Int. J. Environ. Res. Public Health 2011, 8 918  Population and GDP data were drawn from the World Development Indicators [40] and CIA World Factbook [41].  Data on the country specific gini inequality index and area in square kilometers per country (used to compute the population density) are obtained from the CIA World Factbook [41].  Per capita expenditures on health were obtained from the WHO report [14].  Data on the number of hospital beds per 1,000 people were obtained from the Organization for Economic Cooperation and Development [42]. The socio-economic variables were only available in the form of annual observations. Thus we aggregated our other data to an annual basis and for the climate variables computed variances using the monthly observations. As a result, all of our observed variables are in annual frequency. The key summary statistics of all the variables used in the estimation are given in Table 1. Table 1. Summary statistics. Variable CAPCASES TEMP STDTEMP PRECIP STDPRECIP POP POPDENS CAPGDP GINI CAPEXP CAPBED Definition Malaria cases per 1,000 people. Temperature (Degree Celsius) Temperature standard deviation Precipitation (mm/m3) Precipitation standard deviation Population (million) Population Density per km2 Per capita GDP(US$/capita) Gini inequality index Health expenditure ($/capita) Hospital beds per 1,000 people. Mean 95.2 24.24 2.9 777.4 60.0 18.5 51.5 671.4 42.9 93.7 1.2 Std. Dev. 119.64 3.32 1.9 479.3 41.1 22.1 59.3 809.5 7.2 119.4 0.9 Min. 0.0 16.7 0.3 37 1.3 0.5 1.9 110.3 29.8 14 0.1 Max. 947.4 29.2 8.5 1,921.7 220.4 118.9 304.6 3,764.2 61 579 4.8 The summary statistics indicate that there is generally less variability in temperature than in precipitation for most of the countries. Therefore, only variability in precipitation is used in the regression as a measure of climate variability index. 6. Empirical Model Specifications Two specifications of the nonlinear function are assumed and estimated. The first assumes an additive form and the second, a complex function of unknown form of . In the first specification, the function is smooth in the climate variability index measured by monthly standard deviation in precipitation. In such case, climate variability affects the number of malaria cases not only through the intercept but also through the slope of temperature ) and precipitation . That is, the effect of temperature and precipitation on the number of cases will depend on how precipitation variability evolves (consistent with the argument made by Jaenisch and Patz [25]). In other words, the size of the impact of temperature and precipitation on the malaria prevalence is conditioned by fluctuations in climate measured by the standard deviation in precipitation. The empirical statistical relationship between malaria cases, climatic and socio-economic variables can be written as: