# The impact of corporate ownership on residential transaction prices.

A perception exists in the appraisal and brokerage industry that
houses sold by corporate relocation firms (or corporate employers) sell
at a discount in the residential market. The purpose of this article is
to empirically determine if corporately owned houses do sell at a
discount. A sample of 278 residential transactions in one community is
used in a hedonic pricing model to test the hypothesis. The results
indicate that corporate properties sold at a discount of nearly 5%. This
article first appeared in the Spring 1992 (Vol. 7, No. 2) issue of The
Journal of Real Estate Research (pp. 207--216), published by the
American Real Estate Society.

The purpose of this paper is to empirically determine whether houses owned and sold by corporate employee relocation firms sell at a discount when compared to the noncorporate transactions in the same local market.

In many markets in recent years, relocation firms have been unable to sell their houses for the appraised value. While this phenomenon is not unique to the relocation industry alone, it has led to discussions between relocation companies and their appraisers about who is responsible for this situation. Appraisers suggest that relocation companies sometimes wholesale their acquired properties to avoid the holding costs associated with an extended marketing period.(1)

There is evidence that this perception exists in the residential brokerage community as well. "For sale" signs and classified advertising often identify these properties as "corporate owned" or "corporate sellers," as if this is a unique submarket in the single-family market.

The results of this research may have significant implications for the residential appraisal industry. If corporately owned houses are found to sell at a discount in the local market, then they should be classified as atypical, nonmarket transactions and not used as comparable sales for noncorporate appraisals without making appropriate adjustments. If the results indicate no discount exists, then corporate sales could be appropriately used as comparable sales for all appraisal assignments.

LITERATURE REVIEW

Most appraisal texts specify that appraisers must adjust comparable sales for factors such as: nonmarket transactions, atypical financing, changing market conditions, locational differences and physical differences between the comparable sale and the subject property. Comparable sales that are identified as nonmarket transactions are not used if a sufficient number of other comparable sales exist. The sales price of these comparables must be adjusted to estimate the true market value of the comparable sale. If corporately owned houses are shown to sell at a systematic discount in the local market, then appraisers should avoid using them for comparable sales without making an adjustment to the actual sales price.

Dotzour(2) previously identified that corporate sellers may be willing to sell their homes at discount if they can avoid the costs associated with an extended marketing period. These costs include per diem expenditures for amortization, taxes, maintenance, utilities, and insurance.(3) The relocation company may be able to minimize the total cost of the employee transfer if they sell an acquired property quickly and avoid the expected holding costs.

MODELS AND HYPOTHESES

To empirically determine whether corporately owned houses sell at a discount, the following hypothesis was tested using a hedonic pricing model:

Ho: Corporate owned houses do not sell

at a discount, when compared to residen-

tial sales not corporately owned.

Ha: Corporately owned houses do not

sell at a discount.

Hedonic pricing theory postulates that the value of a house is a function of the quantitative and qualitative attributes that are components of the house.(4) Hedonic pricing theory is usually tested using a multiple regression model (linear and/or nonlinear), where: Sales Price of a house = f([X.sub.i], [Y.sub.i]), (1) where

[X.sub.i] = vector of quantitative factors such as

age, size, baths, fireplaces, and

garage;

[Y.sub.i] = vector of qualitative factors such as

neighborhood quality, physical

property condition, and school

district.

To test the above-stated hypothesis, a semi-log multiple regression was constructed according to the following form: Ln(Sales Price) = f([X.sub.i], [Y.sub.i], Z), (2) where

Z = 1, if house was sold by a corporate

employer,

= 0, otherwise.

The Data

The sample data consists of residential transactions that were sold and closed in Wichita, Kansas, between December 1, 1987 and October 31, 1989. Local appraisers were consulted to identify two neighborhoods(5) that have a high level of corporate relocation activity. With the help of appraisers in the area, 58 relocation transactions were identified that sold and closed in the two neighborhoods within the stated time period. In addition, a random sample of 220 noncorporate transactions in the same neighborhoods was gathered. These 278 transactions represented virtually all of the market activity in the two areas during the time period under investigations, except for those not reported through the Multiple Listing Service.

Properties in the sample are similar in age and construction quality. The average age was five years, ranging from zero to fifteen years old. Ninety percent of the sample was ten years old or younger. The sales prices range from $49,950 to $283,000, with a mean of $111,418. The houses range in size from 928 square feet to 3,435 square feet. Additional descriptive statistics of the sample data are presented in Exhibit 1.

