A Study on the Adjustment Process of the Rent to Cheonsei Ratio on the Change of Interest Rate in the Seoul Metropolitan Area^*

The cheonsei system is one of Korea’s unique rental housing systems,⁷⁾ and is a combined system of money lending and rental housing. It is not easy to understand how the rent to cheonsei ratio is determined, because the lessor and the lessee can have a choice between cheonsei and monthly rent (or monthly rent with security deposit) as well as the cheonsei system is a combined system of money lending and rental housing.

Lee (2012) derived equilibrium conditions for the lessor and for the lessee in choosing between cheonsei and monthly rent, and showed that the cheonsei market and the monthly rent market achieve an equilibrium when the two equilibrium conditions are satisfied simultaneously. And he called the rent to cheonsei ratio at a time when the two markets (cheonsei market and monthly rent market) achieve an equilibrium at the same time ‘the market equilibrium rent to cheonsei ratio,’ and showed theoretically how the rent to cheonsei ratio finds a new equilibrium according as the market interest rate changes.

This paper intends to investigate theoretically how the rent to cheonsei ratio varies with the changes in the market interest rate, on the basis of Lee’s (2012) logic.⁸⁾ For this, let us first suppose that there are only cheonsei and monthly rent in the rental housing market, and that the lessor and the lessee choose between cheonsei and monthly rent.⁹⁾ And we suppose that the lessor and the lessee can borrow money at the rate of return on risk-free asset, and deposit money at the same interest rate.¹⁰⁾ In addition, it is supposed that the lessor’s equity capital is the same whether the lessor rents a house on a basis of cheonsei or monthly rent. It is assumed that the lessee’s equity capital is also the same whether the lessee leases a house on a basis of cheonsei or monthly rent.

It is assumed that the lessor purchases and rents a house priced at $P$, raising money for it by borrowing $C$, which is equivalent to cheonsei key money, and providing ($P-C$) from the lessor’s own capital. It is assumed that in case of renting this house on a cheonsei basis, $C$ is raised by cheonsei key money, while in case of renting it on a monthly rent basis, $C$ is borrowed from a financial institution. And it is assumed that in case of leasing a house on a cheonsei basis, the lessee borrows $C$ from a financial institution, while in case of leasing it on a monthly rent basis, he does not borrow money.

In the case of the lessor, the choice between renting on a cheonsei basis and renting on a monthly rent basis becomes indifferent only when the return on equity is the same whether he rents a house on a basis of cheonsei or monthly rent¹¹⁾. The return on equity for a case of renting a house on a cheonsei basis ($r_c$) can be expressed as Eq. (1), and that for a case of renting it on a monthly rent basis ($r_m$) can be expressed as Eq. (2). And the lessor’s equilibrium conditions are as shown in Eq. (3).

$r_c=\frac{\Delta P}{P-C}$

$r_m=\frac{\Delta P+\left(1-k\right)R-iC}{P-C}$

$\frac{\Delta P}{P-C}=\frac{\Delta P+\left(1-k\right)R-iC}{P-C}$

Where $\Delta P$ denotes the expected capital gain, and $R$ denotes rent that can be received in case of renting a house on a monthly rent basis. $k$ is the expected rate of loss due to vacancy or bad tenant in case of renting a house on a monthly rent basis. And $i$ denotes the return on risk-free asset, and it is the same as the interest rate for loan according to assumption.

Eq. (3) can be arranged as Eq.(4).

$\frac{R}{C}=\frac{i}{1-k}=i+{\pi }_o$

where ${\pi }_o=\frac{k}{1-k}i$

In Eq. (4), $R/C$ is the rent to cheonsei ratio,¹²⁾ and ${\pi }_o$ denotes the premium for rental risk (the risk of vacancy, or the arrearage or non-payment of rent) that the lessor should take when he chooses monthly rent. Eq. (4) means that the lessor becomes indifferent between cheonsei and monthly rent only when the rent to cheonsei ratio is the same with the return on risk-free asset plus a premium for rental risk.

If $r_c〈r_m$ (if $R/C〉i+{\pi }_o$), the lessor will choose monthly rent instead of cheonsei. On the contrary, if $r_c〉r_m$ (if $R/C〈i+{\pi }_o$), the lessor will choose cheonsei instead of monthly rent.

On the other hand, the lessee’s choice between cheonsei and monthly rent becomes indifferent only when housing cost is the same whether leasing on a cheonsei basis or on a monthly rent basis. The lessee’s housing cost in case of leasing on a cheonsei basis ($U_c$) is equivalent to Eq. (5). And that in case of leasing on a monthly rent ($U_m$) is equivalent to Eq. (6). The lessee’s equilibrium conditions are as shown in Eq. (7).

