Cognitive Reference Points, Left-Digit Effect and Clustering in Housing Markets Sudheer Chava, and Vincent Yao

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September 17, 2016 Preliminary and Incomplete. Please do not cite or circulate

Abstract We document a significant clustering in the list prices in housing markets and consequently, a left-digit effect in housing transactions. Our identification utilizes a quasi-experiment setting that exploits the sale outcomes of two similar properties that are listed only $100 apart, but with a much greater perceived left digit. We find that properties listed at smaller left digits are 5.7% more likely to sell, stay 8 days shorter on the market and receive 0.8% higher price. The effects are more pronounced in softer housing markets and in less educated regions. In addition, we also find that buyers of left-digit listed homes pay a higher interest rate on their mortgage, receive a lower return on a resale, and are more sluggish in refinancing their mortgages. They are also more likely to be minorities, younger, liquidity-constrained, low credit score, and less financially sophisticated. Our results highlight behavioral biases can affect even significant and high value purchases such as housing.

Keywords: Cognitive Reference Points, Left-Digit Effect, Real Estate, Financial Sophistication JEL Classification: D4, D12, G10, L1, L8,R2, R3, R20 ∗

Sudheer Chava can be reached at [email protected], or at +1 404 894 4371. Vincent Yao can be reached at [email protected]

I.

Introduction

Do behavioral biases affect even large household decisions such as housing transactions? Housing is the dominant asset of a typical household in the United States and housing transactions are the single largest household finance decision that households make. As such, any systematic mistakes in housing decisions are of significant economic importance and have major policy implications. In this paper, we analyze whether households exhibit behavioral biases in housing transactions. Specifically, we analyze whether the left digit of the listing price has a significant impact on the housing sales transaction and whether these buyers make other mistakes in their housing and mortgage decisions. It’s well documented that people use cognitive reference points, i.e. standard benchmarks against which other stimuli are judged (Rosch 1975). The left-digit effect manifests when the left digit dominate how consumers brain works and a change in the left-digit of a price causes people to move from one cognitive reference point to another. For example, $3.99 is perceived to be significantly less than the $4.00 because the left digit dominates and it is considered not just as one penny less (see Thomas and Morwitz 2005; Manning and Sprott 2009). Hence, retail prices are often set ending in 9s (for example, $3.99, not $4.00). In this paper, we examine possible clustering in list price and also consequent left-digit effects in housing markets. Our primary data is the listing and sale records from Multiple Listing Services (MLS) in fourteen largest and diverse Metropolitan Statistical Areas (MSAs) in the United States. List prices largely reflect a sellers reservation price (Gensove and Mayer 1997; Han and Strange 2016). We find there is significant clustering in right digits of list price at either $900 or $1,000 when it is divided by 1,000. 76% of right digits of all list prices are either at $900 (e.g., $329,900) or $1,000 (e.g., $330,000), 34% and 41% respectively. Another 7% of list prices end up with right digits at $500 (e.g., $329,500). These three right digits combined account for 83% of all list prices and all ten right digits at exact multiples of $100 collectively account for 88%. Hence it is most popular to list the property for sale at the price ending with either $900 or $1,000. Our identification strategy for analyzing left-digit effects is thus based on the aforementioned evidence of clustering in list prices. By focusing only on list prices ending with either $900 or $1,000, we create a quasi-experiment setting that exploits the sale outcomes of two similar properties that are listed $100 apart, but with a much greater perceived left digit. We select two properties that 1

appear identical in property attributes, list date and location, with the only difference being they are listed at tiny price difference, i.e. one listed at the exact multiples of $1,000 (e.g., $330,000) and the other at $100 less (e.g., $329,900), to be our control and treatment groups respectively. The one in the treatment could have been listed at the same round price as the one in control group. MLS data allows us to define several outcome variables to represent the success of listings: whether the listing ends up with a successful sale; how many days is the property actively listed on the market before it is under contract; how much it is sold for. Our baseline results indicate that properties listed at smaller left digits, compared to very similar properties that are listed $100 more but perceived much more, are 5.7% more likely to convert the listing into a sale. They also stay on the market 8 days shorter and are sold at higher price by 0.8%. The extra higher sale price is equivalent to $1,508 to $2,287 for an average contract price, to homeowners. The gain represent a net 15 to 23 times return on the initial $100 investment. The 8-day savings of days on the market spent by the listing agents alone is roughly 12% of the average listing time. Assuming the realtor expects to collect standard 3% commission rate when the property is sold, and an annual discount rate of 20%, that is the equivalent $662 extra value for the average contract price. In addition, there are significant benefits associated with not having to wait longer for final contract and avoiding prolonged uncertainty for homeowners. Next, we explore which realtors and sellers utilize the left-digit listing strategy. There is a direct relationship between list agents past performance and the likelihood of choosing to list at smaller left digits. However, realtors share of listings at smaller left digits range between 45% to 55%, suggesting the strategy is not omnipotent. There is a negative relationship between listing at smaller left digits and price level. However, there is really not much variation in the likelihood for all the prices below the median (e.g., $228,000). Among house prices above the median, chance of using left-digit strategy exponentially declines by 30% through the highest price decile. Since MLS data does not provide any information on buyers, we supplement the analysis with a national representative mortgage sample where we have information on both loan application and mortgage origination. Our data also allows us to examine the ex post performance of buyers the interest rate on their the mortgage used to finance the home purchase, their post-purchase refinance and default outcomes, and the resale appreciation when they choose to sell home a few years later.

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Our results indicate that buyers who choose to buy properties listed at smaller left digits, are also consistently underperforming in other mortgage and housing outcomes. They tend to pay higher interest rate on the mortgages by 2.4 bps compared to their peers. Following their home purchase, they are also less likely to refinance by 17% after controlling for a full array of factors that determine the mortgage terminations using a Cox hazard model. When we interact the potential saving with the left-digit indicator, there is a strong interaction effect. Buyers for smaller left digits react more slowly to interest rate savings. Compare two borrowers who can save 1% relative to their original mortgage rate by refinancing, the borrower who bought for listings at smaller left digits has a lower hazard of refinancing by 10% slower. Also when they choose to sell the property at a later date, these buyers receive a lower return by 3.5% for an average holding period of 5 years. These results confirm that the left-digit effect is a truly a behavioral bias. We also explore the characteristics of the buyers of left-digit listed properties based on the mortgage data. Consistent with the household finance literature, we find that these buyers are more likely to be minorities, younger, more liquidity-constrained, have a low credit score, and in general, less financially sophisticated. It is reasonable to expect that the listing strategy and outcome would be influenced by both the housing market conditions and the characteristics of various players in the real estate transaction buyers, sellers and real estate agents. First, we explore whether the listing strategy depends on the housing market conditions in that area. We define the housing market where the property is located as soft/weak if the number of days on the market in prior three months in that zip code is in the top third. Not surprisingly, we find that the left-digit effects are more pronounced in softer housing markets – the left-digit listed properties are 7.1% more likely to be sold in weaker markets, with the effect more than twice as that in the tighter markets (where it take shorter days on the market to sell). Consistently the left-digit effects on days on the market is also much greater in the softer markets – the effect is 14.8 days shorter on the market, more than eight times the effect in tighter markets. Also, the left-digit effects on price are greater in the softer markets. The estimated effect on sale price is 0.9% in soft markets, higher than only 0.6% in the tight markets. In line with these results, we also find that the left-digit effects also have a significant seasonality, i.e., much greater in slow seasons that are September through next February. The evidence broadly suggests that in

