The impact of estimated sub-national purchasing power parity on macroeconomic measures 1

Abstract

Due to the lack of Purchasing Power Parities (PPPs) at sub-national level, regional Gross Domestic Product (GDP) figures have been traditionally adjusted using national PPPs. The simplifying assumption that there are no regional differences in a country, and implicitly that all regions of a country have the same cost of living, might lead to regional GDP figures (adjusted for national PPPs) that are biased and might limit the design and implementation of regional policies. This paper tries to overcome this problem by estimating PPPs at sub-national level for OECD countries (TL2 regions) and EU-27 countries (NUTS2 regions) for a time series 2000–2018 through an econometric method, which uses publicly available data and is based on the Balassa-Samuelson hypothesis. This paper also presents the implications of adjusting regional macroeconomic figures with sub-national PPPs in terms of economic welfare, regional convergence and the impact on EU cohesion funds.

Keywords

Sub-national purchasing power parity Balassa-Samuelson hypothesis sub-national economic variables cohesion funds

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1. Introduction

The cost of goods and services varies across countries and regions. Territorial price differences have been long discussed in the literature [1, 2, 3, 4, 5]. This literature has shown that prices differ not only across countries, but also across sub-national territories inside a country and that differentials in the territorial price levels indicate differences in the cost of living.

Differences in the cost of living within countries have important implications for the welfare of territories [6] and are important from a policy perspective [7]. Regional economic policies are usually sustained by economic analyses and studies which use macroeconomic statistical indicators measuring the region’s economic performance and development (e.g. Gross Domestic Product per capita, disposable income, wages, etc.). Traditionally, these sub-national macroeconomic indicators have been compared across countries by adjusting them using national exchange rates or Purchasing Power Parities (PPPs). However, these methods can lead to significantly distorted adjustments across the regions of a country. While PPPs take into account differences in price levels between countries, they fail to account for differences in regional price levels, leading to biased economic figures at sub-national level. Indeed, when adjusting macroeconomic figures, the use of an average national price deflator will lead to an artificial increase of the macroeconomic indicator in the better developed regions and a decrease in the lagging regions [8]. As a result, the inaccuracy or imprecision of regional economic levels might lead to a biased assessment and, consequently, inadequate policy design.

The available statistical information on prices is still limited in sub-national settings.3 In the preamble of Regulation No. 1445/2007 of the European Parliament and of the Council, of December 11, 2007, which establishes common rules for the provision of basic information on purchasing power parities, and for their calculation and dissemination, it is indicated that “Member States are encouraged to produce data for regional PPPs”. However, and despite the long tradition of the Bureau of Economic Analysis (BEA) in offering PPP data at the national and subnational level, other official statistics offices, provide this information at the national level only.

In fact, Eurostat and the OECD have developed a standard methodology for the computation of PPPs. This is based on the EKS (Éltetö-Köves-Szulc) method which requires data concerning the volume and prices of consumer goods and services in a territory [9]. Despite the existence of this method and the possibility to apply it also at sub-national level, it is often not possible due to the lack of homogeneous sub-national data (prices of and expenditures on goods and services) across countries. In addition, national Consumer Price Index collections, as well as specific price collections implemented across countries, differ in terms of the regional consumption basket data gathered, as well as on the scope of regional prices observed [10].

Despite the need for regional price indices at the international level [7], no homogeneous methodology has been developed for all OECD and EU-27 countries. Due to this lack of data, international sub-national economic analyses are currently done by adjusting regional economic indicators using national PPPs. In order to overcome this limitation, the main goal of this study is to estimate PPPs for more than 300 TL2 regions in OECD countries and more than 200 NUTS-2 regions in EU-27 countries between 2000 and 2018, subject to data availability. This goal has been achieved by estimating regional price indices across regions according to the Balassa-Samuelson hypothesis4 and using sub-national time series on prices from the U.S. Bureau of Economic Analysis (2008–2019) and economic and demographic sub-national figures from the OECD Regional Database (2000–2018) and Eurostat Regional Statistics Database (2000–2018).

This paper is divided into four sections. Following the introduction, Section 2 presents some of the most relevant literature contributions on the computation of sub-national PPPs. Section 3 presents the estimation method used, with reference to its theoretical basis, the databases used and the estimates of the models that allow obtaining regional prices and regional PPPs. Section 4 summarises the practical relevance of the results derived from Section 3. It zooms into year 2018 to show the effect of adjusting regional per capita GDP figures with the estimated sub-national PPPs compared to figures adjusted with national PPPs. It also analyses the effect on regional convergence of adjusting regional per capita GDP figures, between 2000 and 2018, with sub-national PPPs and the corresponding implications on the European cohesion funds. Section 5 presents the conclusions.

2. Previous attempts to compute sub-national PPPs

To date, a number of national statistical offices and academic works have been able to estimate regional price levels within countries. Some of them are cited here in a chronological order and by country.

