AN ECONOMETRIC ANALYSIS OF A CAPITAL GAINS TAX ON LAND*

Transcription

1 The Economic Studies Quarterly Vol. 38, No. 2, June 1987 AN ECONOMETRIC ANALYSIS OF A CAPITAL GAINS TAX ON LAND* By YOSHITSUGU KANEMOTO, FUMIO HAYASHI, AND HAJIME WAGO 1. Introduction A tax on realized capital gains has the well-known lock-in effect of discouraging the supply of residential land.1) The Japanese government reduced the tax rate temporarily between 1970 and 1975 for the purpose of increasing the supply of residential land. This paper empirically estimates the effects of this reduction on the housing market in Japan. Another purpose of this paper is to estimate the structural demand and supply functions of residential land and housing capital.2) Since land and housing are major assets for households, their demand and supply functions must be derived from intertemporal asset-choice decisions. We therefore take into account the asset side of housing in formulating a model of a residential development process. As usual, the model includes expectations on future land prices and we must specify an expectation formation mechanism. In this paper, we use two types of expectation formation mechanisms: rational expectations and optimal ARIMA forecasting. Although there are many empirical studies on asset choice, attempts at estimating both supply and demand functions are rare, and, to our knowledge, there have been no such studies on the housing market. We find that although the effects of the capital gains tax on the supply of residential land are statistically insignificant, the effects on residential capital formation are significant. The reason is that a change in land price induced by the change in capital gains tax has little effects on the supply of residential land but has significant substitution effects on housing capital. The organization of this paper is as follows. A model of residential development is formulated in Section 2 and the estimation procedures are explained in Section 3. empirical results. Section 4 presents Given the estimation results in Section 4, Section 5 calculates the effects of a change in the capital gains tax on the equilibrium residential development process. Section 6 contains conclusions. Appendix describes data sources and the methodologies used to construct * Earlier versions of this paper were presented at seminars at Tokyo Center for Economic Research and University of Tsukuba, and at Rokko Econometric Conference. We thank participants there, especially, Charles Horioka who served as a discussant at the Rokko Conference, for useful comments. Thanks are also due to a referee of this journal for valuable comments and to Masahiro Igarashi for research assistance. Research support from the Japan Economic Research Foundation is gratefully acknowledged. 1) See, for example, Kanemoto (1982, 1985). 2) In the case of housing capital, we estimate only the demand function, assuming that the supply of housing capital is completely price elastic

2 our data series. The Economic Studies Quarterly 2. The Model A tax on realized capital gains has the well-known "lock-in" effect: since the tax is levied when the landowner sells his land, it discourages the sale of land. This causes a decrease in the supply of owner-occupied housing which requires transfers of land ownership. The tax may not reduce the supply of rental housing, however, because the tax is not levied if the landowner rents his land. Substitution from owner-occupied housing to rental housing will increase the supply of rental housing.3) In Japan, however, the two types of housing are not good substitutes for suppliers because of the law which "over-protects" the right of tenants and makes it almost impossible to evict a tenant even when he refuses an increase in rent to the market-prevailing level. The capital gains tax can therefore be expected to cause a reduction in the over-all supply of housing. In this paper, we empirically estimate the effects of a change in the tax rate on the supply of residential land. Concentrating on owner-occupied housing, we consider a residential development process where developers buy land from agriculturalandowners, prepare the land for residential use, and sell it to consumers who build houses on the developed land. At the beginning of period t, *l, units of land are sold to developers at price PLt. The rate of a capital gains tax on land is *t, in period t and, for simplicity, we assume that landowners bought their land at price zero in period t=0. Because of extremely high rate of land price appreciation in Japan, errors caused by this simplifying assumption will be small. Landowners then receive the after-tax price of =(1-*t)PLt. qlt Developers develop the land for residential use, for example, by installing sewerage and constructing roads. The price and the amount of the developed land sold to consumers in period tare PSt and St, respectively. The amounts of land bought and sold, lt and St may not be equal to each other, since developers can carry inventories of land. Taking into account the provision in the tax law that developers are exempt from the capital gains tax when a development project satisfies certain criteria for a "desirable" project, we assume that developers do not pay the capital gains tax. Consumers buy St of developed land and build houses on the purchased land.4) The production function of housing is F(kt, St), where kt is the amount of housing capital purchased in period t. The price of housing capital is denoted by Pkt The equilibrium prices of undeveloped and developed lands are determined endogenously by market clearing conditions. Since land is durable and can be held as an asset, demand for and supply of land are derived from intertemporal optimization of landowners, developers, and consumers, and depend on expectations on future prices as well as current prices. 3) Private rental housing constitutes only about 20% of the total housing stock in Japan. For studies on tenure choice between renting and owing, see Rosen and Rosen (1980), Rosen, Rosen, and Holtz-Eakin (1984) on the American housing market and Seko (1984) on the Japanese market. 4) Of course, instead of consumers, developers may build houses and sell both land and houses tc consumers. This, however, does not significantly change the results

