Data Sources for CPPIs: An Overview and Strategy. Mick Silver Paper Presented at the EC International Conference on Real Estate Statistics, 20-22 February, 2019, Luxembourg. The author acknowledges the support of Eurostat in the writing of this paper. The views expressed are those of the author and should not be attributed to Eurostat.

The context Macroeconomists and central banks need to identify property price bubbles, the factors that drive them, instruments that contain them, and to analyze their relation to recessions. Needs of Monetary Policy Committees: Timely, proper measurement. Guidelines on measurement: On RPPIs: Eurostat et al. (2103) Handbook on Residential Property Price Indices. http://epp.eurostat.ec.europa.eu/portal/page/portal/hicp/methodology/hps/rppi_handbook On CPPIs: Eurostat (2017), Commercial Property Price Indicators: Sources, Methods and Issues. http://ec.europa.eu/eurostat/web/products-statistical-reports/-/KS-FT- 16-001 : Jens’ and Sabine’s paper 4/8/2019

Alternative data sources for CPPIs Transaction-price CPPI compilation highly problematic. Heterogeneous properties with sparse data. The seemingly appealing way around this sparse data and quality-mix adjustment problem is to use price data on broadly the same properties over time and avoid transaction price data. Tax or investment appraisal data. Market valuations of real estate investment trusts (REITs).

Appraisal/Valuation data Appraisals are usually annual; quarterly data are interpolated or (stale) estimates by the manager/owner based on last appraisal. Guidelines are to base appraisals to be base on the transactions of similar properties introducing circularity in the argument that appraisals solve the sparse data problem. Criteria for appraisal varies within and between countries. Reliability of index depends on reliability of appraisers: judgmental; “stale” element; bias. Sample usually of large properties in a portfolio whose composition changes over time. Capital expenditures and depreciation estimates sometimes inappropriately used as a means for quality adjustment. Problems include smoothing and lagging. Diewert, Fisher, Geltner, , Nishimura, Shimizu, Watanabe…

Commercial property price indexes for Tokyo offices, using transaction and appraisal data: 2005Q1=1.00 - Diewert and Shimizu (2017/8) PFMLITS and PFLDHEDS can be seen to be fairly similar. The recession starts in 2007Q3 and 2007Q4 respectively. Appraisal 2008:Q3 and Q4. And thereafter very different. Appraisal 11% over 10 years PFMLITS and PFLDHEDS 43 and 54% resp.

Real estate investment trusts - REITs They do not track the transaction prices; indirectly reflect stock market valuations. Holdings of properties in portfolios change over time as new properties are added and existing ones sold Not all commercial properties are publicly traded. Many will be owned and traded outside of REITs in the private property markets. Bias. Stock market is a more efficient vehicle for trading in commercial property. Its movements not just a best guess the underlying market price. Also the “animal spirits” that drive the stock market. Buyers and sellers in the private market may have different priorities; e.g. long- vs. short-term returns. The market price of a commercial property is something that is only realized when the asset itself is bought and sold. REIT indexes are about investment returns, including rents. They are different phenomena.

CPPIs and REIT-based commercial property price indexes for Germany: 2009: Q4=100.00 – Geltner (2015).

Sampling theory: not sample sizes but confidence intervals. The 95% (confidence) interval estimate for the population mean is 𝑥 ±1.96 𝜎 𝑛 . Heterogeneity and small sample size matter: bad. However, we require a confidence interval for the ratio of sample means. The sample of properties compared are independent samples of transaction prices. The Jevons index is the (exponent of) the difference between the arithmetic means of the logarithms of prices and the SE of this difference is the square root of the sum of the separate variances (standard errors squared) of the two samples. Thus where 𝑑 𝑖 is the difference between the logarithms of prices in the two periods for property i, 𝑑 𝑖 =𝑙𝑛 𝑃 𝑖𝑐 −𝑙𝑛 𝑃 𝑖𝑟 , 𝑑 the mean, 𝑆𝐸(𝑑)= 𝑣𝑎𝑟 𝑃 𝑐 +𝑣𝑎𝑟 𝑃 𝑟 , and the 95% confidence interval for the difference is 𝑑 ±1.96 𝑆𝐸 𝑑 and for Jevons, the exponents of this interval. As such the SE from sparse heterogeneous independent samples of transaction prices will be much higher than would be anticipated from simply judging what it might be based on the sample size in an individual period.

