Free Motion in Limine - District Court of Federal Claims - federal

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EXHIBIT C

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IN THE UNITED STATES COURT OF FEDERAL CLAIMS

CAROL AND ROBERT TESTWUIDE, et al., )

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Plaintiffs, v. THE UNITED STATES OF AMERICA, Defendant. )

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) No.: O1-201L

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Judge Victor J. Wolski

PLAINTIFFS' REBUTTAL TO THE EXPERT REPORT OF DR. DAVID DALE-JOHNSON (Analyses of the Impact of the Realignment on House Values)

JON P. NELSON, PKD.

December 12, 2005

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2 4. In order to evaluate these claims, I will first develop the methodology used to conduct a repeat sales analysis, including an examination of the sampling and measurement procedures used by Dr. DaleJohnson. The methodology of a repeat sales analysis is subject to a number of well-known problems, all of which are largely ignored in his report. Second, building on my criticisms of his work, I present alternative regression estimates for the repeat sales model that demonstrate that the "Change in Noise" coefficient is negative and statistically significant. Furthermore, these negative effects agree with the noise damage estimates presented in my Expert Report (Nelson report, p. 29). Thus, using the same basic methodology and data available to Dr. Dale-Johnson, l demonstrate that plaintiffs" damage formula is statistically sound and correct. Third, I examine selected aspects of Dr. Dale-Johnson's event study analysis. Fourth, I evaluate his hypothesis for his null findings, i.e., the transfer of U.S. Navy personnel to the Virginia Beach area and the possible effects (if any) of this transfer on housing demand and values.

II. Repeat Sales Methodology The repeat sales model is commonly used to construct real estate price indices. It is subject to several methodological and econometric problems that require caution in its application. Two widely discussed problems are aggregation bias and sample selection bias. A. The Repeat Sales Model 5. As an econometric technique, the repeat sales method was first developed in 1963, and it has been widely used in recent years to develop housing price indices. Consequently, the econometric problems or difficulties associated with this technique are well known. The repeat-sales model as applied to environmental effects or damages was pioneered in I982 by Dr. Raymond Palmquist? Assume a significant environmental "event" that occurs at a specific date in time and which has different measurable physical effects on residential properties. In the case ofNAS Oceana, the transfer of 10 squadrons of F/A-l 8 aircraft occurred during December 1998 to September 1999, With 2 squadrons arriving in December 1998, 6 squadrons in July 1999, and 2 squadrons in late September 1999. Thus, in Dr. Dale-Johnson's analysis, the "event date" or "base quarter" is the second quarter of 1999 (April-June 1999), which is the quarter just before the increase in noise levels. The physical effects of this event refer to different changes in noise exposure, e.g., +0, 5, 10, or 15 dB changes measured relative to the

J R.B. Palmquist, "Measuring environmental effects on property values without hedonic regressions," Journal of Urban Economics, t I (1982): 333-47. I am aware of only one other study that uses the repeat sales method for aircraft noise; see N2q. Knickerbocker, "Aircraft Noise and Property Values," Unpub. Ph.D. dissertation, University of Maryland, 1991. This study of National Airport finds negative effects that agree generally with other studies for National Airport and other airports, i.e, the noise discount is -I.29% per dB (p. 149).

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pre-event exposure level. The important reasons for using a sample of repeat sales of residential properties are: (I) it might eliminafe the necessity to collect numerous housing features required for the hedonic price model; (2) it focuses the analysis on the change in environmental quality and damages; and (3) it can be used to construct housing price indices for additional analysis of the event. 6. The repeat sales model is based on the notion that there exists a set of residential properties that were Sold before and after the event, and which did not change except for the differences in noise exposure. Consider two residential properties, both of which were sold for $100,000 in 1998 and which sold again in 2000. Assume that neither property underwent any structural, environmental, or neighborhood quality changes during 1998-2000, except that Property A experienced a I0 dB increase in noise exposure in July 1999 and Property B did not. If Property B was sold for $120,000 in 2000, the appreciation was $20,000 or 20%. According to plaintiffs' damage formula, Property A should appreciate less in value. Suppose that Property A sold for $110,000 in 2000 or a 10% appreciation. Hence, the damage due to the increase in noise was $10,000 or -1% per dB change in noise exposure. 7. A more technical description of the repeat sales model helps reveal some of the assumptions that underlie the model and analysis. The starting point is the standard semi-log hedonic price function

(1)