3 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land Our formulation of demand and supply functions are slightly different from the standard one because of our implicit assumption that the interest rate depends on the net debt position. That is, we assume that the interest rate which an individual faces is high if the individual has large debts. This assumption is introduced to make our model compatible with the empirical observation that until the first oil crisis in 1973 the rate of return on land had been significantly higher than the market interest rate for a long period of time. Under this assumption the rate of return on land, which equals the marginal interest rate, can be higher than the average interest rate which is observed as the market interest rate. First, the supply function of undeveloped land may be written (1) lt=ls[et(qlt+1),qlt,lat-1,at,bt], where Et(qLt+1) is the after-tax price of undeveloped land in period t+1 predicted in period t, is the stock of agricultural land at the end of period t-1, at represents factors affecting LAt-1 productivity and demand conditions in agriculture, and bt those affecting the interest rate schedule for landowners, e.g., the general interest rate level. We normalize at and bt such that an increase in at raises the marginal revenue product of the agricultural sector and an increase in bt causes an upward shift of the interest rate schedule. We expect that a rise in the expected future price of land, i.e., the first argument in the supply function, results in a fall in supply of land because larger capital gains induce the landowner to postpone the sale of land. The effect of the second argument is uncertain. A rise in the current price level lowers the rate of return on agriculturaland, which tends to increase the supply of land. If the landowner cannot borrow and lend money at a constant interest rate, however, there is another effect. A rise in land price increases the revenue from land sale and hence improves the debt position of the landowner. Since the interest rate is higher for an individual who is in larger debt, this lowers the marginal interest rate and reduces the supply of land. The final outcome depends on the relative strength of these two effects. It is natural to expect that, other things being equal, an increase in LAt-1 tends to increase the supply of land. An increase in at, such as technological progress in agricultural production and a rise in the relative prices of agricultural products, raises the rate of return on agriculturaland and reduces the supply of land. A rise in bt, such as a rise in the general interest rate level, increases the supply of land by making financial assets more attractive (or loans more costly). Developers buy undeveloped land at price PLt and sell developed land at price PSt. We assume that servicing costs per unit area of land are Wt and do not depend on the speed of land development. Under this constant average cost assumption, the price of developed land must equal the price of undeveloped land plus the servicing costs: PSt=pLt+Wt. Otherwise, developers would demand or supply infinite amounts of land and the land market could not be in equilibrium. We assume that the inventories of land held by developers yield zero land rent. Then, developers hold inventories only when they expect sufficient capital gains. The rate of return on inventories of land is the expected rate of increase in land price, [Et(PLt+1)-pLt]/PLt. First, consider a case where the interest rate, r, is constant regardless of the amount of borrowing or lending and developers are risk neutral. In this case, we obtain a bang-bang solution: if [Et(PLt+1)-PLt]/PLt>r, then demand for inventory is infinite; if the opposite inequality holds, then developers carry no inventories; and if equality holds, then demand for inventory is in

