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# 2. Theory.

The Ricardian method is a cross-sectional approach to studying agricultural production. It was named after David Ricardo Noun 1. David Ricardo - English economist who argued that the laws of supply and demand should operate in a free market (1772-1823)
Ricardo
(1772-1823) because of his original observation that the value of land would reflect its net productivity. Farmland net revenues (V) reflect net productivity. This principle is captured in the following equation:

V = [SIGMA] [P.sub.i] [Q.sub.i] (X, F, H, Z, G) - [SIGMA] [P.sub.x] X (1)

where Pi is the market price of crop i, [Q.sub.i] is the output of crop i, X is a vector of purchased inputs (other than land), F is a vector of climate variables, H is water flow, Z is a set of soil variables, G is a set of economic variables such as market access and [P.sub.x] is a vector of input prices (see Mendelsohn et al. 1994). The farmer is assumed to choose X to maximize net revenues given the characteristics of the farm and market prices. The Ricardian model is a reduced form In social science and statistics, particularlly econometrics, a reduced form equation is a method of dealing with endogeneity. A reduced form equation is defined by James Stock & Mark Watson (2007) in the following way:  model that examines how several exogenous Exogenous

Describes facts outside the control of the firm. Converse of endogenous.
variables, F, H, Z and G, affect farm value.

The standard Ricardian model relies on a quadratic quadratic, mathematical expression of the second degree in one or more unknowns (see polynomial). The general quadratic in one unknown has the form ax2+bx+c, where a, b, and c are constants and x is the variable.  formulation of climate:

V = [B.sub.0] + [B.sub.1]F + [B.sub.2] [F.sup.2] + [B.sub.3] H + [B.sub.4] Z + [B.sub.5] G + u (2)

where u is an error term. Both a linear and a quadratic term for temperature and precipitation are introduced. The expected marginal impact of a single climate variable on farm net revenue evaluated at the mean is:

E[dV/[df.sub.i]]= [b.sub.1,i] + 2 * [b.sub.2,I] * E[[f.sub.i]] (3)

The quadratic term reflects the nonlinear shape of the net revenue of the climate response function (Equation 2). When the quadratic term is positive, the net revenue function is U-shaped and when the quadratic term is negative, as in Figure 1, the function is hill-shaped. We expect, based on agronomic a·gron·o·my
n.
Application of the various soil and plant sciences to soil management and crop production; scientific agriculture.

ag
research and previous cross-sectional analyses, that farm value will have a hill-shaped relationship with temperature. For each crop there is a known temperature at which that crop grows best across the seasons. Crops consistently exhibit a hill-shaped relationship with annual temperature, although the peak of that hill varies with each crop. The relationship of seasonal climate variables, however, is more complex and may include a mixture of positive and negative coefficients across seasons.

The change in welfare, AU, resulting from a climate change from C0 to C1 can be measured as follows.

[DELTA]U = V ([C.sub.1]) - V ([C.sub.0]) (4)

If the change increases net income it will be beneficial and if it decreases net income it will be harmful.

Cross-sectional observations across different climates can reveal the climate sensitivity of farms. The advantage of this empirical approach is that the method not only includes the direct effect of climate on productivity but also the adaptation response adaptation response See Adaptation, psychology.  by farmers to local climate. This farmer behavior is important because it mitigates the problems associated with less than optimal environmental conditions. Analyses that do not include efficient adaptation (such as the early agronomic studies) overestimate o·ver·es·ti·mate
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
the damages associated with any deviation from the optimum. Adaptation thus explains both the more optimistic op·ti·mist
n.
1. One who usually expects a favorable outcome.

2. A believer in philosophical optimism.

op
results found with the Ricardian method and the generally pessimistic results found with purely agronomic studies.

Adaptation is clearly costly. The Ricardian model takes into account the costs of different alternatives. For example, if a farmer decides to introduce a new crop on his land as climate warms, the Ricardian model assumes the farmer will pay the costs normally associated with growing that new crop. That is, the farmer will have to pay for new seeds and new equipment specific to the crop. The Ricardian model does not, however, measure transition costs. For example, if a farmer has crop failures for a year or two as he learns about a new crop, this transition cost is not reflected in the analysis. Similarly, if the farmer makes the decision to move to a new crop suddenly, the model does not capture the cost of decommissioning Decommissioning is a general term for a formal process to remove something from operational status. Some specific instances include:
• Ship decommissioning
capital equipment prematurely. Transition costs are clearly very important in sectors where there is extensive capital that cannot easily be changed. For example, studies of timber (Sohngen et al. 2002) show that modeling the transition is absolutely necessary in order to reflect how difficult it is to change the forest stock. Although agriculture adapts quickly to changes in prices, many intertemporal agricultural studies argue that farms will have more difficulty adapting quickly to climate change (Kaiser et al. 1993 a,b; Kelly et al. 2005). Given how slowly some innovations in modern agriculture have spread in Africa in particular, transition costs may be very important.

