Risk and Information: a Hedonic Price Study in the New Zealand Housing Market*

S. A. MAANI and S. B. KASK Univenuy of A u c W Univers@ofNorth Carolina,

Asheville

This paper employs the hedonicpriceapprwch developed by Rosen (1 974) and recendy extended to study the effects of potential natural hazards on consumer behavwur. Hedonic prices are used to estimate home buyers’ w W g m to pay to avoid a high-pressure gar pipeline installed in a residential area Studies of risk and information (e.g. BrOokrhLe et aL. 1985, Smith and Johnso4 1988) mggm that the subjective pmbabhty of a hazard occuning differsfivm the objective pmbabduy. If we allow for this and relax the Qlslunption of JW information on the part of home buyers our theomtical anaiysis indicates that a single kdonic price is not mfficienr because hedonic prices are likeiy to change with a change in information O w empirical analysis of cross-sectional data acmss time b in accord with the theoretical moaki although not highly signifiant

I Introduction Hedonic pricing techniques. developed by Rosen

(1974). have been widely applied to the estimation of consumer values for non-market goods. How- ever, the approach has only recently been applied to estimate the value a consumer places upon the avoidance of the risk of losses which may result from natural hazards (e.g. Brookshire et af., 1982 and 1985, and MacDonald etd, 1987). These new studies are of particular interest, because they use the hedonic approach to evaluate consumer

* Dr Maani is a Senior Lecturer in Economics at the University of Auckland in New Zcaland Dr Kask was formerly a research fellow at tbe University of Auckland and is presently an Asistant Professor of Economics at the University of North Carolina in Ashcville. The authors would like to thank the Minisfry of Works and Development in New Zealand for supporting the empirical mearch rcportcd in this paper. The authors are thankful to two anonymous referees and to G. A. F. Sebcr. P. Kennedy, A Siddiqui. J. Nankervis, M. O’Connor. J. Shogrcn, B. h n . and S. Patch for helpful comments. This paper was presented at thc Eastern Economic Association Meeting, USA, March 1989.

behaviour under conditions of risk and uncertainty. where the risk arises from non-market hazards occumng in the natural environment. This characteristic of the studies raises new questions, previously unaddressed in the literature. regarding the application of the hedonic approach under conditions of risk and uncertainty. In particular, the static approach used in hedonic studies and the assumption of full information made inAhe earlier hedonic wage-risk studies (e.g. Thaler and Rosen, 1976) are likely to be invalid in the case of non-market environmental hazards, since the information regarding these risks may not be fully available to consumers in the hedonic markets.

If full information does not hold, or information changes over time, a static hedonic price approach assuming full information is likely to under- or over-estimate the theoretically relevant objective hedonic price. A number of recent studies suggest that the subjective probability of hazardous events is often different from the objective probability (see, for example, Smith and Johnson. 1988; Viscusi and Magat, 1987; Brookshire et af., 1985; Lichtenstein et d. 1978). These studies suggest that the

227

228 THE ECONOMIC RECORD SEPTEMBER

subjective probability is sensitive to information change.

If information and subjective probabilities change over time, a single hedonic price approach based on observations over one time period, as is customary in the literature, is insufficient for estimating the costs or benefits of environmental policy. The theoretical analysis in this paper suggests that if we relax the assumption of full information, and thereby allow the chosen level of self-protection from hazards to be based on subjective probabilities, hedonic prices are likely to change with information over time. This assertion is tested in our empirical study for New Zealand where we examine the homebuyers' willingness to pay to avoid the probability of a hazardous event, in this case the explosion of a high-pressure gas pipeline installed in a residential area. We analyze cross-sectional data across time to illustrate the changing nature of hedonic prices.

Section I1 presents the theoretical framework of the study and a review of the current literature on information and risk. Section 111 presents the empirical results. Section 1V concludes the paper.

I! Hedonic Pricing Subjective Probabikry, and Information

We start with a model similar to the self- protection model, which assumes full information, found in Erlich and Becker (1972). We assume that a consumer maximizes a utility function U ( h ) . where h is a vector of housing characteristics, ( h , , . . . . . , hm), and x is a composite good. In our model, since the consumer is making a decision in the uncertainty that a hazardous event (such as a flood. explosion or earthquake) may occur, we assume that the consumer maximizes an expected value of his or her utility function where the event occurs in state 0.