EXHIBIT 1 Descriptive Statistics

SOURCE: derived by authors from the sample data

Information about the corporately owned houses and the other transactions was gathered from the files of appraisers participating in the project and multiple listing service data.

EMPIRICAL RESULTS

To examine the impact of corporate relocation ownership on transaction prices, a semi-log multiple regression model(6) of the following form was used: Ln(SP) = f(LOT, AGE, ROOF, FINBSMT, SQFT, GAR, FIRE, Q, BRICK, LOC, STORY, TENPOOL, C, FENCE, CORP), (3) where:

Ln(SP) = the natural logarithm of

sales price;

LOT = lot size in square feet;

SQFT = size of the house in square

feet;

AGE = actual age of the housing

improvements;

STORY = 1, if the house was a one-

story "ranch" design,

= 0, if house had more than

one story;

ROOF = 1, if wood roof

= 0, otherwise;

FINBSMT = percentage of basement area

that is finished;

GAR = number of garage parking

spaces;

FIRE = number of woodburning

fireplaces;

TENPOOL = 1, if property has a pool or

tennis court,

= 0, otherwise;

FENCE = 1, if property has a fence,

= 0, otherwise;

C = 1, if condition was rated ex-

cellent (by appraiser),

= 0, if condition was rated

good/fair/poor;

Q = 1, if construction quality was

rated excellent,

= 0, if construction quality was

rated good/fair/poor;

BRICK = 1, if property has a brick or

stone exterior,

= 0, if frame exterior;

LOC = 1, if property is located in

the east area,

= 0, if property is located in

the west area;

CORP = 1, if property was corpo-

rately owned,

= 0, if property was not cor-

porately owned.

The regression results, shown in Exhibit 2, reveal that the model explains more than 90% of the variation in the sales prices of the houses in the sample data. Many of the variables in the model were found to be significant with 95% confidence. The significant variables include square footage of the house, age, roof type, percentage of finished basement, location, and corporate ownership. These results indicate that square footage, roof type, and percentage of finished basement have a positive association with the sales price of houses in the sample. Age was found to have a negative association with sales prices, as expected. The parameter estimate for the location variable (LOC) of .080376 indicates that the sale prices of properties located in the east Wichita neighborhood were 8% higher than similar houses in the west neighborhood.

[TABULAR DATA OMITTED]

The result of particular interest in this study is the relationship between the CORP variable and the sales price of the houses in the sample. The parameter estimate for CORP indicated that corporately owned properties in the sample sold for an average of 4.6% less than other homes in the sample (holding all other variables constant). The reported [tau]-statistic and [rho]-value indicate that this parameter estimate is significantly different from zero with a 98% confidence level. These findings indicate that the null hypothesis can be rejected and that corporately owned houses do sell at a discount in this local market.

The presence of collinearity among variables in hedonic pricing models can create difficulty for the real estate researcher attempting to measure the influence of one specific variable in a regression model on the variation in sales price. If the specific variable of interest is highly correlated with other variables in the model, hypothesis testing of the influence of the specific variable becomes problematic.

Consequently, even though the regression results indicate that corporately owned houses do sell at a discount, further investigation is warranted to determine if these results have been degraded by the influence of collinearity.

First, the correlation matrix of the variables was analyzed to determine if the CORP variable was highly correlated with other variables in the model. The correlation matrix is presented in Exhibit 3. The correlation matrix reveals that the CORP variable is not highly correlated with any of the other independent variables in the model, indicating that the parameter estimate for the CORP variable may not be heavily influenced by collinearity.

EXHIBIT 3 Pearson Correlation Matrix

SOURCE: derived by authors from the sample data

The absence of high simple correlation between the CORP variable and the other independent variables is not sufficient evidence of a lack of collinearity, however, because it is possible that CORP may be correlated in a multidimensional fashion with a linear combination of two or more other variables in the data. Analysis of the correlation matrix will not reveal correlation of linear combinations of the variables.

The variance inflation factors for the variables in the sample data were analyzed to determine if the CORP variable was correlated with any linear combination of other variables in the sample. The variance inflation factor for the CORP variable is defined as

[MATHEMATICAL EXPRESSION OMITTED] where [[R.sup.2].sub.corp] is the multiple correlation coefficient or CORP regressed on the remaining independent variables. Variables with a high measured VIF are highly correlated with other variables in the sample. The variance inflation factors for the sample data are presented in Exhibit 2. The lower bound for VIF is unity, when there is no multiple correlation between the variable in question and the remaining variables. The upper bound of the VIF distribution is unbounded as the multiple correlation approaches unity. The variable CORP has a VIF of 1.069, indicating that the multiple correlation coefficient of the CORP variable is less than 7%, and that the parameter estimate for CORP is not greatly influenced by collinearity.