4 The Economic Studies Quarterly determinate. In a more general case where the interest rate depends on the debt position and/or developers are risk. averse, a smooth inventory demand function may be obtained. We adopt a smooth inventory demand function in this paper: (2) lt-st=*[et(plt+1),plt,b1], where, as in (1), b1 represents factors affecting the interest rate schedule. Note that the inventory demand here is not demand for inventory stocks but demand for net additions to inventory stocks. The inventory demand function is increasing in the expected future price of land, since larger capital gains provide more incentive to hold land. The effect of the current price level, however, depends on the sign of lt-st. If the amount sold exceeds the amount bought, i.e., lt-st<0, then a rise in price improves the debt position of the developer and the marginal interest rate falls. This induces the developer to buy more land. If lt-st>0, the opposite result is obtained. It is also easy to show that a rise in b, reduces demand for land. Consumers buy developed land from developers and build houses. Demand functions of land and housing capital are respectively (3) St=Sd[Et(PSt+1), Et(PKt+1), PSt,PKt,yt,LCt-1,bt], (4) kt=kd[et(pst+1), Et(PKt+1), PSt,PKt,yt,LCt-1,bt], where y, and LCt-1 are respectively income in period t and the stock of residential land at the end of period t-1. Although the stock of housing capital also enters these demand functions, we cannot include it because of the lack of data. The optimization problem for a consumer is too complicated to yield definite comparative statics results. However, we would normally expect that demand for land is increasing in the expected future prices of land and capital, decreasing in the current land price, increasing in income, decreasing in the stock of residential land, and decreasing in bt. The effect of a rise in the current price of housing capital are, however, uncertain. A rise in capital price, on one hand, raises the cost of housing and reduces demand for land through a reduction in demand for housing. On the other hand, it raises the price of capital relative to that of land and induces substitution from capital to land. Final outcome depends on the relative magnitudes of these two effects. In the same way, demand for housing capital is normally increasing in the expected future prices of land and capital, decreasing in the current price of housing capital, increasing in income, decreasing in the stock of residential land, and decreasing in b but the effect of a rise in the current land price is uncertain. Since data on servicing costs are not available, we ignore them by assuming that servicing costs constitute a constant fraction of land price, i.e., wt=*plt for a constant *. Summing (2) and (3) then yields the demand function of undeveloped land, (5) lt=ld[et(pst+1),et(pkt+1),pst,pkt,lct-1,bt] =*[Et(PLt+1),PLt,bt]+Sd[(1+*)Et(PLt+1),Et(PLt+1),(1+*)PLt,PKt,yt,LCt-1,bt]. An equilibrium in the land market requires that demand for and supply of undeveloped land be equal: (6) ls[et((1-*t+1)plt+1),(1-*t)plt,lat-1,at,bt] =ld[et(pst+1),et(plt+1),pst,pkt,yt,lct-1,bt]

5 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land Because of the lack of data on the supply side of housing capital, we assume that the capital price is exogenously determined. Under this assumption, the equilibrium condition (6) yields the equilibrium land price, PLt, given expectations on future prices of land and capitaḷ The equilibrium development process can be characterized if we specify an expectation formation mechanism such as rational and adaptive expectations. In our econometric estimation, we estimate equations (1), (4) and (5) simultaneously, assuming alternative types of expectation formation mechanisms. 3. Empirical Implementation We estimate (1),(4), and (5) with annual Japanese data for 1960 to 1981, where (1) and (5) are respectively the supply and demand functions of undeveloped land, and (4) is the demand function of housing capital. For empirical implementation, we assume the following functional form. (7) DLt=a10+a11(Tt+1+*Lt+1)+a12(Tt+PLt)+a13Rt+a14YAt+a15LAt-1+ult, (8) DLt=a20+a21*Lt+1+a22PLt+a23Rt+a24YCt+a25PKt+a26*Kt+1+a27LCt-1+a28Nt +u2t, (9) DKt=a30+a31*Lt+1+a32PLt,+a33Rt+a34YCt+a35PKt+a36*Kt+1+a37LCt-1 +a38nt+u3t, where DLt: the quantity of undeveloped land supplied in year t, Tt=1-*t:*t, is the effective capital gains tax rate in year t, in year t, DKt: capital formation in the housing sector in year t, LAt-1,: the stock of agricultural land in year t-1, LCt-1: the stock of residential land in year t-1, Nt: the population of individuals between 20 and 40 years of age, with all variables measured in real terms and all variables except the interest rate are in logarithms. Data sources are documented in Appendix. The real agricultural income and the real interest rate serve as at and bt, respectively. The real consumption level, YCt, stands for consumer income yt. The capital gains tax on land is complicated with many provisions for reductions and exemptions. Roughly speaking, however, up to 1969, a half of capital gains income was included in the annual taxable income and taxed according to the progressive income tax schedule. From 1970 to 75, a separate tax for capital gains income was adopted with tax rates of 10% for 1970 and 71, 15% for 1972 and 73, and 20% for 1974 and 75. The separate tax was abandoned in 1976 and

