## Abstract

We explore the questions of why Real Estate Investment Trusts (REITs) pay more for real estate than non-REIT buyers and by how much. First, we develop a search model where REITs optimally pay more for property because (1) they are willing, due to cost of capital advantages and, (2) they are occasionally rushed, due to external regulatory time constraints and internal incentives to deploy capital quickly. Second, using commercial real estate transactions, we find that the extant hedonic pricing models contain an unobserved explanatory variables bias leading to inflated estimates of the REIT premium. Third, using a repeat-sales methodology that controls for unobserved property characteristics, we derive more plausible estimates of the REIT premium. Consistent with our model, we also find the REIT-buyer premium depends on the size of the REIT advantage, the rush to deploy, and the relative presence of REITs in the market.

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## Notes

Search in the presence of deadlines is also a feature of labor market models where unemployment benefits are withdrawn after a deadline. See Akin and Platt (2012) for a survey of the labor market findings.

In 2010, the Getty Museum beat five other bidders to buy William Turner’s “Modern Rome—Campo Vaccino” for nearly $50 million, setting a record for the British artist’s paintings.

For example, REITs could buy retail properties with better ingress, apartments with nicer swimming pools, offices with grander views, and industrial properties with higher ceilings. These characteristics are typically not reported in common sources of transaction data.

Internal Revenue Code, 856(c)(4)

Internal Revenue Code, 856(c)(3)

Internal Revenue Code, 856(c)(5)(B)

Brandon (1998) and Graff (2001) discuss REIT tax issues. Failure to meet the quarterly asset and income requirements can lead to a loss of REIT status. However, Internal Revenue Code, 856(c)(6) and 856(c)(7) allow for REITs who missed just one quarter to retain their status if the failure is due to “reasonable cause” and the REIT takes corrective action, which can include a tax, a penalty, or the selling of “offending” assets.

In practice, REIT managers could satisfy the time constraint by parking money in, say, Fanny Mae securities. This strategy has the same internal costs as holding cash.

Search models include Yavas (1992); Sirmans et al. (1995); and Lambson et al. (2004). The last is most closely related to our paper. In contrast to our paper, Lambson et al. (2004) assume an exogenous price distribution and buyers that differ in their outcomes because some have (permanently) higher search costs and thus a higher reservation price. This disadvantage does not change over time.

Although we model buyer and seller behavior, we do not model an endogenous choice to enter the market (as a seller, a REIT, or a non-REIT). Sellers exogenously enter the market, being unable to manage their offered property. REITs have a clear advantage over non-REITs, but the latter are unable to change their status to the former, perhaps due to legal hurdles.

Horowitz (1992) finds a monotonic (and hence invertible) relationship between asking and purchase prices, suggesting that which is used is immaterial to the analysis.

Arnold (1999) shows that in practice, when a seller lists a higher price in the MLS, some buyers will not even bother investigating the property further since it would require significant negotiation to bring the price to an acceptable range. This reduces the likelihood that the seller encounters an interested buyer in a given period.

Each buyer’s purchase represents one deployment of new capital. A REIT may hold multiple investments, but we do not need to track these holdings since we do not model any interaction among them.

In practice, the consequences can be more severe, including losing REIT status on all properties rather than just the newly-deployed capital. Larger penalties will strengthen the two-price equilibrium presented, creating a wider gap between the prices.

Our model assumes an infinite horizon; the market is expected to exist for infinitely many time periods. The infinite horizon need not be interpreted literally. If a strictly positive probability that the market will function for another period exists, say \( \sigma \in \left( {0,1} \right) \), then the probability can be wrapped into the discount factor, \( \beta \in \left( {0,1} \right) \), so that \( \beta = \sigma /(1 + \rho ) \) where \( \rho \in [0,\infty ) \) is a rate of time preference.

We assume that the market for construction is perfectly competitive so that a seller can only obtain new properties at cost

*x*, which is equal to the expected revenue from sale. Under this assumption, tracking the steady-state population of sellers is unnecessary. Since sellers are indifferent about entering the market, we can assume they enter at whatever rate is needed to ensure that every buyer will encounter one seller each period.CoStar Group Inc. investigates, records, and sells commercial property transaction data after confirming the details of the transaction with the relevant parties, including the buyer, seller, and broker. We thank CoStar for their generous assistance with the data.

