Investigating the Unintended Consequences of the High School Equalization Policy on the Housing Market

: Owing to its potentially far-reaching impact on a large population, an educational policy may lead to unintended consequences beyond the educational area. The High School Equalization Policy (HSEP), introduced into South Korea in the mid-1970s, is representative of such a policy. HSEP prohibits high school entrance exams and randomly assigns students to a high school near their residence. Despite its aim of ensuring equal opportunities in education for all students regardless of socio-economic status, a frequent criticism was that HSEP could prompt students’ families to move to a region near traditional elite high schools, which, in turn, would widen the gap in house prices between di ﬀ erent regions. Thus, we conducted an empirical study to examine the secondary inﬂuence of the HSEP on the housing market via a di ﬀ erence-in-di ﬀ erences (DD) analysis. We used house price data from the Gangwon province, as the partial introduction of HSEP into the province allowed for a quasi-experimental study on the e ﬀ ect of HSEP. The result revealed that, contrary to expectations, the HSEP in Gangwon had the opposite spillover e ﬀ ect of reducing the gap of the average house prices by 5%~9% across regions.


Introduction
Policymakers carefully design and implement government policies or interventions to meet their goals efficiently. Evaluating such policies mainly involves identifying "what works, for whom, and under what circumstances" and the causal mechanisms driving the outcomes within the established scope [1,2]. However, because government interventions may impact a broad population in different ways, unintended consequences may arise from the policies beyond the target population or area [3][4][5]. Whether these are adverse or positive spillover effects, it is meaningful to uncover, monitor, and study them for the effective implementation of such policies in the future [6,7].
Educational polices are not exempt from unintended consequences, because changes in educational policies may affect every student and their family. It may prompt them not only to adopt different educational strategies, but also to alter their expenditure patterns [8][9][10] and their region of residence [11,12]. Empirical studies spanning multiple countries consistently find that the local educational climate is a key factor for families choosing a residential location [13][14][15][16][17]. This suggests that policies influencing the educational environment of a region may also significantly affect its housing market as an unintended consequence [18][19][20]. The High School Equalization Policy (HSEP), which started to be implemented in South Korea in the mid-1970s, exemplifies such an intervention. This policy mainly abolishes the entrance exams of all high schools and randomly assigns students to a high school among the ones nearby their residence. It aims to alleviate the competition among students to get into a highly ranked school and to provide equal educational opportunities for all students regardless of their social economics status [21][22][23]. Despite concerns over potential losses in educational efficiency [24], the policy was initially implemented in 1974 in two large cities, Seoul and Busan, supplemented with follow-up measures and revisions (e.g., the adjustment of school districts), and then adopted nationwide.
Years after HSEP was introduced, an unexpected, interesting phenomenon was observed in the housing market in Seoul. House prices in Gangnam, one of the richest districts in Seoul at present, continued to soar. Critics attributed this result to HSEP, though many other factors could have affected the housing market at that time (e.g., large-scale urban development projects in Gangnam). They argued that HSEP induced households with middle-school students to move into the Gangnam district where many elite high schools would be relocated, thereby increasing the demand for the houses in the district dramatically [12]. That HSEP could inflate house prices in specific districts became a pervasive concern every time HSEP was newly introduced to a different region [25]. If such claims are true, then decision-makers in education must be cautious about introducing HSEP, as their policy for reducing disparities in education may ironically increase disparities in wealth, beyond their original scope. Considering the possibility that this sort of policy can be implemented in other countries (e.g., Japan), it is meaningful to investigate whether introducing HSEP actually affected the housing market and widened the gap of the house prices between different regions.
As the number of regions enacting HSEP has gradually increased in South Korea, we alternatively searched for a region that satisfies quasi-natural experiment conditions and provides reliable data on house prices within the region. Finally, we selected Gangwon province, where HSEP was partially introduced into some of its divisions in the early 2010s, and tested our hypothesis that HSEP influenced the housing market via a difference-in-differences (DD) analysis. To ensure the robustness of the analysis result, three different time periods were considered for the post-treatment period, including six months after, one year after, and two years after the HSEP went into effect.