(1) &v, - puo (b) + (1 -p)ul(icx). where a u i a x x , a w i a x w o and auiahi s 0, a2uiahi2 < 0.

The subjective probability, p , is the consumer's perception of a hazardous event occurring and is a function of an endowed (scientifically deter- mined) probability, p', and the consumer's efforts to self-protect (in this case from a high-pressure gas pipeline explosion), s, as in (2) below:

p - p@:s) (2) where aptapt > 0 and dplds C 0.

The consumer's housing decision is subject to an income constraint where W is the price of a

home and is a function of the attributes of a home, h, and the level of self-protection taken to reduce the risk of the hazardous event occurring, S I The price of the composite good x. Wx, is assumed equal to one, therefore we can write the income constraint as (3):

x - Y - W(ks). (3) If Yo represents income in state 0 when the

hazardous event occurs and Y I is income when the event does not occur? we can substitute (3) into ( I ) , to derive the Expected Value Function given in equation (4) which the consumer maximizes as follows:

Max E(V) -fir. s) V d h , YO- W(h, $1 + (4) [l-P@'. s)lV~lh Yi-W(h, s)l.

in hedonic pricing models such as this, where the consumer is choosing both housing characteristics and the level of self-protection (i.e. choosing to relocate and lower p), we maximize the expected value function over the vector h and s. The first-order conditions of maximizing expec- ted value function (4) with respect to h and s, are the hedonic prices derived for levels of the j household characteristics and the level of self- protection chosen. These prices are given in (5) and (6), below:

Self-protection is chosen such that the price of self-protection is set equal to the trade-off between the gain from self-protection (i.e. the reduction in

I In some of the papcn cited above. a self-insurance model was applied, when the individual remains in a hazardous situation, but buys insurance. In our case the self-protection model (as in Erlich and k k e r , 1972) is more appropriate, since the decision to locate near or away from an area where an uncertain hazardous event may occur is relevant. This decision affects both the pmbability of the event occurring and the level of damages.

2 in this model we wume lossts remain constant for different levels of self-protection. Relaxation of this assumption is not necessary to investigate the impact of information on self-protection bchaviour.

199 I RISK AND INFORMATION 229

expected losses) and the marginal utility of the composite good x.

Hedonic studies which estimate consumer ‘wiliingness to pay’ to avoid uncertain hazardous events estimate the price W, given above. As stated above, these studies assume information is perfect and thus the subjective probability, p. is equal to the objective probability p The assumption that subjective probabilities are independent from information and that they are constant, as above (pp and constant), disregards the recent literature on how subjective probabilities are formed. If we allow imperfect information, as in the model below, we show that the level of self-protection a consumer chooses depends upon the effect of information on the subjective probability. The above model is extended to allow varying levels of information.

The Extended Model The research on probability transformation from

objective to subjective probabilities suggests that subjective probabilities are highly sensitive to information levels and that they change with changes in information (see Lichtenstein et aL, 1978; Fischoff, 1975; and Tversky and Kahneman, 1973). We incorporate the possibility of infor- mation change into our hedonic model by allowing the subjective probability to be a function of information, i, as given in (7) below

p - w. SA. (7) If we substitute this subjective probability into

our model given above, we can derive the same decision results given in (5) and (6). The consumer chooses the levels of h and s such that they equate the marginal costs of each to their respective marginal rates of substitution. These results are not particularly interesting until we consider the effect of changing information on the hedonic price for self-protection. If information is not perfect, and the consumer’s prior subjective probabilities are not equal to the endowed probability (i.e.p+p). we would expect our hedonic price to be different from what it would be based on full and constant information.’ If information changes over time our hedonic prices will also change, thus the usual static hedonic estimates may give biased information on consumer values of risk and safety. Equation 8

3 It can be argued that the endowed probability QP) is itself based on ‘expert’ knowledge. and that it can also change over time. Our paper addruses the simpler case in which the endowed probability remains constant, but the home buyer’s subjective probabilities may change.

below shows the effect of changing information on the hedonic price W, (see Appendix A for the derivation of these results).

Whether consumer expenditures on self- protection increase or decnase in response to new information depends on the effect of information on the subjective probability, aplai k 0. A review of the literature on risk and information provides some insights into the conditions under which the hedonic prices will increase with changes in information and when it may decrease.

