The Illiquidity of Water Markets

Donna and Espín-Sánchez investigate whether a market (sequential English auction) or a non-market institution (fixed quota) more efficiently allocates an intermediate good — irrigation water — when some buyers are liquidity constrained. The setting is Mula, a city in southeastern Spain, where farmers used an unregulated water auction continuously from 1244 until August 1, 1966, when the institution was replaced by a fixed quota system. This 700-year natural experiment, combined with the fact that water demand for a given crop is pinned down by the crop’s production function rather than by farmer wealth, allows the authors to separately identify liquidity constraints from unobserved heterogeneity in productivity.

The empirical context has four features the authors exploit. First, the pre-1966 auction was entirely unregulated, so price differences directly reflect valuations without the confounds of regulatory changes. Second, water is an intermediate good for apricot production; conditional on plot area, tree count, and crop type, demand is determined by the apricot tree’s biological water requirements — not by the farmer’s wealth — so wealthy and poor farmers growing the same bulida apricot variety share the same underlying demand up to an idiosyncratic productivity shock. Third, farmers are classified as wealthy if they held positive urban real estate (non-agricultural wealth) in 1955 tax records; wealthy farmers’ average annual urban rental income (5,702 pesetas) far exceeded their average annual water expenditure (500 pesetas, rising to 1,619 in the highest-expenditure year, 1963), supporting the assumption that wealthy farmers were never liquidity constrained. Fourth, the 1966 institutional shift to quotas — under which each farmer received a fixed water allotment (tanda) every three weeks proportional to plot size, paying only a small annual maintenance fee after the critical season — provides the counterfactual.

The authors build a structural dynamic demand model with three key features: storability (irrigation raises soil moisture, creating intertemporal substitution between periods because water evaporates partially), liquidity constraints (poor farmers cannot always afford water during the critical season when prices peak), and weather seasonality (the critical season, corresponding to apricot fruit growth stages II–III and the Early Post-Harvest period, spans roughly weeks 18–32 and is when trees most need water). Farmers are forward-looking and form expectations about future prices and rainfall. The model’s production function, drawn from the agricultural engineering literature (Torrecillas et al., 2000; Allen et al., 2006), transforms soil moisture into apricot output via a transformation rate parameter gamma, a hydric stress coefficient, and a seasonal dummy.

Demand parameters are estimated using a two-step conditional choice probability (CCP) estimator (Hotz et al., 1994) on wealthy farmers only, then projected onto poor farmers’ welfare calculations. The sample consists of 24 single-crop apricot farmers observed in weekly auction records from January 1955 to July 1966, embedded in a market with over 500 total participants.

The main finding is that the institutional change from auction to quota increased total efficiency. Welfare increased by 23.4 real pesetas per farmer per tree, a 6 percent increase in total apricot production relative to the market. This gain arises because: (1) farmers were relatively homogeneous in productivity (small idiosyncratic shocks), so the primary source of misallocation was not productivity heterogeneity but wealth heterogeneity; (2) liquidity constraints prevented poor farmers from purchasing water during the critical season when their valuation was high, causing them instead to buy earlier (at lower prices but with partial evaporation loss) or later (when their trees had already experienced hydric stress); and (3) the apricot production function is concave in water, so uniform quota allocation is more efficient than market allocation when farmers are approximately homogeneous. The paper provides the first empirical demonstration that liquidity constraints can reverse the standard efficiency ranking of markets over quotas.

Q: What is the core research question? A: The paper asks whether a free market (water auction) or a non-market institution (fixed quota) more efficiently allocates an intermediate good when some buyers are liquidity constrained. The theoretical ranking is ambiguous when agents are heterogeneous in both productivity and wealth, making this an empirical question. The authors find that quotas dominated the auction in the specific Mula setting.

Q: What was the historical water market in Mula and when did it end? A: From 1244 to 1966 — over 700 years — Mula farmers used a sequential ascending-price (English) auction to allocate river water. The auctioneer sold water in discrete units called cuartas (each representing 3 hours of canal flow, or approximately 432,000 liters), holding 40 units per weekly Friday session. Farmers paid in cash on auction day. On August 1, 1966, the farmers’ union (Sindicato de Regantes) replaced the auction with a fixed quota system, having secured a credit line to purchase water property rights share by share.

Q: How did the quota system work, and how did it eliminate liquidity constraints? A: Under the quota, each plot of land received a fixed water allotment (tanda) every three weeks, proportional to plot size. Farmers paid only a small annual maintenance fee to the Sindicato at year-end, after the critical season harvest. Because payment occurred after farmers collected harvest revenue, no farmer was liquidity constrained under the quota. The fee was substantially lower than the per-unit average price under the market.

