Housing Market Dynamics in Korea: A Panel VAR Approach

Table 1 illustrates the recent ups-and-donws in apartment sales and Jeonse prices by region. While apartment sales prices have increased nationwide, some regions show decreases in price. In Daegu, one of the metropolitan cities, the sale price has been dropped in June 2016 and in June 2017. Some non-Seoul metropolitan regions, such as Chungbuk, Gyeongbuk, and Gyeongnam, have suffered from the incessant decrease in the sale price.

In the construction sector, the above-average permits and starts in 2015, 2016, and 2017 resulted in the fall in housing supply in 2018. If we assume that the historical average of apartment construction is about 300,000 units per year, we have witnessed a great deal of expansion in the apartment construction sector from 2013 up to date. In 2017, the flow of construction peaked at 569,209 units. Now, we anticpate a huge drop in the new construction in the coming years.

There are research papers on the housing market dynamics in Korea. Park and Ahn (2009) investigated the factors of housing price functuations in Seoul, Korea. They found that the prices are affected by the macroeconomic condition and the prices in the adjacent locations. Lee (2010) analyzed the linkage between housing prices and Jeonse prices using the vector error correction methodology. The study found the cointegrating relationship between the two. The long-run elasticity of Jeonse to price is estimated as 0.575 with a slow speed of adjustment. Kim and Lee (2011) examined the factors affecting housing prices using the panel unit root and panel cointegration tests. They also found the cointegration between the sale and Jeonse prices. They emphasized that region-specific characteristics are the important factors in determining the prices. Fousing on the macroeconomic liquity on housing prices, Lim (2015) found that interest rates change both stock prices and housing prices. Yoon et al. (2016) applied the panel vector error correction model to investigate the short-run and long-run effects of regional housing prices. They found that the patterns of short-run and long-run dynamics behave differently, and thus the policy responses should be designed to address the discrepancy in the market. A similar research was conducted for the regional housing prices using panel VAR by Koo and Choi (2018). The paper particularly focused on the comparison before and after of the 2008 global financial crisis. They found that it is important to understand the region-specific environment for the determination of housing price movement.

As for the construction sector, Ji et al. (2018) analyzed the factors on the time gap between housing permit and housing construction. They found that the gap resulted from the macroeconomic and socio-economic characteristics, predicting that low birth rate and rapid aging will limit the housing supply. Seo and Kim (2018) looked at the causal relationship between housing and construction. They found a statistically significant negative impact of the interest rate on all of the housing market variables, concluding that the market should keep vigilant watch over the changes in macroeconomic condition. For the role of land prices on housing construction, You (2018) concluded that housing starts are determined by housing prices positively and by land prices negatively.

This study contributes to the existing literature by examining the role of housing supply in the sales and the rental markets. When the positive demand shock arrives at the housing market system, the rental price of housing should rise, and the value of housing correspondingly increases. This short-run disequilibrium between housing stock and prices may excerbate the affordability of housing throughout the market, particularly in the market where the supply is highly inelastic. A new flow of housing supply should result in the adjustments in the stock and prices of housing, ending up with getting to a new, stable equilibrium. This paper tests whether or not this adjustment process exists in the Korea’s housing market.

From Sims(1980), there have been a great deal of studies, which applied the vector autoregressive (VAR) models. In the VAR framework, all the variables entered into the system are considered endogenous. The VAR system has proved to be a highly flexible model in explaining the dynamics of economic and financial markets. Although it is atheoretical per se in that it does not need any identifying assumption to draw the causal interpretation between some factors and the outcome variable of interest, the VAR estimation is very useful to figure out the interconnectivity of the variables and to forecast the future values of the variables considered in the model. The model applies when each variable depends on both its own lags and the ones of the other variables. Consider the following bivariate VAR system (VAR(2)):

where E(ϵ_1tϵ_2s) = σ₁₂ for t = s and zero for t≠s. We can arrage the terms of the lag variables, and yields and E(ϵ_t) = 0, E(ϵ_tϵ_s) = 0 for t ≠ s and

Using the lag operator Φ(L) = I₂−Φ₁L−Φ₂L² such that Φ(L)x_t = I₂x_t−Φ₁x_t−1−Φ₂x_t−2, the moving average, MA(∞), representation of the Equation 1 is

where Ψ(L) = (I₂−Φ₁L−Φ₂L²)⁻¹.

A problem should arise when we apply the VAR approach to model a national housing market: it cannot capture the unobserved random spatial heteogeneity, which indicates each region’s innate time-invariant characteristic. This probem can be solved when we expand the dataset to a panel structure. Suppose we have a set of regions (i = 1,…,n), each of which is observed at multiple periods (t = 1,…,n). Let y_it be the outcome variable of interest. The set of the independent variables that varies over time is denoted as x_it. Then, the model we want to specify takes the following form:

where μ_i is a constant (or an intercept) that could be different in each period, and β is the coefficient vector. One should note that there are two random terms in Equation 3. While ϵ_it varies over time across regions, the term α_i only varies regions, not over time period. The former represents the pure random shock to the system, but the latter captures all the unobserved variations that do not change over time. If we take α_i as the parameters to be estimated, we can obtain the unbiased estimators for β via the following between-groups transformation.

The between-group mean $\overline{{\alpha }_i}$ equals α_i because α_i is time-invariant. Therefore, estimating the Equation 4 is equivalent to cancelling out the effect of spatial heterogeneity. This study utilizes the VAR framework and the panel data structure at the same time, winding up with the use of the panel VAR approach.