In(Pit) = ~t + I3"Zi + YNit + 6Air + uit

where ln(P~) is the log of the sales price of house i at time t; Zi is a vector of housing characteristics that do not vary with time; Nn is the noise exposure level at time t; A~tis the age of the house; and ua is the error term (aka the "residual"). The error term captures the effects of omitted variables, measurement errors, and purely random or stochastic aspects of the data. The depreciation rate due to age is given by 6. The noise damage index or hedonic price of noise in percentage terms is given by "/x 100. The expected sign ofy is negative. 8. For the repeat sales model to be appropriate, there must be a sale of each property before and after the event date. Suppose the earlier sale of the property occurred at time t and the second (or subsequent) sale occurred at time s. The first sale occurs before the event and the second sale occurs after the event. For these houses, the price-relative is given by (P~/P,). Using the log transformation, the rate of appreciation function for the repeat sales model is given by

(2)

In Pa - ln~P~ = ~s- ~ + 13"(Zi - Z~) + y(N~- N-0 + 6(Aa- AO + (u~- uO

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Using an assumption due to Dr. Palmquist, houses are assumed to depreciate geometrically with age. The age variable is eliminated by a uniform adjustment of the price-relative using an independent estimate of the depreciation rate. The values of the constant terms, ccs and cq, form a house price index. These values are the estimated coefficients for dummy variables indicating the quarter(s) of sale.2

B. Aggregation Bias and Sample Selection Bias 9. In the standard hedonic model, [3 is a vector of parameters to be estimated. In the repeat sales model, this is not necessary because the Z variables are constant over time. Hence, the repeat sales model requires a sample of properties for which the structural, environmental, and neighborhood features of the houses are unchanged between time t and time s. This condition is referred to as the constant quality assumption and violation of this assumption is called aggregation bias. 10. While the repeat sales model can eliminate the necessity to collect data on housing characteristics required for the hedonic price model, it does this under stringent conditions. It is clear from equation (2) that the sample of repeat sales must not undergo any changes whatsoeyer- no housing improvements or disrepair other than the uniform effects of age - except for the change in noise level. There also must be no changes in environmental or neighborhood quality variables that vary across properties in the sample, i.e., any important changes in neighborhood quality must be area-wide changes that affect all properties equally. Further, there must be no change in the underlying mathematical reIationship for the hedonic price function, i.e., the [3 parameters must not change over time. 11. The constancy assumption is very difficult to meet in practice, and also leads to features of the repeat sales sample that impose subtle constraints on the data. It is very likely that the sample of repeat sales is not a random draw from all properties or a random draw of those properties that were sold on the market, including properties sold once during a given time period. Hence, past studies using repeat sales have found that properties that sell twice are likely to be different from the rest of the housing stock.3 This is referred to as sample selection bias. In fact, there are two possible selection biases in re]Seat sale studies. First, the repeat sale sample is not a random draw from the existing stock of properties (i.e., not all properties were sold in the time period). Second, all sales are not repeat sales, and

2 Because the repeat sales model is derived from the hedonic price model, it does not avoid various econometric problems that have been the subject of recent discussion for the latter model, including spatial autocorrelation and spatial autoregression. 3 Housing is a unique commodity because it trades infrequently. This is in contrast to other ~ommodities, such as stocks and bonds, that might trade each business day. As a result, transactions are sparse relative to the outstanding stock of houses. As a consequence, external information from other markets, such as that from a metaanalysis, are informative about the effects of environmental disruptions, including the realignment at NAS Oceana.

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a repeat sale sample is biased toward those properties that were re-sold during a specific time period. Hence, properties that sold more than once may not be representative of all residential properties in the market area. Increasing the length of the sample period might reduce selection bias but this aggravates the problem of heteroskedasticity - the price change variability is greater the longer the period between transactions. Further, increasing the length of the sample period increases the likelihood of aggregation bias due to changes in the underlying hedonic price function or unobserved changes in housing quality. 12. The effects of aggregation bias and sample selection bias have been widely discussed in the real estate literature, including a special issue of the Journal of Real Estate Finance and Economics (January 1997). Because Dr. Dale-Johnson was an Editor for this journal and has published several papers in the journal, he was obviously in a good position to take account of the special issue papers. However, these well-recognized econometric problems are not discussed explicitly in his report.

