Tenure security and urban squatting

DISCUSSION PAPER Report No.: TUDD-46 TENURE SECURITY AND URBAN SQUATTING by Emmanuel Jimenez January, 1984 Water Supply and Urban Development Department Operations Policy Staff The World Bank .he . nresented here are those of the authors, and thev should not be nt-rpreted as reflecting those of the World Bank. Professor R. A. Hackenberg, University of Colorado, and Director of the Davao Action Information Centre, provided the data base for this study. The author acknowledges the expert research assistance of Serena Ng and helpful comments received from J. R. Follain, C. Lim, S. Mayo, W. Wheaton, two anonymous referees, and participants of work- shops at MIT and at the Universities of Toronto and Western Ontario, but accepts full responsibility for any remaining errors. Mr. Jimenez is on the faculty of the Department of Economics, University of Western Ontario. An U Abstract While recent studies have shown that up to 35% of the total urban population of the Third World live in squatter settlements, there is a dearth of economic analysis on the phenomenon of squatting. This paper attempts to fill this gap theoretically, by modifying existing models of tenure choice to account for risk and empirically, by using a unique data set for a developing country. The equilibrium model argues that the difference in unit housing prices between the non-squatting (formal) sector of a city and its squatting (informal) sector reflects the premium associated with a secure tenure status. The conditions under which households of different types, such as income groups, allocate themselves among squatting comnunities associated with various risks of eviction are then derived. The empirical portion of this paper uses hedonic price techniques to derive the average premium on tenure security in a medium-sized Philippine city, Davao. Results show that formal-sector unit dwelling prices are about 18% (renters) to 58% (owners) more than in the informal sector. These equilibrium price differentials were found to be greater for lower income groups, larger household sizes and households with older heads for renters and younger heads for owners. These groups would thus tend to be in areas associated with greater eviction probabilities. The paper is based on research conducted as part of RPO 672-46, Housing Demand and Finance in Developing Countries, the first phase of which encompasses (1) the demand for housing as a "composite good," focusing on expenditure patterns for housing, (2) determinants of land and housing rents and values, focusing on estimating the implicit market prices of housing, infrastructure, and neighborhood amenities using hedonic price indices, and (3) demand for individual housing character- istics such as interior space, quality of construction, utilities, and accessibility, focusing particularly on estimating schedules of the public's "willingness to pay" for different types of housing in different markets. Table of Contents Page No. I. Introduction ........................................... 1 II. Conceptual Framework .................................. 3 Household Equilibrium: One Type of Household ...... 4 Household Equilibrium: More Than One Type of Household .................................... 8 III. Empirical Formulation and the Data ..................... 10 IV. Empirical Results ..................................... 14 V. Implications ........................................... 19 Appendix ............................................... 20 References ............................................. 23 I. Introduction It has been estimated that 30-35% of the total urban population of the Third World (and up to 40-50% in some of its largest cities) live in squatter settlements, where households do not own or rent the land on which they live but are illegally dwelling on it (Grimes, 1976). Many communities appear overnight on land which may have been vacant for a number of reasons. The land may have been government owned and reserved for some future use; recreational; or marginal, such as rights- of-way for -transport networks, marshes, floodplains, ravines or hillsides. The land may have been privately owned and kept vacant for speculative purposes, which is an option that is particularly attractive in developing countries where relatively disorganized financial markets constrain other opportunities for investment. One of the goals of the recent innovative attempts, led by inter- national aid agencies such as the World Bank, to upgrade urban shelter standards in low income areas has been the rationalization of land tenure schemes (see World Bank, 1980). These efforts have been handicapped by a lack of information regarding the parameters which determine squatting behavior. For example, in a squatter upgrading project which included, as one of its components, the provision of secure tenure, information regarding how much different types of recipient households would be willing to pay for that security would be essential in evaluating the magnitude of the distributional implications of this type of project or in calculating user charges. This paper is an attempt to begin to fill this substantial gap in the theoretical and empirical literature by introducing the use of economic analysis to the 1 2 study of the issues in squatting, which have heretofore been addressed primarily by noneconomists in the social sciences (see Peattie and Aldrete-Haas, 1981 , for a recent review of the prodigious literature compiled by antropologists, planners, political scientists, sociologists and geographers). The most difficult task in evaluating security of tenure is its measurement. If a time series were available, the solution would be relatively straightforward. The objective probability of being evicted would be the proportions of squatters evicted over, say, any given year. If present or prospective squatters guess correctly and equate their sub- jective probability with the objective probability, then the latter, which is measurable, can be used in economic models of behavior. In practice, such a time series is unavailable in developing countries. However, the literature documents evidence that there is considerable variation in the perception of eviction over a city (Peattie and Aldrete-Haas, 1981). If households are correct and there is also