The Effects of Housing Price Changes on the Distribution of Housing Wealth in Singapore Joy Chan Yuen Yee & Liu Yunhua Nanyang Business School, Nanyang Technological University, Nanyang Avenue, Singapore 639798 Fax: +(65) 792.4217, Tel: +(65) 799. 4949, Email: ayuliu@ntuvax.ntu.ac.sg Abstract Accelerating public housing prices may have resulted in housing wealth distribution changing over time. Measurement of public housing wealth distribution in Singapore from 1984 to 1992 is carried out. Result show that, overall, the distribution was reasonably good from 1984 to 1990. But, starting from 1991, inequality increased. Housing price change is the major reason for the change in equality. The estimated result of the impact of the price change on inequality indicates that a $1000 price increase in a 3-room flat reduces the Gini coefficient by 0.35 percent, while a $1000 price increase in a 5-room flat increases the Gini coefficient by 0.37 percent. The price change of a 4-room flat has an uncertain effect on inequality. 1. INTRODUCTION The resale price of public housing in Singapore has more than doubled in five years from 1990 to 1995. 1 The accelerating public housing prices (due to the growing population and limited land space) could have resulted in the housing wealth distribution in Singapore changing since about 80 percent of Singaporeans own public housing (Table 1). Social problems like inequality might have been the consequence. It is therefore of interest to investigate how and by what percentage the housing wealth distribution changes over time when average housing prices change. The objective of this paper is, firstly, to examine the housing wealth distribution in terms of total housing value in the public housing market by looking at two measures of distribution. They are the Lorenz curve and the Gini coefficient. Secondly, the effect of changes in average housing prices for various flat types on the housing wealth distribution will be analysed by using a regression of flat prices on the Gini ratio. The results provide a better understanding of the current housing wealth distribution in Singapore, how this distribution is derived, as well as how the volume of housing price impacts on housing wealth distribution. 2. MEASUREMENT OF HOUSING WEALTH DISTRIBUTION IN SINGAPORE: 1984 TO 1992 Two types of housing wealth distributions are generally cited: functional distribution and size distribution. Size distribution is considered more relevant to the issue of changing welfare of households. It measures the amount of housing value in the public housing market that is contributed by households living in different flat types. It reveals the degree of inequalities faced among households in Singapore over time. It also allows for the comparison of inequality among households at a given point in time. 1 The National Day speech of Prime Minister Goh Chok Tong, Lianhe Zaobao, 21 August, 1995.
182 Chan and Liu Firstly the Lorenz curve is used to measure the size distribution of housing wealth. Figure 1 shows a typical Lorenz curve. The Lorenz curve itself is the percentage of housing wealth accounted for by the corresponding cumulative percentage of households. Table 2 shows the data that are required to arrive at the X and Y axes for plotting the Lorenz curve. 2 The data collected are of nine years from 1984 to 1992. The sources are from the HDB annual reports for various years and The Straits Times (30 September 1993). To calculate the total value of housing in the public housing market, only the 3- room, 4-room, 5-room and Executive flats are included. Since 1-room and 2-room flats in Singapore are mainly for tenancy and not for owner-occupancy, they are not considered in the calculation of the housing wealth of HDB new flats for home ownership. In addition, HUDC flats are excluded because the required data are not available. Three Lorenz curves are plotted, as shown in Figure 2, to determine the trend of housing wealth distribution in the public housing sector. It shows a clear picture of the distribution in which households face. The year 1992 experienced a relatively greater inequality as the Lorenz curve bends further away from the diagonal line; the year 1989 experienced the least inequality. Overall, households in Singapore do not face a serious unequal distribution of housing wealth as the Lorenz curves are close to the line of perfect equality. Figure 2 also presents a graphic illustration of the actual distribution of housing wealth. Firstly, it illustrates how the total value of housing is distributed among different groups of households. For example, the bottom 20 percent of the households in 1985 contributed about 15 percent of the total value of public housing, the next 20 percent contributed approximately 15 percent, the middle 20 percent contributed about another 20 percent, the upper 20 percent about another 20 percent and the top 20 percent contributed approximately 30 percent. This shows that a small degree of inequality prevailed among the five groups of households in owning public housing. The Lorenz curve also illustrates how actual distribution among the various groups of households varies from year to year. Figure 2 shows that the bottom 40 percent of the households in 1985 and 1989 contributed approximately 30 percent of the housing wealth but approximately 20 percent in 1992. This indicates that the unequal distribution has shifted from households who own relatively bigger and more expensive flats to those who own smaller and less expensive flats. The Lorenz curve will only prove instrumental in visualising the extent of equality in the distribution. It provides only a graphic illustration of the actual distribution of housing wealth for cross-sectional comparison among households as well as over time. The Gini coefficient (G), on the other hand, is defined as a single number that adequately expresses the degree of overall inequality present in the housing wealth distribution. It is derived from the Lorenz curve. The Gini coefficient is the ratio of the area between the Lorenz curve and the diagonal line relative to the total area of the triangle in which it lies. Mathematically, the Gini ratio is Area A divided by Area A plus Area B (See Figure 1), given as below : G = A / (A + B) (1) 2 The vertical Y axis measures the cumulative percentage of housing value going to the households, who are arrayed in percentiles on the horizontal X axis from 3-room flats to Executive flats.
