Price Measures

Real Estate Price Measures

• Prices quantify value; three key types:
  • Fair value – theoretical “average willingness to pay” derived from fundamentals (credit conditions, rents, etc.)
  • Market (ask) price – ex-ante price set by sellers, seen in listings
  • Transaction price – ex-post price actually paid in completed sales

Real Estate Price Indexes

Purpose:

• Compare values across property types/regions

• Track price changes over time

• Inform buyers, investors, policy-makers, forecasting models

Main construction methods (each has pros/cons):

1. Hedonic

2. Repeat-Sales

3. Stratification (Mix-Adjustment)

4. SPAR (Sale-Price–Appraisal-Ratio)

Hedonic Method

• Survey a sample of properties; score $n$ attributes (size, age, location, etc.)

• Estimate regression: $P \sim \beta<em>0 + \beta</em>1 x<em>1 + \dots + \beta</em>n x_n$

• Predicted prices form the index; to compare periods:

  1. Collect new sample; estimate new $\beta$’s

  2. Apply new $\beta$’s to old sample → “new-old” prices

  3. Index = ratio of new vs. new-old prices

• Strengths: captures quality differences, predictive.

• Limits: relies on representative survey; fixed old sample may mis-represent current preferences.

Repeat-Sales Method

• Observe two (or more) sales of the same dwelling; model log price change:
  $\ln\left(\frac{P<em>{t+\tau}}{P</em>t}\right) \sim \beta<em>0 + \sum \beta</em>i D<em>i$ where $D</em>i$ are time dummies (−1 first sale, +1 second sale).

• Advantages: uses actual transactions; no survey needed.

• Limits: requires large matched-sale data; only descriptive of past changes, no quality attributes.

Stratification Method

• Group dwellings into strata (bins) by attributes (e.g. size >100 m², district X, age >5 yrs).

• Compute mean/median price per stratum for two periods.

• Apply weights (share of transaction value or housing stock) → two weighted prices.

• Index = ratio of weighted prices.

• Pros: simple, avoids surveys.

• Cons: attribute/boundary choice can be arbitrary; weight choice affects results.

SPAR Method

• Need sale price and independent appraisal for each dwelling.

• For period $t$: $\text{SPAR}<em>t = \text{mean}\left(\tfrac{P</em>{sale}}{P_{appraisal}}\right)$

• Index between periods $t<em>1$ and $t</em>2$: $\tfrac{\text{SPAR}<em>{t</em>2}}{\text{SPAR}<em>{t</em>1}}$.

• Pros: no matched sales or attribute lists.

• Cons: requires timely, unbiased appraisals (often scarce or outdated).