Estimating the effect of climate on agriculture with the productive value of agricultural land

Jesús Arellano-González

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Abstract

Objective: The Ricardian model, in which market land values are modeled as a function of climate, has been estimated extensively in the context of developing countries where its core assumptions are likely to fail due to missing or incomplete markets. This article proposes a new measure of land valuation that better reflects agricultural productivity in such contexts: the Productive Value of Agricultural Land (PVAL).

Methodology: A three-step empirical strategy is applied to data from a survey of Mexican rural households. The first step is the estimation of an agricultural production function. In the second step, parameter estimates are used to calculate PVAL. In the third step, PVAL is used as the dependent variable in a Ricardian regression.

Results: Suggests that PVAL increases with more precipitation and decreases with by extreme heat. When the Ricardian regression is estimated using market land values, the positive effect of precipitation is underestimated and the effect of extreme heat on land productivity is null.

Limitations: Omitted variables bias could still influence the Ricardian estimates obtained using PVAL.

Originality: A novel version of the Ricardian model is estimated, one that does not rely on market values of land.

Conclusions: Failing to account for the market setting of agricultural producers, particularly in developing countries, may lead to an underestimation of the effects of climate change in agricultural productivity.

jel Classification:Q15, Q24, Q54, Q56.

Keywords: Climate change, adaptation, agriculture, Ricardian model.

Resumen:

Objetivo: El modelo Ricardiano, en el cual el valor de mercado de la tierra se modela como una función del clima, ha sido estimado extensivamente en el contexto de países en desarrollo en donde sus supuestos clave podrían no sostenerse debido a mercados ausentes o incompletos. Este artículo propone una nueva medida de valuación de la tierra que refleja mejor la productividad agrícola en tales contextos: el Valor Productivo de la Tierra Agrícola (VPTA).

Metodología: Una estrategia empírica de tres pasos se aplica a datos de una encuesta a hogares rurales en México. En el primer paso se estima una función de producción agrícola. En el segundo paso, los parámetros estimados se utilizan para calcular el VPTA. En el tercer paso, el VPTA se utiliza como variable dependiente en una regresión Ricardiana.

Resultados: Sugieren que el VPTA aumenta con la precipitación y disminuye con el calor extremo. Cuando la regresión Ricardiana se estima utilizando valores de mercado de la tierra, el efecto positivo de la precipitación se subestima y el efecto del calor extremo en la productividad agrícola es nulo.

Limitaciones: El sesgo por variables omitidas aún podría influenciar las estimaciones Ricardianas obtenidas con el VPTA.

Originalidad: Se estima una nueva versión del modelo Ricardiano que no se basa en valores de mercado de la tierra.

Conclusiones: El no tomar en cuenta el contexto de mercado de los productores agrícolas, particularmente en países en desarrollo, podría derivar en una subestimación del efecto del cambio climático en la productividad agrícola.

Clasificación jel:Q15, Q24, Q54, Q56.

Palabras clave: Cambio climático, adaptación, agricultura, modelo Ricardiano.

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Artículos

Estimating the effect of climate on agriculture with the productive value of agricultural land

Estimando el efecto del clima en la agricultura con el valor productivo de la tierra agrícola

Jesús Arellano-González¹ jesus.arellano@banxico.org.mx

Banco de México, Mexico

EconoQuantum, vol. 21, no. 2, pp. 47-76, 2024
Universidad de Guadalajara

Received: 17 June 2024

Accepted: 29 June 2024

DOI: https://doi.org/10.18381/eq.vi21i2.7344

Introduction

Climate change may increase global temperatures by as much as 2.7°C by 2100 under an intermediate scenario of GHG emissions (IPCC, 2023). Such an increase might have important productivity consequences in agricultural systems around the world. The agriculture of developing countries is expected to be the most affected due to the already warm temperatures in which they produce and their low capacity to adapt (Mendelsohn and Massetti, 2017; Lybbert and Sumner, 2012). Yet, the empirical evidence available is likely to underestimate the negative effects of climate change in developing countries because current models overstate their potential for adaptation (Hertel and Lobell, 2014).

One such model is the Ricardian approach (Mendelsohn et al., 1994), which exploits cross-sectional variation of land values and climate to approximate the welfare consequences of climate change. Under certain assumptions, the Ricardian model is said to account for the adaptation of farmers in the long run. When the market for land is perfectly competitive and farmers maximize profits unconstrainedly, market land values reflect the productivity of land and the capacity of farmers to adapt in the long run. However, such a setting is rarely seen in the developing world where access to credit is typically heterogeneous with a big proportion of small, poor farmers facing credit constraints (Eswaran and Kotwal, 1986; Carter, 1988). Isolation (Taylor and Adelman, 2003), uncertainty in land tenure (Feder and Nishio 1998) and violent conflicts (Ibáñez and Querubin, 2004; CMDPHD, 2018) might also prevent well-functioning land markets. In these settings, the market valuation of land typically used in Ricardian studies, is not the appropriate measure to quantify the effects of climate change on agriculture as it might overestimate their ability to adapt.

The possibility of omitted variable bias has also undermined the reliability of the Ricardian results (Deschenes and Greenstone, 2007; Ortiz-Bobea, 2020). Market land values can be influenced by unobserved on-farm characteristics and off-farm pressures to convert agricultural land to new uses such as urbanization and housing, confounding the true relationship between climate and agricultural productivity. While recent studies have tried to solve this identification issue in the context of the US or other developed countries (Severen et al., 2018; Ortiz-Bobea, 2020; Bareille and Shakir, 2023), little attention has been paid to the plausibility of the core assumptions of the Ricardian approach in developing countries and the implications they might have on the climate change welfare effects derived from it.

In this paper, I implement a novel version of the Ricardian approach that relies on a shadow measure of land valuation that I call the Productive Value of Agricultural Land (PVAL). PVAL is structurally uncovered from the estimation of an agricultural production function and, as a result it only reflects farm productivity, reducing concerns about omitted variable bias. Its estimation is derived from the first order condition in the profit maximization program of a household. As a result, it also internalizes the shadow components of land valuation associated with the markets of land and credit reflecting more properly the market setting in which farmers make decisions.

The empirical application of this paper focuses on the case of Mexico, a country in which the level of competitiveness so far achieved in agricultural land markets is unclear and where access to credit is limited. In 1992, Mexico initiated a land reform that sought to strengthen the individual property rights of agricultural producers through a process of certification. Before 1992, land was held under ejido ownership, a type of collective property in which individual farmers were not allowed to sell, rent, or collateralize their plots. The land reform ended these restrictions and created a legal mechanism to convert ejido land to full private property (de Janvry et al., 2014; de Janvry et al., 2015). As of 2023, 96.0% of ejido agricultural land has been certified with only 6.0% transitioning to private property (RAN, 2023). In addition, land rental markets are not very active with only 6.3% of total agricultural land being rented (INEGI, 2022). As for credit markets, in 2019, 9.4% of the farms apply for a loan while only 8.4% secured it (INEGI, 2019).

This paper relies on a three-step empirical strategy applied to household data from Mexico’s National Rural Household Survey (ENHRUM). The first step is the estimation of an agricultural production function. In the second step, the estimated input elasticities are used to calculate PVAL using the first order condition of the profit maximization problem of the farmer. In the third step, I use PVAL as the dependent variable in a new version of the Ricardian model. Results are compared with a Ricardian estimation that relies on self-reported market land values instead. In these regressions, the non-linear effect of temperature on land productivity is captured by transforming temperature into growing degree days (GDD) and harmful degree days (HDD).

There are four main findings. First, estimates of PVAL are on average, 33.0% larger than self-reported land values. Market land values underestimate land productivity in all regions of Mexico except the Center, where urbanization pressures are high. Second, when estimating a Ricardian regression using PVAL as the dependent variable, it is found that extreme heat is detrimental for land productivity, i.e. an additional HDD reduces PVAL by 1.5%, on average. Results also reveal a concave and robust relationship between precipitation and land productivity with precipitation increases being beneficial, i.e. a 1mm increase in precipitation increases PVAL by 0.15%. When market land values are used instead, results show no significant effects of harmful temperatures and a smaller increase in market valuation resulting from precipitation increases (a 1mm increase in precipitation increases market land values by only 0.07%). Thirdly, access to formal credit significantly increases land productivity only when PVAL is used. Market land values do not seem to internalize the shadow component of agricultural productivity associated with the credit constraints faced by farmers. Fourth, PVAL does not seem to be affected by the urbanization and housing pressures affecting market land values which increase the closer the farm is to a city.

