In table 5 we see that the R-squares for the three equations are between 0.12 and 0.14. We see that population density and road investments have responded over the past to AEP, but not the distance to markets. The coefficient for distance to road is much larger than that of population density. While road investment has been responsive to AEP, market distance has not, suggesting that other factors than AEP determine investments in or emergence of markets.

Urban gravity on the other hand does not affect population density. But instead has a strong impact on distance to road with an elasticity of 0.31, more than twice as high as that of AEP. Market distance is also reduced for EAs subject to more urban gravity, presumably because the density of markets is higher close to major cities.

It is therefore clear that both population and public investment in the past have responded significantly to AEP and UG, which is as we expected. Therefore, cross section regressions explaining any intensification variable (or any other agricultural variable that stems from a public or private decisions), with population density and infrastructure variables will lead to upwardly biased coefficients of the independent variables. To the extent that AEP and UG are constant or evolving at constant rates, the problem can be overcome using panel data with fixed effects as done in Binswanger et al. (1993).

In table 6 we look at the five farming systems indicators. The R-squares or Pseudo R- squares vary between 0.16 for crop and perennial area to 0.77 for area under fallow. We see that AEP does not affect any of the five variables, while UG affects four of the five: Own area, cropped area and crop and perennial area with elasticities from –0.05 to -0.09. UG also increases crop intensity with a smaller absolute elasticity of 0.03. This is the only variable for which the interaction term of UG and AEP is statistically significant, and the elasticity of UG with respect to crop intensity at the mean of AEP is only 0.003 but highly statistically significant.

In table 7 we see that the share of land irrigated is unresponsive to either AEP or UG and seems to be determined by other factors. However AEP has a significant impact on all four technology variables, with the larger elasticity of 0.07 for inorganic fertilizer and the lowest one at 0.03 for organic fertilizer. The interpretation of these finding is that higher input use has significantly higher payoffs in areas of high AEP than low AEP. This, of course, is well known, but it is interesting to see that our AEP variable and the household data can capture this effect. On the other hand, urban gravity has very little to do with use of inputs, except for use of modern varieties. We will discuss the implications of these findings in the conclusion section.

In table 8 we see that for profits per ha the linear term of AEP is positive, while the square term is negative, indicating diminishing returns to improvements of AEP at higher levels. At the mean of AEP the elasticity of profits per ha with respect to AEP is a respectable 0.37. What this means is that higher input use at higher AEPs does not fully equalize profits with those in areas of lower AEP, and in such areas households will need larger areas to reach similar incomes. That this may actually be the pattern across areas is consistent with the total lack of response of household income to either AEP or UG. On the other hand urban gravity has no impact on profits per ha or profits per household, suggesting that differential population growth and migration equalize these measures.

# **Summary and Conclusions**

## **New measures of agro-ecological population pressure and of urban gravity**

This paper first developed internationally comparable measures of agro-ecological potential and urban gravity. These measures impact positively on population densities, public investments in road and markets, and on some indicators of agricultural intensification.

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