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Central bank communication by ??? The economics of monetary policy leaks

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates the economics of monetary policy leaks — anonymous disclosures of confidential information by insiders to the media — focusing on three central questions: (1) Are leaks random accidents, strategic individual disclosures, or institutionally authorized “plants”? (2) Do leaks shape public (financial market) views, and by how much? (3) Can attributed (named) communication by central bank officials mitigate the effects of leaks?

Data and Setting

The authors study the Eurosystem (ECB and euro area National Central Banks) over January 2002 to December 2021. Their primary data source is a novel database of 368 unique policy-relevant leaks — assembled by manually filtering and classifying more than a million news items from Reuters, Bloomberg, and Market News International archives — with precise minute-level timestamps. Topics covered include: policy rates (178 leaks), unconventional monetary policy/UMP (207 leaks), economic growth (47), inflation (41), and euro exchange rate (36); individual leaks may cover multiple topics. They complement this with a dataset of 7,883 attributable public statements by ECB Governing Council members, identified via keyword filtering and machine learning classification of the Reuters News Archive.

Methodology

The paper employs four main empirical strategies. First, high-frequency event studies using asymmetric windows (5 minutes before to 30 minutes after an event) compare absolute market reactions in OIS rates across the full term structure (3M to 10Y) and in the EURO STOXX 50 across leaks, 5,000 randomly sampled placebo events, and attributable statements. Second, Poisson regression models relate the number of leaks per policy meeting to proxies for Governing Council disagreement (Italian-German sovereign yield spread, inter-quartile range of national inflation rates, number of attributable statements per meeting) and a dummy for quarterly macroeconomic projection releases. Third, a regression framework tests whether leaks move market expectations toward the subsequent policy outcome — identifying whether leaks are informative about the direction of policy. Fourth, an augmented version of the Tillmann (2021) model relates end-of-day changes in longer-term OIS rates to high-frequency monetary policy surprises, interacted with dummies for post-announcement leaks and attributable statements.

Main Findings

Incidence and timing. The number of Eurosystem leaks peaked at 36 in 2019 (more than four per policy meeting on average) before declining by more than one third following the start of Christine Lagarde’s presidency in November 2019. Leaks cluster around policy meetings and, since 2015, have shifted notably from before meetings to after meetings, a shift driven by leaks related to UMP. Leaks occur even during the ECB’s quiet period, when policy-makers are formally restricted from public statements on policy-sensitive topics.

Leaks are not accidents. Poisson regressions reveal that the number of leaks per meeting is significantly and positively associated with proxies for Governing Council disagreement: every additional percentage point in the Italian-German sovereign yield spread is associated with approximately half an additional leak per meeting. The propensity of a policy change increases by four to six percentage points with each additional pre-meeting leak (statistically significant at the 5% or 10% level). The specification explains around 15% of the variation in leak counts.

Market impact. Market movements around leaks are up to 85% larger than those around placebo events. Leaks trigger market reactions that are consistently larger than those of attributable statements by individual Governing Council members across the entire OIS term structure and in equities — a result robust to controlling for distance to policy meetings. Rate leaks mainly move the short and medium end of the yield curve; UMP leaks affect the long end and equities. Leaks about general economic conditions (growth, inflation, exchange rate) produce little statistically significant market response.

Leaks are uninformative about policy direction. Conditional on a pre-meeting leak occurring, the average leak does not move market rates closer to the levels prevailing directly after the subsequent policy announcement. By contrast, attributable statements systematically do reduce this distance. This asymmetry implies that leaks predominantly reflect minority opinions within the Governing Council. Consistent with this, leaks counteract prevailing trends in market expectations at the short end of the yield curve (as established by a negative coefficient on the interaction between the prevailing seven-day pre-leak trend and the leak dummy).

Leaks are not plants; attributed communication mitigates their effects. Post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates (negative and significant interaction coefficient in the augmented Tillmann framework). Attributed statements by ECB Executive Board members, by contrast, systematically move in the direction opposite to the preceding leak across most of the yield curve, partially reversing leak-induced market moves. More intense pre-leak attributable communication is also associated with lower market impact of the subsequent leak, across most maturities. These results jointly indicate that most Eurosystem leaks originate from individual insiders with minority opinions rather than constituting institutional plants.

Scope Conditions

Results pertain to the Eurosystem committee setting, where decision-making is broadly consensus-based and voting records are not published; they may not fully generalize to institutions with concentrated decision-making power. The study measures effects on financial markets, not broader public opinion.

In depth

Q1. How is a “leak” defined in this paper, and how are Eurosystem leaks identified empirically?

