We did not use post-tax income because few Malaysians are subject to personal income tax; it is thus unlikely to affect poverty or vulnerability status.

Income data have been adjusted for spatial price differences. We constructed a spatial price index that reflects prices of basic goods, services and housing at the state level, separately for rural and urban areas within the state (see Table A 1 in the Appendix). The index was derived from the household-specific poverty lines that the Department of Statistics Malaysia calculates for each survey year, which depend on the location and demographic composition of the surveyed household.<sup>18</sup> As explanatory variables in our income model, the method requires we only use variables that are time-invariant. We use three such categories. First, we employ dummy variables for the birth cohort of the household head, using five-year bins. The first bin starts in 1949 (those 55 in 2004) and the last bin starts in 1984.<sup>19</sup> Second, we use six dummy variables for the highest level of education enjoyed by the household head. Those with primary education or less form the base category. Third, we use dummy variables for the ethnicity of the household head. The four categories are Bumiputera, Chinese, Indian and Other; Bumiputera is set as the base category.

In addition, we use two location dummies that, strictly speaking, are not time-invariant. These are one dummy for urban or rural location and another for being located in either Peninsular Malaysia or East Malaysia. This restricts the interpretation of results to households that did not migrate from one such classification to another.<sup>20</sup> We opted for this approach because omitting these dummies led to biases in predicted income based on urban or rural location, which would have led us to overestimate downward mobility for rural households. Table A 2 in the Appendix provides the regression results of our income models for each survey year, based on the subsample of households with heads in the age range of 25– 55.

The synthetic panel method requires checks on the stability of the sample, as a means of assessing the assumption of a stable underlying population. We observe some differences in the distribution of explanatory variables between survey rounds, notably in the means of education variables. This seems to be driven by the age of household heads, with the mean age of heads in later rounds being lower

> 18 We are aware that the index is thus based on expenditure patterns at the very low end of the income distribution. However, this is the best we could do in the absence of spatially disaggregated consumer price data.

> 19 The first two bins are taken as base categories, since the first bin alone does not always contain a sufficient number of observations.

> 20 With the caveat that classification of a location as urban or rural may change over time, the cross-sectional data show that the proportion of the population that is living in rural areas is steadily decreasing: from an estimated 36 percent in 2004, it declined to an estimated 23 percent in 2016. Similarly, mean estimated household size decreased from 4.5 in 2004 to 4.0 in 2016.

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