<u>β1</u><sup>2</sup> Var(YCt <u>) β2</u><sup>2</sup> Var(YTt <u>)</u> = = C T , C T = 1, (4) β1<sup>2</sup> Var�Yt �+β22Var(Yt ) β1<sup>2</sup> Var�Yt �+β22Var(Yt ) WW<sup>YYCC</sup> WW<sup>YYTT</sup> , WW<sup>YYCC</sup> + WW<sup>YYTT</sup> where represents the share of the variance of the social indicator driven by income, which is explained by the business cycle. On the other hand, , captures the share of the variance of the WW<sup>YYCC</sup> social indicator driven by income that is explained by the trend component of output. WW<sup>YYTT</sup> The height of the bars in Figure 6 denotes ; that is, the average share of the variance of the social indicator driven by income that is explained by the business cycle for a worldwide sample. This share WW<sup>YYCC</sup> is much higher for the unemployment rate and monetary poverty than for more structural measures of social welfare such as the HDI. We find that, by itself, the business cycle component explains 47.4, 23.3, and 1.7 percent of the variance of the social indicator driven by income for the unemployment rate, monetary poverty, and HDI, respectively. This clearly shows how some indicators such us the unemployment rate or monetary poverty are heavily exposed to sampling bias due to common and well understood ups and downs in economic activity. Moreover, as in the case of Argentina above, and given that is a function of Var(YtC), the potential bias of interpreting trend-driven gains in social conditions for such indicators would mechanically grow with the volatility of the business cycle WW<sup>YYCC</sup> (see equation (4)).<sup>17</sup> The next section zooms on the role of the business cycle driving movements in cyclical social indicators such as monetary poverty using microdata for a set of LAC countries.

# **4. A Microdata Approach on the Importance of Business Cycle Fluctuations on Monetary Poverty: An Application to LAC**

The previous section showed that while some social indicators (such as the unemployment rate) are cyclical in nature, fluctuating considerably in the short run along with the business cycle, others (such as the HDI, especially its non-income components) follow long-term trends and bear very little relation to the business cycle. Interestingly, monetary poverty lies somewhere in between the two extremes with large heterogeneity across countries. In particular, whether monetary poverty behaves more like the unemployment rate (i.e., affected by cyclical considerations) or the HDI (i.e., determined essentially by the long-run trend) crucially depends on the volatility of the business cycle. In highvolatility countries (such as Argentina), changes in monetary poverty are much more closely related to the business cycle than in low-volatility countries (such as Chile).

> 17 We are forced by virtue of the sample length to rely upon a linear deterministic trend. In light of well-established evidence regarding the different stationary nature of real GDP in emerging markets (see for example seminal paper by Aguiar and Gopinath, 2007), a natural concern is the extent to which the findings of Figure 6 are robust to other detrending more “flexible” techniques. While most data for monetary poverty and HDI (and its components) start in mid-1990s to early 2000s, we have 32 countries in our sample with unemployment rate data starting in the year 1980 (which gives us almost 4 decades of continuous data). Using this data, we cannot reject the null hypothesis that the median contribution of the business cycle to the variance in the unemployment rate is the same across well-known more “flexible” detrending techniques. In particular, and based on a nonparametric K-sample test on the equality of medians, a contribution based on a linear trend (45.2 percent) is statistically the same as that based on a Hodrick-Prescott filter (38.5 percent) or a Christiano-Fitzgerald filter (42.2 percent).

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