6 The Economic Studies Quarterly from 1976 to 1981 three quarters of capital gains income were included in the taxable income and the usual income tax was levied. From 1982, the proportion included in the annual income was reduced to a half of capital gains income. In computing the effective tax rates on capital gains income, we assume that the (marginal) income tax rate is 60%. Although this rate is somewhat arbitrary, changing the income tax rate does not significantly change the estimation results. Under this assumption on income tax rate, the effective tax rates are 30% until 1969, 10% for 1970 and 71, 15% for 1972 and 73, 20% for 1974 and 75,45% from 1976 to 81, and 30% from 1982 on. Since changes in the capital gains tax rate were announced beforehand, we assume that the tax rate in the next year is known with certainty. Figures 1-3 illustrate the time paths of three major variables: the rate of land price appreciation, the supply of residential land, and real capital formation in the private housing sector. From Fig. 1, we can see that until the first oil crisis (1973) land price had risen at extraordinarily Figure 1 Rate of Appreciation of Real Land Price: 100*(Pt-Pt-1)/Pt-1 Figure 2 Supply of Residential Land -164-

7 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land Figure 3 Real Capital Formation in the Private Housing Sector (at Market Prices in Calendar Year of 1975) rapid rates: in most years the rate of price appreciation exceeds the interest rate on bank loans. The appreciation rate dropped sharply in 1974, and since then it has not become as high as before. Fig. 2 shows that the supply of residentialand increased dramatically in High levels of supply continued until 1973 but it decreased to the level before 1969 in The years with large supply of residentialand, therefore, overlap but do not coincide with those with low rates of the capital gains tax. As seen from Fig. 3, real capital formation in the housing sector had increased rapidly until 1973, but since then it has not increased much. Comparing Fig. 2 and Fig. 3, we can see that the time paths of supply of residential land and real capital formation are quite different. This indicates that housing construction does not necessarily occur immediately after the conversion of agricultural land into residential use. Some agents (either developers, agricultural landowners, or consumers) have held inventories of residential land for a significantly long period of time. The future prices of land and capital are not observable for economic agents and an expectation formation mechanism must be specified. We use two formulations: rational expectations and the optimal ARIMA forecasting. The rational expectations formulation assumes that expectations are formed rationally based on currently available information. In the estimation, we adopt an instrumental variables procedure used by McCallum (1976) and others. This approach is of a limited-information type in the sense that it does not require specification of the complete auto-covariance function for the observable data. It treats the realized values of future prices as their expected values measured with unpredictable forecast errors. For example, the expected value of PLt+1, denoted by *Lt+1, is obtained based on available information in year t which includes any variable in the model lagged one or more periods, and it is assumed that PLt+1=*Lt+1+*t+1 with E(*t+1 It)=0, where It denotes the information available in period t. Since any variable included in It is uncorrelated with the forecast error, *t+1, this model can be estimated by replacing the expected value, *Lt+1, by the realized value, PLt+1, and using lagged variables in the model as instrument variables. The optimal ARIMA forecasting procedure suggested by Box and Jenkins (1970) is used by Rosen and Rosen (1980) and Rosen, Rosen and Holtz-Eakin (1984) in the estimation of housing -165-

