What crop choices can—and cannot—reveal about patience

A decision can make sense today for two different reasons: it pays well immediately, or it improves future opportunities. That creates a problem for economists studying repeated choices. The same behavior may reflect different combinations of current rewards and concern for the future.

In a preprint, Yu Hao, Hiroyuki Kasahara and Katsumi Shimotsu show how restrictions on current payoffs can help separate those explanations. Their contribution is primarily mathematical, with numerical illustrations and an application to crop choices in Story County, Iowa. This briefing draws on the supplied paper text; the findings remain preprint research.

Separating rewards from patience

The researchers study dynamic discrete choice models: models in which an individual or firm repeatedly selects among distinct actions while considering their consequences. The discount factor, called beta, determines how much weight next period’s payoff receives relative to today’s. A higher value means future payoffs matter more.

Observed choice probabilities alone generally cannot identify beta separately from current payoffs. Here, “identify” means determine which values are compatible with the model and the observable behavior—not necessarily estimate them precisely from a finite dataset.

Instead of specifying an exact payoff formula, the authors impose properties that economic theory may justify in a particular setting. Monotonicity says a payoff does not fall as a relevant variable rises. Concavity describes diminishing increments. Homogeneity specifies how a payoff changes when certain inputs are scaled together.

The method combines these restrictions with choice probabilities, state-transition probabilities and an assumed distribution of unobserved payoff shocks. It translates the resulting conditions into polynomial equations and inequalities in beta. Equations can isolate one value or leave several candidates; inequalities can bound the possibilities.

These results require suitable rank conditions and informative restrictions. Economic shape assumptions do not automatically reveal patience in every model. The framework also assumes a stationary, infinite-horizon decision problem: the rules remain stable and decisions have no fixed endpoint.

Learning patience without learning every payoff

One important distinction is that beta may be identifiable even when some current payoffs remain unresolved.

Economists often fix one action’s payoff at zero to make a model identifiable. Such a normalization can affect predictions about hypothetical policy changes. The paper shows settings where economic restrictions identify beta without fixing an entire action’s payoff this way, although some payoff components can remain unidentified.

The authors also extend the approach to competing firms, allowing each firm to have its own discount factor. Restrictions can include the irrelevance of rivals’ past actions for current payoffs and exchangeability: swapping rivals’ current actions leaves the firm’s payoff unchanged. Under the stated conditions, these restrictions can identify discount factors even when the value recovered on exit is unknown. Numerical examples demonstrate the results within constructed models, not observed industries.

An Iowa illustration

The empirical application uses satellite-derived crop classifications. The sample contains 583,390 interior 30-metre pixels classified as corn or soybeans throughout 2010–2023. Choices are modeled for 2012–2023. These are pixels used as field proxies, not 583,390 independently surveyed farmers.

The researchers estimate three unobserved, time-invariant types with different cropping patterns and discount factors: rotators, partial rotators and corn-heavy fields. Partial rotators account for about 33% of the sample and plant corn after corn roughly 39–43% of the time, depending on the market-profitability regime.

For this application, the authors do normalize soybean payoffs to zero. They require the implied payoff from corn after corn to rise weakly across low, medium and high profitability regimes. Interpreting that normalized payoff as the current corn-over-soybean margin requires an additional condition: the expected effect of this year’s crop on next year’s soybean payoff must be constant across regimes.

For partial rotators, the compatible annual discount factors run from 0.681 to 0.848. This is a model-dependent identified set, not a confidence interval or a direct measurement of farmers’ psychological patience.

The limits carry much of the message

No discount factor satisfies the restriction for the estimated rotator type. The authors interpret that as failure of the restriction for this group, not evidence about its patience. They report no set for corn-heavy fields because an estimated choice probability is too close to one for the calculation to be reliable.

Alternative clustering methods produce substantially different bounds. Removing smoothing from the profitability-transition estimates changes the partial-rotator interval to 0.459–0.629. Those transitions are estimated from only 16 annual observations.

The reported bounds also omit sampling uncertainty; statistical inference is left for future work. The paper therefore offers a way to discover what assumptions and behavior jointly imply—not an assumption-free answer to how patiently farmers or firms make decisions.