before and after the start of the project for households who were able to benefit from the project as compared to households who were unable (or systematically less able) to benefit.

The regression equation of the household-level DiD estimator in Malawi can be written as: where Yijt is the outcome of household i in district j at time t . Postt is a dummy time variable that equals 1 for the post-program year (2019) and 0 for the pre-program year (2013). Treatij is a dummy treatment variable that equals 1 for households residing in districts with project components, and 0 otherwise. The variables Postt and Treatij are interacted to estimate the coefficient β3 , which is the main coefficient of interest. Xijt is a vector of control variables that are included to account for potential imbalances in characteristics between treated and untreated households that might be correlated with the outcome. Some specifications also include district fixed effects (FE).

The estimated coefficients from the model in equation (1) can be interpreted in the following way. The coefficient β1 captures the change in outcome Y between the pre- and post-program year for households residing outside in areas without project components (the control group). The coefficient β2 captures the difference between households benefitting from the project and households in the control group before the start of the project (pre-program difference). The coefficient of interest is β3 which captures the _difference_ in the change in Y for the benefitting households and those in the control group. If the assumptions underlying the DiD approach (see below) hold, then β3 can be interpreted as the change in Y that the households in the treatment group experienced because they benefitted from the project, i.e., the project’s impact on Y over the considered time period.

The DiD strategy relies on the assumption that any pre-existing difference between the households benefitting from the project and those forming the control group would be constant over time in the absence of the project (“parallel trends assumption”). One of the advantages of DiD is that it can account for systematic differences between the treatment and control group that prevailed before the start of the intervention. The existence of such differences is to be expected in the context we study, because the allocation of project locations was not determined randomly. The estimation of the program effect β3 in equation (1) will be robust as long as these differences are constant over time in the absence of the project (i.e., in the absence of the project the households residing in project areas would have featured the same time trend as the control group). There is no statistical test to verify (or reject) this assumption. However, a notion in the literature is to use data on the time before the start of the intervention to visually verify whether trends appear to be parallel. Since the LSMS data are available for Malawi in multiple years (2010, 2013, 2016 and 2019), we are able to follow this approach (see Section V). In addition, it is possible that the parallel trends assumption holds only after conditioning on relevant covariates. Since our data allow us to control for a rich set of household characteristics, it will be sufficient for our identification strategy if trends are parallel when conditioning on these covariates.

In addition to estimating equation (1) based on household survey data for two years (pre and post program implementation), we use grid-level data from satellites (which are available annually for the period 2012-2020) to estimate a more general spatial DiD specification of the form: where Yct is the nighttime radiance in grid cell c at time t , Yeart is a set of dummy variables for each year (i.e., year fixed effects), Cellc is a set of dummy variables for each cell (i.e., grid cell fixed effects), and Treatc is a treatment indicator that equals 1 for grid cells corresponding to project areas and 0 otherwise. Postt is defined analogous to equation (1) as a dummy time variable that equals 1 for the years after the start of project implementation (2015 in Malawi), and 0 for all earlier years. The variables Postt and Treatc 7