In Mexico, under a medium GHG emissions scenario, annual mean temperature is expected to increase by 1.5°C by midcentury. This increase might be accompanied with an increase in the number of high heat days (those with maximum temperature > 35°C) to above 20 days per month during summer. At the same time, annual total precipitation is expected to decrease by 3.4% (TWBG, 2023). The Ricardian estimates of this paper suggest that the negative effect that extre me heat may have on future agricultural productivity may not be captured when market land values are used. Similarly, the negative effect of less precipitation in future agricultural productivity would be underestimated if marked land values are used. This result is explained by the fact that PVAL and market land values capitalize climate in different ways. PVAL reflects agricultural productivity and internalizes the market setting faced by agricultural producers. Market land values do not. When making projections of the potential effect that climate change may have on agricultural productivity it is important to do it using estimates that correctly reflect land productivity in a context of constrained production, otherwise, the conclusions and the policy recommendations de rived may be misleading.

The organization of this paper is as follows. The first section provides a review of the existing approaches and some thoughts on the suitability of their application in the context of developing countries. In the second section, I use a profit maximization setting to show the implications of the Ricardian analysis when the assumptions of competitive and complete markets for land and capital do not hold. In the third section, I lay out the empirical strategy to estimate PVAL and the agricultural data used. In the fourth section, I estimate a version of the Ricardian equation that utilizes PVAL as the dependent variable and present the results and their robustness. The final section provides some conclusions and implications for existing and future work relying on the Ricardian approach.

Existing approaches

In the Ricardian model, farmers are assumed to maximize profits in a context of complete and perfectly competitive markets. With perfect competition in land markets, the market rental price of one unit of land, $v$ , will be set equal to the profit $π^{*}$ that such unit of land will generate (Mendelsohn et al., 1993). Land values then reflect the present value of future land rents or, equivalently, future farm profits. If the interest rate on capital is the same for all farmers, then:

L a n d V a l u e = \sum_{t = 1}^{\infty} \frac{π^{*}}{{(1 + r)}^{t}} = \sum_{t = 1}^{\infty} \frac{v}{{(1 + r)}^{t}} = \frac{v}{r}

(1)

where $t$ stands for time and $r$ is the market interest rate. By relying on cross-sectional variation of farm prices, the Ricardian approach accounts for all the possible forms of adaptations that a profit maximizing farmer would undertake in response to climate change. Given climate, farmers will choose the crop or activity that generates the highest value of $π^{*}$ . Farmers will then optimize input usage within the chosen activity. Consequently, the Ricardian approach relies on land values to draw conclusions about how exogenous changes in climate affect farm productivity. Typically, this relationship is estimated using an equation of the form:

{L a n d V a l u e}_{c} = α + {f (\bar{W}}_{c}) + X_{c}^{'} β + ε_{c}

(2)

where $\bar{W}$ represents climate normals (three-decade averages of climatological variables, generally, temperature and precipitation) at every location $c$ (i.e., counties). $\bar{W}$ is generally estimated from historical meteorological records of temperatures and precipitation for relevant time windows usually associated to growing periods. A set of other relevant determinants of land values, $X$ , is also included. Welfare impacts from different climate change scenarios can then be inferred from the parameter estimates obtained in Equation 2.

The Ricardian model proposed in the mid 1990’s has been applied extensively. In the US, a first application was provided by (Mendelsohn et al., 1994) with subsequent developments aiming to improve upon this seminal work (Schlenker et al., 2005; Schlenker et al., 2006). Econometrically, the cross-sectional nature of the Ricardian approach is its greatest disadvantage. If there exist unobserved factors correlated with climate and land valuation, then, the Ricardian estimates will be affected by omitted variable bias (Mendelsohn and Massetti, 2017). Such unobserved factors could be soil quality, a farmer’s idiosyncratic ability and nonfarm influences such as the option value to convert land to a new use (as with urbanization). To reduce the threat of omitted variables, the usual strategy has been the inclusion of a large set of plot or household characteristics. However, some studies have found that even after controlling for such characteristics, the Ricardian estimates are not stable over time and that such instability is likely due to factors affecting land valuation that remain omitted (Deschênes and Greenstone, 2007; Ortiz-Bobea, 2020).

The panel data approach (Deschênes and Greenstone, 2007), solves the identification issues of the Ricardian approach by regressing agricultural outcomes on weather and individual fixed effects. However, by relying on weather, the panel data approach estimates something that is different from the long run effect of climate. Specifically, short run adaptations to fluctuations in weather can differ from long run adaptations to climate change (Fisher et al., 2009; Fisher et al., 2012; Deschênes and Greenstone, 2012; Auffhammer, 2022). In spite of this potential shortcoming, the panel approach has attracted significant attention. Some of the empirical applications relying on panel data include Burke and Emerick (2016), Schlenker and Roberts (2009) and Ortiz-Bobea and Just (2013) for the US, Welch et al. (2010) for Asia, Gammans et al. (2017) for France and Moore and Lobell (2014) for Europe, Guiteras (2009) for India and Lobell et al., (2011) for a global analysis. The application of the panel data approach in developing countries has been more limited mainly because long panel data sets on agricultural outcomes at a sufficiently disaggregated scale are often not available (Burke et al., 2016). In such contexts, cross-sectional data is more likely to be available. Not surprisingly, the implementation of the Ricardian approach in developing countries has been prolific. Some countries and regions for which Ricardian estimates exist are Mexico (Mendelsohn et al., 2010; Galindo et al., 2015), Sri Lanka (Seo at al. 2005), Brazil and India (Sanghi and Mendelsohn, 2008), Latin America (Seo and Mendelsohn, 2008a and 2008b), Africa (Kurukulasuriya and Mendelsohn, 2007) and Asia (Mendelsohn, 2014).

Efforts to address the omitted variables bias critique to the Ricardian approach are still ongoing. In the context of the US, Ortiz-Bobea (2020) estimates a Ricardian equation using agricultural land rents as the dependent variable. According to the author, this strategy circumvents the effect of nonfarm influences because land rents better reflect agricultural productivity and do not capitalize the opportunity costs of alternative land uses. When comparing his results with a traditional Ricardian equation that relies on market land values, the author concludes that the estimated effect of climate change in US agriculture is actually not distinguishable from zero which is in sharp contrast with the large negative effects found with Ricardian models that use market land values. In a more recent contribution, Bareille and Chakir (2023) estimate a version of the Ricardian approach based on repeated land sales data from France in which plot fixed effects are included in the regression while climate is allowed to vary between sales. The authors argue that the inclusion of plot fixed effects is the only way to remove the bias associated with omitted factors affecting land valuation. This analysis combines the advantages of both, the cross-sectional approach, by still using land values and climate, and the panel approach, by controlling for confounding omitted variables with plot fixed effects. Their results suggest higher positive impacts of climate change in French agriculture compared to traditional Ricardian estimates. Yet, both of these applications are focused on two developed countries, the USA and France, where the assumptions of perfectly competitive markets for land are likely to hold. These contributions, however, pay no attention to the plausibility of such assumptions in the context of developing countries. In addition, both studies rely on decades-long data on land values or land transactions, which is hard to get in the developing world.

Market land values will reflect the true valuation of land only when the markets for land and credit are well-functioning. Perfect competition in the land market will make profits equate the rental value of land. A complete market for capital allows farmers to access any amount of working capital that they require in order to initiate and continue the production process. This, however, is not the case in many developing countries. Empirical evidence shows that land titling increases land values and farm investments (Feder and Nishio 1998). Uncertainty in land tenure introduces a component of risk to future farm profits not likely to be captured by market land values. Violent conflicts and forced displacements make it impossible for a farmer to have certainty about land tenure and the value of land holdings (Ibáñez and Querubin, 2004; CMDPHD, 2018). Isolated villages poorly integrated with regional or national markets might not fit the assumption of perfectly competitive input markets if local markets for some inputs, including land, do not exist (Taylor and Adelman, 2003).

Agrarian economies in developing countries typically have limited access to credit due to the inability of farmers to provide collateral. Often, the amount of land that farmers own represents their most valuable possession. Whenever access to credit is associated to land holdings, small farmers might remain constrained or not have access to capital at all (Eswaran and Kotwal, 1986; Carter, 1988). Because of heterogeneous access to capital, farmers are unlikely to bear the costs of adaptation to climate change homogenously. Credit constraints preventing adaptation might have important consequences on who is able or not to adapt. In the context of incomplete or missing markets, market land values might not reflect the true productive value of agricultural land and the true ability of farmers to adapt, an issue explored in detail with the theoretical model presented in the next section.

