appendices for: unobserved quality and anchoring to home

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Appendices for:

Unobserved Quality and Anchoring to Home Purchase Price and Fundamentals

over a Housing Market Cycle

November 29, 2016

By John M Clapp, University of Connecticut

and Ran Lu-Andrews, California Lutheran University

Updated appendices can be found at:

http://www3.business.uconn.edu/reresume/WWW/SalientFundamentalAppendices.pdf .

Appendix A: Literature review p 1

Appendix B: Fundamental value estimation p 9

Appendix C: Salient gap average by town and year (sort by standard deviation) p 21

Appendix D: Reference point model with salient gap variables: dummy interaction regressions

(common sample) [Substitute gain variables with loss variables] p 23

Appendix E: Summary statistics for counterfactual 7-year fixed gap p 24

Appendix F: Hedonic regression analysis using the initial full sample p 25

Appendix G: A model of sample selectivity p 29

Appendix H: Why an unobserved quality dummy instead of the first residual? p 32

Appendix I: Bivariate analysis of boom (2001 – 2007) and bust (2008-2013) periods p 33

http://www3.business.uconn.edu/reresume/WWW/SalientFundamentalAppendices.pdf

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Appendix A: Literature Review

This appendix provides in-depth reviews of the papers that most influenced our work.

Literature Relevant to the Relationship between House Prices and Fundamentals

Shiller’s seminal work on deviations between market prices and fundamentals stresses the

amplification of a positive feedback loop through news stories and “new era” stories that people tell each

other in informal settings.1 Survey research supports unrealistically high expectations of price

appreciation (Case and Shiller, 2003) – but says little about how the bubble bursts.2

In a summary of his thinking on positive feedback mechanisms, Shiller (2007, page 8) says “the

feedback cannot go on forever, and when prices stop increasing, the public interest in the investment may

drop sharply: the bubble bursts.” This suggests that processes internal to the bubble cause it to end. His

discussion of a boom and bust in US farmland prices Shiller says: “The end of the boom coincides with

President Carter’s Soviet grain embargo, which lowered the price of grains that farms produced, as well

as the sharp rise in interest rates during Volcker’s term, and the recessions of 1980 and 1981-2 (Shiller,

2007, page 30).” This suggests that changes in fundamentals are important in some cases.

A major issue is whether the return to fundamentals is symmetrical with the beginning of the

boom: i.e., does the positive feedback mechanism simply reverse? Akerlof and Shiller (2009) suggest

asymmetry in their discussion of money illusion, where they emphasize the effect of downward wage

rigidity on extending the great depression of the 1930’s.3 Their discussion of the end of a boom in Mexico

1 The title of one of Shiller’s most influential books, Irrational Exuberance, indicates his emphasis on the positive

part of the feedback loop. Akerlof and Shiller (2009) have an interesting discussion of the power of stories to shape

decision making. 2 A bubble cannot exist without limits to arbitrage. The housing literature suggests that short sale constraints,

liquidity constraints, limited price revelation (markets are local) and high transactions costs are major contributors.

A useful summary is contained in Ling, Ooi, and Le (2015). Goswami, Tan, and Waisman (2014) find that 2%

transactions costs can explain substantial deviations from fundamentals. 3 They explain the US depression of the 1890’s by a sudden loss in confidence leading to a run on banks and to

remembered stories of economic failure, as well as corruption and a sense of unfairness (Akerlof and Shiller, 2009,

chapter 6). The depression of the 1930’s is explained in a similar way, with emphasis on the overheated stock

market and industrial growth of the 1920’s, suggesting that the new era stories contained the seeds of their collapse.

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suggests symmetry of fundamentals in that case. The boom began with the finding of oil reserves believed

to be immense and the election of a charismatic president who told a new era story. It ended when the oil

reserves were found to be much smaller than thought, corruption became rampant and the president left

office.

Abraham and Hendershott (1996) explain growth in real house prices in 30 MSA’s with three

fundamental variables designed to capture changes in supply, demand and financial conditions.4 Their

model includes lagged house price appreciation; they interpret the significant value of about .4 (.2 for

inland cities, .5 for coastal cities) to indicate deviation from fundamentals.

Their analysis of the dynamic adjustment path following the bursting of a bubble is most relevant

to this paper. They introduce a term for the deviation between actual price level and the equilibrium level;

a positive sign “captures the tendency for the bubble to eventually burst (pp 194-195).” Their equation

assumes symmetry (negative gaps have the same effect as positive), but this may be due to their short

time period which included a part of one cycle in most MSAs. They find significant positive signs only

for coastal cities; together with other evidence, they conclude that supply constraints generate much larger

bubbles in these cities and that it can take up to 10 years to eliminate a positive deviation.5

Ling, Ooi, and Le (2015) find that lagged changes in national sentiment indices have a strong

positive influence on house price appreciation in a VAR model, and this is true for in a number of large

MSAs as well as at the aggregate national level.6 There findings, which include strong momentum effects

and positive effects of turnover (a measure of market liquidity), are robust to sub-period analysis. Boom

and bust sub-periods are combined and symmetry is assumed by the VAR specification.

4 The variables are real construction cost inflation and employment growth at the MSA level and change in real

after-tax interest rates. They have annual data from 1978 through 1992. 5 Our gap variable differs because we use the salient gap for those selling properties in each year. Our estimation

methods differ by imposing much less structure on the data, and we estimate with local market data, not MSA

aggregates. 6 Dua (2008) uses a VAR to analyze the effect of sentiment on the housing market.

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Agnello and Schuknecht (2011) use a multinomial probit model to estimate the effects of

fundamentals (interest rates, credit supply and GDP) on indicators of boom and bust. They conclude that

“a decrease in interest rates and an increase in the domestic credit growth rate increase significantly the

probability of boom. As expected, the same set of variables has the opposite impact on the probability of

the occurrence of busts (page 172).”7 Symmetry is assumed by the probit specification.

The reasons given for imperfect arbitrage in the housing market – notably short sale and liquidity

constraints, a category which includes high costs of mortgage default – strongly suggest asymmetrical

responses in boom and bust periods, so the lack of attention to this in the literature is surprising.