In Europe, some examples are found in the literature. The first estimations of price levels at NUTS-2 in Spain for the year 1989 were developed by [11] based on price levels from 17 cities. Since then several authors have estimated the price levels in the Spanish NUTS-2 Spain for different years by applying CPI regional variation rates [12, 13, 14]. In [14] two alternative methods were used to estimate PPPs at NUTS-2 level for the year 2012, one macroeconomic method based on the Balassa-Samuelson hypothesis [15, 16] and further extended in [17] using housing prices, and a microeconomic one which uses an adaptation of the method used in [18]. The ONS developed estimates of regional price levels for the NUTS-1 regions in the United Kingdom for the years 2000 and 2003 [19, 20]. Since then, the ONS made two other attempts to estimate regional price indices for the year 2010 [21] and 2016 [22] based on the basic information on the prices of the different goods considered for the calculation of inflation. [6] estimated price levels for 440 German districts (Kreise) and 16 states (Bundesländer) for the year 2002, through the estimation of a price model based on the information of price indices of 50 German cities. Later on, [23] following [6] approach, estimated regional price indices for German NUTS-3 regions between 1995 and 2004, incorporating the information on house prices, not taken into account by [6]. [24], in collaboration with the Guglielmo Tagliacarne Institute and the Union of Italian Chambers of Commerce, estimated spatial price indices for capital cities in Italian regions for the year 2006, making use of price collected to calculate inflation. Later on, the Bank of Italy [25] and ISTAT in collaboration with the University of Florence and the University of Tuscia [7] estimated regional price indices for all NUTS-2 in Italy. In the Czech Republic, regional price levels (NUTS-3) were estimated by [26, 27] for the year 2007, while [28] estimated regional price levels at NUTS-3 and District level (LAU 1) for the years 2011–13. [29] estimated regional price indices in Austrian NUTS-2 for the year 2008. [30] estimated regional price levels in Poland at the NUTS-2 and NUTS-3 for the years 2000 and 2011 based on information on prices. This work was then further extended to the period 2000–2012 by [31]. [32] estimated regional prices (NUTS-2) in 12 European countries. Later on, [33] estimated regional prices (NUTS-2) in 28 EU countries based on a model of regional prices estimated with the information available for 6 European countries (79 observations).

Similar examples are observed outside Europe. [34] estimated regional prices for eight capital cities in Australia using price data from the year 2002. Later on, the Government of Western Australia started providing regional price index estimates for its regions and cities for the period 2000–2019 [35]. [36] estimated provincial-level price deflators in China for the years 1984–2002 based on the prices of the goods in the shopping basket at the provincial level. [37] did a similar analysis for the period 1986–2001. At the same time, [38] estimated regional prices in 38 areas of the United States (U.S.) for the years 2005 and 2006. Later on, [39] provided regional price estimates for the U.S. states and Metropolitan areas between 2006 and 2010. Since then, the Bureau of Economic Analysis (BEA) provides annual estimates of regional price parities for all U.S. states and Metropolitan areas. Recently, [40] provide estimates of price levels in urban and rural regions of India for the year 2010 based on a microeconometric model which exploits the idea that changes in household composition have quasi-price effects.

3. Methodology and estimation

3.1 Conceptual framework

According to the so-called Balassa-Samuelson effect [15, 16], countries with a higher level of income per capita tend to have higher price levels. The Balassa-Samuelson hypothesis states that, richer countries (or territories) show higher levels of productivity in the production of tradable goods (industrial or marketable goods) than poorer countries, thus giving rise to higher wages in the tradable sector. However, and given the fact that wages tend to equalise between the sectors producing tradable and non-tradable goods (services, in general), the prices of non-tradable goods will also be higher in rich countries than in poorer countries. Therefore, the general level of prices will be higher in rich countries. Figure 1 confirms this relationship at the OECD level.

Figure 1.

Relationship between price levels and GDP/Income per capita in OECD countries (2018). Note: All variables are expressed in natural logarithm as relative to the United States levels. Price levels are constructed by dividing Purchasing Power Parities by exchange rates. Colombia is excluded from Panel B due to lack of data on per capita disposable income. Costa Rica is excluded from both Panels due to lack of data on per capita disposable income and GDP per capita for the year 2018. Source: OECD https://dx-doi-org.web.bisu.edu.cn/10.1787/na-data-enNational Accounts. (2021) and https://stats.oecd.org/Index.aspx?DataSetCode=SNA_TABLE4 Prices and Purchasing Power Parity Statistics (2021).

In more formal terms, let us consider a simplified example of only two countries, the domestic one “the richest” and the foreign one “the poorest”, and two types of goods, industrial or tradable and services or non-tradable. Obviously, the real world is constituted of more than the two sectors presented in this example (one fully tradable and the other fully non-tradable). Indeed, all goods produced will be partly tradable, and partly non-tradable. However, following the logic of Balassa-Samuelson, the two-sector model provides a justification for a positive correlation between price levels and income per capita as shown above.