Belsley, Kuh and Welsch(7) developed a rigorous two-step process to determine if a specific regression parameter estimate has been "degraded" by the presence of collinearity among the variables in a sample data set. They concluded that "It is the joint condition of a high variance-decomposition proportion for two or more regression coefficients associated with a high condition index that signals the presence of degrading collinearity."(8)

Their suggested method for assessing the impact of collinearity on regression parameter estimates is a two-step process. First, a principal components analysis is completed to identify the eigenvalues of the data matrix. Then, each eigenvalue is measured by a "condition" index that measures the dispersion between a specific eigenvalue and the largest eigenvalue in the sample. The condition index for a specific eigenvalue "I" is defined as [CI.sub.i] = Max eigenvalue/[Eigenvalue.sub.i] (5)

If the sample data were completely orthogonal, the condition index for each eigenvalue would be unity. As the collinearity among the sample data increases, the condition indexes for some of the eigenvalues increase as well. Consequently, eigenvalues with high condition indexes are associated with collinear variables. The eigenvalues and the measured condition numbers of the sample data are presented in Exhibit 4. Weak dependencies are associated with condition indexes around 5 to 10, while moderate to strong relations are associated with indexes of 30 to 100.(9) The condition indexes for the sample indicate the presence of collinearity within the data.

EXHIBIT 4 Condition Indexes of the Data

SOURCE: derived by authors from the sample data

To determine which parameters in the regression model have been degraded by the presence of collinearity, the second step of the Belsley, et al. technique is utilized. This step, called regression-coefficient variance decomposition, measures the proportion of the variance of each regression coefficient associated with each eigenvalue of the data. Evidence that collinearity has degraded the reliability of regression parameters is found when a high proportion of the variance of the parameter estimates of two or more variables is associated with an eigenvalue with a "high" condition number. The results of the regression-coefficient variance decomposition are presented in Exhibit 5. Eigenvalues numbered 13--16 were identified as having moderately high condition numbers (over 10). Analysis of the regression-coefficient variation decomposition shows that only 1% of the variance of the regression parameter for CORP is associated with eigenvalue 13, and that less than 1% of the CORP parameter variance is associated with eigenvalues 14, 15, and 16.

EXHIBIT 5 Regression-Coefficient Variance Decomposition

SOURCE: derived by authors from the sample data

Additional results in Exhibit 6 show that 44% of the variance of the regression coefficient for CORP is associated with the fourth eigenvalue, and another 44% is associated with the fifth. Both of these eigenvalues have low condition numbers, 3.7 and 3.8 respectively. No other variables are highly associated with these eigenvalues. Consequently, the conclusion can be made that collinearity is present in the sample data set, but that the regression parameter estimate for CORP is not degraded by its presence.

EXHIBIT 6 Regression-Coefficient Variance Decomposition

SOURCE: derived by authors from the sample data

SUMMARY AND CONCLUSIONS

The purpose of this article was to empirically test whether houses owned and sold by corporate relocation companies sell at a discount when compared to houses not owned by corporate relocation firms.

Using a hedonic pricing model, a semilog multiple regression was used to test the hypothesis. The regression results indicated that the null hypothesis was rejected and that corporately owned houses do sell at a discount of approximately 4.6% of the average sales price of houses in the sample. A rigorous analysis of the sample data indicated that a degree of collinearity was present in the data, but that the regression coefficient of interest was not heavily affected by it.

The results of this study indicate that corporate relocation sales may be atypical transactions that should not be used for comparable sales by appraisers if other sufficient data is available. Further research in other cities should be undertaken to determine if this occurs uniformly, or if it varies in magnitude between local markets. The magnitude of this adjustment would have to be measured in each local market, because it could vary between markets depending on the local supply and demand conditions. For example, in markets where demand is relatively high in relation to current supply, the amount of discounting by relocation firms may be negligible. In such a market, the volume of corporate relocation activity may be low because the transferred employees can sell their houses without corporate assistance. However, in a market where supply of available houses exceeds demand, the price discounting by relocation companies may be more substantial as they seek to divest themselves of their acquired inventory. If the discount is measurable and predictable, then these transactions could be used by appraisers as reliable comparable sales (after appropriate adjustment for the observed discount). However, if the discount varies over time, then these transactions should not be used if other data is available.