C. Sampling Methods Used by Dale-Johnson 13. P~epeat-sale aggregation bias results from omission of characteristics that contribute to value (including unobserved characteristics) and parameter instability over time. The effect of this bias on the "Change in Noise" coefficient is difficult to establish without greater knowledge of the omitted characteristics and parameter instability. Only the application of other methodologies or more complete data would resolve this issue. Previous studies of this problem have established that the bias can be substantial for the derived price indices.4 Hence, there is reason to suppose that the event study conducted by Dr. Dale-Johnson is biased statistically. 14. Dr. Dale-Johnson does attempt to ensure that the houses in his sample have not been "improved" between the time of first sale and the second sale. Specifically, he starts with samples of 154,628 "housing units," 141,642 residential properties, and 70,520 properties that were sold at least once between 1/1/1995 and 12/31/2003 (Dale-Johnson report, Exhibit 1). From the latter sample, he omits 4,533 properties that were missing basic information on the living area and 57,085 properties that sold only once or were non-arms-length sales. This leaves him with a raw sample of repeat-sale properties with a sample size of 8,902 (or about 6.3% of the residential housing stock). This raw sample is further reduced by 2,420 properties with recorded improvements and 453 properties with other nonarms-length sales (sales to relatives, banks, etc.). This leaves a final repeat-sale sample of 6,029 properties. The final sample is only 4.3% of the residential stock and 8.5% of all property sales between

4 See J. Dombrow, et al.,"Aggregation bias in repeat-sales indices," Journal of Real Estate Finance and Economics, 14 (1997): 75-88; and J.E. Zabel, "Controlling for quality in house price indices," Journal of RealEstate Finance and Economics, 19 ( 1999): 223-41; i i~i~i /!

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1995 and 2003. While this screening procedure is necessary to ensure a sample of constant-quality repeat sales, it produces a non-random or selected sample of the Virginia Beach housing stock and housing sales. Further, the screening procedures do not ensure parameter stability or ensure that neighborhood and environmental features are constant, other than the measured change of noise levels. 15. The effect of sample selection bias has been investigated in a number of repeat sale studies. These studies indicate that repeat-sales data are biased toward older and smaller properties. Furthermore, repeat-sale properties tend to appreciate more than properties that sold only once during a specific time period. This difference has been attributed to unobserved or unrecorded improvements to the repeat sale properties between the dates of sale:

(1) Clapp, Nanda, and Ross (1991) found that houses selling repeatedly were older and smaller ("starter homes") than houses that sold only once during a ten to twenty year period: (2) Meese and Wallace (1997) found that repeat sale houses were smaller and in.worse condition ("fLxer-uppers') than the average for single-sale properties.6 (3) Goetzmann and Spiegel (1997) found that repeat sale homes in San Francisco tended to be sold more often by higher-income families living in racially-mixed neighborhoods.7 (4) Case, Pollakowski, and Wachter (1997) found that repeat sale homes were smaller, but also tended to appreciate at a higher rate: They believe that this is due to property improvements that are not adequately reflected in the available data. Further, homes that have depreciated in value are less likely to be sold. Both conditions lead to sample selection bias. (5) Gatzlaff and Haurin (1997) found that repeat-sate price indexes tended to be biased upward during periods of economic growth and biased downward during periods of economic weakness.9 This bias is with respect to never-sold homes or less-frequently sold homes. S J.IVL Clapp, C. Giaceotto, and D. Tirtirglu, "Housing price indices based on all transactions compared to repeat subsamples," AREUEA Journal, 19 (1991): 270-85. 6 ILA. Meese and N.E. Wallace, "q'he construction of residential housing price indices: A comparison of repeat-sales, hedonic regression, and hybrid approaches," Journal of Real Estate Finance and Economics, 14 (1997): 51-73. 7 W2q. Goetzmann and M. Spiegel, "A spatial model of housing returns and neighborhood substitutability," Journal of Real Estate Finance and Economics, 14 (1997): 11-31. 8 B. Case, H.O. Pollakowski, and S.M. Wachter, "Frequency of transaction and house price modelling" Journal of Real Estate Findnce and Economics,14 (1997): 173-87. 9 DkI. Gatzlaffand D.R. Haurin, "Sample selection bias and repeat-sales index estimates," Journal of Real Estate Finance and Economics, 14 (1997): 33-50. :
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(6) McMillen and Thorsnes (2005) found that the average price of houses in Chicago rose an average of 7.5% per year during 1993-2002, but repeat sale houses increased by 8.5% annually.~° They attribute this difference to unobserved remodeling and renovation. 16. Summarizing the discussion of the model, a repeat sales study requires a sample of properties that were sold at least twice during a given time period and which, aside from normal "wearand-tear," have not changed in quality. Any unobserved improvements (or major disrepairs) will bias the results, such as improvements done by the first owner or those that go unrecorded at an assessor's office, such as landscaping. The constant quality assumption also applies to other environmental features of the residential area. For example, if traffic noise or air pollution changed in a non-uniform manner across the study area, this will bias the results. There also must be no non-uniform neighborhood quality changes. For example, if one neighborhood had an increase in crime rates, this also can bias the results. Finally, the hedonic price function must not change over time, so that the underlying marginal prices are constant over time. The screening procedures used by Dr. Dale-Johnson are insufficient to ensure that these conditions are met. 17. Using repeat sales and screening the data to delete "improved" properties results in sample selection bias. A sample selected according to various screening procedures is not equivalent to random sampling and a regression analysis based on a non-random sample does not as a general rule produce a true description of the population regardless of the sample size. Previous studies demonstrate that repeat sale samples are biased toward smaller and older properties, and these properties tend to appreciate more than properties that sold only once during a given time period. Due to these problems, the two regression studies conducted by Dr. Dale-Johnson should not be taken as an accurate description of the impact of the realignment on all residential properties in the vicinity ofNAS Oceana.

