The standard Ricardian model relies on a quadratic formulation of climate: where u is an error term. Both a linear and a quadratic term for temperature and precipitation are introduced. The marginal influence of each climate variable consequently depends upon the level of temperature or precipitation:

[dNR/dfi]= [b1,i + 2*b2,i * fi] .

The quadratic term reflects the nonlinear shape of the net revenue of the climate response function. When the quadratic term is positive, the net revenue function is U- shaped and when the quadratic term is negative, the function is hill-shaped. We expect, based on agronomic research and previous cross-sectional analyses, that farm value will have a hill-shaped relationship with temperature. For each crop, there is a temperature range where that crop grows best across the seasons. Sites that are either too cool or too hot have lower productivity. Crops consistently exhibit a hill-shaped relationship with annual temperature, although the maximum of that hill varies with each crop. Seasonal variables, however, can take on many shapes.

There is one important difference between the satellite data in this study and the ground station data that has been used in past studies. The ground stations measure precipitation. Satellites find measuring rainfall very difficult. They can detect when rain clouds are present but they have a hard time measuring actual precipitation. The satellites, however, can measure surface wetness (soil moisture). From an agronomic perspective, surface wetness may be a more attractive measure than rainfall as it reflects the moisture actually available to crops. Soil moisture, however, is a complex measure. First, surface wetness has a memory, it reflects not just precipitation but also past precipitation. Second, surface wetness varies with soil type. Soils with more organic material can hold moisture longer whereas sandy soils cannot. Third, surface wetness can be affected by management decisions. Irrigated land, for example, has more surface wetness simply from diverted water.

Although the Ricardian technique carefully measures the influence of climate, it has been criticized for omitting the influence of water from runoff (Cline 1996; Darwin 1999). The early empirical models did not include runoff from other sources and so they did not capture the value of exogenous water supplies (Mendelsohn et al 1994). This criticism was addressed in Mendelsohn and Nordhaus (1999) and again in Mendelsohn and Dinar (2003) who show that although both irrigation and irrigation water supplies are important, including them has only a minor effect on the measurement of climate sensitivity. Water runoff is not available in this study for all countries and so it is not included.

# **DATA AND EMPIRICAL SPECIFICATIONS**

Historically, global land surface temperatures and wetness have been obtained from weather stations on the ground mainly in populated and industrialized regions (for example, airports). Unfortunately, these stations are neither located evenly nor densely around the globe. Specifically, observations are sparse over large regions of Africa, tropical South America, and southeastern and central Asia. An alternative technique 62