Inequality and Asset Prices during Sudden Stops

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1388 December 2025 Inequality and asset prices during Sudden Stops Sergio Villalvazo Please cite this paper as: Villalvazo, Sergio (2025). “Inequality and asset prices during Sudden Stops,” International Finance Discussion Papers 1388r1. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2025.1388r1. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Inequality and asset prices during Sudden Stops⋆ Sergio Villalvazoa,∗ aDivision of Financial Stability, Federal Reserve Board, 20th Street and Constitution Avenue NW, Washington, DC, 20551, United States of America Abstract This paper studies the cross-sectional dimension of Fisher’s debt-de(cid:29)ation mechanism that triggers endogenous Sudden Stop crises(cid:22)i.e., episodes with large reversals in the current account. Analyzing microdata from Mexico, we show that this dimension has macroeconomic implications that operate via opposing e(cid:27)ects. First, an amplifying e(cid:27)ect by which households with high leverage (cid:28)re-sale their assets during crises, increasing downward pressure on asset prices. Second, a dampening e(cid:27)ect by which wealthy households with low leverage buy depressed assets, relieving downward pressure on asset prices. As a result, the role of inequality during crises is ambiguous. We conduct a quantitative analysis using a calibrated small open economy, asset-pricing model with heterogeneous agents and aggregate risk to measure the e(cid:27)ects of inequality during crises. The model suggests that economies with lower inequality, whether due to reduced idiosyncratic risk or wealth redistribution across agents, experience less severe crises, as observed in the data. Keywords: Inequality, Sudden Stops, Debt-de(cid:29)ation, Asset-pricing, Household leverage JEL: D31, E21, E44, F32, F41, G01 ⋆Correspondence: S. Villalvazo (Sergio.Villalvazo-Martin@frb.gov), Federal Reserve Board, 20th Street andConstitutionAvenue,NW,Washington,DC20551. ThispaperisbasedonmydissertationattheUniversity of Pennsylvania. I am immensely grateful to my advisers, Enrique G. Mendoza and Frank Schorfheide, and to my dissertation committee, Alessandro Dovis and Dirk Krueger. For useful comments and suggestions, IthankBora§anAruoba, HaroldCole, JesusFernandez-Villaverde, PerKrusell, FedericoMandelman, Guillermo Ordoæez, Ignacio Presno, Victor Rios-Rull, Felipe E. Sa(cid:30)e, John Shea, my discussants, Dan Cao, CarlosEsquivelandAndresSchneider,andseminarparticipantsattheMoney-MacroClubattheUniversity of Pennsylvania, the Atlanta Fed, the Federal Reserve Board, ITAM’s Alumni Conference, and the NBER IFM group. I am grateful to the Federal Reserve Bank of Atlanta for their hospitality. The views expressed in this paper are solely the responsibility of the author and should not be interpreted as re(cid:29)ecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. All remaining errors are my own. Declarations of interest: none. ∗Corresponding author Email address: sergio.villalvazo-martin@frb.gov (Sergio Villalvazo)

1. Introduction Over the past four decades, 58 (cid:28)nancial crises of the Sudden Stop type have occurred across both emerging and developed economies.1 These episodes have sparked a substantial literature studying Sudden Stops through the lens of models with (cid:28)nancial frictions(cid:22) typicallywithinrepresentativeagentframeworks. However,suchmodelsmissacriticalaspect of (cid:28)nancial crises: they do not account for the heterogeneity in households’ balance sheets and (cid:28)nancial positions. In this paper, we argue that the distribution of wealth and leverage acrosshouseholdsplaysacentralroleinshapingthemacroeconomice(cid:27)ectsof(cid:28)nancialcrises. This paper examines the cross-sectional dimension of the debt-de(cid:29)ation mechanism introduced by Fisher (1933), which works as follows. After a negative aggregate shock that tightens the (cid:28)nancial conditions, (cid:28)nancially constrained agents sell part of their collateralizable assets, triggering a decline in asset prices. This price drop further deteriorates (cid:28)nancial conditions, pushing more agents into binding credit constraints (extensive margin) and forcing already-constrained agents to liquidate larger asset positions (intensive margin). This feedback loop deepens the asset price collapse and tightens (cid:28)nancial conditions even more.2 Our main insight is that the cross-sectional dimension of the debt-de(cid:29)ation mechanism plays a key role in the macroeconomic dynamics of Sudden Stops through two opposing channels: (1) a crisis-dampening e(cid:27)ect, where unconstrained wealthy households buy depressed assets (cid:28)re-sold by (cid:28)nancially constrained households, mitigating the decline in prices and weakening the debt-de(cid:29)ation spiral; and (2) a crisis-amplifying e(cid:27)ect, where indebted households, once constrained following asset price declines, must also (cid:28)re-sell assets, further depressing prices and tightening (cid:28)nancial conditions. The net impact of inequality on crisis severity is thus ambiguous due to the tension between these forces. Empirical evidence supports this perspective. Panel micro-data from Mexico during the 2009 crisis reveal that wealthy households with low leverage increased their asset holdings 1 Sudden Stops are episodes with large reversals in the current account. See Bianchi and Mendoza (2020) for a recent survey and review of the stylized facts of Sudden Stops. 2 This mechanism is quantitatively signi(cid:28)cant. In the calibrated stationary model, 10 percent of the households are constrained and own 7.7 percent of the assets with a consumption share of 9.0 percent, while 75.9 percent of the household are unconstrained indebted and hold 88.1 percent of the assets with a consumption share of 78.1 percent. 2

by 61.4 percent, while similarly wealthy but highly leveraged households saw their assets fall by 36.6 percent(cid:22)highlighting the sharply divergent dynamics across households during crises. Furthermore, Figure 1 shows descriptive evidence that Sudden Stop crises are more severe in economies with higher income inequality. Hence, cross-country data show larger contractions in consumption and GDP during crises in more unequal economies. Figure 1: Severity of Sudden Stops and inequality (a) Change in consumption (b) Change in GDP Note: Triangle (circle) markers correspond to advanced (emerging) economies. Dates of Sudden Stop episodes come from Bianchi and Mendoza (2020). Gini index measures income inequality; larger numbers mean larger inequality. ∗∗p<0.05,∗p<0.1. Source: Own calculations with data from the World Bank. To examine these dynamics quantitatively, we develop a small open economy model with heterogeneous agents, incomplete markets, aggregate risk, and occasionally-binding collateral constraints. The model includes risk-free bonds and collateralizable risky assets, with households facing persistent idiosyncratic risk in both labor income and dividends. A key feature is the risk-wealth tradeo(cid:27): holding more risky assets relaxes borrowing constraints and smooths consumption, but also increases exposure to income volatility, creating incentives for precautionary savings in safer instruments. This dynamic gives rise to a realistic wealth and leverage distribution, where some households accumulate assets and transition from borrowing to saving. In a version of the model calibrated to an emerging economy (Mexico), the crisisdampeninge(cid:27)ectdominatesrelativetotherepresentativeagentmodel: unconstrainedhouseholds absorb (cid:28)re-sales, helping to stabilize asset prices. However, the model with hetero- 3

geneity generates deeper and more persistent declines in consumption, along with prolonged current account reversals. In contrast, when comparing two economies with di(cid:27)erent nondegenerate levels of inequality(cid:22)the baseline emerging economy and a more equal advanced economy calibration in which idiosyncratic dividend risk is removed but labor income risk remains(cid:22)crises are milder and less frequent in the more equal economy. Moreover, an impulse response analysis, comparing the e(cid:27)ects of simultaneous interest rate and total factor productivity shocks, reveals that in the baseline emerging economy calibration with a perfectly equal initial distribution (perfect redistribution) generates declines in consumption and asset prices that are approximately 0.5 percentage points smaller than in the baseline emerging economy with the stationary distribution as initial condition. Overall, the model suggests that economies with lower inequality, whether due to reduced idiosyncratic risk (as seen in advanced versus emerging economy calibrations) or wealth redistribution across agents (with identical idiosyncratic risk processes but di(cid:27)erent initial conditions), experience less severe Sudden Stop crises, (cid:28)ndings that align with empirical observations. Finally, the paper examines how a redistributive tax policy a(cid:27)ects the dynamics of (cid:28)nancial crises. Implementing a constant tax on dividend income, aimed at reducing wealth inequality, leads to less severe Sudden Stops through a general equilibrium e(cid:27)ect. The tax lowers dividend returns and weakens households’ incentives for precautionary savings by reducing their exposure to dividend risk. As a result, households demand fewer assets, pushing down equilibrium asset prices and reducing debt capacity. With smaller debt positions in normal times, crises involve milder bond adjustments and smaller consumption drops. A welfare analysis further shows that the dividend tax not only mitigates crisis severity but also improves welfare on average, generating a gain equivalent to 2.8 percent of consumption. However, the e(cid:27)ects are heterogeneous: about three-quarters of households bene(cid:28)t, while the more leveraged and wealthier households experience welfare losses due to lower asset prices, declines in net worth, and tighter (cid:28)nancial conditions. After reviewing the literature in Section 2, in Section 3 we describe the empirical descriptive evidence on the cross-sectional e(cid:27)ects of the debt-de(cid:29)ation mechanism. The proposed model is described in Section 4. Section 5 describes the cross-sectional e(cid:27)ects through the lens of the model. Section 6 presents the quantitative analysis, and Section 7 concludes. 4

