https://orcid.org/0000-0002-6471-7292
Figures
Abstract
This study draws on economic index theory to construct a new indicator for adaptation to changing environmental conditions, most notably climate change, which may shift the production technology over time. Such environmental shifts are largely exogenous to firm decision making, for instance investments in research and development, which may also lead to technology change. Few existing measures of total factor productivity (TFP) make this distinction, between exogenous environmental shifts and shifts due to firm decision making or innovation. We introduce a nonparametric Luenberger productivity indicator for adaptation, which allows for decomposition of standard technology and efficiency change measures into both environmental and production components. We apply this framework to agricultural production in the US Mississippi River Basin for recent decades, working with USDA Census of Agriculture data at the county level and key climate conditions. We also match the production and climate data to estimates of Nitrogen loading over time, to incorporate water quality into the adaptation indicator. Our results indicate sustained overall productivity growth, for both agricultural production and nitrogen loading reductions, driven by technology gains outweighing efficiency losses. Decomposing further to the adaptation component, our results indicate modest overall adaptation gains, driven by both adaptation efficiency and technology gains.
Citation: Barnhart BL, Bostian M, Färe R, Grosskopf S, Lochner SM (2023) A productivity indicator for adaptation to climate change. PLOS Clim 2(11): e0000199. https://doi.org/10.1371/journal.pclm.0000199
Editor: Haoying Wang, New Mexico Tech, UNITED STATES
Received: November 11, 2022; Accepted: September 10, 2023; Published: November 14, 2023
This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
Data Availability: Data freely accessible via openICPSR: https://doi.org/10.3886/E192462V1.
Funding: The authors received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
Adaptation of agricultural production to changing environmental conditions generally entails some form of adjustment, either to take advantage of new opportunities or to lessen harmful impacts [1–4]. Changing climate conditions highlight the importance of adaptation for overall productivity, yet few productivity index measures exist to decompose and quantify this adaptation component.
We employ economic index theory to construct a new productivity indicator for adaptation to changing environmental conditions, most notably climate change, which may shift the production technology over time and lead to changes in efficiency relative to the new technology. Such environmental shifts are largely exogenous to firm decision making, like investments in research and development. This may also lead to technology change, while changes to efficiency are often more directly linked to production practices.
Our approach to measure adaptation using a productivity indicator contributes to the broader literature related to agricultural productivity and climate change in several ways. First, very few existing agricultural productivity index measures account for climate, let alone adaptation to changing climate conditions. Those that do include [5], who adjusts measures of efficiency change for exogenous environmental change, as well as [6, 7], who introduce a weather index change component to agricultural TFP. Each of these measure adaptation in terms of changing efficiency to a climate-adjusted technology. We build on these existing studies by introducing a new indicator to measure adaptation both in terms of efficiency change and technology change.
Second, we extend the indicator framework to also account for non-marketed environmental externalities of agricultural production, in this case nitrogen pollution from fertilizer use. This form of pollution is particularly relevant for considering adaptation to climate change, as changing climate conditions (e.g., warmer temperatures, heavier rainfall) can exacerbate pollution levels [8, 9]. To our knowledge, we are the first to model climate adaptation both in terms of productivity and associated environmental condition.
Third, we develop the first non-radial productivity indicator for adaptation to climate change. This provides a more general framework for assessing productivity, and also allows for the inclusion of undesirable outputs, such as nitrogen pollution, in the production technology. Our decomposition uses the Luenberger productivity indicator [10–13] to distinguish adaptation efficiency and technology change components to overall productivity. The Luenberger indicator is constructed from directional measures of inefficiency which can be specified to jointly expand desirable production output and contract undesirable output. Existing radial approaches to measure adaptation only allow for expansion of the desirable production output. In a radial framework, undesirable output can only be contracted if modeled as an input.