an objective variation in tenure security, then cross-section data can be used to characterize that variation. This paper attempts to obtain a measure of the value of security of tenure among squatter households in Davao, a medium-sized city in the southern Philippines, by taking advantage of the dispersion in probabilities of eviction. This dispersion may be due to differences in the opportunity cost of the land which is the subject of the squatting; differences in the cost to the government of evicting squatters from particular settlements, due perhaps to varying degrees of community organization (see Jimenez, 1982b); or differences in the tenure status of certain plots of land, as ownership may be disrupted. A choice-theoretic conceptual framework is used to argue 3 that, in equilibrium, the difference in unit housing prices between otherwise identical units in the non-squatting (formal) sector and the squatting (informal) sector reflects the premium associated with a secure tenure status. Moreover, if there is a discrepancy in this premium among households who face similar risk levels but are otherwise different in terms of socio- economic characteristics, the various premia can be expected to measure differences in attitudes toward risk. The conceptual framework for the analysis is an adaptation of the model described in Jimenez (1982b), and is outlined in Section II. The equilibrium value of tenure security associated with a particular location is the unit price differential between formal and informal sector housing which equilibrates utility in the two sectors and which represents the highest "bid" in the informal sector. The empirical measure of this differential is described in Section III and is based on data from a medium-sized city, Davao, in the Philippines. Section IV is an attempt to infer how squatter households of various socioeconomic characteristics will sort themselves out among squatter locations which are associated with different risk levels. II. Conceptual Framework Consider a city of a fixed site in which there is an amount of land (which is also fixed in size) that is available for squatting. These assumptions are made in order to simplify the model. Squatting land is available due to the institutional reasons described earlier. Housing is assumed to be a composite commodity that yields a continuous flow of services and that is characterized by an upward sloping supply curve. Moreover, in the squatting sector, this supply is situated on land associated with various levels of security of tenure. This is consistent with what has been documented for developing countries, where some older communities are considered "low risk" types. 4 (See Peattie and Aldrete-Haas, 1981.) Some of thr reasons for this have already been discussed in the previous section. The probabilities of eviction associated with different sites are exogenous to the model. Each household is presumed to behave as one individual agent and accepts housing prices,which are market-determined in each sector, as given. This section then examines what are the parameters which a prospective squatter about to enter the city faces in a simple one period world. Household Equilibrium: One Trie of Household In this subsection, all households are assumed to be alike. Each. household maximizes utility with respect to a flow of housing services, h, and a composite comodity, x, under the parameters faced in the formal sector market and under squatting. The household chooses the mode of tenure which yields the greater utility.2 If the representative household were to choose not to squat, it would maximize utility u(x,h) subject to the constraint that W-ph+x, where W- income and p the price per unit of formal housing services. The price p can be interpreted as an implicit rental price of housing or as some unit ownership cost. If p is to be interpreted as Che latter, it would include financing costs, depreciation, maintenance, foregone interest income, differences in the income tax treatment of renters and owners, net of expected capital gain, per unit of housing services. It is assumed that x is the numeraire. The usual first-order condition would be: uh/Ux'P* Solving for the optimal values of x and h would yield the indirect utility funrtion: V = ulW- ph*(W,p), h*(w,p)} v(W,p). (1) The household who squats and who is "successful"--i.e., is not evicted--obtains a price of housing ps and faces a budget constraint 5 W = x n +p h . The subscript n signifies the consumption of the composite n n commodity and housing services under the "not evicted" state of nature. However, if a squatter household were evicted, it would have to incur moving costs and, possibly, a penalty. These are assumed to be a lump-sum cost C. Moreover, in this model, the squatter household must precommit itself and spend money on housing services ex ante, that is, before the household finds out whether it is evicted or not. Thus, the evicted squatter would lose whatever it has invested in the settlement and, in addition, would have to find alternative accommodation. It is assumed that it must buy housing in the formal sector at a given price p if it is evicted. The budget constraint in this state of the world would thus be W = x + ph + C + ph , where e signifies the "evicted" state of nature. Squatters thus face two possible budget constraints, depending upon whether or not they are evicted. The perceived probability of eviction, 17, is assumed to be accepted as given to the squatting household. Faced with two possible budget constraints and the probabilities that one would apply rather than the other, the squatter household is assumed to choose its ex post consumption bundle by maximizing its expected utility: Eus =-u(x ,h )+ --- e e (1-,)u(xn,hn). Substitution of the budget constraint into Eus and the solution of the maximization problem would yield, -pux +uh =0 and e e -p s[17/(1-TT)]u +u J+Uh =0. These conditions can be used to solve for e n n demand equations for optimal amounts of housing services under both states of nature: h* =h*(W,C,p,p ,1) and h* =h (W,C,p,p ,T). Substituting h* and h* into e e s n n s e n Eus would yield the following indirect expected utility function: Vs = nVe+ (1-1)Vn , (2) 6 where ve e (W,C,p,p '=uW-C-ph*(W,C,p,p s h*(WC2pYp s,),h* (W C,p,ps )1 wLer e S,pp s nsr s e and vn=vn(W,Cyp,p , ) =u[W-p h*(W,C,p,ps ,),h*(W,C,p,ps,T), The v(*)'s are thus the indirect utility function under both states of nature and ve v The amount, per unit of housing services, that a representative household is willing to pay to achieve a given level of expected utility, Vs, can be derived by solving (2) for ps =ps(,W,C,p,Vs)- W, C and the distribution of TT's are determiped outside the model. For the moment assume there is only one level of aT in the city. The equilibrium levels of p and p are the prices which would clear the markets in the td residential sectors. The representative household compares its utility under the illegal sector with that under the formal sector to decide whether to squat or not. Analytically, this implies that a household will squat if V<Vs. If the level of utility available in the formal sector were less than that in the informal sector, households would become squatters and raise housing prices until the difference i p and ps was sufficient to compensate for taking the rislc as a squatter. This would be a level of ps which equated utility in the two sectors. For all households to be in equilibrium, then, prices 5 must be such that V equal V . Thus, there would be no incentive for a household to prefer squatting over living in the legal sector. Equilibrium is therefore characterized by: v(W,p) _ V s = TTve(W,C,p,p ,r) + (1-)vn(W,C,p,s where the "o" subscript denotes equilibrium levels of utility, which is determined by a market-clearing condition. The equilibrium gap between ps and p is the amount, per unit of housing service, which would be sufficient to induce a household to be indifferent between living in the formal sector and being a squatter with a given chance, 7, of being evicted. 7 The analysis in the preceding paragraph assumes only a unique value of i. However, as described in the introduction, there is usually a given range, TTk, for various squatter settlements, where k=0,...,1 . A settlement that was reasonably well- established would have a TT that would be close to zero. Thus, in equilibrium, ps should be close to p. For settlements with higher levels of nT, if house- holds are risk averse, households would be willing to settle only for relatively lower values of ps. Since Tk is fixed for each location, observed unit housing prices, ps, are equivalent to what a household would be willing to bid for that particular level of risk. th The locus of combinations of p and TT which would make the j household indifferent between squatting and not squatting is depicted by Vs. in 03 e n Figure 1, under the assumption that v and v are monotone and continuous in. TT and ps. The farther away is the locus from the origin, the worse off will the household be (V <V15). This locus is downward sloping, as rigorously shown in equation (A2) of the Appendix. Intuitively, this is so because, from any given point on a locus, an increase in the cost of being a squatter, ps, would'result in a loss of utility, which would have to be compensated by a drop in TT. The "height" of Vs in equilibrium would depend on the level of V, utility in the formal sector, and, ultimately, the population, income and other exogenously determined characteristics which determine the demand and supply for housing in the city. The convexity of the locus is assumed since, as is shown in equation (A5) of the Appendix, it depends upon behavioral parameters. The exact shape is not important to the analysis. If there is no segmentation in the formal sector so that there is a unique level of p, Figure 1 shows that the difference between p and ps will increase as TT increases (at a given level of utility) . This difference can be interpreted as the amount that a household's bid for squatter housing will differ from the formal sector price at given levels of 7T. Given risk aversion, p > ps' so that Vs is everywhere to the left of p. 8 Household Equilibrium: Mre Than One Type of Household The previous subsection examined the case in which households are homogeneous in terms of income and other characteristics. However, if there were more than one type of household, (1), (2) and (3) would have to be indexed to denote an equilibrium relationship only for a particular household type. Let a represent a set of characteristics which affect behavior (taste, household composition, etc.). For the jth type squatter household, for example, its utility level in the "kth" type of settlement is: V i keW, p k' j k3n ' sk' k where rr denotes the probability of being evicted associated with a particular settlement, and psk is the household's willingness to pay for a unit of housing services at that settlement. The derivation of an equilibrium vector of informal sector housing prices follows the arguments developed in the literature on bid rents in housing markets (see Henderson, 1977, Ch. 6; Rosen, 1974; and Wheaton, 1977). Otherwise homogeneous housing units which are associated with different probabilities of being evicted are rented or sold to the highest bidder. In equilibrium the number of units over which each household type has the highest bid must equal the number of households in that'group. The number of house- holds, in turn, depends upon the level of utility in the formal sector for that household type. Let subscript "k." be the index of that location household j occupies at an equilibrium. At equilibrium: Vo * i"n (e(w ,C4,p,p)k'"k.)j k) n ,C.,p,pk.'7k. j oj o k. ik . v ( 13ci3p,j'PPk k for the jth type of household. To obtain equilibrium across all household types, indifference curves must be compared for each group of consumers to determine the highest bidder for a particular location. 