We empirically investigate the welfare effect of a historical institutional change from markets to quotas in the presence of frictions. Both systems allocated water to farmers for irrigation.
A market institution was active for more than 700 years in the southern Spanish town of Mula. In 1966, a fixed quota system replaced the auction. Under the quota system, farmers who owned a plot of land in the irrigated area were entitled to a fixed amount of water, proportional to the size of their plot. In the absence of frictions, a market is efficient because it allocates water according to the valuation of farmers. When frictions are present, however, markets may not be efficient. Frictions arose in Mula because farmers had to pay in cash for the water that they purchased, but did not always have enough cash during the critical season, when they needed the water the most. When farmers are liquidity constrained, the efficiency of auctions relative to quotas is theoretically ambiguous.
It is then an empirical question to assess which institution is more efficient. We show that some farmers were liquidity constrained in Mula, as some historians have suggested. Poor farmers bought less water than wealthy farmers during the critical season, and obtained lower revenue per tree as a result. To compute welfare under auctions and quotas, we estimated the dynamic demand system under the auction accounting for three main features of the empirical setting: intertemporal substitution, liquidity constraints, and seasonality.
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We used the estimated demand system to compare welfare under markets, quotas, and the highest-valuation allocation.
The contributions of this paper are twofold. First, from a historical perspective, we pro-vide empirical epro-vidence of a source of inefficiency in water markets. Second, from an indus-trial organization perspective, we propose a dynamic demand model that includes storability, seasonality, and liquidity constraints. Ignoring the presence of liquidity constraints biases the estimated inverse demand and demand elasticity downwards. To perform the estimation we used only the choices of farmers who were not liquidity constrained; then, we used the model to infer the conduct of all farmers in a counterfactual setting in which no one was liquidity constrained. Our approach may also be applied to other settings by identifying, for example, rational agents, informed consumers, buyers affected by inertia, or other frictions, and simulating counterfactuals where those features are not present.
Our analysis is subject to several limitations. First, the empirical results in this paper apply only to the empirical setting in Mula. One should not conclude that all water markets are inefficient. We have presented an empirical framework incorporating the main compo-nents found in other water markets: seasonal demand, storability, and liquidity constraints.
Our framework can be adapted to assess the efficiency of water markets in other empirical settings. Second, the results from our welfare analysis in Mula only apply to the 24 apricot farmers used in our sample. Finally, our model does not allow for systematic (or perma-nent) differences in productivity across farmers. We believe this is sensible in the empirical context of Mula for the reasons discussed in the paper. Our goal was to investigate how the institutional change, from markets to quotas, affected efficiency for apricot farmers in Mula. However, allowing for systematic or serially correlated differences in productivity may generate dynamic sample selection on unobservables, and may be a central explanation in favor of the efficiency of markets in general. Enriching the model in such dimension is an avenue for future research.
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