Land valuation in the context of missing and incomplete markets

To illustrate the fact that market land values do not reflect land productivity in the presence of credit and land constraints, consider a household ( $i$ ) that engages in agricultural production using land ( $T_{i}$ ), labor ( $L_{i}$ ), and intermediate inputs ( $I_{i}$ ) (i.e. fertilizers, pesticides). Agricultural output is given by $Q (T_{i}, L_{i}, I_{i}, A)$ which is assumed to be increasing, twice continuously differentiable and quasi-concave. $A$ is a productivity parameter. Output and inputs are all traded using market prices. The household is also endowed with an amount of land ${\bar{T}}_{i}$ .

When renting land, hiring labor and purchasing intermediate inputs, the household is subject to a working capital constraint $B_{i}$ that is equal to the amount of credit for which it is eligible based on the amount of collateral that it can offer.² For simplicity, let us abstract away from the potential endogeneity of access to credit and assume that the credit amount $B_{i}$ is exogenously determined.³

The household seeks to maximize profits from agriculture by solving the following problem⁴:

\max_{T_{i}, L_{i}, I_{i}} p_{Q} Q (T_{i}, L_{i}, I_{i}; A) - v (T_{i} - {\bar{T}}_{i}) - p_{L} L_{i} - p_{I} I_{i} - r B_{i}

(3)

s.t.

v (T_{i} - {\bar{T}}_{i}) + p_{L} L_{i} + p_{I} I_{i} \leq B_{i}

where $p_{Q}$ , $v$ , $p_{L}$ and $p_{I}$ are the market prices of output, land, labor and intermediate inputs respectively. The household repays the loan at the interest rate $r$ . When $v (T_{i} - {\bar{T}}_{i})$ is positive, the household rents land in and this expenditure tightens the credit constraint as it uses liquidity. Conversely, when $v (T_{i} - {\bar{T}}_{i})$ is negative, the household rents land out and the cash generated relaxes the constraint as it creates liquidity (Sadoulet and de Janvry, 1995). Let $λ_{i}$ the Lagrange multiplier associated with the credit constraint. The First Order Condition (FOC) with respect to $T_{i}$ is given by:

p_{Q} \frac{\partial Q}{\partial T_{i}} = v (1 + λ_{i})

(4)

The price used by the household to optimally determine land use is a shadow rental price that is household specific and a function of the shadow price of credit, $λ_{i}$ , and the market rental value of land $v$ . As a result, in the presence of credit constraints the market rental value of land does not entirely reflect its full opportunity cost. Equation 4 clearly differs from the Ricardian result. Whenever credit constraints are present, the shadow rental value of land will differ from the market rental price. The Ricardian assumption stated in Equation 1 will result from profit maximization only when the credit constraint is not binding (i.e. $λ_{i} = 0$ ).

When the market for land is missing, the household cannot rent land in or out, $v$ is equal to zero and the household cannot devote an amount of land larger than its land endowment to agricultural production. The profit maximization program becomes:

\max_{T_{i}, L_{i}, I_{i}} p_{Q} Q (T_{i}, L_{i}, I_{i}; A) - p_{L} L_{i} - p_{I} I_{i} - r B_{i}

(5)

s.t.

p_{L} L_{i} + p_{I} I_{i} \leq B_{i}

T_{i} \leq {\bar{T}}_{i}

Let $μ_{i}$ be the Lagrange multiplier associated with the land constraint. When the market for land is missing the shadow rental value of land is given by:

p_{Q} \frac{\partial Q}{\partial T_{i}} = μ_{i}

(6)

In turn, the shadow rental price of land is household specific and the opportunity cost of land is given by a shadow measure only known to the farmer.

Equation 4 and Equation 6 illustrate that in the presence of credits constraints and/or when the market for land is missing, the marginal value of an additional unit of land is not necessarily equal to an exogenous price determined in a competitive market. Depending on the market setting, this value could be a combination of market and shadow valuations. When the market for land exists and no credit constraints affect the decision making of the farmer, then, the market value of land, $v$ , tells us all we need to know about its productivity. However, if credit constraints are present, the marginal value of an additional unit of land is higher due to the increased productivity caused by accessing an additional unit of credit. This is the shadow price of credit $λ_{i}$ , and the market rental price of land fails to internalize it. Finally, if a market for land does not exist, farmland productivity is endogenously determined and given by the shadow price of land, $μ_{i}$ .

Market measures of land productivity might lead to erroneous conclusions as they might omit other important determinants of land productivity, particularly in developing countries where farmers are expected to face different types of constraints. To investigate the effects of climate change on long-run farm productivity one must use a measure that genuinely reflects it, free of other non-agricultural confounders affecting its market valuation and inclusive of the market setting directly affecting agricultural productivity. If access to credit boosts productivity, then the shadow price of credit $λ_{i}$ should be part of its productive value. In the absence of a competitive market for land, the shadow rental price of land $μ_{i}$ should be interpreted as its productive value. Such a measure is what I have defined as PVAL. Although not directly observed, PVAL can be inferred from the left-hand side of Equation 4 or Equation 6. The next section outlines the empirical strategy to estimate it and the results obtained.

PVAL estimation

Empirical strategy

The first step of the empirical strategy of this paper is to estimate PVAL. The shadow rental price of land given by the right-hand side of Equation 4, and Equation 6 is not observed as the idiosyncratic component of land valuation is only known to the farmer. However, regardless of the market setting faced by the farmer, the left-hand side of the FOC is always the same. The marginal value of an additional unit of land should always equate the shadow rental price of land and it is possible to approximate it by estimating an agricultural production function. I assume a Cobb-Douglas production function of the form:

G_{i t} = A_{i t} T_{i t}^{β 1} L_{i t}^{β 2} I_{i t}^{β 3}

(7)

where $G_{i t}$ represents gross output value of household $i$ at time $t$ . As before, $T_{i t}$ , $L_{i t}$ and $I_{i t}$ represent land, labor and intermediate inputs. Taking natural logs of Equation 7 results in the familiar linear production function:

{l n G}_{i t} = β_{0} + β_{1} {l n T}_{i t} + β_{2} l n L_{i t} + β_{3} l n I_{i t} + q_{i t} + η_{t} + ε_{i t}

(8)

where the productivity parameter $A_{i t}$ has been decomposed in $β_{0}$ , the mean efficiency level common to all households, $q_{i t}$ , a productivity parameter that represents unobserved household-specific characteristics such as the managerial ability of the farmer and, $η_{t}$ , a productivity shock common to all households within a time period $t$ . $ε_{i t}$ , is an i.i.d. error component composed of unexpected shocks to agricultural productivity.

The correlation between input levels and unobserved productivity factors generates an endogeneity issue. Inputs levels in agricultural production are not independently chosen but are rather determined by the characteristics of the firm including the unobserved factor $q_{i t}$ . Panel estimates of Equation 8 would generate unbiased estimates of the structural parameters of the production function if we are willing to assume that $q_{i t}$ is time-invariant. Recent theoretical developments have moved away from such an assumption and treat the idiosyncratic unobserved productivity as time-variant. Of particular relevance for this empirical application are the works of Olley and Pakes (OP, 1996) and Levinsohn and Petrin (LP, 2003). OP use the firm’s investment decisions to proxy for unobserved productivity shocks. LP favors the use of intermediate inputs as proxies arguing that in some settings the proportion of observations with zero investment is high enough to cast doubts on the validity of the assumptions made by OP. This is particularly true for the case of agriculture where investment decisions are not observed on a frequent basis. The preferred results of this empirical application are derived using LP. For comparison purposes, estimates using standard OLS and panel techniques are also provided.⁵

Having estimated the structural parameters of the production function, PVAL is recovered from the capitalization of the shadow rental value of land. Equation 4 and Equation 6 state that regardless of the market setting, the shadow rental value of land will always equate to the marginal value of land given by the left-hand side of the equations. Taking the first derivative of Equation 7 with respect to $T$ and using $r$ to capitalize it we have:

{P V A L}_{i t} = \frac{{\hat{β}}_{1} [e^{({\hat{β}}_{0} + {\hat{q}}_{i t} + {\hat{η}}_{t}}] T_{i t}^{{\hat{β}}_{1}} L_{i t}^{{\hat{β}}_{2}} I_{i t}^{{\hat{β}}_{3}}}{r T_{i t}} * \hat{φ}

(9)

where $\hat{φ} = \frac{1}{N} \sum_{n = 1}^{N} e x p ({\hat{ε}}_{n})$ , with N equal to the total number of observations in the sample and ${\hat{ε}}_{n}$ equal to the estimated residual from Equation 8. $φ$ is the Duan smearing transformation factor, a correction needed to account for the fact that $\ln [\ln (G)] \neq \ln [E (G)]$ (Duan, 1983).⁶ As opposed to the market valuation of land, PVAL is the household’s reservation price of land that internalizes the market settings faced by the farmers. It is also uncovered from the structural estimation of a functional form that synthetizes the way in which agricultural inputs are transformed in agricultural output thus reflecting only agricultural productivity.