If $P_{I}$ are the prices of domestic industrial products and $P^{*}_{I}$ are the prices of foreign industrial products that are fully tradable goods without transport costs, competition will make both prices equal ( $P_{I}=P^{*}_{I}$ ). However, productivity in the industrial sector will be higher in the richest than in the poorest country. If ${\prod}_{I}$ and ${\prod}^{*}_{I}$ are the respective productivities, the following inequality will be fulfilled: ${\prod}_{I}>{\prod}^{*}_{I}$ . Considering that there is correspondence between wages and productivity in the industrial sector, the following will be verified: $W_{I}={\prod}_{I}$ ; $W^{*}_{I}={\prod}^{*}_{I}$ .

However, and due to an effect derived from competition, wages in the industrial sector will tend to extend to the services sector. If this were not the case, to the extent that productivity in industry grows faster than in services, wages in this sector would also grow at a faster pace than in services. This would originate a transfer in the supply of labour from services to industry. The shortage of people willing to work in services and the abundance of people willing to work in industry would lead to an equalisation of salaries in both sectors. In this case, wages in the richest country will be $W={\prod}_{I}$ ; while the wages in the poorest country will be $W^{*}={\prod}^{*}_{I}$ , since equality of wages is assumed in both sectors.

Focusing now on the services sector and assuming that prices in services are determined by the ratio between wages and productivity, the following equalities will be verified: $P_{S}={W}/{{\prod}_{S}}$ ; $P^{*}_{S}={W^{*}}/{{\prod}^{*}_{S}}$ . Let us assume also that productivity in services is the same in the richest country as in the poorest country. Therefore, if $W$ is greater than $W^{*}$ and productivity in the services sector is the same, the price of services in the poorest country will be lower than the price of services in the richest country and the following inequality will occur $P_{S}={W}/{{\prod}_{S}}>W^{*}/{\prod}^{*}_{S}=P^{*}_{S}$ .

Figure 2.

Relationship between price levels and GDP/Income per capita in 51 U.S. states (2018). Note: US01 (Alabama), US02 (Alaska), US04 (Arizona), US05 (Arkansas), US06 (California), US08 (Colorado), US09 (Connecticut), US10 (Delaware), US11 (District of Columbia), US12 (Florida), US13 (Georgia), US15 (Hawaii), US16 (Idaho), US17 (Illinois), US18 (Indiana), US19 (Iowa), US20 (Kansas), US21 (Kentucky), US22 (Louisiana), US23 (Maine), US24 (Maryland), US25 (Massachusetts), US26 (Michigan), US27 (Minnesota), US28 (Mississippi), US29 (Missouri), US30 (Montana (US)), US31 (Nebraska), US32 (Nevada), US33 (New Hampshire), US34 (New Jersey), US35 (New Mexico), US36 (New York), US37 (North Carolina), US38 (North Dakota), US39 (Ohio), US40 (Oklahoma), US41 (Oregon), US42 (Pennsylvania), US44 (Rhode Island), US45 (South Carolina), US46 (South Dakota), US47 (Tennessee), US48 (Texas), US49 (Utah), US50 (Vermont), US51 (Virginia), US53 (Washington), US54 (West Virginia), US55 (Wisconsin) and US56 (Wyoming) Both variables (per capita GDP and per capita disposable income) are expressed relative to the national value. Price levels refer to the variable SAIRPD (Implicit Price Deflators by state) (July, 2021). Source: https://www.bea.gov/itable/index.cfm Bureau of Economic Analysis (2021).

Since average prices in a country are a weighted average of prices of industrial and services products, prices in the rich country will be $P=(1-\lambda)P_{I}+\lambda P_{S}$ , while prices in the poor country will be $P^{*}=(1-{\lambda}^{*})P_{I}+{\lambda}^{*}P^{*}_{S}$ . Here $\lambda$ and ${\lambda}^{*}$ correspond to the weight of services in Gross Domestic Product (GDP) in the rich country and in the poor country, respectively. Only in the case where the structure of GDP is the same in both countries, namely, $\lambda={\lambda}^{*}$ would the following hold: $P>P^{*}$ . However, if the weight of services in GDP is higher in rich countries than in poor ones, then the previous inequalities will be reinforced.

Based on this example, it is presented how productivity differentials in the tradable goods would lead to wage differentials across territories. Additionally, these wage differentials also lead to differences in the price of services and consequently differences in prices across territories. According to [41], high price of services in developed countries are mainly explained by the relative high demand of services respect to the supply. Similarly, [42] state that the scarcity of land available in urban areas will limit the supply of services (e.g. housing) and will therefore explain increases in prices in certain areas leading to price differences across cities and across countries.