Another drawback of the Ricardian approach is that it cannot measure the effect of variables that do not vary across space. Specifically, this approach cannot detect the effect of different levels of carbon dioxide carbon dioxide, chemical compound, CO2, a colorless, odorless, tasteless gas that is about one and one-half times as dense as air under ordinary conditions of temperature and pressure.  since carbon dioxide levels are generally the same across the world. Changes in carbon dioxide levels have occurred over recent decades. In principle, one might be able to detect the effect of these increases in C[O.sub.2] by looking at productivity over time. However, it is impossible to distinguish the effect of the carbon dioxide changes from the much larger effect of technical changes that have occurred across the same time period (Mendelsohn 2005). The best evidence about the magnitude of the fertilization fertilization, in biology, process in the reproduction of both plants and animals, involving the union of two unlike sex cells (gametes), the sperm and the ovum, followed by the joining of their nuclei.  effects of carbon dioxide comes from controlled experiments. These studies report an almost universal fertilization effect for all crops, although the magnitude of this effect varies from crop to crop (Reilly et al. 1996). Reilly reports an average improvement in productivity of 30% associated with a doubling in C[O.sub.2]. However, these results must be interpreted cautiously because the conditions in the controlled experiments may not be representative of farms across the world. In most cases, the laboratory experiments have been done in near ideal conditions where other nutrients are freely available. In practice, if nutrients are scarce, the fertilization benefits from increased carbon dioxide levels may be lower. Thus in many developing countries, where fertilizers are not fully applied, the actual carbon fertilization benefits may be less than 30%.

Another potential drawback is that the variation in climate that one could observe across space may not resemble the change in climate that will happen over time. For example, the temperature range across space could be small relative to the change in temperature over the next century. This explains why one may not be able to estimate a Ricardian model in small countries. If the range of climates in a country is small, one cannot detect how climate might affect crops. This specific problem does not apply to this study as there is a wide range of climate variation across the sample. However, it may still be true that climates in the future will not resemble any existing climates. For example, the climate could become erratic, leading to precipitation events that are simply not common today. The analysis cannot measure the impact of such changes.

The Ricardian model also assumes that prices remain constant. As argued by Cline cline, in biology, any gradual change in a particular characteristic of a population of organisms from one end of the geographical range of the population to the other.  (1996), this introduces a bias in the analysis, overestimating benefits and underestimating damages. The Ricardian approach, by relying on a cross section, cannot adequately control for prices since all farms in the same country effectively face the same prices. However, calculating price changes is not a straightforward task, since prices are a function of the global market. Studies that have claimed to take price changes into account have had to make gross assumptions about how world output would change with climate change. These global assumptions also may introduce bias if they are not correct. Further, even analysts who have assumed large agronomic impacts from global warming global warming, the gradual increase of the temperature of the earth's lower atmosphere as a result of the increase in greenhouse gases since the Industrial Revolution.  predict that greenhouse gases would have only a small net effect on aggregate global food supply (Reilly et al. 1996). If aggregate supplies do not change a great deal, the bias introduced by the Ricardian assumption of constant prices is likely to be small (Mendelsohn & Nordhaus 1996). If the supplies of some commodities increased and others decreased, welfare effects would offset each other. In this case the bias could be large relative to the remaining small net effect. However, even in this case the absolute size of the bias would remain small. In a separate analysis, Kumar and Parikh (2001) include prices in their interannual analysis of Indian agriculture. The inclusion of the price terms appears to have little impact on the climate coefficients.

Another valid criticism that has been leveled against the Ricardian analysis concerns the absence of explicit inclusion of irrigation irrigation, in agriculture, artificial watering of the land. Although used chiefly in regions with annual rainfall of less than 20 in. (51 cm), it is also used in wetter areas to grow certain crops, e.g., rice. . Cline (1996) and Darwin (1999) both argued that irrigation should be explicitly included in the analysis. This problem has been addressed in the literature by explicitly modeling irrigation (Mendelsohn & Nordhaus 1999; Mendelsohn & Dinar 2003). This study explicitly includes irrigation and also includes measures of flow and runoff Runoff

The procedure of printing the end-of-day prices for every stock on an exchange onto ticker tape.

Notes:
If the "tape is late" then it can take a long time to print off all the closing prices.
.

A final concern about the Ricardian method is that it reflects current agricultural policies. If countries subsidize specific inputs or regulate crops, these policies will affect farmer choices. The Ricardian results will consequently have these distortions embedded in the results. For example, if a country mandates that a fraction of cropland be devoted to a certain crop, one may well see more of that crop in that country than elsewhere. We can control for such effects using country dummies. In general, we prefer not to place dummies unless there is evidence of a distortion. Nonetheless, if future decision makers eliminate these subsidies or introduce new ones, the empirical results may no longer hold. Policies that differ across countries could contribute to some of the differences in farm net revenue.
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