Data

ENHRUM is a nationally representative panel of Mexican households located in 80 villages with fewer than 2,500 inhabitants and across 14 states. It provides information for the 2002 and 2007 cropping seasons and a complete characterization of the agricultural activities of rural households including total output value and input use and detailed information on socio-demographics, plot characteristics (size, ownership regime, self-reported market land values, access to irrigation, etc.) and access to credit (formal and informal).

Table 1 reports the summary statistics of the variables used to fit the agricultural production function. The sample is composed of 720 agricultural households, 182 present in the 2002 round, 154 present in the 2007 round and 384 present in both rounds of the survey. The pooled sample is composed of 1,104 observations. Agricultural variables in this table represent the aggregated values of every crop grown by the household.⁷ For example, in 2002, the average output value per hectare (ha) of $9,540.8 includes the market value of all crops grown by the household (staples, non-staples, annuals, perennials) in the Spring-Summer and Fall-Winter cropping seasons. Double cropping has been mentioned in the literature as a potential way of adaptation to climate change (Seifert and Lobell, 2015). Thus, it is important to account for it when valuing land productivity. Between 2002 and 2007, average output value per hectare increased by 18%.

Table 1
Summary statistics of agricultural variables

Note: Monetary values are expressed in real pesos of June 2012.

Average land in production amounts to 4.6 has on average. Total labor is defined as the sum of family and hired labor from the beginning of the production process before planting and up to harvest, and the pooled sample reflects an average of 65.2 days of total labor per ha. We observe an increase of 23% in total labor usage from 2002 to 2007. The cost of intermediate inputs is defined as the sum of seed, fertilizer, manure and pesticide purchases. It also includes the rent of agricultural machinery (i.e. tractors, harvesters, yuntas, etc).⁸ On average, households spent $4,984.5 per ha on the purchase of intermediate inputs. Finally, average agricultural value added (output value minus the cost of intermediate inputs) is equal to $4,556.3 per ha and between 2002 and 2007 it increased by 50%.

Results

Table 2 reports the parameter estimates of the agricultural production function. OLS, fixed effects and LP estimates of Equation 8 are presented in columns (1), (2) and (3) respectively. In OLS and fixed effect, standard errors are clustered at the household level. In LP standard errors are derived using 50 bootstrap replications. In all three specifications, it is found that increases in labor and land lead to increases in agricultural value, i.e. all estimated elasticities are positive and statistically significant at the 5% level. Failing to control for unobserved idiosyncratic productivity leads to an overestimation of the magnitude and significance of the elasticity of intermediate inputs, i.e. the OLS estimate is larger compared to the fixed effects and LP estimates. This result indicates that, while all three inputs are potentially correlated with q it , the correlation between intermediate input usage and $q_{i t}$ is likely to be the highest.⁹ In the event of unexpected productivity shocks, farmers have more flexibility to adjust the use of intermediate inputs compared to land or labor which may have been already committed in the production process. Thus, the omission of $q_{i t}$ artificially inflates the parameter estimate of intermediate inputs. In fact, according to the LP estimates (column (3)), the estimated elasticity of intermediate inputs is not statistically significant. Finally, the LP estimates indicate that the hypothesis of constant returns to scale cannot be rejected.

Table 2
Production function parameter estimates

Note: In OLS and fixed effect, standard errors are clustered at the household level In LP, standard errors are derived using 50 bootstrap replications. * p<0.10, ** p<0.05, *** p<0.01.

PVAL estimates are obtained from substituting the parameter estimates of column (3) of Table 2 into Equation 9. The interest rate used for the capitalization of PVAL is 4.61% which corresponds to the return of a Mexican treasury bond on June, 2012 (Banxico, 2023). PVAL and self-reported land values are both available for only 727 observations. Table 3 reports summary statistics and the paired t-test for the difference of these two measures. In the pooled sample, the average PVAL per hectare is $100,202.8. This value is 33% higher than the mean self-reported land value of $75,597.3 and the difference is statistically significant. On average, PVAL estimates are significantly larger than self-reported land values in the southern and northern regions. For example, the Northwest displays an average PVAL estimate that is 245.0% higher than the average self-reported land value. Between 2002 and 2007, average self-reported land values increased by 54% while average PVAL increased by only 10%. This result indicates that the rapid increase in self-reported land values is possibly associated to off-farm factors not related to agricultural productivity.

Table 3
Market land values vs PVAL estimates (pesos per hectare)

Note: The regional distribution of the 14 states of the ENHRUM sample is as follows: a) Southeast: Oaxaca, Veracruz and Yucatan; b) Center: Estado de Mexico, Puebla; c) Midwest: Guanajuato, Nayarit, Zacatecas; d) Northwest: Baja California, Sinaloa, Sonora; e) Northeast: Chihuahua, Durango, Tamaulipas.

The overall correlation between observed land valuation and the PVAL estimates is only 0.173. Thus, there is little agreement between what households report as market land values and the actual productive value of their plots. Self-reported land values could be affected by measurement error but its magnitude is unknown since there is not an official source of market land values that could be used as comparison. Alternatively, households might report an estimation of the market value of their land but not its shadow components. As detailed before, in the presence of credit constraints, there is an additional component in a household’s reservation price for land, the shadow price of credit. If this is true, then Table 3 provides evidence that such credit constraints are present and economically important, particularly at the regional level. Other empirical findings have also highlighted the economic importance of shadow prices to explain agricultural labor supply responses (Skoufias, 1994) and crop valuation (Arslan and Taylor, 2009).

Ricardian estimation

Empirical strategy

The final step of the empirical application of this paper is the estimation of a version of the Ricardian equation that has PVAL as the dependent variable. To estimate the effect of climate change on land productivity, I use the pooled sample of PVAL estimates (1,104 obs) to estimate the following specification:

{l n P V A L}_{i v t} = α + θ_{1} {G D D}_{v t} + θ_{2} {H D D}_{v t} + θ_{3} P_{v t} + θ_{4} P_{v t}^{2} + S_{v t}^{'} γ + X_{i t}^{'} ϕ + τ_{r} + η_{t} + ϵ_{i t}

(10)

where the natural logarithm of PVAL of household $i$ in village $v$ at time $t$ is expressed as a function of the following climate variables at the village level: Growing Degree Days (GDD), Harmful Degree Days (HDD), precipitation (P) and precipitation squared (P²). $S_{v t}$ is a vector of soil types at the village level and $X_{i t}$ is a vector of household characteristics. Regional ( $τ_{r}$ ) and time ( $η_{t}$ ) fixed effects are also included to control for unobserved time-invariant determinants of land productivity common to all households within the same region and during the same year. Versions of Equation 10 with region-by-year fixed effects are also estimated to control for the possibility that such unobserved determinants are time-varying.

As long as there is correlation between climate and other unobserved determinants of agricultural productivity not included in the regression, the Ricardian estimation could still be biased. However, PVAL only reflects land productivity which greatly reduces concerns about omitted factors polluting land market valuation. Also, PVAL internalizes the market setting in which farmers make decisions and is thus a better representation of land valuation in places where markets are less likely to function perfectly. For comparison purposes, Equation 10 is also estimated using self-reported land values.

Data

Household data

Table 4 reports summary statistics on the household characteristics included in the estimation of Equation 10. There is not much evidence of competitive and complete markets for land and credit. Only 30% of households have predominantly private ownership over their plots¹⁰ with the rest still being under the ejido figure. Only 10% of the households participate in land rental markets while an additional 14% engage in informal mechanisms such as borrowing and crop-sharing. Only 8% of households had access to formal credit while an additional 19% had credit from informal sources. Finally, only 27% of the households use irrigation. The table also indicates that rural households in the sample rely heavily on government transfers (from PROCAMPO and PROGRESA) and that household heads in rural Mexico have low levels of education.