$U_c=iC+H$

$U_m=R$

$iC+H=R$

H is a sort of contingent cost that the lessee may incur by choosing cheonsei. It includes cost caused by the lessor’s bankruptcy and by failing to get back cheonsei key money timely.

Eq. (7) can be arranged as Eq. (8) below.

$\frac{R}{C}=i+\frac{H}{C}=i+{\pi }_l$

where $\frac{H}{C}={\pi }_l$

In Eq. (8), ${\pi }_l$ denotes the lessee’s premium for risk of choosing cheonsei. Eq. (8) means that the lessee becomes indifferent between cheonsei and monthly rent only when the rent to cheonsei ratio is the same with the return on risk-free asset plus a risk premium on private lending (lending the cheonsei key money to the lessor).

If $U_c〈U_m$ (if $R/C〉i+{\pi }_l$), the lessee will choose cheonsei instead of monthly rent. On the contrary, if $U_c〉U_m$ (if $R/C〈i+{\pi }_o$), the lessee will choose monthly rent instead of cheonsei.

If the lessor and the lessee are in equilibrium at the same time, the cheonsei market and the monthly rent market are also in equilibrium. That is, if Eq. (9) is valid, the cheonsei market and the monthly rent market achieve an equilibrium at the same time.

$\frac{R}{C}=i+{\pi }_o=i+{\pi }_l$

Eq. (9) indicates that the cheonsei market and the monthly rent market are in equilibrium at the same time only when the lessor’s risk premium coincides with the lessee’s risk premium. Is this possible? There exists an equilibrium point at which Eq. (9) is satisfied because lessors and lessees have different risk premiums according to their own demographic and economic characteristics. For example, if a lessee has a lending risk premium lower than the equilibrium risk premium (${\pi }_0^{*}={\pi }_l^{*}$), he/she will choose cheonsei. On the contrary, if a lessee has a lending risk premium higher than the equilibrium risk premium, he/she will choose monthly rent. Similarly, if a lessor has a renting risk premium lower than the equilibrium risk premium, he/she will choose monthly rent. On the contrary, if a lessor has a renting risk premium higher than the equilibrium risk premium, he/she will choose cheonsei.

For the simplification of the theoretical model, we assumed above that both lessor and lessee can borrow money at the rate of return on risk-free asset. However, borrowing interest rates for the lessor and the lessee may be different. Generally, the lessor’s loan interest rate is low because a house is used as a guarantee, whereas the lessee’s loan interest is high because of having to borrow money on credit. This, however, also varies according to the lessor’s and the lessee’s demographic and economic characteristics. If even a lessor is heavily in debt, the financing cost will be high. If a lessee has good credit, the financing cost will be low. When the credit spread on the lessor’s financing is denoted by $s_o$ and the credit spread on the lessee’s financing is denoted by $s_l$, Eq. (9) is modified as follows:

$\frac{R}{C}=i+\left(s_o+{\pi }_o\right)=i+\left(s_l+{\pi }_l\right)$

To think about the credit spread alone, among lessors, a lessor who have difficulty in financing will require a rent to cheonsei ratio higher than the equilibrium rent to cheonsei ratio in the market because he/she should pay a high premium. In this case, this lessor will choose cheonsei because of ${\left(R/C\right)}^{*}\langle i+\left(s_0+{\pi }_0\right)$. As for a lessor who can finance money easily, he/she will choose monthly rent on the contrary for ${\left(R/C\right)}^{*}\rangle i+\left(s_0+{\pi }_0\right)$ due to a low credit spread.

In addition, among lessees, a lessee who can finance money easily (in particular, one who has his own money or can get cheonsei key money from parents) will require a rent to cheonsei ratio lower than the equilibrium rent to cheonsei ratio in the market. Thus, this lessee will choose cheonsei for ${\left(R/C\right)}^{*}\rangle i+\left(s_0+{\pi }_0\right)$. As for a lessee who has difficulty in financing money will choose monthly rent on the contrary because of ${\left(R/C\right)}^{*}\langle i+\left(s_0+{\pi }_0\right)$ due to a high credit spread.

If the market interest rate drops (if $i$, the rate of return on risk-free asset, drops to $i\text{'}$) under the condition of the simultaneous equilibrium of the cheonsei market and the monthly rent market, some of lessors who chose cheonsei will choose monthly rent because of ${\left(R/C\right)}^{*}=i+{\left(s_0+{\pi }_0\right)}^{*}\rangle i\text{'}+{\left(s_0+{\pi }_0\right)}^{*}$ (a decrease in the supply of cheonsei, an increase in the supply of monthly rent). Also, some of lessees who chose monthly rent will choose cheonsei because of ${\left(R/C\right)}^{*}=i+{\left(s_l+{\pi }_l\right)}^{*}\rangle i\text{'}+{\left(s_l+{\pi }_l\right)}^{*}$(an increase in demand for cheonsei, a decrease in demand for monthly rent). As a result, the rent to cheonsei ratio comes to fall as the cheonsei price rises and the monthly rent price falls. Through this process, the cheonsei market and the monthly rent market come to find a new equilibrium.

