℎ𝑝𝑡
ℎ𝑝𝑡
⇏
𝑦𝑡
𝑢𝑐𝑡
⇏
ℎ𝑝𝑡
ℎ𝑝𝑡
⇏
𝑢𝑐𝑡
𝑛𝑡
⇏
ℎ𝑝𝑡
ℎ𝑝𝑡
⇏
𝑛𝑡
𝑑𝑡𝑖𝑡 ⇏
ℎ𝑝𝑡
ℎ𝑝𝑡
𝑑𝑡𝑖𝑡
⇏
Obs.
81
81
81
81
F-Statistic
Prob.
5.015
0.003
13.241
0.000
3.955
0.011
0.541
0.656
1.389
0.253
2.360
0.078
3.098
0.032
0.314
0.815
2.124
0.104
1.286
0.285
Note: Test results show that the null hypotheses that real house prices (ℎ𝑝𝑡 ) do not Granger cause real income (𝑦𝑡 ), the
user cost of house ownership (𝑢𝑐𝑡 ), the economically active population (𝑛𝑡 ) and the household debt-to-income ratio
(𝑑𝑡𝑖𝑡 ) are not rejected, at a 5% significance level, which implies that these independent variables have exogeneity to
the dependent variable, real house prices(ℎ𝑝𝑡 ).
31