A Quantifiable Lower Bound

Since the informational requirements for measuring TSB are prohibitive, economists have looked to define a simpler measure that might lend itself to estimation in the real world. It turns out that one such measure is the sum of QCS measures presented in Equation 3. All that is required to calculate this measure is knowledge o f the bid function o f households in the affected area, details o f their current residential choices and information on the level o f environmental change experienced by each household.

Encouragingly, Bartik (1988) has given a theoretical justification for choosing to measure the welfare changes resulting from a change in environmental quality as the sum o f households’ QCS. He shows that the sum o f QCS across all affected households provides a lower bound estimate o f the TSB.

Bartik’s intuitive proof involves partitioning the welfare changes affecting households and landlords into a series o f three stages. Whilst these stages help in the analysis o f welfare changes they are not meant to represent a realistic sequence o f events. The three stage decomposition is presented in Table 3.

In the first stage, some or all of the residential locations in the urban area experience an improvement in environmental quality. It is assumed that neither landlords, nor households nor the hedonic market adjust in response to this change.

• Since households do not move property, the benefit to households will be simply their WTP for the environmental improvement at their original location.

This is the QCS measure presented in Figure 2 and Equation (2).

• Since landlords do not change rents or adjust the attributes o f their properties, they will only be affected by the change in environmental quality if it affects their costs. Since we assume they make no changes to their properties at this stage, the measure o f cost savings is that given by the vertical distance between

W and X in Figure 7.

In the second stage, the HPF shifts precipitating a change in the rental price for each property. However, at this stage households and landlords are constrained to their original location and supply choices. As such the change in rents simply acts so as to transfer money from one to the other. Indeed, whatever the pattern o f rent changes in the second stage, there is no overall welfare effect.

Notice, however, that whilst there is no change in the aggregate welfare change in stage two, welfare changes for each individual household and landlord may be positive or negative depending on the particular pattern of rent changes.

In the third stage, households and landlords respond to the new HPF. Households will move to the property that offers them the highest possible utility. This must be at least as beneficial as remaining in the original property since they could always opt not to move house. Similarly, landlords may adjust the attributes o f their properties.

Clearly, any such adjustments must increase profits since the landlord could just as well choose to leave the property as it is. Hence, in stage 3, both households and landlords must enjoy an increase in welfare.

This is not to say that every household and landlord experiences an increase in welfare over all three stages. Whilst households and landlords only benefit in stages

1 and 3, they may just as well lose as gain in the rental changes isolated in stage 2.

As shown in Table 3, summing all three stages for households results in the total welfare gains given by the sum o f household C S ’s given in Equation (5). Similarly, summing all three stages results in the sum o f landlords CP's given in Equation (13).

Thus the three stage decomposition, whilst not reflecting the simultaneous nature o f responses to the change in environmental quality, accurately represents the overall change in welfare.

The insight o f Bartik’s decomposition is to isolate all individual welfare losses as price changes in stage 2. Since price changes simply represent pecuniary transfers between agents in the property market, these losses must be offset by equivalent gains elsewhere. In other words, when we are interested in the aggregate welfare change, we can ignore the losses incurred by certain landlords and households by netting these out as a price change.

As a result TSB, that is the total welfare change experienced by all households and landlords in the urban area, can be regarded as the sum o f the four non-negative values defined in stages one and three. In words, these are;

1. WTP of households at improved locations to enjoy the change in environmental quality whilst staying in their original property ( ^ QCSh )

h e H t

2. Cost savings for landlords at stage 1

3. Household utility gains from relocation at stage 3 4. Landlord profit gains from changes in supply at stage 3

Since all four values are non-negative, QCSh must also be a lower bound to TSB.

h e H l

Table 3: A decomposition of the welfare effects of a change in environmental quality from Bartik (1988)

-Net landlord gain, sum over all landlords, Equation (13) in text

Sum of 1st and 2nd columns is same as Equation (15)

84

This is an extremely important insight since it gives us a good theoretical reason for

improvement. There are a number o f reasons why this might be desirable.