We apply the adaptation indicator framework to agricultural production in the U.S. Mississippi River Basin, spanning the years 1987-2012. Our results indicate sustained overall productivity growth, for both agricultural production and nitrogen loading reductions, driven by technology gains outweighing efficiency losses. Decomposing further to the adaptation components, our results indicate modest overall adaptation gains, driven by both adaptation efficiency and adaptation technology gains.
2 Climate and agricultural productivity
2.1 The impact of climate change on agriculture
Perhaps more so than any other economic sector, agriculture and climate are intimately linked. Much of the literature on climate change and productivity focuses on the agricultural sector, with growing emphasis on adaptation, as well as some debate surrounding the extent of the effect for overall yields [14–16]. Early evidence suggests overall negative effects of climate change for US agriculture, with minimal mitigation of these effects due to adaptation [4, 17, 18]. A lack of adaptation may be due to limited opportunities available to farmers, or to options that are only economically feasible over some range of the production technology [4], as well as uncertainty and risk management [19–21]. On a global scale, [22] find that climate change has lowered agricultural TFP by roughly 20% since 1961, and that the negative effects tend to be more concentrated in warmer regions.
There is also growing work to use historical estimates of climate effects on agriculture to project future effects for agricultural TFP. [18] provide a comprehensive analysis of long term climate effects on US agricultural productivity, covering the entire sector for the continental US states. Using stochastic frontier analysis (SFA) methods, they find that effects vary largely by region, with average losses to production efficiency due to both increasing aridity and heat stress. They also construct future projections based on their results, finding future efficiency losses most concentrated in the Mississippi Delta, greater Southeast, Corn Belt, and Plains regions.
[23] exploit geographic and seasonal variation in climate variables to measure regional climate correlation to national agricultural TFP change. They then use these correlation measures to estimate the effects of variation in longer term climate trends on changing contributions to TFP, in order to simulate future Climate-TFP effects. They find that while sustained technical progress has outweighed the negative effects of changing climate trends, allowing for continued productivity growth thus far, this relationship will eventually reverse. Namely, given current rates of technical progress and medium to high emissions scenarios, the authors estimate that TFP will begin to fall around the year 2035, and that by 2050 TFP could fall below pre-1980 levels.
2.2 Climate-adjusted measures of agricultural TFP
Few existing measures of total factor productivity (TFP) distinguish exogenous environmental shifts from shifts due to firm decision making or innovation. [24] review the US Department of Agriculture Economic Research Service (USDA ERS) methods for calculating agricultural productivity. [5] introduces a new TFP decomposition which includes an Environmental Efficiency (EE) component, relating the production technology for a given set of environmental conditions to an encompassing metatechnology for all environmental conditions. [25, 26] build on this in the context of climate change, by further distinguishing short term weather variation from longer term climate trends. [25] introduce separate environmental scale/mix efficiency and technical efficiency index decompositions, to distinguish exogenous shifts of the technology from managerial inefficiency. [26] introduce an explicit adaptation component to the TFP decomposition, to estimate the effect of long term climate trends on production. Each of the above employ parametric SFA methods for estimation of the associated distance functions in the first case, and production function in the latter.
[6], and the related [7] introduce the first nonparametric decomposition of TFP to include a weather index component, and associated weather change indicator. Also similar to the SFA framework of [6, 7, 25, 26] include weather conditions as exogenous inputs to estimate the production frontier. They then interpret conventional measures of efficiency change relative to the production frontier as measures of adaptation to changing weather conditions. Results from [7] suggest that the decline in agricultural productivity growth for Australia [27, 28] is due to struggling climate-related adaptation to technological advances, rather than a slowdown in technological innovation. For US agriculture, [6] find that adaptation to the frontier and technical change significantly impact the average state TFP.
2.3 Incorporating environmental effects into agricultural TFP
We take a production theoretical approach to model nitrogen pollution as part of the agricultural production technology. This draws on more general methods for incorporating undesirable outputs, along with intended output, into measures of efficiency and productivity. See [29–31] for recent reviews of this literature, as well as [32] for a review of environmental adjustments to agricultural TFP specifically.