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stronger housing markets, the listing price may be set to convince the sellers (who perceive the $100 higher price to be much larger) and in weaker housing markets, the listing price is set to attract buyers (who perceive the $100 lower price to be much larger). Although listings at smaller left digits are less popular for more expensive properties, their leftdigit effects on sale price and days on the market are much higher, except for those in the top price decile, suggesting significant more benefits to these seller and list agents. In addition, there is a large variation in the left-digit effect across geographic regions given that location is an important determinant of real estate transactions. Since we do not directly observe demographic information on buyers from MLS data, we explore the heterogeneity in effects by county-level education. The leftdigit effects are higher in less educated markets where there are more less-educated people the effect on sale likelihood and days on the market are both twice or more as that in more educated markets. The county level education results suggest that it is possible that there is greater heterogeneity across the borrowers and some borrowers don’t pay attention to the left-digit. Our analysis broadly contributes to the literature that documents mistakes in household financial decision making in general (Agarwal, Driscoll, Gabaix, and Laibson, 2009; Agarwal, Green, Rosenblatt and Yao, 2015; Campbell, 2006; Campbell, Jackson, Madrian, and Tufano, 2011). Related to the phenomenon we document here, DellaVigna and Malmendier (2006) show that gym members underutilize their gym memberships. Akin to the current study, these gym members overstate the benefits from offered contracts and pick the wrong one. Examples of other mistakes made by households include individuals leaving money on the table in their 401K decisions (Choi, Laibson, and Madrian, 2011), borrowers taking payday loans with astronomical annual percentage rates (APRs) when other cheaper forms of credit are available (Agarwal, Skiba, and Tobacman, 2009; Bertrand and Morse, 2011), and consumers with multiple credit card offers failing to optimally choose the right one (Agarwal, Chomsisengphet, Liu, and Souleles, 2015). More broadly, it is puzzling that less than 30% of U.S. households directly participate in equity markets (Cole and Shastry, 2009; Li, 2014), and among those who do hold stocks, many have highly concentrated portfolios and trade excessively (Korniotis and Kumar, 2011; 2013). Stango and Zinman (2009) find that U.S. borrowers regularly underestimate the APR of a loan if they are given only the loan principal and repayment stream. Bertrand and Morse (2011) find that payday loan borrowers who are shown information on

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the aggregate cost of their loan or the time to repayment frequently borrow significantly less per pay cycle. Buyers for the left digits are another example of behavior bias. This paper also contributes to our knowledge about the (lack of) sophistication of households and financial education. Agarwal and Mazumder (2013) find that borrowers who make financial mistakes have lower cognitive ability. Agarwal, Amromin, Ben-David, Chomsisengphet, and Evanoff (2010) document the effects of a successful financial education program on mortgage defaults, and Agarwal, Amromin, Ben-David, Chomsisengphet, and Evanoff (2014) find that mandatory mortgage counseling does not achieve the expected change in behavior that regulators hoped for. Agarwal, Liu, Torus and Yao (2014) find that sophisticated households are less likely to pay too high a mortgage rate and more likely to refinance when financially advantageous to do so. This paper is also linked to the literature that studies implications of compensation in the real estate brokerage industry (e.g., Levitt and Syverson 2008; Hsieh and Moretti 2003; Hendel et al. 2009; Han and Hong 2011; Han and Strange 2015). Barwick, Pathak and Wong (2016) analyze the direct consequences of the commission compensation structure. Our paper is also related to th literature on clustering of prices in various markets. Osborne (1962), Nierderhoffer (1965), Harris (1991), Christie and Schultz (1994) document that integerdollar prices are more common than stock prices at half-dollar, quarter or eighths. Goodhart and Curcio (1990) find clustering in foreign exchange markets. Kahn, Pennacchi and Sopranzetti (1999) document that retail deposit interest rates cluster around integers and even fractions. We contribute to this literature by showing that there is clustering in listings of major assets such as housing prices. The remainder of the paper is structured as follows. Section II explains the data and our identification strategy. Section III presents our baseline results. Sections IV and V analyze seller and buyer attributes of those subject to left-digit effects. Section VI examine the heterogeneity in the left-digit effects. Section VII concludes the paper.

II.

Data and Identification Strategy

In this section, we describe the data sources we use, clustering in list price and our identification strategy.

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A.

Data Sources Our primary data source is the listing and sale records from MLS in fourteen largest and diverse

MSAs in the United States. All these MLS are covered in the Case-Shiller Twenty-City Home Price Indices. They represent more than half of housing transactions in the country, with good data coverage since 1990 to date. MLS is the clearinghouse through which realtors in each market advertise the properties for sale to other realtors and more recently, the general public. Although many platforms offer to display and visualize the listing information (e.g., Realtors, Refin, and Zillow), each independent MLS board remains the primary data source for all of them. There are many advantages in using the MLS data. First, they cover virtually every house put up for sale in a local market, regardless whether the house is eventually sold. Therefore, there is selection bias. Second, the data contains detailed information about properties on the market such as their exact location, detailed housing characteristics, initial list price, list date and the date when the house is under contract as well as the contract price. From these information, we can define several variables to measure the listing outcomes from perspectives of listing agents or sellers: SOLD is 1 when the listing ends up with a successful sale; DOM is the days on the market from initial list date to the final contract date; Price is the sale price the property is sold for. Sale price can be also measured as a ratio to initial list price that measures whether the house is sold at premium or discount. Third, each listing is associated with a hired realtor or real estate agent. With their unique id, we can track past performance of individual realtors. Fourth, since property address is geocoded, we can track sales history of individual properties to explore resale returns of the buyers even though we cant link MLS data to public records. There are, however, some important limitations of the MLS data. For example, because the information is typed by the realtors themselves, there is no independent check on the accuracy of the description of the properties, especially when compared to other sources such as public information used by tax assessors or collected by appraisers in the field. As pointed out in other studies, there are substantial amounts of missing data for some variables, such as property age which is one of the most important attributes of propertys condition and market value. Other fields like lot size of the land lack uniform standard regarding units (e.g., square foot vs acre) or precision (e.g., exact number vs. range). Therefore, we restrict our sample to only records with valid data values.

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We also supplement the MLS data with decennial Census information at county level. The purpose is to explore degree of behavior bias by markets delineated by either percent of higher education, minorities or age in the absence of such information at individual level from MLS. MLS data, however, does not provide any information on buyers. We use mortgage data to supplement, which, although not matched to MLS data directly, captures mortgages taken by buyers to finance their home purchases. Our third data is a national representative loan-level mortgage sample from one of the largest mortgage insurers in the country. The data contains detailed information on origination as well as dynamic performance tracked monthly. Our sample covers mortgage origination from 2001 to 2013 with performance updated through 2014. The information at origination includes the borrowers credit score (FICO), loan to value ratio (LTV), debt-to-income ratio, loan purpose, occupancy status (e.g., owner occupied versus investment); property type (e.g., single-family houses, condominiums), the level of documentation (low documentation versus full documentation), loan amount, interest rate type (fixed-rate versus adjustable-rate), and so forth. We restrict our sample to fully-documented and fully-amortized 30-year fixed rate mortgages, which accounts for vast majority of prime conforming loans, in order to focus on the more consistent and pristine mortgage profile. We derive the purchase price from loan amount and LTV given that LTV is the ratio of the two. The derived price here, however, may contain other upfront charges/discounts (e.g., points, closing costs or capitalized items) in some cases. To minimize possible measurement errors, we only keep purchase prices that end at exact $100s (e.g., $279,900 or $278,000), a pattern we observe on list price from MLS data. Each loan is tracked in dynamic files until the borrower defaults or prepays the loan. Default is defined as when the borrower misses at least three consecutive payments, so-called serious delinquency or SDQ. Borrower may prepay the loan for the purpose of moving or refinancing.

B.

