Capital as a factor of production in OECD agriculture: measurement and data

Abstract

This article provides a farm sector comparison of levels of capital input for fourteen OECD countries for the period 1973 to 2002. The starting point for construction of a measure of capital input is the measurement of capital stock. Estimates of depreciable capital are derived by representing capital stock at each point of time as a weighted sum of past investments. The weights correspond to the relative efficiencies of capital goods of different ages, so that the weighted components of capital stock have the same efficiency. Estimates of the stock of land are derived from balance sheet data. We convert estimates of capital stock into estimates of capital service flows by means of capital rental prices. Comparisons of levels of capital input among countries require data on relative prices of capital input. We obtain relative price levels for capital input via relative investment goods prices, taking into account the flow of capital input per unit of capital stock in each country.

Notes

¹The countries are Belgium, Denmark, Germany, Greece, Spain, France, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Sweden, the United Kingdom and the United States.

²In this study, depreciation is defined as the decline in the ability of the asset to produce at a given output level, i.e. the physical decay of the asset or a decline in its productivity. Efficiency loss is assumed to be a function of age of the asset.

³Data on investment for most member countries of the European Union are from Capital Stock Data for the European Union (Beutel, 1997). The series were extended through 2002 using Eurostat's NewCronos database (http://europa.eu.int/comm/eurostat/newcronos/). Additional data sources include Contabilidad Nacional de España (Instituto Nacional de Estadística), Anuario de Estadística Agraria (Ministerio de Agricultura Pesca y Alimentación) and Cuentas de Sector Agrario (Ministerio de Agricultura Pesca y Alimentación); ISTAT, Dipartimento di Contabilità Nazionale ed Analisi Economica; and Instituto Nacional de Estadística, Departamento de Estatísticas da Agricultura e Pescas, Serviço de Estatísticas Económicas Agrícolas.The Investment data is reported on pages 53–60 of Fixed Reproducible Tangible Wealth in the United States (US Dept. of Commerce (2003)). This data is also available online at the US Dept. of Commerce website www.bea.gov/national/FA2004/SelectTable.ASP#52. The data is also available for the period 1901–2004.

⁴The expression in (1) gives the quantity of capital available for production. In the dual problem, the factor price function relates the price of an asset to the flow of services derived from that asset. This dual relationship between an asset's relative efficiency and its price can be used to construct estimates of the replacement value of the capital stock, or wealth.

⁵The hyperbolic decay function was employed in Ball et al . (1993, 2001, 2004).

⁶To determine the effects of changes in the value of β on estimates of capital stock, various values of β were used to construct a series of capital stocks. Changes in the value of β produce significant changes in the magnitude of the estimates of capital stock. However, there is much similarity in the rates of growth in the series over the time interval. Thus the choice of β, while having a pronounced effect on the level of capital stock, has little impact on the long-term trends.

⁷Very little data exist on the form of the distribution around the mean life. The only study available was conducted by Winfrey (1935) detailing the actual service lives of a group of assets. Winfrey's S-3 distribution had a bell-shaped appearance somewhat akin to the normal distribution. No rigorous tests were performed to determine if the distribution was, in fact, a normal distribution, but based on this admittedly sparse evidence it is assumed that there exists a normal distribution about the mean life of a particular type of asset. This assumption is used mostly for convenience since tables of values for the normal distribution are readily available.

⁸If r>0, then Substituting this result in (15) and rearranging terms yields expression (16).

⁹For the special case where d _τ = δ(1 − δ)^τ − 1, which was assumed by Jorgenson (1963, 1973), and c = w(r + δ).

¹⁰A number of European countries offer subsidies on purchases of new capital goods at the rate s of their price, in which case the rental price falls to: c = [rw/(1 − F)](1 − s). To fully realize the reduction in capital costs made possible by the subsidy, the firm would have to sell its existing capital stock and replace it with new units of capital which are eligible for the subsidy. In a simply model with no adjustment costs and perfect resale markets, this would be possible. The subsidy would create a one-time capital loss on existing capital. The prices of used capital goods would have to decline to keep the services from them competitive with the lower cost of services available from subsidized, new capital goods.

¹¹The nominal rate was taken to be the average annual yield over all maturities.

¹²Observed real rates are expressed as an AR(1) process. We use this specification after examining the correlation coefficients for autocorrelation, partial and inverse autocorrelation, and performing the unit root and while noise tests. We centered each time series by subtracting its sample mean. The analysis was performed on the centred data.

¹³Purchasing power parities for investment goods are from OECD (1999, p. 162).

¹⁴See Eswaren et al . (2003). They develop a procedure for evaluating inherent land quality and use this procedure to assess land resources on a global scale. Given the Eswaran et al . database, we use GIS to overlay country and regional boundaries. The result of the overlay gives us the proportion of the land area of each region that is in each of the soil stress categories.

¹⁵A number of characteristics are common to only a few regions. In this case, we indicate environmental stress by a dummy variable equal to unity if more than 10% of the land area is affected and zero otherwise.

¹⁶We use the PROC QLIM procedure in SAS 9.1 to estimate the Box–Cox parameters.

¹⁷The results in Table 9 are based on translog multilateral indexes of relative prices in the base year (See Caves et al ., 1982). The base-year purchasing power parities are then extrapolated to earlier and later years in the sample via translog time series indexes of capital rental prices for the individual countries.