Literature relevant to identification of the disposition effect

The literature on the disposition effect, often known as “loss aversion,” provides a well-

established method for allowing asymmetrical responses to boom and bust market conditions. This

literature motivates us to use repeat sales and the salient market gap to analyze the return to fundamentals.

Genesove and Mayer (2001) (hereafter, GM) model the effect of reference dependence on house

prices.8 Their model is motivated by some puzzling empirical regularities, notably the positive association

between price change and volume. Their model says that, in the down market, risk averse owners decide

upon a reservation price that exceeds the level they would set in the absence of a loss, and so set a higher

asking price, spend a longer time on the market, withdraw from the market at high rates and receive a

higher transaction price if they do sell. Subsequent literature indicates that buyers anchor to higher asking

prices, so it is possible to successfully “fish” for a willing buyer at above market prices.

GM’s estimation model is designed to explain the second sales price as a linear function of the

expected sales price of that property estimated from all sales including one-only; town-year dummies

control location in our version of this model. The model is explained by equations (1) and (2) in our

7 A strength of this paper is its international cross-country comparison. 8 Ben-David and Hirshleifer (2012) finds little evidence to support loss aversion in stock trading, suggesting that

speculative behavior is a better explanation. But that paper notes that real estate markets may exhibit more loss

aversion due to short sale constraints, scarce local information and the like. See page 2522 for more details.

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paper. Bokhari and Geltner (2011) elaborate on the importance of the difference between the coefficients

on loss and on gain: if the two are the same, there is no loss aversion, only reference dependence. They

found that the coefficient on the loss variable is greater in absolute value than the gain coefficient, a

finding that supports loss aversion but that could be due to liquidity constraints faced by sellers with

losses. In the art market, Beggs and Graddy (2009) find no significant difference between the two

coefficients.

The main issue with this model is controlling for unobserved variation over time and space in

quality.9 Our database is better than most in that we observe major structural characteristics (notably

interior square footage, number of rooms and number of bathrooms) at the time of sale. Since renovations

such as a luxury kitchen are not observed, we follow Genesove and Mayer (2001), Beggs and Graddy

(2009), Bokhari and Geltner (2011), and others by including a term for unobserved quality estimated as

an indicator variable if the residual from the first sale is greater than zero.

GM point out that the coefficient of interest may be biased upward by unobserved quality and

downward by errors in variables:

“Unfortunately, estimation of this “true” relationship is not feasible, since for any given unit we

cannot separately identify its unobservable quality from the extent to which the owner over- or

underpaid relative to the market value at the time of purchase. We show, however, that regressing

the list price on observed loss, while controlling for the previous sale price, yields a lower bound

for the true coefficient on loss, while not controlling for the previous sales price provides an

upper bound for the true effect (GM, p. 1238).”

The unobserved quality variable can be included in one regression, then excluded from another; GM

argue that this provides bounds on the value of the true coefficient.

9 Our discussions with housing professionals suggest that sellers typically do some cosmetic repairs to improve the

curb appeal of their houses. Owners of houses being sold at a loss may have additional incentive to invest in their

house before sale, even though such behavior might be viewed as a form of money illusion.

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GM’s results support the salience of the first price as a reference point:10

- Sellers whose unit's expected selling price falls below their original purchase price (i.e., those

with expected losses) set an asking price that exceeds the asking price of other sellers by between

25 and 35 percent of the percentage difference between the two.

- Those with losses exit the market without selling their property at a much higher rate than others.

- If they do not exit the market, sellers with losses realize higher sales prices than others.

- Losses are relevant when calculated in nominal not real terms.

- Both investors and owner-occupants behave in a reference-dependent fashion, although investors

exhibit about one-half of the degree of dependence of owner-occupants.

An alternative explanation for the positive price-volume correlation is down-payment requirements in

the mortgage market. Genesove and Mayer (2011) add LTV to their models but find little effect on the

coefficients. They conclude that LTV is not strongly binding in their market.11

Beggs and Graddy (2009) apply the GM model to the market for art separated into auctions of

impressionist paintings and modern art. Their findings may be summarize by the following key points:

The anchoring effect is significant and positive.

The anchoring effect is stronger when the sample is restricted to items re-sold within a

short period (42 months). They suggest that the reason for this is the salience of recent

prices.

As expected, the “observed quality” variable has a coefficient not significantly different

from 1.

The “unobserved quality” proxy variable is positive and significant.

10 They interpret their findings as evidence for loss aversion. Here we rely on subsequent literature emphasizing

reference dependence; i.e., the salience of the first sales price. 11 They find that LTV greater than .8 has a small positive effect (.04 for LTV of 100%) on list prices for unsold

properties and a slightly larger effect (.06) for sold property.

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Beggs and Graddy (2009) find no evidence for loss aversion in the art market: i.e., the anchoring

effect they identified is symmetric, meaning the magnitude of loss and gain effects are the same but the

signs are opposite.12 They report using nonlinear models of the unobserved quality effect; they find no

evidence of bias.

Anenberg (2011) develops the GM model by allowing equity constraints and nonlinear price

trends between sales. His locally linear regression allows time effects to exhibit some variation across

individual houses, where the amount of variation is constrained by imposing a smoothness criterion. He

argues that this method for controlling heterogeneity helps identify the effects of losses.13 He further

develops the role of down payment constraints by including a term for low down payment purchases. He

concludes that “in a downturn, the selling prices of homes do not drop as fast as their fundamental value

because equity constrained sellers and sellers facing nominal losses are reluctant to accept lower prices

(Anenberg, 2011, p 75).” He finds that repeat sales price indices might be higher than fundamental value

by as much as 4% during downturns.

Bokhari and Geltner (2011) estimate the Genesove-Mayer (GM), model with market data on

asking and sales prices of all U.S. commercial property greater than $5,000,000 from January 2001

through December 2009. They find that “commercial property sellers faced with a loss relative to their

purchase price tend to post asking prices higher than otherwise-similar sellers not facing a loss, by a

magnitude of about 38% of their loss exposure. The comparable finding in the GM housing study was

25–35% (page 649).” They found that a gain reduces asking price by about 22%. The asymmetry is in the

direction suggested by prospect theory; a symmetrical relationship would support anchoring as in Beggs

and Graddy (2009). Unlike GM, Bokhari and Geltner (2011) find that more experienced and sophisticated

investors are at least as loss averse as others. Their data do not show much influence of reference

12 Small samples (50 to 100 observations in most regressions) and a limited time period (12 years of mostly

increasing prices) might explain these results 13 For example, houses differing in size and location are allowed to have different trends in market value between

sales.

