expressed as a function of household expenditure (or income), and by consequence as a function of the model error and idiosyncratic errors when relying on imputed household expenditure. An estimate of average welfare is obtained by evaluating the expected value of the welfare function, which involves taking expectations over the error terms. The corresponding standard errors are obtained by evaluating the variance of the welfare function, where again the model error and idiosyncratic errors denote the random variables. While this can in principle be done analytically, for general non-linear welfare functions (i.e. non-linear functions of the error terms) the evaluation of the expected value and variance can pose a challenge. A practical alternative is to estimate average welfare along with the corresponding standard error by means of simulation (see Fujii and van der Weide 2012, 2013).

Another possibility relates to the use of the _estimated poverty series as a dependent or independent variable in cross-sections models_ . This application is also explored in Elbers et al. (2005). The latter paper considers the use of small area estimates of poverty and inequality obtained by combining household income survey with population census data in regression analysis. The difference with our approach is that the household incomes are imputed into a second survey (the LFS) instead of a population census, which introduces sampling error as an additional source of error (in addition to model error). Provided that this dual error structure is accounted for, the results of Elbers et al. (2005) should directly carry over; they show how the imputation-based poverty estimates can be used as both dependent and independent variables, and how accurate standard errors of the regression coefficients can be obtained. It is important to note however that the imputed household consumption data cannot be treated as if it were observed data; for example, counting the percentage of households with imputed consumption below the poverty line would provide a biased estimate of poverty (as it ignores the error term that separates observed consumption from predicted consumption).

Exploring the time variation in estimated poverty rates, possibly disaggregated by sub-regions, can also be a powerful instrument to _understand the causes of poverty using the newly obtained panel data_ . Suppose for example that the researcher has (as for Morocco) 48 points in time and also representative data for 20 regions. This would amount to a panel of 960 observations that can be used to study the determinants of poverty when combined with regional quarterly macro and micro data. Such a wealth of poverty points is rare in poverty studies and could substantially expand the poverty work that is routinely undertaken in country poverty assessments.

Another possible application is poverty _forecasting_ . Using the most recent LFSs, Morocco today can count on 12 years of quarterly statistics for a total of 48 points in time. This time series can be used to produce poverty forecasts for the future using dynamic panel data models. Note that one will have to account for the fact that one is dealing with imputed data and not observed data in order to obtain consistent estimates of the parameters of the panel data model.

It is also possible to use the imputation-based poverty estimates for _simulations of policy reforms and economic shocks_ . For example, one could simulate how an increase in the unemployment rate or an increase in female labor force participation might affect the poverty rate.

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