A Hierarchical Linear Model Approach for Assessing the Effects of House and Neighborhood Characteristics on Housing Prices

Abstract. This pedagogical paper illustrates by what mode a hierarchical linear model (Raudenbush and Bryk 2002) can be used through researchers and practitioners to estimate housing prices as a function of one as well as the other house and neighborhood characteristics. While traditional hedonic regression moulds allow researchers to include the pair house and neighborhood characteristics in the investigation of housing prices, hedonic regression does not account for the inherent hierarchy in the housing purchase decision, namely that houses reside in neighborhoods, which in turn round exist within cities and states. upon the other hand, multinomial logit protoplasts incorporate such hierarchy but focus primarily upon the housing purchase decision and not the housing price. Thus, the hierarchical linear original gives researchers a more flexible tool to design housing prices.

Introduction

A hedonic regression design has traditionally been used to prototype housing prices. The hedonic approach regresse the price of the house against various characteristics of the house to determine the importance of specific characteristics (such as the number of bathrooms) to explain housing prices. For pick outed examples and extensions of the hedonic approach, diocese Downes and Zabel (2002), Cheshire and Sheppard (1998) Palmquist (1984) Paterson and Boyle (2002) and Yinger, blossom Borsch-Supan and Ladd (1988). greatest in quantity hedonic regression models include characteristics of the community where a house is located, as well as the house's characteristics. Since houses are located within neighborhoods, neighborhoods within cities, and thus forth, residential location decisions are inherently hierarchical, proceeding in stages. In other words, and as pointed on the outside by Quigley (1985), households begin the search proces through choosing a town to live in, followed through a neighborhood to live in given the town, and finally a house to live in given the neighborhood and the town. The hedonic regression original however, does not take advantage of this hierarchy when modeling housing prices.

An alternative approach used in the housing literature is the multinomial logit original (McFadden, 1978). This is a discrete choice approach that attempts to identify the importance of various housing characteristics upon the housing purchase decision. This design does account for the inherent hierarchy in the data (Chattopadhyay, 2000; Nechyba and Strauss, 1998; and Quigley, 1985) Unlike the hedonic archetype however, this approach does not attempt to explain housing prices, on the contrary instead examines the variables that determine whether a household purchases a dwelling or not.

A relatively fresh approach to modeling hierarchical data is the hierarchical linear mould (HLM). Raudenbush and Bryk (2002) outline the various applications and statistical techniques associated with the protoplast HLM has been widely used, particularly in the education literature (see Aitkin, Anderson and Hinde, 1981; Aitkin and Longford, 1986; Goldstein, 1987; Rumberger and Thomas, 1993) Its use in economics has been limited, admitting Kahane (2001) employed the HLM to determine the importance of team and player attributes upon National Hockey League player salaries. His approach exhibits that the HLM can separate the results that different levels of the hierarchy have upon an outcome variable. Thus, the HLM can be exerciseed to model housing prices, as the hedonic archetype does, while at the same time incorporating the hierarchical nature of the data into the analysis, as the multinomial logit does.

The objective in this paper is to demonstrate in a simple way, for the benefit of researchers and practitioners alike, in what manner HLM can be used to make known models that account for the inherent hierarchy in determining housing prices. This paper does not attempt to build a perfect model of housing prices using HLM Therefore, a two-level pattern is considered that specifies housing prices as a function of dwelling and neighborhood characteristics, and includes alone one variable for each horizontal While this limits the intention of the study, it does permit a discussion of the lock opener ideas of the HLM original and the statistical results obtained from similar models in a pedagogical framework. subsequent time research should, of course, expand the list of explanatory variables at each horizontal to develop a more clean model.

An HLM Model of Housing Prices

The goal in this paper is to demonstrate by what means HLM can be used to separate the variation in housing prices into that portion that hangs on house-specific characteristics and that portion that hangs on neighborhood-specific characteristics. The HLM archetype is detailed in Raudenbush and Bryk (2002) and summarized in Kahane (2001)

Raudenbush and Bryk (2002) consign to Equation (5) as the "combined" protoplast As they point out, while Equation (5) is linear, it cannot be estimated using traditional ordinary least squares (OLS) [i]modus operandi[/i]s Standard OLS methods require the random errors to be independent and to have constant variance. The error arrangement in Equation (5) does not fit these requirements for two reasons. First, the errors are hanging within each neighborhood since u^sub 0j^ and u^sub 1j^ are for the use of all to every house in neighborhood j next to the first the errors have unequal variances since u^sub 0j^ + u^sub 1j^(X^sub ij^ - X^sub j^) be pendent on u^sub 0j^ and u^sub 1j^ which vary across neighborhoods and upon (X^sub ij^ - X^sub j^) which varies across houses. In this instance, OL estimates will be the couple biased and inconsistent. For a derivation of the optimal estimator for this pattern see Raudenbush and Bryk (2002)