Before analyzing the data, we eliminate transactions with missing or questionable values. Specifically, we drop 12,700 observations with inconsistent building square feet; 21,433 condominium conversions; 7,243 non-conventional CoStar property type labels (flex, healthcare, hospitality, specialty, and sports/entertainment); 67,903 observations that have missing data on critical variables, i.e., sales price, building age, building area, and land area; 202 unusual sales conditions such as property contamination or auction sale; 3,716 observations with questionable price data (price per square foot less than $20 or greater than $2,500), and 5 observations with comments indicating the recorded price pays for more than the recorded property. The remaining dataset contains 139,527 observations.

The test computes the integrated squared density difference between the estimated densities/probabilities of two samples having identical variables/data types. We used 999 bootstrap replications for each of the five variables under scrutiny, and the bandwidths used for each density are standard rule of thumb bandwidths. See Li et al. (2009) for further details.

Ling and Petrova (2009) truncate their sample at a sales price of $500,000. In practical terms, our 20,000 square foot conditioning translates into a cut-off price of $405,000. We use building size rather than price because price is our dependent variable. All of our results are slightly stronger if we use all 139,527 observations, rather than just the 33,252 largest properties.

Hardin and Wolverton (1999) empirically examine acquisition premiums by REITs in Atlanta, Phoenix, and Seattle. They find that REITs paid a statistically significant premium of 21.6 % in Atlanta and a premium of 27.5 % in Phoenix; however, they find no evidence of a REIT premium in Seattle. Lambson et al. (2004) also find a substantial overpayment for apartment properties by REITs in the Phoenix market, and Ling and Petrova (2009) find strong empirical support for a REIT buyer premium in nine large metropolitan areas.

Clauretie and Thistle (2007) find that evidence for the search cost and anchoring explanations for the buyer-out-of-state premium weakens after accounting for time on the market and exact location. Ong et al. (2006), and Benjamin et al. (2008) use out-of-town or out-of-state variables in their studies of foreclosure and condo conversions, respectively.

Bank sales were identified by matching the names of the sellers of each transaction to a list of financial institutions.

Clapham et al. (2006) review four approaches to creating house price indices. Their purpose is not to investigate a REIT-buyer premium; rather, it is to compare and contrast the stability of each index as data is added over time.

Repeat transactions control for unobserved tangibles but not necessarily intangibles. The observed REIT buyer premium could arise if zoning and tenant leases were consistently more valuable when the REITs bought the property compared to when the same property was purchased, either earlier or later in time, by a non-REIT. However, this would require that REITs were systematically more likely to purchase properties after favorable zoning changes or advantageous new leases and sell them after unfavorable changes.

The coefficient on the

*REITBUYER*variable can be transformed into an indication of the percentage of price increase by using the relationship PERCENT INCREASE\( = 100\left[ {{e^{{0.261}}} - 1} \right] \) or 29.8 % (Halvorsen and Palmquist 1980).We start testing for robustness across years in 1991 because of insufficient data (not full rank) in the first 2 years (1989 and 1990), particularly for Clark County, Nevada. We also checked for robustness using finer spatial resolution and shorter horizons for our market condition (time) dummies. Using cities, rather than counties, and using quarters, rather than years, has little if any effect on the REIT buyer premium. Additionally, when we included all 139,527 observations (no conditioning on building size) the REIT coefficient is 0.460 (

*p*-value less than 0.0001).Ling and Petrova (2011) document another advantage of being public—a higher probability of becoming a purchase target.

Examination of a smaller, but more complete, dataset of apartments in the Phoenix metro area supports our suspicion about unobserved explanatory variables. The Phoenix data include explanatory variables not available in our full dataset such as clubhouse, swimming pool, on-site laundry facility, tennis courts, and a ranking of condition. In this subsample, the properties purchased by REITs have, on average, more club houses, swimming pools, laundry facilities, tennis courts, and were more likely to be in CoStar’s superior condition category. Thus in this subsample, one reason REITs pay an apparent

*price premium*is because they buy*premium property*.Estimating the modified repeat-transaction model for each property type separately results in limited subsamples; nevertheless, we find that the REIT-buyer premium is largest for retail and is not significant for apartments. Further research with more data is needed to test for robustness across property types, counties, and years.