Table 4
Summary statistics of household characteristics

Notes: 1) PROCAMPO is direct income support program for farmers; 2) PROGRESA is a conditional cash transfer program for poor families; 3) obtained using village information and urban polygons of the 2010 National Census (INEGI, 2010). An urban center is defined as a locality with at least 2,500 inhabitants.

Climate and soil data

Daily weather data for 5,422 weather stations were obtained from the meteorological service repository CLICOM¹¹ which provides information on daily precipitation, maximum and minimum temperatures that date as far back as 1920. Entry and exit are observed for many weather stations, and as a result, daily weather data are missing for the dates in which a station did not exist or did not operate. Missing data are a common issue when using information from weather stations and could introduce a bias in parameter estimates (Auffhammer et al., 2013). To minimize the potential effects of missing data, I restrict the sample of eligible weather stations to those with at least 75% of daily information for the period of 1972 to 2007. This period is long enough to cover 30 years before each round of ENHRUM. After this exclusion, I am left with information from 1,713 stations for precipitation and 1,510 stations for temperature. This procedure keeps the set of stations used to calculate each climate variable constant ensuring that its resulting variation is not caused by changes in station coverage (Auffhammer et al., 2013).

I define weather $w$ , in village $v$ at time $t$ as the weighted average of weather in the 5 nearest weather stations:

w_{v t} = \frac{\sum_{t = 1}^{5} α_{n} w_{n t}}{\sum_{t = 1}^{5} α_{n}}

(11)

with $α_{n} = \frac{1}{\sqrt{d_{n}}}$ , where $d_{n}$ stands for distance of weather station $n$ to each village $v$ . Weights are normalized so that their sum over all stations in a village sum to 1. On average, the 5 closest weather stations used to interpolate precipitation and temperature are located at a distance of 36km and 39km, respectively. A map showing the location of villages and weather stations is provided in Figure 1.

Figure 1
Location of ENHRUM villages and weather stations
Note: The map shows the location of the 80 ENHRUM villages and the weather stations used to interpolate weather data to each village. The interpolation is limited to the 5 closest weather stations.

Following Jessoe et al. (2018), I predict missing data by regressing weather in the closest station, on weather of the remaining 4 stations assigned to the village. I use the predicted values from this regression to fill in missing values. Weather at time $t$ in station $n$ will remain missing if it is also missing in at least 1 of the other 4 stations. To fill in the remaining missing observations, this regression is repeated while dropping the most distant station in each iteration until there are no more stations to predict weather (i.e. after weather in the closest weather station is regressed on weather of the second closest station). This process is subsequently applied to the second, third, fourth and fifth closest stations. The number of predicted missing observations varies by village, however, on average, it represents about 10.0% of the total number of observations.¹² After completing the interpolation procedure, weighted averages of temperature and precipitation were successfully obtained for about 98.0% of the sample days.¹³

The calculation of climate variables relies on daily weather information for the 30 years preceding each survey round. That is, I use information from the period of 1972-2001 to represent climate in 2002 and information from the period of 1977-2006 to represent climate in 2007. PVAL is estimated from an agricultural production function that aggregates all the different crops grown by the households over the whole year. Consequently, the main Ricardian specification of this paper associates PVAL with measures of annual climate.

The climate measure for annual precipitation is calculated as the 30-year average of yearly accumulated precipitation for each of the two periods previously defined. With regards to temperature, the simple calculation of annual or seasonal averages would not take advantage of the rich daily variability in temperature observed in weather station data. Moreover, plant growth does not benefit from heat over the whole temperature range. Above and below certain thresholds, temperatures might be harmful for plant health. To capture the importance of optimal growing conditions and extreme temperatures, I transform daily observations of temperature into Growing Degree Days (GDD) and Harmful Degree Days (HDD) adopting the 8-32°C range used in related literature (Schlenker et al., 2006; Schlenker and Roberts, 2009; Jessoe et al., 2018). Daily temperature 𝑇 was calculated as the average of daily maximum and minimum temperatures and converted to GDD and HDD using the following definitions:

G D D (T) = \{\begin{matrix} 0 i f T \leq 8 \\ T - 8 i f 8 < T \leq 32 \\ 24 i f T > 32 \end{matrix}

(12)

H D D (T) = T - 32 i f T \geq 32

(13)

Climate measures of GDD and HDD are constructed by calculating a 30-year average in each period. Table 5 presents summary statistics of the climate variables. The Southeast region of Mexico displays the highest average annual precipitation while the mostly-semiarid northern regions have the lowest levels. On average, the Southeast is the hottest region but the Northwest has comparable average temperatures. HDD are highly concentrated in the Northwest. Overall, the difference between climate in 2002 and 2007 is minimal.

Table 5
Summary statistics of the climate variables

Note: Climate variables are calculated using daily information for the 30 years preceding each survey round.

When estimating the Ricardian equation, one might be worried that the climate variability observed in the sample might not be enough to estimate the effects of climate on agricultural productivity after conditioning on different sets of location and time fixed effects. An a priori evaluation of the residual variability on climate shows that the inclusion of state and state-by-year fixed effect soaks up a large fraction of the variation in climate, (see Table A.1). It is important to consider this residual variation when deciding the level of location fixed effects to be included in the regression. On one hand, we want to control as flexibly as possible for unobserved time-invariant and time-varying factors potentially correlated with agricultural productivity. On the other hand, we also want the residual variation in climate left after the inclusion of such location and time fixed effects to be sufficiently large so that results are still informative of the effect of climate on agricultural productivity. Taking this into account, the estimation of Equation 10 only controls for region and year fixed effects. A robustness test using region-by-year fixed effects is also provided.

Soil data for each village were obtained from FAO’s Digital Soil Map of the World (FAO, 2007). Using each village’s location, the class of dominant soil was extracted and then grouped into the following 15 major soil types: Acrisols, Cambisols, Rendzinas, Gleysols, Phaozems, Litosols, Fluvisols, Kastanozems, Luvisols, Nitosols, Regosols, Andosols, Vertisols, Xerosols and Yermosols.

Results

Results obtained from the estimation of Equation 10 are reported in Table 6. The dependent variable in column (1) is the natural logarithm of the estimated PVAL while in column (2) the natural logarithm of self-reported land values is used instead. In columns (3) and (4) region-by-year fixed effects are included in lieu of region and year fixed effects. Table 6 only reports results for relevant variables but other controls include the variables in Table 4 and 14 categories of major soil types. Standard errors are clustered at the village level which accounts for the potential heteroscedasticity arising from the fact that the dependent variable is estimated (Lewis and Linzer, 2005; Auffhammer, 2022).

Table 6
Ricardian regressions of PVAL and self-reported land values on annual measures of climate

Note: Clustered standard errors at the village level are reported in parentheses. Regressions include all the variables summarized in Table 4 and 15 categories of major soil types. The age and indigenous background of the household head have a negative effect on PVAL and are the only sociodemographic with statistical significance. Altitude and soil types are highly significant in all regressions. * p<0.10, ** p<0.05, *** p<0.01.

Extreme temperatures (HDD) have a large negative and statistically significant effect on PVAL. A one-unit increase in HDD decreases agricultural productivity by 1.5%. This result is consistent with Jessoe et al., (2018) who find that extreme temperatures affect local employment choices using the same dataset. GDD have the expected sign in all specifications but do not achieve statistical significance. Self-reported market land values fail to capitalize the effect of good or bad growing conditions, i.e. the coefficients on GDD and HDD have the expected direction but are not statistically significant.¹⁴ All of the regressions document a concave and statistically significant relationship between precipitation and agricultural productivity. The middle section of Table 6 displays the implied optimal level of precipitation ( $P^{*}$ ) and the marginal effect when evaluated at its sample mean ( $\bar{P}$ ). According to the PVAL specifications, the optimal level of accumulated precipitation is found around 2,050mm. Self-reported land values place this level at around 1,580mm. Also, all of the marginal effects are positive and statistically significant. Results using PVAL indicate that a 1mm increase in precipitation increases agricultural productivity by 0.15%, or approximately $150 Mexican pesos relative to the average estimated PVAL (see Table 3). When using market land values, the marginal effect is 0.07%, which is equivalent to $53 Mexican pesos relative to the average market land value observed in the sample (see Table 3). Thus, market land values underestimate the positive effect that more precipitation has on agricultural productivity.¹⁵

Access to formal credit has a positive and statistically significant effect on agricultural productivity only when PVAL is used. This result suggests the existence of binding credit constrains in rural Mexico. Access to credit boosts productivity and self-reported land values do not capitalize the marginal gain associated to an additional unit of working land.¹⁶ Access to irrigation is positive and statistically significant in all specifications but the estimated coefficient is higher when PVAL is used, meaning that the productivity returns to irrigation are higher than its capitalization on land valuation. Also, factors like urbanization and housing affect self-reported market land values but not PVAL. The coefficient on the distance to the nearest city is negative and significant in columns (2) and (4). The closer the village is to an urban center, the higher its market land value. PVAL is unaffected by the proximity to a city which suggest that off-farm factors affecting land valuation do not affect PVAL.

