On the relationship between the number of a broker’s real estate listings and transaction outcomes

Abstract

This paper documents that sellers who employ brokerage offices that list a large number of properties (“active brokerages”) obtain higher selling prices, smaller negotiated discounts from the corresponding list prices, and shorter times on the market for their listed properties. Sellers who employ active brokerages list their properties at prices that are closer to our hedonic model’s predicted prices. Interestingly, properties that are listed at discounts relative to their predicted prices are snapped up more quickly only if they are associated with brokerages that list a relatively small number of properties. In addition, properties listed by active brokerages are less likely to be listed “as is” and are more likely to have their defects repaired prior to being listed. Moreover, because the efficacy of brokerage services varies across brokerage offices, the results also suggest that the use of an indicator variable for the use of brokerage services is not sufficient to capture the complete impact of the use of a real estate broker on transaction outcomes. In addition, the Appendix discusses the concern for potential endogeneities between the number of brokerage listings and transaction outcomes. It documents that the Durban–Wu–Hausman test indicates that exogeneity cannot be rejected.

Appendix: Test for potential endogeneity

A concern for potential endogeneity between LLISTINGS and the dependent variables (LIST, SALE, and SOVERL) arises because the identity of the broker is chosen by the seller. Econometrically, endogeneity exists when one or more of the explanatory variables is correlated with the error term. Note that the residuals are, by construction, orthogonal to all the explanatory variables. However, the theoretical specification may be such that the error term (what should be attributed to all things other than the specified function of the explanatory variables) is correlated with one of the explanatory variables. If endogeneity exists, then ordinary least squares regressions (OLS) would yield inconsistent estimates, and the use of instrumental variables techniques (IV) would be appropriate. To test for endogeneity between LLISTINGS and our dependent variables, we implement the Durban–Wu–Hausman Test.

The Durbin–Wu–Hausman test takes its name from James Durbin, De-Min Wu, and Jerry Hausman for their seminal work in the field of econometrics (see Durbin 1954; Wu 1973; Hausman 1978). The test is often used to determine whether a given estimator, in our case, OLS, is consistent relative to a second estimator, IV, when IV is known to be consistent, but less efficient. In other words, the Durban–Wu–Hausman test determines whether the existence of endogeneity warrants the use of IV rather than OLS. Davidson and MacKinnon (1993) interpret the Durbin–Wu–Hausman test as an examination of whether possible endogeneity of the right-hand-side variables not contained in the instruments has any significant impact on the coefficient estimates: whether an IV regression is inefficient relative to OLS. This test is implemented by using an IV regression to test the null hypothesis that an OLS estimator of the same equation would yield consistent estimates. A rejection of the null hypothesis indicates that the effects of endogeneity on the OLS estimates are meaningful, and that IV methods are required.

The original OLS specifications for LIST, SALE, and SOVERL are given in Eqs. (1), (3), and (4), respectively. To perform the Durbin–Wu–Hausman test, we estimate a new IV structural model as follows:

$$y = \alpha + \varvec{BX} + \gamma \hat{u} + \varepsilon$$

where y is either LIST, SALE, or SOVERL, the vector X includes the explanatory variables in Eqs. (1), (3), and (4), respectively. Since we wish to test endogeneity between LLISTINGS and the three dependent variables, the additional instrumental variable $\hat{u}$ represents the residuals from the following regression:

$$\begin{aligned} LLISTINGS_{i} & = \alpha + \beta_{1} FT_{i} + \beta_{2} AGE_{i} + \beta_{3} LOT_{i} + \beta_{4} BED_{i} + \beta_{5} FULL_{i} + \beta_{6} HALF_{i} \\ & \quad + \beta_{7} POOL_{i} + \beta_{8} ASIS_{i} + \beta_{9} DEFECT_{i} + \beta_{10} L900_{i} + u_{i} \\ \end{aligned}$$

(7)

where the first nine explanatory variables are discussed in Table 1 and L900 is an indicator variable that equals one if the property’s list price ends in the digits “900”. Palmon et al. (2004) find that this last variable, L900, is correlated with LLISTINGS, but does not have any significant impact on the transaction prices. The inclusion of L900 is important to identify the reduced form equation for LLISTINGS, since the other explanatory variables also are included in X.