I n formarion and S&j& hbabilities A recent article by Smith and Johnson (1988)

and the many articles preceding it (Lichenstein et d, 1978; Fischoff, 1975; TFenky and Kahneman, 1973; and Kunreuther a d, 1978) stress the importance of information on the transformation of objective probabilities to subjective probabilities. These studies validate the presumption that information will alter a consumer’s perception of risk and thus the assumption of perfect information is likely to be invalid when using the hedonic approach under conditions of uncertainty. In addition, they show that subjective probability may consistently under- or over-estimate the objective probability, and thereby these studies provide insight into the possible biases in estimated hedonic

Lichenstein et d find that individuals consis- tently misjudge the possible frequency of hazardous events by under-estimating high frequencies and over-estimating low frequencies. The consistent bias was found to occur as a result of: the recency of a past event, the impact of an occurrence on an individual, anchoring,’ and the ability of individuals to retrieve information from their memory.5 In addition, the authors found that media reporting, which may provide inadequate or misleading information, or may sensationalize an

prices.

The individual anchors on to a specific frequency level and adjusts hidher Subjective probability up or down as information changes This anchoring level can come from any source.

5 Usually referred to as ‘AvailabiIity’ (Tvenky and Kahneman, 1973).

230 THE ECONOMIC RECORD SEPTEMBER

event, also biases subjective probabilities upward by affecting an individual's ability to retrieve information. Finally, they found that mass events (i.e. events not distributed over time) were over- estimated due to sensationalized information.

Smith and Johnson (1988) examine the res- ponsiveness of individuals to information about a hazardous chemical, Radon, and find that changes in information cause consumers to alter their perceived risks.

Brookshire cf al. (1985) and Kunreuther d d, (1978). find that consumers behave as if their probability is essentially zero for hazardous events when objective probabilities are below some threshold level, even when these events are catastrophic. Both the Brookshire ct ul. and the Kunreuther et ul. results suggest that at some low probability level the subjective probability is zero.

Vixusi and Magat (1987) find that individuals behave in a manner consistent with the Bayesian learning model, i.e. that increases in the size of the loss lead to increases in precautionary efforts; and that an increase in the endowed risk relative to the consumer's prior probability increases the consumer's level of self-protection. They find that increases in information raise a consumer's posterior probability when the endowed risk, p', is below average. However, increased information lowers the posterior probability when the consumer's prior probability is above average.

They further show that information with a low

i FIGURE I

Subjective Probability and Information with Low Endowed Probability

i FIGURE 2

Subjective Probability and Information with High Endowed Probability

endowed probability and initially high subjective probabilities leads to a posterior probability that decreases with increases in information, i.e. dpldi < 0, as may be shown in Figure 1. This will result in a decrease in a consumer's expenditure on self-protection (according to equation 816 In contrast. a high endowed probability and an initially lower subjective probability lead to an increasing probability with incrcases in informa- tion, i t . aplai X, as shown in Figure 2 above. In this case, with an increase in information, the consumer's expenditures on self-protection are expected to increase.

If. as the above studies indicate, in a market involving hazardous risks, information is imperfect or may change over time, applying a static hedonic price approach to estimate a consumer's willing- ness to pay to avoid an uncertain hazardous event is insufficient. Such static estimates only capture consumers' valuations for a single point in time, while the willingness to pay may change. Therefore, since the applied policy goal undedying most

While information is expected to bring subjective probabilities closer to objective probabilities with increased information, sensationalizing of the risks involved is likely to c a w sudden jumps in the subjective probabilities Such sudden increases in subjective probabilities arc likely to adjust gradually towards the objective probability.

1991 RISK AND INFORMATION 23 I

hedonic studies is to estimate consumer valuations as part of some stream of benefits or costs, the static cross-sectional approach applied can result in erroneous findings for policy or compensation.

The next section gives an example of an empirical study where information was changing over time and shows the results using multiple periods of data to illustrate this problem.

