6 not on constructing highly accurate rainfall maps as such, necessary for example for the design of weather index insurance programs, but rather on the household welfare effects of weather related events, a pragmatic approach has been pursued here, aimed at minimizing measurement error of the disaggregated rainfall measures at a reasonable cost, while maintaining maximum replicability of the approach in other settings.

In particular, using the historical daily rainfall records over 1980‐2006 in 166 geo‐referenced weather stations from across Vietnam (see Figure 1)<sup>9</sup> , monthly rainfall grids of 0.1 degree resolution are constructed<sup>10</sup> using both inverse distance weighting (IDW) and inverse elevation difference weighting (IEW). In IDW, one of the most widely used spatial interpolation techniques in practice (Tomczak, 2003), the rainfall value in a particular grid cell is obtained as the weighted average of the rainfall data from a predetermined set of neighboring weather stations (e.g. the 5 closest or all the neighboring stations within a certain distance) using the inverse distance between the station and the center of the grid cell (raised to a power) as weight and normalized by the sum of the weights.<sup>11</sup> The squared inverse distance to the five nearest stations for which data were available was chosen in the empirical application below. IDW exploits the intuition that the further away the station is, the less its rainfall pattern will resemble this at the point of interest. However, even over short distances rainfall patterns can still diverge widely, especially among locations at different altitudes (Hutchinson, 2003). Given its mountainous range, high slope gradients are frequently observed in Vietnam, with some grids displaying within grid elevation differences of more than 1,000 meters. To exploit this largely neglected insight (Dubois and Shilbi, 2003), an elevation difference weighted rainfall index based on the ten nearest stations is also constructed.<sup>12</sup> The relative importance of both the IDW and IEW indices in determining rainfall in a grid is subsequently estimated through an ordinary least square regression of the log of the observed monthly rainfall patterns in the 166 stations during 1980‐2006 on the log of their IDW and the log of their IEW index, monthly dummies and their interactions to allow for monthly variations in the better than this for IDW (6.3 mm), which is negligible compared to the average rainfall of 18.51 mm among the 367 omitted data points for which rainfall was interpolated from the remaining 100 rainfall stations. 9 The average distance between rainfall stations is 32 km.

10 While the satellite based rainfall maps produced by CPC/NOAA could also be used in principle, they only dated back to 2001, preventing us from constructing disaggregated historical rainfall patterns, necessary to explore patterns of adaptation. There is an additional concern as the satellite based CPC / NOAA data for Vietnam appear calibrated on a rather small number of rainfall stations (10 or so) from within Vietnam.

> 11 � ����� To be precise, ���������∑��� ∑�� ����� �� with r(x) the inverse distance weighted rainfall at interpolated point x, based on observed rainfall values rk at k=0,1, ..., N known interpolating (known) points xk, with � ������ ���,���<sup>�</sup> as weight, x _k_ an interpolating (known) point, d a given (Euclidean) distance from the known point xk to the unknown point x and p a positive real number, the power parameter.

12 Further corrections for anisotropy can be taken. This is important if nearness in one direction is more important than nearness in the perpendicular direction in determining the distance weights. This may be the case when mountain ranges are oriented at particular angles, or when prevailing winds are from a specific direction. This has not been pursued here, given the inclusion of the elevation difference in our final predictions and the reasonable prediction precision obtained when using both inverse distance squared and inverse elevation weighted indicators (see below).