Surprisingly, private ownership does not increase agricultural productivity or market land values. A possible explanation of this result is that the process of transitioning from ejido to private ownership in Mexico has been slow which has prevented land consolidation and the investments incentives associated with it (de Janvry et al., 2015; Binder, 2015). Thus, in practice, private land in small agricultural communities, such as the villages in our sample, might not be much different from ejido land in terms of productivity or market valuation. Finally, smaller farms (as measured by the amount of land in production) have a larger productive or market values per unit of land, a result consistent with findings from the development literature (Kagin et al., 2016).

Robustness

In Table 6, PVAL measures and self-reported land values are regressed on annual measures of climate. The rationale is that PVAL is estimated using information from the two cropping seasons throughout the year. Double cropping could be, by itself, a form of adaptation to climate change. Similarly, market land values are expected to capitalize the full flow of annual profits when farmed in one or in both seasons. However, agricultural production in Mexico is highly concentrated in the Spring-Summer season (55.3% of the total farmed land in 2007; SIAP, 2023). In columns (1) and (2) of Table 7, the annual climate variables have been substituted with seasonal climate variables constructed using weather information for the months of March to September, the period officially considered as the Spring-Summer season in Mexico (SADER, 2017). Results are qualitatively similar to those reported in Table 6.

Table 7
Robustness of the results to alternative definitions of climate

Note: Clustered standard errors at the village level are reported in parentheses. Regressions include all the variables summarized in Table 4 and 15 categories of major soil types. Regressions include region-by-year fixed effects. When region and year fixed effects are included separately, results are similar. * p<0.10, ** p<0.05, *** p<0.01.

The main findings of Table 6 are also robust to the exclusion of precipitation from the Ricardian equation (columns (3) and (4) in Table 7) proving that the result is not due to correlation among the climate variables.

Conclusions

In this paper, I propose a novel version of the Ricardian approach that relies on a shadow valuation of land recovered from the estimation of an agricultural production function. This measure, that I call the productive value of agricultural land, or PVAL, internalizes any shadow components associated with the constraints that farmers face, reflecting more properly the market setting in which farmers make decisions. Also, this measure purely reflects land productivity and is thus free of the other factors polluting market land values that have prompted the omitted variable bias criticism raised around the Ricardian model. I argue that the use of this shadow measure as the dependent variable in a Ricardian estimation leads to more accurate estimates of the relationship between climate and land productivity, particularly in settings where markets are not perfectly competitive.

When the proposed approach is applied to data of rural households in Mexico, I find that indeed, when using PVAL, the relationship between climate and agricultural productivity is stronger and more precisely estimated. Specifically, extremely high temperatures decrease land productivity while more precipitation increases it. Market land values fail to capitalize the negative effects of extreme temperatures and underestimate the positive effect of more precipitation. Altogether, the findings of this article suggest that in settings where markets are incomplete, the use of market land values to represent long-run farm productivity in the Ricardian approach may lead to an underestimation of the effect that climate change may have on agriculture.

The Ricardian approach continues to be a useful tool to get insights about the potential effects of climate change on agricultural productivity but future researchers considering implementing it should also pay attention to the market setting of the context in which it is going to be applied. In a developing country setting, it is important to estimate those losses with a methodology that rightfully captures land productivity in the context of constrained production, particularly if public policies promoting adaptation in developing countries will be designed based on such estimations.

The methodology that I propose in this paper addresses an issue so far ignored in the application of the Ricardian approach: non-competitive markets. It also addresses the issue of omitted factors polluting the Ricardian estimates by relying on a shadow valuation of land that only reflects agricultural productivity. Yet, there are still several caveats that apply to this analysis. First, omitted variables could still affect the Ricardian estimates based on PVAL, particularly those affecting farm productivity and not accounted for in the estimation of the production function. Second, the implementation of the Ricardian approach using PVAL relies on getting unbiased estimates of the parameters governing the agricultural production function, which is only plausible when panel data is available for such purpose. As a result, the implementation of the approach proposed in this paper might be limited in settings where panel data does not exist. Finally, the panel I use in this paper is only two-years long. The shortness of my data prevents me from including fixed effects more geographically disaggregated such as at the state, village or household levels. The residual variation left in climate once such fixed effects are included might be so small that the estimated relationship between climate and agricultural productivity could vanish, either using PVAL or market land values. This highlights the enormous advantage of having access to long data sets when estimating the Ricardian approach.

Supplementary material

Appendices

Appendix

Table A.1
Residual variation in climate. Number of household-year observations for which predicted climate differs from observed climate by more than

Note: This table (adapted from Jessoe et al., 2018) reports the extent of the residual variation of climate left after controlling for the different sets of location and time fixed effects listed in the Fixed effects column. Each panel shows the number of observations for which the absolute value of predicted climate differs from observed climate by more than the number in the head of each column. For example, in panel a), the cell at the intersection of the first row and column (1) indicates that after regressing annual temperature on state and year fixed effects, the absolute value of the predicted temperature was at least 0.5°C higher than observed temperature in 745 (out of 1,104) observations. When conditioning on regional and year fixed effects, this number increases to 1,030 or 93% of the total number of observations. The interpretation of columns (2) to (5) and of panels b) to d) is similar.

Table A.2
Ricardian regressions of PVAL and self-reported land values on temperature and precipitation

Table A.3
Ricardian regressions of PVAL and self-reported land values omitting access to formal credit

References:

Arslan, A., & Taylor, J. E. (2009). Farmers’ subjective valuation of subsistence crops: The case of traditional maize in Mexico. American Journal of Agricultural Economics, 91(4), 956-972. https://doi.org/10.1111/j.1467-8276.2009.01323x

Auffhammer, M. (2022). Climate Adaptive Response Estimation: Short and long run impacts of climate change on residential electricity and natural gas consumption. Journal of Environmental Economics and Management, 114(102669), 1-19. https://doi.org/10.1016/j.jeem.2022.102669

Auffhammer, M., Hsiang, S. M., Schlenker, W., & Sobel, A. (2013). Using weather data and climate model output in economic analyses of climate change. Review of Environmental Economics and Policy, 7(2), 181-198. https://doi.org/10.1093/reep/ret016

Bareille, F., & Chakir, R. (2023). The impact of climate change on agriculture: A repeat-Ricardian analysis. Journal of Environmental Economics and Management, 119(102822). https://doi.org/10.1016/j.jeem.2023.102822

Banxico. (2023). Información económica y financiera. Retrieved from https://www.banxico.org.mx/Indicadores/consulta/Instrumentos.action

Binder, C. (2015). Mexico’s Second Land Reform. Berkeley Review of Latin American Studies. https://clacs.berkeley.edu/mexico-de-janvry-mexicos-second-land-reform

Burke, M., Craxton, M., Kolstad, C. D., & Onda, C. (2016). Some research challenges in the economics of climate change. Climate Change Economics, 07(02). https://doi.org/10.1142/s2010007816500020

Burke, M., & Emerick, K. (2016). Adaptation to climate change: Evidence from US agriculture. American Economic Journal: Economic Policy, 8(3), 106-140. https://doi.org/10.1257/pol.20130025

Comisión Mexicana de Defensa y Promoción de los Derechos Humanos (CMDPH). (2018). Episodios de desplazamiento forzado masivo en México: Informe 2017. https://www.cmdpdh.org/publicaciones-pdf/cmdpdh-informe-de-desplazamiento-interno-masivo-en-mexico-2017.pdf

Carter, M. R. (1988). Equilibrium credit rationing of small farm agriculture. Journal of Development Economics, 28(1), 83-103. https://doi.org/10.1016/0304-3878(88)90015-6