(1.)M. Dotzour and D. Levi, "Reducing the Cost of Corporate Employee Relocation," Journal of Real Estate Research, vol. 4, no. 3(1989): 157--168.

(2.)M. Dotzour, "Quantifying Estimation Bias in Residential Appraisal," Journal of Real Estate Research vol. 3, no. 3 (1988): 1--16.

(3.)For a complete discussion of the costs associated with employee relocation, see Dotzour, footnote 2.

(4.)R. Edmonds, "A Theoretical Basis for Hedonic Regression: A Research Primer," AREUEA Journal, vol. 12, no. 1 (1984): 72--85.

(5.)One neighborhood was located in east Wichita, while the other was in west Wichita. These neighborhoods have different schools, shopping, recreational opportunities, and other locational differences. Hence, a binary variable was used in the hedonic model to explicitly measure these locational differences between neighborhoods.

Some locational and neighborhood differences of houses within each of the two neighborhoods exist, but additional data was not available to measure these differences. However, the size of the neighborhoods was restricted to minimize within-neighborhood locational differences.

The two neighborhoods used in this study were identified specifically because of the high level of corporate relocation activity within them. Houses in these neighborhoods are newer, larger, and more expensive than the average for the entire city. It is possible that the high level of corporate sales activity in these areas could influence the degree of price competition in the individual neighborhoods. Consequently, the results of this study may not be applicable to corporately owned houses that are sold in other neighborhoods where the volume of corporate relocation activity is smaller.

(6.)Other variables such as air-conditioning, heating, carpet, dishwasher, disposal, and existence of a basement were not included in the model because every house in the sample had these features. Inclusion of these variables would have caused the matrix to be non-singular. Local appraisers advised that the trend in property values was stable over the period of time in which the sample properties were sold. Hence, no time adjustment was included in the model. To confirm this, the regression residuals were regressed against the month in which the houses were sold. The results indicated no relationship between the residuals and time of sale.

(7.)D. Belsley, E. Kuh, and R. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (New York: John Wiley and Sons, 1980).

(8.)Ibid., 112.

(9.)Ibid., 105.

The purpose of this paper is to empirically determine whether houses owned and sold by corporate employee relocation firms sell at a discount when compared to the noncorporate transactions in the same local market.

In many markets in recent years, relocation firms have been unable to sell their houses for the appraised value. While this phenomenon is not unique to the relocation industry alone, it has led to discussions between relocation companies and their appraisers about who is responsible for this situation. Appraisers suggest that relocation companies sometimes wholesale their acquired properties to avoid the holding costs associated with an extended marketing period.(1)

There is evidence that this perception exists in the residential brokerage community as well. "For sale" signs and classified advertising often identify these properties as "corporate owned" or "corporate sellers," as if this is a unique submarket in the single-family market.

The results of this research may have significant implications for the residential appraisal industry. If corporately owned houses are found to sell at a discount in the local market, then they should be classified as atypical, nonmarket transactions and not used as comparable sales for noncorporate appraisals without making appropriate adjustments. If the results indicate no discount exists, then corporate sales could be appropriately used as comparable sales for all appraisal assignments.

LITERATURE REVIEW

Most appraisal texts specify that appraisers must adjust comparable sales for factors such as: nonmarket transactions, atypical financing, changing market conditions, locational differences and physical differences between the comparable sale and the subject property. Comparable sales that are identified as nonmarket transactions are not used if a sufficient number of other comparable sales exist. The sales price of these comparables must be adjusted to estimate the true market value of the comparable sale. If corporately owned houses are shown to sell at a systematic discount in the local market, then appraisers should avoid using them for comparable sales without making an adjustment to the actual sales price.

Dotzour(2) previously identified that corporate sellers may be willing to sell their homes at discount if they can avoid the costs associated with an extended marketing period. These costs include per diem expenditures for amortization, taxes, maintenance, utilities, and insurance.(3) The relocation company may be able to minimize the total cost of the employee transfer if they sell an acquired property quickly and avoid the expected holding costs.

MODELS AND HYPOTHESES

To empirically determine whether corporately owned houses sell at a discount, the following hypothesis was tested using a hedonic pricing model:

Ho: Corporate owned houses do not sell

at a discount, when compared to residen-

tial sales not corporately owned.