8 The Economic Studies Quarterly tenure choice. In this approach, forecasts of a variable are based only on its past values. For example, if an ARIMA (1, 1, 0) equation is used to make forecasting, the following equation is estimated: (10) PLi-PLi-1=A(t)(PiL-1-PLi-2)+ui (i=0,...,t-1), where ui is a normally distributed white noise error and A(t) is a parameter to be estimated. Equation (10) is re-estimated each year t with observations from year 0 to year t-1. Since (7) and (8) simultaneously determine land price, PLi, some sort of simultaneousequations method is required in both formulations of expectation formation. We use the threestage least-squares method because it is likely that the error terms, u1, u2, and u3, are correlated due to common omitted variables. 4. Estimation Results Tables 1-3 report the estimated parameters. RE and ARIMA indicate the estimation results of the rational expectations model and the optimal ARIMA forecasting model, respectively. In ARIMA1, the expected price *Lt+1 is that in the next year. In ARIMA5, it is replaced by the average of the expected prices in the next five years. If a landowner supplies a strictly positive amount of land every year, we have to use the price in the next year. Few landowners, however, sell land every year. In such a case, the appropriat expected price to use is the price in the year when the landowner expects to sell land. Since there are many landowners who expect to sell land in many different years, some sort of average price over future years may be better than the price in the next year. RE uses instrument variables, Tt, Tt+1, Rt, YAt, YCt, Nt, LCt-1, LAt-1, PKt, PCt-1, Rt-1, YAt-1, YCt-1, PKt-1, and a constant. ARIMA1 and ARIMA5 use*lt+1, *Kt+1, Tt+1+*Lt+1, Tt, Rt, YAt, YCt, PKt, Nt, LCt-1, LAt-1, and a constant. Table 1 shows that some of the estimated parameters of the land supply function do not conform to our theoretical prediction. The parameter for the interest rate has the "correct" sign in all estimations, but the estimated coefficient for the expected price is positive and significant, which constradicts the usual asset choice theory. As seen in Section 2, the coefficient for the Table 1 Estimated parameters of the supply function of land Note: Numbers in parentheses are t-values. * significant at the 1% level ** significant at the 5% level ** significant at the 10% level * -166-

9 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land Table 2 Estimated parameters of the demand function of land Note: See Footnotes in Table 1. Table 3 Estimated parameters of the demand function of housing capital Note: See Footnotes in Table 1. current price can be either positive or negative on theoretical grounds. Its estimates are positive in all cases, although it is insignificant in the RE case. The coefficient for agricultural income is positive and significant at the 1% level in all estimations. This result is caused by the fact that both agricultural income and the supply of land have the declining trends over time. Some omitted variables which are correlated with agricultural income might have caused a decline in the supply of land. land. From Table 2, it can be seen that very few coefficients are significant in the demand function of In RE, only the population variable, Nt, is significant (at the 5% level); and in ARIMA1, only the stock variable, LCt-1,, is significant (at the 1% level); and in ARIMA5, both the stock variable (at the 1% level) and the population variable (at the 10% level) are significant. Even the coefficients for the current and expected price variables are insignificant, although their signs are "correct" in RE and ARIMA5. Finally, Table 3 shows that very few variables are significant also in the demand function of housing capital. In RE, the expected capital price (5%) and the population variable (1%) are significant; in ARIMA1, only the population variable (1%) is significant; and in ARIMA5, the current land price (10%), the consumption level (5%), and the population variable (5%) are significant. All significant coefficients have "correct" signs. Although there are some differences between different models and estimation methods, they are minor and the estimation results are similar. The values of the Durbin-Watson statistic do -167-

10 The Economic Studies Quarterly not suggest serious serial correlation except in ARIMA1 estimation of the supply function of land. 5. The Effects of a Change in the Capital Gains Tax The parameter estimates obtained in Section 4 allow us to examine the effects of a change in the capital gains tax rate. If the error terms are ignored and the path of capital price is exogenously given, then (7) and (8) yield a difference equation for land price which characterizes the perfect foresight equilibrium path: (11) (a11-a21)plt+1=(a22-a12)plt-a11tt+1-a12tt+xt+a20-a10, where (12) Xt=(a23-a13)Rt+a24YCt-a14YAt+a25PKt+a26PKt+1+a27LCt-1-a15LAt-1+a28Nt. The general solution of this difference equation is (13) PLt=(a20-a10)/(b1-b2)-(1/b1)**i=0(b1/b2)i+1[Xt+i-a11Tt+1+i-a12Tt+i] +c(b2/b1)', where b1=a11-a21 and b2=a22-a12, and c is an arbitrary constant. The long-run perfect foresight requires a convergent solution and c=0 must hold.5) If a permanent change in tax rate is considered, the tax rates in (13) are all equal, i.e., T1=T for any t, and we obtain (14) PLt=(a20-a10)/(b1-b2)-[(a11+a12)/(b1-b2)]T -(1/b1)**i=0(b1/b2)i+1Xt+i. The effect on land price of a permanent change in tax rate is then (15) *P1/*T=-(a11+a12)/(b1-b2), for any t. From (8) and (9), the effects on the supplies of land and housing capital are (16) *DL1/*T=(a21+a22)*Pt/*T, and (17) *DKt/*T=(a31+a32)*Pt/*T. Table 4 The effects of a permanent change in the capital gains tax Note: Numbers in parentheses are r-values 5) See Kanemoto (1985) for a more detailed discussion