When we condition on properties greater than 40,000 square feet (7,500 repeat transactions), the premium drops to about 4.9 % (

*p*= 0.0027), and when we condition on properties greater than 80,000 square feet (3,703 repeat transactions), the premium drops to 3.5 % (*p*= 0.1380). The importance of conditioning on size helps explain the wide range of REIT premiums found in prior empirical research.For example, Master Limited Partnerships (MLPs), although originally designed for natural resources–related assets, have been extended to real estate. MLPs combine the tax benefits of a limited partnership with the liquidity benefits of a publicly traded corporation, mimicking REIT advantages. Additionally, some pension funds are allowed (limited) exposure to real estate; they too have tax advantages without capital access concerns mimicking REITS.

The calibration’s resulting 24.3 % advantage seems reasonable. The advantage REITs have over publicly traded corporations is the avoidance of corporate income tax, where large companies pay a flat rate of 34 or 35 % due to the structure of the marginal rates. Relative to most of the buyers in our sample (individuals, partnerships, and Limited Liability Corporations), the REIT advantage is the liquidity associated with publicly traded securities. Amihud and Mendelson (1986, 1991), Silber (1991), and Longstaff (1995) find liquidity discounts in the 20 to 40 % range using bond and stock market data. More relevant to our setting is Benveniste et al. (2001) finding of a 23 % liquidity premium in real estate markets.

The size of the discount factor depends on the length of a search round. If it takes 1 month to complete a search, then a discount factor of 0.99 is reasonable.

The rejection of normality results from high power (14,949 observations), not high levels of skewness or kurtosis.

A typical property in our sample experienced approximately a 130 % increase in price from a low near 1995 to a high in 2007; we therefore consider a 400 % price increase as suspicious. Our repeat-sales results do not materially change when a stronger or weaker screen is imposed.

The 268 residual differences have a standard deviation of 0.3187, a median of 0.0244, a low of −0.8970, a high of 1.1897, and the 25th and 75th percentiles are −0.1520 and 0.2624, respectively. Thus, our subsequent finding of a REIT−buyer premium is not driven by a few outliers.

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## Author information

### Authors and Affiliations

### Corresponding author

## Additional information

The authors thank Troy Carpenter and Greg Adams for programing support and Chris Parmeter and participants at BYU, the University of Utah, and the AREUEA 2011 Midyear Meetings for helpful comments. This work was partially supported by the William Edwards professorship, the J. Cyril Johnson Fellowship, and the Harold R. Silver Fund at BYU.

## Appendices

### Appendix A: Multiple Opportunity Extension

In our model presented in Section 2.2, we assumed REITs had one period to make a purchase and considered only one property during that period. Here, we consider a richer model in which REITs may be able to view multiple properties during the limited time in which they are eligible for extra benefit *b*. We find this easiest to illustrate in a continuous time framework. This model shares some features with the unemployment search model of Akin and Platt (2012); the reader can find additional exposition there.

### Buyers

In this multiple-offer environment, a buyer encounters properties at Poisson rate *λ*; that is, encountering *λ* properties on average over one unit of time. Having found a property, the buyer observes the seller’s asking price for that property and chooses to either purchase the property or continue searching. As in the Section 2 model, suppose there are two prices, *p*
_{
l
} and *p*
_{
h
}, and the fraction of sellers offering the low price is *φ*.

As before, all buyers derive benefit *x* from owning the property; a REIT obtains an additional benefit *b* if it acquires a property within the first *T* units of time searching. Buyers and sellers both discount at rate *ρ*.

We denote the state of a buyer by the remaining time *s* until the extra REIT benefit is lost. Since expired REITs are identical to non-REITs, we represent both with state *s* = 0. All REITs enter the market with *s* = *T*, while all non-REITs enter with *s* = 0. Let *V*(*s*) denote the expected net present value of a REIT buyer who has s time remaining before losing the benefit.