9 At equilibrium, the outer envelope of crnsumer bids exactly represents the price profile observed when consumers maximize utility. In Figure 1, there are two types of individuals, types i and j, whose equilibrium utility levels are Vs. = V and Vsi iV Household j will outbid household i above rr but not below. Thus, the equilibrium set of bid rents would be the outer envelope of the utility-maximizing households' indifference curves in probability-price space. The concavity or convexity of the equilibrium price locus will depend upon the assumptions regarding the shape of the utility locus for each household type. An interesting issue is which type of households will locate at "safer" locations. Suppose that all households were imilar except for wealth. Once again, for this example, the problem is limited to two types of households. rich and poor. If it were determined that rich households are like the type "i" households discussed above, then, they would outbid the poorer households for the settlements which have lower probabilities of eviction. In Figure 1, higher income households would outbid lower income households for locations with more security.of tenure (lower 1T) if, at 17, (g- lRich) > (7 "-IPoor). s s Since -< 0, this would, of course, mean that the absolute value of the slope s of the rich-group utility locus would be less than that of the poor-group. Conversely, if the reverse condition held, the poor would locate where the probability of eviction was lower. Thus it is not unambiguously true that poor households will locate in the riskiest settlements. To determine the conditions under which this holds, the change in (rn/ps) with respect to a change in W is determined at T, ceteris paribus. The resulting expression is derived as equation (A7) in the Appendix. 10 The direction of change in the slope of the equilibrium rent locus with respect to a change in income depends upon parameter values measuring the responsiveness of housing demand to income and the attitudes towards risk. The use of empirically estimated values indicate that the change in the slope is ambiguous. However, what can be said is the following: the greater is the measure of relative risk aversion in relation to the income elasticity of housing demand, the more likely it is that rich people will outbid poorer, people for locations which are "safer". The intuition underlying the result described above follows from the propooition that if housing demand were relatively income inelastic, the amount of decline in housing prices which would be needed to compensate for a greater risk will be greater for high income households than low income households. This is because the benefit from the lower housing prices is dependent upon housing consumption. If the difference in housing consumption between the rich and poor were less than proportional to the difference in income, the poor would benefit more if ps were to decline by the same amount for a slight increase in Tr. To keep utility constant, ps must fall more for richer households. (The analytical justificationis in the Appendix.) It can also be shown that the greater are costs, C, the less steep would the (,,p ) locus be and thus, the more likely are households to be located in safer areas. The analytics of this intuitive result can be found in Jimenez (1982b). III. Empirical Formulation and the Data The theoretical results outlined in the preceding section indicate that a greater ooserved differential in equilibrium unit housing prices between the formal sector and a squatting community implies that households associate a greater probability of eviction with that squatting community. This can 11 be seen in Figure 2 where type i households outbid type j households for safer locations. The heavy line is the equilibrium set of bid prices for the city. The goal of this section of the paper is to measure this average price differential, and thus, the average probability of eviction for the informal sector of a medium-sized city in the Philippines. This differential varies by household characteristics to determine the types of households which locate in safer parts of the city. The primary difficulty lies in a reliable measure of unit housing prices, p and ps, which are unobservable, since h and hs are composite commodities which are made up of a vector of characteristics, z. A rough but useful measure would be to use the hedonic price technique to hold constant for housing characteristics in comparing actual (or, in the case of owners, implicit) rental values in the formal and informal sectors. Let R and R denote observed rents in the formal and informal sectors, s respectively: R = ph(z) = R(z,p) (5) R = p h (z )= R (z ,pS) . (6) S SS S S5 These equations assume that unit housing prices are independent of the level of characteristics consumed. For any given mix of characteristics, f, h(2) =hs () or the consumption technology is assumed to be such that a similar bundle of characteristics in either sector implies the same service flow of the composite commodity. Under these assumptions the following ratio can be calculated for each squatter household: 12 R(z s,p)/Rs(z Ss * (7) That is, the ratio of what a squatter's home would rent out for in the formal sector relative to its actual rental value would be equal to the relative difference in unit housing prices. The equilibrium price ratio p/ps is, in general, expected to be greater than unity because of the uncertainty in the squatting sector and risk averse behavior. The step that remains to be explained then, is how R(z s,p) is to be generated. The hedonic equation that relates R to the characteristics in the formal sector is first estimated, to yield R(z,p). Then the vector of characteristics of the squatter sector, zs, is inserted into this estimated equation describing the structure of formal sector rents, to derive R(z ,p). This is .s. 4 then used to calculate (12), where R (z ,p ) is the actual squatter rent. The arpropriate functional form for the hedonic equaticn cannot, in general, be specified & 2riri on theoretical grounds. Recently, urban economists have imbedded their choice of functional form in a Boz-Cox framework (see, for examplei Quigley, 1982; Goodman, 1978). In this paper, the following transformation is used: * m R+ E + P.Z. + (8) o i=1 ( 1 where R 3 dwelling unit rent (or sale value, for the case of owners); z. is the consumption of the ith characteristic; P 's are parameters to be estimated; C is the random error term; m is the number of characteristics; and R (R-1)/, To simplify the estimation procedure it is assumed that the independent variables are not to be transformed. 