2. Related Literature This paper contributes to several strands in the economics literature. Firstly, in the broader literature on (cid:28)nancial crises, representative agent models with occasionally-binding credit constraints, as pioneered by Mendoza (2010), have been crucial in understanding the dynamics of Sudden Stops and economic downturns. Further work, such as Mendoza and Smith (2006), Bianchi and Mendoza (2018) and Jeanne and Korinek (2018), explores pecuniary externalities in (cid:28)nancial crises, while Lorenzoni (2008), Bianchi (2011), and Benigno et al. (2013) examine the impact of collateral constraints on over-borrowing and the design of optimal macroprudential policies. Our paper extends this literature by focusing on the cross-sectionale(cid:27)ectsofthedebt-de(cid:29)ationmechanism. Unlikepreviousmodels, weintroduce marketincompletenessattheindividuallevelinamodelwithaggregateriskandanalyzehow household distributions of bonds, assets, and individual productivity in(cid:29)uence asset prices, portfolio choices, and consumption dynamics during crises. Asecondstrandoftheliteratureexploresassetpricesinclosedeconomieswithincomplete individual markets. Aiyagari and Gertler (1991), Heaton and Lucas (1996), Aiyagari and Gertler (1999) and Storesletten, Telmer, and Yaron (2007) examine the equity premium puzzle (Mehra and Prescott 1985) in a closed economy with bonds, stocks, adjustment costs, and labor income risk. More recently, Gomez (2025) studies the interplay between asset prices and wealth inequality in a model with two types of agents with di(cid:27)erent exposures to shocks. Our paper complements this literature by proposing a model with (cid:28)nancial frictions and heterogeneous agents that can generate a high equity premium. Additionally, we derive a cross-sectional decomposition of the equity premium into constraint, individual risk, risk persistence, trading cost, and short-sales e(cid:27)ects. A third line of research explores macroeconomic models with individual heterogeneity, starting with Krusell and Smith (1997), who developed quantitative tools to analyze economies where market prices depend on the distribution of agents, not just on the mean aggregate state. Mendoza, Quadrini, and Rios-Rull (2009), Kaplan and Violante (2014), Guerrieri and Lorenzoni (2017) and Kaplan, Mitman, and Violante (2020) study the role of 5

heterogeneity in models with (cid:28)nancial frictions.3 Extending this literature, this paper develops a small open economy model with heterogeneous agents facing a loan-to-value credit constraint. Unlikethewealthyhand-to-mouthframeworkintroducedbyKaplanandViolante (2014), due to the LtV constraint, households in our model can become credit-constrained at varying levels of asset holdings, depending on their leverage. Moreover, this constraint generates a pecuniary externality, as households fail to internalize how their decisions in(cid:29)uence both their own borrowing limits and those of others through changes in the endogenous aggregate asset price. This feature of the model generates a debt-de(cid:29)ation spiral during (cid:28)nancial crises and allows us to study Sudden Stops. Finally, in a series of empirical papers that study the relationship between income inequality, capital (cid:29)ows and crises, Bordo and Meissner (2012), Morelli and Atkinson (2015), Liu, Spiegel, and Zhang (2023), and Paul (2023) examine the predictive power of rising income inequality for (cid:28)nancial crises with mixed conclusions. Lastly, Guntin, Ottonello, and Perez (2023) use microdata to show that, in line with the permanent income hypothesis, high-income households with liquid assets sharply reduce consumption during large aggregate consumption adjustments.4 The present paper adds to the literature by using the proposed model to study the responses on asset prices and macroeconomic aggregates for economies with di(cid:27)erent degrees of inequality whether due to reduced idiosyncratic risk or wealth redistribution across agents. 3 On a related literature that studies exchange rates, De Ferra, Mitman, and Romei (2020), Auclert et al. (2021), and Ferrante and Gornemann (2022) study how depreciation ampli(cid:28)es household spending via the real income channel and its distributional e(cid:27)ects. Biljanovska and Vardoulakis (2024) show that distinguishing between workers and entrepreneurs introduces a distributive externality in macroprudential policy. Empirically, ? (cid:28)nd that mortgage revaluations during exchange rate depreciation raise household default rates and reduce consumption, based on Hungarian data. 4 On the modeling side, Kumhof, RanciŁre, and Winant (2015) examine how changes in the top income distribution a(cid:27)ect household leverage and crises. Additionally, Hong (2023) examine excess consumption volatilityinemergingeconomies,RoldÆn(2020)analyzeshowincomeinequalityin(cid:29)uencessovereignspreads, Guo, Ottonello, and Perez (2023) explore monetary policy’s distributional e(cid:27)ects in open economies with heterogeneoushouseholds,Berger,Bocola,andDovis(2023)quantifytheimpactofimperfectrisksharingon aggregate (cid:29)uctuations, Bayer, Born, and Luetticke (2024) analyze how much inequality in the U.S. matters forbusinesscycles. Regardingheterogeneityonthe(cid:28)rmside,Benguria,Matsumoto,andSa(cid:30)e(2022)explore the creative destruction framework to jointly study productivity and trade dynamics during (cid:28)nancial crisis, andLanteriandRampini(2023)studycapitalallocatione(cid:30)ciencyineconomieswithpecuniaryexternalities and heterogeneous (cid:28)rms. 6

3. The Cross-Sectional E(cid:27)ects in the Data This section (cid:28)rst describes the data used to show descriptive evidence that the crosssectional e(cid:27)ects of the debt-de(cid:29)ation mechanism are empirically relevant. Then, sorting households according to their net wealth and leverage ratio, we obtain the changes in their individual asset values during the 2009 Sudden Stop. The (cid:28)ndings indicate that households in the highest decile of both wealth and leverage ratio experienced the largest decline in asset holdings, while low-leverage households exhibited the greatest accumulation of assets. 3.1. Description of the Data We use data from the Mexican Family Life Survey (MxFLS) for the three available waves: 2002, 2005, and 2009. The MxFLS is a longitudinal household survey that collected information from a representative sample of approximately 8,400 households in 150 localities throughout Mexico. The survey covers information on expenditures, income, assets, and liabilities. The MxFLS is representative at the national, urban-rural, and regional levels. The sample selection criterion we use corresponds to households that answered the survey in all three waves. The resulting subsample includes 78 percent of the households in 2005. The next subsection will analyze the asset holding dynamics for households grouped by their level of leverage ratio, de(cid:28)ned as the household’s total debt over the sum of the household’s total assets, and net wealth, de(cid:28)ned as the household’s total assets minus the household’s total debt.5 3.2. Di(cid:27)erentiated Individual E(cid:27)ects In 2008-09, the Mexican economy, like many small open economies, faced a severe Sudden Stop. Aggregate data indicate a current account reversal of 1.5 percentage points relative to GDP, a 7 percent decline in per capita consumption, and housing prices falling 4 percent below their pre-crisis trend by 2010.6 Additionally, data from the MxFLS survey reveal that between 2005 and 2009, the total value of households’ gross assets decreased at an 5 As a representativeness check, per capita private consumption declined by 5.1 percent in the National Accounts and by 5.7 percent in the household survey between 2005 and 2009. See the Online Appendix for more details on the distribution of households in 2005 and for a detailed description of the survey, see Rubalcava and Teruel (2003, 2006, 2013). 6 For a detailed overview of the aggregate time series, refer to the Online Appendix. 7

annualized rate of 0.5 percent. However, the impact of the crisis varied across households, largely depending on the composition of their balance sheets. Regarding the evolution of the household leverage ratio distribution before, during, and after the crisis. We classify households as (cid:28)nancial savers if they report positive holdings of (cid:28)nancial assets, as indebted but unconstrained if their leverage ratio falls below the 90th percentile (0.168 in 2005), and as (cid:28)nancially constrained if their leverage ratio exceeds this threshold. We use the 90th percentile following that from 2004 to 2008, the average delinquency rate for commercial bank household credit is 10.3 percent. Between 2002 and 2005, prior to the crisis, the share of (cid:28)nancial savers rose by 1.7 percentage points, while the share of (cid:28)nancially constrained households declined by 2.3 percentage points. However, from 2005 to2009, asthecrisisunfoldedandaggregateliquiditycontracted, theshareof(cid:28)nancialsavers dropped signi(cid:28)cantly by 5.0 percentage points likely re(cid:29)ecting the need to draw down savings to smooth consumption. Over the same period, the share of (cid:28)nancially constrained households increased by 1.7 percentage points, consistent with tightening (cid:28)nancial conditions. Additionally, Table 1 shows descriptive evidence of the di(cid:27)erentiated individual e(cid:27)ects. Speci(cid:28)cally, it shows the annualized median percent change in the real value of real estate (de(cid:29)ated with an aggregate house price index) owned by households from 2005 to 2009 relative to the average and sorted according to their net wealth and leverage ratio in 2009.7 Wealthy households correspond to the top decile of net wealth, and the (cid:28)nancially constrained households correspond to the top decile of the leverage ratio. As shown in the table, the real estate held by wealthy households declines as leverage increases. Speci(cid:28)cally, the wealthy low-leveraged households (top-right cell) increased their real estate the most, by 61.4 percent. This descriptive evidence supports the dampening e(cid:27)ects from the cross-sectional dimension, where declining asset prices allow wealthy, unconstrained agents to increase their asset positions. Assuming no creation or destruction of real estate, the increase in assets held by uncon- 7 The survey data correspond to the value of real estate. To obtain the quantity change, we de(cid:29)ated the value change with an aggregate house price index. To sort the households with zero leverage we de(cid:28)ned an auxiliary (cid:28)nancial negative savings leverage variable where we replaced the zero debt with the negative (cid:28)nancial savings. In the Online Appendix we show evidence that these dynamics are not driven by a mean reversion mechanism using the surveys from 2002 and 2005. 8