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dependence on the aggregate volume of transactions. They find that the aggregate effect of anchoring on

market prices is 18% pre 2007, 23% in 2007 and 15.5% after 2007.

Einiö, Kaustia, and Puttonen (2008) exploits sales of nearly 200,000 repeat sales of Helsinki

apartments over 1989-2003, a period covering one and a half market cycles. They find a relatively high

frequency of transactions at exactly the same price as purchase, suggesting loss aversion in the

negotiation process. Like GM, Anenberg (2011) and Bokhari and Geltner (2011), Einiö, Kaustia, and

Puttonen (2008) control loan to value, but find that it has little influence on the main results.

We do not have data on loan to value, and our focus is not on the bias in the repeat sales

estimator. Instead, we develop the reference price model by documenting the role of a local positive gap

at the time of the second sale relative to the zero gap (by construction) at the time of the first sale.14 We

exploit the fact that we have a complete boom and bust cycle of large amplitude in most towns during our

sample period whereas GM (2001) and Anenberg (2011) rely on more mild cycles.

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Appendix B: Fundamental Value Estimation

Census Data

In this study, we use Connecticut census tract data from 1990, 2000 and 2010. The following

variables are available by tract and year: centroid latitude, centroid longitude, land area (square miles),

housing units, occupied units, vacant units, owner-occupied units, renter-occupied units, and median

household income. Median household income for census year 2010 is from the American Community

Survey 5-year estimate for the period 2008-2012. All the income data are in 2012 U.S. dollars. All the

different types of housing units are scaled by land area for each census tract.

Transaction Data

We have housing transaction data on 53 major towns in Connecticut. Each transaction address is

geocoded to obtain its latitude and longitude15.

Methodology

1. Sample Division

The full sample is from January, 1994 to December, 2013. In order to use census data properly,

we divide the sample into three subsamples. We interpolate census tract data of year 1990 and year 2000

to the subsample of January 1994 – April 2000. We interpolate census tract data of year 2000 and year

2010 to the subsample of May 2000 – April 2010. The subsample of May 2010 – December 2013

extrapolates census data from the year 2010 using growth rates from the previous decade. Details below.

2. Radius search

For transaction i and census tract j, we calculate the distance between the transaction address and

census tract centroid, using the following equation:

15 We use the geocoding service provided by Texas A&M University Geoservices. https://geoservices.tamu.edu/

https://geoservices.tamu.edu/

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𝐷𝑖𝑗 = 69√(𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒𝑖 − 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒𝑗)2 + (𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒𝑖 − 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒𝑗)2 (B.1)

The distance is in miles. We use 2 miles as a cut-off value to select the census tracts that are close to the

transaction address. It is likely to find that one sale is close to multiple census tract centroids.

3. Interpolation

For each transaction i, we calculate the averages of median household income, housing units/sq.

mile, occupied units/sq. mile, vacant units/sq. mile, owner-occupied units/sq. mile, and renter-occupied

units/sq. mile of all the census tracts of which centroids are within two-mile radius of the transaction

address.

a. For the subsample of January 1994 to April 2000, we have the averages of each census variable

for each transaction i for census 1990 and 2000.

First, we calculate the monthly growth rate, 𝑔𝑘, of census variable k:

𝑔𝑘 = √𝑐𝑒𝑛𝑠𝑢𝑠 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑘2000 𝑐𝑒𝑛𝑠𝑢𝑠 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑘

1990⁄120

− 1 (B.2)

Second, we interpolate the variable values for month t of the subsample period:

𝑐𝑒𝑛𝑠𝑢𝑠 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑖,𝑘,𝑡 = 𝑐𝑒𝑛𝑠𝑢𝑠 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑘1990 × (1 + 𝑔𝑘)𝑡 (B.3)

This means that if the sale occurred close to year 2000, the census variable for that sale has more

weight on the data from Census 2000 than Census 1990. Month t is the month during which transaction i

occurred.

b. For the subsample of May 2000 to April 2010, we have the average of each census variable for

each transaction i for census 2000 and 2010.


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2000⁄120

− 1 (B.4)




weight on the data from Census 2010 than Census 2000.

c. For the subsample period of May 2010 to December 2013, we make the assumption that the

monthly growth rates of all the census variables from 2000 to 2010 remain the same for the subsample of

May 2010 and December 2013. Therefore, before we can interpolate data to each transaction, we need to

extrapolate data to December 2013. We also assume that there will be no changes of tract ID numbers or

centroids between 2010 and 2013. After we generate the “centroid data” for December 2013, we calculate

the averages of all the census variables for 2013. Then, we follow the similar procedures of interpolation

for each transaction as described in (a) and (b).

For the subsample of May 2010 to December 2013, we have the averages of each census variable

for each transaction i for census 2010 and 2013.



2010⁄44

− 1 (B.6)




weight on the data from hypothetical 2013 than Census 2010.

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Fundamental Value Estimation

In this research, we use the following equation to estimate the fundamental value of each property

at the time of the transaction:

𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙𝑖,𝑡 = 0.15 ∗ 𝛼𝑇 ∗ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑖,𝑡∗𝑤𝑒𝑚𝑝𝑇,𝑡

𝑢𝑠𝑒𝑟𝑐𝑜𝑠𝑡𝑜𝑓ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡 (B.8)

𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙𝑖,𝑡 is the estimated fundamental value of property i at transaction time of t, 𝛼𝑇 (town alpha)

is a constant for town T, ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑖,𝑡 is the interpolated average household income of the census tracts

within two-mile radius of property i at transaction time t, 𝑤𝑒𝑚𝑝𝑇,𝑡 is employment in town T at time t, and

𝑢𝑠𝑒𝑟𝑐𝑜𝑠𝑡𝑜𝑓ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡 is the user cost of housing at transaction time t. Employment provides annual

variation over the cycle (see details below), whereas income is interpolated from decennial census data.

We estimate 𝛼𝑇 (town alpha) using year 200016 as a benchmark for every town in our sample.