The lesson is not to compare (geometric) average transaction prices for sparse heterogeneous data. Appraisal data uses matched/paired prices for the same property in the two periods. The (exponent) of the average difference between the logarithm of these prices is the Jevons index and its SE is based on the standard deviation of these differences, much smaller than the sum of the SEs for the two independent samples. This may argue for appraisal data. The question is whether transaction-based data can be used to compile a quality-mix adjusted CPPI that phrases the calculation as matched-paired price comparisons, not independent samples? The answer is “yes.” Best-practice hedonic imputation approach does exactly that. It is the confidence interval associated with an estimate that matters. Small sample of heterogeneous transactions result in large the confidence intervals. Dressing up a small sample in an abundance of appraisal prices - estimated in a subjective and inconsistent manner with documented bias - does not negate this statistical principle.

ln 𝑝 𝑖 0 = 𝛽 0 + 𝑘=1 𝐾 𝑧 𝑘,𝑖 0 ln 𝛽 𝑘 + 𝜀 𝑖 0 Hedonic regression A semi-logarithmic form is usually appropriate for a period 0 hedonic regression with prices 𝑝 𝑖 for property i regressed on each of k=1,…,K price-determining characteristics 𝑧 𝑘,𝑖 given as:  ln 𝑝 𝑖 0 = 𝛽 0 + 𝑘=1 𝐾 𝑧 𝑘,𝑖 0 ln 𝛽 𝑘 + 𝜀 𝑖 0 Hill and Melser (2008), Diewert, Heravi and Silver (2009), Hill (2013), de Haan and Diewert (2013), and Silver (2018)

Hedonic imputation indices: geo-means; double imputation: period 0→𝒕. Constant period 0 characteristics Constant period t characteristics

A question Why not weight each transaction using “quasi-superlative” index number formula?

And .. Why is it only quasi-superlative? Use of period 0 and period t transactions requires: Feenstra (1995); Ioannidis and Silver (1999); Silver and Heravi (2005); Diewert (2005); Hill and Melser (2008); Diewert, Heravi, Silver (2009); de Haan (2009); de Haan and Gong (2013); de Haan and Diewert (2013); Hill (2013); Rambaldi and Rao (2013); Hill et al. (2018); and Silver (2018); and on stock vs transaction weights, Mehrhoff and Triebskorn (2016).

Also, .. In the practical context of thin markets – sparse data - and vagrancies of regular hedonic estimation: Use an extended reference period for thin markets – sparse data - with regular re-linking, re-estimation. Only estimates a reference period hedonic regression – with regular re- linking.

The political economy: context G-20 Data Gaps Initiative (DGI), responsibility of (IMF) and the Financial Stability Board (FSB). The work is coordinated by the Inter-Agency Group on Economic and Financial Statistics (IAG) which comprises representatives from BIS, ECB), Eurostat, IMF, OECD), UN, and the World Bank Also the Inter-secretariat Working Group on Price Statistics (IWGPS) comprising representatives from Eurostat, ILO, IMF, OECD, UNECE, and the World Bank. Task force.

Get things done. RPPI success: Handbook on methods, widespread compliance, BIS Property database CPPI less so: no agreed methodology; poor take up; few countries on data base.

Of note.. DGI-2 IMF-FSB Progress Report of Sept 2018 The summary of the Conference on RPPIs and CPPIs Argentina, January 29–30, 2018: “The participants agreed that the way forward with real estate statistics, especially CPPI, should be pragmatic, data-oriented, and take account of available private data sources for economies where no official indicators exist.” IMF and FSB (2018, paragraph 5). Table 1 is a dashboard of achievements—Overall Implementation Status and Progress for the DGI-2 Recommendations. “No harmonized methodological framework nor detailed methodological guidance available yet. Action plan still to be elaborated” are included as Early stages of implementation or lack of timely progress. IMF and FSB (2018, page 9). The Traffic light monitoring dashboard for Recommendation II.19 is less than inspiring with 10 of the G-20 countries boxes shaded in red (target of publishing a CPPI not met, and 9 in green, target met, the Euro area being partially met, orange).

Way forward… CPPIs not used for market segments with unduly large interval estimates. Transparency guided by statistical principles. Ratios of means not used, even if (minimal) quality-mix adjustment, e.g. price per square foot. Appraisal and REIT data not be used for CPPIs. Transaction-based CPPIs using hedonic imputations should be the recommended methodology, preferably (i) with weights at the level of the individual property transaction; (ii) an extended time period for the reference period; and (iii) by estimating the hedonic regression periodically. The specification of the hedonic regression is expected to improve over time as more characteristic data becomes available. There will be a natural synergy with the RPPI measurement team.   International organizations meet data initiatives by setting and promoting standards of measurement. Doing something, rather than nothing, may be to mislead, rather than lead - a disservice especially when an alternative transaction-based methodological approach is available, albeit one that requires more effort and care in its development.

The doers: Commercial property price indicators: Papers at this conference : Ireland Poland Portugal Denmark, Germany, Netherlands, USA BIS (Robert Szemere) ECB (Andrew Kanutin) and Jean-Marc Israël, Catherine Ahsbahs and Arek Wyka on Funding, S-T indicators, Business sentiment; data needs for asset managers Jones Lang LaSalle MSCI Real Capital Analytics Japan: (Erwin Diewert and Chihiro Shimizu) Plug: RPPI US BEA