strained wealthy households implies that they were purchasing assets from other households, who were therefore selling. Hence, the amplifying e(cid:27)ect originates from households nearing (cid:28)nancial constraints; once triggered, these households become (cid:28)nancially constrained and further exacerbate the downward pressure on asset prices. The right column in Table 1 suggests that wealthy, (cid:28)nancially constrained households(cid:22)those in the top deciles of both net wealth and leverage ratio(cid:22)experienced the largest asset (cid:28)re-sales, reducing their holdings by 36.6 percent, thus intensifying the downward pressure on prices. Additionally, wealthy but (cid:28)nancially vulnerable households(cid:22)those in the top decile of net wealth and the ninth decile of leverage ratio(cid:22)also engaged in (cid:28)re-sales as (cid:28)nancial conditions worsened, though to a lesser extent. This descriptive evidence supports the amplifying e(cid:27)ects from the crosssectional dimension, where wealthy, highly leveraged households reduce their asset positions, further driving down asset prices. Table 1: Median annualized percent change in real value of real estate by deciles, 2005(cid:21)09 Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII 0.0 61.4 VIII 1.5 31.9 IX -1.7 -15.0 X 0.0 -36.6 Source: MxFLS. Having documented stylized facts about households’ cross-section, we describe the proposed model that accounts for households’ balance sheet heterogeneity in the next section. 4. Model The proposed framework is a Bewley model of a small open economy with international bonds, domestic equity, an endogenous occasionally-binding constraint and aggregate risk. 4.1. Environment Time is discrete and in(cid:28)nite: t = 0,...,∞. The economy is populated by a unit measure of households. There are two (cid:28)nancial assets: a one-period risk-free international bond that households can trade with the rest of the world and a risky domestic asset (land) that is 9

tradable only between households and is subject to a trading cost.8 Borrowing is subject to anLtVcollateralconstraintbywhichhouseholds’internationaldebtcannotexceedafraction of the market value of their assets(cid:22)i.e., the domestic asset is collateralizable (see the Online Appendix for a micro-foundation of the collateral constraint). Regarding the (cid:28)nancial market’s structure in the economy, markets are incomplete at the aggregate and individual levels. With respect to aggregate risk, the economy is subject to aggregate shocks that determine the international interest rate and total factor productivity. Concerningindividualrisk, householdsfacenon-insurableidiosyncraticlaborincomeriskand dividend income risk. The latter risk means that households buy ex-ante identical shares of the risky domestic asset but get ex-post heterogeneity in the return.9 4.2. Households There is a continuum unit measure of households. Each household i ∈ [0,1] maximizes (cid:34) (cid:35) ∞ (cid:88) E βtu(ci) , (1) 0 t t=0 where ci is the consumption of household i, β ∈ (0,1) is the common discount factor, t and the utility function, u(·), has a common constant relative risk aversion (CRRA) form. Households have access to the international bond market and the domestic asset market. However, since debt markets are imperfect, only secured debt is available, and households’ domestic assets serve as collateral. At the beginning of the period, each household holds bi t risk-freeinternationalbondsandai sharesoftheriskydomestic assetthathasanendogenous t price q and pays a dividend A di. The household receives labor endowment income A wi and t t t t t uses funds to buy consumption goods ci, bonds to carry for the next period at an exogenous t priceequaltotheinverseofthegrossinternationalrateR , andassetholdingstocarryforthe t 8 The assumption of only domestic trading follows the representative agent literature (see Bianchi and Mendoza (2018) and Jeanne and Korinek (2018)) but could be relaxed to allow foreign ownership up to a certain percentage of the shares in the economy. With an exogenous foreign demand for domestic shares, asset prices could become more volatile. See the Online Appendix for an impulse response analysis after a permanent shock in which foreigners sell domestic asset holdings. 9 Evidence of a similar individual return on wealth is documented by Fagereng et al. (2020), and related individualcapitalincomeriskhasbeenusedbyAngeletos(2007),Mendoza,Quadrini,andRios-Rull(2009), Benhabib, Bisin, and Zhu (2011), and Hubmer, Krusell, and Smith Jr (2020). 10

next period, subject to a quadratic trading cost of the form Φ(ai ,ai) = ϕ(ai −ai)2. This t+1 t 2 t+1 t cost re(cid:29)ects that trading the domestic asset requires a higher level of (cid:28)nancial knowledge relative to the bond market and that physical assets are relatively less liquid than bonds.10 Lastly, A corresponds to the aggregate level of total factor productivity. The household’s t budget constraint is ci +R−1bi +q (ai +Φ(ai ,ai)) = A wi +ai(q +A di)+bi. (2) t t t+1 t t+1 t+1 t t t t t t t t Households face an LtV constraint that limits their ability to leverage foreign debt on domestic asset holdings. Next-period debt (negative bonds) cannot exceed a constant fraction κ of the market value of asset holdings. The collateral constraint is R−1bi ≥ −κq ai . (3) t t+1 t t+1 In addition, there is a short-sales constraint on the risky asset ai ≥ 0.11 Note that the t+1 portfolio choice problem is well de(cid:28)ned, given the combination of the trading costs in the asset market and the LtV debt constraint. Lastly, the income of households is composed of an idiosyncratic and an aggregate part, as in Benhabib, Bisin, and Zhu (2015). The individual wage takes the form wi = ϵi,ww¯, and t t the individual rate of return di = ϵi,dd ¯ , where {ϵi,w,ϵi,d} correspond to the idiosyncratic risk t t t t ¯ components, which will be speci(cid:28)ed in the next subsection, and {w¯,d} correspond to the aggregate, exogenous, and constant components. 10 Similar to the wealthy hand-to-mouth literature introduced by Kaplan and Violante (2014), the householdsinourmodelhaveaccesstotwoassetsthatdi(cid:27)erintheirliquidity. However,inourframeworktheLtV constraintgeneratesanadditionalmarginbywhicheachhouseholdcana(cid:27)ecttheirdebtcapacitybychoosing di(cid:27)erent asset positions. This constraint generates a pecuniary externality, as households fail to internalize how their decisions in(cid:29)uence both their own borrowing limits and those of others through changes in the aggregate asset price. This feature of the model generates a debt-de(cid:29)ation spiral during (cid:28)nancial crises. 11 The short-sales constraint is needed to ensure that the state space of asset holdings is compact and that the LtV constraint is not irrelevant. If unlimited short selling of assets were possible, households could always undo the e(cid:27)ect of Equation 3. 11

4.3. Exogenous Stochastic Processes The economy is exposed to two aggregate shocks. The process for the international interest rate is R = ϵRR ¯ and log(ϵR) = ρ log(ϵR ) + ηR, with ηR ∼ N(0,σ2), and the t t t R t−1 t t R process for the total factor productivity is A = ϵAA ¯ and log(ϵA) = ρ log(ϵA ) + ηA, t t t A t−1 t with ηA ∼ N(0,σ2). Regarding the individual shocks, the individual wage takes the form t A wi = ϵi,ww¯ and log(ϵi,w) = ρ log(ϵi,w ) + ηi,w , with ηi,w ∼ N(0,σ2), and the individual t t t w t−1 t t w dividendtakestheformdi = ϵi,dd ¯ andlog(ϵi,d) = ρ log(ϵi,d )+ηi,d ,withηi,d ∼ N(0,σ2). Note t t t d t−1 t t d that the idiosyncratic labor and dividend risk that households face does not have aggregate 1 1 1 1 implications on the returns:12 (cid:82) didi = (cid:82) ϵi,dd ¯ di = d ¯ and (cid:82) widi = (cid:82) ϵi,ww¯di = w¯. t t t t 0 0 0 0 4.4. Closing the Domestic Asset Market ¯ The domestic asset is in constant positive net supply equal to K, and in equilibrium, it is equal to the total asset holdings (demand) of households. Hence, market clearing in the 1 asset market requires (cid:82) aidi = K ¯ for every t. t 0 4.5. Recursive Formulation To characterize the problem of the agents and the equilibrium in recursive form, we start by de(cid:28)ning the states of the economy. Households are heterogeneous in their current holding of bonds, assets, idiosyncratic labor, and dividend productivity. The individual states are (b,a,ϵw,ϵd). We need to keep track of both the individual bonds and assets, given the asset trading costs and the imperfect debt market. Let Ω(b,a,ϵw,ϵd) be the endogenous distribution of households according to their bonds, assets, and individual productivities. Regardingaggregatestates, toforecastassetprices, householdsneedtoknowthedistribution of wealth. Hence, the aggregate states correspond to the endogenous distribution Ω, the exogenous shock to the international interest rate ϵR, and the exogenous shock to the total factor productivity ϵA. Letting the superscript ′ correspond to the variables in the next 12 However, as noted in Hubmer, Krusell, and Smith Jr (2020), the idiosyncratic dividend risk will impact theaggregateendowment,whichwillbeafunctionofhouseholds’distributionofassetsanddividendreturns. 12

period, the recursive problem of a household becomes v(b,a,ϵw,ϵd,ϵR,ϵA,Ω) = max u(c)+βE[v(b′,a′,ϵw′,ϵd′,ϵR′,ϵA′,Ω′)] s.t. {c,b′,a′≥0} c+(ϵRR ¯ )−1b′ +q(Ω,ϵR,ϵA)(a′ +Φ(a′,a)) = ϵAA ¯ ϵww¯ +a(q(Ω,ϵR,ϵA)+ϵAA ¯ ϵdd ¯ )+b, (ϵRR ¯ )−1b′ ≥ −κq(Ω,ϵR,ϵA)a′, ϕ Φ(a′,a) = (a′ −a)2, 2 Ω′ = HΩ(Ω,ϵR,ϵA), (4) where HΩ(·) corresponds to the aggregate law of motion of the distribution of households, and the individual multipliers on the budget constraint, the collateral constraint and the short sales constraint are λ(·), µ(·) and ψ(·), respectively. The de(cid:28)nition of the recursive competitive equilibrium can be found in the Online Appendix. 5. The Cross-Sectional E(cid:27)ects in the Model In this section, we study the cross-sectional e(cid:27)ects on the credit and equity channel of the economy. For tractability, we will abstract from aggregate risk and keep the interest rate ¯ ¯ and the total factor productivity constant at their average levels, R and A, respectively. 5.1. Market Incompleteness and Risk Exposure Householdsareexposedtotwosourcesofnon-insurableidiosyncraticriskthathavedi(cid:27)erent equilibrium implications. Note that the standard Bewley non-insurable persistent labor income risk, ϵw, together with the constant aggregate labor income endowment assumption implies a (cid:28)xed labor risk exposure, which means that the exposure to labor earnings risk is independent of households’ decisions. In contrast, the idiosyncratic persistent dividend productivity, ϵd, allows households to change future risk exposure by changing the next-period holdings of the asset. This endogenous dividend risk exposure, combined with the LtV collateral constraint, generates a risk-wealth tradeo(cid:27). To see this point, (cid:28)rst, note that when households are in an adverse individual state, they can smooth consumption in two ways(cid:22)by lowering their bond holdings b′ (if these are already negative, this means borrow more) or by reducing their asset 13