13 The random sample used in the analysis is of 3,344 households in Davao, a medium-sized city in the southern Philippines. Of these households, 1,505 were squatters (489 were renters and 1,016 were owners of the structure). The rest were non-squatters and included 887 renters and 952 owners. The interviews were conducted in 1979 by the Davao Action Information Center, a private research foundation, which kindly provided cleaned tapes for this analysis. Separate equations for renters and owners were estimated because the data base does not have similar measures of monthly rent, to be used as the dependent variable in (13), for these two groups. For renters, actual monthly rent is used. The equivalent variable for owners is the estimated sale value, as appraised by tho occupiers. A recent study for another group of squatters in the Philippines (see Jimenez, 1982a) indicated that the latter measure tends, on average, to be similar to that obtained from a professional appraiser. Covariance tests indicate that squatter equations are different from non- squatter equations. The mean housing and household characteristics which are used in this analysis are reproduced in Table I for each bf the subsamples. Some interesting comparisons can be made between the squatter and non-squatter groups. Non- squatters have larger dwellings than squatters but the former's advantage in terms of dwelling unit quality and access to essential urban services is not significant. As expected, squatters live in poorer neighborhoods and have a significantly lower proportion of houses with covered drains. The income in their neighborhoods also appears to be, on average, significantly more concentrated than in the formal sector. Finally, when one examines household characteristics, while there are significant differences in average income, the differences (207. for renters and 34% for owners) are not as large as one 14 might expect. Indeed the income profile (not shown) indicates that about 15% of squatters belong in the top 20% of the overall Davao income distribution. These figures tend zo confim the "new view" among social scientists (see Peattie and Aldrete-Haas) that squatters are not marginal households who have no other choice but to forego the formal sector. 17. Empirical Results The first step in the empirical analysis is the estimation of the hedonic relationship (8) for renters and owners of the formal sector. The results for linear, semi-log, and Box-Cox specifications are presented in Table 2. It should be noted that the statistical package used to estimate the Box-Cox equation via maximum likelihood methods may produce underestimates of the standard errors (see Blackley, I_t a). However, the extent of this bias has yet to be determined in the literature. Thus, few statements about significance are made below. For renters, the functional form which maximizes Box-Coz likelihood function is one in which % approaches zero, which makes this equivalent to the semi-log, The results for the hedonic equation indicate that most of the coefficients are of the proper sign. The variables which measure quantity (number of rooms) and quality (structural condition, wall material quality and floor material quality) are all positively related to rent or sale value. The coefficients for basic urban services display less consistent behavior. For renters, the coefficients of the other urban services such as the provision of water services, sanitazy facilities, garbage collection, electrical and phone connections, and drainage have the expected signs. For owners, three of these are of the wrong sign, although they also have low levels of significance, even with standard errors which are underestimated. 15 As expected, distance from the city center and the average income of the neighborhood are negatively and positively related, respectively, to the dependent variable. An interesting finding is that an increase in the heterogeneity of the neighborhood in terms of income leads to a decline in hous*.ng value. In the second stage of the empirical analysis, the results summarized in Table 2 are used to predict the rental or sale value of squatter housing. Since these coefficients ref7ect the role of formal sector housing characteristics in formal sector value, this procedure predicts the rent that squatter housing, with a particular set of characteristics, would obtain, had that housing been in the formal sector: 13 R (zsp= [(1+10 )+ Z 4 as s'p xo Xj=l P i s This calculation of R(z ,p) can be compared with Rs (z s,p), the rent that is actually paid for a house with a set of zs characteristics. Since the level of housing services is held constant, the ratio must reflect differences in unit prices to compensate for risk. In relative terms: R(zs,p)/Rs(z s = s These ratios, averaged for each of the squatter subsamples, are 1.177 for renters and 1 .578 for owners. The results indicate that, on average, a squatter dwelling would rent out for approximately 18% more if it were in the formal sector. For squatter owners, the mean difference is considerably greater--the sale value for the same dwelling unit would increase by over half. This result is to be expected given the costs of eviction for these two tenure groups, although the two ratios are difficult to compare because of different measures of rent. The strict comparison of renter and owner behavior will be the subject of future work. 16 The relative difference for each subgroup can be interpreted as the market valuation of the security of tenure. According to the theory outlined in the previous section, if households are in equilibrium, the reciprocal of this ratio is the discount in formal sector housing prices which is necessary to induce an average household to accept a particular level of risk of being evicted in the squatting sector. This disccunt would be expected to be larger, the greater is the perceived risk. It is impossible to rigorously test whether the magnitude of the average discount fully reflects rr, since measures of T are unavailable, However, there is indirect evidence to support the conclusion. First of all, Davao had a history of planned, and a lower level of actual, squatter eviction in the period prior to data collection. Hackenberg states in 1974 that "present plans for squatter removal.. .may affect as many as 17,000 households or 28% of -the city's population" (p. 46). Knowledge of such plans and several court decisions that went against the squatters in the more valuable areas (Doeppers, p. 365) likely led some squatters to perceive significant amounts of risk. Secondly, while differential length-of-residence rates do not fully reflect such risk (since age of homes may exceed length of residence), they can