III The Empirical Modei Data and Results A study conducted in Auckland, New Zealand,

which evaluates a consumer’s willingness to pay to avoid exposure to the risk of a hazardous event, Wn provides an example of the problems arising from the assumption of perfect infomation.’ In this study, the hazard was the possibility of an explosion from a high-pressure natural gas pipeline installed in urban neighbourhoods. A consumer’s expenditure on self-protection was reflected in his/ her decision to pay a higher price for a comparable home that was not exposed to the hazard, therefore we can estimate a hedonic price for self- protection.8

The empirical model estimates the hedonic prices for the various home attributes and the hedonic price, w, to avoid exposure to the risk of explosion. The model includes housing charac- teristics: gross floor area, number of bathrooms and the number of bedrooms. lot size, quality of construction, condition of the home, age of the house, and the pipeline variable. Equation 9 below presents the general housing sale price model:

(9) where Log W,: the natural logarithm of the sale

CP: gas pipeline on the street The hedonic price paid for safety is &. Therefore,

the pipeline variable (Gp) which represents the

Log Wh, - a + Zbljh,,+ & Ge + 6,

price h: vector of housc characteristics

J. Y a m (1981) applies the hedonic price approach to the Australian housing market for the purpose of estimating the income elasticity of housing demand. R. A. Williams (1984) estimates price equations for houses in A d i a , accounting for inflation, income and financial assets

8 Based upon engineering staristics from the United Kingdom. the endowed probability of an explosion from this pipeline is less than 1 per cent However, the New Zealand experience of two ruptures between 1969 and 1984 suggests subjective probabilities may be significantly higher. See the Ministry of Works and Development Environmental Impact Report, February 1987.

location of the pipeline on the street, is of special interest in the study. This variable is included as a zero-one binary variable where a home adjacent to the pipeline will have a pipeline value of 1, and it is used to examine whether there is a statistically significant level of expenditure to self- protect from the hazard of the high-pressure pipeline.

The data used consist of the population of houses sold in 1983, 1984 and 1986 in the Mt Roskill ‘area in Auckland, through which a high-pressure gas pipcline was installed in 1983. In this area, the housing charcteristics are variable across homes in a single neighbourhood but there is little variation in area characteristics, such as zoning, crime rate, school quality, distance to the city and ocean, racial and age configuration etc. Therefore, these characteristics are not included in the empirical model.9

In 1986, the housing market was much more active during the second half of the year due to expectations of increased housing prices. Therefore a binary variable was included for 1986 to control for this effect on prices. In 1983 and 1984, however, general housing market conditions were stable during the year, and therefore control variables were not needed for these years The data for the study were collected from the statistics of the Department of Government Valuation, floor plans of the Auckland city council, and field surveys conducted by the authors.

As mentioned in the previous section, the transformation of objective to subjective probabilities may change over time because of changing information. To determine whether the hedonic price. Wn has changed, this study includes a set of years when the information available to home buyers may have been reduced as a result of changes in the level of media attention. The yean 1983, 1984 and 1986 provide conditions of changing publicity, being respectively, the year of pipeline construction, one year later, and three years later.10

9 Due to the nature of the pipeline impact we were not required to usc a p a i d sampling technique since the pipcline passes through a part of a neighboumood

10 The data for 1985 were not considered. Instead. 1986 was chosen so that more time had elapsed since the pipcline construction and subsequent public attention to its potential hazards. During this period expcrt information on the risks remained constant, while information available to home buyers changed Therefore. p can be reasonably assumed as constant, and i as changing in the study.

SEPTEMBER 232 THE ECONOMIC RECORD

Most publicity was given to the pipeline in 1983. In this year. media attention focused on the issue of locating the pipeline, and government infor- mation was circulated throughout the city. Articles about the possible hazards of the pipeline appeared regularly in the newspapers prior to and during its construction. In itself, construction drew attention to the pipeline's presence.

In the following years, in contrast. the infor- mation on the hazards of the pipeline received very little public attention. and media coverage stopped after its construction. Although small signs were posted regularly along the pipeline route, providing information to potential buyers in the area, they only provided information on the pipeline's presence, not its hazards This reduction in media and government attention may have resulted in a decrease in the information used by home buyen due to a potential increase in the cost of obtaining information in the later years. This. in addition to the fact that the pipeline was by then covered up from public view, is likely to have decreased the information available to home buyers in the years following 1983. Therefore, we expect our 1983 sample to reflect either a greater awareness,~' or an exaggerated awareness, of the pipeline hazards as compared to the 1984 and 1986 samples.