A non-REIT’s decision can be represented by the following Bellman equation:

The right hand side indicates that properties arrive at rate *λ*. Yet only the low price is acceptable to non-REITs, so, conditional on encountering a property, they make a purchase with probability *φ*, which changes their payoff from *V*(0) to *x*–*p*
_{
l
}.

A REIT with *s* >0 has the following Bellman equation:

Note the following changes, relative to those with no benefits. First, REITs are willing to pay either price. Second, when a purchase is made at price *p*, the buyer’s payoff changes from *V*(*s*) to *x* + *b*–*p*. Finally, the looming deadline is reflected in \( - {V^{\prime }}(s)\kern-3pt \), since the state *s* deterministically falls until the buyer either makes a purchase or the benefit expires.

### Sellers

Sellers face a stationary problem. If they decide to ask for the low price, they encounter buyers at rate *λ*, all of whom are willing to purchase at the low price. This results in the following Bellman equation:

so the net present value of profit is \( {\Pi_l} = \frac{\lambda }{{\rho + \lambda }}{p_l} \) from this strategy.

Suppose instead that, having encountered a buyer, the seller were to ask the high price; then only fraction γ of buyers will make the purchase. This produces the following Bellman equation:

with a net present value of \( {\Pi_h} = \frac{{\lambda \gamma }}{{\rho + \lambda \gamma }}{p_h} \). For both prices to occur in equilibrium, sellers must be indifferent between them. Thus\( { }{\Pi_h} = {\Pi_l} \), which is to say:

### Steady State

Let *H*(*s*) denote the measure of buyers who have *s* or less time remaining, while \( {H^{\prime }}(s) \) is the relative density of this distribution. To keep this distribution constant over time, it must obey the following three steady state conditions.

First, REITs enter the market at a constant Poisson rate *N*
_{
r
}, so \( {H^{\prime }}(T) = {N_r} \). Second, REITs encounter properties at rate *λ* and purchase them at either price. Thus, the density must fall at rate \( \lambda {H^{\prime }}(s) \):

Third, the mass of buyers at state *s* = 0 increases at rate \( {H^{\prime }}(0) \), due to expiring REITs, and rate *N*
_{
n
}, due to newly entering non-REITs. At the same time, these buyers encounter properties at an acceptable price at rate *λφH*(0):

The fraction of consumers willing to pay the high price is:

### Equilibrium Solution

As before, the price *p*
_{
l
} should make non-REITs indifferent about making the purchase. Thus, \( x - {p_l} = V(0) \). Combining this withs the Bellman equation at *s* = 0 yields *p*
_{
l
} = *x* and *V*(0) = 0.

The rest of the Bellman equation can be solved as a first-order differential equation, with boundary condition *V*(0) = 0. The result is:

The high price is chosen to make the REIT at *s* = *T* indifferent between making the purchase and continuing search, so \( {p_h} = x + b - V(T) \)
*.* By doing so, all buyers whose benefit has not expired will be willing to purchase at price *p*
_{
h
}, since those with 0 < *s* < *T* have *V*(*s*) < *V*(*T*) and thus strictly benefit from such a purchase. This allows us to solve for *p*
_{
h
} as:

Note that as long as 0 < *φ* < 1, then *p*
_{
h
} > *p*
_{
l
}.

The steady state distribution is a second-order differential equation with two boundary conditions. Its unique solution is:

Next, the equal profit condition simplifies to \( \left( {1 - \frac{{\rho H(0)}}{{\left( {\rho + \lambda } \right)\left( {H(T) - H(0)} \right) }}} \right){p_l} = {p_h} \). Substitution for prices and the steady state distribution results in:

This value of *φ* can be substituted back into previous answers to calculate the final solution. Two consistency conditions must be checked to verify that the two-price equilibrium exists. The first is that 0 < *φ* <1, but it turns out that if *φ* <1, we automatically obtain *φ* <0. Thus, this requirement amounts to:

If this inequality does not hold, REITs are sufficiently scarce that sellers face too much delay in asking the higher price. Thus, a single-price equilibrium occurs. Also note that the transition between the two equilibria is continuous. For instance, as *b* falls, *φ* increases until it reaches 1; any further decline in *b* will violate the condition above, and hence maintain the single-price equilibrium (*i.e., φ* = 1).