11 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land Table 4 reports the magnitudes of these partial derivatives and their t-values. Note that a rise in the tax rate reduces T=log(1-*). In all three cases, a rise in the tax rate raises land price. Although the estimated values of the partial derivatives are large, their t-values are small and the effects on land price are not statistically significant. The reason for this result is that, as seen in the preceding section, the coefficients for expected and current land prices are not significant in the estimated demand functions of residential land. However, the t-values for the effects on capital formation is fairly large in RE and ARIMA5 cases. This shows that a rise in the capital gains tax has statistically insignificant effects on the supply of land but significantly reduces housing capital. The reason is that, although an induced rise in land price has small effects on supply of land, it causes a fairly large increase in capital formation through the substitution effect. On the average, a 10% rise in 1-t reduces housing capital formation by about 5%. 6. Conclusion We have estimated structural demand and supply functions of residentialand and a demand function of housing capital, and examined the effects of a change in capital gains tax on land. Since the coefficients for expected and current land prices are not significant in the estimated demand function of land, a rise in the capital gains tax has statistically insignificant effects on the supply of residential land. The capital gains tax, however, significantly reduces housing capital formation. The reason for this result appears that a rise in land price caused by the capital gains tax induces a fairly large increase in capital formation through the substitution effect. In many of the estimated equations, the expected and current land prices are either insignificant or do not have "correct" signs. Possible reasons for this result can be classified into three types: (1) neither RE nor ARIMA forecasting provides a good approximation of the actual expectation formation mechanism; (2) the working of the Japanese housing market cannot be explained by the asset choice theory; (3) there are statistical problems in our estimation. First, because very few people (if any) anticipated a sudden fall in the rate of appreciation of land price which occurred after the first oil crisis, it is natural that the performance of a rational expectations model is not good. The optimal ARIMA forecasting does not have this problem, but it is unlikely to approximate the process of expectation revisions after the oil crisis. Second, the asset choice theory may not be applicable to the Japanese housing market because of imperfections in the housing market. There is a long list of market imperfections in the housing market: (1) significant transactions costs including search costs, (2) asymmetric information between buyers and sellers, (3) asymmetric information between owners and tenants, (4) various taxes such as income taxes, property taxes, inheritance taxes, and gift taxes, in addition to the capital gains tax which is analyzed in this paper, and (5) various subsidies such as an implicit subsidy which reduces the interest rates of housing loans. These imperfections may have prevented the land market from functioning smoothly. Furthermore, because of imperfections in the capital market, credit availability (instead of the expected rate of return from land) may have been the major determinant of demand for land. Third, we cannot exclude the possibility that there are statistical problems in our estimation: (1) The sample size (21) may be too small to provide sufficient information on the asset choice -169-