Definitions of the model variables are given in Table 1, and a summary of the statistics is provided in Appendix B. An examination of the statistical summary reveals that the mean sale price of the houses adjacent to the pipeline was 21 per cent lower than the mean price of the other houses in 1983. A further examination reveals that a statistically significant difference in the mean prices at which houses were sold cannot be observed in 1984 and 1986, one year and three years after the pipeline installation. These statistics further reveal that a similar proportion of the houses sold were on the pipeline in these years (23 per cent in 1983, and 24 per cent in 1984 and 19861, while some other sample characteristics were variable. Therefore, in the next section, our empirical model which controls for those housing characteristics formally tests the effect of the pipeline on the sale price of houses.

The Results The regression coefficients and the associated

t statistics for our model. employing the ordinary least squares method, are presented in Table 2.

I ' Depending upon the level of the endowed probability.

TABLE 1

&jhtwnof Vatiabks

Log Price Sold- Natural logarithm of the total sale price of residential properties in the dollars of the year studied. The sale price includes the price of the property and chattels.

Log Floor Area: Natural logarithm of the gross floor

Bedrooms: Bathroomr Age:

On-Pipeline:

Condition of Walls:

Construction Quality:

Section Size:

Time:

area of a home in square metres. Number of bedrooms in a home. Number of bathrooms in a home. Age of a how measured in terms of decades, i.e. when age - I the h o w was built in the 1970s and thus is approximately I decade olb A house built in the 1960s has a value of 2 for 2 decades The location of the house using a binary variable - I if it is adjacent to the pipeline and 0 othenvise. Represents the condition of the walls of a dwelling, bascd on the 1982 government valuation. Qualitative variable - 1 for good condition, 2 for very good, and 0 for poor or very poor condition. Represents the quality of construction ofthe walls and roof. based on the 1982 government valuation. Binary variable, where a dwelling with brick and tile materials is rated as good quality with a value of I, and all others have a value of zero. Area of the lot sold with the house in 100 square metres. Binary variable - 1 if the h o w sold in the second half of 1986. This variable controls for the especially booming housing market in the second half of 1986. due to expectations of higher p i c a .

Results for 1983, 1984 and 1986 are reported in columns 1.2 and 3 respectively.

An examination of these results and the reported Rz and F statistics (significant at the .OOO1 level) indicates that the model explains the variation in housing sale prices for our samples well. The coefficients exhibit the expected signs, and we find consistencies across the three years in both the significance and sign of several of the household characteristics (i.e. floor area, bedrooms, age, wall condition, quality of construction and section size). The variation in coefficients across years can be explained by either data set variation or changing

1991 RISK AND

TABLE 2

OLS Rcnh of the Housing f i e MOM Lkpndenr V& Natuml Log of the f i e Sold'

Independent Variables 1983 1984 1986

Intercept 8.94*** 8.69*** 8.3 I***

Log Floor Area .39*** .3 I *** .47***

Bedrooms .02 .15*** .08**

Bathrooms -0.002*+ .21*** .09+

Age -0.04** -.05**+ .04

(39.49) (30.41) (24.20)

(7.90) (5.44) (5.69)

(0.70) (4.26) (2.01)

(.02) (3.17) (.60)

(2.27) (3.07) (1.77)

(2.41) (.13) (.02)

(3:03) (3.71) (2.88)

construction (1.27) (1.51) (.09) Section size 0.0 1 *** 0.0 I I** 0.003

(2.48) (259) (.46) Time of the Year Sold +++ +++ ,17*** (in 1986) (2.48) Sample size: 85 87 83 F value: 25.96*** 27.94*** 12.85***

F(9.76) F(9,78) F(10.73) R: .73 .73 .5 9-

On-pipeline. -0.11*** .006 -.001

Condition of walls lo**** ,19*** .17***

Good quality of 0.04 .06 .005

market conditions. For example, in 1983 and 1986 there was very little variation in the number of bathrooms (only one observation in each case with more than one bathroom), which can explain the lack of significance of this variable in those yean'*

In this study the multiple year estimates of the pipeline coefficient are expected to capture the changing nature of the willingness to pay to avoid the risk of explosion in different time periods. Our

12 Tests for the assumptions of normality and homoscedasticity of the crror terms were conducted Kolmogorov-Smirnov D statistics of .063 for 1983, .067 for 1984 and .069 for 1986, and the graphical analyses conducted support the normality ossumptioD The Park test was conducted for h c t e m d a s t ~ 'city. which resulted in Fs between .01 and .001 and very insignificant F and r statistics, supporting the assumption of homoscedasticity of the error terms Plots of residuals were consistent with Park test results