holdings a′. Given the (cid:28)nancial frictions in the debt market (see Equation 3), to have credit capacity and hence borrow, the household needs (cid:28)rst to buy domestic assets. Note that although the current dividend return is given since the current asset holdings are (cid:28)xed (they are an individual state variable), the household chooses how much future exposure to have by choosing the next-period asset holdings a′. Because the (cid:29)ow income of the household is given by FI(a,ϵw,ϵd) = A ¯ ϵww¯ +aA ¯ ϵdd ¯ , with independent idiosyncratic risks its variance is V[FI(a,ϵw,ϵd)] = (A ¯ w¯)2σ2 +a2(A ¯ d ¯ )2σ2 , which is a convex function with respect to asset ϵw ϵd holdings. This convexity translates into more income volatility for asset-rich households. This property of (cid:29)ow income gives rise to the risk-wealth tradeo(cid:27) associated with acquiring more assets. On one hand, households bene(cid:28)t from a higher debt capacity (Equation 3), which facilitates greater consumption smoothing and reduces consumption volatility. This allows for lower precautionary savings. On the other hand, accumulating assets also exposes households to greater future income risk, increasing consumption volatility and thereby strengthening the incentive for precautionary savings. In equilibrium, asset-poor households with debt tend to increase their borrowing as they acquire more assets. In contrast, households earning high dividend returns begin to deleverage once they become asset-rich, as precautionary saving motives become more prominent, and some households eventually transition into net savers due to the rising income risk. To better understand this mechanism, Figure 2 shows the policy functions and the nonlinearities generated in the model. In the upper row of Figure 2, the solid lines correspond to the bond policy for the high- (low-) dividend shock in blue (red) and the average labor income shock as a function of the current asset holdings in panel (a) and current bond holdings in panel (b). Additionally, the colored dashed lines represent the corresponding debt limits, and the black dashed lines correspond to the bottom 1 and top 99 percentiles of bond and asset holdings obtained from the model’s simulated cross-section. Panel (a) shows that for low-dividend shocks (red lines), a household lowers its bond holdings (or gets more debt) as it increases its asset holdings. In contrast, the risk-wealth tradeo(cid:27) generates the convex form of the bond policy for high-dividend shocks (blue lines). For asset-poor households, as they increase their assets, they also lower their bond holdings (or get more debt if the holdings are negative), and there is a certain level for which the dividend risk exposure overcomes 14

the bene(cid:28)t from more debt capacity that makes households increase their bond holdings. This behavior generates unconstrained wealthy households, which endogenously have a diversi(cid:28)ed portfolio, whereby asset-rich households end up holding both positive international bonds and domestic assets.13 In panel (b) we can see the standard bond policies under an occasionally-binding debt limit: the LtV constraint becomes binding when households accumulate enough debt. Regarding the middle row of the (cid:28)gure, in panel (c) we can see the asset policy function that is highly linear and behaves as expected: for high-dividend shocks, households accumulate more assets, and for low-dividend shocks, households decumulate assets. With respect to the cross-sectional (cid:28)re-sales in the model, in panel (d) we can see that households accumulate less assets as they increase their debt holdings. However, this relation is highly strengthened (households incur (cid:28)re-sales) when the debt limit becomes binding. In Figure 2(e), we show the dynamics of the portfolio choices of a hypothetical household that has zero assets and bonds in period one and draws low dividend and wage shocks for 20 periods, then draws high dividend and wage shocks from period 21 to 180 and draws low shocksfromperiod181onward. The(cid:28)gureshowsthatinthe(cid:28)rst20periods, thehouseholdis asset-poor and hand-to-mouth, then from period 21 to period 100, the household transitions to being wealthy hand-to-mouth as they begin accumulating assets while simultaneously taking on debt, keeping their debt at the maximum level (the debt limit). From period 100 onward, the precautionary savings motives becomes stronger and the household starts accumulating more debt but at a lower pace than the accumulation of assets, hence they become unconstrained. This behavior continuous and eventually the household starts to deleverageandbyperiod150becomesasaverinbonds. Inperiod181, thehouseholdgetsthe low idiosyncratic shocks and starts to decrease both asset and bond positions, with a faster bond decline due to the asset transaction costs. At around period 190, the household hits 13 Similar tradeo(cid:27)s have been examined in the literature, notably by Mendoza, Quadrini, and Rios-Rull (2009)andBenhabib, Bisin, andZhu(2011), butthroughdi(cid:27)erentmechanisms. Ourapproachdepartsfrom these studies by combining persistent dividend risk with a loan-to-value constraint, enabling the stationary model to produce an empirically plausible distribution of constrained households, (cid:28)nancially vulnerable borrowers,andsaversholdingpositivebondpositions. Agraphicalanalysisoftheremainingpolicyfunctions for the calibrated stationary model is provided in the Online Appendix. 15

Figure 2: Stationary Bond and Asset Policies and Simulated Dynamics 0.1 0.1 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 -0.5 0 2 4 6 8 -0.4 -0.2 0 (a) Bond Decision Rule (b) Bond Decision Rule 1 8 6 0.8 4 0.6 2 0 0.4 0 2 4 6 8 -0.4 -0.2 0 (c) Asset Decision Rule (d) Asset Decision Rule 12 10 8 6 4 2 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 (e) Simulated Dynamics Note: The upper (middle) row corresponds to the bond (asset) policies given median asset (bond) holding and mean labor shock ϵ¯w. The solid blue (red) line corresponds to the policy function with the high- (low-) dividend shock, and the dashed blue (red) line corresponds to the debt limit with the high- (low-) dividend shock. Dashed black lines correspond to the bottom 1% and top 99% of bond and asset holdings obtained from the model’s simulated cross-section. Dotted black lines correspond to the 45-degree line. The missing values across the state space correspond to the infeasible individual states that would imply a negative consumption. The bottom row, panel (e), shows the simulated dynamics for a household that has zero assets and bonds in period one and draws low dividend and wage shocks for 20 periods, then draws high dividend and wage shocks from period 21 to 180 and draws low shocks from period 181 onward. the debt constraint and again becomes wealthy hand-to-mouth that keeps on selling assets 16

at a faster pace ((cid:28)re-selling) which in turn decrease their debt capacity. Around period 280, the household has depleted their asset position and becomes asset-poor hand-to-mouth. In summary, this subsection showed the cross-sectional behavior of households through the lens of our model. Households with high-dividend shocks will accumulate more assets, and, while they are still asset poor, they decumulate bonds. Once they become asset rich, because of the risk-wealth tradeo(cid:27), they start accumulating more bonds. This behavior generates wealthy unconstrained households that drive the dampening cross-sectional e(cid:27)ect. Moreover, low-dividend households decumulate assets as they increase their debts, and this relation strengthens (households incur (cid:28)re-sales) when the debt limit is reached, driving the strength of the amplifying e(cid:27)ect. Note that the representative agent model misses both key e(cid:27)ects. First, in the absence of idiosyncratic shocks, all households behave identically(cid:22) either wanting to buy or sell assets(cid:22)but actual asset holdings remain unchanged. Second, in the representative agent model, the average debt constraint multiplier will be the same as the individual debt multiplier. In contrast, in the heterogeneous agents model, even if only a small fraction of households are constrained, their individual multipliers can be much larger due to their individual states, amplifying the aggregate e(cid:27)ect. 5.2. Financial Premia In this subsection, we study the e(cid:27)ects that households’ balance sheet heterogeneity introduces to (cid:28)nancial premia. Speci(cid:28)cally, we analyze the cross-sectional dimension of the debt-de(cid:29)ation mechanism in terms of the external (cid:28)nancing premium and equity premium at the individual and aggregate levels. For simplicity, we omit state variables and reintroduce the superscript i to identify household-speci(cid:28)c variables. Let λi, µi, and ψi be the individual multipliers on the budget constraint, the collateral constraint, and the short-sales constraint, respectively, and let µ˜i = µi and ψ ˜i = ψi . Lastly, let the fraction I ¯ ∈ [0,1] refer to λi λi the households that are credit constrained and, without loss of generality, sort by µ˜i the ¯ constrained households from 0 to I. Similar to the analysis done by Mendoza and Smith (2006) but for an economy with heterogeneous agents, the (cid:28)rst-order conditions of household i’s problem imply an Euler equation for individual bonds, λiR ¯−1 − µiR ¯−1 = βE[λi′], where µi ≥ 0 and µ˜i = µi ∈ λi 17