When extending this analysis to the regional level, the positive relationship between prices and the weight of services in the GDP structure is also verified. Indeed, when using state level data from the U.S. Bureau of Economic Analysis and splitting GDP figures into three components, agriculture, industry and services, it can be observed that the higher the share of the services sector, the higher the prices. Similarly, states in which the services sector accounts for a greater share of the GDP appear to be those characterized by higher prices.

Additionally, considering that salaries are the main component of household disposable income levels, it seems that there is a higher positive correlation between price levels and income levels than between price levels and GDP per capita. When using state figures on GDP per capita, price and per capita income levels from the U.S. Bureau of Economic Analysis, it can be observed that the elasticity is lower between regional prices and GDP per capita than between regional prices and per capita household disposable income levels (Fig. 2). Additionally, the explanatory capacity of the former is lower than the latter. Based on these results, it is plausible to think that in the same country there are income transfers that weaken the relationship between GDP and household disposable income and, consequently, also the relationship between GDP per capita and price levels.

3.2 Data and territorial coverage

The data used in this paper were collected from the OECD Regional Database, the Eurostat Regional Database and the U.S. Bureau of Economic Analysis (BEA).

The BEA is the only official statistical agency that offers a series of prices parities by state with temporal continuity and with the standard dissemination degree of official statistics. Although there are other approaches to regional prices, they all lack continuity and have been developed in the context of isolated studies, even those in which official statistical offices participate. The data used for the estimations were 2008–2019 time series of regional price parities, available at the time of writing this text.

Time series data at regional level (TL2) for all OECD countries (between 2000 and 2018) have been obtained from the OECD Regional Database, while regional data at NUTS-25 for EU-27 countries (between 2000 and 2018) come from the Eurostat Regional Database. National Purchasing Power Parity figures were obtained from the OECD National Accounts Database. The former provides a unique set of comparable statistics at regional level. The set of TL2 variables used to compute the regional prices are Regional Disposable Household Income, Regional economic structure of GDP (percentage weight of services and industrial sector in total Gross Value Added (GVA)), as well as population.

The current analysis is carried out through a cross section of more than 300 OECD large regions6 across OECD countries and more than 250 NUTS-2 regions across EU-27 countries. Countries such as Colombia, Costa Rica, Iceland and Israel, were excluded from this analysis due to the lack of regional data on the weight (percentage) of services and industry in total Gross Value Added at regional and national level or for the lack of regional data on household disposable income. French overseas territories were also excluded from this analysis.

3.3 Methodology and results

The method builds on the work of [14]. Taking into account the theoretical framework presented in Section 3.1, and considering the availability of regional data from the U.S. Bureau of Economic Analysis (for more details see Section 3.2), the process used to estimate regional prices in OECD countries was developed in three steps:7

Step 1: The relationship between U.S. state prices and state household disposable income per capita including also data on the industrial composition of the GVA by State in the United States is defined by the following function:

$\displaystyle{\mathrm{ln}P_{it}}={\beta}_{0}+{\beta}_{1}{\mathrm{ln}\textit{% HDIpc}_{it}}+{\beta}_{2}{\textit{Ind}}_{it}{}\!\!+{\beta}_{3}{\textit{Serv}}_{% it}+u_{it}$ (1)

where $P_{it}$ are the prices in Purchasing Power Parities of the state “i” in the period “t”, $\textit{HDIpc}_{it}$ is the corresponding value of the available household disposable income per capita, ${\textit{Ind}}_{it}$ is the weight of the industry8 and ${\textit{Serv}}_{it}$ the weight of the services9 over GVA in each state “i” in the period “t”.

Table 1

Estimation results of the relationship between state prices and state household disposable income per capita. Dependent variable: Regional prices in U.S. states (in natural logarithm), 2008–2019

	Model 1: Pooled OLS and clustered standard errors			Model 2: Between-group estimator
	Coef.	Std. Err.	$t$	Coef.	Robust Std. Err.	$t$
Constant	3.272	0.242	13.50	3.200	0.310	10.32
HDIpc	0.346	0.037	9.25	0.339	0.042	8.00
IND	1.015	0.264	3.85	1.066	0.334	3.20
SERV:	1.414	0.244	5.79	1.491	0.313	4.77
n. obs.	612			51
$R^{2}$	0.770			0.770
$R^{2}$ – within				0.022
$R^{2}$ – between				0.790
Root MSE	0.041

Note: HDIpc stands for “Regional household income (in natural logarithm)”, IND for “Share of GVA of industry of the region” and SERV for “Share of GVA of service of the region”. In Model 2, Std. Err. adjusted for 51 clusters. Source: Own elaboration based on the U.S. BEA (2021) and OECD Regional database (2021).

