The simulation analysis on the accuracy and efficiency of MIT transaction index

Abstract

The paper aims to investigate the improvement that Ridge regression brings to the commercial real estate index estimation. The MIT transaction based index extends the use of the last model by Fisher, Gatzlaff, Geltner and Haurin (2003.) They address the sample selection bias and the noise effect of the transaction prices in small sample. To correct sample selection bias, MIT transaction index use the Heckman two-step. In addition to the correction of sample selection bias the MIT transaction based index applies the Ridge filters into the index creation procedures to dampen the effect of noise in transaction prices on estimations. Among them, this paper primarily focuses on: (1) investigating error structures, defined by the difference between the true market return and the estimated index return; (2) examining the efficiency improvement of the Ridge Regression as estimation method over Ordinary Least Square (OLS); (3) selecting the proper value of weight factor "k." The findings on the error structures are as follows. First, MIT transaction index does not suffer from smoothing and lagging which is apparent in the appraisal based index. Second, with larger sample size, the estimated market indexes become close to the true market values. In addition, the estimated market index is more biased when it uses small number of sample. Third, the error does not cumulate over time regardless of the sample size. To correct noise effect on the estimation procedure under the observation poor scenario, this study examines the efficiency of the Ridge regression. First, we examine the qualitative form of relationship between ridge coefficients and the control factor of "k." Generally, ridge trace is not significantly changed with respect to "k." It might be argued that the noise effect is not severe in the estimation procedure, yet the introduction of ridge regression apparently improves the estimation. Indeed, between k =4 and 5 ridge coefficients stabilize. Second, to investigate the improvement of ridge regression, we examine the mean square error.

(cont.) Between k = 4 and 5, mean square error, defined by the difference between the true and estimated market index, achieve the lowest value. Taken together, the system stabilizes between k = 4 and 5 and achieve the minimum mean squared error. This result leads to the conclusion that we can obtain better estimation using the control factor of 5.