𝛼𝑇 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 [𝑠𝑎𝑙𝑒𝑠𝑝𝑟𝑖𝑐𝑒𝑖,𝑡

𝑇,2000

(0.15 ∗ ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑖,𝑡 𝑢𝑠𝑒𝑟𝑐𝑜𝑠𝑡𝑜𝑓ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡⁄ )⁄ ] (B.9)

Where, 𝑠𝑎𝑙𝑒𝑠𝑝𝑟𝑖𝑐𝑒𝑖,𝑡𝑇,2000

is the sales price of property i at transaction time t in year 2000, ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑖,𝑡 is

the interpolated average household income of the census tracts within two-mile radius of property i at

transaction time t, and 𝑢𝑠𝑒𝑟𝑐𝑜𝑠𝑡𝑜𝑓ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡 is the user cost of housing at transaction time t. 𝛼𝑇 is the

average of the ratios for each town T in year 2000. After we obtain 𝛼𝑇 from Equation (B.9), we plug it

into Equation (B.8) to estimate the fundamental value of each property at the time of sale in our sample.

The user cost of housing is a percentage of house value that represents the after tax annual cost of

owning a house. The following is based on Hendershott and Slemrod (1982):

𝑅𝑉⁄ = (𝑖 + 𝑇)(1 − 𝑡𝑦) + 𝑐 − 𝑔 (B.10)

16 Cheshire only had 1 transaction in year 2000. Therefore, to avoid outlier problem, we use year 2002 as the

benchmark year for Cheshire.

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Where R is the user cost in dollar terms, V is the value of the house, ty is the marginal income tax rate, .30

for most home owners who are itemizing deductions. The 30 year fixed rate mortgage interest, i, is

variable over time; T is the property tax rate in Connecticut, averaging .02; c is maintenance, between .01

and .03; g is the expected appreciation rate of appreciation, expected to average .02, the rate of inflation.

We do not attempt to estimate the expectations of homeowners in the g term since that is captured

in our model by the salient gap between market values and fundamentals. We use nominal interest rates

because of money illusion; previous research suggests that decisions are made in nominal terms. We have

done robustness checks with real interest rates: this does not change our results with respect to gains

versus losses or the influence of a salient gap. Given the most likely assumptions about fixed quantities:

R/V = (i+ .02)(.7) + 0 = .7i+.014.

Employment data (50 towns)

We obtain annual town-level employment data from Connecticut Department of Labor17 for the

period of 1996 to 2013. Because of the structural changes in the employment data in 2000, we use a

backward interpolation method to interpolate the town-level employment data for the period of 1994 to

1999 in our sample.

a. Backward interpolation

First, we calculate the average annual growth rate in employment for each town between 1996

and 1999. Second, we calculate the actual yearly growth rate in employment for each town year by year

from 1996 to 1999. Third, we assume that the average annual growth rates remain the same from 1999 to

2000, then we interpolate employment data for year 1999 for each town backward using the employment

data in year 2000. Fourth, we apply the actual yearly growth rates to interpolate the employment data for

years 1996-1998 backward using the interpolated data for year 1999 in the previous step. Lastly, to

backward interpolate the employment data for 1994 and 1995, we assume that the growth rates between

17 http://www1.ctdol.state.ct.us/lmi/laus/default.asp

http://www1.ctdol.state.ct.us/lmi/laus/default.asp

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1994 and 1996 are the average annual growth rates between 1996 and 2000. Then we use the interpolated

1996 employment data for each town to backward interpolate the employment data for years 1994 and

1995. Thus, we have a consistent employment data series for each town in our sample for the period of

1994 to 2013.

b. Weighted-average Employment Data Estimation

In our hedonic regression analysis, we control for town-year fixed effects. We save the

coefficients on the town-year dummies as the estimated housing price index (HPI) for each town each

year. Next, we combine the town-level employment data (emptownindx), New York City employment

index (nycempindx)18, and the HPI data together. We standardize all three indices, and run a regression of

standardized HPI on standardized emptownindx and standardized nycempindx.

To calculate the weights on the town-level employment and NYC employment, we save the

coefficients from the regression. The weight on town-level employment (weightemptown) is the ratio

between the coefficient on standardized emptownindx and the sum of the two coefficients. The weight on

NYC employment (weightnycemp) is 1-weightemptown. Because the regression is based on standardized

variables, there are occasions that the coefficients are negative. Therefore, to avoid negative weights and

weights that are higher than 1, we assume that if an estimated weight is negative, the weight is set to be 0,

and if an estimated weight is higher than 1, the weight is set to be 1. Thus, all the weights for all the 50

towns in our sample are within the range of [0, 1]. The weighted-average employment data for each town

is estimated by Equation (B.11) for town T at time t:

𝑤𝑒𝑚𝑝𝑇,𝑡 = 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑚𝑝𝑡𝑜𝑤𝑛𝑇 × 𝑒𝑚𝑝𝑡𝑜𝑤𝑛𝑇,𝑡 + 𝑤𝑒𝑖𝑔ℎ𝑡𝑛𝑦𝑐𝑒𝑚𝑝𝑇 × 𝑛𝑦𝑐𝑒𝑚𝑝𝑡 (B.11)

18 New York City employment data is from http://labor.ny.gov/stats/lslaus.shtm. It is a monthly data series for the

period of 1994-2013. We regress the monthly employment data on the year dummies to obtain New York City

employment index (nycempindx) for each year. In the same regression, we also save the predicted annual

employment value of New York City (nycempy) to be used later in the weighted average employment calculation.

http://labor.ny.gov/stats/lslaus.shtm

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Appendix C: Salient gap average by town and year (sort by standard deviation)