In one of the first analyses of nitrogen loading and agricultural TFP, [33] find that at the time, agricultural TFP measures for US agriculture should be adjusted downward by 12-28 percent, due to environmental effects of nitrogen use. At the micro-level, [34] distinguish environmental efficiency (including excess nitrogen) from standard output technical efficiency for a sample of dutch dairy farms. A number of studies adopt a materials balance accounting approach to model nitrogen use and excess pollution for larger scale production [35–37], generally finding potential for increases to agricultural production while also reducing nitrogen use.
A key insight from the broader literature on agricultural nitrogen pollution concerns the importance of spatial relationships, both for productivity and for runoff and loading in surrounding watershed systems [38–40]. Advances in computational optimization methods and integrated modeling for agriculture have made possible large scale modeling of these spatial relationships, linking economic production to environmental systems [41–48]. See also [49] for a review of the integrated modeling literature. Better understanding of these spatial relationships can facilitate spatial targeting of conservation policies for improved efficiency [44, 45] and individual management practices [41, 43, 47].
3 Methodology
3.1 The production technology
Our indicator relies on the underlying production technology, which we define for a vector of inputs x = (x1, …, xN) and a vector of outputs y = (y1, …, yM) as
(1)
As defined, the technology in (1) tells us how inputs can be used to produce output, without accounting for environmental factors. [5] likens this to a set of basic instructions or recipe, which can be counted upon under control conditions, and is generally neither lost nor forgotten over time. As a result, at any given point in time, there is some cumulative knowledge for how to use x to produce y. Following [5], we define a second metatechnology to represent this accumulation of knowledge at time t as
(2)
where Tt encompasses the technologies of all preceding periods. In other words, what was possible yesterday is still possible today, so that there can be no technical regress. We refer to this as the time t metafrontier. We note that other studies also refer to this use of a metafrontier to encompass all preceding technologies as the sequential technology approach [50], and that the use of this approach to exclude technical regress dates back to even earlier work, for example [51].
But, just as changes in altitude may call for modifying a bread recipe, changes in environmental conditions may shift the production technology and require some form of adaptation by the firm.
We let w = (w1, …, wL) represent the set of relevant exogenous environmental conditions, and define a second environmental production metatechnology subject to these conditions as
(3)
where the conditions in wt remain outside the firm’s control. We refer to this as the environmental metafrontier for time t. Production possibilities for given environmental conditions remain over time, while both changing environmental conditions and technical advance may expand this frontier over time.
We note this also draws on the earlier work of [52], who introduces environmental factors to the production technology, for both desirable and undesirable factors.
To also model undesirable outputs, such as pollution, we let u = (u1, …, uJ) represent the set of undesirable output resulting from the production technology. Taking an output orientation of the production technology for both goods and bads yields the corresponding output sets, Pt(xt) and Pt(xt; wt),
(4)
(5)
3.2 Optimal production
Distance functions can be used to represent the technology for multi-input and multi-output production processes, either radially [53, 54] or by using the additive directional distance function [11, 12]. [55] show that the Shephard distance function can be recovered as a special case of the directional distance function. We use the more general directional distance function here, defined for the output orientations in (4) and (5) as
(6)
(7)
where the vector
specifies the direction of desirable output expansion and undesirable output contraction. Note, setting the direction vector
equal to observed output values specifies a radial expansion and contraction of goods and bads, while choosing the unit directional vector (gy, −gu) = (1, −1) facilitates aggregation across technologies [55]. Given our interest in changing technologies over time, as well as adjusting for changing climate conditions, we employ the unit directional vector for this analysis. It is also possible to endogenize
for both nonparametric [56–58] and parametric models [59, 60].
The directional distance function satisfies a number of key axiomatic properties from production theory. See [55] for more complete review and associated proofs. For a given technology, these axiomatic properties include:
- i. Translation property.
- ii. Homogeneity of degree -1 in
.
- iii. Representation property.
if and only if (y, u) ∈ P(x)
- iv. Monotonicity of outputs.