A leak is defined as a disclosure of confidential information by an insider to the media with an expectation of anonymity. Eurosystem leaks are identified from Reuters, Bloomberg, and Market News International archives (2002–2021) using keyword-driven pre-filtering followed by manual classification of “candidate” items. The resulting database contains 1,253 news items that aggregate to 368 unique policy-relevant leaks with minute-level timestamps. Policy-relevant leaks touch on: policy rates, unconventional monetary policy tools, economic growth, inflation, or the euro exchange rate; leaks about local economic conditions, banking regulation, or managerial appointments are excluded.

Q2. What are the broad trends in the number and topic composition of Eurosystem leaks over 2002–2021?

The number of leaks rose sharply in the second half of the sample, peaking at 36 in 2019 (more than four per meeting on average). Since Christine Lagarde took over the ECB presidency in November 2019, leaks fell by more than one third from that peak. The topic composition shifted substantially over time: policy-rate leaks predominated in the earlier period, while leaks related to UMP came to dominate in the 2015–2021 sub-period.

Q3. How does the timing of leaks within the policy meeting cycle change across sub-periods?

In the full sample, leaks cluster in the run-up to policy meetings and immediately following announcement days (both on the announcement day itself and the following Friday). Since 2015, a notable shift occurs from pre-meeting to post-meeting timing, driven specifically by leaks related to UMP. The authors attribute this shift to the expectation-management role of UMP: post-meeting leaks allow dissenting insiders to reshape market expectations that are otherwise guided by official press releases and press conferences.

Q4. What regression evidence supports the view that leaks are not random accidents?

Poisson regressions of the number of leaks per meeting on disagreement proxies find significant positive coefficients on: the lagged Italian-German sovereign yield spread (about half a leak more per meeting for each additional percentage point of spread), the inter-quartile range of national inflation rates, and the number of attributable statements per meeting. Meetings coinciding with the release of quarterly macroeconomic projections also attract significantly more leaks. These results are robust to replacing the disagreement proxies with a binary dissent index based on Q&A sessions at ECB press conferences (Tillmann, 2021), even after excluding disagreement-related leaks from the dependent variable to address endogeneity. The model explains about 15% of the variation in leak counts.

Q5. Does the number of pre-meeting leaks predict policy changes?

Yes. The propensity of a monetary policy change increases by four to six percentage points with each additional pre-meeting leak (significant at the 5% or 10% level). This signal about the propensity of change (not the direction) is hard to square with the random accidents hypothesis.

Q6. How large are the financial market reactions to leaks relative to placebo events and to attributable statements?

Market movements around leaks are up to 85% larger than the average size of market reactions to 5,000 randomly sampled placebo events. When leaks are compared directly to attributable statements (with leaks as the baseline and fixed effects for year, month, weekday, and hour), average absolute market moves around leaks are consistently larger across the entire term structure of OIS rates and for the EURO STOXX 50. This result is robust to differences in distance to policy meetings, with size differences across the full term structure persisting for periods far from meetings; near meetings, differences narrow but the average market reaction to leaks never falls below that to attributable statements.

Q7. Do the market effects of leaks differ by topic?

Yes. Leaks about policy rates primarily move the short and medium end of the yield curve. Leaks about UMP tools affect the long end of the curve and equities. Leaks about general economic conditions (growth, inflation, euro exchange rate) do not produce statistically significant market reactions, consistent with the interpretation that economic condition leaks require more interpretation before their implications for the policy path become apparent.

Q8. Do leaks move market expectations in the direction of the subsequent policy outcome?

No. The average pre-meeting leak does not reduce the absolute distance of market rates to post-announcement levels. This result holds across maturities from 3M to 10Y and is robust to separating leaks inside and outside the ECB’s quiet period. Attributable statements, by contrast, systematically reduce this distance (Table 7). The failure of leaks to align expectations with outcomes is interpreted as evidence that leaks predominantly reflect minority views within the Governing Council rather than information held by the decisive voter.

Q9. Do leaks counteract or reinforce prevailing trends in market expectations?

Leaks counteract prevailing trends. The regression of market reactions to leaks and placebo events on the seven-day pre-event trend reveals a significantly negative interaction between the trend and the leak dummy at the short end of the yield curve. This result is driven specifically by leaks about policy rates.

Q10. Do post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates?

Yes. In the augmented Tillmann (2021) framework, the interaction of the high-frequency 2Y monetary policy surprise with a dummy for post-announcement leaks is negative and significant for 2Y, 5Y, and 10Y OIS rates. In contrast, the interaction with a dummy for post-announcement attributable statements is positive and significant across maturities, indicating that attributed communication reinforces the official policy signal. These two results jointly show that leaks weaken official policy announcements while attributed communication strengthens them.

Q11. Does more intense pre-leak attributable communication reduce the market impact of subsequent leaks?

Yes. Using an intensity measure that weights each attributable statement by the inverse of its distance in hours to the subsequent leak (covering a window from 36 hours to 30 minutes before the leak), the paper finds a significant negative relationship between pre-leak communication intensity and the absolute market reaction to the leak, controlling for year, month, weekday, and hour fixed effects. This holds across most maturities.