The Effects of Housing Price Changes on the Distribution of... 183 Area B has to be calculated first before Area A can be obtained. Area B is obtained by summing all trapezoid areas under the Lorenz curve. The area under the Lorenz curve (i.e. Area B) is calculated as follows: n Area B = 1 ( Xi Xi 1)( Yi Yi 1) (2) 2 i= 1 where X = co-ordinates of the points on the X axis, percentage of households; Y = co-ordinates of the points on the Y axis, percentage of housing wealth; i = 1,2,3,..., n Area B can also be obtained by method of integration; that is, B = yxdx ( ) where y is a function of x. To find Area B, we can integrate the equation between a limit zero and n integers. However, it is not always possible to derive a non-linear equation from the data so we omit its calculation here. Area A also requires calculation. Since the area under the equality line is a 45- degree line, the area is (1/2) x 100% x 100% = 5000. To obtain Area A, we subtract 5000 from Area B. Table 3 presents calculations of Gini coefficient. The Gini ratios are plotted onto a line chart to detect any noticeable trend in the coefficient, as shown in Figure 3. The Gini ratio varies from zero (in the case of perfect equality where everyone is contributing the same share of housing value) to one for perfect inequality (where one individual contributes the entire housing wealth). The lower the Gini ratio, the more equal the distribution of income. In practice, the Gini ratio will only fall between these two extremes. Between the years 1984 to 1989, the Gini coefficients were stable, ranging between 0.15 and 0.17 and with a mean value of 0.162. Figure 3 also shows that the distribution in housing value was very close to equality with a zero mean value. In other words, the degree of inequality experienced by households in Singapore is small. From 1990, it started to increase meaning the distribution of total value of public housing had shifted further away from the perfect equality line. In 1992, the Gini ratio reached 0.2370. The degree of inequality experienced was still rather small. Possible explanations may be the growing affluence of households and the evolution of housing programmes, especially towards home ownership. As Singapore progresses from a developing to a newly industrialised nation, per capita income has increased that enables more and more households afford more expensive flats and apartments, thereby resulting a shift in the distribution. Housing policies, on the other hand, such as the housing financing, home ownership and upgrading policies have encouraged households to spend on larger and better well-designed flats, such as the 4-room, 5-room, executive and HUDC flats. These flats are relatively better in quality and higher in prices as compared to the 1-room, 2-room and 3-room flats and therefore contribute to the greater proportion of the total value of public housing in terms of home ownership. Those who belong to the relatively low-income groups and are unable to afford those flats will choose to purchase smaller flats that comprise lower value.
184 Chan and Liu The Gini ratio is a simple mathematical measure of inequality that allows for a very large number of observations be taken into account. Hence, the Gini ratio provides a picture as to the extent to which the distribution of wealth is closer to perfect equality or to perfect inequality. It also shows how much inequality differs over time by allowing us to see a vivid trend in the distribution of wealth. The Gini ratio has shortcomings. Firstly, it is insensitive to changes in the distribution of wealth. The Lorenz curves can intersect implying nonuniqueness; curves with different shapes can generate the same Gini ratio. The Lorenz curves must not cross if the Gini ratio is to be a good measure of comparison. The three Lorenz curves plotted (see Figure 2) do not intersect indicating that they are good measures of inequality. The Gini coefficient does not give any indication of where the inequality lies, nor, when a distribution changes, where the change has taken place. If our intention is to examine the source of inequality, the Gini coefficient is of limited help; a table of percentile shares would be more revealing. 3. THE PRICE EFFECT ON INEQUALITY A regression model is used to estimate the effect of price change on inequality in housing wealth distribution. The model is defined by a dependent variable, the Gini coefficient, and four independent variables the average housing prices for 3-room, 4-room, 5-room and Executive flats: G = a + b 1 P 1 + b 2 P 2 + b 3 P 3 + b 4 P 4 + u (3) where G = the Gini coefficient; P 1 = the average housing price for a 3-room flat; P 2 = the average housing price for a 4-room flat; P 3 = the average housing price for a 5-room flat; P 4 = the average housing price for an Executive flat; u = the error term; and a, b 1, b 2, b 3, and b 4 = parameters The data used for the regression analysis are found in Tables 2 and 3. The estimated results are shown below. G = 13.13-0.35P 1-0.015P 2 + 0.37P 3-0.10P 4 (4) (12.5) (4.46) (0.12) (2.60) (1.77) Adj R-sq = 0.99 N = 9 (numbers in parenthesis are T-values of the estimated parameters) 4. ANALYSIS OF THE RESULTS The results reveal that the overall regression model is significant in explaining variation of the Gini coefficient. The adjusted R-square, which takes into account the number of explanatory variables in the model and the sample size, shows that a large proportion (99 percent) of variation in the Gini ratio is explained by the set of average housing prices.