Carter, M. R. (1994). Sequencing capital and land market reforms for broadly based growth. Research in Agricultural and Applied Economics. https://doi.org/10.22004/AG.ECON.12689

de Janvry, A., Emerick, K., Gonzalez-Navarro, M., & Sadoulet, E. (2015). Delinking land rights from land use: Certification and migration in Mexico. American Economic Review, 105(10), 3125-3149. https://doi.org/10.1257/aer.20130853

de Janvry, A., Gonzalez-Navarro, M., & Sadoulet, E. (2014). Are land reforms granting complete property rights politically risky? Electoral outcomes of Mexico’s certification program. Journal of Development Economics, 110, 216-225. https://doi.org/10.1016/j.jdeveco.2013.04.003

Deschênes, O., & Greenstone, M. (2007). The economic impacts of climate change: Evidence from agricultural output and random fluctuations in weather. American Economic Review, 97(1), 354-385. https://doi.org/10.1257/000282807780323604

Deschênes, O., & Greenstone, M. (2012). The economic impacts of climate change: Evidence from agricultural output and random fluctuations in weather: Reply. American Economic Review, 102(7), 3761-3773. https://doi.org/10.1257/aer.102.7.3761

Duan, N. (1983). Smearing estimate: A nonparametric retransformation method. Journal of the American Statistical Association, 78(383), 605-610. https://doi.org/10.1080/01621459.1983.10478017

Eswaran, M., & Kotwal, A. (1986). Access to Capital and Agrarian Production Organization. Economic journal (London, England), 96(382), 482-498. https://doi.org/10.2307/2233128

FAO. (2007). Digital Soil Map of the World. Food and Agriculture Organization of the United Nations. Data retrieved from https://data.apps.fao.org/map/catalog/srv/eng/catalog.search#/metadata/446ed430-8383-11db-b9b2-000d939bc5d8

Feder, G., & Nishio, A. (1998). The benefits of land registration and titling: Economic and social perspectives. Land Use Policy, 15(1), 25-43. https://doi.org/10.1016/s0264-8377(97)00039-2

Fisher A.C., Hanemann, W.M., Roberts, M.J. and Schlenker, W. (2009). Climate change and agriculture reconsidered. University of California at Berkeley, Department of Agricultural and Resource Economics. CUDARE Working Paper 1080.

Fisher, A. C., Hanemann, W. M., Roberts, M. J., & Schlenker, W. (2012). The economic impacts of climate change: Evidence from agricultural output and random fluctuations in weather: Comment. American Economic Review, 102(7), 3749-3760. https://doi.org/10.1257/aer.102.7.3749

Galindo, L.M., Reyes, O. & Alatorre, J.E. (2015). Climate change, irrigation and agricultural activities in Mexico: A Ricardian analysis with panel data. Journal of Development and Agricultural Economics 7(7): 262-273.

Gammans, M., Mérel, P., & Ortiz-Bobea, A. (2017). Negative impacts of climate change on cereal yields: statistical evidence from France. Environmental research letters, 12(5). https://doi.org/10.1088/1748-9326/aa6b0c

Guiteras, R. (2009). The impact of climate change on Indian agriculture. Department of Economics, University of Maryland, College Park, Maryland. https://nswai.org/docs/The_Impact_of_Climate_Change_on_Indian_Agriculture.pdf

Hertel, T. W., & Lobell, D. B. (2014). Agricultural adaptation to climate change in rich and poor countries: Current modeling practice and potential for empirical contributions. Energy Economics, 46, 562-575. https://doi.org/10.1016/j.eneco.2014.04.014

Ibáñez, A. M., & Querubín, P. (2004). Acceso a tierras y desplazamiento forzado en Colombia. Documento CEDE 2004-23, Centro de Estudios sobre Desarrollo Económico, Bogotá.

Instituto Nacional de Estadística y Geografía (INEGI). (2022). Censo Agrícola, Ganadero y Forestal 2022. Data retrieved from https://www.inegi.org.mx/programas/ca/2022/#tabulados

Instituto Nacional de Estadística y Geografía (INEGI). (2019). Encuesta Nacional Agropecuaria 2019. Data retrieved from https://www.inegi.org.mx/programas/ena/2019/#tabulados

Instituto Nacional de Estadística y Geografía (INEGI). (2010). Marco geoestadístico 2010 versión 5.0 (Censo de Población y Vivienda 2010) https://www.inegi.org.mx/app/biblioteca/ficha.html?upc=702825292812.

IPCC. (2023). Summary for Policymakers. In: Climate Change 2023: Synthesis Report. A Report of the Intergovernmental Panel on Climate Change. Contribution of Working Groups I, II and III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Core Writing Team, H. Lee and J. Romero (eds.). IPCC, Geneva, Switzerland, 1-36. (in press).

Jessoe, K., Manning, D. T., & Taylor, J. E. (2018). Climate change and labour allocation in rural Mexico: Evidence from annual fluctuations in weather. Economic Journal (London, England), 128(608), 230-261. https://doi.org/10.1111/ecoj.12448

Kagin, J., Taylor, J. E., & Yúnez-Naude, A. (2016). Inverse productivity or inverse efficiency? Evidence from Mexico. The Journal of Development Studies, 52(3), 396-411. https://doi.org/10.1080/00220388.2015.1041515

Kurukulasuriya, P., & Mendelsohn, R. (2007). A ricardian analysis of the impact of climate change on African cropland. The World Bank. https://doi.org/10.1596/1813-9450-4305

Levinsohn, J., & Petrin, A. (2003). Estimating production functions using inputs to control for unobservables. The Review of Economic Studies, 70(2), 317-341. https://doi.org/10.1111/1467-937x.00246

Lewis, J. B., & Linzer, D. A. (2005). Estimating regression models in which the dependent variable is based on estimates. Political Analysis: An Annual Publication of the Methodology Section of the American Political Science Association, 13(4), 345-364. https://doi.org/10.1093/pan/mpi026

Lobell, D. B., Schlenker, W. , & Costa-Roberts, J. (2011). Climate trends and global crop production since 1980. Science(New York, N.Y.), 333(6042), 616-620. https://doi.org/10.1126/science.1204531

Lybbert, T. J., & Sumner, D. A. (2012). Agricultural technologies for climate change in developing countries: Policy options for innovation and technology diffusion. Food Policy, 37(1), 114-123. https://doi.org/10.1016/j.foodpol.2011.11.001

Mendelsohn, R. (2014). The impact of climate change on agriculture in Asia. Journal of Integrative Agriculture, 13(4), 660-665. https://doi.org/10.1016/s2095-3119(13)60701-7

Mendelsohn, R., Nordhaus, W. D. & Shaw, D. (1994), The impact of global warming on agriculture: A ricardian analysis. American economic review, 84, 753-71. (2017). En Climate Change (pp. 131-150). Routledge.

Mendelsohn, R., Nordhaus, W. D. & Shaw, D. G. (1993). The Impact of Climate on Agriculture: A Ricardian Approach. In Costs, impacts, and benefits of CO2 mitigation, Y. Kaya, N. Nakicenovic, W. Nordhaus, and F. Toth, eds. Luxemburg, Austria: International Institute of Applied Systems Analysis, pp. 173-208.

Mendelsohn, R., Arellano-Gonzalez, J., & Christensen, P. (2010). A Ricardian analysis of Mexican farms. Environment and Development Economics, 15(2), 153-171. https://doi.org/10.1017/s1355770x09990143

Mendelsohn, R. O., & Massetti, E. (2017). The use of cross-sectional analysis to measure climate impacts on agriculture: Theory and evidence. Review of Environmental Economics and Policy, 11(2), 280-298. https://doi.org/10.1093/reep/rex017

Moore, F. C., & Lobell, D. B. (2014). Adaptation potential of European agriculture in response to climate change. Nature Climate Change, 4(7), 610-614. https://doi.org/10.1038/nclimate2228

Olley, G. S., & Pakes, A. (1996). The dynamics of productivity in the telecommunications equipment industry. Econometrica: Journal of the Econometric Society, 64(6), 1263-1297. https://doi.org/10.2307/2171831

Ortiz-Bobea, A. (2020). The role of nonfarm influences in Ricardian estimates of climate change impacts on US agriculture. American Journal of Agricultural Economics, 102(3), 934-959. https://doi.org/10.1093/ajae/aaz047

Ortiz-Bobea, A., & Just, R. E. (2013). Modeling the structure of adaptation in climate change impact assessment. American Journal of Agricultural Economics, 95(2), 244-251. https://doi.org/10.1093/ajae/aas035

