Anatomy of regional price differentials: evidence from micro-price data

ABSTRACT

Micro-price data collected from Germany's consumer price index are used to compile a highly disaggregated regional price index for the 402 counties and cities of Germany. A multistage version of the weighted country-product-dummy (CPD) method is introduced. The unique quality of the price data allows one to depart from previous spatial price comparisons and to compare only exactly identical products. It is found that the price levels are spatially autocorrelated and largely driven by the cost of housing. The price level in the most expensive region is about 27% higher than in the cheapest region.

KEYWORDS:

• spatial price comparison
• regional price index
• purchasing power parity (PPP)
• country-product-dummy (CPD) method
• hedonic regression
• consumer price data

JEL:

• C21
• C43
• E31
• O18
• R10

ACKNOWLEDGEMENT

The authors are indebted to the Research Data Centre (RDC) of the Federal Statistical Office and Statistical Offices of the Länder for granting access to CPI micro-data of May 2016. They also express their gratitude to Alexander Schürt and Rolf Muller from the Federal Institute for Research on Building, Urban Affairs and Spatial Development (BBSR) for providing the results of their rent data sample from May 2016. The authors also received valuable support from the Statistical Office of Bavaria, as well as from Timm Behrmann, Florian Burg, Marc Deutschmann, Bernhard Goldhammer, Florian Fischer, Malte Kaukal, Karsten Sandhop and Stefan Schulz. Helpful suggestions made by Bettina Aten, Jan Pablo Burgard and Henning Weber are gratefully acknowledged. The authors presented their research at staff seminars at the European Central Bank (ECB), Frankfurt, as well as at the ifo Institute, Munich, and at the conferences ‘Messung der Preise, 2018’ (Dusseldorf) and ‘Regionale Preise, 2018’ (Munich). Helpful comments and suggestions from participants are gratefully acknowledged. For an extended version of this study, see Weinand and Auer (2019). The recommendations of three referees and the editors improved the paper considerably. The opinions expressed in this paper are those of the authors alone and do not necessarily reflect the views of the Deutsche Bundesbank, the Eurosystem or their staff.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1 This issue is well known from the ICP 2005, where CPD regressions use average prices of product groups. Hill and Syed (2015, p. 524) convincingly demonstrate that this practice is inferior to a CPD regression based on individual price quotes. We fully agree with this assessment and add the recommendation that each product dummy must relate to a tightly defined product and not to a group of seemingly very similar products.

2 The expenditure data necessary for the weighting could be incorporated into the analysis only after one stage of aggregation of the original price data.

3 Studies that compare the regional price levels of individual products or groups of products without transforming these results into the regions’ overall price levels are not included in this survey. Examples are Hoang (2009) and Majumder et al. (2012), who investigate regional food prices in Vietnam and India, respectively. Léonard et al. (2019) analyze French scanner data of industrial food products. For a recent alternative literature review, see Janský and Šedivý (2018).

4 For the Turkish index numbers, see http://www.turkstat.gov.tr.

5 For example, Biggeri et al. (2017b) subdivide Italy into 19 regions, where each region is represented by its most important city.

6 In Table 1, the studies with a full coverage of Germany do not include 402 regions, because different studies use slightly different regional demarcations.

7 The German consumer price data represent a stratified sample where the products are selected non-randomly within the basic headings. One exception are rents. Since 2016, they are collected from a stratified random sample (Goldhammer, 2016).

8 For summary statistics for the respective variables, see Weinand and Auer (2019, pp. 12–13).

9 Faller et al. (2009) find an overall deviation of 8% between quoted and transactional prices for purchases of flats and houses. For rents, they expect that this deviation becomes smaller.

10 The classification of basic headings into goods and services follows ILO et al. (2004, pp. 465–482).

11 Weinand and Auer (2019, pp. 35–37) show that exactly the same estimates, $\widehat{\ln P^r}$, are obtained when we apply another weighted CPD regression or the GEKS approach where the underlying bilateral price index numbers are computed as weighted Jevons indices.

12 Referring to the analysis of Goldberger (1968), Kennedy (1981, p. 801) points out that the expected value of the estimator $\exp \left(\widehat{\ln P^r}\right)$ is not $\exp \left(\ln P^r\right)$, but $\exp (\ln P^r+0.5\mathrm{var}(\widehat{\ln P^r}\left)\right)$. This implies that the values of $P^r$ should be estimated by $\exp \left(\widehat{\ln P^r}-0.5\widehat{\mathrm{var}}\left(\widehat{\ln P^r}\right)\right)$ and not by $\exp \left(\widehat{\ln P^r}\right)$. In our regression, however, we cannot estimate the variances, $\widehat{\mathrm{var}}\left(\widehat{\ln P^r}\right)$ reliably. Therefore, we have to do without this adjustment.

13 Hoffmann and Kurz (2002, p. 18) report values that range from 0.53 to 0.65 for multiple cross-section analysis of West German rent data of the German Socio-Economic Panel. Kholodilin and Mense (2012, p. 17) use rent data of flats located in Berlin, collected from internet adverts within the period 2011–2012. The goodness of fit of their hedonic regression is 0.65. Behrmann and Goldhammer (2017, p. 22) use the 2017 rents of the German CPI data for 12 of the 16 federal states. They report a value of 0.77.

14 Some cities with a population size smaller than $100,000$ are pooled with their neighbouring regions. Therefore, the total number of regions considered is smaller than the actual number in 2007.

15 For the computation of Moran's $I$ (Cliff & Ord, 1981; Moran, 1950), we use a row-standardized spatial weights matrix where each neighbouring region receives a weight according to its population size. Consequently, the spatial lag is a population-weighted average of the neighbouring price levels.

16 Montero et al. (in press) propose a novel method that imposes penalization conditions leading to a spatially penalized CPD model.

17 Technically, ${lag}^r$ is computed by multiplying the spatial weights matrix with the vector of regional price levels, $\widehat{\ln P^r}$.