Patterns in List or Asking Price Compared to contract price or final close price, the initial list is the pure asking price. The list

price is determined prior to any price concession and financing-related charges demanded by the buyers. Gensove and Mayer (1997) first explore the role of original list price and find that sellers motivation to sell, measured by their equity position, operates primarily through the original list price and variations in it reflect most of the variation in sellers reservation price. With the professional role of listing agent, list price also reflects listing agents best estimate of the most probable selling 7

price subject to sellers reservation price. We first analyze the patterns of list price by decomposing it into left (i.e., mod) and right digits (i.e., reminder) in order to identify any clustering of the right digits. For example, a list price at $359,900 can be decomposed to left digit of $359 (000) and right digit of $900 if divided by 1,000, or left digit of $35 (0,000) and right digit of $9,900 if divided by 10,000, or left digit of 3 (00,000) and right digit of $59,900 if divided by 100,000. The three left digits are exact multiples of 1,000, 10,000 and 100,000 respectively. The density distributions of right digits from dividing the list price by 100,000, 10,000 and 1,000 are plotted in Panels A-C of Figure 1 respectively. Panel A plots the distribution of right digits after we divide the list price by 100,000. Less than 1.5% of all list price are exact multiples of $100,000 (e.g., $300,000) which have right digit exactly at zero. There are less than 9% of list prices whose right digits are exact multiples of $10,000 (e.g., 330,000 or 350,000) and 90% plus of all list prices end up with right digits that are not exact multiples of $10,000 (e.g., 335,000 or 334,000). This suggests right digits of list prices are not clustered at multiples of $100,000 or $10,000. Panel B plots the distribution of right digits when the list price is divided by 10,000. Consistent with Panel A, there are about 9% of list prices clustered around right digits exactly at zero, whose list prices are exact multiples of $10,000 (e.g., $330,000). Another 11% of list prices are clustered around right digits exactly at $9,000 (e.g., $339,000) and 13% of list prices are clustered around right digits exactly at $5,000 (e.g., $335,000). The single most popular category of right digits from dividing by 10,000 lie between 9,000 and 0, which can be anywhere from 9,100 to 9,900 (e.g., $339,100 - $339,900). Panel C plots the distribution of right digits when the list price is divided by 1,000. From the chart, list prices are clearly clustered around right digits at either $900 or $1,000. 76% of right digits of all list prices are either at $900 (e.g., $329,900) or $1,000 (e.g., $330,000), 34% and 41% respectively. Another 7% of list prices end up with right digits at $500 (e.g., $329,500). These three right digits combined account for 83% of all list prices and all ten right digits at exact multiples of $100 collectively account for 88%. The other 12% of list prices have right digits are not at exact multiple of $100 and they can be anywhere from $10 to $90 (e.g., $329,950). This suggests it is most popular to list the property for sale at the price ending with either $900 or $1,000. 8

C.

Identification Strategy Based on the above observed clustering pattern, our identification strategy for analyzing left-

digit effects is focused on only list prices ending with either $900 or $1,000. Comparing two similar list prices, e.g., $329,900 vs $330,000, while the actual difference between two right digits $900 and $1,000 is only $100, the implied left digits of these two right digits can be perceived to differ by a much greater $1,000. The setting is very similar to the penny wise and pound foolish experiments where researchers compare consumers perception and purchase attitude of two products: one priced at $2.99 and the other at $3.00. Although $100 is 10,000 times of one penny, it only accounts for 0.036% of the average list price, much less important than one penny relative to a dollar. We thus explore the possible differences in listing outcomes resulting from buyers perception of much larger left-digit effects with very negligible dollar differences. Because our data contains a large number of listings in housing market, we do so using a regression discontinuity design between two list prices or pairs that are only $100 apart and comparing the listing outcomes within each of these price pairs. By controlling for MSA, list date fixed effects, and an array of property attributes, we create a quasi-experiment that contains two comparable properties that are listed in the same time and same market, and could have been listed at the same price and had similar listing outcomes. But because one is listed $100 lower that leads to a much greater left digit that appears $1,000 lower than the other, they may have different listing outcomes. More formally, to analyze the effect of the left digit on listing outcomes, we run linear regressions of the following form:

Yi,t = β i ∗ Hi + β2 ∗ M SAi + β3 ∗ Y Y M Mt + β4 ∗ Price Pairi + β5 ∗ Price Pairi ∗ Smaller Left Digiti + i,t

Where Yi , t is the listing outcome of individual listed property i in time t; Hi is various property attributes that determine the value of the property such as square foot of the living area, lot size and age of the property; M SAi is the MSA location fixed effects; Y Y M Mi is the list year and month fixed effects to capture the market conditions in local markets. P riceP airi is a large number of fixed effects for every pair of list price that is only $100 apart. For example, a house listed for 9

$329,900 and another listed for $330,000 are defined as the same pair; a house listed for $330,900 and another listed for $331,000 are defined as another same pair. The interaction term of Price Pairi and Smaller Left Digiti indicates the properties listed at smaller left digit, i.e. those listed with right digits at $900 relative to those listed with right digits at $1,000. Thus while captures the common attributes at very fine price level, captures the incremental differences of those that are listed at $100 less that bears possible left-digit effect. We then explore the heterogeneity in the left-digit effects across different market conditions as well as markets with different demographics defined by level of education.

D.

Summary Statistics The key variables used in the analysis are summarized in Table 1. Panel A reports detailed

statistics based on the overall sample. Our sample contains about 7.33 million listings from 1990 to 2014 in fourteen largest MSAs. Among them, about half or 3.53 million listings are sold. By comparing the final contract and original listing, we derive several important listing outcomes: SOLD is an indicator of listing being sold; DOM is the days on market from initial list date to the contract date; Log(Price) is logged contract price; SALE/LIST is the ratio of final contract price to original list price. If SALE/LIST is at 100%, the property is sold at list price; if above 100%, it is sold at premium; if below 100%, it is sold at discount. We restrict our sample to list price ranging between $49,900 and $1,000,000 exclude extreme prices. The average list price is $281,665, of which 48% are sold. The average contract price is $234,627, about 97% of average list price. The average DOM is 68 days or about 2 months. The average house living area is 1,796 square foot, lot size 0.52 acres and property ages round 29.5 years old. The average percent of bachelor or higher education at county level is 28.5% based on Census county data. We also use average DOM in the previous three months in a given zip code to measure the real-time market conditions, which averages at 2 months too. Low DOM indicates an potential overheating market with more demand than supply while high DOM indicates an slow market that takes longer to clear. The overall listings are split exactly 50/50 between smaller left digits and those larger. Panel B of Table 1 compares the characteristics between the two. The average list price for the smaller 10

left-digit subsample is $230,655, only 71% of that for the greater left-digit subsample. This reflects less expensive properties are more likely to be listed at smaller left digits. We plot the share of smaller left-digit listings by decile of list price in Figure 2 plots the patterns of the left-digit listings by price or year. From Panel A we find that about 60% of listings in the lowest four deciles are listed with smaller left digits, the share gradually drops below 50% in 7th decile and further down to 20% in the last decile with the highest list price. The pattern is similar in percentiles as well, i.e., left-digit appear to be more commonly used in the less expensive houses and less so in more expensive houses. However, at any price level, neither smaller nor greater left digits ever accounts for more than 90% of entire market. They coexist in every single market. The same share by year, depicted in Panel B, suggests that listings at smaller left digits are much more popular in early years, declining from 70% of all listings over time to 49% in recent years. There is also variation across different MSAs, though as great as the pattern over time. Back to Panel B of Table 1, the likelihood of listings at smaller left digits being sold is 51.8%, five and half points higher than otherwise. The average DOM is 66.7 months, 3 months shorter than otherwise. Consistent with lower list price, the contract price for smaller left-digit subsample is also lower, but with very similar SALE/LIST ratio. All the other variables including house characteristics and county-level education level as well as prior DOMs in the same zip code are very similar between the two subsamples, suggesting they are comparable properties. Panel C of Table 1 reports overall summary statistics of variables contained in the loan-level sample where we observe information on the borrowers who bought the property listed at smaller or greater left digits. There are 524,369 loans in our sample that are restricted to purchase price between $49,900 and $1,000,000 and also right digits at either $900 or $1,000. These mortgages are conventional, conforming loans (not government insured) made to prime borrowers. Conforming mortgages meet the government sponsored enterprise (GSE) conforming loan limit, which has been $417,000 since 2006 for single-family one-unit properties in most of the U.S with higher limits in high-cost areas. The average note rate of the mortgages is 6.1%. The average FICO of all borrowers is high at 717 since they are all prime conforming loans. 8% of borrowers have FICO below 620. The average LTV is 86.5 with 37% of loans having LTV at and above 90. Borrower on average are aged

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at 40 years old with 43% are younger than 35. The average monthly income is $6,249 and we define those lowest 25% as low income borrowers. 9% of the loans in the sample are for investment purpose opposed to those used for primary residence. 51% of loans are originated by brokers as opposed to those by retail banks. The average backend debt to income ratio that includes monthly mortgage payments is 38%. The average loan amount borrowed is $146,300. With LTV, the derived purchase price is on average at $169,058. In our sample, 35% of borrowers are first-time homebuyers, who may lack of experiences managing their mortgage accounts. 24% of borrowers are non-White minorities who are often underrepresented in credit market. Loans may terminate due to refinancing to a new loan for the purpose of rate savings, default due to adverse events such as unemployment or divorce, or resale in order to move. In our sample, 68% of loans have refinanced by end of 2014 which include both true refinance and a move; 12% of loans defaulted; the others are still active. From public records, we are able to match resale deeds for some movers, who represent 27% of the sample. Of them, the average resale appreciation (or return) is 12.9% over the holding period. The average duration is 59 months or barely 5 years. Compared to the listing sample, our mortgage sample contains much fewer purchases that have smaller left digits, probably due to the fact that the final purchase price computed from loan amount and LTV may differ from the initial listing price due to buyers negotiation, upfront financing charges and other factors following the initial listing. The summary of the key variables are compared between smaller left-digit subsample and those greater ones in Panel D of Table 1. Compared to buyers for the greater left-digit properties, those who buy the smaller left-digit properties have lower FICO (by 10 points), higher LTV (by 2.6 points), younger (by 1.5 years), earn less (by 11%), have higher backend debt ratio, and more likely to be first-timer (by 7 percentage points). Regarding the loan outcomes, their average note rate is 13 basis points (bps) higher, reflecting their relative poor quality. They have much higher default rate, 17% vs 12% for the other subsample. They have slightly less refinancing, 67% vs 69%. In terms of resale outcomes for the movers, their resale appreciation is much lower, 4.8% vs 14% for the other subsample. Their other characteristics are about the same.

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III.

Baseline Results

We first run equation (1) on the entire sample to test if listing at smaller left digits make any difference to listing outcomes. The baseline regression results are reported in Table 2. Columns (1) (3) are regressions of three different listing outcomes on property attributes and list year and quarter fixed effects, but without the location control and price pairs fixed effects. Since the price pairs are not included, the coefficient on smaller left-digit capture both the difference between smaller left-digit listings and their counterparts as well as between low and high list prices, which have different shares of smaller left-digit listings. Columns (4) (6) include both the MSA and list price pair fixed effects. By including list price pair fixed effects, we can test the incremental effects due to the perceived left digits. In both specifications, there are consistent and significant positive effects of listing properties at smaller left digits on sale outcomes: more likely to sale, shorter days on market and higher sale price. The magnitudes from full specification where location and list price are controlled for are much greater. When listed at smaller left digits, although just $100 less, properties are 5.7% more likely to be sold, days on market is 8 days shorter and sale price is actually 0.8% higher than they otherwise would. The higher sales price is equivalent to $1,508 to $2,287 for average contract prices to homeowners in two different subsamples. The gain represent a net 15 to 23 times return on the initial $100 investment. The 8-day savings of days on the market spent by the list agents alone is roughly 12% of the average listing time. Assuming the realtor expects to collect standard commission rate, 3% of sale price, when the property is sold, and annual discount rate of 20% (consistent with Genesove and Mayer 2007; Levitt and Syverson 2008), that is the equivalent of 0.35% of contract price or $662 for the average contract price. In addition, there are also significant benefits from not having to wait longer for final contract and avoiding prolonged uncertainty for homeowners that we cannot monetarize. In the absence of seller constraints, such as those equity-constrained sellers studied by Genesove and Mayer (2007), both the seller and listing agent should be more incentivized to choose to list at smaller left digits.

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IV.

Analysis of Sellers

Our baseline results confirm that it is listing agents and sellers best interest to exploit the left-digit effects. We now explore what determine listing at smaller left digits not otherwise from perspective of sellers. Table 3 reports the linear probability models of whether to list at small left digits on property attributes, list agents past history, seasonality, time, location and price arranges in a multivariate setting. Regression (2) differs from (1) by directly controlling for all the list price pairs as fixed effects instead of linear effect. Figure 3 plots estimated coefficients on price decile and year fixed effects from these regressions. There is a negative relationship between likelihood of listing at smaller left digits and property age as well as lot size, but little relationship with living area. Thus the newer and smaller houses are more considered for the left-digit listing strategy. List agents past performance seems to matter a lot. The more business and higher price they have achieved in the past, the more likely they choose to list at smaller left digits. However, for any realtor who have reasonable business success, no one exercise the left-digit strategy all the time their share of listings at smaller left digits all range between 45% to 55%, suggesting many other factors jointly determine the optimal listing strategy. Consistent with Panel A of Figure 3, there is a negative relationship between listing at smaller left digits and price level. However, there is not much variation in the likelihood for all the list prices below the median (e.g., $228,000). For properties above the median price, chance of using left-digit strategy exponentially declines by 30% through the most expensive price decile. While controlling for the price level, it is increasingly less popular to list at smaller left digit now compared to the 1990s (Panel B of Figure 3). This could be driven by the rapid deployment of new technologies that make the listings much more accessible to the general public. For example, listings used to be an exclusive right for viewing to realtors who pay regular dues. It is now available to almost anyone, free of charge, on applications such as Redfin, Zillow, Realtors and etc. There is also a great variations across different markets while controlling for the time and price. Unlike the raw statistics, there is also some interesting seasonal patterns of adopting the leftdigit strategy while controlling for other factors. It starts high at the beginning of the year and gradually decline through the end of each year. This seems to correlate with the seasonal patterns of market conditions busy from March through June and then slows down from summer through

14

holiday seasons. There is, however, not much information on seller from MLS. Based on Genesove and Mayer (2007)s findings on the listing strategy of sellers with low equity who list higher relative to fundamental value of the property and end up with taking longer to sell, but sell as higher price when sold, homeowners that align with the smaller-left-digit strategy may not be the equity-constrained sellers. The fact they are willing to list at lower price than they otherwise would, suggests that they are more unconstrained.

V. A.

Analysis of Buyers

Ex Post Performance The significant left-digit effects suggest net gains for sellers and listing agents. Does it also suggest

buyers for smaller left digits are subject to consistent behavioral bias? We study this by examining the ex post performance of buyers based on other mortgage outcomes: interest rate they pay on the mortgage used to finance their home purchase, their post-purchase refinance and default outcomes, lastly the resale appreciation when they choose to sell home a few years later. The last outcome is a most direct test on buyers performance related to price if they cannot sell for higher return from resales to compensate for higher price they paid, then the higher price they paid for the home purchase is a behavioral bias. The tests on refinance are used to explore whether buyers for smaller left digits are inattentive to their finances. Specifically, we test whether points takers fail to refinance their mortgages when interest rates decrease. Finding such evidence would support the hypothesis that a lack of financial sophistication among some buyers is the reason that left-digit effects can be exploited by some sellers. Borrowers refinance their mortgages to lower their interest rate or monthly payments. An extensive literature estimates the optimal time for a borrower to refinance. The initial work in this area uses continuous time option valuation models (Dunn and McConnell, 1981). Later studies relax some of the assumptions of the early models, for example by allowing borrowers to endogenously choose to default (Hendershott and Van Order, 1987). Finally, Agarwal, Driscoll, and Laibson (2013) derive a closed-form solution showing that it is optimal to refinance when the refinancing rate is between 100