The Effects of Housing Price Changes on the Distribution of... 185 The findings also suggest that the individual average housing prices for the 3-room, 5-room flats and the Executive flats are significant predictors of the Gini coefficient. The t-values for P 1, P 3 and P 4 indicate that changes in the price values for the respective flat type do bring about changes in the housing wealth distribution, holding other prices constant. The price and Gini ratio variables in the regression model are measured in terms of $ 000 and percentage respectively. The negative coefficient (-0.35) for P 1, indicates that a $1,000 increase in the average price for a 3-room flat leads to a decrease of 0.35 percent in inequality, holding other independent variables unchanged. On the other hand, the positive coefficient (0.37) for P 3 indicates that a $1,000 increase in the average housing price for a 5-room flat increases inequality by 0.37 percent brings about a corresponding increase of 0.37 percent in inequality, holding other prices constant. However, it is hard to explain the statistically significant and negative P 4 estimate for the Gini coefficient. It contradicts our theory and prediction that an increase in the average prices for the bigger and larger flats will result in a rise in inequality. This could be due to the small sample size of nine observations used. Thus we must be careful in interpreting our empirical results. On the other hand, the model indicates that a change in P 2 is statistically insignificant in determining a change in Gini ratio. The explanation for the insignificance of P 2 as a predictor could be that the overall effect on inequality is uncertain when there exists a change in the average housing price for the majority of households in Singapore residing in 4-room flats. It could also mean that the inequality gap between households who live in 3-room flats and those in 4-room flats widens when P 2 increases. On the contrary, the inequality gap between those residing in 4-room flats and those in relatively larger flats narrows down. As a result, the overall offsetting effect could be positive or negative. The above results lead to two noticeable points. Firstly, they prove our intuition that as the housing price for the smaller flat (bigger flat) increases, the unequal distribution of housing wealth becomes smaller (greater). For example, as P 1 (P 3 ) increases (while holding other housing prices constant), the housing value rises will bring about the narrowing (widening) of the inequality gap between those who own 3-room flats and those who own 5-room flats. The findings also show that the majority of households is not significantly affected by a change in the average prices of their type of flats. The unequal distribution of housing wealth contributed by this majority group could become relatively greater or smaller when there is a price change for the 4-room flat; the resultant effect is uncertain. 5. CONCLUSIONS This paper has analysed housing wealth distribution in Singapore using different measures of inequality the Lorenz curve and the Gini coefficient. A regression analysis has also been conducted to gauge the effect of price change on inequality.
