According to the best global practices, residential and commercial real estate price indices are calculated using several measures, namely the Laspeyres index or the Paasche index. Another popular measure, the Fisher real estate index is a combination of the two. These indices heavily depend on the available sample and do not take into account sample volatility across time (for example, the quality of purchased units in the sample may increase over time, which will be reflected in higher prices). One way of remedying this issue is to construct a standardized real estate unit in each time period (using a hedonic regression technique) and to use this unit to obtain quality-adjusted indices. The latter indices are called the Laspeyres hedonic imputation index and the Paasche hedonic imputation index (Handbook on Residential Property Price Indices, Eurostat Methodologies and Working Papers, 2013).

To implement this methodology, we first determine the characteristics of a “typical” real estate unit in each month. This is done for both real estate categories (residential and commercial). For example, to determine a typical flat in any given month we calculated the median of the log area of the property advertised in that month, mode of renovation type, mode of district, median of the number of bedrooms, median of the number of bathrooms, and median of the number of balconies. Similarly, to determine a typical commercial area, we calculated the median of the log area of the property, mode of renovation type, mode of district, median of the number of rooms, and median of floor.

Second, we construct a linear regression model on the data in each month using unit price in log form as a dependent variable and controlling for various characteristics of the real estate unit. In the case of flats, we control for the following: the log area of the property, type of renovation (We combine nine categories (black frame, white frame, not finished white frame, no renovation, renovation needed, renovated long ago, renovation in progress, renovated, newly renovated, euro-renovation) into three renovation types: frame, old, and new), district (Vake-Saburtalo, Old Tbilisi, Isani-Samgori, Didube-Chughureti and Gldani-Nadzaladevi), number of bedrooms, number of bathrooms and number of balconies. In the case of commercial units, the log area, type of renovation, district, number of rooms, and the floor the property is on were used as control variables. In short, the general exposition of the model is the following:

method form-1
Where Pt is the price of the real estate unit in period t, Z1, ..., ZK is the characteristics vector of the unit, and is the error term. (The dependent variable is transformed due to the fact that real estate prices tend to have a log-normal distribution).

The regression coefficients tell us how different characteristics of the real estate unit (e.g. location, number of rooms, etc.) affect the price of the property. Clearly, when we repeat the regression for every month, we will obtain different estimates of the coefficients for each month.

The coefficient estimates and the characteristics of a “typical” real estate unit are then combined to calculate both the Laspeyres and Paasche monthly indices.

The two indices differ in the way they combine the coefficients and the “typical” unit characteristics. The exact formula for the Laspeyres hedonic imputation index is:

method form-2

Where a vector is the standardized real estate unit of period (the base period. March 2013 was taken as the base month).

As one can see, the Laspeyres index keeps the unit characteristics constant over time. It takes the “typical” housing unit from the base period (March 2013 in our sample) and compares the price of this unit in any given month t to its price in the base month. The Laspeyres index answers the question: what would be the relative price today of a real estate unit that was typically offered for sale (or rent) in the base month?

The Paasche hedonic imputation index is somewhat different:

method form-3
The Paasche index takes the characteristics of a “typical” real estate unit advertised in month t, and compares the current price of this unit to the price it would have had in the base month. Essentially the Paasche index answers the question: what is the price of a typical real estate unit today relative to the price of the same unit in the base month?

Both of these indices have advantages and disadvantages. The Laspeyres index could possibly overstate any price increase, as it would not account for substitutions towards cheaper (e.g. smaller or in a less prestigious area) real estate units as prices increase. At the same time, the Paasche index could understate any price increase for the same reason – it would “allow” people to substitute lower quality housing options as prices go up.

The best way to reconcile both measures is to obtain a Fisher-type hedonic imputation index – the geometric average of the Laspeyres and Paasche indices:

method form-4
The Fisher index is used as the main indicator of real estate price movement in our report.

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