Ha: Corporately owned houses do not

sell at a discount.

Hedonic pricing theory postulates that the value of a house is a function of the quantitative and qualitative attributes that are components of the house.(4) Hedonic pricing theory is usually tested using a multiple regression model (linear and/or nonlinear), where: Sales Price of a house = f([X.sub.i], [Y.sub.i]), (1) where

[X.sub.i] = vector of quantitative factors such as

age, size, baths, fireplaces, and

garage;

[Y.sub.i] = vector of qualitative factors such as

neighborhood quality, physical

property condition, and school

district.

To test the above-stated hypothesis, a semi-log multiple regression was constructed according to the following form: Ln(Sales Price) = f([X.sub.i], [Y.sub.i], Z), (2) where

Z = 1, if house was sold by a corporate

employer,

= 0, otherwise.

The Data

The sample data consists of residential transactions that were sold and closed in Wichita, Kansas, between December 1, 1987 and October 31, 1989. Local appraisers were consulted to identify two neighborhoods(5) that have a high level of corporate relocation activity. With the help of appraisers in the area, 58 relocation transactions were identified that sold and closed in the two neighborhoods within the stated time period. In addition, a random sample of 220 noncorporate transactions in the same neighborhoods was gathered. These 278 transactions represented virtually all of the market activity in the two areas during the time period under investigations, except for those not reported through the Multiple Listing Service.

Properties in the sample are similar in age and construction quality. The average age was five years, ranging from zero to fifteen years old. Ninety percent of the sample was ten years old or younger. The sales prices range from $49,950 to $283,000, with a mean of $111,418. The houses range in size from 928 square feet to 3,435 square feet. Additional descriptive statistics of the sample data are presented in Exhibit 1.

EXHIBIT 1 Descriptive Statistics

Standard Variable Mean Deviation Minimum Maximum LOT 10708.010 2978.710 4730 23240 AGE 5.043 3.733 0 15 ROOF 0.539 0.499 0 1 FINBSMT 34.862 29.674 0 99 SQFT 1893.859 553.059 928 3435 GAR 2.046 0.227 1 3 FIRE 1.245 0.501 0 3 Q 0.358 0.480 0 1 BRICK 0.123 0.329 0 1 LOC 0.496 0.500 0 1 STORY 0.465 0.499 0 1 TENPOOL 0.047 0.212 0 1 C 0.765 0.424 0 1 FENCE 0.447653 0.498152 0 1 CORP 0.208633 0.407064 0 1 N = 278

SOURCE: derived by authors from the sample data

Information about the corporately owned houses and the other transactions was gathered from the files of appraisers participating in the project and multiple listing service data.

EMPIRICAL RESULTS

To examine the impact of corporate relocation ownership on transaction prices, a semi-log multiple regression model(6) of the following form was used: Ln(SP) = f(LOT, AGE, ROOF, FINBSMT, SQFT, GAR, FIRE, Q, BRICK, LOC, STORY, TENPOOL, C, FENCE, CORP), (3) where:

Ln(SP) = the natural logarithm of

sales price;

LOT = lot size in square feet;

SQFT = size of the house in square

feet;

AGE = actual age of the housing

improvements;

STORY = 1, if the house was a one-

story "ranch" design,

= 0, if house had more than

one story;

ROOF = 1, if wood roof

= 0, otherwise;

FINBSMT = percentage of basement area

that is finished;

GAR = number of garage parking

spaces;

FIRE = number of woodburning

fireplaces;

TENPOOL = 1, if property has a pool or

tennis court,

= 0, otherwise;

FENCE = 1, if property has a fence,

= 0, otherwise;

C = 1, if condition was rated ex-

cellent (by appraiser),

= 0, if condition was rated

good/fair/poor;

Q = 1, if construction quality was

rated excellent,

= 0, if construction quality was

rated good/fair/poor;

BRICK = 1, if property has a brick or

stone exterior,

= 0, if frame exterior;

LOC = 1, if property is located in

the east area,

= 0, if property is located in

the west area;

CORP = 1, if property was corpo-

rately owned,

= 0, if property was not cor-

porately owned.