15

and 200 basis discount points below the original mortgage rate. The actual behavior of mortgage holders sometimes differs from the predictions of the optimal refinancing model. Keys, Pope, and Pope (2014) find that borrowers, in general, refinance their mortgages too late and consequently incur substantial losses. On the other hand, Agarwal, Rosen, and Yao (2015) note that some borrowers error by refinancing too early without getting enough rate savings. We adopt the similar specifications in Equation (1) with additional controls for a full array of borrowers and mortgage attributes including FICO, LTV, investment property, broker-originated loans, backend debt ratio. For default and refinance outcomes, we control for marked-to-market combined LTV as well as interest rate changes from origination date to last performance date, two most important measures of option values that determine the termination decisions. While all the other regressions are estimated on loan-level data, those for refinance are based on loan-quarter panel using a standard Cox hazard model. Agarwal, Ben-David, and Yao (2016) also adopt the similar specification to test for inattentive behavior of points takers. For the buyers who have resold their properties by 2014, we also control for the sale date year and quarter fixed effects so that holding period returns are comparable. Results for these regressions are reported in Table 4. Across different ex post performance measures, buyers who favor the smaller left digits tend to show consistent behavioral bias. Column (1) report the regression of origination note rate on left digits while controlling for a full array of borrower and mortgage attributes. They pay higher interest rate on the mortgages used for financing their home purchases by 2.4 bps. Assuming borrowers hold on to their mortgages for 5 years in average, that implies $176 extra financing costs for an average mortgage. The sample we use for refinance analysis is a panel dataset of all mortgage-quarter. We use Cox hazard model regressions in which the dependent variables are indicators for whether the borrower refinance by end of the performance period. Columns (3) and (4) address the hazard rate of refinancing. Controlling for the potential saving from refinancing, the regression in Column (3) shows that points takers are 17% less likely to refinance than others. When we interact the potential saving with the left-digit indicator, there a strong interaction effect. Buyers for smaller left digits react more slowly to interest rate savings. A lower interest rate change means more savings. The coefficient on the interaction in Column (4) is positive, meaning that it reduces the sensitivity of the hazard

16

of refinancing to the interest rate savings. To see the effects of rate savings and discount points on the hazard of refinancing, consider the following example. Compare two borrowers who can save 1% relative to their original mortgage rate by refinancing. The borrower for larger left digits increases the hazard of refinancing by 38% (= exp(-3.22 * -0.01) - 1). In contrast, the borrower for smaller left digits in the past has a lower hazard of refinancing: 28% (= exp(0.056 + (-3.22 * -0.01) + (0.299 * -0.01)) - 1). The difference is 10% slower. These results are consistent with inattentiveness of borrowers, suggesting that these homeowners are not actively managing their finances and do not make optimal financial decisions. Also when they choose to sell the property later, these buyers tend to have negative return relative to similar houses in the same market that are bought as well as sold in the same time The return is lower by 3.5% for an average holding period of 5 years. This is the equivalent of a loss at $1,285. These results support that buyers of the smaller left-digit listed properties have underperforming outcomes consistently compared to those otherwise.

B.

Who are the Buyers? Given that buyers for smaller left digits have shown consistent behavioral bias, it is important from

a policy standpoint to explore who they are. In our mortgage data, we observe some demographic information about the homeowners at the time of their loan application, including their income, age and race / ethnicity. One possibility is that borrowers lack financial sophistication. For example, borrowers might have the mindset of lowering purchase price; however, they do not properly weight the benefits against the costs involved. Second possibility is unexpected demand. When many buyers prefer smaller left-digit list price, they end up bidding with one another and pushing up the final contract price. Third possibility is that these buyers are liquidity constraint and value the $100 difference very much. To test these predictions, we explore the characteristics of borrowers who buy at smaller left digits. The dependent variable in our analysis is an indicator for whether a borrower bought a house listed at lower left digits. The explanatory variables are mortgage and borrower characteristics at the time of origination as well as loan application. The results are presented in Table 5. The regressions show that the most important predictor of buying smaller left-digit listings is the high LTV indicator 17

for those who do not have enough money to put down more downpayment. Borrowers with low credit score as well as those first-time homebuyers are also more likely to prefer listings at smaller left digits when buying their homes. They generally lack of experience managing their credit and mortgage accounts. Third set of significant characteristics are younger homebuyers who just started to enter homeownership as well as the minorities who are generally underrepresented in access to credit and housing. These findings are consistent with the existing literature that studies financial mistakes household make (e.g., Calvet, Campbell and Sodini 2009; Agarwal, Liu, Torous and Yao 2016).

VI.

Heterogeneity in the Left-Digit Effects

Although there are significant left-digit effects on sale outcomes based on overall sample, we next explore the heterogeneity in the left-digit effects across different cohorts, including price level, calendar month, calendar year, geographic regions, housing market conditions, and average level of education in order to nail down intertwining relationship among realtors, sellers, buyers and various constraints. The estimated left-digit effects by various cohorts are plotted in Figures 4 7 as well as reported in Table 6.

A.

Price Levels Figure 4 show great variations of left-digit effects across price levels. Panel A suggests that left-

digit listings has the highest effect on sale likelihood among the least expensive houses (e.g., those below $10,000) and the effect is significant but similar elsewhere. Panels B-D, however, suggest while the effect on sale likelihood is the greatest in the lowest price decile, the effects on other outcomes are actually worse. The effect on days on the market in the lowest price decile is about the same as the overall effect, but much smaller than more expensive homes especially those in the last decile which include properties listed at $554,900 or higher. The left-digit effect on sale price in the first decile is actually the lowest among all, suggesting while smaller left-digit listings may help sell the cheap houses sooner, it could not sell at enough gains to even offset the $100 cost. Houses in the other 90% market see significant more left-digit effects on days on the market and sale price. The left-digit effect on sale price is higher for more expensive homes especially those above 18

the median price so these sellers are more motivated to exploit left-digit strategy. Effect on days on the market, which is the primary incentive for the list agents since they can earn the pre-negotiated commission in shorter time, are also higher for more expensive houses except for the most expensive ones possibly because the most luxurious homes are more illiquid. Then why is share of listing at smaller left digits less popular as the price increases? Maybe the $100 difference as a percentage of list price is much smaller for more expensive homes that fewer sellers would believe its effects. Maybe there are other factors that limit the left-digit effects.

B.

Seasonality Residential real estate market is well known for its seasonal pattern. Figure 5 shows that markets

are generally slow (e.g., fewer listings and higher days on market) after August especially around holiday seasons, and resume busy from March till when the summer vacation begins. The seasonality reflects the timing of family planning and school calendars. The left-digit effects are much greater in slow seasons than in busy seasons. Listings at smaller left digits are more likely to be sold , stay on the market shorter and sell for higher sale prices in September through next February.

C.

Time We discussed in Sections II and III that left-digit strategy was more popular in early years. To

isolate different time-varying factors, Figure 6 shows housing market conditions vary by years can be broadly classified into four distinct phases: markets grow increasingly tight from 1990s through 2000 as stipulated by various national homeownership initiatives; markets remain very tight in early 2000s during the unprecedented housing boom with very low days on market and high sales to list ratio; markets are generally depressed during the foreclosure crisis from 2007 through 2011 and have recovered since then. Because we only observe the sale outcomes by end of 2014, data for 2014 listings is censored. The estimated left-digit effects vary significantly by housing cycles. There is a large swing in the effects on sale likelihood as well as days on the market. When there is a potential oversupply issue in the market characterized of longer time on the market, the left-digit effects are usually the strongest. Average effects on sale likelihood in 2009-2010 are about 2-3 times of that in late 1990s and early 19

2000s. Average effects on days on the market in the same three years are about 3-5 times of that in other years. The effects on sale price are significantly greater in early years but not significant in years after 2010. This may be attributable to the strong recovery in some housing markets following the foreclosure crisis.

D.

