Theoretical Production Restrictions and Agricultural Technology in the United States

Abstract

Agricultural production studies are usually conducted using classical econometrics that make it difficult, if not impossible, to impose conditions derived from economic theory on flexible functional forms. Therefore, such conditions need not hold in estimation. We apply Bayesian econometrics to estimate a flexible production function using U.S. agricultural data under alternative restrictions dictated by theory, including a fully theoretically consistent model that satisfies all restrictions at each point of the data. The probability density functions of parameters, output elasticities, scale elasticity, and productivity gains vary substantially across models. Output elasticities from the fully theoretically consistent model suggest that agricultural production in the United States has typically been more responsive to land than to other factors of production. However, output became more responsive over time to changes in materials, and less responsive to changes in land and labor. By the early 2000s, the elasticity of output to materials was very similar to the elasticity of output to land. The elasticity of output to capital remained relatively stable over the entire sample. The estimates from the fully theoretically consistent model also show a slight increase in the average rate of productivity gains between the 1960s and the 1970s, a relative slowdown in the 1980s and 1990s, and a relative stabilization afterwards. All inputs are substitutes in production; all the elasticities of substitution have increased through the decades, though at different rates.

How weather affects the decomposition of total factor productivity in U.S. agriculture

“…Following Plastina and Lence (2018, 2019), to control for the potential endogeneity problem associated with having variable input quantities as regressors in the distance function, we simultaneously estimate (9) with a system of auxiliary translog equations relating the weather‐filtered input ratios and the weather‐filtered quasi‐fixed inputs to all weather‐filtered output levels and input prices. If the cross‐equation correlation between (9) and any of the auxiliary equations is significant, the appropriate estimation consists of the system rather than the single regression.…”

“…The system of equations to be estimated comprises the IDF (9) and three auxiliary equations with labor, capital, and land ratios as dependent variables (to control for endogeneity). We use Bayesian methods to estimate the system because they allow us to (1) fully impose the desired monotonicity restrictions and partially impose concavity restrictions in estimation, (2) enforce homogeneity on the recovered (as opposed to estimated) parameters and the concavity restriction (ex post) by dropping any Monte Carlo draw that does not meet the conditions, and (3) perform the corresponding inferences with a set of fully theoretically consistent posterior estimates (e.g., O'Donnell & Coelli, 2005; Plastina & Lence, 2018, 2019). By means of the Bayesian approach, we can ensure that parameter restrictions stemming from production economics theory are satisfied over their entire credible intervals, which is generally not possible when the latter are computed with classical approximations such as the delta method.…”

“Are They Aware, and Why?” Bayesian Analysis of Predictors of Smallholder Farmers’ Awareness of Climate Change and Its Risks to Agriculture

“…Girolami and Caderhead [67] further demonstrate that both Gibbs sampling and Metropolis-Hastings algorithms are in general less efficient than HMC. Due to its advantages, some agricultural economics research that employed Bayesian methods has used HMC techniques (e.g., [68][69][70]). Since HMC and the no-U-turn sampler are the default choice in Stan software, all our estimations were done in R and Stan [60,[71][72][73][74].…”

Economics of the Greenseeder Hand Planter, Discrete Choice Modeling, and On-Farm Field Experimentation

“…Gelman and Rubin's idea is that if → , then ̂→ 1, which would be strong evidence that the Markov chains converged. In practice, ̂ should be estimated across all parameters until all their respective ̂′ s satisfy ̂< 1.10 Rubin 1992, Gelman et al 2013;Lambert 2018;Plastina and Lence 2019). As discussed above, corn levels would then be generated in a Monte Carlo simulation using the stochastic plateau function as the true data generating mechanism from which another Bayesian estimation to recover the true parameter vector is conducted.…”