The regression results, shown in Exhibit 2, reveal that the model explains more than 90% of the variation in the sales prices of the houses in the sample data. Many of the variables in the model were found to be significant with 95% confidence. The significant variables include square footage of the house, age, roof type, percentage of finished basement, location, and corporate ownership. These results indicate that square footage, roof type, and percentage of finished basement have a positive association with the sales price of houses in the sample. Age was found to have a negative association with sales prices, as expected. The parameter estimate for the location variable (LOC) of .080376 indicates that the sale prices of properties located in the east Wichita neighborhood were 8% higher than similar houses in the west neighborhood.

[TABULAR DATA OMITTED]

The result of particular interest in this study is the relationship between the CORP variable and the sales price of the houses in the sample. The parameter estimate for CORP indicated that corporately owned properties in the sample sold for an average of 4.6% less than other homes in the sample (holding all other variables constant). The reported [tau]-statistic and [rho]-value indicate that this parameter estimate is significantly different from zero with a 98% confidence level. These findings indicate that the null hypothesis can be rejected and that corporately owned houses do sell at a discount in this local market.

The presence of collinearity among variables in hedonic pricing models can create difficulty for the real estate researcher attempting to measure the influence of one specific variable in a regression model on the variation in sales price. If the specific variable of interest is highly correlated with other variables in the model, hypothesis testing of the influence of the specific variable becomes problematic.

Consequently, even though the regression results indicate that corporately owned houses do sell at a discount, further investigation is warranted to determine if these results have been degraded by the influence of collinearity.

First, the correlation matrix of the variables was analyzed to determine if the CORP variable was highly correlated with other variables in the model. The correlation matrix is presented in Exhibit 3. The correlation matrix reveals that the CORP variable is not highly correlated with any of the other independent variables in the model, indicating that the parameter estimate for the CORP variable may not be heavily influenced by collinearity.

EXHIBIT 3 Pearson Correlation Matrix

LOT AGE ROOF FINBSMT SOFT GAR LOT 1.000 AGE 0.095 1.000 ROOF 0.189 -0.298 1.000 FINBSMT 0.120 0.260 -0.001 1.000 SQFT 0.365 -0.348 0.625 -0.138 1.000 GAR 0.429 -0.197 0.158 -0.055 0.368 1.000 FIRE 0.230 -0.006 0.122 0.078 0.162 0.342 Q 0.147 -0.255 0.319 -0.023 0.356 0.244 BRICK 0.325 0.220 0.117 0.125 0.130 0.175 LOC 0.280 -0.025 0.153 -0.071 0.351 0.143 STORY -0.090 0.345 -0.326 0.206 -0.618 -0.160 TENPOOL 0.162 0.025 0.066 -0.002 0.055 0.029 C -0.024 -0.352 0.189 -0.037 0.156 0.113 FENCE -0.008 0.493 -0.310 0.180 -0.261 -0.089 CORP 0.093 0.140 0.083 0.067 0.010 0.011 FIRE Q BRICK LOC STORY TENPOOL FIRE 1.000 Q -0.012 1.000 BRICK 0.103 0.061 1.000 LOC -0.023 0.272 0.114 1.000 STORY -0.033 -0.210 0.147 -0.264 1.000 TENPOOL -0.007 0.100 0.228 -0.085 -0.000 1.000 C 0.081 0.399 0.003 -0.011 -0.089 0.045 FENCE -0.030 -0.251 0.064 -0.033 0.241 0.145 CORP -0.057 0.110 0.076 0.056 0.035 0.053 C FENCE CORP C 1.000 FENCE -0.184 1.000 CORP -0.070 0.089 1.000

SOURCE: derived by authors from the sample data

The absence of high simple correlation between the CORP variable and the other independent variables is not sufficient evidence of a lack of collinearity, however, because it is possible that CORP may be correlated in a multidimensional fashion with a linear combination of two or more other variables in the data. Analysis of the correlation matrix will not reveal correlation of linear combinations of the variables.

The variance inflation factors for the variables in the sample data were analyzed to determine if the CORP variable was correlated with any linear combination of other variables in the sample. The variance inflation factor for the CORP variable is defined as

[MATHEMATICAL EXPRESSION OMITTED] where [[R.sup.2].sub.corp] is the multiple correlation coefficient or CORP regressed on the remaining independent variables. Variables with a high measured VIF are highly correlated with other variables in the sample. The variance inflation factors for the sample data are presented in Exhibit 2. The lower bound for VIF is unity, when there is no multiple correlation between the variable in question and the remaining variables. The upper bound of the VIF distribution is unbounded as the multiple correlation approaches unity. The variable CORP has a VIF of 1.069, indicating that the multiple correlation coefficient of the CORP variable is less than 7%, and that the parameter estimate for CORP is not greatly influenced by collinearity.