186 Chan and Liu The results obtained from the two measures illustrate consistency in the trend of wealth distribution over the nine-year period; earlier years show a stable and nonfluctuating inequality while there exists an upward trend in inequality from 1989 to 1992. The results point towards an increasing gap between the two extreme groups those who own bigger flats and those who own smaller flats. The regression analysis shows that a change in housing prices influences the distribution of housing wealth in Singapore from 1984 to 1992, especially the significant price change effects of P 1 and P 3 on the Gini coefficient while other prices are held constant. A change in the average price for a 3-room flat will bring about a change in the Gini ratio in the same direction while a change in the average price for a 5-room flat will result in a change but in the opposite direction. On the contrary, the analysis has indicated that the change in the average price for a 4-room flat does not play a significant role in the determination of a change in the housing wealth distribution. The majority of households residing in 4-room flats are not significantly (or are only slightly) affected when there is a change in the price for the 4- room flats. We consider only the government or HDB prices for new flats that contribute to the housing wealth in Singapore. This is due to the incomplete and non-available data set for resale prices of public housing. Resale prices would be more representative and would contribute a greater accuracy for total housing value in the public housing market since the resale prices are market prices and not determined by the government. Because the price trends in the resale market were closely related to price increases for new flats 3 for the periods of 1979 to mid 1984 4 and 1987 to 1991, 5 the results obtained by using the government prices are not significantly distorted and thus can be used for evaluation in this paper. A broker who specialises in HDB resale flats pointed out that resale prices are now more independent of the primary market for new flats 6. This could be due to the growing portion for HDB resale flats out of the total supply of HDB flats. Another broker said demand conditions in the resale market increase cause the resale prices to rise since HDB relaxed its resale rules. Hence, it will not be appropriate to use the government prices for new flats for the recent years like 1993 onwards. Another limitation is the small sample size of only nine observations. Ability to carry out more precise inferences would require more observations. As a result, we cannot rely strongly on the empirical testing in the regression model that results in a contradiction of the effect of the average prices for executive flats, P 4 on the Gini ratio with our theory and prediction. The small sample size used is due to the non-availability of data for the 3- room flats after 1992 and for the Executive flats before 1984. 3 The periods between 1984 and 1987 cannot be assessed whether the trends of resale prices were closely related to price increases for new flats from any sources. 4 See Augustine HH. and Phang Sock Yong, (1991), The Singapore Experience in Public Housing, Times Academic Press. 5 Source: The Business Times, 23 June 1992. 6 Source: The Business Times, 23 June 1992.
The Effects of Housing Price Changes on the Distribution of... 187 In the regression model, the value of average housing prices in dollar terms is used in the analysis due to the non-availability of a Public Property Index in any publication; only the Private Property Index is available. It would be more representative and more accurate to use a Public Property Index since the Gini coefficient is measured in terms of percentages. Future research could be conducted to determine other factors that may affect the distribution of housing wealth such as income growth, population size, growth, qualitative factors and housing policies over time. REFERENCES Coehr, W. and Powelson, J. P. (1981): The Economics of Development and Distribution, Harcourt Porace Jovanorich, Inc. Department of Statistics, Singapore (1994): Yearbook of Statistics, Singapore: Mentor Printers Pte Ltd. Gillis, Perkins, Roemer & Snoddgrass (1992): Economics of Development, 3rd Edition, New York: W. W. Norton and Co. Gujarati, D. N. (1995): Basic Econometrics, New York: McGraw-Hill. Housing and Development Board (various years): Annual Report, Singapore: Teck Wah Printing Pte Ltd. Lianhe Zaobao (1995): Singapore, 21 August. Poulson, B. W. (1994): Economic Development - Private and Public Choice, New York: West Publishing Company. Singapore Press Holdings (various years): The Business Times, Singapore, various issues. Singapore Press Holdings (various years): The Straits Times, Singapore, various issues.
188 Chan and Liu TABLE 1 Percentage of Total Population living in Public Flats & Home ownership Public Flats % of total population living in* Year Public Flats Owner-occupied Public Flats 1975 54 22 1976 60 27 1977 64 31 1978 68 37 1979 71 39 1980 73 42 1981 74 43 1982 75 50 1983 77 54 1984 81 60 1985 84 64 1986 85 66 1987 86 69 1988 87 71 1989 88 79 1990 87 80 1991 87 82 1992 87 82 1993 87 81 1994 86 80 Note: Before 1990 it includes non-resident population. Source: Department of Statistics, Yearbook of Statistics 1994, Singapore.