• Since the QCS measure does not require information on how the market price or agents in the market adjust to a change in market conditions, it can be calculated in advance o f a public programme to improve environmental quality.

• QCS is a measure o f household welfare change. Consequently using the sum of QCSs as a lower bound estimate o f TSB removes the need to examine the supply side o f the market. Researchers can ignore the considerable difficulties associated with estimating landlord cost and offer functions.

• QCS is only defined for households in an affected area. As a result, the researcher only requires information on which households will be affected by the environmental improvement and the extent of improvement enjoyed by each.

• QCS is based solely on underlying preferences for environmental quality as captured in the bid function. The measure is not particular to a specific property market. Indeed, if a researcher could derive the bid function from one market then this could be used to evaluate the QCS in another property market, provided the researcher was prepared to assume that preferences for environmental quality were stable across the two markets.

Clearly, using the sum o f households’ QCS as a lower bound approximation to the TSB makes it practical to carry out ex-ante assessments o f the welfare gains from environmental improvements. The accuracy o f this approximation will depend on the size o f the values taken by the other three elements of TSB isolated in Bartik’s analysis. Certainly, the approximation will tend to be more accurate when the environmental change is less extensive as the benefits o f household relocation and landlord change in supply will tend to be smaller.

to measure the welfare change resulting from an environmental

8. Conclusions

This chapter has demonstrated how the benefits o f an environmental improvement can be measured in the property market. In the simplest case, the environmental improvement is a localised phenomena that causes no change in the HPF. If households can move freely and landlords do not enjoy cost savings and are constrained not to alter the supply o f property attributes, then the welfare benefits o f the improvement accrues to landlords as the change in the rental price o f their properties (Equation 13).

This measure is easy to calculate for any property market for which the HPF is known. Unfortunately, the fact that the measure is based on the unique HPF o f a particular market means that there is no theoretical substance to transferring such values across property markets.

Clearly, estimating the welfare change o f an environmental improvement by the increase in prices of affected properties is to impose severe restrictions on the reactions o f the economic agents in the market to the improvement. Indeed, a completely comprehensive measure o f the welfare benefits o f an environmental improvement is given by the TSB measure (Equation 15).

However, the TSB measure is little more than a theoretical construct. To estimate such a measure researchers would require detailed knowledge o f how the equilibrium HPF would be affected by changes in environmental quality and how households’ and landlords’ choices would respond to both changes in environmental quality and changes in the hedonic price schedule.

Unfortunately, hedonic market equilibria are too complex to derive satisfactory analytical solutions by which to predict such outcomes. Indeed, the TSB measure is almost impossible to calculate ex-ante, making it o f little use to practitioners attempting to measure the potential benefits of a program seeking to change environmental quality in an urban area.

Nevertheless, in an important analysis, Bartik (1988) showed how a third measure the QCS, when summed over all households directly affected by the change in environmental quality, could always be taken as a lower bound to the TSB. There are a number o f reasons why using the QCS measure might be desirable. In particular,

the QCS measure is based solely on the household bid function. As a result, it is not necessary to consider the supply side o f the market nor predict market conditions following environmental change. Further, the QCS measure is not particular to a specific property market. Indeed, if a researcher could derive the bid function from one market then, provided the researcher was prepared to assume that preferences for environmental quality were stable across the two markets, this could be used to evaluate the QCS in another property market.

In Part 3 o f this thesis, therefore, we investigate the possibilities for deriving estimates o f the bid function from which the QCS measure o f welfare change can be derive.

P ^{a r t} 2

E m p ir ic a l E s t im a t io n o f t h e

H ^{e d o n ic} P ^{r ic e} F u n c t io n

C

3: T

H

P

F

T

P

1. Introduction

The five chapters that make up Part 2 o f this thesis concern themselves with the estimation o f the hedonic price function (HPF);

P = P(z)

the function that relates a property’s characteristics, represented by the vector o f attribute levels z, to the price at which that property sells in the market, P.

Chapter 4 provides a description o f the data set for which the HPF is to be estimated.