, for freely disposable y
, for weakly disposable u
- v. Homogeneity of degree +1 in outputs.
, for constant returns to scale (CRS)
Given these properties, the directional distance function provides a complete representation of the production technology. The resulting distance value provides a measure of inefficiency in the direction (gy, gu), where for efficient firms operating on the frontier and
for inefficient firms operating below the frontier, increasing in value with inefficiency.
We estimate the technology models defined in (2) and (3), and corresponding directional distance functions defined in (6) and (7), nonparametrically, using Activity Analysis [61, 62] or Data Envelopment Analysis (DEA) methods [63, 64].
Beginning with the metatechnology output set, Pt(xt), we solve for each observation k = 1, …, K, in each time period (t, τ) = 1, …, T,
(8)
where zτ = zτ1, …, zτK are also known as intensity variables. The intensity variables serve as endogenous weights, chosen to construct the cumulative output set metafrontier as the convex combination of the outermost output values in each time period, t. Note, by setting the sum of the intensity variables to be less than or equal to one, we assume non-increasing returns to scale for the production technology. This, coupled with the null joint condition, imposes weak disposability for the undesirable outputs. [65] provide additional conditions which can be used to satisfy weak disposability and the null joint condition under variable returns to scale. The constraints for
and
allow for strong or free disposability of desirable outputs and inputs, while the
constraints impose weak disposability for undesirable outputs. To include environmental conditions (namely, climate), we add to (8) the environmental constraint,
, which also imposes weak disposability for environmental conditions.
This nonparametric approach to estimation allows us to directly impose the axiomatic properties of the directional distance function model on a given set of empirical data observations, as well as the null joint and weak disposability assumptions for undesirable outputs. Beyond these axiomatic properties, this approach makes no additional assumptions for functional form.
Fig 1 illustrates the production metatechnology conceptually, for time periods t, and t + 1, focusing for simplicity on desirable output only. In this example, both technologies expand from t to t + 1, though by different amounts. The ray extending from observation k to the Tt frontier represents the directional technology distance in the g direction (here contracting inputs, and expanding outputs) where the corresponding point kt* on the frontier represents efficient production in time t. A similar interpretation holds for the ray extending from k to the environmental frontier, where the corresponding point represents efficient production in time t, under environmental conditions w. The dashed ray from kt* to
represents the change in the production technology due to environmental conditions at time t, or alternatively, the difference in distance to the frontiers, with and without changing environmental conditions.
3.3 The Luenberger adaptation indicator
Adaptation to changing environmental conditions depends on the change in the cumulative metatechnology, the extent of environmental change and the change in efficiency relative to the new environment. We use the Luenberger productivity indicator to identify these adaptation components to overall productivity from one time period to the next. We begin with the Luenberger productivity indicator (maintaining the output orientation), LUEN(t, t + 1), for time periods (t, t + 1),
(9)
which can be decomposed [11] into separate measures of efficiency change,
(10)
and technology change,
(11)
where overall productivity LUEN(t, t + 1) = LECH(t, t + 1) + LTCH(t, t + 1). [66] provide recent theoretical justification for weighting the indicator equally across time periods, in order to satisfy the time reversal property for aggregation. We let LUEN(w) denote the environmental technology analogues to (9)–(11).
Our adaptation indicator considers changes in efficiency relative to the environmental frontier, as well as changes to the environmental technology relative to changes in the cumulative metatechnology. We use the Luenberger framework above to define the adaptation indicator, which we denote AI(t, t + 1), as
(12)
with the corresponding efficiency and technology change components,
(13)
(14)
Intuitively, the indicator measures adaptation as the difference in productivity, with and without including environmental conditions in the production technology. As productivity is itself a measure of change in output to change in input over time, this lends a difference in differences interpretation to the adaptation indicator. In Fig 1, observation k loses efficiency over time, relative to both technologies, Tt,t+1, Tt,t+1(w). However, the loss of efficiency to the environmental frontier is smaller, implying a positive adaptation efficiency change component, AIEC > 0. Likewise, while both technologies expand, the environmental technology expands by less, implying a negative adaptation technology change component, AITC < 0. The sign of the overall adaptation productivity indicator, AI, would depend on the relative magnitudes of the adaptation efficiency gain and technology loss.