Belsley, Kuh and Welsch(7) developed a rigorous two-step process to determine if a specific regression parameter estimate has been "degraded" by the presence of collinearity among the variables in a sample data set. They concluded that "It is the joint condition of a high variance-decomposition proportion for two or more regression coefficients associated with a high condition index that signals the presence of degrading collinearity."(8)

Their suggested method for assessing the impact of collinearity on regression parameter estimates is a two-step process. First, a principal components analysis is completed to identify the eigenvalues of the data matrix. Then, each eigenvalue is measured by a "condition" index that measures the dispersion between a specific eigenvalue and the largest eigenvalue in the sample. The condition index for a specific eigenvalue "I" is defined as [CI.sub.i] = Max eigenvalue/[Eigenvalue.sub.i] (5)

If the sample data were completely orthogonal, the condition index for each eigenvalue would be unity. As the collinearity among the sample data increases, the condition indexes for some of the eigenvalues increase as well. Consequently, eigenvalues with high condition indexes are associated with collinear variables. The eigenvalues and the measured condition numbers of the sample data are presented in Exhibit 4. Weak dependencies are associated with condition indexes around 5 to 10, while moderate to strong relations are associated with indexes of 30 to 100.(9) The condition indexes for the sample indicate the presence of collinearity within the data.

EXHIBIT 4 Condition Indexes of the Data

Principal Condition Component Eigenvalue Number 1 10.11325 1.000 2 1.24628 2.848 3 1.06142 3.086 4 0.73325 3.713 5 0.67289 3.876 6 0.50233 4.487 7 0.45471 4.716 8 0.28628 5.943 9 0.26901 6.131 10 0.20272 7.063 11 0.17705 7.557 12 0.13968 8.508 13 0.08658 10.808 14 0.03771 16.376 15 0.01288 28.021 16 0.00406 49.933

SOURCE: derived by authors from the sample data

To determine which parameters in the regression model have been degraded by the presence of collinearity, the second step of the Belsley, et al. technique is utilized. This step, called regression-coefficient variance decomposition, measures the proportion of the variance of each regression coefficient associated with each eigenvalue of the data. Evidence that collinearity has degraded the reliability of regression parameters is found when a high proportion of the variance of the parameter estimates of two or more variables is associated with an eigenvalue with a "high" condition number. The results of the regression-coefficient variance decomposition are presented in Exhibit 5. Eigenvalues numbered 13--16 were identified as having moderately high condition numbers (over 10). Analysis of the regression-coefficient variation decomposition shows that only 1% of the variance of the regression parameter for CORP is associated with eigenvalue 13, and that less than 1% of the CORP parameter variance is associated with eigenvalues 14, 15, and 16.

EXHIBIT 5 Regression-Coefficient Variance Decomposition

Eigenvalue Eigenvalue Eigenvalue Eigenvalue 13 14 15 16 LOT 0.0321 0.8434 0.0000 0.1096 AGE 0.0908 0.0072 0.1496 0.0788 ROOF 0.0188 0.0165 0.2340 0.0172 FINBSMT 0.0033 0.0029 0.0026 0.0001 SQFT 0.0334 0.0477 0.9111 0.0000 GAR 0.0059 0.0059 0.0966 0.8893 FIRE 0.7410 0.0020 0.0096 0.0262 Q 0.0082 0.0006 0.0054 0.0138 BRICK 0.0001 0.0410 0.0785 0.0118 LOC 0.0717 0.0308 0.0113 0.0129 STORY 0.0069 0.0030 0.2202 0.0176 TENPOOL 0.0118 0.0216 0.0003 0.0086 C 0.0174 0.0153 0.0495 0.0008 FENCE 0.0038 0.0210 0.0000 0.0004 CORP 0.0109 0.0060 0.0082 0.0002 INTERCEPT 0.0064 0.0221 0.1210 0.8488

SOURCE: derived by authors from the sample data

Additional results in Exhibit 6 show that 44% of the variance of the regression coefficient for CORP is associated with the fourth eigenvalue, and another 44% is associated with the fifth. Both of these eigenvalues have low condition numbers, 3.7 and 3.8 respectively. No other variables are highly associated with these eigenvalues. Consequently, the conclusion can be made that collinearity is present in the sample data set, but that the regression parameter estimate for CORP is not degraded by its presence.