IlL Noise Measurements and Alternative Repeat Sale Estimates The post-realignment noise measurements used by Dr. Dale-Johnson - BASE 2000 DNL levels - have not been universally adopted for analyses of the realignment. Due to errors of measurement, this feature of his study alone could bias his regression results toward a null outcome. Regressions using ARS2 noise exposure data yield significantly negative noise coefficients that agree with my meta-analysis and plaintiffs' damage formula. A. Noise Data Used by Dale-Johnson 18. The repeat sales analysis requires damon sales prices before and after 1999Q2; dates of the

t0 D.P. McMillen and P. Thorsnes, "Housing renovations and the quantile repeat sales price index," Unpub. paper, University of Illinois at Chicago, August 2005.

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No other study of aircraft noise and property values has applied the event study methodology used by Dr. Dale-Johnson. A lack of prior studies suggests that his econometric results are premature as a basis for litigation. A regression on the individual indices, rather than their ratio, suggests that there may be unaccounted events occurring in the "control sample" that are not revealed by his event study method. 28. I am not aware of any other study that has applied the event study method to aircraft noise, at least in the form used by Dr. Dale-Johnson.~ A lack of prior studies suggests that his results are premature as a basis for litigation. There are two major problems with this methodology as applied to aircraft noise exposure. First, it is unclear how market processes incorporate the new information abotrt noise exposure and reflect it in "constant quality" price indices for Virginia Beach. Dr. Dale-Johnson used a "shift" or event dummy model that changes only the Constant term in his regressions. 29. Second, the "control area" sample is subject to all of the criticisms Ievied against the samples used in repeat sale models. The larger and more diverse the control area sample, the more likely it is that the constant quality assumption is violated. The "control sample" is defined as the subset of properties with a BASE 2000 DNL <45 dB. The sample size is 1,685 repeat sales. He argues that this subset of sales should not be affected adversely by the change in noise exposure (Dale-Johnson report, p. 17). The 45 dB cut-off is based on an EPA report that identifies noise levels less than 45 dB as within the normal indoor activity interference and annoyance levels. However, the BASE 2000 DNL for the "control area" is measured for aircraft noise only, and ignores other sources of noise (traffic, commercial and industrial activity, etc.). While the area in question might be removed from the Naval air bases, the noise levels and changes are measured inaccurately if they ignore other noise sources. This is the errors in measurement problem. In general, too little is known about the houses in the "control sample" to justify its use as a basis for normal returns in the Virginia Beach housing market. 30. Dr. Dale-Johnson's Exhibit 8 shows a graph of the housing price indices. This graph shows variation of the individual indices that is largely eliminated when ratios of the indices are constructed (Exh~it 9). However, the sample size is small (36 quarters), so it may be that the time span is simply too short for thi~ type of study or the frequency of the data should be different (e.g., constructing the indices

tl I am aware of two recent studies that incorporate airport announcement effects within the hedonic price model. A study by Jud and Winkler examined the announcement of a new Greensboro/Winston Salem AirportHub on housing prices near the airport_ They found housing prices declined in the post-announcement period by 5.7% to 9.2%; see G.D. Jud and D,T. Winkler, "The announcement effect of an airport expansion on housing prices," Unpub, paper, University of North Carolina at Greensboro, April 2005. A second study by Konda examined the announcement effect from coustruction of a new airport for Austin, TX on housing prices in the vicinity of the old airport, which is a complex setting with multiple announcements. Using hedonic methods and repeat sales, she found a positive effect of the dosing, especially for properties located in the noisier areas (70 dB and above); see L.S. Konda, "A comparison of methodologies to measure the effects of airport siting decisions," Unpub. paper, University of Texas at Austin, October 2002. Neither of these studies uses the method employed by Dale-Johnson. iiii~~