[0,1). Let the individual expected e(cid:27)ective interest rate be the inverse of the individual (cid:104) (cid:105)−1 stochastic discount factor E[Ri,eff] = E[SDFi]−1 = E βλi′ . Then, from the previous λi Euler equation, we get an individual expected external (cid:28)nancing premium on debt: µ˜i E[Ri,eff]−R ¯ = R ¯ ≥ 0. (5) 1−µ˜i This individual premium re(cid:29)ects the fact that when the constraint binds (µ˜i > 0), the household would want to borrow more than what the collateral constraint allows. Also, note that the individual premium is increasing in µ˜i, which means that as the constraint tightens, ¯ the household would be willing to pay an interest rate higher than R for more debt. Similarly, from the (cid:28)rst-order conditions of household i’s problem, we obtain the Euler equation for individual assets, q(λi(1+Φi)−κµi)−ψi = βE[λi′(q′ +di′ −q′Φi′)], where Φi 1 2 j corresponds to the partial derivative with respect to argument j. Let d ˜i,′ = di′ −q′Φi′ and 2 (cid:16) (cid:17) the individual return on the risky asset be R ˜i,q = q′+d˜i,′ . Then, from the aforementioned q Euler equation, we get an individual expected equity premium: (cid:16) (cid:17) R ¯ (1−κ)µ˜i −COV[SDFi,R ˜i,q]+Φi −ψ ˜i 1 E[R ˜i,q]−R ¯ = . (6) 1−µ˜i In Equation 6, we see a direct positive e(cid:27)ect on the individual equity premium coming from the collateral constraint: as µ˜i increases, the individual equity premium increases by an additive term that multiplies R ¯ (1−κ) and by a multiplicative factor (1/(1−µ˜i)). When the collateral constraint binds, a larger equity premium re(cid:29)ects that buying an extra unit of the asset provides an additional bene(cid:28)t since this additional unit also relaxes the constraint. However, this additional bene(cid:28)t is imperfect, since only κ fraction of the assets is pledgeable as collateral. Additionally, there is a positive risk e(cid:27)ect coming from the covariance term, which will become more negative due to the precautionary savings.14 There is an ambiguous e(cid:27)ect coming from the marginal trading costs, Φi. This e(cid:27)ect is expected to be negative for 1 14 This risk e(cid:27)ect also includes the next period’s marginal trading cost e(cid:27)ect that is expected to increase theprecautionarymotives. Theintuitionforthis(cid:28)ndingisthefollowing. Notethatthehouseholdthat,next period, gets a high dividend return will buy more shares. Hence, ai′′ >ai′ ⇒Φi′ <0⇒d˜i,′ >di′. That is, 2 e(cid:27)ectively, the individual dividend risk increases because of the trading costs. 18

(cid:28)nancially constrained households, because when µ˜i > 0, the household will sell assets to smooth consumption and ai′ < ai implies Φi < 0. Lastly, there is a negligible e(cid:27)ect coming 1 from the no short-sales constraint, ψ ˜i. Theaggregateexpectedequityrateofreturn, E[Rq] = E (cid:104) q′+ (cid:82) ai′di′di (cid:105) , canbeobtainedby q (cid:28)rst integrating the individual expected asset returns over all households. Then we use the expected returns derived in Equation 6 to obtain a decomposition of the aggregate expected equity premium: I¯ 1 (cid:90) µ˜i (cid:90) −COV[SDFi,R ˜i,q] E[Rq]−R ¯ = R ¯ (1−κ) di +R ¯ di 1−µ˜i 1−µ˜i 0 0 (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) ConstraintE(cid:27)ect: +I¯and+µ˜ RiskE(cid:27)ect: (cid:16)+" 1 1 1 (cid:90) COV[ai′,di′]di (cid:90) Φi R ¯ (cid:90) −ψ ˜i + + R ¯ 1 di + di. (7) q 1−µ˜i q 1−µ˜i 0 0 0 (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) PersistenceE(cid:27)ect: (cid:16)+" TradingCostE(cid:27)ect: (cid:16)≈0" NoShort-SalesE(cid:27)ect: (cid:16)−" Equation 7 shows that aggregate excess returns can be decomposed into di(cid:27)erent e(cid:27)ects. First, a positive direct e(cid:27)ect coming from the measure of constrained households and from how (cid:16)strongly(cid:17) the constraint binds. Second, the risk e(cid:27)ect coming from the covariance between the individual stochastic discount factor and the individual return on equity (note that the integral becomes a weighted average of the covariances, with larger weights on constrainedhouseholdssinceµ˜i > 0implies1/(1−µ˜i) > 1). Sinceconstrainedhouseholdsare expectedtohavemorenegativecovariancesbecauseoftheirincreasedindividualconsumption volatility and the implied precautionary savings behavior, we expect a positive risk e(cid:27)ect. Third, a positive persistence e(cid:27)ect coming from the covariance between the idiosyncratic dividend return and the asset holdings. Since there is persistence in the idiosyncratic shocks and after a positive dividend shock households are expected to accumulate more assets, we expect this e(cid:27)ect to be positive. Fourth, there is the trading cost e(cid:27)ect(cid:22)again, the weighted 1 (cid:82) average puts more weight on constrained households, and since Φi di = 0, we can expect 1 0 the aggregate e(cid:27)ect to be close to zero and decreasing with respect to ϕ. Fifth, we observe a no short-sales e(cid:27)ect that decreases the equity premium, since households with a binding short-sales constraint contribute to the aggregate demand for assets, with no e(cid:27)ect on the 19

marginal bene(cid:28)t of saving in assets. Finally, the debt-de(cid:29)ation cross-sectional e(cid:27)ects on risk premia operate through two opposing channels. First, the dampening e(cid:27)ect arises when a greater proportion of unconstrained wealthy households are present, reducing the equity premium by mitigating the risk e(cid:27)ect, as these households can better smooth consumption. Conversely, the amplifying e(cid:27)ect occurs when (cid:28)nancially constrained households become more prevalent, leading to a higher equity premium. This increase results from both a larger constraint e(cid:27)ect, driven by a higher ¯ I and a larger risk e(cid:27)ect, as these constrained households experience greater consumption volatility. In the next section, we use the model as a measurement device to quantitatively study the cross-sectional e(cid:27)ects of a Sudden Stop episode. 6. Quantitative Analysis This section presents the quantitative results of the model. Because of the computational intensity of the solution method, we calibrate the parameters using the stationary model without aggregate risk.15 6.1. Calibration To calibrate the model, we use data for Mexico. Table 2 shows the calibrated parameters. Regarding the set of parameters that are calibrated outside of the model, we set the households’riskaversion, ν, equalto2, whichisstandard, andthecollateraldebtfraction, κ, equal to 0.168, which is the 90th percentile of the leverage ratio distribution in 2005, following that from 2004 to 2008, the average delinquency rate for commercial bank household credit is 10 percent. Lastly, the net asset supply is normalized at 1. Then we calibrate by simulation the discount factor β = 0.90 to match the average net foreign asset position relative to GDP for Mexico, equal to -35 percent, and we also calibrate the trading cost parameter ϕ = 3.0 to obtain an average transaction cost of 5 percent, which is consistent with the estimates from Aiyagari and Gertler (1999) and Kaplan and Violante (2014). 15 Since the economy has an endogenous occasionally-binding constraint, the household’s policy functions are highly nonlinear, a global solution method is needed. We use the FiPIt algorithm proposed by Mendoza andVillalvazo(2020)tosolvethehousehold’sproblemcombined,withthestochastic-simulationapproachby Maliar, Maliar, and Valli (2010) and Krusell and Smith (1997) to solve the aggregate uncertainty problem. 20

Table 2: Parameters Parameter Value Source or Target Calibrated outside of the model ν Risk aversion 2 Common in the literature κ Debt fraction of collateral 0.168 90th percentile lev. ratio in 2005 K¯ Net asset supply 1 Normalization Calibrated by simulation β Discount factor 0.90 Average NFA/GDP ratio of -35% ϕ Trading cost 3.0 Average transaction cost of 5% Individual labor income risk w¯ Average wage 0.17 See Section 6.1 ρ Autocorrelation 0.906 w σ Std. dev. (%) 19.8 w Individual dividend income risk d¯ Average dividend yield 0.0425 See Section 6.1 ρ Autocorrelation 0.905 d σ Std. dev. (%) 69.4 d Aggregate interest rate risk and TFP R¯ Average interest rate 1.047 See Section 6.1 ρ Autocorrelation 0.81 R σ Std. dev. (%) 1.9 R σ Std. dev. (%) 0.5 A To estimate the exogenous earning process, we apply the methodology described in Krueger, Mitman, and Perri (2016) using Mexican data. First, we estimate a Mincer logearningsequationwithtime(cid:28)xede(cid:27)ects: log(Yi ) = β′Xi +D +yi ,whereeachobservation a,t a,t t a,t corresponds to an individual i, with quarterly age a and in quarter t. Yi corresponds to the a,t annual income of the person, and the vector of controls Xi includes a cubic polynomial on a,t age, dummy variables for the education level, and a dummy variable that identi(cid:28)es whether the worker is in the informal sector. Finally, D corresponds to the time (cid:28)xed e(cid:27)ects. After t running the regression, we obtain the residuals yi and assume the income risk follows a a,t stationary process with a persistent and transitory component. The stationarity assumption allows us to drop the time dimension, and the income risk model becomes yi = zi +ϵi, zi = ρ zi +ηi,w, ηi,w ∼ (0,σ2), zi ∼ (0,σ2 ), ϵi ∼ (0,σ2). (8) a a a a w a−1 a a w 0 z0 a ϵ In section 6.2.1 we do a model validation for both the stationary and aggregate risk models. 21

