## _wp1472

## Source details

**Canonical URL:** [_wp1472](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1472.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1472.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1472.pdf.json)

---

### I. Introduction — motivation and framing
- Residential (house) and commercial property price indexes (RPPIs and CPPIs) should be at least quarterly measures of change in actual transaction prices of a constant-quality basket of representative properties.
- Hedonic regressions and matched (repeat) transactions are the two primary methods used to control for changes in the quality-mix of properties transacted.
- Accurate measures of RPPIs and CPPIs are important for economic analysis, monetary policy, financial stability and prudential supervision.
- The IMF/FSB G-20 Data Gaps Initiative (DGI) includes CPPIs in its 20 recommendations on data gaps.
- Measurement of CPPIs remains highly problematic due to property heterogeneity and irregular transactions.

### II. Data and empirical scope
- Empirical work is based on panel granular transaction-based CPPIs by metropolitan area and type of transaction for the United States from 2000Q4–2012Q4 (RCA series; later granular series use 2000:Q1 onward).
- Two panel data sets used:
  - RCA CPPIs 2000:Q1–2012:Q4 for “apartments” broken down by 34 metros/markets.
  - RCA CPPIs 2000:Q1–2012:Q4 for “other properties” (industrial, office, retail) grouped as “core commercial”.
- RCA transaction coverage and filters:
  - From 2000 RCA covered transactions of over $5 million; in 2005 extended to transactions over $2.5 million (inflation-adjusted to December 2010).
  - RCA filters: exclude “flipped” properties (sold twice in 12-months or less); exclude transactions not at arm’s-length; exclude properties where size or use has changed; exclude properties with extreme price movements (more than 50 percent annual gain/loss).

### III. Methodological innovations and estimator choices
- Primary estimator: two-way fixed effects panel regression estimating time dummies of price inflation using least squares dummy variable (LSDV) method (restriction 1 0γ and include a constant). Both OLS and counts-based WLS are used.
- Use of counts:
  - Counts C_{n,t} are number of observed price transactions for area n in period t (for RCA CPPI, count is number of transactions in the period with earlier transaction-pairs on same property).
  - WLS uses counts as explicit weights with assumption var(V_{n,t})=f(C_{n,t}): as counts increase variance decreases; WLS improves efficiency by down-weighting less precise observations.
  - Measurement error model: observed Y_{n,t} = Y_{n,t}^* + Ε_Y; measurement error increases variance of error term; explicit WLS counts target var(Ε_Y) component to improve precision of ˆγ_t estimates.
- Spatial modeling — SAR model:
  - Specification: Y = ρ W Y + Z μ + Z γ + V (reduced form (I - ρ W)^{-1} (Z μ + Z γ + V)).
  - Marginal effects matrix: B_t = (I - ρ W)^{-1} γ_t. Direct effects = diagonal(B_t); indirect effects = off-diagonals; total effects = column sums.
  - SAR rationale: inclusion of ρ W Y ameliorates omitted variable bias and captures spillovers.
- Relaxing fixed ρ and W:
  - Estimate annually for 4-quarter windows (2000, 2001, …, 2012) allowing ρ^τ and W^τ fixed within year but varying between years.
  - Spatial weight matrix W^n generated from longitudes and latitudes of areas; for nine less-concentrated metro areas employment-weighted average longitudes/latitudes used to represent centers.
- Weighted aggregation:
  - Decompose B_t into n components and apply explicit weights S (n×n diagonal matrix of area relative shares in stocks or transactions) to obtain weighted direct and total effects.
  - Compare fixed-base weighted and annually chain-weighted estimates (48 quarterly inflation rates in 12 independent windows of 4 quarters).

### IV. Appraisal-based vs transaction-based CPPIs — features and limitations
- Appraisal-based indexes:
  - Definition: ratio of a simple aggregation of appraised values in each period of a selected group of properties.
  - Example: NCREIF Property Index (NPI) is a quarterly total rate of return of individual commercial real estate properties; members submit appraised fair market values and NOI each quarter.
  - Limitations: valuations differ from transaction prices, are often irregular (stale values), methods differ across valuers, evidence of dampening/smoothing and lagging market price volatility.
  - User preference: end-users prefer transaction-based CPPIs; ECB considered valuation indexes “a second best option”.
- Transaction-based indexes (RCA CPPI):
  - Repeat-sales regression is used for building-block CPPIs: pair transactions for same property and regress on time dummies (Shiller, 1991).
  - Advantages: controls for changes in quality mix by comparing same-property transactions.
  - Disadvantages: quality changes between sales (depreciation/renovation), small sample sizes → sampling error and potential sample selectivity bias, asymmetric/positive variance of error term, heteroskedasticity materially affects index, volatile revision history as new pairs added.
  - ECB “transaction-linked” mixed approach uses prior appraised capital value to predict prices for non-traded properties but sparse transaction data remains an issue.

### V. Empirical results — sparse-data insights and numerical findings
- Panel/unit-root diagnostics (inflation rates):
  - Core commercial property inflation: Im, Pesaran and Shin W-statistic = -28.62 (p-value=0.0000); ADF Fisher Chi-squared statistic = 773.7 (p-value=0.0000); Phillips and Perron Fisher Chi-squared statistic = 832.3 (p-value=0.0000) — null of individual unit roots rejected.
  - Apartments: IPS = -1.33 (p-value=0.092) (rejection at 10 percent), ADF = 5.02 (p-value=0.081), PP = 2.92 (p-value=0.232) — mixed evidence.
- Counts association with inflation (bivariate correlations, 2001Q1:2012Q4 and subperiods):
  - Whole period 2001Q1:2012Q4:
    - All: 0.298**
    - Office: 0.215
    - Retail: 0.286*
    - Industrial: 0.312**
    - Apartment: 0.239
  - Pre-recession 2000Q4:2007Q4:
    - All: 0.538***
    - Office: 0.702***
    - Retail: 0.007
    - Industrial: 0.721***
    - Apartment: 0.168
  - Recession 2008Q1:2012Q4:
    - All: 0.612***
    - Office: 0.487**
    - Retail: 0.601***
    - Industrial: 0.578***
    - Apartment: 0.622***
  - Significance notation: ***, **, * denotes statistically significant at 1, 5, and 10 percent levels respectively.
- Causality and pooled regressions:
  - Pooled regressions of inflation on counts show significant positive coefficients for each property type in pre-recession and recession sub-periods (sole exception: retail during the recession).
  - Chow F-statistic for difference between pre-recession and recession periods = 113.1 (p-value 0.0000).
  - Granger-causality: no evidence in pre-recession; during recession mixed/limited: office counts Granger-cause inflation; apartments inflation Granger-causes counts; remaining cases mixed.
- OLS vs counts-based WLS (efficiency and bias):
  - Sample sizes for pooled regressions: 48 quarterly observations × 34 areas = 1,632 observations.
  - Pooled OLS R2 for apartments and core commercial properties reported as 0.47 and 0.48 respectively.
  - For US apartments, WLS and OLS/RCA inflation estimates converge before, during, and after the recession; the trough around 2009:Q1 as estimated by WLS was smaller by over 1.5 percentage points compared with OLS.
  - For core-commercial properties (industrial, retail, office aggregated) counts are larger and sparsity less problematic; counts-based WLS has little impact on aggregates.
- SAR panel models — diagnostics and numeric results:
  - Spatial weight matrix nW is a row-standardized inverse distance matrix; for nine less-concentrated metros employment-weighted centers used; nW allowed to vary annually.
  - Null hypothesis ρ = 0 rejected for whole period for both apartments and core commercial properties.
  - ˆρτ statistically significant in just over half of the 12 individual years for apartments and in only 3 years for core commercial properties; with a single exception significant ˆρτ values are positive.
  - Standard deviation of ˆρ: apartments = 0.34 percent; core commercial = 0.14 percent.
  - OLS estimates biased upwards relative to SAR total (fixed) by:
    - On average: 1.78 percentage points (apartments) and 1.68 percentage points (core commercial).
    - In 2009:Q1: 2.47 percentage points (apartments) and 2.48 percentage points (core commercial).
  - SAR total effect primarily constituted by direct effect with smaller indirect effect except at troughs:
    - Example: apartments in 2009:Q1 — total fall 12.0 percent comprised of 8.6 percent direct effects and 3.4 percent indirect effects.
- Spatial regression diagnostics (selected):
  - Period 2001Q1–2012Q12: Apartments Log-likelihood = -4408.646; R-sqrd = 0.498; rho = 0.30059*** (std. error (0.0433741)).
  - Period 2001Q1–2012Q12: Core commercial Log-likelihood = -4,427.100; R-sqrd = 0.483; rho = 0.24722*** (std. error (0.04370)).
  - Observations: 34 areas × 48 quarters = 1,632; annual windows: 34 × 4 = 136.
  - Significance notation: ***,**, * denote statistically significant at 1, 5, and 10 percent levels respectively. Driscoll-Kraay standard errors reported in parentheses.
- Weights and aggregation — Moody’s/RCA vs BEA comparisons:
  - Moody’s/RCA CPPI weights approximate share of outstanding stock using 10-year rolling average of transaction volume.
  - Table 3 selected entries (2011 comparison):
    - National All-Property Index: 100.0 (both)
    - Core Commercial: Moody’s/RCA 73.0; BEA 73.8
    - Retail: Moody’s/RCA 19.564; BEA 18.6
    - Office CBD: Moody’s/RCA 19.491; BEA 26.9
    - Office Suburban: Moody’s/RCA 19.345; BEA 45
    - Industrial: Moody’s/RCA 14.6; BEA 28.3
    - Apartment: Moody’s/RCA 27.0; BEA 26.2
  - Notable divergence: industrial share 14.6 (RCA) vs 28.3 (BEA) percent of estimated stock in 2011.
  - Recompiled indexes using BEA weights (2000:Q4 – 2012:Q4):
    - Average quarter-on-quarter change for BEA-weighted indexes: 3.51 percent.
    - Average quarter-on-quarter change for Moody’s/RCA index: 3.69 percent.
    - Largest single-period difference noted: BEA-based -9.53 percent vs Moody’s/RCA -10.1 percent for one two-way aggregation stage.