The region-level, monthly data are provided by the Ministry of Land, Infrastructure and Transport, and publicly available. The data set is constructed by region (metroplitan cities or provinces) with the time period of 2012.1∼2017.11. The data from 2017.12 to the current month are excluded from the anlaysis because the data delivery organization (Korea Appraisal Board) has applied a new sampling and weighting scheme so that the data for the later period do not seem to be comparable to the previous time periods. The PPG variable refers to the growth rate of apartment sales price, the JPG variable means the growth rate of apartment Jeonse price, and the PJRD variable is the percentage change of the sales-to-Jeonse price ratio.

As for the sales prices and Jeonse prices, areas in the Seoul Metorpolitan region, that are Seoul, Incheon, and Gyeonggi, show the similar patterns. While Jeonse prices have gone up gradually during 2012 to 2017, the sales prices have decreased from 2012 to 2013 and picked up since 2014. The units completed show seasonaility and local flunctuation. The Gyeonggi region exhibits general upward trend in construction, reflecting the fact that there have been a continuous designation of new town development and land development in the region in order to decentralize the population in Seoul to the region.

The ratios of price to Jeonse for the Seoul Metropolitan areas gradually increase while Ulsan exhibits ups and downs. The ratio in Gwangju already picked up over the 80 percent around 2016 and keeps up, reflecting the use value and the transaction value of houses do not show much difference in that region.

The Harris-Tzavalis unit-root tests for the VAR variables are performed whether or not the time series variables are non-stationary and contain unit roots. The tests for PRICE, JEONSE, and PJR variables cannot reject the null hypothesis that the variables contain unit roots. As the result from the panel unit root test suggests that unit roots exist in PRICE, JEONSE, and PJR, I converted PRICE and JEONSE to the growth rate metrics (PPG and JPG, respectively) while transforming the price-to-Jeonse ratio to the percent change measure (PJRD). The null hypothesis that the number of housing units (COMP) has a unit root was strongly rejected, meaning that the COMP variable can be entered into the PVAR system as its original level form.

In order to select the final appropriate model, several models are estimated by specifying different instrument lags (see Table 5). Instrumenting the explanatory variables in each equation with their own lags makes the model to yield more significant coefficients and to be more stable. Among the models with instruments, the model with first to ninth lags as instruments is chosen to produce impulse response functions and variance decompositions.

After choosing the model with 1-9 lags of the variables as instruments, the PVAR systems with different lags were specified. In the completion equation, adding more lags makes the coefficient of the 1st lag of the complition smaller (from 0.3998 to 0.269). Except for the own variable, only the ratio of sales to Jeonse negatively influence the completion.

Housing supply (completion) affects the sales price, the Jeonse price, and the ratio. Those effects are all negative in the short run. The growth in the sales price results in the growth in the Jeonse price, but the growth in the Jeonse price reduces the growth in the sales price. The latter does not mean that the Jeonse price (level) decreases the sales price (level). When the sales price goes up, the buyers can or should raise more Jeonse deposit to purchase a unit. This works as the sales market is in the buyer’s market. When the growth in the Jeonse price increases in the short run, the speed in the growth in the sales price does not catch up the growth in the Jeonse price, which makes the ratio of sales-to-Jeonse price to increase higher.

This study chooses the 1st-lag and 1-9th instrumental lags specification as the final model because it shows the dynamics explained above more significantly (Model 2-1 in Table 6).

The main research focus is whether or not the newly-supplied housing units have an impact on the rental (Jeonse) housing market. Indeed, the units completed Granger-causes the growth of Jeonse price, but the opposite direction is not statistically significant in the PVAR(1) system (the p-value for the JPG to COMP causality test is 0.123). JPG Granger-causes only PPG. Then, PPG Granger-causes PJRD, which is in line with the PVAR(1) with 1∼9 lags of instruments model. The PJRD variable then Granger-causes the units completed. The PVAR Granger causality test, therefore, suggests the interretionships among construction and prices in the Korea’s housing market are described as COMP → JPG → PPG → PJRD. Furthermore, all the eigenvalues (not reported here) for the PVAR system lie inside the unit circle, meaning the system is stable.

First of all, all the impulse response functions illustrate that the PVAR model is stable. When the positive shocks in impulse variables move the response variables, and then go back to the original states. When the positive shock arrives at the housing supply, the growth in the Jeonse price initally slows down in the very short time period around 2 months, then slowly goes back to the original state (or a new equilibrium point). The positive shock in the Jeonse price growth shoots up the sales price growth, and then after 3 month or so, the change goes to 0 (zero). The difference in the sales-to-Jeonse ratio negatively responses and goes back as the sales price increses higher. Finally, housing supply decreases very shortly and goes back as the ratio of sales-to-Jeonse prices gets bigger.

The proportion of the variability of the housing units completed get smaller as time (months) elapses. After ten month, the completion accounts for only 50 percent of the variance of the completion itself. Rather, the Jeonse market does not seem to be explained much by other market variables.

The variability of the ratio of the sales price-to-Jeonse is explained by 74.4 percent in JPG and only by 25.2 percent in the ratio variable. When it comes to the growth in the sales price, the JPG and PJRD variables together explain more than 50 percent of the variance of the price growth after 10 months from the initial shock. It seems that much of the volatility in the housing market come from the flunctuation in the Jeonse market. And it is expected that the movements in the Jeonse market are originated from the positive shocks in the demand for space and in the housing supply.