The Durban–Wu–Hausman test examines whether employing an IV regression technique improves the efficiency of the estimators relative to OLS estimates. In our case, if the LLRESID coefficient is significantly different from zero, then the OLS estimates are also not consistent and an IV technique should be employed. The only way that LLISTINGS could be endogenous to y (and hence correlated with ε) is if and only if u is correlated with ε. If u is correlated with ε, then the coefficient on LLRESID should be significantly different from zero in the IV regression. The Durban–Wu–Hausman null hypothesis is that the coefficient on LLRESID is zero, which implies that LLISTINGS is not correlated with the error term, and thus exogenous with y (LIST, SALE, or SOVERL). A rejection of the null hypothesis implies that OLS is consistent.

To implement the Durbin–Wu–Hausman test, we extract the residuals, called “LLRESID,” from regression (7). The results of this regression for LLISTINGS are reported in Table 8. We next append LLRESID to the specifications for LIST, SALE, and SOVERL [Eqs. (1), (3), and (4), respectively]; that is, LLRESID is included along with LLISTINGS in each of the regressions. As a result, Eq. (1) becomes:

$$\begin{aligned} LIST_{i} & = \alpha_{i} + \beta_{1} LLISTINGS_{i} + \beta_{2} FT_{i} + \beta_{3} AGE_{i} + \beta_{4} LOT_{i} + \beta_{5} BED_{i} \\ & \quad + \beta_{6} FULL_{i} + \beta_{7} HALF_{i} + \beta_{8} POOL_{i} + \beta_{9} FC_{i} + \beta_{10} ASIS_{i} + \beta_{11} DEFECT_{i} \\ & \quad + \beta_{12} REPAIR_{i} + \beta_{13} TIME_{i} + \beta_{14} NEW_{i} + \beta_{15} NEW1_{i} + \beta_{16} SUMMER_{i} \\ & \quad + \beta_{17} LLRESID_{i} + \varepsilon_{i} \\ \end{aligned}$$

(8)

Equation (3) becomes

$$\begin{aligned} SALE_{i} & = \alpha_{i} + \beta_{1} LLISTINGS_{i} + \beta_{2} FT_{i} + \beta_{3} AGE_{i} + \beta_{4} LOT_{i} + \beta_{5} BED_{i} \\ & \quad + \beta_{6} FULL_{i} + \beta_{7} HALF_{i} + \beta_{8} POOL_{i} + \beta_{9} FC_{i} + \beta_{10} ASIS_{i} + \beta_{11} DEFECT_{i} \\ & \quad + \beta_{12} REPAIR_{i} + \beta_{13} TIME_{i} + \beta_{14} NEW_{i} + \beta_{15} NEW1_{i} + \beta_{16} LISTRES_{i} \\ & \quad + \beta_{17} SUMMER_{i} + \beta_{18} LLRESID_{i} + \varepsilon_{i} \\ \end{aligned}$$

(9)

And, Eq. (4) becomes

$$\begin{aligned} SOVERL_{i} & = \alpha_{i} + \beta_{1} LLISTINGS_{i} + \beta_{2} FT_{i} + \beta_{3} AGE_{i} + \beta_{4} LOT_{i} + \beta_{5} BED_{i} \\ & \quad + \beta_{6} FULL_{i} + \beta_{7} HALF_{i} + \beta_{8} POOL_{i} + \beta_{9} FC_{i} + \beta_{10} ASIS_{i} + \beta_{11} DEFECT_{i} \\ & \quad + \beta_{12} REPAIR_{i} + \beta_{13} TIME_{i} + \beta_{14} NEW_{i} + \beta_{15} NEW1_{i} + \beta_{16} SUMMER_{i} \\ & \quad + \beta_{17} LLRESID_{i} + \varepsilon_{i} \\ \end{aligned}$$

(10)

A coefficient on LLRESID that is significantly different from zero in a given regression indicates a rejection of the null hypothesis of exogeneity between LLISTINGS and the dependent variable in question. Tables 9, 10, and 11 present the results of the Durban–Wu–Haussman Test for LLISTINGS and LIST, SALE, and SOVERL, respectively. Note the insignificant coefficients on LLRESID in each of these regressions indicates that we cannot reject the null hypothesis of exogeneity between LLISTINGS and any of the dependent variables. Consequently, ordinary least squares regression yields consistent estimates is an appropriate methodology.

Table 8 OLS regression of LLISTINGS, the natural logarithm of the number of properties listed by an individual brokers

Table 9 OLS regression of LIST, the property’s list price, on the variables specified in Eq. (1) with the addition of LLRESID

Table 10 OLS regression of SALE, the property’s transaction price, on the variables specified in Eq. (3) with the addition of LLRESID

Table 11 OLS regression of SOVER, the ratio of the property’s transaction price to its list price, on the variables specified in Eq. (4) with the addition of LLRESID