Materials and Methods
The data used in this study came from the public database of the Ministry of Land, Infrastructure, and Transport in South Korea (the data can be downloaded from the website in [26]). It includes the actual price of a transacted apartment, the final transaction date, address, size (m 2 ), floor, and construction year in Gangwon province. As transactions of apartments account for more than 70% of house transactions in South Korea [27], we focused on the change of apartment prices in the study. To control for the effect of the size of an apartment on its price, we used the actual transaction price per square meter of an apartment for the individual house price.
As mentioned in Introduction, we conducted a difference-in-differences (DD) analysis for testing our hypothesis about the secondary effect of HSEP on the housing market in Gangwon province. The DD analysis is a statistical technique that is often used in social sciences to identify the effects of policies from observational data [28,29]. For the DD analysis, observations must be classified into two groups: a treatment group, where a policy is applied, and a control group, where the policy is not applied. Then, the average difference in the amount of change of an outcome variable between the two groups after the treatment is computed and statistically tested, as the average difference may represent the treatment effect under the parallel trends assumption (i.e., that changes in the outcome variable of the two groups would be parallel absent any treatment).
In our analysis, the treatment group is the group of districts in Gangwon province where HSEP was implemented, whereas the control group includes the districts that did not adopt HSEP. HSEP was implemented only for the three cities (Chuncheon, Wonju, and Gangneung), in which most of the elite Sustainability 2020, 12, 8496 3 of 9 high schools within the Gangwon province were located. Figure 1 depicts the lists of districts in the two groups. . The three districts in the treatment group (HSEP was implemented) are orangecolored, whereas the rest in the control group (HSEP was not implemented) are in gray [30] As the outcome variable of our study is house price, we pre-examined whether the average house prices in the two groups show the parallel trends in the year before the HSEP was legislated. Figure 2 depicts the trends of the average house prices in the two groups from the third quarter 2009 to the second quarter 2014. As the local law for implementing HSEP in Gangwon province was passed and promulgated in December 2011, we focused on the trends during the one-year period from the third quarter of 2010 to the same quarter of 2011. As shown in Figure 1, the two trends during the period were nearly parallel, indicating that the DD analysis can be applied to this data.  As the outcome variable of our study is house price, we pre-examined whether the average house prices in the two groups show the parallel trends in the year before the HSEP was legislated. Figure 2 depicts the trends of the average house prices in the two groups from the third quarter 2009 to the second quarter 2014. As the local law for implementing HSEP in Gangwon province was passed and promulgated in December 2011, we focused on the trends during the one-year period from the third quarter of 2010 to the same quarter of 2011. As shown in Figure 1, the two trends during the period were nearly parallel, indicating that the DD analysis can be applied to this data.
The DD model used in this study can be expressed as where ln p igt is the log price per square meter of the ith apartment (i = 1, 2, ···, N) in the gth group (g = 0 for the control group and 1 for the treatment group) at the tth time point (t = 0 for the pre-treatment period and 1 for the post-treatment period), β k is the regression coefficient of the model (k = 1, 2, and 3), Time t is a time dummy whose value is 0 before the treatment and 1 after the treatment, HSEP g is a group dummy whose value is 0 for the control group and 1 for the treatment group, δ = [δ 1, δ 2, δ 3 ] is a 3 by 1 vector of regression coefficients for three covariates (x igt = [Floor it , Age igt , Age igt 2 ]), and ε igt is the error term for ln p igt . The covariates are individual characteristics of apartments including a dummy (Floor it ) for the floor of an apartment whose value is 0 for the low floor apartment (lower than the fifth floor) and 1 for the high floor apartment (higher than the fourth floor), the age of an apartment Sustainability 2020, 12, 8496 4 of 9 (Age igt ), and the squared age of an apartment (Age igt 2 ). β 3 is the parameter of interest that represents the causal effect of HSEP on the house prices while controlling for the effect of the other covariates. As the results from the DD analysis can be sensitive to the choice of time period for Time t , we considered the three different time periods for the post-treatment period and built three corresponding models, while setting the pre-treatment period at the third quarter of 2011 in all conditions. We chose the first quarter of 2012 as the first post-treatment period (Model 1), to capture the immediate response from the housing