Q: How do the authors identify liquidity constraints separately from unobserved heterogeneity in productivity? A: The key insight is that water is an intermediate good whose demand is determined by the apricot tree’s biological production function, not by farmer wealth. Two farmers growing the same bulida apricot variety with the same number of trees should have the same water demand up to an idiosyncratic shock. The authors use wealthy farmers (those with positive urban real estate in 1955 tax records) to estimate preferences, under the assumption that wealthy farmers are never liquidity constrained. They then verify that outside the critical season, wealthy and poor farmers purchase similar amounts of water; the purchasing divergence appears only during the high-price critical season, consistent with a cash constraint rather than a preference difference.

Q: What empirical evidence shows poor farmers were liquidity constrained rather than simply less interested in water? A: Poor farmers display a bimodal purchasing pattern inconsistent with the apricot tree’s biological water needs: they buy water before the critical season (when prices are low) in anticipation of not being able to afford it during the critical season, and again after the critical season (when prices fall) to prevent their trees from withering from dehydration. Wealthy farmers, by contrast, delay purchases strategically to the critical season when trees most need water (weeks 18–32). Regression analysis confirms that wealthy farmers purchase significantly more water per tree during the critical season than poor farmers growing identical bulida apricots, while the difference outside the critical season is not statistically significant.

Q: How were wealthy farmers defined and why does their wealth validate the non-constrained assumption? A: A farmer is defined as wealthy if the value of their urban real estate (from 1955 urban tax records) is positive, and as poor if it is zero. Urban real estate constitutes non-agricultural wealth uncorrelated with the apricot production function. Wealthy farmers’ average annual urban rental income was 5,702 pesetas, while their average annual water expenditure was only 500 pesetas (rising to 1,619 pesetas in 1963, the highest-expenditure sample year). This large gap supports the assumption that wealthy farmers could always afford water purchases.

Q: What is the model’s treatment of soil moisture dynamics and why does it matter? A: Soil moisture (M_it) evolves according to an agricultural engineering formula: it increases with rainfall and irrigation purchases (each unit adding 432,000 liters divided by plot area) and decreases via evapotranspiration (ET), subject to a full-capacity ceiling (FC) and a permanent wilting point (PW) lower bound. This storage structure creates intertemporal substitution — water purchased early partially substitutes for future purchases, but at a cost (evaporative loss). The dynamics mean poor farmers who pre-buy water before the critical season lose some of that investment to evaporation, generating a real efficiency loss relative to the quota that delivers water closer to when it is biologically needed.

Q: What are the two sources of potential inefficiency the authors identify? A: The first is inefficiency due to heterogeneity: if farmers differ in ex-post productivity (captured by idiosyncratic shocks epsilon_it), allocating water to a less productive farmer at a given moment is wasteful. Markets correct this inefficiency (they direct water to highest-valuation buyers) while quotas do not. The second is inefficiency due to decreasing marginal returns (DMR): because the production function is concave in water, giving water to a farmer with already-high soil moisture is less productive than giving it to a farmer with low moisture. Quotas naturally avoid DMR inefficiency by allocating uniformly; markets with liquidity constraints exacerbate DMR inefficiency by directing scarce critical-season water to wealthy farmers who may have already accumulated moisture from prior purchases.

Q: What is the main quantitative result of the welfare analysis? A: Switching from the market auction to the fixed quota system increased welfare by 23.4 real pesetas per farmer per tree, representing a 6 percent increase in total apricot production relative to the market counterfactual. This is computed as the difference in yearly mean welfare per tree per farmer (net of irrigation costs, excluding water expenditures which are transfers) between the quota and market allocations using the estimated structural model.

Q: Under what conditions is a quota more efficient than a market with liquidity constraints? A: Quotas dominate markets when three conditions hold simultaneously: (1) farmers are relatively homogeneous in productivity (so the market’s advantage of directing water to high-valuation buyers is small), (2) liquidity constraints are significant (so the market misallocates water away from constrained high-valuation farmers), and (3) the production function is concave in water (so uniform allocation is efficient when farmers are homogeneous). The authors find all three conditions hold in Mula. Conversely, markets dominate quotas when heterogeneity in productivity is large relative to heterogeneity in wealth.

Q: How is the transformation rate parameter gamma estimated and interpreted? A: The transformation rate gamma measures how soil moisture above the permanent wilting point converts into apricot output (in pesetas) during the critical season, via the production function h() = gamma * (M_it - PW) * KS(M_it) * Z(w_t). It is identified from variation in purchasing patterns across seasons and variation in moisture across farmers within the same season. The preferred specification (column 3 of Table 3) yields gamma_L = 0.05. With average moisture per tree (accounting for the hydric stress coefficient) of 873.93 during the critical season, a farmer earns on average 29.09 pesetas per tree per week during the critical season, or 407.25 pesetas per tree per year.