In some sense, the standard production technology, estimated without considering environmental variables, suffers from omitted variables bias. By ignoring the additional constraints imposed by environmental conditions, this is likely to overstate what is truly possible for a given observation. Namely, the standard technology compares each observation to a reference set which can include more favorable environmental conditions. Our indicator exploits this form of bias, by comparing productivity given the added constraints of changing climate conditions to the standard reference technology, which omits any changes to climate. In the spirit of differences in differences estimation, the standard reference technology serves as the counterfactual point of comparison to the actual climate-adjusted technology.
3.4 A long differences approach to climate trends
To consider adaptation over longer time horizons associated with climate change, we follow the recent long differences approach of [4] to distinguish longer term climate trends from annual weather variation. Let represent a vector of P successive climate time periods, each of length Sp, p = 1, …, P. We use
,
,
, and
, to represent the climate period average values for the production variables. We then estimate both the metatechnology and environmental metatechnology for each climate period, using these period average values, in order to model longer term change. This yields the climate period technologies,
and
, defined as in (1) and (3), as well as corresponding output sets,
and
, defined as in (4) and (5). Note that the technology for each climate period represents the cumulative metatechnology, including all preceding climate periods.
For our analysis, we construct three 5-year climate periods (i.e., P = 3 and Sp = 5, p = 1, 2, 3) based on USDA Census of Agriculture years: 1987-1992, 1997-2002, and 2007-2012. We refer to these as the 1990, 2000, and 2010 climate periods. We employ the Luenberger framework for productivity and adaptation outlined in (9)–(12) to measure change between climate periods.
4 Application to US Mississippi River Basin
4.1 Data construction
We apply the productivity indicator framework to agricultural production and nitrogen loading in the US Mississippi River Basin, one of the most productive regions for agriculture globally. Nitrogen runoff from agricultural production in the basin also remains a leading contributor to in-stream eutrophication and annual hypoxia in the Gulf of Mexico, commonly known as the “Dead Zone” [42, 67]. This makes the region particularly relevant for analysis of management practices and policy design to reduce nitrogen runoff and subsequent loading in the basin [43, 46, 47, 68–71].
Following [4], we limit our analysis to areas east of the 100th Meridian, to mitigate the role of irrigation in production. We refer to this as the Eastern Mississippi River Basin (EMRB). We extend the [4] production data, originally drawn from [17], to now include USDA Census of Agriculture years 1978—2012. Our analysis considers the subset years, 1987-2012. We restrict this subset to overlap available nitrogen loading estimates from [8]. The production data include county-level aggregate values for agricultural sales and expenditures. Our use of aggregate sales and expenditure data is similar to previous related studies combining production and nitrogen loading data for the Mississippi River Basin, including [46, 47, 72], as well as the use of aggregate input and output quantity data by [6, 7]. We use the USDA national PPI and CPI to convert all monetary values to 1990-1992 base year values. Table 1 summarizes the production data.
We use GIS to aerially prorate the county-level production data to 4 km grid resolution climate data, drawn from the PRISM Climate Group (Oregon State University, https://prism.oregonstate.edu), and to subbasin-level estimates for nitrogen loading, drawn from [8]. This data construction follows related work to match subbasin-level nitrogen loading to agricultural production data [44, 46, 72]. Figs 2 and 3 present the spatial distribution for precipitation in the EMRB for the 1990-2010 study climate periods, while Figs 4 and 5 presents similar spatial distributions for the production variables and nitrogen loading. Note, all climate data are reported in terms of 30-year climate normals, computed as the average value from the preceding 30 years.
Looking at these spatial distributions, we see increases to precipitation over much of the middle regions of the basin, with northern and southern-most regions becoming drier for growing season months. We also see varying levels of temperature increase over most of the basin, with more extreme increases in the northern-most regions. The expenditure ratio generally improved for most of the basin, and most so in the upper midwest regions, areas where nitrogen loading levels also became more concentrated.