INFORMATION 233

earlier analysis suggests that a higher willingness to pay is expected in 1983 due to the pipeline construction and a higher level of publicity in that year. It can be noted in Table 2 that the pipeline coefficient is -.I 1 in 1983, but close to zero in the two later years13 This change is consistent with the hypothesis that consumers were willing to pay more for a home off the pipeline route to avoid exposure to the risk of explosion in 1983 compared to the later years Since the objective risk of the pipeline was likely to have remained constant, a change in the willingness to pay across years is more likely to be attributable to a change in the subjective risk.

It should be noted that although the change in the pipeline coefficient in the three years is con- sistent with our theoretical analysis, the statistical significance of the change cannot be firmly established based on formal stability tests. An F test based on restricted and unrestricted models with the use of binary variables and pooled data over the three years was conducted (see Dufour, 1980 or Kennedy, 1985). The Chow test, and a Wald test (see Watt, 1979) were also performed.

The Chow test indicated that the coefficients had changed across the three years and that, therefore, an unrestricted specification was appro- priate for the thrte years.14 The F test further indicated that some of the non-pipeline coefficients had changed in the three years, possibly due to the differences in the characteristics of homes sold in different years and the different market

13 The 1983 model was also tested using two separate pipeline variables, one controlling for the sale of a house on the pipline during conuruction (during the first quarter of that year). and a variable controlling for its sale after construction The regrcsrion coefficient for the pipeline variable during cOllStnrtion war -.I4 with a rstatistic of215,and thecoefficient for afterconstruction was -.09 with a r statistic of 1.73. However, since the resulting incremental F values w m highly insignificant, we did not pursue using a separate pipeline variable for the construction period.

14 The Chow test examined whether the explanatory power of the model estimated for thrcc separate years was superior lo the mults of a similar model with pooled data. The test results with an 99228) - 7.26 (significant at the 1 per cent level), indicated that the separate re@m had superior explanatory power, and therefore the coefficients based on separate regressions are emphviztd in tt# paper. The results of the Chow test were consistent in two versions of the model, one with time of sale variable included for all y e m for similarity of models, and one excluding i t

234 T H E ECONOMIC RECORD SEPTEMBER

conditions.15 Once we allowed a non-restricted specification for all other coefficients. the change of the pipeline coefficient was not statistically significant at the 10 per cent level.16 The Wald test of the quality of the pipeline coefficients also failed to reject at the 10 per cent level.'' Therefore, the results should not be regarded as firm evidence on the effect of information change on the willingness to pay to avoid hazardous events. Our results, nevertheless, arc consistent with

those of Brookshire ef aL (1985) who found changing willingness-to-pay values when they evaluated consumers' willingness-to-pay levels before and after information legislation had been implemented. Their results, and those above, suggest that information legislation, and public attention to a hazard, can change consumers' subjective probability and thus their willingness- to-pay to avoid risky situations.

IV Conchion In this paper we have relaxed the assumptions

of full information in estimating the willingness to pay to avoid hazardous events. We have incorporated the effect of a change in information on the subjective probability of hazardous events and consequently on hedonic prices. Our analysis indicates that since consumer transformations of objective to subjective probabilities are imperfect,

I J The pooled sample in the stability tests (we Kennedy. 1985) consisted of 255 obsmations The unrestricted model included 28 coefficients allowing all coefficients to be different in the three years The d c t c d model included 14 coefficients constraining the non-pipeline coefficients to be q u a l in the three years. Both models included an intercept, two binary variables for 1983 and 1986 to adjust for general changes in the housing prices, and a binary variable for the second half of 1986. The F(14 227) - 2.79 obtained was significant at the I percent level.

16 The unrrstricted model in this test included 28 coefficients as before. The restricted model included 27 cocfticients and constrained the 1983 pipeline coefficient to be equal to the other ycan. This test resulted in F (1227) - 2.28 which is not significant at the 10 per cent level.