Town Peak Trough Amplitude Standard Deviation R2 Driving Distance

Weston 0.253 -1.101 1.354 0.372 0.679 58

Norwich 0.305 -0.687 0.992 0.346 0.022 135

West Haven 0.442 -0.509 0.950 0.337 0.658 78.2

Stratford 0.447 -0.472 0.919 0.335 0.780 65.1

Naugatuck 0.279 -0.588 0.866 0.326 0.745 87.1

Bethel 0.329 -0.588 0.917 0.320 0.552 69.2

Danbury 0.315 -0.625 0.940 0.314 0.640 66

East Hartford 0.304 -0.610 0.914 0.312 0.751 118

Monroe 0.279 -0.589 0.868 0.305 0.711 73.9

Stamford 0.354 -0.418 0.772 0.298 0.713 40.7

Southbury 0.143 -0.826 0.970 0.290 0.278 82.4

New Milford 0.296 -0.568 0.864 0.288 0.740 80.3

Ledyard 0.251 -0.542 0.793 0.283 0.904 134

New Britain 0.386 -0.447 0.833 0.282 0.726 110

Trumbull 0.457 -0.430 0.887 0.280 0.737 65.7

Meriden 0.382 -0.377 0.759 0.276 0.658 101

New Canaan 0.447 -0.313 0.761 0.273 0.748 49

Shelton 0.343 -0.434 0.777 0.270 0.806 74.1

Middletown 0.290 -0.498 0.788 0.268 0.778 106

New Haven 0.381 -0.473 0.853 0.268 0.801 81

East Haven 0.336 -0.465 0.802 0.265 0.693 83.2

Fairfield 0.263 -0.493 0.755 0.260 0.862 57.3

Westport 0.361 -0.298 0.659 0.259 0.805 52.3

Hamden 0.345 -0.434 0.779 0.257 0.705 85.5

Norwalk 0.450 -0.371 0.821 0.256 0.781 49.1

Windsor 0.285 -0.479 0.763 0.249 0.523 124

Enfield 0.244 -0.471 0.715 0.248 0.731 137

Wilton 0.287 -0.460 0.748 0.247 0.668 55

Hartford 0.351 -0.389 0.739 0.247 0.712 118

Greenwich 0.358 -0.267 0.625 0.246 0.805 35.1

South Windsor 0.355 -0.339 0.694 0.243 0.702 126

Manchester 0.212 -0.482 0.695 0.242 0.760 124

Wallingford 0.311 -0.404 0.715 0.241 0.739 92.9

Torrington 0.269 -0.414 0.682 0.238 0.576 112

Darien 0.363 -0.266 0.628 0.238 0.819 44.7

Cheshire 0.183 -0.401 0.584 0.233 0.907 103

Madison 0.292 -0.373 0.666 0.231 0.780 99.4

Groton 0.259 -0.383 0.642 0.230 0.849 128

North Haven 0.285 -0.306 0.591 0.229 0.839 87.9

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Town Peak Trough Amplitude Standard Deviation R2 Driving Distance

Branford 0.230 -0.403 0.634 0.228 0.826 86.3

Tolland 0.193 -0.415 0.608 0.212 0.634 134

Bristol 0.210 -0.376 0.586 0.209 0.480 105

Southington 0.325 -0.258 0.583 0.206 0.838 104

Simsbury 0.157 -0.401 0.558 0.205 0.787 128

Farmington 0.212 -0.334 0.546 0.205 0.824 116

Newington 0.278 -0.328 0.607 0.204 0.772 110

Newtown 0.151 -0.519 0.670 0.203 0.004 76.3

Wethersfield 0.198 -0.408 0.607 0.198 0.846 112

West Hartford 0.244 -0.300 0.544 0.193 0.866 119

Glastonbury 0.192 -0.353 0.545 0.183 0.749 121

Notes. This is the repeat sales analog of Case and Shiller (2003), Table 2. The salient gap by town and year is the

average of difference between change in log market values (predicted values for each sale from a standard hedonic

regression) and change in log local fundamental value (computed from tract income, households, town employment

and the user cost of housing). Changes are averaged from the date of the first sale (the salient date) to date of the

second sale. These changes were averaged annually by town from 2000 through 2013 based on data from 1994 to

allow for adequate first sales. Amplitude is the town-year average in the peak year (Peak) minus the average in the

trough year (Trough). Peak and Trough can be interpreted as log percentage difference between market value and

salient fundamental value. E.g., a value of 1.0 is one order of magnitude on the log scale, a doubling of the

difference. R2 is the correlation coefficient between the salient gap and fundamentals. Driving distance is minutes to

New York City without substantial traffic estimated from Google maps on Saturday September 13, 2014 at 10am to

noon.

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Appendix D: Reference point model with salient gap variables: dummy interaction regressions

(common sample) [Substitute gain variables with loss variables]

Dependent variable: lnprice2

1 2 3 4 5 6 7 8

Intercept 0.987*** 0.981*** 1.036*** 1.049*** 1.030*** 1.068*** 1.071*** 1.063***

(3.91) (3.88) (3.97) (4.19) (4.09) (4.29) (4.29) (4.26)

lnprice2_f 0.969*** 0.969*** 0.972*** 0.967*** 0.967*** 0.966*** 0.966*** 0.966***

(49.79) (49.84) (48.04) (50.23) (50.08) (50.57) (50.37) (50.37)

1stResiddum 0.193*** 0.192*** 0.222*** 0.191*** 0.193*** 0.190*** 0.190*** 0.191***

(17.00) (17.17) (14.89) (16.92) (16.72) (17.01) (16.92) (16.92)

gapd -0.019 -0.006 0.022* -0.001 -0.003 -0.008

(-1.48) (-0.47) (1.98) (-0.06) (-0.30) (-0.64)

lossd 0.096*** 0.064*** 0.063*** 0.083*** 0.056*** 0.054*** 0.059***

(7.46) (6.69) (5.43) (7.26) (4.62) (4.34) (4.90)

bglossd 0.040***

(4.00)

gapdlossd 0.106*** 0.125*** 0.151*** 0.170***

(5.46) (4.62) (6.00) (4.82)

bggapd -0.032***

(-4.05)

bggapdlossd 0.206***

(5.48)

loss24d 0.084***

(3.65)

gapdloss24d -0.112***

(-5.63)

loss36d 0.043***

(3.64)


(-4.91)

loss48d 0.012

(1.42)


(-3.12)

Town-Year FE Yes

No. Obs 34584 34584 34584 34584 34584 34584 34584 34584

Adj. RSQ 0.868 0.868 0.866 0.869 0.869 0.869 0.869 0.869

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Appendix E: Summary statistics for counterfactual 7-year fixed gap regressions