The PRISM climate data include monthly values for temperature, dew point and precipitation. Rather than include these weather variables directly in the technology model, we follow [18] to construct two separate weather indexes: The Oury (1965) aridity index for crop production and a temperature-humidity index (THI) to measure heat-stress conditions for livestock production.
The Oury index for time t is constructed as:
(15)
where temperature is measured in degrees Celsius and precipitation in millimeters. The THI is constructed as:
(16)
where temperature is again measured in degrees Celsius. Following [18], we restrict the Oury index to the growing season months, April-August and construct annual THI values. Table 1 presents summary statistics for the climate variables and index values. Note, as with the raw weather variables, all weather index values are reported in terms of 30-year climate normals.
We use this weather index approach to better satisfy the production technology axioms for monotonicity. Raw temperature and precipitation values often present thresholds, below which, more rain or warmer temperatures may be production-increasing, but above which, the opposite holds [72]. For instance, [17] find that after gradual yield growth increases up to 29-32 degrees Celsius, corn, cotton, and soy experience rapid decreases in yield growth. By contrast, the Oury and THI values imply consistent production relationships over their range of possible values. For the Oury, higher values imply lower aridity, and more favorable conditions for crop production. The THI increases with heat stress, implying less favorable conditions for livestock production [73, 74]. Oury index values below 20 indicate drought conditions, while THI values greater than 70 indicate stress to cattle livestock [18, 75].
Table 1 presents summary statistics for all model variables. We note to clarify, the data in Table 1 represent the 5-year climate period averages. For the production and nitrogen loading data, these are the average annual values within the climate period. For the climate variables, these are the same 5-year window average values, but in this case using the 30-year climate normals. While there is no overlap of the 5-year windows, there is some overlap of the underlying 30-year climate normals, so that the main variation in the climate normals comes from the underlying periods of non-overlap.
To overview the data in Table 1, while land in agriculture remained relatively stable over the study period, both sales and expenditures increased in real terms. The 30-year climate normals for growing season temperature and precipitation increase on average, while the resulting Oury and THI index values remain relatively stable. Nitrogen loading increases, peaking during the 2000 climate period.
4.2 Inefficiency results
To consider inefficiency under different environmental conditions and production objectives, we estimate four versions of the directional distance model from (8). The first model (Production-Only) considers only the agricultural production objectives, setting (gy, −gu) = (1, 0), without including climate normals or nitrogen loading. The second model (Climate) includes the climate normals, still setting (gy, −gu) = (1, 0), while the third (Nitrogen) includes nitrogen loading, setting (gy, −gu) = (1, −1), but omits the climate normals. The fourth model (Climate-Nitrogen) jointly maximizes production output and minimizes nitrogen loading, while also including the climate normals. In each case, the model considers time t observations, relative to the time t metatechnology frontier. Table 2 presents the corresponding model results.
Average inefficiency values range from approximately 20 to 38 percent of mean production values, and generally increase over the study period. Lower inefficiency with the inclusion of climate normals implies an inward shift of the environmental frontier, relative to the production metatechnology, similar to the conceptual depiction in Fig 1. This pattern holds across climate periods, and both with and without adding the nitrogen loading objective. For the nitrogen loading models, we see the greatest inefficiency levels for the 2000 climate period, which corresponds to the concurrent peak in nitrogen loading for the basin. Including the nitrogen loading objective also generally lowers inefficiency estimates, implying less potential for increases to agricultural output when also working to reduce nitrogen loading.
4.3 Productivity and adaptation indicator results
As with the underlying inefficiency models, we construct four versions of the Luenberger productivity indicator, with and without the nitrogen objective and climate normals. We also consider shorter-term changes in productivity between climate periods (1990-2000, 2000-2010), as well as longer term productivity over the entire study period (1990-2010). Table 3 presents the corresponding model results.