Based on data from 50 U.S. states and the Federal District of Columbia, two approaches were considered to estimate this equation (Table 1). A first approach (Pooled OLS, presented as Model 1) was used to simply pool the data from all regions in the United States, estimating the variance and covariance matrix of the beta coefficients through a robust method that takes into account the potential autocorrelation and heteroscedasticity within each state (clustered standard errors). The second approach (Between group estimator, presented as Model 2) consisted of regressing the averages of regional prices on the average of explanatory variables in the states in the United States.10

Table 1 shows that for both approaches (Model 1 and Model 2) the price-income elasticity is estimated to be around 0.3, which means that a 10% difference in nominal income between states tends to become a real difference in income of the order of 7%, given that the remaining 3% is absorbed by higher prices. These results also show that the states with the greatest weight of services are those that tend to have higher price levels, followed by the states in which industry has a greater weight.11 Given that both approaches provide similar results it was decided to use the results of Model 2 in Step 2.

Step 2: OECD regional prices are estimated based on the relationship between price level, income level and composition of the GVA derived from Step 112 This step will be the result of three subsequent steps:

Step 2.1: Obtaining the unadjusted prices of region “ $h$ ” that belongs to country “ $J$ ” in period “ $t$ ”, by directly using the estimated equation to predict prices (Model 2):

$\displaystyle{\hat{p}}_{\textit{Jht}}=\exp(\textit{Const}+\widehat{\beta}_{{1}% }\textit{lnHDIpc}_{\textit{Jht}}{}+{\widehat{\beta}}_{{2}}{\textit{Ind}}_{% \textit{Jht}}+{\widehat{\beta}}_{{3}}{\textit{Serv}}_{\textit{Jht}})$ (2)

Step 2.2: This step consists in obtaining the price levels after adjusting them with the adjustment factor. This Step is necessary to guarantee the internal consistency of the estimates. The price adjustment factor is thus obtained to ensure that the weighted average of the regional price levels matches the reference national price levels. The procedure is as follows:

$\displaystyle p_{Jt}={\tau}_{Jt}\sum\limits^{H}_{h=1}w_{\textit{Jht}}\cdot\hat% {p}_{\textit{Jht}}$ (3)

Figure 3.

Percentage difference between estimated and official prices in the United States (2018). Note: Deviations are expressed in percentage. Deviations presented in the grey bar are the result of ((estimated regional PPP-official regional PPP)/official regional PPP) while deviations in the black bar are the result of ((National PPP – official regional PPP)/official regional PPP). Source: Own elaboration based on data from the U.S. BEA (2021).

Figure 4.

Deviations between Regional and National PPPs in OECD countries, 2018. Note: Deviations are expressed in percentage ((estimated regional PPP-national PPP)/national PPP). Data not available for Colombia, Costa Rica, Iceland and Israel. Source: Own elaboration.

where, $p_{Jt}$ refers to the price level of country J in period t; $w_{\textit{Jht}}$ refers to the weight of the GDP in region “h” over GDP in country “J”; and ${\tau}_{Jt}=p_{Jt}\left/\sum\limits^{H}_{h=1}\right.w_{\textit{Jht}}{\cdot}{% \hat{p}}_{\textit{Jht}}$ is the adjustment factor.

Step 2.3: Obtaining adjusted regional prices. For each country and each year the average of the weighted regional price levels must coincide with the price level of the country in PPPs.

$\displaystyle{\hat{p}}^{*}_{\textit{Jht}}={\tau}_{Jt}\cdot{\hat{p}}_{\textit{% Jht}}={\tau}_{Jt}\cdot\exp$ $\displaystyle(\textit{Const}+{\widehat{\beta}}_{1}\textit{lnHDIpc}_{\textit{% Jht}}+{\widehat{\beta}}_{2}{\textit{Ind}}_{\textit{Jht}}+$ (4) $\displaystyle{\widehat{\beta}}_{3}{\textit{Serv}}_{\textit{Jht}})$

Step 3: OECD regional price parity indices (regional PPPs) are estimated by using the adjusted regional prices derived from Step 2 and the PPPs at national level.13

$\displaystyle{\textit{PPP}}_{\textit{Jht}}={\hat{p}}^{*}_{\textit{Jht}}*{% \textit{PPP}}_{Jt}$ (5)

where ${\textit{PPP}}_{\textit{Jht}}$ refers to the PPPs at regional level (in $), ${\hat{p}}^{*}_{\textit{Jht}}$ refers to the adjusted regional price derived from Step 2, and ${\textit{PPP}}_{Jt}$ refers to the PPPs at national level (in $).