The second consistency issue is to verify that asking a higher price is not profitable, e.g., \( p(s) = x + b - V(s) \) for \( s \in \left( {0,T} \right) \). Buyers with more than *s* time until the deadline would reject such a price, as would those who have passed the deadline, creating a smaller fraction of potential buyers compared to *p*
_{
h
}. Indeed, the lower likelihood of acceptance outweighs the increase in price as long as 0 < *φ* <1. This can be verified by taking the derivative of:

and verifying that it is positive at *s* = *T*. That is, charging a price just below *p*(*T*) = *p*
_{
h
} will decrease profits.

The two-price equilibrium requires a larger benefit, *b*, or flow of REIT buyers, *N*
_{
r
}, than the discrete model calibration in Section 5.3, but is still within the range of plausibility. For instance, suppose that the annual discount rate is *ρ* = 5 %, REITs constitute 20 % of the flow of buyers, their benefits expire in *T* = 1 year, and they encounter an average of *λ* = 2 properties in that time. Then a benefit *b* = 0.84*x* would sustain a two-price equilibrium, with 64.5 % of sellers offering the low price and REITs paying on average \( \frac{{\rho \left( {{N_r} + {N_r}{e^{{ - \lambda T}}}} \right)}}{{{N_r}\left( {\lambda + \rho } \right)\left( {1 - {e^{{ - \lambda T}}}} \right)}} = 6.4\% \) more than non-REITs. Also, with these parameter values, only 13.5 % of REIT buyers would fail to encounter any properties (at either price) before the deadline.

The comparative statics on *φ* are quite intuitive. As *N*
_{
r
} increases, sellers are more likely to encounter a REIT and thus more sellers ask for *p*
_{
h
} (*i.e., φ* falls). A larger benefit *b* allows the sellers who target REITs to charge even more, which increases their expected profit. This in turn decreases *φ* because asking for *p*
_{
l
} is relatively less attractive.

The comparative static with respect to *λ*, on the other hand, does not have a monotonic relationship. If properties arrive infrequently, few REITs will encounter a property while eligible for the extra benefits. Thus, sellers are not sufficiently likely to make a sale at price *p*
_{
h
} to justify the long wait needed to encounter a REIT, and the single-price equilibrium occurs. On the other hand, if properties arrive frequently, REITs have no reason to rush into purchasing at price *p*
_{
h
}, since they expect a number of more opportunities to find the lower price before their benefits expire. For intermediate values of *λ*, however, the two-price equilibrium can be sustained, and increases in *λ* cause *φ* to fall initially (as sellers become more willing to wait for REITs) and then rise (as REITs become more willing to wait for the low asking price). An increase in *T* has similar competing effects, but for parameters anywhere near those above the net effect is to reduce the REIT premium.

An increase in *λ* will always reduce the REIT premium in percentage terms. Intuitively, as REITs expect more offers before expiration, they can be more patient in their search and hold out for lower prices. This forces sellers to reduce *p*
_{
h
}, lest everyone (except the few REITs near their deadline) turn them down.

The effect of *λ* on the REIT premium explains our empirical finding that the premium falls as property size increases. For instance, buyers of large properties may put forth greater effort to investigate the majority of what is on the market, effectively raising *λ* for larger *x*. Since less money is at stake for small properties, buyers expend less search effort, equivalent to a lower *λ*.

Figure 1 illustrates these comparative statics in a contour plot. The contours indicate the fraction of sellers, *φ*, asking the low price under the specified combination of *b* (relative to *x*) and *λ*. The white region indicates where the single-price equilibrium occurs; that is, all sellers ask the low price so *φ* = 1. All other parameters are fixed at their values used in the numerical example above. The plot looks nearly identical if *b*/*x* is replaced with *N*
_{
r
} on the horizontal axis.

