where �= [(1 � �) (�� � �) = (1 � �)]�[� (1 � ��) =�] > 0. From STM expression (13) it is straightforward to show that: (i) dSTM=d�� < 0 (a larger �� makes Ricardian agents cut their consumption more as the real interest rate goes up), (ii) dSTM=d'<sup>�1</sup> > 0 (due to larger labor supply e¤ects), (iii) dSTM=d�< 0 (because a lower � reduces the need of Ricardian agents to cut their consumption due to lower labor supply e¤ects), (iv) dSTM=d�p > 0 (demand shocks have larger e¤ects on output rather than on prices), (v) dSTM=d�> 0 (mainly because a larger share of HtM agents, �, increase the average marginal propensity to consume of the economy), (vi) dSTM=d�> 0 (as social transfers particularly reach those HtM agents with high marginal propensity to consume).<sup>23</sup> It is important to note that while having a larger share of HtM agents, �, or a bigger share of social transfers reaching the HtM agents, �, increases the size of the STM, these increases are in and of itself associated with lower and higher levels of well-being, respectively. Why? Because a larger � points to more individuals not being able to smooth consumption, whereas a bigger � depicts more social transfers being allocated to constrained individuals. In other words, while having a larger � ampli...es the e¤ect of a social transfer shock, it is not something that, naturally, should be commended as desirable.

# 4 The share of HtM individuals and the share of social transfer reaching them in data

Given the nature of our contribution, it is essential to be able to measure the share of HtM individuals, �, as well as the share of social transfers reaching them, �. As discussed in the introduction, no paper disciplines the share of social transfers reaching HtM agents, �, by data. It is generally assumed that social transfers solely reach HtM agents (i.e., � = 1), which is referred to as perfect social transfers targeting. Regarding the share of HtM agents, �, quantitative papers estimating STMs for the United States (Giambattista and Pennings, 2017; Pennings, 2020) discipline the share of HtM agents to one-third based on Kaplan et al. (2014). There have been two main strategies to identify HtM agents in the United States and other developed countries.

A ...rst group of studies relies on survey data on household portfolios, with an emphasis on savings, net worth, and the liquidity of assets (e.g., Kaplan and Violante, 2014; Kaplan et al., 2014; Aguiar et al. 2020). In their seminal paper, Kaplan et al. (2014) ...nd that between 25 and 40 percent of United States households are HtM, with their preferred estimate being one-third. Of all HtM households, about one-third are poor HtM (who hold little or no liquid wealth and no illiquid wealth) and two-thirds are wealthy HtM (who also hold little or no liquid wealth but have signi...cant amounts of illiquid assets on their balance sheets, led by real estate properties).

> 23 It is worth noting that the empirical evidence obtained from properly adding interaction terms to empirical speci...cation (3) with respect to country-varying variables �, �, and � (see Sections 4 and 5 for measurement details) delivers the model-based sign estimates. Results are not shown for brevity.

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