Development Accounting with Spatial Effects

Abstract

The aim of this paper is to show how the spatial autocorrelation phenomenon often observed in the world distribution of income per capita, can be introduced structurally as the outcome of spillovers effects into a development accounting equation. Neglecting spatial autocorrelation potentially biases our vision of the role played by physical capital in the development process. We show that the total contribution of physical capital accounts for almost 90% of the differences between developing countries and the richest countries.

RÉSUMÉ

Comptabilisation du developpement avec effets spatiaux

La presente communication a pour effet de demontrer la fagon dont le phénoméne d'autocorrelation spatiale, que I'on releve souvent dans la répartition mondiale des revenus par habitant, pent être introduit defagon structurelle comme résidtat d'effets d'entrainement dans une équation de comptabilisation du developpement. Lefait de nepas tenir compte de la correlation spatiale influe sar notre vision du role joue par le capital physique dans le processus de developpement. Nous demontrons que la contribution totale de comptes de capital physiques represente pres de 90% des differences entre les pays en voie de developpement et les pays les plus riches.

RESUMEN

Contabilidad del desarrolio con efecto espaciales

El objetivo de este estudio es mostrar como el fenómeno de autocorrelación espacial a menudo observado en la distribución mundial del ingreso per capita, puede ser introducido estructuralmente como el resultado de los efectos derrame dentro de una ecuación de contabilizar el desarrollo. Si ignoramos la autocorrelación espacial, nuestra visión delpapel quejuega el capital jisico en el proceso del desarrollo se verá posiblemente afectada. Demostramos que la contribución total del capital físico explica casi 90% de las diferencias entre los países en desarrollo y los países más ricos.

Keywords:

• Development accounting
• total factor productivity
• spatial autocorrelation
• technological interdependence

JEL CLASSIFICATION:

• C21
• 033
• 040

Acknowledgements

I would like to thank C. Ertur, B. Fingleton, J. LeSage as well as an anonymous referee for valuable comments and suggestions. The usual disclaimer applies.

Notes

1. King & Levine (1994) and Easterly & Levine (2001), using & Denison's methodology, found that these differences account for 28–59% of the development gap between the richest and the poorest countries.

2. Keller (2004) reviews the recent literature on technological change and diffusion.

3. Actually, (I − γW)⁻¹ exists if and only if |I−γW|≠0. This condition is equivalent to: |γ||W−(1/γ)I|≠0, where |γ|≠0 and |W−(1/γ)I|≠0.

4. Its expression follows directly from the row stochastic property of matrix W. In fact, since γ < 1 and 0 < w _ij <1, expression (9) can be rewritten as: (α+φ)I+γW+γ2W2 + … If we take the sum of the elements of row i of this expression, for i=1,…, N, we have: α + φ(1 + γ+γ ²+…), since: for i=1,…, N, where is the element of the W matrix to the power of r, for r=1,…, ∞. Because of |γ| < 1, the expression in the text follows directly.

5. See also equation (8)

6. This property of this inverse matrix is equivalent to those of the Leonticff matrix with γ = 1.

7. Le Gallo et al. (2005) use the spatial diffusion effect to simulate random shock on the distribution of growth in Europe.

8. As underlined by Temple (1999) and recently motivated by LeSage & Pace (2008), the spatial autocorrelation phenomenon may simply reflects? omitted variables like common shocks or characteristics whereas our model suggests that it is due to TFP spillovers. These questions need to be investigated further but are outside the scope of this paper.

9. In this paper, we use the maximum likelihood estimator with the spatial econometric toolbox of J. LeSage: spatial-econometrics.com.

10. They show instead that variation in growth rates is consistent with each country having the same constant returns to scale production function and with a stochastic process for technical change that is the same across different countries but starts from different initial positions.

11. We note that, in general, the spatial lag variable is a weighted average of other observations but not necessarily contiguous neighbours. Indeed, countries could be related by trade or FDI, for instance.

12. The great circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). It is computed using the equation:where radius is the Earth's radius, lat and long are, respectively, latitude and longitude for i and j.

13. The results are given for W1 and δ=6%. They are robust for δ=4% and δ=10% or the other spatial weight matrix W2. Thees are available upon request.

14. Sincc there is no substantive modification in the distribution of TFP with respect to the value of δ, we present results only for δ = 6%. All results are available upon request.

15. Recall that we work with the per-worker income.

16. This value is close to those of King & Levine (1994) who take a conservative value (0.4) in order to criticize the potential contribution of capital accumulation to output. We use the implied α in our estimation result in the spatially augmented TFP model. The results, using α = 0.33 lead to similar results and are available upon request.