To overview, we begin with the composite productivity indicator values. Across models, productivity increases over the study period, with average inter-climate period gains ranging from 5.4 to 12.5 percent, and greater gains for the 2000-2010 period. Average productivity estimates for the entire 1990-2010 period range from 12.9 to 17.2 percent. Using the decomposition, we can attribute overall productivity gains mainly to gains in the production technology, or an outward shift of the production frontier across time. Average technology gains range from 6.2 to 15.3 percent for the inter-climate period models, and from 17.6 to 25.6 percent for entire study period. Technology gains generally outweigh efficiency losses, which range on average from -0.3 to -9.0 percent for the inter-climate period models and from -0.47 to -9.3 percent for the entire study period. We do find modest average efficiency gains for the 2000-2010 nitrogen loading model, still outweighed by technology gains in that case. This general pattern of technology gains outweighing efficiency losses, resulting in overall productivity gains, is consistent with previous recent analyses of climate and US agricultural productivity [6, 25].
Comparing the nitrogen loading results to the production only results, we generally see smaller overall productivity gains when taking nitrogen into account. The same pattern of technology gains outweighing efficiency losses (or modest efficiency gains) holds.
We note, it is important to interpret the productivity results in Table 3 as measures of change relative to each model’s respective frontier. A higher productivity value for the climate adjusted models versus the non-adjusted models simply implies greater relative gains from the initial climate-adjusted basis for comparison, rather than greater overall increases to production or a beneficial effect of climate. Indeed, our inefficiency results in Table 2 indicate that the climate-adjusted frontier generally lies below the non-adjusted frontier. Fig 1 also illustrates this difference in frontiers conceptually. Our indicator framework interprets this difference in proportional change for the climate-adjusted model as the adaptation component.
Figs 6–9 present the spatial distributions for the productivity indicator results from each of the models. We see similar spatial patterns across models, with the highest productivity gains concentrated in the upper-Midwest region of the basin, and losses mainly in the South and eastern regions. We see a similar pattern for the nitrogen loading models, but with more areas of productivity loss in the Midwest, where nitrogen loads became more concentrated over the study period.
The adaptation indicator takes the difference between the productivity indicator (and sub-component) values, with and without the change in climate normals. In Table 3, average productivity gains with climate normals included outweigh those without, to varying degrees. To better understand the underlying components to this difference, Table 4 presents the adaptation indicator and sub-component results.
The overall adaptation indicator values range from 1.2 to 2.8 percent for the inter-climate periods, versus 0.1 to 0.9 percent for the entire study period. For the 1990-2000 period, efficiency losses to the climate-adjusted frontier were less than those to the metatechnology frontier, indicating net adaptation efficiency gains. This pattern reverses for the 2000-2010 period, while for the 1990-2010 period as a whole, we find average net adaptation efficiency gains of 1.3 percent for the production only model, versus net adaptation efficiency losses of 0.8 percent for the nitrogen loading model. We find overall adaptation technology losses of -0.4 percent for the production only model over the entire period (i.e., the climate-adjusted metafrontier expanded by less than the production metafrontier), but average gains of 2.8 percent for the 2000-2010 period. Technology gains persist on average for the nitrogen loading model, with overall adaptation gains of 0.9 percent over the entire period. Adaptation technology gains indicate the climate-adjusted frontier expanded more, proportionately, than the production metatechnology frontier.
Figs 10 and 11 presents the spatial distributions of the adaptation indicator values. Compared to the previous productivity results, we find greater spatial dispersion of adaptation indicator values, for both the production-only and nitrogen loading models. Areas extending from the upper-Midwest to lower South exhibit adaptation gains above 2 percent, with additional positive gains over much of the eastern regions of the basin as well. Adaptation losses are more pronounced in the upper portions of the basin for the production-only model, while more dispersed over the center regions for the nitrogen loading model.