NAME N mean min max q1 median q3 std

avglnprice2_f 34584 12.369 11.252 14.359 11.893 12.251 12.710 0.643

bggapd7 34584 0.298 0 1 0 0 1 0.457

bggapd7gaind 34584 0.253 0 1 0 0 1 0.435

bggapd7lossd 34584 0.045 0 1 0 0 0 0.207

fundR27 34584 0.178 -6.157 5.559 0.026 0.181 0.331 0.261

gap7 34584 0.079 -5.926 5.885 -0.230 0.115 0.398 0.481

gapp7 34584 0.233 0 5.885 0 0.115 0.398 0.300

gapd7 34584 0.595 0 1 0 1 1 0.491

gapd7bggaind 34584 0.455 0 1 0 0 1 0.498

gapd7bglossd 34584 0.092 0 1 0 0 0 0.289

gapd7gain 34584 0.206 0 4.313 0 0 0.375 0.296

gapd7gain24d 34584 0.061 0 1 0 0 0 0.240

gapd7gain36d 34584 0.132 0 1 0 0 0 0.339

gapd7gain48d 34584 0.202 0 1 0 0 0 0.402

gapd7gaind 34584 0.481 0 1 0 0 1 0.500

gapd7loss 34584 0.022 0 2.388 0 0 0 0.088

gapd7loss24d 34584 0.029 0 1 0 0 0 0.167

gapd7loss36d 34584 0.057 0 1 0 0 0 0.232

gapd7loss48d 34584 0.079 0 1 0 0 0 0.269

gapd7lossd 34584 0.115 0 1 0 0 0 0.319

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Appendix F: Hedonic Regression Analysis using the initial full sample

Appendix Table F1: Hedonic regression analysis variable definitions

Variable Name Definition

age Age of the property, calculated as the difference between the transaction year

and the year built

age2 Age of the property squared

bath2or3 A dummy variable that is equal to 1 if the number of bathrooms is between 2

and 3; 0 otherwise

bath3 A dummy variable that is equal to 1 if the property has more than 3 bathrooms;

0 otherwise

bathrooms Number of bathrooms in the property

intersize Interior size of the property (sf)

intersize2 Interior size squared

lint

Natural logarithm of the ratio between assessed building value and assessed

land value of the property

lnprice2 Natural logarithm of the sales price of the property

lnprice2_f

Predicted natural logarithm of the price of the property from hedonic regression

using all sales (258,538 observations)

lnprice2_p Natural Logarithm of the previous sale price

lnprice2_f_p

Predicted natural logarithm of the price of the property in the previous sale

from hedonic regression

lotsize Lot size of the property (sf)

lotsize2 Lot size squared

totroom2 Number of total rooms squared

totrooms Number of total rooms in the property

unobsq Unobserved quality, 1st sale residual from the hedonic regression using all sales

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Appendix Table F2: Descriptive statistics for hedonic regression

Variable N mean min max q1 median q3

price2 258538 387507.87 50100.00 6850000.00 160000.00 245000.00 405000.00

lnprice2 258538 12.51 10.82 15.74 11.98 12.41 12.91

age 258538 47.61 0.00 113.00 29.00 47.00 62.00

age2 258538 2934.77 0.00 12769.00 841.00 2209.00 3844.00

bath2or3 258538 0.47 0.00 1.00 0.00 0.00 1.00

bath3 258538 0.08 0.00 1.00 0.00 0.00 0.00

bathrooms 258538 1.98 1.00 11.50 1.00 2.00 2.50

intersize 258538 1877.55 206.22 92928.00 1242.00 1606.00 2220.00

intersize2 258538 4.65E+06 4.25E+04 8.64E+09 1.54E+06 2.58E+06 4.93E+06

lint 243233 0.35 -10.24 10.82 0.03 0.42 0.75

lotsize 258538 29728.83 1505.00 435164.00 9148.00 16117.00 40000.00

lotsize2 258538 2.22E+09 2.27E+06 1.89E+11 8.37E+07 2.60E+08 1.60E+09

totroom2 258538 51.32 16.00 7569.00 36.00 49.00 64.00

totrooms 258538 6.93 4.00 87.00 6.00 7.00 8.00

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Appendix Table F3: Interior Size Regression

Modeling Intersize to interpolate about 5% of the sample with missing Intersize

Variable Parameter

Intercept -450.9317***

(-18.18)

lotsize 0.0068***

(74.80)

lotsize2 -1.49E-08***

(-42.43)

bath2or3 -321.9759***

(-71.76)

bath3 -163.3418***

(-15.56)

age -13.5988***

(-74.04)

age2 0.1055***

(65.58)

totrooms 247.3405***

(171.25)

totroom2 -2.6205***

(-53.86)

bathrooms 498.1300***

(137.49)

Town-Year FE YES

No. Obs 258532

Model DF 988

Adj. RSQ 0.65

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Appendix Table F4: Hedonic Regression Result with Standard Errors Clustered at the Town Level

Variable Parameter

Intercept 11.7551***

(629.20)

lint -0.0999***

(-58.28)

intersize 0.0003***

(242.80)

intersize2 -4.16E-09***

(-127.63)

lotsize 2.61E-06***

(56.58)

lotsize2 -6.76E-12***

(-38.89)

bath2or3 0.1251***

(81.88)

bath3 0.2394***

(71.60)

age -0.0050***

(-52.03)

age2 0.00002***

(28.62)

Town-Year FE YES

No. Obs 243179

Model DF 963

Adj. RSQ 0.85

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Appendix G: A model of sample selectivity

This appendix provides a formal model for the effect of persistent unobserved quality on the residual

from the GM model, equation (3), where our analysis is conditional on loss or gain. It is well established

in previous research that the first residual is positively related to unobserved quality, and that the

inclusion of this residual in equation (3) is a proxy for unobserved quality. Here we present the

additional assumptions required to use the coefficients from equation (5) as measures of the proportion

of the first residual that persists as unobserved quality conditional on a gain or a loss.

Start with equation (5) from the paper.

𝑃𝑠 − �̃�𝑠 = 𝛾0 + 𝛾𝑙(𝑃𝑝 − �̂�𝑝)𝑙

+ 𝛾𝑔(𝑃𝑝 − �̂�𝑝)𝑔

+ 𝜀�̃� (G.1)

The 𝐹𝐸𝑠 terms have been dropped because they shift the constant term. Recall definitions:

𝑃𝑠 − �̃�𝑠 is the residual from the GM equation (3). Note that �̃�𝑠 includes the effect of the first

residual (log of first sale price less its predicted value from a hedonic), but not the interaction of

the first residual with gain and loss at the time of the second sale.