TABLE 2 Assessed Housing Wealth on Households in the Public Housing Sector Assessed Flat Type Categories Cumulative Assessed Households Cumulative % Households, X Average Housing Prices ($) Cumulative Assessed Total Value of Public Housing ($) Cumulative % Assessed Total Value of Housing, Y 1984 3-room flat 186,782 61.22 36,300 6,780,186,600 45.89 4-room flat and smaller 270,535 88.67 62,600 1.20231244 10 81.38 5-room flat and smaller 302,769 99.24 77,200 1.45115892 10 98.22 Executive flat and smaller 305,089 100.00 113,500 1.47749092 10 100.00 1985 3-room flat 210,556 56.10 37,300 7,853,738,800 41.20 4-room flat and smaller 328,423 87.51 62,600 1.5232213 10 79.91 5-room flat and smaller 369,472 98.45 77,200 1.84011958 10 96.53 Executive flat and smaller 375,294 100.00 113,500 1.90619928 10 100.00 1986 3-room flat 221,583 53.60 37,300 8,265,045,900 38.61 4-room flat and smaller 358,198 86.64 62,600 1.68171449 10 78.56 5-room flat and smaller 404,355 97.81 77,200 2.03804653 10 95.20 Executive flat and smaller 413,409 100.00 113,500 2.14080943 10 100.00
TABLE 2 (CONT) Assessed Housing Wealth on Households in the Public Housing Sector Assessed Flat Type Categories Cumulative Assessed Households Cumulative % Households, X Average Housing Prices ($) Cumulative Assessed Total Value of Public Housing ($) Cumulative % Assessed Total Value of Housing, Y 1987 3-room flat 226,041 51.54 40,800 9,222,472,800 37.79 4-room flat and smaller 375,484 85.62 64,948 1.892849676 10 77.56 5-room flat and smaller 427,068 97.38 80,163 2.306362496 10 94.51 Executive flat and smaller 438,558 100.00 116,632 2.440372664 10 100.00 1988 3-room flat 231,594 48.94 40,800 9,449,035,200 35.21 4-room flat and smaller 397,143 83.93 65,021 2.021319673 10 75.33 5-room flat and smaller 457,621 96.71 80,098 2.505736357 10 93.38 Executive flat and smaller 473,172 100.00 114,216 2.683353659 10 100.00 1989 3-room flat 237,322 46.58 45,800 1.08693476 10 33.72 4-room flat and smaller 423,389 83.10 71,900 2.42475649 10 75.22 5-room flat and smaller 491,263 96.42 84,704 2.99967642 10 93.05 Executive flat and smaller 509,490 100.00 122,916 3.223715413 10 100.00
TABLE 2 (CONT) Assessed Housing Wealth on Households in the Public Housing Sector Assessed Flat Type Categories Cumulative Assessed Households Cumulative % Households, X Average Housing Prices ($) Cumulative Assessed Total Value of Public Housing ($) Cumulative % Assessed Total Value of Housing, Y 1990 3-room flat 237,199 45.52 45,800 1.08637142 10 31.01 4-room flat and smaller 431,464 82.81 76,147 2.565641116 10 73.23 5-room flat and smaller 501,377 96.23 95,171 3.231010128 10 92.22 Executive flat and smaller 521,038 100.00 138,652 3.503613825 10 100.00 1991 3-room flat 237,026 44.42 48,000 1.1377248 10 27.56 4-room flat and smaller 439,925 82.45 88,794 2.939346181 10 71.21 5-room flat and smaller 511,874 95.93 114,228 3.761205218 10 91.12 Executive flat and smaller 533,590 100.00 168,849 4.127877706 10 100.00 1992 3-room flat 235,848 43.36 53,000 1.2499944 10 24.80 4-room flat and smaller 442,821 81.41 103,387 3.389826155 10 67.24 5-room flat and smaller 519,296 95.47 143,400 4.486477655 10 89.00 Executive flat and smaller 543,952 100.00 224,960 5.041139031 10 100.00 Source: HDB Annual Reports & The Straits Times, 30 September 1993.
Housing Price Change and The Effect on Housing Wealth Distribution in Singapore 192 TABLE 3 Calculation of Gini Coefficients (G) from 1984 to 1992 Year Area A + B * Area B Area A Gini Coefficient = A/(A+B) 1984 5,000 4,175.98 824.02 0.1648 1985 5,000 4,175.13 824.87 0.1650 1986 5,000 4,154.59 845.41 0.1691 1987 5,000 4,205.99 794.01 0.1588 1988 5,000 4,191.65 808.35 0.1617 1989 5,000 4,240.82 759.18 0.1518 1990 5,000 4,121.85 878.15 0.1756 1991 5,000 3,973.25 1,026.75 0.2054 1992 5,000 3,815.18 1,184.82 0.2370
The Effects of Housing Price Changes on the Distribution of... 193 FIGURE 1 The Typical Lorenz Curve 100 Cumulative % of Housing Wealth 90 80 70 60 50 40 30 20 10 45-degree line, Line of perfect equality The Lorenz Curve A B Curve of complete inequality 0 0 20 40 60 80 100 Cumulative % of Households
194 Chan and Liu FIGURE 2 The Lorenz Curves for 1985, 1989 & 1992 100 Cumulative % of Total Value of Housing, Y 90 80 70 60 50 40 30 20 10 0 1989 1992 1985 0 20 40 60 80 100 Cumulative % of Households, X FIGURE 3 Gini Ratios from 1984 to 1992 0.25 Gini Coefficients 0.2 0.15 0.1 0.05 0 1984 1985 1986 1987 1988 1989 1990 1991 1992 Years