Education Our analysis of buyers suggests that buyers for the smaller left digits are subject to consistent

behavior bias related to many financial decisions. To explore the role of education, we run the baseline regression by level of education measured by percent of bachelor or higher degree at the county level from U.S. Census. The entire sample is divided in thirds equally based on the level of education, but we only report the results for top and bottom thirds in Panel A of Table 6 to save space (full results are available in online Appendix). The left-digit effects on sale likelihood is higher in less educated markets where there are more less-educated people the effect is 6.6% more likely to be sold, almost twice as that in more educated markets. Consistently the left-digit effects on days on the market is also higher in less educated markets the effect is 9.3 days shorter on the market, more than twice of more educated places. However, the left-digit effects on price are greater in the more educated places where most expensive houses are located.

E.

Housing Market Conditions As we have shown above, the left-digit effects have a great deal to with housing market conditions

either by time or location. We explore this further by estimating the baseline regressions by real-time market conditions measured by the days on the market in prior three months in the zip code where properties are located. The entire sample is divided in thirds equally based on the prior days on the market, but we only report the results for top and bottom thirds in Panel B of Table 6. The left-digit effects on sale likelihood is higher in the softer markets characterized of longer days on the market the effect is 7.1% more likely to be sold, more than twice as that in the tighter markets where it take shorter days on the market to sell. Consistently the left-digit effects on days on the

20

market is also much greater in the softer markets the effect is 14.8 days shorter on the market, more than eight times of more tight markets. Also, the left-digit effects on price and sale to list ratio are greater in the softer markets. The estimated effect on sale price is 0.9% in soft markets, higher than only 0.6% in the tight markets.

F.

House Characteristics Certain houses are more conforming than others in a given market. We also find from the analysis

above that new and smaller lot are more likelihood to be listed at smaller left digits. We next run the baseline regressions by different house characteristics. The entire sample is divided in thirds equally based on gross living area. Results for top and bottom thirds are reported in Panel C of Table 6. There is significant, but not as great variation in estimated left-digit effects across different house characteristics. The left-digit effects on SALE likelihood is higher for smaller houses the effect is 6.3% more likely to be sold, about 1.5 times as that for the larger houses. Consistently the left-digit effects on days on the market is also much greater for smaller houses the effect is 8.2 days shorter on the market, about 0.7 days shorter than larger houses. However, the left-digit effects on price are greater for the larger houses, 1.1% higher relative to 0.4% higher for the small houses.

VII.

Conclusion

In this paper, we analyze the role of behaviorial biases in housing transactions. The extant literature (Rosch 1975 and subsequent work) has shown that people use cognitive reference points, i.e. standard benchmarks against which other stimuli are judged. One manifestation of these cognitive reference points is the left digit effect, where in, a change in the left-digit of a price causes people to move from one cognitive reference point to another. For example, $3.99 is perceived to be significantly less than the $4.00 because the left digit dominates and it is considered not just as one penny less, the so called, penny wise, dollar foolish phenomenon. In this paper, using MLS data, we document a significant clustering in the house listing prices with 76% of right digits of all list prices are either at $900 or $1,000, 34% and 41% respectively. We use this clustering as quasi-experiment setting, where two similar properties are identical in property attributes, list date and location, but that are listed $100 apart, say $329,900) and $330,000). We 21

find that properties listed at smaller left digits, compared to very similar properties that are listed $100 more (but perceived to be more expensive), are 5.7% more likely to sale, stay on the market shorter by 8 days and are sold at higher price by 0.8%. We also find that these left-digit effects are more pronounced in softer housing markets, as defined by zipcodes with higher average days on the market, as well as markets there are lots of less-educated people based on Decennial Census. Further, we examine the subsequent mortgage and resale transactions of the buyers of the leftdigit listed properties. In line with their purchase decisions, we find that buyers of left-digit listed homes pay higher interest rate on their mortgages, receive a lower return on a resale, and are more likely default and more sluggish refinancing their mortgages. In addition, we find that in general, buyers of left-digit listed properties are more likely to be minorities, younger, liquidity-constrained, low credit score, and less financially sophisticated. These findings are consistent with the existing household finance literature that documents mistakes in household financial decision making and find lack of financial sophistication contributes to these mistakes. Our results highlight how behavioral biases can affect even significant and high value purchases such as housing. It appears that even in significant and large value transactions such as housing, home buyers make penny wise, dollar foolish mistakes.

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Figure 1: Clustering in List Price A. Distribution of Right Digits from List Price / 100,000 We plot the relative frequency of right digits from list price / 100,000 to identify any evidence of clustering. Right digits are the reminder from list price / 100,000. Y axis is the relative frequency. The chart shows no significant clustering in the right digits from list price / 100,000.

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B. Distribution of Right Digits from List Price / 10,000 We plot the relative frequency of right digits from list price / 10,000 to identify any evidence of clustering. Right digits are the reminder from list price / 10,000. Y axis is the relative frequency. The chart shows some clustering in the list price ending with between $9,000 and $10,000.

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C. Distribution of Right Digits from List Price / 100,000 We plot the relative frequency of right digits from list price / 1,000 to identify any evidence of clustering. Right digits are the reminder from list price / 1,000. Y axis is the relative frequency. The chart shows a significant clustering in the list price ending with between $900 and $1,000.

29

Figure 2: Patterns of Left-Digit Listings A. Percent of Left-Digit Listings by Price We plot the percent of listings at smaller left digits, as defined as those list price ending with $900, by list price deciles. The percentage numbers in the figure are the raw statistics based on data. There are two types of listings in the sample: one list price ending with $900 and the other ending with $1,000. Data is based on the all listings in 1990-2014 from MLS in fourteen largest MSAs in the country.

30

B. Percent of Left-Digit Listings by Year We plot the percent of listings at smaller left digits, as defined as those list price ending with $900, by list year. The percentage numbers in the figure are the raw statistics based on data. There are two types of listings in the sample: one list price ending with $900 and the other ending with $1,000. Data is based on the all listings in 1990-2014 from MLS in fourteen largest MSAs in the country.

31

Figure 3: Analysis of Seller and Listings A. Estimated Probability of Left-Digit Listings by Price We plot the estimated coefficients on price levels from a linear probability model that control for many listing information. The dependent variable is 100 if listing is at smaller left digits and 0 otherwise. Right-hand sided variables include list price, property age, living area, lot size, sale to list ratio of the list agent in the past one year, number of sales of the list agent in the past one year, MSA fixed effects, year fixed effect effects and quarterly dummies. The purpose of the regression is explore what listings are more likely to be listed at smaller left digits vs otherwise.

32

B. Estimated Probability of Left-Digit Listings by Year We plot the estimated coefficients on year fixed effects from a linear probability model that control for many listing information. The dependent variable is 100 if listing is at smaller left digits and 0 otherwise. Right-hand sided variables include list price, property age, living area, lot size, sale to list ratio of the list agent in the past one year, number of sales of the list agent in the past one year, MSA fixed effects, year fixed effect effects and quarterly dummies. The purpose of the regression is explore what listings are more likely to be listed at smaller left digits vs otherwise.

33

Figure 4: Left-Digit Effects by Price A. Effect on Sale Likelihood This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is SOLD, defined as 100 if listing is sold and 0 otherwise. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on sale likelihood. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

34

B. Effect on Days on the Market This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is DOM, defined as number of days from initial listing to contract date. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on days on the market. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

35

C. Effect on Sale Price This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is logged sale price. Righthand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. Coefficients can be interpreted as the percentage difference in prices. The purpose of the regression is explore whether there is any effect of left-digits on sale price. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

36

D. Effect on Sale to List Price Ratio This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is sale to list ratio x 100, defined as ratio of sale price to list price multiplied by 100. They are above 100 if the property is sold above the list price and below 100 if sold below list price. This is a measure of sale success relative to initial list price. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on sale to list ratio. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

37

Figure 5: Left-Digit Effects by Calendar Month A Seasonal Patterns of Market Conditions The numbers in the figure are the raw statistics based on data. The bars are relative frequency of listings in each month, which add up to 100. The line chart is the average days on the market by calendar month.