Now the objective is to estimate the vector of parameters θ = (ρ ,σ2,σ2 ,σ2). These w w z0 ϵ parameters are identi(cid:28)ed with the following theoretical moments: COV[yi,yi ] ρ = a a−2 , w COV[yi ,yi ] a−1 a−2 σ2 =V[yi ]−ρ−1COV[yi,yi ], ϵ a−1 a a−1 σ2 =V[yi ]−COV[yi,yi ]−σ2, w a−1 a a−2 ϵ σ2 =V[yi]−σ2 . (9) z0 0 ϵ We use data from the National Survey of Employment and Occupation (ENOE) to do an over-identi(cid:28)ed GMM estimation with an identity weighting matrix.16 The ENOE survey is a quarterly household rotating panel with a representative sample of 120,000 households that started in 2005:Q1. Every household is interviewed for (cid:28)ve consecutive quarters, and, each quarter, 20 percent of the sample is replaced. Consistent with the standard practice in the literature, our sample selection criteria are male individuals with ages between 20 and 60 and with positive earnings. We (cid:28)nd that the persistence and variance of the income risk are 0.906 and 0.039, respectively. The estimated persistence is smaller, and the variance is larger, for Mexico compared with the U.S. A reason for this di(cid:27)erence could come from the informal market structure that is common in emerging economies (Leyva and Urrutia 2020). The Mexican labor market is characterized by a high informality rate(cid:22)more than 50 percent informal employment. Since the informal sector is relatively more (cid:29)exible than the formal sector, it could create a less permanent e(cid:27)ect of idiosyncratic shocks. Moreover, Gomes, Iachan, and Santos (2020) (cid:28)nd that informality is associated with more volatile earnings. Finally, the combination of a large informal sector and the lack of unemployment insurance could also cause a higher income risk.17 To explore this reason, we re-estimate the income process with a subsample of only formal employment. As expected, the di(cid:27)erence narrows, althoughthechangeissmall, withapersistenceandvarianceof0.922and0.038, respectively. 16 Notethattojust-identifytheparameters, weneeddataonlyforages(a,a−1,a−2). Sinceweareusing data for 160 quarterly ages, the system is over-identi(cid:28)ed. 17 Bosch and Esteban-Pretel (2015) study the consequences for the labor market of implementing an unemployment bene(cid:28)t system in economies with large informal sectors and (cid:28)nd that an unemployment bene(cid:28)t could increase the formality rate. 22

Given that in the model we do not explore speci(cid:28)c heterogeneity in the labor, we still use as a benchmark the results from the estimates that include all the employment. Lastly, the discretelaborincomeriskprocessisapproximatedusingasymmetrictwo-stateMarkovchain that employs a simple persistence rule following Mendoza (2010). The discretized risk takes the values ϵw ∈ {ϵw = 0.80,ϵw = 1.20}, and the probability that the next-period realization L H of the shock is the same as that of the current period is Pr[ϵw′ = ϵw|ϵw = ϵw] = 0.953 for j j j ∈ {L,H}. The dividend income risk plays a key role in the decision rules of households and drives therisk-wealth tradeo(cid:27) discussedinSection5.1. However, aproperestimationofthisprocess is infeasible due to the lack of available data in most economies.18 Because of the restrictions of the available data for Mexico, we take the following estimation strategy. We jointly esti- ¯ mate the three parameters that characterize the dividend income risk (d,ρ ,σ ) to match the d d leverage ratio distribution of households in 2005. Speci(cid:28)cally, we focus on three distribution statistics: the measure of savers who have (cid:28)nancial assets and no debt, indebted households that have positive debts but are not close to their debt limit, and (cid:28)nancially constrained households that have a leverage ratio above 0.168, which corresponds to the 90th percentile. The model (data) distribution for the three statistics is 14.1 (14.2), 75.9 (75.8), 10.0 (10.0), ¯ respectively, and the calibrated parameters are d = 0.0425, ρ = 0.905 and σ = 0.694. Simd d ilarly to the labor risk, the discrete dividend risk process is approximated using a symmetric two-state Markov chain that employs a simple persistence rule. Hence, the discretized risk takes the values ϵd ∈ {ϵd = 0.31,ϵd = 1.69}, and the probability that the next-period real- L H ization of the shock is the same as that of the current period is Pr[ϵd′ = ϵd|ϵd = ϵd] = 0.9525 j j for j ∈ {L,H}. These estimates imply that the e(cid:27)ective dividend yield (ϵdd ¯ ) households will face can take the following two values in percent: {1.3,7.2}. Lastly, the aggregate wage ¯¯ level, w¯, is set equal to 4dK such that the average household has a total (cid:29)ow income that corresponds to four-(cid:28)fths labor income and one-(cid:28)fth dividend income. The last exogenous process that needs to be estimated corresponds to the international 18 One exception is the work by Fagereng et al. (2020), who estimate the wealth risk using administrative data from Norway and (cid:28)nd that there is high heterogeneity in the wealth returns and that these di(cid:27)erences are highly persistent. 23

interest rate. This process was estimated using data from Kehoe and Ruhl (2009) and Uribe ¯ and Schmitt-GrohØ (2017). The parameter estimates are (R = 1.047,ρ = 0.81,σ = 0.023). R R Similarly,theinterestrateprocessisapproximatedusingasymmetrictwo-stateMarkovchain that employs a simple persistence rule. Hence, the discretized interest rate takes the values R ∈ {R = 1.070, R = 1.024}, and the probability that the next-period realization of H L the interest rate is the same as that of the current period is Pr[R′ = R |R = R ] = 0.905 j j for j ∈ {L,H}. The total factor productivity (TFP) shock is assumed to have a perfect negative correlation with the interest rate shock and standard deviation σ = 0.005. Hence, A whenevertheinterestratetakesthevalueR (R ),theTFPwilltakethevalueofA = 0.995 H L L (A = 1.005). These values are common in the literature of small open economies and are H close to the estimates obtained in studies of the Mexican economy (see Mendoza 2010 and Bianchi 2016, among others). 6.2. Aggregate Risk Model To solve the aggregate risk model, we adapt the nontrivial market clearing algorithm proposed by Krusell and Smith (1997) to a small open economy framework. Speci(cid:28)cally, 1 (cid:82) we use the current aggregate net foreign asset position, B = bidi, and a dummy variable 0 that indicates the current value, high or low, of the interest rate, D , to forecast the next R period’s net foreign asset position, B′. Additionally, to forecast the domestic asset price, q, we also use last period’s asset price, q . This algorithm is computationally intensive since −1 the current market clearing asset price depends on the whole distribution of asset holdings and not only on the aggregate holdings (which are constant). Hence, to obtain a simulated time series, each period we use the aggregate law of motion to forecast the next period’s aggregate net foreign asset position and the next period’s asset price. With these forecasts, we then solve a (cid:28)xed-point problem for every period, which gives as a solution the current equilibrium market clearing price. The solution of the aggregate law of motion is as follows, 24

with all the coe(cid:30)cients statistically signi(cid:28)cant at 1 percent con(cid:28)dence:19 B′ = −0.015+0.807 B +0.004 D , R2 = 0.99, R q = 0.509+0.229 B −0.008 D +0.059 q , R2 = 0.93. (10) R −1 6.2.1. Model Validation In this subsection, we analyze the stationary equilibrium for an economy in which the interest rate is constant at its steady state value of 4.7 percent and TFP is equal to 1(cid:22)i.e., a Bewley economy without aggregate risk, as well as moments from the ergodic distribution from the the model with aggregate risk. In Figure 3, we show the average net wealth, assets, and debts by deciles relative to the median level of each variable for simulated data and observed data in 2005. As we can see in panels (a) and (b), the net wealth and assets distributions generated by the model are very close to the ones obtained from the MxFLS in 2005(cid:22)with the exception of the top deciles. Although, in the model with aggregate risk, the precautionary savings motives deliver slightly lower wealth inequality. Regarding the total debt shown in panel (c), the only decile that is signi(cid:28)cantly di(cid:27)erent is the bottom decile. One possible reason for this di(cid:27)erence is that we do not allow households to default in the model, and households cannot hold more debt than the collateral limit(cid:22)in contrast to the observed data, where households in the bottom decile have negative net wealth. However, for the rest of the deciles, the model does a good job of capturing the inequality in terms of net wealth, total assets, and debt. Moreover, notice that the debt-de(cid:29)ation mechanism a(cid:27)ects a household’s consumption when two things happen. First, the household must be highly leveraged, so when the collateral constraint tightens, the household is close to (or at) the binding region and needs to adjust its asset holdings. Second, the household must have a large debt-to-expenditure ratio, so when it has to deleverage, there is a signi(cid:28)cant e(cid:27)ect on their consumption. As a model validation exercise, Figure 4 shows how well the model replicates the distribution of 19 Wevalidateourresultsusinganalternativeaccuracymeasurefortheaggregatelawsofmotionproposed by Den Haan (2010), we (cid:28)nd that the max (percentile 95) forecast error is 2.8 (1.6) and 1.1 (0.5) for the current account and asset price aggregate laws of motion, respectively. See the Online Appendix for a description of the solution algorithm. 25

Figure 3: Variables relative to the median 25 25 25 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 I IIIIIIV VVIVII VIIIIX X I IIIIIIV VVIVII VIIIIX X I IIIIIIV VVIVII VIIIIX X (a) Net wealth (b) Assets (c) Debt Note: Deciles ordered by net wealth. Blue bars correspond to the distribution of Mexican households in 2005. Red bars correspond to the simulated distribution of the stationary model, while yellow bars correspond to the simulation from the model with aggregate risk. Source: MxFLS. (cid:28)nancially included households (with positive (cid:28)nancial savings and/or debts) with respect to the joint leverage ratio and debt-to-expenditure ratio. In overall terms, the model does a good job of replicating the joint distribution, with a slight underestimation of the measure of households in the top quintile for the leverage ratio and debt-to-expenditure ratio. 6.2.2. Simulation and Event Study of Sudden Stops Using the solution to the aggregate laws of motion, we simulate a panel of 1,000 households for 2,100 periods and drop the (cid:28)rst 100 periods. Table 3 columns (1) and (2) report moments of the main macro aggregates from both the benchmark model with heterogeneous agents and a representative agent version without idiosyncratic risk and a lower leverage limit, κ, which matches the average leverage ratio of 0.12 obtained in the model with heterogeneity. Regarding variable means, the current account as a percentage of GDP (CA/GDP = (B −B )/GDP ) is zero and aggregate consumption is the same for both t t+1 t t models. In the heterogeneous agents model, the net foreign asset position relative to GDP is 5.5 percentage points larger in absolute value, and the asset price is 12 percent higher. Since households do not need to self-insure against idiosyncratic shocks in the representative agent model, there is less precautionary savings and lower demand for the domestic asset. This equilibrium e(cid:27)ect lowers the average asset price, tightening aggregate (cid:28)nancial conditions andloweringthetotaldebt. Regardingstandarddeviations, consumptionvolatilityishigher, and the asset price is about one-third as volatile, in the benchmark heterogeneous agents economy compared with the representative agent economy. This result comes from the larger 26

