Memorandum, Nov. 2007

Joan R. Rosés (UC3M)

Nikolaus Wolf (Warwick)

1. Introduction

This short memo presents a review of the basic methodology to be employed in the European network 'Historical Economic Geography of Europe, 1900-2000' The basic objective is to generate regional GDP estimates for most European countries with a common methodology.

2. Basic Methodology

The basic methodology was developed by Geary and Stark in their article “Examining Ireland's post-famine economic growth performance”, Economic Journal, 112 (2002), pp. 919-935, although several improvements will be introduced along the following pages. For a discussion of the method see also Nicholas Crafts “Regional GDP in Britain 1871-1911: some Estimates”, LSE Dept of Economic History WP 03/04 (2004).

These authors base their estimates of regional GDP on data on the structure of regional employment (agriculture, industry, services) and regional wages for these sectors together with data for national output for each sector. They assume that regional sectoral productivity relative to the country average is reflected in sectoral regional wages relative to the national average. There are no adequate data for service sector wages which are taken to be equal to a weighted average of agricultural and industrial wages. More formally, country GDP is defined as

YUK = ΣYi

where Yi is GDP of region i which is in turn defined as

Yi = ΣyijLij

where yij is average value-added per worker in region i in sector j and Lij is the corresponding number of workers. This can be estimated as:

Yi = Σ[yjβj(wij/wj)]Lij

where wij is the wage paid in region i in sector j and wj is the national average wage in that sector. β is a scalar which preserves the relative regional differences but scales the absolute levels so that region totals for each sector sum to the known country total. The data required to implement this procedure are agricultural and industrial wages by region and a breakdown of employment by region into agricultural, industrial and service-sector components.

3. Minimum data requirements. The minimum data requirements are:

• Working population breaking down by sector and region.
• Nominal Wages by sector (at least for industry and agriculture) and by region.
• Consumer price levels by region (but see section 5).
• Real GDP national estimates.

4. Improvements in GDP nominal estimates. There are many possible improvements into these basic estimates. We will present several of them:

• Employ wages for service sector.
• Use data on income taxes to take non-wage income into account (Crafts 2004).
• Break down working population by sex and age (this would be important if different regions differ in the age/composition of their workforce).
• Adjust wages by sex-age. This requires a regression approach as the one developed in Chad Turner, Robert Tamura, Sean E. Mulholland and Scott Baier, “Education and income of the states of the United States: 1840–2000”, Journal of Economic Growth 12, 2 (2007), pp. 101-158. (Although data requirements are not too limiting the amount of work required to get final estimates increases dramatically).
• Adjust working population for working hours. This is only important if working hours differ by region (differences by sector are already subsumed in the original methodology).
• Adjust for regional differences in production functions in agriculture. This seems fairly important for big countries with different regional climates and agrarian specializations (for example Spain). This requires the availability of regional estimates for land rents, agricultural land, wages and different regional production functions. More formally, National Agrarian value added is defined as:

YAGRARIAN = ΣYi

where Yi is Agrarian VA of region i which is in turn defined as

Yi = α (wiLi ) + (1- α) (riLdi )

where wi is average wage per worker in region i in agriculture, Li is the corresponding number of workers, ri is average land rents (it could be assumed that this is identical across all regions in the same country if capital markets are integrated), Ldi is the corresponding amount of land, and α is the share of labour in regional agriculture.

5. Constructing real regional GDP estimates

Up to now, data that we have constructed is nominal regional GDP estimates from the production side. However, we need to convert these nominal into real regional GDP estimates.

We can derive easily a regional deflator by the demand side as the weighted sum of ac consumer deflator (cost-of-living) and an investment deflator (which could be assumed identical across all regions if national capital markets are integrated). Then, we need to elaborate new cost-of- living deflators for each region. More specifically, we should use purchasing-power parity (PPP) price indices with a common market basket. Basically, we strongly recommend to follow the Cobb-Douglas PPP indices methodology suggested by J.G. Williamson (“The Evolution of Global Labor Markets since 1830: Background Evidence and Hypotheses”, Explorations in Economic History 32, 2 (1995) pp. 141-196) which weights all regions with a population-weighted common (national) basket.