A Stochastic Model with Penalized Coefficients for Spatial Price Comparisons: An Application to Regional Price Indexes in Italy

• Published date: 01 September 2020
• Author: José‐María Montero,Tiziana Laureti,Román Mínguez,Gema Fernández‐Avilés
• Date: 01 September 2020
• DOI: http://doi.org/10.1111/roiw.12422

© 2019 Internation al Association for Re search in Inco me and Wealth

512

A STOCHASTIC MODEL WITH PENALIZED COEFFICIENTS FOR

SPATIAL PRICE COMPARISONS: AN APPLICATION TO REGIONAL

PRICE INDEXES IN ITALY

José-María Montero

University of Ca stilla-La Manc ha

tiziana Laureti*

University of Tuscia

roMán Mínguez

University of Ca stilla-La Manc ha

AND

geMa Fernández-aviLés

University of Ca stilla-La Manc ha

This paper focuses on a new strand of research that uses stochastic approach for making spatial price

comparisons. We propose a novel method to account for the presence of spatial dependencies in con-

sumer prices and consequently in price indexes by imposing penalization conditions on the estimation of

traditional CPD models leading to the spatially-penalized country-product-dummy (SP-CPD) model.

The paper proposes an appropriate estimation strategy, which enables us to simultaneously estimate all

the parameters in the model, including the smoothing parameter of the penalization term instead of

determining it externally. In order to estimate spatial price indexes for areas lacking in price data, we

suggest applying the kriging methodology to the price indexes obtained from the SP-CPD model. This

new approach is applied to official Italian CPI data for constructing regional spatial price indexes for

2014. The results show that price levels are higher in the Northern-Central regions than in the South.

JEL Codes: C21, D12, E31

Keywords: hedonic country product dummy models, regional price comparisons, spatial dependence,

spatial price indexes, stochastic approach

1. introduction

Spatial price indexes provide measures of price level differences across coun-

tries or across regions within a country and are widely used by researchers and

Note: The authors would like to thank Prof. DS Prasada Rao and three anonymous referees for

their helpful comments and suggestions. This work has been partially funded by the Spanish Ministry

of Economy and Competitiveness grants MTM2014-52184 and ECO2015-65826-P.

*Correspondence to: Tiziana Laureti, Department of Economics, Engineering, Society and

Business Organization, University of Tuscia, Via del Paradiso 47, Viterbo 01100, Italy (laureti@unitus.

it).

Review of Inc ome and Wealth

Series 66 , Number 3, September 2020

DOI : 10.1111 /roi w.124 22

bs_bs_banner

Review of Income and Wealth, Series 66, Number 3, September 2020

513

© 2019 Internation al Association for Re search in Inco me and Wealth

policy-makers for comparing real income, standards of living and consumer

expenditure patterns.

In all spatial price comparisons, the concept of Purchasing Power Parity (PPP)

is used to measure the price level in one location compared to that in another loca-

tion1; therefore PPPs are essentially spatial price index numbers. At international

level, PPPs facilitate cross-country comparisons of Gross Domestic Product

(GDP) and its major aggregates as they can be used in converting aggregates into

a common currency. Likewise, sub-national PPPs allow for intra-country spatial

comparisons and can serve as inputs and/or improve other inputs for estimating

key economic indicators produced by countries, such as real regional price com-

parisons, real income dimensions and poverty estimates. The process of compiling

PPPs is quite complex and is carried out in two stages.2 First, elementary spatial

price indexes are computed by aggregating, without using weights, prices of items

belonging to a group of similar well-defined goods or services (called Basic

Headings, BHs). In the second stage, the elementary PPPs are aggregated using

expenditure weights to obtain PPPs for higher-level aggregates such as consump-

tion, investment and GDP.

In order to improve the quality and reliability of PPP estimates, this paper

focuses on methodological issues that arise when constructing spatial price indexes

at the lowest level of aggregation since it is essential to obtain reliable PPPs at

BH level because they are the foundations of overall comparisons (Hill and Syed,

2015). One of the main issues when constructing spatial price indexes is to cap-

ture the spatial dependence which is inherent in consumer price levels (Aten, 1996,

1997; Rao, 2004). Several researchers have found that consumer prices are more

similar in geographically proximate locations, thus observing a significant positive

correlation between the Law of One Price (LOP) deviations and distance (Choi

and Choi, 2014, 2016; Crucini et al., 2015). This spatial effect may reflect transport

costs as well as local distribution costs, which are likely to be similar in nearby

locations if the distribution of goods is labor intensive and labor markets are geo-

graphically integrated (Choi and Choi, 2016). However, in spite of its theoretical

attraction, as yet only a few studies have been carried out to explore the issue of

spatial dependence in consumer price index construction (Aten, 1996, 1997; Rao,

2001; Biggeri et al., 2017; Majumder et al., 2017).

In order to compare consumer price levels, this paper focuses on the sto-

chastic approach, where uncertainty and statistical ideas play central roles since

index number construction is viewed as a problem of signal extraction from the

messages on price changes for different commodities over space (Summers, 1973).

Clements and Izan (1987), Selvanathan (1989) and Selvanathan and Rao (1994)

have emphasized the versatility and usefulness of the stochastic approach which

leads to familiar index-number formulae under certain circumstances (Clements

et al., 2006; Diewert, 2010). Over the last two decades there has been a steady

1Purchasing power parities of currencies are defined as the number of currency units of a country

that can purchase the same basket of goods and services that can be purchased with one unit of cur-

rency of a reference currency.

2At international level, PPPs are compiled by the International Comparison Program (ICP), which

is administered by the World Bank and overseen by the United Nations Statistical Commission with the

collaboration of the OECD, EUROSTAT and other regional organizations (see Rao, 2013 for details).