be an indicator. The median non-squatter owner has been in his/her current residence 33% longer than his/her squatter counterpart (6.8 years). For renters, the difference is almost 30%. It is interesting to note that the risk premium declines as length of residence rises for owners. No trend is discernible for renters. Sincj there is a given distribution of risks associated with different plots in the community, differences in household characteristics and risk preference would imply different discounts for various socioeconomic groups. These differences in household characteristics would have certain implications for the costs of being evicted, relative risk aversion, and so on. In BEST COPY AVAILABLE 17 equilibrium, those with the smallest discount for a particular level of risk would obtain the plot associated with that risk. In order to gain some insight into which types of households bid for and obtain riskier areas, the ratio, R(z s,p)/R s, is regressed on socioeconomic characteristics such as income, household size and the age of head. Once again, in this analysis, households are assumed to perceive the same level risk associated with a dwelling unit. The regression results for the semi-log and double-log forms are reported in Table 3. The results for other functional forms (quadratic and linear) are quite similar and are not reproduced here. The means of the independent variables are at the bottom of Table 1. Permanent income is obtained from a predicted value of an equation that regressed current income on a number of relevant variables.5 The most consistent result is that income is negatively related to relative prices. The coefficients for current (not shown) and permanent income measures are less than zero and significantly so for all the specifications. The interpretation of this result can be seen by first recalling that, in equilibrium, there is a dowrward sloping relationship between Tr and ps. If there were no segmentation in the formal housing market, this implies that, at higher levels of eviction probabilities, there should be greater differences in the ratio of unit prices in the formal sector relative to unit prices in the informal sector. This equilibrium relationship was shown. to be the envelope of "highest bids" by various socioeconomic groups. The empirical result indicates that higher income households are willing to pay more for security (RATIO is lower) than poorer households. This result is in accord with prior expectations, as discussed in the theoTetical section, given prevailing estimates for the income elasticity of housing demand and priors about the Arrow-Pratt measure of relative risk aversion. REST COPY AVAILALE 18 The results for the demographic variables indicate that larger households are willing to pay less for security than smaller households. While this, at first, seems surprising since the larger families probably have to incur greater costs if evicted, it should be noted that household income is being held conmstant and larger families would imply lower income per person. For renters, age of head is positively (although weakly) associated with relative differences in housing prices, which indicates that. older renter households will tend to locate :n squatter neighborhoods with higher eviction probabilities. For owners, the trend is exactly the opposite and owner occupying households with older heads tend to outbid younger ones for safer locations. One explanation for this is that, among owners, older households have greater eviction costs due to loss of status. Moreover, they have had a greater opportunity to consolidate their dwelling and, indeed, even their property rights to a location. For renters, such considerations are unimportant and renter families with older heads are likely to be those with little to lose and who would prefer the chancier locations at a lower price. Because of the relatively low explanatory power of the equations in Table 3, the empirical results of the second part of this analysis should be interpreted with the appropriate caveats. Household characteristics other than the ones included in this study may be important in determining which households bid for what type of site. However, the low R2's are not iurprising given the cross-section nature of the data base. The findings for the characteristics which are included still yield interesting insights. 1* 4BEST COPY AVAILABLE 19 V. Imlications The results show that formal-sector unit dwelling prices are about 18% (renters) to 58% (owners) more than equivalents in the informal sector. These equilibrium price differentials were found to be greater for lower income groups, larger household sizes and households with older heads for renters and younger heads for owners. These groups would thus tend to be in areas associated with greater eviction probabilities. While these figures are derived through a technique based on some simplifying assumptions for a city in a particular environment and thus should not be accepted as widely applicable for every city with a squatter community, they are indicative that premia for tenure security do exist. One important application of the results of this research is in the design and pricing of urban development projects which grant tenure security to their beneficiaries. For the city of Davao, this paper has been able to obtain average estimates of the market valuation of tenure security. Moreover, tho benefits of secure tenure will differ depending upon the perceived risk of eviction, which is capitalized into the price of dwellings. If the structure of risks were not taken into account into its design, a project which uniformly provided tenure to all types of squatter communities would have significant distributional implications. For example, if the conclusions for the Davao sample are correct, low income households would benefit more than their high income counterparts from such a project. The findings also offer one explanation why it would not be unusual to find relatively low-priced squatter dwellings in vacant areas among properties which are quite attractive and which may be settled by the city's elite. Since the risks of eviction are likely to be greater in these areas, the findings of this study would indicate that poorer squatter house- holds would "outbid" richer ones for such locations. 