### VI. Annex findings — aggregation and counts applications
- Apartment CPPI aggregation:
  - Moody’s/RCA aggregate for “apartments” is weighted average of two building-block indexes: Major Markets (six MMs: Boston, Chicago, DC, Los Angeles, New York, San Francisco) and Non-Major Markets (remaining 28).
  - Apartment building CPPI inflation for major and non-major markets estimated using OLS and counts-based WLS as pooled regressions.
  - Deviations for apartments:
    - Bottom of trough in 2009:Q1 underestimated by OLS vs WLS by 2.4 percentage points for non-major markets and by 1.7 percentage points for major markets.
- Core-commercial non-major market deviations (specific numeric deviations):
  - Trough overestimated (deeper) using OLS by 1.34 percentage points in 2001:Q4.
  - Trough overestimated by 1.70 percentage points in 2009:Q2.
  - Trough overestimated by 2.19 percentage points in 2012:Q4.
  - In 2010:Q3 OLS inflation exceeded WLS inflation by 1.49 percentage points.

### VII. Conclusions and methodological recommendations
- Two-way fixed effects panel models with counts-based WLS improve efficiency of inflation estimates from granular transaction-based CPPIs by down-weighting sparsely observed, imprecise series.
- SAR models that incorporate spatial spillovers reduce fixed-effects bias and better account for spatial autocorrelation; OLS without spatial terms is biased upwards for apartments and core commercial properties.
- Relaxing fixed ρ and nW and introducing weighted aggregation within SAR models is feasible, but chain-weighting produced limited empirical gains in this application.
- Recommended practices:
  - Test ρ = 0 for sub-periods τ and consider wider windows for panel regressions as applicable.
  - Consider SAR formulations that allow for varying spatial weights where appropriate.
  - Use counts-based WLS to reduce leverage from sparsely observed series, particularly in downturns.
- Overall: the proposed methodology demonstrates gains in efficiency and bias reduction and should inform CPPI estimation despite mixed results for chain-weighting.

*Source: _wp1472 - Section IIA. Estimates of commercial property price inflation are based on ˆtγ in equation (1) (PDF chapter/section).*

### References ........................................................................................................24

_wp1472 - References ........................................................................................................24

### I. INTRODUCTION

- Residential (house) and commercial property price indexes (RPPIs and CPPIs) should be at least quarterly measures of change in actual transaction prices of a constant-quality basket of representative properties.
- In practice, residential and commercial properties are heterogeneous and transactions irregular, complicating comparisons of average transaction prices for a fixed-quality bundle of properties over time.
- Hedonic regressions of price on the quality characteristics of the properties and use of only matched (repeat) transactions are the two primary methods used to control for changes in the quality-mix of properties transacted.
- Both hedonic and repeat-sales methods can be estimated as panel regressions using the parameter estimates of dummy variables on time (see Eurostat et al., 2013) to derive the index.
- Accurate measures of RPPIs and CPPIs are important for economic analysis, monetary policy, financial stability and prudential supervision.
- The International Monetary Fund (IMF)/Financial Stability Board (FSB) G-20 Data Gaps Initiative (DGI), endorsed by the G-20 Finance Ministers and Central Bank Governors, as well as the IMF’s International Monetary and Financial Committee (IMFC), includes CPPIs in its 20 recommendations on data gaps (see Heath, 2013).
- Measurement of CPPIs remains highly problematic.

### Data and empirical scope

- Empirical work is based on panel granular transaction-based CPPIs by metropolitan area and type of transaction for the United States (US) from 2000Q4–2012Q4.
- Regression formulations are commonly used in aggregation to control for quality-mix changes in transactions data.
- The paper’s concern is not with quality-mix methods per se, but with the efficiency and bias of estimates of aggregate price movements arising from panel regression frameworks often used.

### Methodological innovations proposed

- The concern is with sparse data and, akin to normal statistical practice when faced with limited sample sizes, increasing the efficiency of the estimator.
- Use of “counts”—number of transactions—in each quarter for each area/type of property to improve the efficiency of estimates of US commercial property price inflation.
- Inclusion of a spatial autoregressive (SAR) term in the regression thus removing potential bias by incorporating spillover effects — a SAR model.
- Improvements sought for parameter estimates by allowing the spatial weighting matrix and autoregressive parameter to vary over time.
- The nn matrix (for n cross-sectional areas) that comprise each parameter estimate for each period is deconstructed and explicitly-weighted (direct, total, and indirect) averages of matrix elements provide estimates of commercial property price inflation, as opposed to the unweighted ones provided by standard software.
- Fixed and chained-weighted parameter estimates are provided for comparison.
- Consideration of the use of weights based on perpetual-inventory stock estimates for higher level aggregation.

*Source: _wp1472 - References ........................................................................................................24*

### Section II briefly outlines select features of appraisal and transaction-based CPPIs with a focus

### _wp1472 - Section II briefly outlines select features of appraisal and transaction-based CPPIs with a focus

### II. APPRAISAL AND TRANSACTION-BASED INDEXES — overview
- The section contrasts appraisal-based (valuation) CPPIs and transaction-based CPPIs, with a focus on United States data and methodology used later in the paper.
- Motivation: sparse transactions on heterogeneous properties are particularly severe for CPPIs and become more problematic in and during recessions; valuations allow coverage irrespective of transactions.

