hypothesis of equality because the projection is noisy. In other words, if a projection is very imprecise and its standard error is large, the test is less likely to find the difference is statistically significant.

For rural areas and estates, even after including the wage data, the projected poverty estimates for rural areas and estates are outside the 95 confidence interval of the direct estimates and the differences are statistically significant at the one percent level. The projected poverty estimate for urban areas performed slightly better. The difference between the projected and the direct estimates is not statistically significant at the 95 percent level, but the projected estimate lies outside the 90 percent confidence interval of the direct estimate. At the national level, the projected poverty estimate is above the upper bound of the 95 percent confidence interval of the direct estimate, and the difference is statistically significant at the one percent level.

# _Backward projections_

We now reverse the direction of the survey-to-survey imputation. We estimate the consumption model in the 2009 HIES, and impute household expenditure into the 2006 LFS. To assess the accuracy of the prediction, we compare the imputed poverty rates with those directly estimated from the 2006 HIES.

When the wage variable is excluded, the results are dismal. In urban areas, the imputation predicts that poverty in 2006 was 4.1 percent when the direct estimate was 7.4 (Table 6). Therefore, the imputation suggests that poverty increased from 4.1 to 6 percent between 2006 and 2009 when in fact it declined. The rural model predicts that poverty in 2006 was 8.8 percent, implying virtually no change between 2006 and 2009, when in fact rural poverty fell 6.5 percentage points. Similarly, the imputation suggests little movement in the estate sector, despite a huge reduction in poverty of 23 percentage points. At the national level, the imputed poverty estimate of 2006 is 8.3 percent. This is 7 percentage points lower than the actual national poverty rate of 15.3 percent, and slightly lower than the 2009 direct estimate of 8.6 percent. This method therefore predicts a small increase in poverty between 2006 and 2009, when in fact poverty fell substantially.

The estimates after adding the wage variable are slightly closer to the direct estimates, but remain far off the mark. For example, the imputed poverty rate for urban areas increases from 4.1 percent to 4.6 percent, but the direct estimate is 7.4 percent. For rural areas, the imputed poverty rate rises from 8.8 percent to 10.3 percent, as compared to a direct estimate of 15.4 percent. At the national level, the imputed poverty rate increases slightly to 9.8 percent but remains far lower than the direct estimate of 15.3 percent.

Like the forward projection, for rural areas and estates, the projected poverty estimates of 2006 are outside the 95 percent confidence intervals of the corresponding direct estimates. Also, the differences between the projected and the direct estimates are statistically significant at the one percent level. For urban areas, the projected poverty estimate lies outside the 95 percent confidence interval of the direct estimate. Furthermore, the difference is also statistically significant at the 10 percent level. At the national level, the imputed poverty rate is below the 95 percent confidence interval of the direct estimate and the difference is statistically significant at the one percent level.

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