As shown above, a change in the market interest rate changes the rent to cheonsei ratio through demand and supply changes in the cheonsei market and the monthly rent market. These changes, however, may not occur immediately in the real world. For example, even though the market interest rate changes, the supply and demand changes in the cheonsei market and the monthly rent market may happen slowly due to the remaining period of a rental contract, costs of house moving, time taken to borrow money, etc. As a result, changes in the cheonsei price and the monthly rent price and the change of the rent to cheonsei ratio may occur with time lags. That is, while the rent to cheonsei ratio finds a new equilibrium according to changes in the market interest rate in the long term, it may be said that equilibrium error caused by the change of the market interest rate is slowly adjusted in the short term.

Let us model this process in which the rent to cheonsei ratio finds an equilibrium in the short and long term.¹³⁾ As shown above, the condition for the simultaneous equilibrium of the cheonsei market and the monthly rent market is $R/C=i+\left(s+\pi \right)$, where the risk premium, ($s+\pi$), is not observable. And the Korea Treasury Bond yield, which represents the market interest, is usually used as the rate of return on risk-free asset. However, the Korea Treasury Bond yield is not exactly equal to the theoretical rate of returns on risk-free asset because the yields of the bonds vary in liquidity risk according to their maturities. Accordingly, the long-run equilibrium relationship between the rent to cheonsei ratio and the market interest rate can be estimated with the following equation.

As shown above, a change in the market interest rate changes the rent to cheonsei ratio through demand and supply changes in the cheonsei market and the monthly rent market. These changes, however, may not occur immediately in the real world. For example, even though the market interest rate changes, the supply and demand changes in the cheonsei market and the monthly rent market may happen slowly due to the remaining period of a rental contract, costs of house moving, time taken to borrow money, etc. As a result, changes in the cheonsei price and the monthly rent price and the change of the rent to cheonsei ratio may occur with time lags. That is, while the rent to cheonsei ratio finds a new equilibrium according to changes in the market interest rate in the long term, it may be said that equilibrium error caused by the change of the market interest rate is slowly adjusted in the short term.

Let us model this process in which the rent to cheonsei ratio finds an equilibrium in the short and long term.¹³⁾ As shown above, the condition for the simultaneous equilibrium of the cheonsei market and the monthly rent market is $R/C=i+\left(s+\pi \right)$, where the risk premium, ($s+\pi$), is not observable. And the Korea Treasury Bond yield, which represents the market interest, is usually used as the rate of return on risk-free asset. However, the Korea Treasury Bond yield is not exactly equal to the theoretical rate of returns on risk-free asset because the yields of the bonds vary in liquidity risk according to their maturities. Accordingly, the long-run equilibrium relationship between the rent to cheonsei ratio and the market interest rate can be estimated with the following equation.

$\begin{array}{l}{\left(\frac{R}{C}\right)}_t=Y_t=\alpha +\beta r_t+e_t\\ t=1,2,\cdots ,n\end{array}$

Where $Y$ denotes the rent to cheonsei ratio, and $r$ denotes the market interest rate that acts as proxy for the rate of return on risk-free asset. It may be said that $\widehat{Y_t}=\widehat{\alpha }+\widehat{\beta }{r}_t$ estimated by Eq. (11) is the equilibrium rent to cheonsei ratio that achieves the simultaneous equilibrium of the cheonsei market and the monthly rent market.

If the rent to cheonsei ratio and the market interest rate are non-stationary time series, Eq. (11) becomes the so-called cointegration function. In this case, an error correction model (ECM) in the form of difference shows the process in which the rent to cheonsei ratio adjusts equilibrium error in the short term. The error correction model in the form of difference is as shown in Eq. (12).

$\Delta Y_t=\alpha +\delta \Delta r_t+\gamma \left(Y_{t-1}-\widehat{Y_{t-1}}\right)+u_t$

Where $\left(Y_{t-1}-\widehat{Y_{t-1}}\right)$ denotes the degree of disequilibrium of the rent to cheonsei ratio in the previous period. Eq. (12) means that when the market interest rate changes, the rent to cheonsei ratio reflects some of the change, and corrects some of disequilibrium in the previous period at the same time. The rent to cheonsei ratio converges to equilibrium only when the sign of $\gamma$ is ‘negative (-).’ That is, if the rent to cheonsei ratio is higher than the equilibrium level, the rent to cheonsei ratio should drop in the following period to converge to the equilibrium. In the opposite case, the rent to cheonsei ratio should rise in the following period.¹⁴⁾

For the estimation of Eq. (11) and Eq. (12), this study uses three types of rent to cheonsei ratio data mentioned in the Introduction (Data on the rent to cheonsei ratio published by KB; data on monthly rent interest rate in the Monthly Rent Price Trend Survey published by KAB; and data on the rent to cheonsei ratio in the National Housing Price Trend Survey announced by KAB).