### A. Appraisal-based indexes — features and limitations
- Definition: an appraisal-based index is the ratio of a simple aggregation of appraised values in each period of a selected group of properties.
- Example: National Council of Real Estate Investment Fiduciaries (NCREIF) Property Index (NPI) is a quarterly total rate of return of individual commercial real estate properties acquired in the private market for investment purposes covering office, retail, industrial, apartment/hotel properties.
- Measurement concept: total return of a property includes both net operating income (NOI) and capital return, measured as if purchased at beginning and sold at end of quarter with investor receiving all net cash flows during the quarter; members submit appraised fair market values and NOI each quarter.
- Identified limitations and concerns:
  - Appraisal-based measures differ from transaction prices and have an informed subjective basis not fully consistent with System of National Accounts valuation principles (SNA 2008, chapter 2, C3).
  - Valuations are often conducted irregularly (e.g., annually); quarterly series may use manager/owner estimates based on last formal appraisal (stale values).
  - Valuation methods differ across countries and valuers (Kanutin, 2013).
  - Evidence of dampening/smoothing of market price volatility and tendency to lag market price indexes (Devaney and Diaz (2011), Fisher and Geltner (2007), Geltner et al., (2003)).
  - User preference: end-users prefer transaction-based CPPIs; ECB viewed valuation indexes as “a second best option” and developed quarterly valuation-based CPPIs as a second-best solution given sparse transaction data.

### B. Transaction-based indexes — RCA CPPI characteristics
- Data source used in the US study: Real Capital Analytics (RCA CPPI).
- Time coverage used in study: from 2000:Q4 to 2012:Q4 (RCA series used; later empirical work uses 2000:Q1 onward for granular series).
- Transaction size coverage:
  - From 2000 RCA covered transactions of over $5 million.
  - In 2005 RCA extended to transactions over $2.5 million (at constant dollars inflation-adjusted to December 2010).
- Data filters applied by RCA:
  - Exclude “flipped” properties (sold twice in 12-months or less).
  - Exclude transactions not at arm’s-length.
  - Exclude properties where size or use has changed.
  - Exclude properties with extreme price movements (more than 50 percent annual gain/loss).
- Aggregation structure:
  - RCA National CPPIs aggregate from detailed CPPIs: “Major” and “Non-Major” metro markets for each of five property types (apartment, retail, industrial, office CBD, and office suburban).
  - Building-block CPPIs and individual granular CPPIs use repeat-sales regression.
- Repeat-sales regression details:
  - For each quarter since 1988, identify sales; pair transactions for the same property and estimate a repeat sales price index using prices of transaction pairs in a regression on time dummies (Shiller, 1991).
  - Advantages: controls for changes in quality mix by comparing same-property transactions.
  - Disadvantages:
    - Quality of repeat purchases may change (depreciation or renovations).
    - Increased sampling error due to small sample sizes and potential sample selectivity bias (properties not sold or new properties sold once are excluded; sample may over-represent frequently sold atypical properties).
    - Asymmetric and positive variance of error term; longer gaps between sales may require less weight; heteroskedasticity assumptions materially affect index (Leventis, 2008).
    - Index may have volatile revision history as new transaction pairs are added.
- Mixed transaction-appraisal approaches:
  - ECB “transaction-linked” indexes regress log transaction prices on prior appraised capital value (preceding two quarters) plus country/property-type dummies; coefficients predict transaction prices for non-traded properties to increase sample, but sparse underlying transaction data remains an issue.

### III. METHODOLOGY — estimator choices, spatial modeling, and weighting
- Goal: develop efficient estimators for higher-level commercial property price inflation from granular CPPIs given sparsity.
- Primary estimator: two-way fixed effects panel regression estimating time dummies of price inflation using least squares dummy variable (LSDV) method (restriction 1 0γ and include a constant). Both OLS and counts-based WLS are used.
- Use of counts:
  - Counts data ,ntC are number of observed price transactions for area n in period t (for RCA CPPI, count is number of transactions in the period with earlier transaction-pairs on same property).
  - WLS uses counts as explicit weights with assumption var(Vnt)=f(Cnt): as counts increase variance decreases; WLS improves efficiency by down-weighting less precise observations.
  - Measurement error model: observed Ynt = Ynt* + ΕY; measurement error increases variance of error term; explicit WLS counts target var(ΕY) component to improve precision of tγ estimates.
  - Literature note: measurement error in dependent variable causes OLS to be unbiased but inefficient with larger SEs and lower R2.
- Modeling spatial dependency — SAR model:
  - Include first-order spatial autoregressive term: Y = ρ W Y + Z μ + Z γ + V (equation (3)) where W is row-standardized spatial proximity matrix and ρ is spatial autoregressive parameter.
  - Reduced form: (I - ρ W)^{-1} (Z μ + Z γ + V).
  - Marginal effects: matrix B_t = (I - ρ W)^{-1} γ_t; direct effects are diagonal elements of B_t, indirect effects are off-diagonals, total effects are column sums. Software reports average direct effect as tr(B_t)/n and average total effect as average column sum.
  - Interpretation: direct effects include feedback from proximate areas due to spatial dependence; direct, indirect, and total effects depend on W, ρ, and γ_t.
  - Rationale: SAR helps ameliorate omitted variable bias via inclusion of ρ W Y; example cited where conventional FE coefficient reduced when applying SAR.
- Relaxing constant ρ and W:
  - Standard software holds ρ and W constant; the paper relaxes this by estimating equation (5) annually for 4-quarter windows (2000, 2001, …, 2012), allowing ρ^τ and W^τ to be fixed within year but vary between years.
  - Spatial weight matrix W^n is generated from longitudes and latitudes of areas; in some cases centers are represented by relative employment weighted averages of conurbations; annual estimation accounts for changing center-of-gravity of commercial property.
- Weighted averages of commercial property price inflation:
  - Standard software averages marginal effects unweighted; the paper decomposes total and direct effects into n components and applies explicit weights S (nn× matrix with diagonal area relative shares in stocks or transactions) to obtain weighted averages per Diewart (2005) WLS analytic weights idea.
  - Weighted direct effect for γ_1 given by sum_n (S B_t)_{nn} (equation (6)).
- Relaxing fixed weights:
  - Allow weights S^τ to vary annually by estimating 48 quarterly inflation rates in 12 independent windows of 4 quarters, producing annually chain-weighted estimates and comparing these to fixed-base weighted estimates.