Registro Agrario Nacional (RAN). (2023). Estadística Agraria. http://www.ran.gob.mx/ran/index.php/sistemas-de-consulta/estadistica-agraria

Secretaría de Agricultura y Desarrollo Rural (SADER). (2017). El ciclo de cultivo Primavera/Verano. https://www.gob.mx/agricultura/es/articulos/el-ciclo-de-cultivo-primavera-verano

Servicio de Información Agroalimentaria y Pesquera (SIAP). (2023). Estadística de Producción Agrícola. Data retrieved from http://infosiap.siap.gob.mx/gobmx/datosAbiertos_a.php

Sadoulet, E., & de Janvry, A. (1995). Quantitative Development Policy Analysis (2a ed.). Johns Hopkins University Press

Sanghi, A., & Mendelsohn, R. (2008). The impacts of global warming on farmers in Brazil and India. Global Environmental Change: Human and Policy Dimensions, 18(4), 655-665. https://doi.org/10.1016/j.gloenvcha.2008.06.008

Seifert, C. A., & Lobell, D. B. (2015). Response of double cropping suitability to climate change in the United States. Environmental research letters, 10(2), 1-7. https://doi.org/10.1088/1748-9326/10/2/024002

Schlenker, W. , Hanemann, W. M. , & Fisher, A. C. (2005). Will U.S. Agriculture Really Benefit from Global Warming? Accounting for Irrigation in the Hedonic Approach. The American Economic Review, 95(1), 395-406. http://www.jstor.org/stable/4132686

Schlenker, W. , Hanemann, W. M. , & Fisher, A. C. (2006). The impact of global warming on U.s. agriculture: An econometric analysis of optimal growing conditions. The Review of Economics and Statistics, 88(1), 113-125. https://doi.org/10.1162/rest.2006.88.1.113

Schlenker, W. & Roberts, M.J. (2009). Nonlinear temperature effects indicate severe damages to US crop yields under climate change. Proceedings of the National Academy of sciences, 106(37):15594-15598.

Seo, S.-N. N., Mendelsohn, R., & Munasinghe, M. (2005). Climate change and agriculture in Sri Lanka: a Ricardian valuation. Environment and Development Economics, 10(5), 581-596. https://doi.org/10.1017/s1355770x05002044

Seo, N. & Mendelsohn, R. (2008a). A Ricardian Analysis of the Impact of Climate Change on Latin American Farms. World Bank Policy Research Series Working Paper 4163. World Bank, Washington DC., USA.

Seo, N. & Mendelsohn, R. (2008b). A Ricardian Analysis of the Impact of Climate Change on South American Farms. Chilean Journal of Agricultural Research 68(1): 69-79.

Severen, C., Costello, C., & Deschênes, O. (2018). A Forward-Looking Ricardian Approach: Do land markets capitalize climate change forecasts? Journal of Environmental Economics and Management, 89, 235-254. https://doi.org/10.1016/j.jeem.2018.03.009

Skoufias, E. (1994). Using shadow wages to estimate labor supply of agricultural households. American Journal of Agricultural Economics, 76(2), 215-227. https://doi.org/10.2307/1243623

Taylor, J. E., & Adelman, I. (2003). Agricultural Household Models: Genesis, Evolution, and Extensions. Review of economics of the household, 1(1/2), 33-58. https://doi.org/10.1023/a:1021847430758

The World Bank Group (TWBG). (2023). Climate Risk Country Profile: Mexico.

Van Beveren, I. (2012). Total factor productivity estimation: A practical review: Total factor productivity estimation. Journal of Economic Surveys, 26(1), 98-128. https://doi.org/10.1111/j.1467-6419.2010.00631.x

Welch, J. R., Vincent, J. R., Auffhammer, M., Moya, P. F., Dobermann, A., & Dawe, D. (2010). Rice yields in tropical/subtropical Asia exhibit large but opposing sensitivities to minimum and maximum temperatures. Proceedings of the National Academy of Sciences of the United States of America, 107(33), 14562-14567. https://doi.org/10.1073/pnas.1001222107

Notes

2 In less-developed agrarian economies, land holdings are typically the most valuable asset in a household’s portfolio. Thus, access to credit in such economies is heavily determined by a household’s ability to collateralize its land and by the size of its land endowment (Carter, 1994; Eswaran and Kotwal, 1986). If access to credit is linked to the size of land holdings, then

B_{i}

would be an increasing function of

T_{i}

rand as long as land endowments are heterogeneous across households, access to credit will also be heterogeneous.

3 Results are qualitatively similar if we explicitly model

B_{i}

as a function of

{\bar{T}}_{i}

4 The theoretical results of this section are qualitatively similar if households are modeled as consumers. Assume for example, that households derive utility from the consumption of market goods, self-produced agricultural goods and leisure. Assume also that the market for labor is perfectly competitive and that credit constraints still exist. In this setting, households would maximize utility subject to an income constraint equal to the sum of agricultural profits and any other exogenous income given to the household. In this case, the first order condition with respect to land will still have a shadow component associated with the shadow price of credit and the marginal utility of income.

5 The interested reader could refer to Van Beveren (2012) for a comprehensive survey of this and other available methodologies on the matter.

6 When

ε_{i}

follows a normal distribution with

E [ε_{i}] = 0 a n d V a r [ε_{i}] = σ^{2}

, it can be shown that

E [\hat{φ}] = e^{\frac{σ^{2}}{2}}

. However, in many settings, the true distribution of the error term is unknown. Duan´s (1983) general result suggests that in such cases, the smearing correction factor can be estimated with the mean exponentiated residual from the model.

7 Production for self-consumption was valued using average market prices calculated at the village level. When market prices for a particular crop were not found at the village level, average market prices were calculated at the state, region and national levels, in that order.

8 The 2002 round of the survey recorded the total machinery-hours used in the production process. Unfortunately, this is not the case in the 2007 round, which only recorded machinery rent expenditures. Ideally, one would treat this form of capital as an additional factor of production in the estimation of an agricultural production function. The unavailability of a physical measure of machinery in both rounds and the high frequency of zero expenditures in the sample makes it necessary to treat machinery expenditures as an intermediate input.

9 This hypothesis is corroborated when looking at the actual correlations of the input variables and the estimated

{\hat{q}}_{i t}

from column (3). Such correlations are 0.027, 0.047 and 0.185 for land, labor and intermediate inputs, respectively.

10 At least 50% of all of the household’s plots have these characteristics.

11 Weather station data retrieved from http://clicom-mex.cicese.mx/.

12 The interpolation of weather to every village uses the information of 5 weather stations. Between January 1st, 1972 and December 31, 2007 there are 13,149 days giving a total of 65,745 observations.

13 There are 13,149 days in the sample period which gives a total of 1,051,920 sample days for the 80 ENHRUM villages.

14 These results also highlight the importance of exploiting daily variation in temperature when estimating its effects on agricultural productivity. Estimate relying on average temperatures might fail to identify the negative effects of extreme temperatures on agricultural productivity (see Table A.2).

15 Ricardian estimates for Mexico have been previously reported by Mendelsohn et al. (2010) and Galindo et al. (2015). However, the results of this paper are not directly comparable with their results due to different methodological approaches, particularly with regard to the construction of the temperature and precipitation variables. Specifically, they express land values (Mendelsohn et al., 2010) or agricultural net revenues (Galindo et al., 2015) as a quadratic function of quarterly temperature and precipitation. In this paper, temperature is transformed into GDD and HDD. Then, PVAL and market land values are expressed as a function of GDD, HDD and (quadratic) precipitation accumulated over the whole cropping season year. Both studies document negative effects of marginal increases in annual temperature and precipitation. The estimated negative effect of precipitation is mainly explained by increases in winter and fall precipitation that are detrimental for land valuation or profitability.

16 This result, however, should be interpreted with caution as access to credit may be determined by agricultural productivity and agricultural productivity could also be determined by having access to credit. This endogeneity, potentially arising from simultaneity, could bias the estimated parameters. Table A.3 (in the Appendix) shows that the exclusion of the variable identifying access to formal credit does not fundamentally change the main results, which suggest that the potential endogeneity of access to credit might not be a large issue in the working sample.

1 I am grateful to Katrina Jessoe, Frances Moore, Pierre Mérel, J.E. Taylor and Steve Boucher for their valuable feedback and suggestions to this article. The conclusions and opinions expressed in this document are mine and are not official positions of the Bank of Mexico. Any errors contained herein are also mine.