### Appendix B: Repeat Sales Pricing Errors with Bootstrapped *P*-Values

In Section 4.2, we use a modified repeat-sales model to directly measure the REIT-buyer premium. That model has the advantage of only using observations where properties are sold more than once, eliminating the unobserved characteristics problem. At the same time, relying only on repeat transactions reduces the quantity of data, discarding useful information. Furthermore the residuals from the repeat-sales regression are slightly right skewed (third standardized moment = 0.347) and leptokurtic (fourth standardized moment = 5.591). A Kolmogorov-Smirnov test rejects the null of normally distributed residuals.^{Footnote 36}

Here we present an alternative to the modified repeat-sales model that utilizes all of the data and measures the significance of the REIT-buyer premium without assuming normally distributed errors. The new methodology exploits the error term from our initial hedonic estimation, narrows the focus to residuals among properties that sold more than once, and then bootstraps the significance level of the test in the following three steps:

### Residuals

Directly comparing the two raw prices is inappropriate because, while the property (e.g., location and size) are the same, market prices change over time and with the age of the property. Consequently, we compare residuals from the hedonic model (Eq. (10) excluding the REIT buyer variable). Note the hedonic model is not used to estimate a REIT premium, rather it controls for changes in year and age between the two transactions of the same property, where these controls are estimated with the full data set. The fitted value includes controls for all known property and transaction characteristics with the exception of the type of buyer (REIT versus non-REIT). We then identify all repeat sales and retain the residual on these 14,393 observations.

### Test statistic

Where available, each REIT-buyer observation is paired with a twin observation or observations (same street address and city) where the buyer is not a REIT. Initially, we have 276 such *REITBUYER*/*nonREITBUYER* pairs. To make sure the two properties are actually twins without significant modifications, we further require that the twin properties be within 10 % of each other in square footage and that the raw price had not changed by more than 400 %.^{Footnote 37} These restrictions eliminate eight pairs, leaving 268 twins for our repeat transaction tests. Whereas in the paper’s body we criticize the hedonic model because of unobserved characteristics, here we use the model, along with its large sample, to adjust for changes in a property’s age and year between transactions. Then we eliminate this unobserved characteristics problem by looking at only repeat transactions. For each pair of transactions, we subtract the *nonREITBUYER* from the twin *REITBUYER* residual, which should be zero on average under the null hypothesis of no REIT price premium. Our test statistic, \( \bar{D} \), is the mean of 268 differences in residuals and equals 0.0419.^{Footnote 38} That is, REITs tend to pay a premium, even when the same property is involved. However, size of the premium is only about 4.19 %, close to the 6.36 % found in the paper’s body using fewer, but higher quality, observations.

### Bootstrapped p-value

The bootstrap recreates the test statistic, \( \overline{D} \), one thousand times using the same process as the actual test, except neither of the pair of transactions has a REIT buyer. Specifically, we run 1,000 pseudo-tests where we randomly draw 268 pairs of non-REIT twins, randomly assign one to be subtracted from the other, calculate the differences between the residuals and then the mean of all 268 differences (a pseudo \( \bar{D} \)). The marginal significance level (*p*-value) for the tests of the actual REIT price premium is the fraction of realized pseudo \( \bar{D}s \) greater than the actual \( \bar{D} \) of 0.0419 found using REIT buyers. The mean of the one thousand pseudo \( \bar{D}s \), −0.0027, is close to zero, as expected, and they range from −0.0813 to 0.0537. Figure 2 provides a histogram of the bootstrapped pseudo \( \overline{D}s \), along with an arrow pointing to the actual \( \overline D \) found using the REIT-purchased property and their twins.

Only twelve out of 1,000 times is the mean difference in residuals above 0.0419. That is, we can reject the null hypothesis of no REIT premium with a *p*-value of 0.012 (compared to 0.0025 in Section 5.2). Thus, the alternative approach yields a slightly lower and slightly less significant REIT-buyer premium than the modified repeat-sales model used in the body of the paper.

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### Cite this article

Akin, S.N., Lambson, V.E., McQueen, G.R. *et al.* Rushing to Overpay: Modeling and Measuring the REIT Premium.
*J Real Estate Finan Econ* **47**, 506–537 (2013). https://doi.org/10.1007/s11146-012-9372-1

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DOI: https://doi.org/10.1007/s11146-012-9372-1

### Keywords

- Real Estate Investment Trusts (REITs)
- Equilibrium search
- Hedonic price analysis
- Repeat-sales analysis
- Market efficiency
- Deadlines

### JEL classification

- R33
- R32
- D83