### IV. EMPIRICAL RESULTS — data and sparse-data insights
A. Data used
- Transaction-based CPPIs from Real Capital Analytics (RCA CPPI).
- Coverage notes reiterated:
  - From 2000 RCA covered transactions over $5 million; extended in 2005 to transactions over $2.5 million (inflation-adjusted to December 2010).
  - RCA filters applied: exclude flips, non-arm’s-length, size/use-changed properties, extreme price movements (>50 percent annual gain/loss).
- Two panel data sets used in empirical work:
  - RCA CPPIs from 2000:Q1 to 2012:Q4 for “apartments” broken down by 34 metros/markets areas.
  - RCA CPPIs from 2000:Q1 to 2012:Q4 for “other properties” (industrial, office, retail) grouped as “core commercial”.
- The paper uses all 34 area inflation rates as the left-hand-side Y_{n,t} in the regressions.
- Panel unit-root tests (on inflation rates):
  - Core commercial property inflation: Im, Pesaran and Shin W-statistic = -28.62 (p-value=0.0000); ADF Fisher Chi-squared statistic = 773.7 (p-value=0.0000); Phillips and Perron Fisher Chi-squared statistic = 832.3 (p-value=0.0000) — null of individual unit roots rejected.
  - Apartments: IPS = -1.33 (p-value=0.092) (rejection at 10 percent), ADF = 5.02 (p-value=0.081), PP = 2.92 (p-value=0.232) — mixed evidence.
B. Sparse data — counts association with inflation
- RCA provided confidential counts (number of transactions underlying each granular index per period).
- Expectation: positive association between counts and commercial property price inflation because counts fall during recessions and rise during recovery.
- Empirical bivariate correlations (counts vs. commercial property price inflation) reported in Table 1 for 2001Q1:2012Q4 and subperiods:
  - Whole period: 2001Q1: 2012Q4
    - All: 0.298**
    - Office: 0.215
    - Retail: 0.286*
    - Industrial: 0.312**
    - Apartment: 0.239
  - Pre-recession: 2000Q4: 2007Q4
    - All: 0.538***
    - Office: 0.702***
    - Retail: 0.007
    - Industrial: 0.721***
    - Apartment: 0.168
  - Recession: 2008Q1: 2012Q4
    - All: 0.612***
    - Office: 0.487**
    - Retail: 0.601***
    - Industrial: 0.578***
    - Apartment: 0.622***
  - Significance notation: ***, **, * denotes statistically significant for two-tailed test at 1, 5, and 10 percent levels respectively.
- Summary findings:
  - A consistent positive association exists between inflation and counts for office, retail, industrial, and apartment properties across 2001Q1 to 2012Q4 and within pre-recession and recession sub-periods.
  - The association is statistically significant at a 5 percent level for each property type during the recession and for the aggregate of all properties in each period considered.
- Additional notes on causality and robustness:
  - Assigning causality between inflation and counts is problematic a priori.
  - Reported pooled regressions of inflation on counts show significant positive coefficients for each property type in pre-recession and recession sub-periods (sole exception: retail during the recession).
  - Chow F-statistic for difference between pre-recession and recession periods = 113.1 (p-value 0.0000).
  - No evidence of Granger-causality between inflation and counts during the pre-recession period; mixed/limited results during the recession (office: counts Granger-cause inflation; apartments: inflation Granger-causes counts; remaining cases mixed).

*Italic: Source: _wp1472 - Section II briefly outlines select features of appraisal and transaction-based CPPIs with a focus (PDF chapter section).*

### Section IIA. Estimates of commercial property price inflation are based on

### Section IIA. Estimates of commercial property price inflation are based on ˆtγ in equation (1)

### Estimation approach and data
- Proportionate impact of period t time dummy estimated using the Kennedy (1981) consistent approximation: (expexp(   (/ 2))1ˆˆV[ ]ttγγ−, where ˆtγ is the OLS estimator and ( )ˆVtγ its estimated variance. Giles (2011) shows the approximation is extremely accurate.
- Sample sizes for pooled regressions: 48 monthly observations on 34 areas → 1,632 observations.
- Pooled OLS R2 for apartments and core commercial properties reported as 0.47 and 0.48 respectively; corresponding figures for core commercial properties reported as 0.43 and 0.44 in other contexts.
- Counts-based weighted least squares (WLS) estimator used to improve efficiency where sparse data raises leverage from extreme observations.