The data relate to residential house sales in the City o f Birmingham in the UK. As described in that chapter, the data set is remarkably comprehensive compiling information from numerous sources with the aid of geographical information systems (GIS). Chapters 5, 6 and 7 concern themselves with the actual estimation o f the HPF for the City of Birmingham data set. The particular focus o f the analysis is the identification of the implicit price o f transport related noise; that is the amount by which property prices decline for each extra decibel of noise to which they are exposed.

One key research theme introduced in Chapter 4 and further developed in Chapter 6 is the application o f data-driven techniques for partitioning property market data into relatively homogeneous subsets. For example, each subset might identify groups o f properties exhibiting similar structural characteristics. Alternatively each subset might identify properties inhabited by residents with similar socioeconomic attributes. Whilst numerous previous studies have sort to partition property market data, the innovation presented in this thesis is the application o f techniques o f model- based cluster analysis. The great advantage o f these techniques is that they provide an independent statistical indication o f the nature and number o f homogenous subsets to be found in the data. These techniques represent the cutting edge in cluster analysis and have not previously been employed in hedonic analysis nor, as far as

can be ascertained by the author, in any other field o f empirical economics. Whilst Chapter 4 presents a standard application o f model-based clustering, Chapter 6 adds another level o f sophistication, allowing for outliers in the data; that is properties that cannot easily be allocated to a particular partition.

Following the substantial literature in this field, Chapter 4 motivates the partitioning o f the data through the assumed presence o f market segments. In particular, it is argued that a significant difference in the HPFs o f different partitions provides evidence that these partitions identify different market segments. Chapter 6 readdresses this motivation and represents a development in thinking over that presented in Chapter 4. In this later Chapter it is argued that the conditions that lead to market segmentation are unlikely to hold in the property market for one urban area. Rather it is argued that significant differences in the HPF between partitions o f the data are evidence of substantial non-linearity in the HPF for Birmingham.

Indeed, this observation provides an alternative and original justification for partitioning property market data. In this case, the data are partitioned to facilitate an estimation strategy that seeks to locally approximate a possibly highly non-linear equilibrium HPF.

A second major concern in Part 2 of this thesis is the econometric estimation o f the HPF. Two major themes are developed through these chapters. The first theme concerns the econometric specification o f the HPF. The second concerns spatial autocorrelation in the regression residuals.

In Chapter 5 sophisticated econometric techniques are used to analyse the Birmingham data. In particular, a well-known semiparametric estimator (Robinson, 1988) is used to introduce flexibility into the specification o f the HPF. Improvements on previous applications o f this model are made by allowing both selected property characteristics and the influence o f location to enter the econometric model nonparametrically. Analysis o f the regression residuals from the hedonic price regressions reveals evidence o f spatial correlation. As such, a general method o f moments estimator proposed by Kelejian and Prucha (1999) is used in a second stage regression. This estimator specifically accounts for spatial autocorrelation in regression residuals returning robust estimates o f the model’s parameters and their variance. As far as the author is aware, this is the first application to combine

semiparametric methods with the Kelejian and Prucha GMM estimator to provide robust estimates o f the parameters o f a HPF.

Chapter 7 concerns itself with issues o f spatial autocorrelation o f regression residuals. In particular, it is argued that spatial autocorrelation o f residuals is evidence o f omitted variables describing spatial features influencing property prices that are not observed by the researcher. As such an estimation approach championed by Gibbons and Machin (2001) is adopted. This approach accounts nonparametrically for omitted spatial variates by spatially smoothing the data. A major innovation of this Chapter is the introduction of a procedure (similar to that proposed by Ellner and Seifu, 2002, in a more general context) that uses the data to prescribe the optimal areal extent o f smoothing.

This Chapter, Chapter 3, brings together many of the theoretical and econometric issues relevant to the estimation o f Equation (1) and held in common by all the Chapters in Part 2 of this thesis. Further, since the key motivation o f Chapter 5 is to identify the impact of noise pollution on property prices, it provides a brief review o f other hedonic analyses that have dealt with this issue. These results provide a point of comparison against which the results o f the research reported here can be evaluated.