The three rent to cheonsei ratios to be used in empirical analysis vary in time periods and data sources, and show differences in regions covered and house types. And there are also differences in the sources of price data (data on cheonsei and monthly rent), which serve as the grounds for the calculation of the rent to cheonsei ratio.

As for the data on the rent to cheonsei ratio published by KB, its time series began from August 2001, but was not published after March 2011. This data was based on licensed real estate agents’ appraisal price, and was subdivided by region into the whole nation, the Seoul metropolitan area, provinces, metropolitan cities, and Seoul. But it was not subdivided by houses type.

As for the data on monthly rent interest rate published by KAB, it was based on appraisal price like KB’s data, and its time series began from August 2010. This data was published until December 2014 only. This data is limited to the Seoul metropolitan area, Seoul, and metropolitan cities, and was not subdivided by house type.

On the other hand, the data on the rent to cheonsei ratio announced by KAB has been estimated on the basis of transaction data, and differs in characteristics from the above two data on the rent to cheonsei ratio. This data has been published since January 2011, and includes the whole nation, the Seoul metropolitan area, eight Dos (provinces), and metropolitan cities by region. It also subdivides house types into all houses, apartment, detached house, and row house.

The investigation of the long-run relationship between the rent to cheonsei ratio and the market interest rate requires a long period time-series, if possible. In this regard, the KB data on rent to cheonsei ratio has no problem in investigating the long-run relationship with the market interest ratio because it has a time series as long as 10 years. It, however, has the disadvantage that it can’t show the recent relationship. On the other hand, the KAB data on monthly rent interest rate or the rent to cheonsei ratio can show recent relationship, but has difficulty in showing the long-run relationship sufficiently for they have short time periods.

Given the above, this paper intends to generate a long-term time series data of the rent to cheonsei ratio by combining the KB data and the KAB data, and to investigate the long-run relationship between the rent to cheonsei ratio and the market interest rate. The KAB’s rent to cheonsei ratio shows the average difference of about 2%p in the KAB’s monthly rent interest rate and the KB’s rent to cheonsei ratio. On the other hand, it seems that there is almost no difference between the KB’s rent to cheonsei ratio data and the KAB’s monthly rent interest rate data, which are based on appraisal price.¹⁵⁾

Thus, we decided to combine the KB’s rent to cheonsei ratio and the KAB’s monthly rent interest rate into one time series,¹⁶⁾ to estimate the long-run equilibrium relationship between this time series and the market interest rate, and to analyze the process of short-term adjustment. ‘But the common regions of the two time series are limited to the Seoul metropolitan area and Seoul. So we decided to make analysis using the data of rent to cheonsei ratio on the basis of all houses in the Seoul metropolitan area because ‘all houses’ is the only house type available from the data.¹⁷⁾

For the market interest rate, which represents the return on risk-free asset, data on Korea Treasury Bond yields was used, provided that the three-year bond yield was used given that the term of a cheonsei agreement is about three years on average.

If the degree of financial inclusion changes, the adjustment process of rent to cheonsei ratio may change. As for the volume of cheonsei key money loan guarantee by the Housing Finance Credit Guarantee Fund, the rate of an increase in the guarantee of cheonsei key money loan was very slow until 2006. Then, the rate of an increase in the guarantee becomes very fast after 2007. Given that the cheonsei key money loan is a kind of credit loan, the increase in cheonsei key money loan by the credit guarantee by the government may be interpreted as the expansion of financial inclusion of households.

On the other hand, as for the trends of the Korea 3-year Treasury Bond yield and the mortgage interest rate, although they show a downward trend in the long term, they showed a downward trend and an upward trend alternately before the mid to late 2008. Then, they have showed a continuous downward trend since 2009. There may be differences in the long-run equilibrium and the short-term adjustment process of the rent to cheonsei ratio between when the market interest rate repeats fluctuations and when it continues to fall.

Consequently, we will investigate whether there are differences in the long-run equilibrium and the short-term adjustment process of the rent to cheonsei ratio by dividing the analysis period into before and after 2008. And with the KAB’s data on the rent to cheonsei ratio and the monthly rent interest rate, we will investigate whether there are differences in the long-run equilibrium relationship or the process of short-term adjustment between the rent to cheonsei ratio based on appraisal price and that based on transaction price.