Finally, we further explore both spatial and temporal heterogeneity of our results, beginning with the kernel density estimates for the adaptation indicator distributions in each time period in Figs 12 and 13. These density estimates align closely over time, especially for the production-only model. However, based on Kruskal-Wallis test results, we can reject the null hypothesis of equality of populations for our adaptation indicator over time, with p = 0.0001. Similarly, Kruskal-Wallis test results also indicate differences in the adaptation indicator populations by state. Taken together, along with the mappings in Figs 10 and 11, we see clear evidence of both spatial and temporal heterogeneity. While our indicator framework does not lend a causal interpretation to explain this heterogeneity, it could be used to inform parametric stochastic frontier models with corrections for serial and spatial autocorrelation (see, e.g., [76, 77]).
5 Conclusion
Changing climate conditions highlight the importance of adaptation for sustained agricultural productivity growth. We contribute to recent efforts to measure the adaptation component to overall productivity by developing a Luenberger productivity indicator for adaptation. Our indicator measures adaptation as the difference in productivity, with and without including climate in the production technology, lending a differences in differences interpretation to resulting indicator values. This framework also allows for decomposition of adaptation to both efficiency and technology change components.
We also extend recent analyses of adaptation and agricultural productivity to consider agricultural production jointly with nitrogen loading, which too can be affected by climate conditions. We construct a new data set, matching historical agricultural production data to nitrogen loading estimates and 30-year climate normals, spanning the years 1987-2012, for the eastern Mississippi River Basin.
Across models, we find productivity gains, driven mainly by technology gains outweighing efficiency losses, over the study period. We also find evidence of average adaptation gains, meaning productivity with climate included increased by more proportionately than without, on average for the study region. This suggests that producers are adapting, both in terms of technical advance and efficiency improvements. Average overall adaptation indicator values are modest, ranging from 0.01 to 2.8 percent, depending on model and period, but when considered in aggregate for agricultural production in the region, imply sizeable gains. Mapping these results also reveals substantial spatial variation in productivity and adaptation, as well as areas of concentration for both gains and losses.
Admittedly, adaptation to climate change can be defined and measured in different ways. We introduce a nonparametric productivity-based indicator here, which is consistent with economic index theory. Our indicator builds on similar recent productivity index decompositions [6, 7], which define adaptation in terms of efficiency change to a climate-adjusted production technology, by adding a second technology change component to overall adaptation. While our indicator framework is useful for measuring adaptation in terms of standard productivity components, this is just one of many possible ways to define and measure adaptation. For instance, moving away from productivity-based approaches, production function-based causal econometric frameworks can be used to measure adaptation in terms of the causal effect of climate change on production yields (see, e.g., [4]).
We also note a number of empirical limitations. First, the analysis is aggregated to county-level production and environmental variables, and does not consider individual producer behavior. Related to this, we work with aggregate sales and expenditures, which does not allow for further decomposition of the indicator into input or output mix components, which might shed additional light on adaptation measures. Our main focus in this study is to develop a new adaptation productivity indicator framework. For greater robustness of the empirical results, we could also extend this framework to stochastic frontier estimation of the underlying technology models.
Caveats aside, we believe our developed adaptation productivity indicator framework offers a novel approach to measuring and decomposing producer adaptation to changing climate conditions, while being grounded in economic index theory. This framework can also be extended to include environmental objectives.
Acknowledgments
We would like to especially thank Spiro Stefanou, Ariel Ortiz-Bobea, Robert Chambers, Eric Njuki, and Christopher Parmeter for their comments on previous drafts and presentations. In addition, we thank participants in the 2022 Allied Social Sciences Association (ASSA 2022) special session on Climate Change and Agricultural Production, University of Miami Department of Economics Seminar, the 2022 Ulvön Conference on Environmental Economics, U.S. Federal Reserve Money Market Analysis Brownbag Seminar, and the Organization for Economic Cooperation and Development (OECD) Network on Agricultural Total Factor Productivity and the Environment (TFPEN). Finally, we would also like to thank our two anonymous reviewers for their comments, which have helped us to greatly improved this paper. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Board or other members of its staff.
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