### Main empirical findings — OLS vs WLS and RCA/Moody’s comparisons
- For US apartments, WLS and OLS/RCA inflation estimates converge before, during, and after the recession; however, the trough around 2009:Q1 as estimated by WLS was smaller by over 1.5 percentage points.
- Explanation: less precisely measured values from smaller sample sizes are more likely to be extreme with relatively high leverage; WLS down-weights these extremes in downturns.
- For “core-commercial properties” (aggregated industrial, retail, office), counts are larger and data sparsity is less problematic; use of counts (WLS) hardly matters for these aggregates.
- Moody’s/RCA CPPI aggregation differs by using repeat-sales regressions over two sub-aggregates (major and non-major metro markets) and 10-year rolling average transaction-volume weights.

### SAR panel models and spatial dependence (method and diagnostics)
- Panel regressions: apartments and core commercial inflation on 34 areas by 48 quarters (2001:Q1–2012:Q4). OLS two-way fixed effects model used as benchmark.
- Spatial autoregressive (SAR) models estimated by ML with Driscoll-Kraay standard errors; data transformed per Lee and Yu (2010) with little substantive effect.
- Spatial weight matrix nW derived as a row-standardized inverse distance matrix; for nine less-concentrated metro areas employment-weighted average longitudes/latitudes used and nW allowed to vary annually for these areas.
- Null hypothesis 0ρ = rejected for whole period for both apartments and core commercial properties.
- Spatial autocorrelation more prevalent for apartments than core commercial properties:
  - ˆτρ statistically significant in just over half of the 12 individual years for apartments, and in only 3 years for core commercial properties; 12 of these at a 10 percent level.
  - With a single exception, significant ˆτρ values are positive.
- Standard deviation of ˆτρ: apartments = 0.34 percent; core commercial = 0.14 percent.
- OLS estimates biased upwards relative to SAR total (fixed) by:
  - On average: 1.78 percentage points (apartments) and 1.68 percentage points (core commercial).
  - In 2009:Q1: 2.47 percentage points (apartments) and 2.48 percentage points (core commercial).
- SAR total effect primarily constituted by the direct effect with little indirect difference except for the trough in 2009:
  - Example: apartments in 2009:Q1 — total fall 12.0 percent comprised of 8.6 percent direct effects and 3.4 percent indirect effects.

### Fixed vs varying rho and spatial weights; fixed vs chain (metro-area) weights
- SAR models estimated with fixed and annually varying ρ and nW (annual windows).
- Fixed vs chain (metro area) weighted SAR panel inflation rates compared against unweighted SAR:
  - Mean absolute deviation between unweighted and fixed base-weighted variants: 0.13 percentage points (apartments) and 0.11 percentage points (core commercial).
  - Annual updating of weights vs fixed weights produced average differences of 0.03 percentage points (apartments) and 0.11 percentage points (core commercial).
- Interpretation: incorporating a spatial component removes some inter-area price change, reducing the need for variable weights.
- Two-way unweighted OLS panel fixed effects measures are substantially biased upwards for apartments.

### Weights and higher-level aggregation: Moody’s/RCA vs BEA comparisons
- Three methods to estimate market capital value of real estate: i) direct measurement of stock; ii) perpetual inventory calculations; iii) extrapolation using proxies.
- Moody’s/RCA CPPI weights approximate share of outstanding stock using 10-year rolling average of transaction volume.
- Table 3 (selected entries) — Moody’s/RCA CPPI Composite Index weights vs BEA-based Index Weights (2011):
  - National All-Property Index: 100.0 (both)
  - Core Commercial: Moody’s/RCA 73.0; BEA 73.8
  - Retail: Moody’s/RCA 19.564; BEA 18.6
  - Office CBD: Moody’s/RCA 19.491; BEA 26.9
  - Office Suburban: Moody’s/RCA 19.345; BEA 45 (table format issues preserved as in source)
  - Industrial: Moody’s/RCA 14.6; BEA 28.3
  - Apartment: Moody’s/RCA 27.0; BEA 26.2
- Table 4 (BEA and Moody’s/RCA weights, percentages for apartments and core commercial CPPIs) reports annual time series (2000–2012) showing relative stability of apartment vs core commercial shares (examples):
  - 2001: Moody’s/RCA core commercial 0.273 / apartments 0.727; BEA core commercial 0.256 / apartments 0.744 (and breakdowns for industrial, office, retail as reported).
  - 2012: Moody’s/RCA core commercial 0.272 / apartments 0.728; BEA core commercial 0.255 / apartments 0.745 (and breakdowns).
- Notable divergence: industrial share 14.6 (RCA) vs 28.3 (BEA) percent of estimated stock in 2011.
- Recompiled indexes using BEA weights (2000:Q4 – 2012:Q4):
  - Average quarter-on-quarter change for BEA-weighted indexes: 3.51 percent.
  - Average quarter-on-quarter change for Moody’s/RCA index: 3.69 percent.
  - Largest single-period difference noted: BEA-based -9.53 percent vs Moody’s/RCA -10.1 percent for one two-way aggregation stage.