38

B. Effect on Sale Likelihood This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is SOLD, defined as 100 if listing is sold and 0 otherwise. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on sale likelihood. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

39

C. Effect on Days on the Market This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is DOM, defined as number of days from initial listing to contract date. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on days on the market. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

40

D. Effect on Sale Price This figure is based on estimated coefficients on listings at smaller left digit dummy from ten OLS regressions by price decile. The dependent variable is logged sale price. Righthand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. Coefficients can be interpreted as the percentage difference in prices. The purpose of the regression is explore whether there is any effect of left-digits on sale price. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

41

Figure 6: Left-Digit Effects by Year A. Market Conditions Over Time The numbers in the figure are the raw statistics based on data. The blue line chart is the average days on the market by list year and the orange line chart s the average sale to list ratio by list year. Two series are used to gauge the market conditions. A market is tight when the days on the market is short and sale to list ratio is higher. A market is cold when the days the market are long and sale to list ratio is lower. Data is the complete listings from MLS data in fourteen largest MSAs in the country.

42

B. Effect on Sale Likelihood This figure is based on estimated coefficients on listings at smaller left digit dummy from many OLS regressions by list year. The dependent variable is SOLD, defined as 100 if listing is sold and 0 otherwise. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on sale likelihood. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

43

C. Effect on Days on the Market This figure is based on estimated coefficients on listings at smaller left digit dummy from many OLS regressions by list year. The dependent variable is DOM, defined as number of days from initial listing to contract date. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on days on the market. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

44

D. Effect on Sale Price This figure is based on estimated coefficients on listings at smaller left digit dummy from many OLS regressions by list year. The dependent variable is logged sale price. Righthand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. Coefficients can be interpreted as the percentage difference in prices. The purpose of the regression is explore whether there is any effect of left-digits on sale price. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

45

Table .1: Summary Statistics A. Overall MLS Sample This table reports the summary statistics based on overall MLS sample. Please refer to Data section for data definitions. Data is the complete listings in 1990-2014 from MLS data in fourteen largest MSAs in thecountry. Variable List Price SOLD DOM Contract Price SALE/LIST Square Foot Lot Size Property Age Pct of Bachelor Degree or Higher DOM in Prior 3 Months Smaller LeftDigit

N 7330589 7330589 3529555 3910630 3529555 7330589 7330589 7330589 7322754 7256041 7330589

mean 281665 48 69 234627 97 1796 22410 29 28 67 .47

Source: MLS Sample

46

sd 188446 50 85 181454 9.6 890 56279 20 7.7 31 .5

min 49900 0 -3619 0 .0001 0 0 -21 9 -187 0

p25 143900 0 16 114900 95 1190 6534 12 25 45 0

p50 228000 0 44 189900 98 1597 10019 27 28 64 0

p75 369900 100 91 320000 100 2218 23158 46 34 83 1

max 999000 100 5071 2000000 2022 19970 999266 84 52 674 1

B. MLS Sample Comparison This table reports the summary statistics based on overall MLS sample by smaller and larger left digits. Smaller left digits are the listings with price ending with $900 and larger left digits are those with price ending with $1,000. Please refer to Data section for data definitions. Data is the complete listings in 1990-2014 from MLS data in fourteen largest MSAs in the country. Variable List Price SOLD DOM Contract Price SALE/LIST Square Foot Lot Size Property Age Pct of Bachelor Degree or Higher DOM in Prior 3 Months Smaller LeftDigit

Larger Left Digit mean sd 326665 209589 45 50 71 92 284794 203911 97 10 1856 934 23423 58792 30 20 0 0 28 7.2 66 33

Source: MLS Sample

47

Smaller Left Digit mean sd 231137 145725 52 50 67 77 187765 142459 97 9.3 1729 833 21272 53293 29 20 1 0 28 8.2 68 30

C. Overall Mortgage Sample Tables C and D report the summary statistics based on overall loan-level sample from a national entity. Please refer to Data section for data definitions. Data is a nationally representative sample that contains mortgages used to finance home purchases in 1990-2014 in the country. These are restricted to fully documented and fully amortized 30-year mortgages. All the purchase prices, calculated from LTV and loan amount, are restricted to those ending with 900and$1, 000. Variable N mean sd min p25 p50 p75 max Note Rate 524369 6.1 1 2.7 5.5 6.3 6.8 14 FICO 524369 717 62 300 674 726 768 899 FICO ≤ 620Indicator 524369 .077 .27 0 0 0 0 1 LTV 524369 87 11 4 80 80 95 120 LTV ≥ 90Indicator 524369 .37 .48 0 0 0 1 1 Borrower Age 524369 40 13 18 30 38 48 99 Age ≤ 35Indicator 524369 .43 .5 0 0 0 1 1 Monthly Income 524369 6249 6097 406 3575 5116 7397 1213427 Low Income Indicator 524369 .25 .43 0 0 0 0 1 Investor Indicator 524369 .088 .28 0 0 0 0 1 Broker Indicator 524369 .51 .5 0 0 1 1 1 Backend ratio 524369 .38 .13 .0001 .29 .37 .45 1 Loan Amount 524369 146300 63736 7500 99200 134900 180000 417000 First-time Homebuyer 524369 .35 .48 0 0 0 1 1 Minority 467139 .24 .43 0 0 0 0 1 Refinance 524369 .68 .46 0 0 1 1 1 Default 524369 .12 .33 0 0 0 0 1 Duration (months) 524369 55 38 0 24 45 78 179 Resale Appreciation 143787 13 48 -99 -6.7 9.4 31 6548 Resale Duration 143787 59 36 1 30 53 83 168 Smaller LeftDigit 524369 .11 .31 0 0 0 0 1 Source: Mortgage Sample

48

D. Mortgage Sample Comparison Larger Left Digit Smaller Left Digit Variable mean sd mean sd Note Rate 6.1 1 6.2 .96 FICO 718 62 707 65 FICO ≤ 620Indicator .074 .26 .1 .3 LTV 86 11 89 11 LTV ≥ 90Indicator .36 .48 .49 .5 Borrower Age 40 13 39 13 Age ≤ 35Indicator .42 .49 .48 .5 Monthly Income 6318 6225 5690 4905 Low Income Indicator .24 .43 .29 .45 Investor Indicator .092 .29 .055 .23 Broker Indicator .52 .5 .49 .5 Backend ratio .37 .13 .39 .13 Loan Amount 146818 63965 142104 61689 First-time Homebuyer .34 .47 .41 .49 Minority .24 .43 .24 .43 Refinance .69 .46 .67 .47 Default .12 .32 .17 .37 Duration (months) 54 38 58 38 Resale Appreciation 14 50 4.8 37 Resale Duration 59 37 60 34 Source: Mortgage Sample

49

Table .2: Baseline Results on Listing Outcomes This table reports the baseline results on the left-digit effects on sale outcomes. Please refer to Data section for data definitions. All the regressions are OLS regressions. The dependent variable is column title. DOM and Log(Sale Price) are only available for sold listings. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is any effect of left-digits on sale outcomes. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

Smaller Left Digit Property Attributes List YYQQ FE MSA FE List Price Pairs N adj. R2 t statistics in parentheses;

(1) SOLD 2.500∗∗∗ (69.96) Yes Yes No No 7128229 0.116 ∗

p < 0.10,

(2) DOM -4.199∗∗∗ (-47.62) Yes Yes No No 3436714 0.060 ∗∗

p < 0.05,

(3) Log(Price) -0.277∗∗∗ (-390.44) Yes Yes No No 3439081 0.231 ∗∗∗

50

p < 0.01

(4) SOLD 5.695∗∗∗ (31.38) Yes Yes Yes Yes 7128229 0.158

(5) DOM -8.414∗∗∗ (-24.31) Yes Yes Yes Yes 3436714 0.081

(6) Log(Price) 0.008∗∗∗ (4.28) Yes Yes Yes Yes 3439081 0.712

Table .3: Characteristics of Sellers This table reports the results on the listing profiles of those ending with $900. Please refer to Data section for data definitions. All the regressions are OLS regressions. The dependent variable is left-digit dummy x 100. Right-hand sided variables include list price pair fixed effects or list price as continuous variable, property age, living area, lot size, average sale to list ratio of the list agent in the past year, total sales of the list agent in the past year, MSA fixed effects, year fixed effect effects, quarterly dummies. The purpose of the regression is explore what listings are more likely to be listed at smaller left digits. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