(𝑃𝑝 − �̂�𝑝)𝑙 is the first residual if there is a loss at the time of the second sale, otherwise zero.

(𝑃𝑝 − �̂�𝑝)𝑔

is the first residual if there is a gain at the time of the second sale, otherwise zero.

Sum equation (G.1) over all transactions that have a loss.

∑ (𝑃𝑠 − �̃�𝑠)𝑙 = 𝛾0𝑛𝑙 + 𝛾𝑙 ∑ (𝑃𝑝 − �̂�𝑝)𝑙

𝑙 + 𝛾𝑔 ∑ (𝑃𝑝 − �̂�𝑝)𝑔

𝑙 + ∑ 𝜀�̃�𝑙 (G.2)

Where 𝑛𝑙 is the number of transactions with losses.

Divide by 𝑛𝑙 and note that the 𝛾𝑔 term equals zero because each element of the sum is equal to

zero.

∑ (𝑃𝑠 − �̃�𝑠)𝑙 /𝑛𝑙 = 𝛾0 + 𝛾𝑙 ∑ (𝑃𝑝 − �̂�𝑝)𝑙

𝑙 /𝑛𝑙 + ∑ 𝜀�̃�𝑙 /𝑛𝑙 (G.3)

Assume that the intercept is zero (𝛾0 ≈ 0) and that the expected value of the residual is zero E𝜀�̃� = 0.

These are weak assumptions given that we are working with residuals that have zero mean in the

equations that generate them. 𝛾0 ≈ 0 is testable. Then it follows that:

P.1: The mean of the GM residual conditional on loss equals the proportion of the first residual

representing unobserved quality given a loss, 𝛾𝑙 times the mean of the 1st residual conditional

on a loss at the time of the second sale.

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The proof is by contradiction. Assume counterfactually that 𝛾𝑙 = 1. Then if any random component

in the GM residual has mean zero, the two conditional means are equal, as illustrated by the 45

degree line in Figure G.1. This implies that all of the mean 1st residual conditional on loss is

persistent unobserved quality. If the ratio of conditional means equals 𝛾𝑙 then this is the part of

the first residual due to persistent unobserved quality.

Figure G.1: Proportion of unobserved quality as a function of gain and loss

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This reasoning leads directly to:

P.2: The mean of the GM residual conditional on gain is the proportion of the first residual

representing unobserved quality given a gain, 𝛾𝑔 times the mean of the 1st residual conditional

on a gain at the time of the second sale.

We further assume that any unobservable variables omitted from equation (G.1) have the same effect

on a gain as on a loss. Then:

P.3: The difference between loss and gain in unobserved quality equals 𝛾𝑙 − 𝛾𝑔 .

The numerical calculations indicating that 70% of the discount on gains relative to losses is due to

unobserved quality is based on P.3. Empirical evidence for the assumptions is contained in Table 5A. We

find an intercept of -.005 for Model 2 (and similar for all models), which is economically insignificant

compared to differences in coefficients of .15 to .20. Even with the hedonic residual Table G.1 below,

the .034 coefficient is small compared to the .3 difference in slope coefficients.

Table G.1. This is Table 5A except that we use the 2nd residual instead of the GM residual.

Panel A: Dependent variable: 2nd Residual

1 2 3 4 5 6

Intercept 0.045*** 0.034** 0.071*** 0.052** 0.071*** 0.045**

(3.47) (2.61) (3.48) (2.51) (3.45) (2.08)

1stResid 0.461*** 0.462*** 0.429***

(16.65) (16.66) (11.14)

1stResidlossd 0.661*** 0.659*** 0.633***

(9.02) (9.02) (5.57)

1stResidgaind 0.361*** 0.363*** 0.268***

(14.94) (14.86) (7.76)

gapd -0.030** -0.021 -0.030** -0.014

(-2.36) (-1.62) (-2.32) (-0.96)

gapd1stResid 0.060*

(1.72)

gapdunosbqlossd 0.077

(0.67)

gapdunosbqgaind 0.148***

(3.92)

Town-Year FE Yes

RSQ 0.199 0.213 0.200 0.213 0.201 0.217

No. Obs 34584 34584 34584 34584 34584 34584

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Appendix H Why an unobserved quality dummy instead of the first residual?

This section explains why an indicator function I(1st residual>median) is preferred to the 1st residual in

equation (3). To summarize, the dummy breaks obvious collinearity with loss and gain and therefore

gives more precise estimates of the coefficients of interest. To see this, start with equation (3):

𝑃𝑠 = 𝛽0 + 𝛽𝑠�̂�𝑠 + 𝛼𝑙(𝑃𝑝 − �̂�𝑠)+ + 𝛼𝑔(𝑃𝑝 − �̂�𝑠)− + 𝜆𝐼[(𝑃𝑝 − �̂�𝑝) > 𝑚𝑒𝑑𝑖𝑎𝑛] + 𝐹𝐸𝑠 + 𝜀𝑠𝑞 (H.1)

The first two terms in parentheses can be replaced by:

𝑃𝑝 − �̂�𝑠 = (𝑃𝑝 − �̂�𝑝) + (�̂�𝑝 − �̂�𝑠) (H.2)

If we had estimated the version of equation (H.1) considered by GM (2001) – and we do

estimate this version in Table 8 – then we would have estimated:

𝑃𝑠 = 𝛽0 + 𝛽𝑠�̂�𝑠 + 𝛼𝑙[(𝑃𝑝 − �̂�𝑝) + (�̂�𝑝 − �̂�𝑠)]+ + 𝛼𝑔[(𝑃𝑝 − �̂�𝑝) + (�̂�𝑝 − �̂�𝑠)]− + 𝜆[(𝑃𝑝 − �̂�𝑝)] +

𝐹𝐸𝑠 + 𝜀𝑠𝑞 (H.3)

The obvious collinearity between the last term in brackets of equation (H.3) and the loss and

gain terms causes variance inflation, reducing the precision of the parameters of interest, 𝛼𝑙

and 𝛼𝑔. We test this by estimating (H.3) and find evidence for using the indicator variable.