market. For comparing the average house prices between the same quarter, we selected the third quarter of 2013 for the second post-treatment period (Model 2). Lastly, we chose the third quarter of 2013 (two years after the pre-treatment period) for the third post-treatment period (Model 3) because HSEP was implemented in the school in the first half of 2013. Figure 1. A map of the administrative districts in Gangwon province. Note: Each block with a number represents an administrative district (1 = Wonju, 2 = Chuncheon, 3 = Gangneung, 4 = Donghaey 5 = Sokcho, 6 = Samcheok, 7 = Taebaek, 8 = Hongcheon, 9 = Cherwony 10 = Hoengseongy 11 = Pyeongchang, 12 = Jeongseon, 13 = Yeongwol, 14 = Inje, 15 = Goseong, 16 = Yangyang, 17 = Hwacheon, and 18 = Yanggu). The three districts in the treatment group (HSEP was implemented) are orangecolored, whereas the rest in the control group (HSEP was not implemented) are in gray [30] As the outcome variable of our study is house price, we pre-examined whether the average house prices in the two groups show the parallel trends in the year before the HSEP was legislated. Figure 2 depicts the trends of the average house prices in the two groups from the third quarter 2009 to the second quarter 2014. As the local law for implementing HSEP in Gangwon province was passed and promulgated in December 2011, we focused on the trends during the one-year period from the third quarter of 2010 to the same quarter of 2011. As shown in Figure 1, the two trends during the period were nearly parallel, indicating that the DD analysis can be applied to this data.   Table 1 presents the descriptive statistics of the price per square meter of an apartment, apartment size (m 2 ), apartment age (years), apartment floor, and the number of observations (or transactions) in the two groups for each time period. In all the time periods, the average price per square meter of apartments in the treatment group was higher than that of the control group, but the difference between the two groups became relatively smaller in the post-treatment period (Q1, 2012; Q3, 2012; Q3, 2013), compared to that of the pre-treatment period (Q3, 2011). For instance, the difference in the average price per square meter of apartments between the two groups was KRW 524,000 in the third quarter of 2011 but became KRW 275,400 in the first quarter of 2012. The difference between these two differences from pre-treatment to post-treatment periods was KRW 248,600, implying that the gap of the average house price between the two groups may have narrowed due to the HSEP. The similar patterns were observed in the rest of the two post-treatment periods. The average size of transacted apartments in the treatment group (69 m 2~7 6 m 2 ) was a bit larger than that of the control group (60 m 2~6 2 m 2 ), whereas there were no substantial differences in their ages and floors. The total number of samples was 10,827 in the two periods for   Table 2 reports the result from the DD analysis with the three models involving different post-treatment periods. The result indicated that all models explained more than 50% of the variance of the house price (for Model 1, R 2 = 0.530, F(7, 10820) = 2035.3, p < 0.001; for Model 2, R 2 = 0.553, F(7, 9380) = 1934.5, p < 0.001; for Model 3, R 2 = 0.525, F(2, 9808) = 1803.9, p < 0.001). The coefficient estimate for the interaction term (β 3 ; Time x HSEP), which is our main interest, was consistently negative and statistically significant in every model (for Model 1, β 3 = −0.092, t(10820) = −7.960, p < 0.001; for Model 2, β 3 = −0.060, t(9380) = −4.906, p < 0.001; for Model 3, β 3 = −0.054, t(9809) = −4.222, p < 0.001), suggesting that HSEP contributed to reducing the house price gap between the two groups of districts by 5%~9%.

Difference in Differences Analysis
The rest of the coefficient estimates were also all statistically significant at the 0.001 α level and their direction was consistent with the theoretical expectation. The coefficient estimate for Time (β 1 ) was 0.108 (Model 1), 0.089 (Model 2), and 0.165 (Model 3), respectively, in each model, showing that house prices in Gangwon province increased by 8%~9% per year on average. The coefficient estimates for HSEP (β 2 ) were between 0.33 and 0.34, implying that the average house price in the treatment group was 33%~34% higher than that of the control group at the pre-treatment period, which is in accord with the result presented in Table 1. There was an 8%~9% premium for high-floor apartments, compared to low-floor ones (δ 1 = 0.076 for Model 1, 0.086 for Model 2, and 0.091 for Model 3). The age of apartments negatively affected their prices (δ 2 = −0.061 for Model 1, −0.056 for Model 2, and −0.053 for Model 3), but when their age became larger than some point, it rather started to affect the price positively (δ 3 = 0.001 for all models). It reflects the characteristic of the Korean housing market where the reconstruction of an apartment complex is allowed in a profitable manner if their apartments are older than the certain age (e.g., 30 years old) [31]. Table 2. Results from the difference-in-differences analysis for the three models involving different post-treatment periods.