### Conclusions and methodological recommendations
- Two-way fixed effects panel models with counts-based WLS improve efficiency of inflation estimates from granular CPPI transaction data.
- SAR models incorporating spatial spillovers remove fixed-effects bias and better account for spatial autocorrelation.
- Relaxing restrictions on fixed ρ and nW and introducing weights within SAR models (fixed-base and chained weights) are feasible; however, chain-weighting produced disappointing empirical gains in this application.
- Recommend:
  - Testing 0τρ = for sub-periods τ and using wider windows for panel regressions as applicable.
  - Considering SAR formulations that allow for varying spatial weights where appropriate.
  - Using counts-based WLS to reduce leverage from sparsely observed series in downturns.
- Overall: proposed methodology demonstrates gains in efficiency and bias reduction and should be of interest despite mixed results for chain-weighting.

*Source: _wp1472 - Section IIA. Estimates of commercial property price inflation are based on ˆtγ in equation (1).*

### References

### _wp1472 - References

### References (bibliography)
- Anselin, L 2008. Errors in variables and spatial effects in hedonic house price models of ambient air quality". Empirical Economics, 34, 1, 5–34.
- Anselin L., Le Gallo J., Jayet H. 2008. Spatial Panel Econometrics, in Matyas L. and Sevestre P. Eds., The Econometrics of Panel Data, Fundamentals and Recent Developments in Theory and Practice, 3rd Edition, chapter 18, 627-662, Berlin, Springer-Verlag.
- Belotti, Federico, Hughes, Gordon, and Andrea Piano Mortari 2013. XSMLE - A command to estimate spatial panel models in Stata, German Stata Users Group Meeting, Potsdam, June 7, 2013.
- Bokhari, Sheharyar and David Geltner 2012. Estimating real estate price movement for high-frequency tradable indexes in a scarce data environment, Journal of Real Estate Finance and Economics 45, 2, 522-43.
- Debarsy, Nicolas and Cem Ertur 2010. Testing for spatial autocorrelation in a fixed effects panel data model, Regional Science and Urban Economics 40, 453–470.
- Devaney, Steven and Roberto Martinez Diaz 2011. Transaction Based Indices for the UK Commercial Real Estate Market: An Exploration using IPD Transaction Data, Journal of Property Research, 28, 4, 269-289.
- Diewert, W. Erwin 2005.Weighted country product dummy variable regressions and index number formulae, Review of Income and Wealth, 51, 561–70.
- Diewert, W. Erwin and Chihiro Shimizu 2013. A conceptual framework for commercial property price indexes, University of British Columbia, School of Economics Discussion Paper 13-11.
- Driscoll, John C. and Aart C. Kraay 1998. Consistent covariance matrix estimation with spatially dependent data, Review of Economics and Statistics 80, 4, 549-60.
- Elhorst, J. Paul 2010. Applied Spatial Econometrics: Raising the Bar, Spatial Economic Analysis 5, 1, March.
- Eurostat, European Union, International Labor Organization, International Monetary Fund, Organisation for Economic Co-operation and Development, United Nations Economic Commission for Europe, The World Bank 2013. Handbook on Residential Property Prices Indices RPPIs, Luxembourg, European Union.
- Feldstein, Martin and Charles Yuji Horioka 1980. Domestic saving and international capital flows, Economic Journal 90, 314–29.
- Florance, Andrew C., Miller, Norm G., Peng, Ruijue, and Jay Spivey 2010. Slicing, dicing, and scoping the size of the U.S. commercial real estate market, Journal of Real Estate Portfolio Management, 16, 2, 101-18.
- Geltner, David and Jeffrey Fisher 2007. Pricing and index considerations in commercial real estate derivatives, The Journal of Portfolio Management 33, 5, 99–118.
- Geltner, David and Henry Pollakowski 2007. A set of indexes for trading commercial real estate based on the Real Capital Analytics Transaction Prices Database, MIT Center for Real Estate Working Paper, Release 2.
- Giles, David E. 2011. Interpreting dummy variables in semi-logarithmic regression models: exact distributional results, University of Victoria, Department of Economics, Econometrics Working Paper EWP1101, January.
- Hann, Jan de and W. Erwin Diewert, Hedonic regression methods, and Jan de Hann, Repeat sales methods. In Eurostat et al. 2013 op. cit.
- Hausman, J. 2001. Mismeasured variables in econometric analysis, problems from the right and problems from the left. Journal of Economic Perspectives 15, 4, 57-67.
- Heath, Robert 2013. Why are the G-20 Data Gaps Initiative and the SDDS Plus Relevant for Financial Stability Analysis? Journal of International Commerce, Economics and Policy, 4, 3.
- Kanutin, Andrew 2013. ECB progress towards a European commercial property price index. Paper presented at the 13th Ottawa Group Meeting held from 1–3 May, 2013, Copenhagen, Denmark. Available at: http://www.dst.dk/da/Sites/ottawa-group/agenda.aspx.
- Kennedy, Peter, E. 1981. Estimation with correctly interpreted dummy variables in semilogarithmic equations, American Economic Review 71, 4, 801.
- Lee, Lung-fei and Jihai Yu 2010a. Estimation of spatial autoregressive panel data models with fixed effects, Journal of Econometrics 154, 165–185.
- Lee, Lung-fei and Jihai Yu 2010b. Some recent developments in spatial panel data models. Regional Science and Urban Economics 40, 255–271.
- LeSage JP, Pace RK 2009. Introduction to Spatial Econometrics. Taylor & Francis, New York, FL.
- Leventis, Andrew 2008. Revisiting the Differences between the OFHEO and S&P/Case-Shiller House Price Indexes: New Explanations, Office of Federal Housing Enterprise Oversight, January, Available at: http://www.fhfa.gov/webfiles/1163/OFHEOSPCS12008.pdf.
- Levin, Andrew, Chien-Fu Lin, and Chia-Shang James Chu 2002.Unit Root Tests In Panel Data: Asymptotic and Finite-Sample Properties, Journal of Econometrics, 108, 1–24.
- Manski, C. F. 1993. Identification of endogenous social effects: The reflexion problem. Review of Economic Studies 60: 531-42.
- Mason, Phil and Gwilym Pryce 2011. Controlling for transactions bias in regional house price indices, Housing Studies, 26, 5, July, 639-660.
- Picchetti, Paulo 2013. Estimating and smoothing appraisal-based commercial real-estate performance indexes. Paper presented at the 13th Ottawa Group Meeting held from 1–3 May, 2013, Copenhagen, Denmark. Available at: http://www.dst.dk/da/Sites/ottawa-group/agenda.aspx.
- Shiller, R.J., 1991. Arithmetic repeat sales price estimators, Journal Housing Economics, 1, 1, 110–126.
- Silver, Mick 2012. Why house price indexes differ: measurement and analysis, IMF Working Paper WP/12/125.
- Silver, Mick 2013. Understanding commercial property price indexes, World Economics 14, 3, September, 27-41.
- Van Garderen, K. J. and C. Shah 2002. Exact interpretation of dummy variables in semilogarithmic equations, Econometrics Journal, 5, 149-159.
- Wooldridge, Jeffrey M. 2002. Econometric Analysis of Cross Section and Panel Data, Cambridge, Massachusetts and London, England: The MIT Press.
- Zellner, Arnold 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias, Journal of the American Statistical Association, 57, 298, June, 348-368.