The Wald test allows the variancesof the error terms to be different in the thm periods. while the Chow test and the F test assume equal variances. The results of thc three tcsts were. however, compatible. For example, the Wald test X * statistics for thc hypothesiis that thc thrcc pipeline coefficients were equal was 4.19 with 2 degrus of freedom. which is not significant at the 10 per cent level.

hedonic prices may under- or over-estimate the objective willingness to pay under conditions of uncertainty, especially if the information set is incomctly assumed to be full. when in fact it is incomplete or changing. Our analysis further suggests that hedonic prices

are likely to change over time with changes in information and subjective perceptions of hazardous risk. This indicates that the use cf a static model when estimating hedonic prices may lead to misleading price information. The multiple year approach to hedonic price estimation, suggested here, can provide a range of estimates, and in some cases upper and lower bounds for the level of self-protection chosen with full information. When only one period is examined, as in the literature, and if information changes, the estimates of a particular year may reflect sensationalism due to publicity, or insufficient information in that year as opposed to the true willingness to pay.

Our empirical results for different time periods which are reflective of possible changes in information show changes in the willingness to pay consistent with the predictions of the theoretical model. However, this empirical result is tentative in nature since although we find that consumers were willing to pay prices 11 per cent higher to avoid the pipeline in 1983 compared to estimates close to zero in the later years, the c h g e in the pipeline coefficients across the three years was only significant at levels between the 10-20 per cent levels in three different stability tests. Stronger empirical evidence can be regarded in future research if it can be shown that the actual information level has changed as a result of publicity or legislation, and that change in the coefficients due to information change is statistically significant. It would be Fruitful to examine in future research the sensitivity of our model results to different types of hazardous events such as earthquakes and floods.

APPENDIX A rn Modd

If we have a subjective probability of a hazard occurring. p . as a function of the endowed probability, p'. and the effort to self-protect, J ; and we have two states of the world, state 0 when tbc hazard occurs and state 1 when the hazard does not occur, we can write an Expected Value function 1s

1991 RlSK AND INFORMATION 235

The consumer is choosing a vector of housing attributes, h. a level of self-protecti0n.s. and a level of the composite good, x. The price of a home, W, is a function of the housing anributes and the level of self-protection, and the price of x. P, is I. The consumer has income Yo in state o and rI in state 1. ~oss*i are then rl-ro. if the hazard occurs. Maximizing the expected value with mpcct of h, and s gives first-order conditions 2A and 3A. respectively

Extending the model to include information, i, as an independent variable affecting the subjective probability, p, we get an Expected Value function as in 4A below.

L - E(v) - (p. SAVdh,Yo - W(h.d) +

( 1 -p(p.sJ) VI (h, YI - W(h.s)). (4A) The first-order conditions do not change from 2A and 3A above.

To determine the impact of changing information on the decision to wlf-protect we take the derivative of our hedonic price (see equation 6 in the main text) with respect to informationbm and get

If we assume information docs not affect our individual’s perception of how self-protection, s. affects hidher subjective probability, p (is. 2- 0). we can rewrite equation 5A as ddi

-- dw, (6A)

dx . d W Substituting ds for the first term on the right-hand side

we get:

I m We have assumed the level of information, i. does not affect the utility gained from the composite good, x nor is information a direct element in V. thus

d2Vo F V I avo d V 0, - -- 0,and- A- dxdi ’ dxdi di ’ di

di

APPENDIX B srarirricnlswnmary

Variables

Price Sold (Houses on the pipeline) Price Sold (Houses off the pipcline) Floor area (in 4u. metres) Bedrooms Bathrooms Age (in decades) Proportion of houses on the pipeline Condition of walls Good quality of conrtnrction Section size (in 100 sq. metres) Sample size

I983 M e a s Standard

Dcvianbn

59 476.2

72 123.5

125.7 2.6

1.03 2.3

0.23

2.2 0.3

6.8 1

85

I2 865.4

I8 929.5

46.4 0.6

0.1 1 1.2 0.4

0.5 0.4

4.3 I

I984 Means Standard

h i a t i o n

85 369.6

83 841.1

140.1 2.7 1.1 2.2

0.24

2.4 0.2

7.10

87

30 282.0

29 029.9

65.6 0.6 0.3 1.5 0.4

0.5 0.4

3.99

I986 Means Srandurd

Dcvianbn

90718.7

91 267.3

113.2 2.7

1.02 2.4

0.24

2.2 0.2

7.09

83

36 087.8

26 205.7

39.4 0.7 0.1 I .3 0.4

0.5 0.4

4.77

236 THE ECONOMIC RECORD SEPTEMBER

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