20 APPENDIX As described in equation (3) of the text, the following equation holds in equilibrium: n v(W,p) =V o e(W,C,p,p ,T) + (1-T-,)v (W,C,p,p,T) (Al) 0 0 S Preference orderings are assumed to be continuous, monotonic, convex and homothe-tic.6 The slope (r/ ps) for a given level of utility Vs, in (TT,p ) space, can then be determined by solving the last equality of (Al) for p =p (r,W,C,p,V s s o and totally differentiating: (T/8p IV) -[nve + (1-T)vn Mv -v n S Ps It is useful to rewrite this expression by using the first order conditions in the text and deriving analogs to Roy's identity, i.e., ve =-h* e(1+)/( -m ) and Ps nvW vns _h*n W+ TT/ (1-T)]hn e to derive: (On/3p so) =h*le + (1_TT)v ]/(ve v (A2) where 3 (h /3p )(p /h ), the price elasticity of housing demand, a-p h /W, n s s n sn a share equation, and eE (3h */W)(W/h*), the income elasticity of housing demand. n n Since vW,vW>0 and v v, (A2) implies that the locus slopes downward. In order to derive the conditions under which the locus is concave, differentiate (A2) with respect to ps holding everything else constant: (0 2Ta Vo a n) h nl"Tv+ (1 -T)vW]1p * e n e n e n2 -lan TvW + (1-TT)vW]6(v - v )/ ps In the first term of (A3)'s bracketed expression: 6hnl* + (1-n)va] s = h [y s+ (1-TT)v s +ES C + (O -rr)AV LhL WvW n s BEST COY AVAILIK 21 To evaluate the above Roy's identity and Young's theorem are used to derive v vn = p p e + (1-T)v = _h* Ire + (1_ )v n; which imply Wps ps s s p s en e ne n * that Tves + (1-T)v = ([ny + (1-) +h* r + (1-T)v.](Bhn/W)). With p W p W n +['W + WWJ the appropriate substitutions: 6haTv.+(1-Tn)v]/ps = hn[ny + (1-T)vn(] TD/p - h[ re + (1 -1) vrn s (A4) e e a, n. n n where r e . fr , r =-n/rW, Arrow-Pratt absolute risk aversion measures. Under the assumption of constant absolute risk aversion (r =rn=r), p = rW, the Arrow-Pratt measure of relative risk aversion in (A4) and (A2), This implies that (A3) can be rewritten as: (6 2nT/3p2 oVS s s("T/6 )(a(S -p)- (A5) e n e n - r (v - v )/(v - v n1W/p a s in order to find out whether or not, at any given level of r,, this utility locus becomes less or more steep as income changes, simply differentiate (A2) with respect to W: 8(ir/½ps IVo)/6W = ,:ny + (1-I)v (Bh/8W) * e _Ta n + h (TTvW+ (1-T)v }/(v - v ) -h w + (1-_)v v n)/( e v ) 2 From (A2), the terms defined earlier, and 6=W(ve -v )/(ve Vn W W' the income elasticity of the spread in utility between the evicted and the unevicted states of nature, (A6) can be expressed as: O(T/6p IVs)/W = (NT/6p IVs)(( -p) - 6AV (A7) s a s o BEST CO PY AVAILABLEr 22 Suppose that f,,p and 8 were invariant with respect to income. The slope (A2) denotes the amount of price decline which would induce a squatter household to accept another unit of uncertainty while holding its level of well-being fixed. According to (A7), since p approaches unity and assuming 8<0 (which is reasonable given diminishing marginal utility of income), a sufficient condition for this price decline to be less for richer than poorer households is that c>1. This implies, of course, that the slope (A2) of the probability-price locus decreases (becomes more steep) as income rises, given rr. Thus a sufficient condition for richer households to outbid poorer households for riskier locations is that housing demand be income elastic. However, recent empirical studies have shown that the demand for housing is relatively income inelastic (see Mayo, 1981, for evidence on developed countries; Ingram, 1981, and Jimenez and Keare, forthcoming, for evidence on developing countries). Thus the sign of (A7) is ambiguous. What can be said is the following: the greater is the measure of relative risk aversion in relation to the income elasticity of housing demand, the more likely it is that rich people will outbid poorer people for locations which are "safer". 23 References Arrow, K. (1971), Essays in the Theory of Risk Bearing, Markham. Blackley, P., Follain, J. R. and Ondrich, J. (forthcoming), "Box-Cox Estimation of Hedonic Models," Review of Economics and Statistics. Doeppers, D. (1971), "Squatting in Davao City," in his Ethnicity and Class in the Structure of Philippine Cities, unpublished Ph.D. dissertation, Syracuse University, pp. 347-488. Goodman, A. (1978), "Hedonic Prices, Price Indices and Housing Markets," Journal of Urban Economics 5: 471-484. Grimes, 0. F. (1976), Housing for Low-Income Urban Families, Baltimore: Johns Hopkins University Press. Hackenberg, B. H. (1974), "Planning More Poverty: Cost and Consequences of Squatter Removal in Lanang District, Davao City," Philippine Planning Journal 5: 45-64. Henderson, J. V. (1977), Economic Theory and the Cities, New York: Academic Press. Ingram, G. K. (1981), "Analysis of Housing Demand in Bogota and Cali," paper presented to the Meetings of the Eastern Economic Assoc. (Philadelphia). Jimenez, E. (1982a), "The Value of Squatter Dwellings in Developing Countries," Economic Development and Cultural Change 30(4): 739-752. Jimenez, E. (1982b), "Urban Squatting and Community Organization in Developing Countries: A Conceptual Framework," Centre for the Study of International Economic Relations, University of Western Ontario, Working Paper No, 8209CDSU. Jimenez, E. and Keare, D. H. (forthcoming), "Housing Consumption and Permanent Income in Developing Countries," Journal of Urban Economics, Kihlstrom, R. and Mirman, L. (1981), "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," Review of Economic Studies 48: 271-280. Mayo, S. (1981), "Theory and Estimation in the Economics of Housing Demand," Journal of Urban Economics 10(1): 95-116. Peattie, L. and Aldrete-Haas, J. A. (1981), "Marginal Settlements in Developing Countries," Ann. Rev. Sociol. 7: 157-175. Quigley, J. (1982), "Nonlinear Budget Constraints and Consumer Demand: An Application to Public Programs for Residential Housing," Journal of Urban Economics 12: 177-201. Rosen, S. (1974), "Hedonic Prices and Implicit Markets," Journal oi Political Econom: 34-55. Wheaton, W. (1977), "A Bid Rent Approach to Housing Demand," Journal of Urban Economics 4(2): 200-219. World Bank (1980), Shelter, Washington, D.C. 24 Footnotes The assumption that housing can be treated as a composite flow of services is standard. It is beyond the scope of the present version to explore the relationships between secure tenure and housing characteristics because data limitations prevent direct measures of tenure security. 