### Annex 1 — Aggregation of Moody’s/RCA CPPIs and use of Counts Data

Subsection: Apartment CPPIs: composition and estimation
- The RCA/Moody’s aggregate CPPI for “apartments” is a weighted average of two building-block indexes: the CPPI for apartments in “Major Markets” and the CPPI for apartments in “Non-Major Markets.”
- Major markets comprise six of the 34 MMs: Boston, Chicago, District of Columbia (DC), Los Angeles, New York, and San Francisco.
- Moody’s/RCA CPPIs for each of the 34 building blocks are estimated using repeat-sales regression, as are their CPPIs for major and non-major markets.
- Following the methodology outlined in section III the authors use equation (1) to estimate commercial property price inflation based on ˆtλ for US apartments using OLS and counts-based WLS to take account of the sparse data.
- Apartment building property price inflation for major and non-major markets was estimated using OLS and WLS as pooled regressions on the six major-market CPPI series and on the remaining 28 non-major market CPPIs.

Findings from apartment CPPI comparisons (Figure A2)
- All three estimates (OLS, WLS, Moody’s/RCA) for both major and non-major market CPPIs track each other fairly closely with respect to turning points, but significant differences are apparent.
- The bottom of the trough in 2009:Q1 is underestimated by OLS, compared with WLS, by 2.4 percentage points for non-major markets and by 1.7 percentage points for major markets.
- The authors note discrepancies are smaller for major markets given their larger sample sizes, but in both cases they are sizable.

Subsection: Core-commercial property price inflation (Figure A3)
- Analysis disaggregated by major and non-major markets shows little difference for major markets, attributed to aggregation across major regional metropolitan markets and property types (industrial, office, and retail) with relatively large numbers of transactions.
- Marked differences arise when comparing OLS and WLS estimates for non-major markets.

Specific numeric deviations reported for non-major markets (core-commercial)
- The trough in commercial property price inflation was overestimated (deeper) using OLS by 1.34 percentage points in 2001:Q4.
- The trough was overestimated by 1.70 percentage points in 2009:Q2.
- The trough was overestimated by 2.19 percentage points in 2012:Q4.
- In 2010:Q3 OLS inflation exceeded WLS inflation by 1.49 percentage points.

Figures referenced
- Figure A1: Schemata of the Aggregation of Moody’s/RCA CPPIs (lists numerous CPPI building blocks by property type and major/non-major breakdown).
- Figure A2: US apartment property inflation: quarter-on-quarter rates (series plotted: Major Mkts OLS; Major Mkts WLS; Major Mkts Moody's/RCA; Non-Major Mkts OLS; Non-Major Mkts WLS; Non-Major Mkts Moody's/RCA).
- Figure A3: US commercial property inflation: quarter-on-quarter rates (series plotted: Major Mkts OLS; Major Mkts WLS; Major Mkts Moody's/RCA; Non-Major Mkts OLS; Non-Major Mkts WLS; Non-Major Mkts Moody's/RCA).

*Source: _wp1472 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1472.pdf_