Q12. Does the market impact evidence support the “plant” hypothesis?

No. If leaks were institutional plants intended to prepare markets for new policy, one would expect the ECB Executive Board — which controls official communication — to subsequently reinforce the signal from leaks. Instead, attributable statements by ECB-affiliated Governing Council members are systematically negatively correlated with the market direction of the preceding leak across the yield curve, with significant coefficients at medium maturities. NCB Governor statements show weaker and more ambiguous effects, potentially because their statements generate smaller average market movements rather than reflecting a lack of willingness to counteract leaks.

Q13. Why do markets react to leaks even though leaks are generally uninformative about policy outcomes?

The paper offers three candidate explanations: (1) automated trading algorithms that do not distinguish between attributed and anonymous communication; (2) leaks serve as a coordination device in the spirit of Morris and Shin (2002), amplifying even noisy signals; (3) media-reporting models such as Nimark (2014) and Chahrour et al. (2021) predict that “man-bites-dog” news — unusual events such as revelations of committee disagreement — shift beliefs beyond their true information content. Leaks are unusual both in frequency (far less common than attributed statements) and in content (they reveal disagreement that rarely surfaces in official communication).

Q14. What are the implications for the measurement of monetary policy shocks from high-frequency identification?

The paper notes that Eurosystem leaks frequently occur shortly before or after official policy announcements. Pre-announcement leaks can shift market expectations before the start of standard event windows, reducing the measured surprise component of official announcements. Post-meeting leaks dampen the end-of-day effects of announcements. In both cases, standard high-frequency surprise instruments extracted from official announcements alone may miss the full extent of new information available to market participants, suggesting that accounting for leaks could improve the relevance of high-frequency instruments used in monetary policy identification.

Q15. What are the implications for the design of central bank quiet periods?

The ECB’s quiet period ends with the policy announcement, whereas the Federal Reserve’s extends to the day after the meeting. Based on the finding that post-announcement leaks dampen policy announcement effects while post-announcement attributed statements reinforce them, the paper suggests that permitting attributed communication shortly after policy decisions may help mitigate the market impact of post-announcement leaks.

Key Concepts

Monetary policy leak (“sources story”): In this paper, a leak is defined as a disclosure of confidential information emanating from an insider within the Eurosystem (ECB or NCB staff or policy-makers) that is transmitted to financial media with an expectation of anonymity for the source. The paper excludes whistle-blower cases and focuses on leaks where anonymity keeps attention on the content rather than the identity of the source. Leaks are distinct from “plants” (formally authorized institutional disclosures intended to advance the institution’s goals) and from “pleaks” (the middle ground).

Plant: An authorized or semi-authorized anonymous disclosure of confidential information made for the purpose of advancing the public institution’s own goals and interests, as distinct from a leak that originates from an individual insider’s personal agenda. The paper tests and rejects the plant hypothesis for most Eurosystem leaks on the basis that ECB Executive Board members’ attributed statements systematically counteract the market impact of leaks.

Single voice principle: The ECB’s communication norm requiring that Governing Council members discuss and resolve disagreements internally while publicly representing the official policy stance. This principle creates a setting where individual members with minority views may resort to anonymous communication as a way to express dissent “off-protocol.”

Quiet period (purdah): The ECB’s rule requiring policy-makers to refrain from public statements on policy-related topics in the seven days before each Governing Council monetary policy meeting. Leaks cluster during this period despite the restriction, supporting the non-random interpretation of leaks.

Attributable (named) statement: A public statement clearly attributed to a specific, named member of the ECB Governing Council, reported as a breaking-news headline. Attributable statements serve both as a comparison benchmark for measuring the market impact of leaks and as a mitigation instrument when they counteract leak-induced market moves.

Pre-leak communication intensity (lambda): The paper’s measure of the intensity of attributable communication in the 36-hour window before a given leak, defined as the sum of inverse time distances (in hours) from each attributable statement to the leak. A higher value means more recent and/or more numerous attributed statements precede the leak.

High-frequency event study window: The paper uses an asymmetric window starting 5 minutes before and ending 30 minutes after a leak’s timestamp. Market reactions are measured as the change in the median OIS quote during the 10 minutes after the window versus the 10 minutes before, matching methodology used for both leaks and attributable statements to ensure comparability across communication types.

Post-announcement leak dummy: An indicator taking the value of one if at least one leak occurs between the end of the official ECB monetary policy announcement window (15:50 CET) and end of trading hours on the announcement day. Used in the augmented Tillmann (2021) regression to measure whether leaks dampen the transmission of monetary policy surprises to longer-term rates.

The Illiquidity of Water Markets

Mon, 01 Jan 0001 00:00:00 +0000

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).