List Price (000s) List Agent’s SALE/LIST Ratio Last Year List Agent’s Sales Last Year Seasonal Effect: 1st QTR Seasonal Effect: 2nd QTR Seasonal Effect: 3rd QTR Seasonal Effect: 4th QTR Property Attributes List Year FE MSA FE Price Pairs N adj. R2 t statistics in parentheses;

∗

p < 0.10,

∗∗

p < 0.05,

51

(1) (2) Smaller LeftDigit x 100 -0.057∗∗∗ (-288.86) 0.896∗∗∗ 0.904∗∗∗ (33.29) (9.23) 0.271∗∗∗ 0.057∗∗ (13.91) (2.00) ∗∗∗ 0.530 0.630∗∗∗ (7.53) (8.58) 0.322∗∗∗ 0.330∗∗∗ (4.66) (4.43) 0.206∗∗∗ 0.154∗∗ (2.90) (2.21) 0.000 0.000 (.) (.) Yes Yes Yes Yes Yes Yes No Yes 4002716 4002716 0.131 0.328 ∗∗∗

p < 0.01

Table .4: Ex Post Performance of Left-Digit Buyers This table reports the results on the ex post performance of mortgage outcomes of buyers. Please refer to Data section for data definitions. All the regressions are OLS regressions. The dependent variable is the column title. Right-hand sided variables include list price pair fixed effects, left-digit dummy, LTV, borrower FICO, investment property dummy, loans originated by broker dummy, backend debt to income ratio, MSA fixed effects, origination year and month fixed effect. For default and refi regressions, regressors also include marked to market CLTV, positive interest rate change, negative interest rate change, all measured from origination to last month. For resale return regression, sale date year and quarter fixed effects are controlled since the dependent variable is the total holding period return. The purpose of the regressions is explore if the buyers have behavioral bias consistently across all mortgage outcomes. Data is a nationally representative sample. Regressions of rate, default and resale return are all based on loan level data while two regressions of refi are based on loan-quarter panel data. Please refer to data section for sample restrictions. Standard errors are clustered around zip codes.

Smaller LeftDigit

(1) Rate 0.024∗∗∗ (12.49)

(2) Default 1.063∗∗∗ (-5.39) 0.383∗∗∗ (58.32) 2.836∗∗∗ (7.83) -1.541∗∗∗ (-14.63)

(3) Refi -0.172∗∗∗ (-7.61) -0.067∗∗∗ (-114.22) -0.552∗∗∗ (-15.16) -3.179∗∗∗ (-145.92)

Yes Yes YYMM MSA Yes

Yes Yes YYMM MSA Yes

Yes Yes YYQQ State Yes

(4) Refi 0.056∗∗ (2.08) -0.067∗∗∗ (-114.30) -0.549∗∗∗ (-15.10) -3.218∗∗∗ (-144.66) 0.299∗∗∗ (9.88) Yes Yes YYQQ State Yes

524369 0.847

285234 0.222

6730951 0.023

6730951 0.023

MtM CLTV Positive Rate Change Negative Rate Change x Smaller LeftDigit Borrower Attributes Mortgage Attributes Time FE Location FE Price Pairs Sale YYQQ FE N adj. R2 t statistics in parentheses;

∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

52

p < 0.01

(5) Resale Return -3.807∗∗∗ (-12.61)

Yes Yes YYMM MSA Yes Yes 143787 0.298

Table .5: Characteristics of Left-Digit Buyers This table reports the results on the demographics of buyers for the properties listed at smaller left digits. Please refer to Data section for data definitions. All the regressions are OLS regressions. The dependent variable is left-digit dummy x 100. Right-hand sided variables include list price pair fixed effects, high LTV dummy, low FICO dummy, young household dummy, low income dummy, first-time homebuyer dummy, minority borrower dummy, investment property dummy, loans originated by broker dummy, backend debt to income ratio, MSA fixed effects, origination year and quarter fixed effect. The purpose of the regressions is explore profile of the buyers for the smaller left digits. Data is a nationally representative sample. Please refer to data section for sample restrictions. Standard errors are clustered around zip codes.

FICO ≤ 620Indicator LTV ≥ 90Indicator Age ≤ 35Indicator Low Income Indicator First-time Homebuyer Minority Mortgage Attributes Origination YYQQ FE MSA FE Price Pairs N adj. R2 t statistics in parentheses;

∗

(1) (2) Smaller LeftDigit x 100 1.079∗∗∗ 1.027∗∗∗ (6.20) (5.33) ∗∗∗ 3.851 3.841∗∗∗ (37.03) (34.23) 0.505∗∗∗ 0.607∗∗∗ (5.22) (6.29) 0.264∗∗ -0.163 (2.37) (-1.28) ∗∗∗ 1.068 1.059∗∗∗ (10.11) (9.91) ∗∗∗ 0.885 0.819∗∗∗ (7.74) (6.82) Yes Yes Yes Yes Yes Yes No Yes 467139 467139 0.034 0.077 p < 0.10,

53

∗∗

p < 0.05,

∗∗∗

p < 0.01

Table .6: Table 6 Heterogeneity in Left Digit Effects The three tables report the results on the left-digit effects on sale outcomes by three different classifications of the MLS sample. Please refer to Data section for data definitions. All the regressions are OLS regressions. The dependent variable is column title. DOM and Log(Sale Price) are only available for sold listings. Right-hand sided variables include list price pair fixed effects, left-digit dummy, property age, living area, lot size, MSA fixed effects, year and quarter fixed effect effects. The purpose of the regression is explore whether there is more or less effect of left-digits on sale outcomes in different subsamples. Data is the complete listings from MLS data in fourteen largest MSAs in the country. Standard errors are clustered around zip codes.

Smaller LeftDigit Property Attributes List YYQQ FE MSA FE List Price Pairs N adj. R2 t statistics in parentheses;

A. Level of Education (1) (2) (3) (4) (5) (6) Low-Education Counties High-Education Counties SOLD DOM Log(Price) SOLD DOM Log(Price) 6.582∗∗∗ -9.305∗∗∗ 0.003∗∗∗ 3.377∗∗∗ -4.262∗∗∗ 0.015∗∗∗ (23.11) (-22.35) (4.13) (15.85) (-12.09) (3.36) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 2771696 1260754 1260754 2336326 1131271 1131271 0.142 0.093 0.862 0.169 0.090 0.458 ∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

54

p < 0.01

Smaller LeftDigit Property Attributes List YYQQ FE MSA FE List Price Pairs N adj. R2

B. Market Tightness (1) (2) (3) (4) (5) (6) Low-DOM Zip Codes Low-DOM Zip Codes SOLD DOM Log(Price) SOLD DOM Log(Price) ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ 2.595 -1.788 0.006 7.063 -14.821 0.009∗∗∗ (13.81) (-9.66) (2.45) (29.06) (-22.48) (5.43) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 2372822 1086156 1086156 2338493 1150928 1150928 0.266 0.054 0.754 0.118 0.041 0.713

t statistics in parentheses;

Smaller LeftDigit Property Attributes List YYQQ FE MSA FE List Price Pairs N adj. R2 t statistics in parentheses;

∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

p < 0.01

C. Different House Size (1) (2) (3) (4) (5) (6) Small Houses Large Houses SOLD DOM Log(Price) SOLD DOM Log(Price) 6.314∗∗∗ -8.243∗∗∗ 0.004∗∗∗ 4.379∗∗∗ -7.530∗∗∗ 0.011∗∗∗ (26.92) (-23.35) (4.64) (22.60) (-14.40) (3.54) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 2376475 1175810 1176453 2321334 1048016 1048421 0.161 0.080 0.836 0.155 0.079 0.444 ∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

55

p < 0.01