Estimated regional prices for the United States offer similar results compared to the official price levels derived from the BEA. Figure 3 presents the magnitude and the location of the percentage difference between the regional prices estimated by the BEA and the national prices, as well as the percentage differences between the regional prices estimated by the BEA and the ones derived from this study. This Figure shows that the typical percentage point difference between the estimated prices derived from this study and the ones reported by the BEA at subnational level is between 5% and $-$ 5%. Slightly larger in-sample relative errors (between $-$ 5% and $-$ 10% as well as between 5% and 10%) seem to be located mainly in eastern and western states such as California, District of Columbia, New Jersey, Ohio and Oregon, as well as central states such as Alaska, Connecticut, Missouri, Nebraska and Tennessee. However, the number of states showing a significant relative error seems to be considerable when comparing regional prices reported by the BEA and the national official price levels (Fig. 3).

Estimates of regional PPPs derived from this study suggest the existence of sub-national price differentials across regions in OECD countries. Indeed, according to these estimates the cost of goods and services would vary not only across countries but also across regions. Figure 4 presents the differences, expressed in percentage, between the estimated PPPs indices at regional level and the national ones. Deviations from the national PPPs imply differences in purchasing power of a “basket of goods” across regions. Positive differences in the cost of living seem to be higher in urban regions while negative differences in the cost of living appear in more rural areas. Therefore, the cost of living in capital cities seems to be higher than in rural areas. For example, the 2018 regional PPP for Madrid is 16% above the national average while the regional PPP is at least 16% below in regions such as Extremadura and Castilla-La Mancha. In France, the region Île-de-France displays regional PPPs that are 12% above the national average while the regions of Hauts-de-France and Grand Est account for regional PPPs which are 6% below the national average.

3.4 Comparison with previous results

To date, only a limited number of studies have been able to estimate prices at regional level (TL2). These studies are mainly focused on European countries, and can be divided in two main groups. On the one hand, there are studies where National Statistical Offices developed a methodology in accordance with the Eurostat/OECD guide and using actual observed prices such as [24] in Italy, [21, 22] in the United Kingdom and [39] and then followed by the BEA in the United States. On the other hand, there are academic papers where regional price indices are identified based on model data, such as [6] in Germany, [29] in Austria, and [14, 17] in Spain.14

Estimated regional PPPs derived from this study do not show any significant difference when compared with the results presented in previous studies using actual observations or modeled data. Figure 5 shows that most of the correlations between the current results and those from previous studies are between 0.7 and 1. Moreover, the correlations between the regional prices obtained from this study and the ones offered by the statistical offices on the basis of statistical methodologies have high correlations (e.g. ISTAT $r=$ 0.95, ONS $r=$ 0.94 and BEA $r=$ 0.88).

Table 2
Histogram and descriptive statistics of GDP per capita adjusted with national and regional PPPs, 2018

Note: Data not available for Colombia, Costa Rica, Iceland and Israel. GDP per capita figures are expressed in thousands of USD dollars. Source: Own elaboration.

Figure 5.

Correlation between regional prices derived from the literature review and regional prices derived from this study. Note: Figures presented in this chart are in accordance with the reference year of all the studies. Source: Own elaboration.

4. Relevance of the estimated subnational PPPs

The basic purpose of regional PPPs is to enable the comparison of macroeconomic figures at the regional level in real prices. The following sub-sections show some applications of the use of sub-national PPP estimates when adjusting regional macroeconomic figures.

Figure 6.

Per capita GDP in OECD regions (2018). Note: Data not available for Colombia, Costa Rica, Iceland and Israel. Source: Own elaboration.

Table 3

Change of the typology of regions after adjusting nominal per capita GDP using estimates of regional price deflators

	Using national prices	Using regional prices
		More developed	Transition	Less developed
More developed	105	102	3	0
Transition	65	5	56	4
Less developed	64	0	10	54
Total	234	107	69	58

Source: Own elaboration.

Figure 7.

Regional disparities across a selection of OECD countries (2000–2018). Theil inequality index of GDP per capita. Note: 1. The Theil index measures inequality in GDP per capita between all TL2 OECD regions analysed. It breaks down the overall inequality into inequality due to differences within countries and inequality due to discrepancies between countries. 2. Countries were selected based on data availability and only if they had more than one sub-national region. The sample covers 30 OECD countries with a complete data series between the year 2000 and 2018. The list of countries considered are: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, Korea, Lithuania, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, United Kingdom, United States. Source: Own elaboration based on data from OECD National Accounts (2021) and OECD Regional Database (2021).

Figure 8.

Typology of regions in EU-27 according to the national and regional prices (2015–2017). Note: The Eurostat GDP per inhabitant for the EU-27 used for the computations is USD 38 833 when adjusting regional figures with National PPPs PPS and USD 39 300 when adjusting with estimated sub-national PPPS. Source: Own elaboration.