Moreover, errors-in-variables (EIV) in the estimation of 𝜆 is substantially reduced by fitting a straight line

from below to above median. We obtain a more precise estimate of that parameter. The proof of this

follows immediately from the discussion of the first residual in connection with equation (5): there is a

random component as well as a persistent unobserved quality component.

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Appendix I Bivariate analysis of boom (2001 – 2007) and bust (2008-2013) periods

Conditional means for one period are compared to the other period.

Boom period: 2001-2007

Variable N Mean std Comments based on comparison of mean to

bust and mild recovery period, 2008-2013

(not shown).

1stResid 17897 -0.010 0.26 About the same

1stResiddum 17897 0.49 0.5 About the same

1stResidgaind 16096 -0.05 0.24 Over 2x more sales with gain in boom, and

these have smaller discount by -.09 (-.05 vs

-.14). Average quality is .09 greater.

1stResidlossd 1801 0.31 0.25 Number with losses is 9% of bust. But the

average quality is .21 greater: .31 vs .1. With

1stResidgaind results, this indicates that

quality increases substantially with boom, on

average for both gain and loss. Results for

gapd1stResidlossd indicate that about 25% of

the quality response is associated with

changes in the salient gap.

anchor 17897 -0.38 0.33 Much lower (-.38)

bggaind 17897 0.86 0.34 Compare to .38 during bust

bggapp2d 17897 0.52 0.5 Big positive gap is .52 vs .05 in bust.

fundamental 17897 4.30E+05 4.30E+05 Level variable.

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fundRatio2to1 17897 0.13 0.16 For typical repeat sale, F increased less

between sales during the boom: .13 vs .22.

gain 16096 0.44 0.29 Realized gains conditional on gain are much

higher during boom: .44 vs. .32. This likely

reflects higher prices for all properties.

gaind 17897 0.9 0.3 90% have a gain vs 43% in bust

gap 17897 0.24 0.19 The average gap is .24 in boom, -.22 in bust,

suggesting that the gap is a good indicator of

cycle.

gapd 17897 0.95 0.21 95% have positive gap vs 19% during bust

gapd1stResid 17059 -0.01 0.26 About the same even though there are many

more gapd observations here. Conclude that

gap is an important control regardless of

cycle.

gapd1stResidgaind 15484 -0.04 0.23 About the same. Gap is a good control for

quality.

gapd1stResidlossd 1575 0.33 0.25 About .05 more quality during boom

conditional on a positive Gap. Losses are of

much higher quality than gains when there is a

positive gap in both subperiods. The

difference between gain and loss (.37) is

about the same as if unconditional on gap

(.36)

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gapdbggaind 17897 0.83 0.37 As expected.

gapdbglossd 17897 0.06 0.24 As expected.

gapdgain 15484 0.44 0.29 About the same. The average amount of gain

does not depend on gap (see .44 above) or on

sub period.

gapdgaind 17897 0.87 0.34 As expected.

gapdloss 1575 0.15 0.2 Similar to results for gapdgain.

gapdlossd 17897 0.09 1 As expected. Shows that there are a significant

number of losses even with a pos gap. In the

bust, 3% of sales still have positive gap and

losses, about 500 sales.

lnavbldgs 17897 11.37 0.62 Hard to draw conclusions since time and

location not controlled. These are level

variables.

lnavland 17897 10.97 0.91 Hard to draw conclusions since time and


variables.

lnprice1 17897 12.3 0.7 Hard to draw conclusions since time and


variables.

lnprice1_hat 17897 12.31 0.65 Hard to draw conclusions since time and


variables.

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lnprice2 17897 12.71 0.7 Hard to draw conclusions since time and


variables.

lnprice2_f 17897 12.68 0.66 The average market value decreased in bust

from 12.68 to 12.57, about .11. This should be

compared to the quality changes.

loss 1801 0.16 0.2 Realized losses conditional on loss are lower

during boom: .16 vs. .25. Possibly because of

higher quality losses, or more bargaining

power as market ratchets up. But, it is more

likely that this reflects higher prices for all

properties.

lossd 17897 0.1 0.3 10% of sample has losses during boom.

months 17897 55.77 32.8 Shorter time between sales. The 2008-2013

allows mechanically for more time between

sales. But months is not a strongly significant

variable. See the "sum of gain coeff's" for

different holding periods in Table 4. Also,

results in Beggs and Graddy (2009) and

related papers.

price2 17897 4.50E+05 5.10E+05 The average price decreased by $40k from

$450 to $410 from boom to bust period

(averages).

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Analysis of boom to bust part of cycle: numbers are boom

minus bust unless otherwise indicated.

Result or

coefficient

unit

Change in house prices on average -0.09 decimal %

Change in 1st resid 0 decimal %

change in 1st resid conditional on a gain- implies lower quality

in bust

-0.09 log change unobs Q

number of sales with gain in boom 16096

number of sales with gain in bust 7192

change in 1st resid conditional on a loss - implies lower quality

in bust


number of sales with loss in boom 1801

number of sales with loss in bust 9495

total second sales in a boom 17897

total second sales in a bust 16687

Analysis of change in average 1st residual, boom to bust

Percent sales gain in boom 0.90 decimal %

Percent sales loss in boom 0.10 decimal %

Percent sales gain in bust 0.43 decimal %

Percent sales loss in bust 0.57 decimal %

change boom to bust in average 1st residual conditional on

gains


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change boom to bust in average 1st residual conditional on

losses


weighted average change. Weights = % in boom -0.05 log change unobs Q

How much of these changes is permanent lower quality in bust

of second sale using paramaters in Table 5?

Losses reflect on average about .045 of every unit in 1st resid 0.00

Gains reflect on average about .2 of every unit in 1st resid -0.02

Weighted average change in quality, boom to bust - Weights =

% in boom

-0.004

Weighted average change in quality, boom to bust - Weights =

% in bust

-0.014

Conclude that between 5 and 15% of the change in hpi from

boom to bust can be accounted for by lower quality trading in

bust.

0.16 Calculations for

lower bound not

shown.

Note: conclusions are only suggestive primarily because I am

using averages over 6 and 7 year periods.

appendices for: unobserved quality and anchoring to home

Documents