EXHIBIT 6 Regression-Coefficient Variance Decomposition

Eigenvalue Eigenvalue 4 5 LOT 0.0001 0.0001 AGE 0.0006 0.0003 ROOF 0.0008 0.0001 FINBSMT 0.0004 0.0012 SQFT 0.0003 0.0000 GAR 0.0001 0.0000 FIRE 0.0020 0.0002 Q 0.0001 0.0041 BRICK 0.1994 0.3176 LOC 0.0000 0.0287 STORY 0.0111 0.0011 TENPOOL 0.1550 0.1594 C 0.0070 0.0001 FENCE 0.0148 0.0044 CORP 0.4412 0.4411 INTERCEPT 0.0001 0.0000

SOURCE: derived by authors from the sample data

SUMMARY AND CONCLUSIONS

The purpose of this article was to empirically test whether houses owned and sold by corporate relocation companies sell at a discount when compared to houses not owned by corporate relocation firms.

Using a hedonic pricing model, a semilog multiple regression was used to test the hypothesis. The regression results indicated that the null hypothesis was rejected and that corporately owned houses do sell at a discount of approximately 4.6% of the average sales price of houses in the sample. A rigorous analysis of the sample data indicated that a degree of collinearity was present in the data, but that the regression coefficient of interest was not heavily affected by it.

The results of this study indicate that corporate relocation sales may be atypical transactions that should not be used for comparable sales by appraisers if other sufficient data is available. Further research in other cities should be undertaken to determine if this occurs uniformly, or if it varies in magnitude between local markets. The magnitude of this adjustment would have to be measured in each local market, because it could vary between markets depending on the local supply and demand conditions. For example, in markets where demand is relatively high in relation to current supply, the amount of discounting by relocation firms may be negligible. In such a market, the volume of corporate relocation activity may be low because the transferred employees can sell their houses without corporate assistance. However, in a market where supply of available houses exceeds demand, the price discounting by relocation companies may be more substantial as they seek to divest themselves of their acquired inventory. If the discount is measurable and predictable, then these transactions could be used by appraisers as reliable comparable sales (after appropriate adjustment for the observed discount). However, if the discount varies over time, then these transactions should not be used if other data is available.

(1.)M. Dotzour and D. Levi, "Reducing the Cost of Corporate Employee Relocation," Journal of Real Estate Research, vol. 4, no. 3(1989): 157--168.

(2.)M. Dotzour, "Quantifying Estimation Bias in Residential Appraisal," Journal of Real Estate Research vol. 3, no. 3 (1988): 1--16.

(3.)For a complete discussion of the costs associated with employee relocation, see Dotzour, footnote 2.

(4.)R. Edmonds, "A Theoretical Basis for Hedonic Regression: A Research Primer," AREUEA Journal, vol. 12, no. 1 (1984): 72--85.

(5.)One neighborhood was located in east Wichita, while the other was in west Wichita. These neighborhoods have different schools, shopping, recreational opportunities, and other locational differences. Hence, a binary variable was used in the hedonic model to explicitly measure these locational differences between neighborhoods.

Some locational and neighborhood differences of houses within each of the two neighborhoods exist, but additional data was not available to measure these differences. However, the size of the neighborhoods was restricted to minimize within-neighborhood locational differences.

The two neighborhoods used in this study were identified specifically because of the high level of corporate relocation activity within them. Houses in these neighborhoods are newer, larger, and more expensive than the average for the entire city. It is possible that the high level of corporate sales activity in these areas could influence the degree of price competition in the individual neighborhoods. Consequently, the results of this study may not be applicable to corporately owned houses that are sold in other neighborhoods where the volume of corporate relocation activity is smaller.

(6.)Other variables such as air-conditioning, heating, carpet, dishwasher, disposal, and existence of a basement were not included in the model because every house in the sample had these features. Inclusion of these variables would have caused the matrix to be non-singular. Local appraisers advised that the trend in property values was stable over the period of time in which the sample properties were sold. Hence, no time adjustment was included in the model. To confirm this, the regression residuals were regressed against the month in which the houses were sold. The results indicated no relationship between the residuals and time of sale.

(7.)D. Belsley, E. Kuh, and R. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (New York: John Wiley and Sons, 1980).

(8.)Ibid., 112.

(9.)Ibid., 105.

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Author: | Dotzour, Mark G.; Levi, Donald R. |
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Publication: | Appraisal Journal |

Date: | Apr 1, 1993 |

Words: | 3736 |

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