12 behavior of consumers and landowners. The Economic Studies Quarterly (2) Pesaran (1981) showed that the identification problem is much more severe in a rational expectations model than in a static equilibrium model without expectation variables. It is, therefore, possible that demand-supply parameters are not identified in our estimation. (3) We have used the aggregate data for the entire Japan. There have been considerable differences in the rate of increase of land price, i.e., extremely high in large cities (especially, in the Tokyo metropolitan area) and not so high in rural areas. The standard aggregation problem might have prevented us from obtaining the "correct" parameter estimate. (4) The supply of residentical land in a certain year may not coincide with the sale of land in that year. Since our data on the supply of residential land are based on the permission of conversion of land granted by the government, it does not necessarily coincide with the sale of land from agricultural landowners. For example, an agricultural landowner may get permission of conversion of land use several years before the land is actually sold as residential land. It is left for future work to resolve these problems. Appendix This appendix describes the sources of our data and the methodologies used to construct our data series. 1. Land Price: PLt. The source of data is the residential land price index (1975=100) in Zenkoku Shigaichi Kakaku Shisu (National Urban Land Price Indices) published by Japan Real Estate Institute. The original index which is in current prices is converted into real terms by dividing it by the consumer price index. The consumer price index is obtained from Bukka Tokei Geppo (Price Statistics, Monthly) published by Statistics Bureau, Prime Minister's Office. 2. Supply of Undeveloped Land: Lt. The source is the amount of land converted from agricultural use to residential use reported in Norinsuisansho Tokeihyo (Statistics Tables of the Ministry of Agriculture, Forestry and Fisheries). The data include only conversions from agricultural land use and do not include those from other uses such as foresty. 3. Capital Formation in the Residential Sector: Kt. The real capital formation in the private residential sector reported in Kokumin Shotoku Tokei Nenpo (Annual Report on National Accounts) published by Economic Planning Agency is used for this variable. 4. The Price of Housing Capital: PKt. For this variable we use the implicit deflator for the real capital formation in the private residential sector reported in Kokumin Shotoku Tokei Nenpo (Annual Report on National Accounts). 5. The Interest Rate: Rt. The source of data is Zenkoku Ginko Kashidashi Yakujo Heikin Kinri (the average interest rate on bank loans) reported in Keizai Tokei Nenpo (Economic Statistics Annual) published by the Bank of Japan. The interest rate is converted into a real rate by subtracting the rate of increase of the consumer price index

13 Y. Kanemoto, F. Hayashi and H. Wago: An Econometric Analysis of a Capital Gains Tax on Land 6. Agricultural Income: YAt. The sources are the net agricultural income and the number of agricultural households in Norinsuisansho Tokeihyo (Statistics Tables of the Ministry of Agriculture, Forestry and Fisheries). The net agricultural income is divided by the consumer price index to obtain real agricultural income. 7. The Consumer Income: YCt. In order to approximated the permanent income, we use the consumption level instead of the income level. The data source is the index of living expenditure level for non-farm households reported in Kakel Chosa (The Family Income and Expenditure Survey) published by the Statistics Bureau, Prime Minister's Office. 8. The Stocks of Residential Land and Agricultural Land: LCt and LAt. The source is the private land area by prefectures in Japan Statistical Yearbook. The agricultural land is obtained by summing paddy fields and fields. 9. The Population of Individuals Between 20 and 40 Years of Age: Nt. The source is Jnko Dotai Tokei (Vital Statistics Japan) by Koseisho (the Ministry of Health and Welfare). (Yoshitsugu Kanemoto and Hajime Wago, the University of Tsukuba) (Fumio Hayashi, Osaka University) First draft received January 21, 1986; final draft accepted October 22, REFERENCES Box, G. E. P. and G. M. Jenkins (1970) Time SeriesAnalysis: Forecasting and Control, San Francisco: Holden- Day. Kanemoto, Y. (1982)"Tochi Shijo to Tochi Zeisei no Dogakuteki Kinko Bunseki," (A Dynamic Analysis of the Land Market Equilibrium and Land Taxes), Economic Studies Quarterly, Vol. 33, pp (1985) "Housing as an Asset and the Effects of Property Taxation on the Residential Development Process," Journal of Urban Economics, Vol. 17, pp McCallum, B. T. (1976)"Rational Expectations and the Natural Rate Hypothesis: Some Consistent Estimates," Econometrica, Vol. 44, pp Pesaran, M. H. (1981)"Identification of Rational Expectations Models," Journal of Econometrics, Vol. 16, pp Rosen, H. S. and K. T. Rosen (1980)"Federal Taxes and Homeownership: Evidence from Time Series," Journal of Political Economy, Vol. 88, pp Rosen, H. S., K. T. Rosen, and D. Holtz-Eakin (1984)"Housing Tenure, Uncertainty, and Taxation," Review of Economics and Statistics, Vol. 66, pp Seko, M. (1984)"Japanese Homeownership: Relative Tenure Prices Versus Demographic Factors-Theory and Evidence-," Nihon Daigaku Keizaigakubu Keizaikagakukenkyusho Kiyou, Vol. 8, pp