Q: How does ignoring liquidity constraints bias demand estimates? A: If one estimates demand using the full sample (poor and wealthy farmers pooled), a decrease in demand during the critical season when prices rise conflates two effects: (1) the standard price effect (fewer farmers have valuations above the price) and (2) the liquidity constraint effect (some farmers with valuations above the price still cannot buy because they lack cash). Attributing the second effect to price sensitivity overstates the demand elasticity, biasing its absolute value upward.

Q: What robustness checks do the authors provide against unobserved heterogeneity? A: The authors provide four pieces of evidence that wealthy and poor farmers do not have systematically different underlying preferences: (1) wealthy and poor farmers are not geographically sorted into different locations (both groups appear in subareas 1, 2, 4, and 7); (2) wealthy and poor farmers grow the same bulida apricot variety; (3) outside the critical season, wealthy and poor farmers purchase statistically similar amounts of water; and (4) the purchasing divergence is significant only during the critical season when prices are high, precisely the pattern predicted by the liquidity constraint mechanism.

Q: What are the policy implications for water allocation in developing countries? A: The paper implies that before introducing water markets in regions where farmers may be liquidity constrained, policymakers should assess the magnitude of those constraints. If liquidity constraints are significant and farmers are relatively homogeneous in productivity, a quota system or a market supplemented with credit provision may deliver higher efficiency than a pure market. The standard presumption that markets outperform quotas can reverse when poor farmers cannot access credit to purchase water at the times they most need it.

Q: How does this paper relate to Che et al. (2013)? A: Che, Gale, and Kim (2013) assume agents consume at most one unit with linear utility and find that markets always dominate quotas, though some non-market mechanisms with resale outperform markets. Donna and Espín-Sánchez extend this framework by allowing multiple discrete units, a concave utility function, and intertemporal dynamics. Under these extensions, the efficiency ranking between markets and quotas is theoretically indeterminate, and the authors show empirically that quotas can dominate markets. Both papers agree that non-market mechanisms with resale outperform both markets and simple quotas.

Liquidity constraint (paper’s sense): A farmer is liquidity constrained when they lack sufficient cash to purchase water at the prevailing auction price, even if their valuation (marginal productivity of water) exceeds that price. In Mula, poor farmers without urban real estate income faced this constraint during the critical season when prices peaked, because they had already spent their harvest proceeds from the prior year and lacked access to credit markets.

Soil moisture (M_it): The state variable measuring water accumulated in a farmer’s plot, computed using the agricultural engineering evapotranspiration formula. Moisture increases with rainfall and irrigation purchases (each auction unit contributing 432,000 liters divided by plot area) and decreases via evapotranspiration. It is bounded below by the permanent wilting point (PW) — below which trees die — and above by field capacity (FC). Moisture creates intertemporal substitution in demand.

Critical season: The period corresponding to apricot fruit growth stages II and III and the Early Post-Harvest (EPH) period, spanning approximately weeks 18–32 (early May to early August). This is when the bulida apricot tree transforms water into fruit at the most rapid rate, when water demand peaks biologically, and when auction prices rise to their highest levels. It is the season during which liquidity constraints are binding.

Transformation rate (gamma): The parameter in the apricot production function that measures the rate at which excess soil moisture (above the permanent wilting point) converts into apricot output (measured in real pesetas) during the critical season. Estimated at gamma_L = 0.05 in the preferred specification (column 3). It is identified from cross-seasonal variation in purchasing patterns and cross-farmer variation in moisture levels.

Inefficiency due to decreasing marginal returns (DMR): One of two sources of allocation inefficiency identified in the paper. It arises when a farmer with already-high soil moisture receives water, yielding less additional output than if that water had gone to a farmer with lower moisture, given the concavity of the production function. Quotas avoid this inefficiency by allocating uniformly; markets with liquidity constraints exacerbate it by directing critical-season water to wealthy farmers who may have accumulated moisture from earlier purchases.

Cuarta (quarter): The unit of water sold at Mula auctions, representing the right to use water flowing through the main channel for three hours. At approximately 40 liters per second of flow, each cuarta carried approximately 432,000 liters of water. Water rights and land rights were held independently; farmers who participated in auctions owned only land, while waterlords separately owned canal usage rights.

Conditional choice probability (CCP) estimator: The two-step estimation procedure used to recover demand parameters from wealthy farmers’ purchasing choices. In Step 1, transition probability matrices for observable state variables (moisture, week, price, rainfall) are computed and CCP is estimated via multinomial logit. In Step 2, the value function is forward-simulated using these transition matrices and parameters are estimated by GMM, following Hotz et al. (1994).