4.1 Effects on the per capita GDP

Regional GDP is typically adjusted using national PPPs, however the cost of goods and services varies across regions. As such, the adjustment of regional GDP figures with national PPPs might lead to an artificial increase of the GDP in the most developed areas and a decrease in the lagging regions. Indeed, as Table 2 shows, the application of regional PPPs derived from this study to GDP per capita figures shows lower kurtosis, lower skewness and lower variance and range than the ones obtained when applying the national PPPs. However, they show similar mean values.

The differences derived from the application of national or regional prices can be seen in Fig. 6. These maps show clearly that when adjusting GDP per capita figures with national PPPs, some of the rural regions appear to be poorer than when applying estimated regional ones.15 For example, the state of Tasmania (Australia), with a GDP around USD 41 000 appear to be richer after adjusting GDP per capita figures with regional PPPs (above USD 46 000). In contrast, we also observe that wealthy regions (e.g. Yukon region in Canada and Madrid region in Spain), after applying the regional PPPs, appear less well off than when national PPPs were applied.

4.2 Effects on regional convergence

Over the first two decades of the 21 ${}^{\text{st}}$ century, national disparities in GDP per capita have been decreasing while regional ones have remained fairly stable. Figure 7 shows the evolution of the differences in real GDP per capita within and between countries between the years 2000 and 2018.16 These data show that regional differences have remained stable (after observing a divergence between the years 2000 and 2008 and a convergence of the regional disparities after the year 2008) while national ones have declined during the period taken into account. This evidence is consistent with the findings of [43] who observe that OECD countries are converging while regions are diverging.

Overall, in the OECD area, regional disparities are smaller when applying the estimated regional PPPs derived from this study than when applying national PPPs (Fig. 7). The application of regional PPP deflators (instead of national average) lowers the overall level of inequalities since it reduces the real per capita GDP in wealthier regions and it increases it in the less developed ones (e.g. from a Theil index of 0.039 to 0.026 in the year 2018). A conclusion supported by [8], in which similar evidence is reported for Poland and the United States. These results show the overestimation of regional disparities when using national PPPs deflators.

Disparities within countries (when adjusting with regional PPPs derived from this study) are still lower than disparities between countries. Disparities between countries have been higher than disparities within countries for all the period analysed. However, these disparities were almost identical in the year 2008. After this point, disparities in both within countries and between countries have been declining, even if the decline is more significant within countries (Fig. 7).

4.3 Effects on the EU regional cohesion policy

The overestimation of regional GDP per capita disparities can have important policy implications. In fact, GDP per capita figures, and more concretely the difference between regional GDP per capita figures and the EU average, are the main criterion used by the European Commission to allocate the financial aid derived from the EU Cohesion Policy. Therefore, the adjustment of GDP per capita figures with regional price deflators could lead to adjustments in the funds allocated to certain regions and could also change the assessment of the effectiveness of the EU structural funds [8].

Resources from the ERDF and ESF $+$ for the Investment for jobs and growth will be allocated according the following three categories of NUTS level 2 regions [44]: i) less developed regions are those whose per capita GDP in purchasing power parities is less than 75% of the EU-27 average; ii) regions in transition are those whose per capita GDP is between 75% and 100% of the EU-27 average; iii) most developed regions are those whose per capita GDP is greater than 100% of the EU-27 average. These three categories are determined on the basis of GDP per capita measures of each NUTS-2 region measured in purchasing power standards (PPS) and calculated for the period 2015–2017. These figures will be relative to the average GDP per capita of the EU-27 for the same reference period.

The EU cohesion typology of regions will vary when applying estimates of regional PPP figures derived from this study. Concretely, and as presented in Fig. 8 and Table 3, show that following the current EU instructions, might lead to an adjustment in the classification of around 10% of regions, also in line with [33]. The misclassification or regions are mainly seen in Spain, France, Finland and Greece, leading to some of these regions to lose their elegibility for EU Eohesion funds.

5. Conclusions

The approach followed in this work aims at contributing to the topic of regional price levels by using an indirect method applied to OECD and EU-27 countries. The sub-national PPPs estimated and the method used in this paper are a relevant contribution to the literature on this topic for several reasons. Firstly, the method applied here uses publicly available data at the international level and does not require the collection of new information on, for instance, the expenditure on and prices of consumer goods and services in a given territory, which is required when computing Consumer Price Indices. Secondly, the results derived from the application of this method are internationally comparable, since the method applied and the data used are homogeneous across sub-national entities. Thirdly, the method can be easily replicated over time as soon as new raw data become available. Finally, these estimates allow adjusting macroeconomic sub-national measures traditionally adjusted with national PPPs, thus helping to better assess regional development and to better implement adequate policy interventions at sub-national level.

Estimated regional PPPs derived from this study are in line with the results derived from a limited number of national statistical offices or academic works. Despite the slight dispersion observed, the results obtained are highly correlated with the regional prices obtained from other studies.