Figure 4: Joint leverage ratio and debt-to-expenditure ratio distribution 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 I II III IV V I II III IV V I II III IV V (a) Lev. Ratio q=I (b) Lev. Ratio q=II (c) Lev. Ratio q=III 20 20 15 15 10 10 5 5 0 0 I II III IV V I II III IV V (d) Lev. Ratio q=IV (e) Lev. Ratio q=V Note: Joint distribution by quintile. Blue bars correspond to the distribution of Mexican households in 2005. Red bars correspond to the simulated distribution of the stationary model, while yellow bars correspond to the simulation from the model with aggregate risk. Source: MxFLS. consumption adjustments that high-leveraged households have to make in the model with heterogeneity when they get hit by a negative idiosyncratic shock. Because of the risk-wealth tradeo(cid:27) described in Section 5.1, the model does a good job of capturing wealth inequality. The wealth Gini index is 0.61, which is close to the untargeted 2005 estimate for Mexico at 0.73. With respect to the aggregate equity premium, the model generates a high premium of 5.1 percent, which is close to the 6.5 percent estimated in the data by Damodaran (2013). As expected, the risk component contributes the most to the equity premium, about 55.3 percent, while the persistence e(cid:27)ect accounts for 35.9 percent and 8.6 percent corresponds to the constraint e(cid:27)ect. Note that the calibration was done to capture the measure of constrained households in 2005 in the stationary model, equal to 10 percent. Hence, even if only these households have an active debt constraint, there is a signi(cid:28)cant contribution to the aggregate equity premium. This is in contrast to the representative agent model where most of the equity premium is coming from the constraint e(cid:27)ect. 27

Table 3: Simulated statistics (1) (2) (3) (4) Het. Agents Rep. Agent Het. Agents Het. Agents Benchmark Same Mean (σd =0) (τd =0.30) Eme. Eco. Lev. Ratio Adv. Eco. Eme. Eco. Long-run mean CA/GDP (%) 0.00 0.00 0.00 0.00 Consumption 0.22 0.21 0.21 0.22 NFA/GDP (%) -30.17 -24.72 -36.41 -34.51 Leverage ratio 0.123 0.123 0.160 0.146 Asset price 0.52 0.41 0.46 0.47 Standard deviation (%) CA/GDP 0.73 0.05 0.21 0.47 Consumption 1.81 1.03 1.48 1.58 NFA/GDP 3.11 0.10 0.31 1.76 Leverage ratio 1.44 0.00 0.45 0.98 Asset price 0.71 2.31 0.63 0.52 Inequality Measures Gini net wealth 0.61 - 0.29 0.55 Gini consumption 0.18 - 0.11 0.14 Equity premium decomposition (%) Equity Premium 5.12 5.63 4.35 5.05 Constraint E(cid:27). 0.44 5.49 0.78 0.53 Risk E(cid:27). 2.83 0.15 3.66 3.17 Persistence E(cid:27). 1.84 - -0.05 1.35 Trading Cost E(cid:27). 0.01 - -0.04 -0.01 No Short-Sales E(cid:27). 0.00 - 0.00 0.00 Sudden Stop dynamics CA/GDP (p.p.) 1.56 0.09 0.54 1.02 Consumption (%) -2.97 -1.17 -2.07 -2.34 Asset price (%) -0.99 -2.57 -0.77 -0.61 Prob. of crisis (%) Benchmark threshold 4.30 0.00 0.00 1.83 To construct an event study of simulated Sudden Stops, we average across all identi(cid:28)ed crisis periods. Sudden Stop episodes are de(cid:28)ned as the periods when the current account as a percentage of GDP is 1.5 standard deviations above its mean. Figure 5 shows the percent deviations from the steady state, where the crisis period corresponds to t = 0. The average of the simulated crisis episodes in the heterogeneous agents economy corresponds to the solid lines, and the average of the data for Mexico around the 1995 and 2009 Sudden Stops corresponds to the dashed line. 28

Figure 5: Event study of a Sudden Stop 1.5 2 1 0 0.5 0 -2 -0.5 -4 -1 -6 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (a) Current Account / GDP (b) Consumption 3 4 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (c) Asset Price (d) Interest Rate Shock Note: Solid lines correspond to the simulated data using the heterogeneous agents model calibrated to the Mexican economy, and dotted lines correspond to the average of the Mexican data around the 1995 and 2009 Sudden Stops. Panels (a) and (d) correspond to the level di(cid:27)erence from the long-run mean in percent. Panels (b) and (c) correspond to percentage point deviations from the long-run average. In Figure 5(a), we can see that a crisis episode is preceded by periods with the current account below its long-run average. Then, when the crisis happens (t = 0), there is a sharp reversal in the current account, which means that international capital stops (cid:29)owing into the economy. Consistentwiththedata, thecrisisispersistent, andittakesmorethanthreeyears for international capital to (cid:29)ow back into the economy. Furthermore, in Figure 5(b), we can see that the model is able to generate a large and persistent aggregate consumption drop. Regarding the asset price drop, in Figure 5(c), we can see that the simulated price falls 1.0 percent below the steady state, which is less than the asset price drop observed for Mexico.20 20 It is worth noting that while the model successfully reproduces the untargeted magnitude of current account dynamics, it underestimates the observed volatility and persistence of asset prices. As shown in the OnlineAppendix,introducinganad-hoctighteningofthecollateralconstrainttogetherwithasaleofforeign asset holdings generates asset price movements that more closely resemble those observed in the data. This suggests that future work could endogenize these mechanisms, which amplify the pecuniary externality and 29

Lastly, Figure 5(d) shows that Sudden Stops occur when there is a negative aggregate shock. For simplicity, the (cid:28)gure displays only the interest rate; however, this is accompanied by a decline in TFP, which is perfectly negatively correlated with the interest rate. However, not all interest rate increases cause a crisis. Speci(cid:28)cally, the long-run probability of a Sudden Stop in the simulated benchmark economy is 4.3 percent, while the probability of moving from a low to a high interest rate is 4.9 percent. The bottom part of Table 3 reports Sudden Stop dynamics. Speci(cid:28)cally, it shows the average percent deviations from the steady state for the current account as a percentage of GDP, consumption, and asset prices across the di(cid:27)erent simulated economies. In the benchmark calibration to an emerging economy (column 1), the asset price decline is smaller than the drop in consumption, aligning with empirical observations. In contrast, the representative agent model (column 2) shows a larger decline in asset prices than in consumption. Comparing these two columns reveals that in the heterogeneous agents economy, the crisisdampening e(cid:27)ect dominates, leading to a smaller asset price drop. However, there is a larger adjustment in aggregate consumption, driven mainly by the leveraged households. Regarding the di(cid:27)erentiated individual e(cid:27)ects during a Sudden Stop, in Table 4 we show the dynamics of asset holdings according to the leverage ratio and wealth of households, as we did for the empirical results presented in Section 3.2 and reproduced in parenthesis. We can see that the model does a good job of capturing the dampening e(cid:27)ect coming from the wealthy unconstrained households that buy assets during a crisis and relieve the downward pressure on the price. In particular, these households increase their asset holdings by 6.6 percent during a crisis. Moreover, in line with the empirical evidence on the amplifying e(cid:27)ect, (cid:28)nancially constrained wealthy households (cid:28)re-sell their assets the most during the crisis, decreasing their asset holdings by 15.8 percent. Although in the model households in decile IX of the leverage ratio do not sell their assets, we can see that they increase their holdings by a smaller amount than households in deciles I through VIII. Hence, the model is able to capture both cross-sectional e(cid:27)ects. transmitshocksmorestronglytoassetprices,byincorporatingricherpreferencestructures,suchasrecursive Epstein(cid:21)Zinpreferencesornon-homotheticpreferencesasinRojasandSa(cid:30)e(2022). Suchextensionswould enhance the feedback between asset prices, consumption, and borrowing, thereby improving the model’s ability to replicate asset price dynamics. 30

Table 4: Median asset holdings percent change in a crisis Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII -0.7 (0.0) 6.6 (61.4) VIII 4.7 (1.5) 5.3 (31.9) IX 4.1 (-1.7) 2.9 (-15.0) X 1.9 (0.0) -15.8 (-36.6) Note: To facilitate comparison between the model and data, empiricalmomentsfromTable1arereportedinparenthesis. 6.2.3. E(cid:27)ect of Zero Variance in the Dividend Risk In this subsection, we compare the severity of Sudden Stops in economies with di(cid:27)erent degrees of inequality. As described in the introduction, Figure 1 shows descriptive evidence suggesting that emerging economies are more unequal than advanced economies and that crisesaremoresevereinmoreunequaleconomies. Toquantitativelyassessthee(cid:27)ectsoflower income inequality, we calibrate the model to an advanced economy in which the dividend risk has zero variance, resulting in a wealth Gini index of 0.29. The results, summarized in Table 3 column (3), show that in the model calibrated to an advanced economy, the longrun average net foreign debt relative to GDP position is 6.2 percentage points larger, and consumption drops 1.0 percentage points less, while asset prices drop 0.2 percentage point less, during crises. The implied slope coe(cid:30)cient from the relation between the severity of a Sudden Stop in terms of consumption declines and the income Gini in the data is -11.5 while the implied coe(cid:30)cient from the di(cid:27)erent calibrations of the model is -11.1. An economy with an income Gini index 0.10 points lower experiences a decline in consumption 1.1 percentage points smaller during a crisis. Hence, the model predicts that economies with less inequality have less severe Sudden Stop crises, as observed in the data. 6.2.4. Impulse Response Analysis Lastly, this subsection looks at the impulse response functions after a two standard deviations aggregate shock.21 We compare the model with heterogeneity for di(cid:27)erent initial 21 The aggregate shock consists of a simultaneous impact on the international interest rate and aggregate TFP, with the latter being perfectly negatively correlated with the interest rate. For simplicity, Figure 6(d) only shows the response in the interest rate. 31