2Because data limitations prevent the strict comparison of renter and owner housing expenditures, the paper does not consider the more general problem in which households also choose whether to rent or own. 3The one period framework and the precommitment allows us to determine ex ante prices, without having to solve an intractable rational expectations problem concerning what prices are likely to be, given who is evicted. Moreover, the analytical solution would become more complex in a multi-period framework in which ex Zost and ex ante prices must be reconciled since households would then have to make comparisons at each point in time. Covariance tests are first carried out to ensure that the hedonic relation- ship differs for squatters and nonsquatters. It should also be noted that the alternative specification, to insert the nonsquatter characteristics into the squatter regression, was also attempted with substantially similar results. 5These variables include: household size, age of head, sex of head, regularity of meat consumption, furnishings, vehicle ownership, appliance ownership, years of education, whether or not the household is self-employed, whether the head has a white collar job and home ownership. 6' The conditions under which the Arrow-Pratt measure of risk aversion can be extended to a utility function which has more than one commodity are discussed in Kihlstrom and Mirman (1981). They obtain the result (Theorem 1) that if the preference orderings are continuous, monotonic, convex and homothetic and if a direct utility function u is an increasing (decreasing, constant) relative or absolute representation of these preference orderings, then the indirect utility function u inherits this property when considered as a function of income. This theorem is invoked to justify the use of the Arrow-Pratt measure with indirect utility. 7In Arrow's (1971) words "broadly speaking, the relative risk aversion must hover around 1, being if anything somewhat less for low wealths and somewhat higher for high wealths" (p. 98). 25 TABLE 1: Average Housing and Household Characteristics in the Two Sectorsa Renters Owners n=489 n=887 n=1016 n=952 Housing Characteristics: Squatters Non-Squatters Squatters Non-Squatters NROOMS Number of rooms in 2.99 3.25 3.65 4.01 d.u. (1.15) (1.22) (1.22) (1.46) STRUCCON Structural Condition 2.79 2,84 2.78 2.89 Index (.61) (.62) (.58) (.62) WALLQ Wall Quality Index 2.34 2.43 2.31 2.45 (.51) (.53) (.55) (.54) FLOORQ Floor Quality Index 2.23 2.22 2.15 2.24 (.51) (.45) (.44) (.52) FLUSHWC Prop, of HH with .56 .66 .45 .58 flush toilet (.50) (.47) (.50) (.49) COLLGAR Prop. of HH with .21 .67 .13 .50 garbage collection (.41) (.47) (.34) (.50) OWNPHONE Prop. of HE with .02 .10 .04 .12 phone access (.15) (.30) (.18) (.32) WATER Water Facilities 1.99 2.12 1.92 2.18 Index (.56) (.74) (.42) (.46) WIRE Prop. of HH with .75 .87 .70 .86 elec. connection (.44) (.33) (.46) (.35) MEANY Avg. income in 1294.20 1513.80 '1182.30 1459.00 neighborhood (545.6) (609.85) (467.24) (625.52) SDMEANY Avg. std. deviation 1174.50 1617.10 1204.80 1517.90 of neigh. income (844.46) (1316.30) (1010.70) (1256.80) DIST Distance in meters 3502.1 1665.3 4436.6 2481.5 from the CBD (2411.5) (1432.8) (2755.3) (2138.7) COVDRN Prop. of HH with .17 .27 .11 .28 covered drains (.38) (.45) (.31) (.45) RENT Monthly Rent 97.99 128.54 -- -- (119.45) (139.15) SALE Owner-assessed ** -- 7938.5 11889.00 sale value (12613.0) (17447.00) Household Characteristics: INCOME Monthly current 1133.60 1357.40 1223.20 1646.50 income (1112.40) (1537.60) (1362.20) (2482.90) PERMINC Estimated permanent 964.76 1117.80 1047.00 1276.40 incomeb (561.69) (624.15) (569.26) (694.99) HHSIZE HH Size 5.33 5.43 6.45 6.42 (2.07) (2.34) (2.49) (2.65) AGEH Age of Head 36.69 38.10 43.29 46.37 '(10.39) (11.30) (11.95) (12,83) a Standard deviation in parentheses. bThis is a predicted value based on certain household characteristics. The equation is explained in the text. REST COPY AVAILALE 26 TABLE 2: Hqdoqac a Renters b -0imer Linear Semi-Los Linear Semi-Log Bo3-Cox (X = .06) , CONSTANT -329.49 1.1975 -45634. 3.0654 2.0454 (25.10) (.1418) (2775.7) (.1986) (.3283) NROOMS 20.178 .2113 1922.8 .2159 .3590 (3.544) (.0020) (368.5) (.0264) (.0436) STRUCCON 35.886 .2320 5726.4 .6783 1.1070 (7.469) (.0422) (890.4) (.0637) (.1053) WALLQ 23,955 .1382 1280.8 .4361 .7084 (8.343) (.0471) (978.5) (.0700) (.1157) FLOORQ 64.916 .3369 10922.0 .3684 .6933 (9.018) (.0509) (1050.0) (.0751) (.1242) FLUSHWC 15.542 .3317 1155.3 .2245 .3744 (8.910) (.0503) (1016.6) (.0727) (.1202) COLLGAR 8.977 .1142 -723.83 . -.0297 -.0454 (8.072) (.0456) (919.58) (.0658) (.1988) WIRE -6.956 .0962 -1976.2 .2960 .4243 (11.100) (.0627) (1289.6) (.0923) (.1525) OWNPHONE 63.873 .2156 2526.2 -.0616 -.0745 (12,526) (.0708) (1470.1) (.1052) (.1793) WATER 6,678 .0167 356.66 .0073 .0165 (4.758) (.0269) (436.35) (.0312) (.0516) COVDRN 38.084 .1318 1437.5 -.1114 -.1670 (8.407) (.0475) (1035.0) (.0740) (.1224) DIST -.0012 -.000025 .0264 -.000020 -.000028 (.0025) (.000014) (.2173) (.000016) (.000026) MEANY .0498 .000416 3.6256 .000322 .000577 (.0163) (.000092) (1.5244) (.000109) (.000180) SDNEANY -.0160 -.000155 .1621 -.000041 -.000075 (.0071) (.000040) (.7075) (.000051) (.000084) N 887 887 952 952 952 -2 .49 .62 .50 .60 .61 aStandard errors are in parentheses. bThe coefficients of the Box-Cox specification are the same as those of the semi-log form. 27 TABLE 3: Relative Unit Price Regressionsa Renters Owners (1) b (2) b (3) b (4)b Dep. Var. LRATIO LRATIO LRATIO LRATIO CONSTANT -.04536 .8539*** .4962*** 2.6395*** (.09190) (.3457) (.1147) (.4042) PERMINC -.000156*** -.000306*** (.000045) (.000051) AGEH .003589 -.004051* (.002310) (.002292) HSIZE .01645 .01414t (.01229) (.01136) LPERMINC -.19843*** -.3806*** (.05344) (.0589) LAGEH .10767* -.0408 (.05897) (.0757) LHRSIZE ..07886 .1130* (.06181) (.0677) .020 .024 .043 .042 N 489 489 1016 1016 F 4.37 5.02 16.07 . 15.96 a"'L" indicates the natural Log of a number; Significance levels: ***= .01, ** =.05, *=.10, t =coefficient >standard error. b A RATIO = R(z ,P)/R s 5 28 V s s V <V I oj A VA-j --o ITI B vSI oi ~sk isk1 Psk sk iS s sksk. sk. PIPs NOTE: pk Household i's bid for a location in j's equilibrium location. sk. . FIGURE 1 Vs Vs A o- vs, oi C P PFPI FIGURE 2