Our analysis estimates the variation of the cost of goods and services across regions within a country. Differentials in the cost of living have important implications on the welfare of territories. In this line, it has been shown that the adjustment of nominal GDP per capita figures by using the estimated regional price deflators (PPPs) lowers the measures of real GDP per capita in the more developed regions and increases it in the lagging regions (compared to the results obtained when national price deflators are used). This suggests that adjusting macroeconomic figures with regional PPPs has the potential to affect assessments of regional convergence of regions.

These new estimates underline the importance of accounting for price differentials when assessing regional economic disparities. In this respect, National Statistical Offices of all OECD countries are requested to intensify their efforts to produce regional PPPs. This would dramatically improve the support that statistics could provide to well-designed regional development policy initiatives.

The estimates also suggest the need to use sub-national PPPs for the new EU cohesion policy 2021–27. Indeed, with these estimated figures it is observed that around 10% of regions would be misclassified if national PPPs are used. The use of sub-national PPPs would thus have an impact on the eligibility of these regions for EU cohesion funds.

Footnotes

Regional price differences (except for housing costs) are typically small in small countries.

According to the Balassa-Samuelson, countries with a higher level of income per capita tend to have higher price levels. For more details, see Section 3.1.

The differences with the Eurostat NUTS classification concern Belgium, Greece and the Netherlands where the NUTS-2 level correspond to the OECD TL3 and Germany where the NUTS-1 corresponds to the OECD TL2 and the OECD TL3 corresponds to 97 spatial planning regions (Groups of Kreise). For France and the United Kingdom the Eurostat NUTS1 corresponds to the OECD TL2. For more information about NUTS classification, please refer to https://ec.europa.eu/eurostat/fr/web/nuts/background.

Large regions refer to the 2020 Territorial Level 2 (TL2) regions, which according to [] refers to the first administrative tier of subnational government, for example, the Ontario Province in Canada.

The model presented in this section is in line with the Balassa-Samuelson hypothesis and omits other variables that might explain regional prices differences (e.g. rent, tourism, ..) which might not be easily available globally at the sub-national level.

The industry sector comprises categories C to F of ISIC Rev.4.

The service sector comprises categories G to T of ISIC Rev.4.

The main objective of the regressions presented in is not to obtain estimators of the coefficients of the regression equation to which a causal interpretation can be given, but only to estimate a model that enables us to forecast regional values based on the sub-national information available for OECD and EU-27 countries.

These results have also been confirmed when including as an independent variable the share of urban population in each state. In fact, it is confirmed that, ceteris paribus, the more rural states tend to show lower price levels. Moreover, it should be noted that when the same equations are estimated using GDP per capita instead of income, the estimated elasticity is reduced, but the simple predictions obtained using GDP or income are practically coincident given that the lower Price-to-GDP elasticity is compensated by a greater inter-state variability in GDP than in income.

Cross-validation was also implemented to evaluate the good fit of the model independently of the sample used. The cross-validation was carried out by using a random sample of 75% of the states to estimate the price levels of the remaining 25%. This process was repeated ten times. Results of this exercise confirm that the estimated model offers unbiased estimated when comparing them with the official prices derived from the BEA.

Estimated regional PPPs are available upon request.

Other studies presented in the introduction of this article have not been analysed in this section due to discrepancies in the NUTS classification. While this study uses NUTS 2016 classification most of the studies presented in the introduction section use NUTS 2013 classification.

This conclusion is expected as the estimated subnational PPPs are based on the Balassa-Samuelson hypothesis.

The countries and period used in the analysis were selected according to the data availability. The sample used in the analysis covers 30 OECD countries and all of them have a complete data series between the year 2000 and 2018.

Acknowledgments

The authors gratefully acknowledge comments on a preliminary version of this document from Javier Sanchez-Reaza (World Bank), Lewis Dijkstra (European Commission) and staff from OECD (Sean Dougherty, Michael Jacobs, Francette Koechlin, Alexander Lembcke, Karen Maguire, Joaquim Oliveira Martins, Pierre-Alain Pionnier, Simon Scott and Paolo Veneri) for their comments and suggestions. The authors also benefited of comments provided by delegates of the OECD Working Party on Territorial Indicators, when presented to them at the 37th Meeting of the Working Party on Territorial Indicators on 19 November 2019 as an information item.

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The impact of estimated sub-national purchasing power parity on macroeconomic measures 1

Abstract

Keywords

1. Introduction

2. Previous attempts to compute sub-national PPPs

3. Methodology and estimation

3.1 Conceptual framework

3.3 Methodology and results

Table 2 Histogram and descriptive statistics of GDP per capita adjusted with national and regional PPPs, 2018

4.2 Effects on regional convergence

4.3 Effects on the EU regional cohesion policy

5. Conclusions

Footnotes

Acknowledgments

References

Table 2
Histogram and descriptive statistics of GDP per capita adjusted with national and regional PPPs, 2018