Trade in Virtual Water: Do Property Rights Matter?

Abstract

This paper examines the determinants of virtual water trade – embodied in agricultural products – and tests the relationship between property rights and the export of water-intensive products. Using two different measures of property rights protection, I show that countries with weaker property rights have an apparent comparative advantage in the export of water-intensive products. After controlling for economic size, natural resource endowments and bilateral trade determinants, the trade flow of virtual water is negatively and significantly correlated with the property rights index of the exporting country. The results are robust across different estimation methods.

Appendix

1.1 Proof: Resource Supply and Property Rights

Suppose the supply of environmental resources is price-dependent, i.e. E^s = E^s(p _E ), where p _E is the price of the environmental resources. Assume that environmental resource E is extracted from a resource pool using an input x which has opportunity cost q. Under an unregulated common-property regime, the extraction of the input E is carried out by N farmers, indexed i = 1,...,N. Let x _i be the input of harvester i, and let $x={\sum }_{i = 1}^{N}{x_{i}}$.

The total harvest can be expressed as a function E = F(x) of the total input. I assume F(0) = 0, F^′(x) > 0, and F(x) is strictly concave, so there are strictly diminishing returns. The concavity assumption is realistic in the case of exhaustible natural resources. The diminishing returns arise from the use of an increasing amount of input x to a fixed body of natural resources.

Assume also that all farmers are symmetric, so that each farmer obtains as its output a fraction of the total output equal to the fraction that it supplies of the total input, E _i = F(x)(x _i /x). Each farmer chooses its input level x _i to maximize the value of its share of output net of costs, p _E E _i (x _i ) − qx _i , here p _E is the market-induced price of the resources, and q is the “opportunity cost” of the input x _i .

The private-property marginal product of the input is denoted MP^P and the common-property marginal product is MP^C. Denote $x_{-i}={\sum }_{j\neq i} x_{j}$, the marginal product under common property rights regime is:

$$ M{P^{C}_{i}}=d{F(x)(x_{i}/x)}/d{x_{i}}\\ =F(x)/x+(x_{i}/x)[F^{\prime}(x)-F(x)/x] $$

(7)

The marginal product of input is F^′(x), the average product is F(x)/x. When N →∞, x _i /x → 0, and the common-property marginal product becomes the average product.

Under private property rights regime, on the other hand, the individual marginal product of input equals the aggregated marginal product, hence $M{P_{i}^{P}}=F^{\prime }(x)$. The difference between the common-property marginal product and the marginal product under private property regime would be:

$$\begin{array}{@{}rcl@{}} M{P^{C}_{i}}-M{P^{P}_{i}}&=&F^{\prime}(x)-F(x)/x-(x_{i}/x)[F^{\prime}(x)-F(x)/x]\\ &=&[F^{\prime}(x)-F(x)/x]-[1-x_{i}/x] <0 \end{array} $$

(8)

The last inequality is derived from the strict concavity, whereby F(x)/x > F^′(x). Therefore, the common-property marginal product is always lower than the private-property marginal product.

For each P^E, the farmer’s objective is to find x _i which optimizes p _E E _i (x _i ) − qx _i . For each fixed q, the solution to this problem, denoted x _i (p _E ,q), is an increasing function of p _E : as the market price of E increases, the marginal productivity of x _i which maximizes the objective function of the farmer must satisfy p _E (∂E _i /∂x _i ) = q. For each p _E and q, this maximization problem defines E _i = E _i (x _i (p _E ,q)).

Under common-property regimens, more is supplied at any given price.