distributions and the representative agent model. In the baseline model with heterogeneity, the responses are obtained by conditioning the economy to start at the stationary ergodic distribution when the aggregate interest rate is kept constant at its mean value. We also look ataheterogenousagentmodelinwhichtheinitialdistributionisperfectlysymmetric, sothat all households initially hold the long-run average levels of bonds and the risky asset, but can then diverge as they receive idiosyncratic shocks going forward (a complete redistribution before the shock). The representative agent model results are obtained by conditioning the economy to start at the long-run mean bond position. All three simulations start at the long-run mean interest rate. Figure 6: Impulse responses to an aggregate shock 1 1.5 0 1 -1 0.5 -2 0 -3 -0.5 -4 -1 0 2 4 6 8 10 0 2 4 6 8 10 (a) Current Account / GDP (b) Consumption 0 4 -1 3 -2 -3 2 -4 1 -5 0 0 2 4 6 8 10 0 2 4 6 8 10 (c) Asset Price (d) Interest Rate Shock Note: Impulse response functions after an interest rate (and simultaneous TFP) shock of two standard deviations. In the baseline model with heterogeneity (red line), the responses are obtained by conditioning the economy to start at the stationary ergodic distribution. In the symmetric initial condition model (black dashed line), the responses are obtained by conditioning the economy to start with all households holding the long-run average levels of bonds and the risky asset. In the representative agent model (blue line), results are obtained by conditioning the economy to start at the long-run average bond position. Bands represent 68% credible intervals, and solid lines are averages over 10 simulations. In line with the results from the previous subsection, Figure 6(a) shows that the baseline 32

modelwithheterogeneity(solidredline)generatespersistentcurrentaccountreversals,which are1.9percentagepointslargerthanintherepresentativeagentmodel(solidblueline),which produces a near-zero response in the current account. In panels (b) and (c), we see that the response of the model with heterogeneity is about four times larger for consumption, and about a third as large for asset prices, compared with the representative agent economy. Lastly, comparing both red solid and black dashed lines, we see that the e(cid:27)ect of doing a perfect redistribution and starting with a perfectly symmetric initial distribution is relevant in the (cid:28)rst three periods after the shock. Moreover, in line with the results of the previous subsection, under the perfectly symmetric initial conditions (dashed black line), the drops in consumption and the asset price are approximately 0.5 percentage points smaller compared to the ergodic distribution initial condition baseline. In the Online Appendix, we present two additional exercises that illustrate how to generate a more pronounced response in asset prices. The (cid:28)rst introduces a permanent shock, while the second combines a permanent shock with an ad-hoc tightening of the LtV limit and an exogenous increase in asset supply, motivated by foreign investors selling o(cid:27) their asset holdings. 6.2.5. E(cid:27)ect of a Dividend Income Tax According to OECD (2018), Mexico has one of the lowest tax rates among OECD countries. The marginal e(cid:27)ective tax rate on bank deposits and dividends is close to zero compared to an OECD average of around 30 percent. In this subsection, we use the model to examine the e(cid:27)ects of introducing a redistributive dividend income tax.22 Speci(cid:28)cally, the government taxes dividend income at a (cid:29)at rate of τd = 0.30 across all households and periods, and redistributes the revenue through lump-sum transfers T , maintaining a balanced t 1 (cid:82) budgeteachperiod. Thispolicyresultsinatime-varyingtransferfunctionT = aiA diτddi. t t t t 0 22 We consider a simple policy rule that remains constant across households and over time. Implementing sucharulerequirescommitmentfromthetaxauthorityandisknowntobetime-inconsistentinmodelswith forward-looking asset prices. The source of this inconsistency comes from the fact that a benevolent social plannercanin(cid:29)uencecurrentassetpricesbyannouncingafuturetaxpaththatshapesexpectations. However, oncethefutureperiodarrivesandassetholdingsarepredetermined,theplannermayfaceincentivestodeviate from the announced rule to achieve a welfare-improving outcome, thus breaking the initial commitment. A fullcharacterizationoftheoptimal,time-consistentpolicyisbeyondthescopeofthispaper; seeBianchiand Mendoza (2018) for a detailed analysis of optimal time-consistent macroprudential policies. 33

The budget constraint of household i becomes ci +R−1bi +q (ai +Φ(ai ,ai)) = A wi +ai(q +A di(1−τd))+bi +T . (11) t t t+1 t t+1 t+1 t t t t t t t t t Implementing this tax reduces the severity of Sudden Stops. As shown in column (4) of Table 3, the average current account reversal during a crisis is 0.54 percentage points smaller. The underlying mechanism behind this result is the following: the dividend tax lowers the average dividend returns and reduces households’ exposure to dividend risk, weakening the precautionary savings motive. As a result, households demand fewer bonds(cid:22)leading to a more negative average net foreign asset (NFA) position(cid:22)and reduce their demand for domestic assets. To clear the market under lower demand, the price of the domestic asset declines, on average, by 9.6 percent relative to the benchmark economy. This asset price decline tightens borrowing constraints economy-wide due to the pecuniary externality embedded in the collateral constraint, increasing the share of (cid:28)nancially constrained households from 5.6 to 7.8 percent. Nevertheless, the overall contraction in domestic absorption is more moderate. Aggregate consumption falls by 0.63 percentage points less than in the benchmark economy. The reason is that lower asset prices reduce the e(cid:27)ective debt of vulnerable households. Consequently, their bond adjustment in response to external shocks is more limited. Combined with the redistributive transfers from the lump-sum policy, this results in a milder decline in consumption.23 Regarding the frequency of crises, it is worth noting that the probability of a crisis increases slightly because the reduced volatility of the current account lowers the threshold used to identify crisis episodes. However, as shown in the bottom row of Table 3, when the crisis thresholds from the benchmark economy are applied, the probability decreases to 1.83 percent(cid:22)less than half of the benchmark value. Finally, we conduct a welfare analysis using the simulated ergodic distribution from the model. We simulate 10 economies with 1,000 households over 220 periods, discarding the 23 The Online Appendix provides further results, such as event studies and asset-holding dynamics, for both the no-dividend risk and dividend-tax economies. Additionally, it also shows that the policy is also e(cid:27)ective, although in a lower magnitude, under a representative agent framework. The consumption and asset price change during a Sudden Stop are -0.95 and -2.39 percent, respectively. These declines are less severe than in the representative agent model however the dividend tax policy is less e(cid:27)ective than in the benchmark heterogeneous agents framework because there is no role and hence no gain from redistribution. 34

(cid:28)rst 20 periods, for both the baseline and the dividend tax economies. For each household, we compute the standard compensating consumption variation associated with the introduction of the dividend tax, accounting for the transition to the new tax policy. On average, households experience a welfare gain equivalent to 2.8 percent of consumption. However, this improvement is heterogeneous across the households: 73.3 percent of households experience welfare gains averaging 6.2 percent, while 26.7 percent experience welfare losses averaging 6.8 percent in consumption-equivalent terms. The households that experience welfare losses are more leveraged and three times wealthier than those that bene(cid:28)t. These results indicate that, on average, the dividend tax policy is welfare-improving, but its negative impact on asset prices disproportionately a(cid:27)ects wealthy, leveraged households by reducing their net worth and tightening their (cid:28)nancial constraints, leading to sizable welfare losses. 7. Conclusion This paper studies the cross-sectional dimension of the debt-de(cid:29)ation mechanism that triggers endogenous (cid:28)nancial crises of the Sudden Stop type. This dimension is relevant for the macroeconomy for two reasons. First, there is a dampening e(cid:27)ect on the de(cid:29)ation of asset prices coming from the unconstrained wealthy households that buy distressed assets, relieving the downward pressure on asset prices. Second, there is an amplifying e(cid:27)ect on the asset price de(cid:29)ation coming from the (cid:28)nancially vulnerable households that (cid:28)re-sell assets, generating a stronger downward pressure on asset prices. Because these two crosssectional e(cid:27)ects move asset prices in opposite directions, the role of inequality during crises is quantitatively ambiguous. Hence, this paper examines how the severity of Sudden Stop crises is a(cid:27)ected by inequality in an economy. First, with a panel microdata for Mexican households, we document descriptive evidence that supports both e(cid:27)ects. Speci(cid:28)cally, the 2009 crisis had di(cid:27)erent e(cid:27)ects on households depending on the composition of their balance sheets. The real estate holdings of low-leveraged wealthy households increased 61.4 percent during the crisis, while wealthy households with high leverage (cid:28)re-sold and decreased their assets the most during the crisis. Then, using the proposed asset-pricing Bewley model of a small open economy, we (cid:28)nd that a version of the model calibrated to an emerging economy (Mexico) can explain Sudden 35

Stops’ key stylized facts. Regarding the cross-sectional forces, in contrast to the representative agent framework, the model with household heterogeneity produces an empirically plausible leverage ratio distribution and generates persistent current account reversals with larger drops in consumption driven by the most leveraged households, consistent with the data. Furthermore, when calibrated to an advanced economy with zero dividend risk, the model predicts that the average net foreign debt position relative to GDP is 6.2 percentage points higher, consumption declines are 1.0 percentage point smaller, and asset price drops are 0.2 percentage points less severe. An impulse response analysis reveals that a heterogeneous agent economy with a perfectly equal initial distribution (complete redistribution) generates declines in consumption and asset prices that are 0.5 percentage points smaller than in the baseline economy with the stationary distribution as initial condition. Lastly, we show that a constant tax on dividend income, designed to reduce wealth inequality, makes (cid:28)nancial crises less severe by lowering asset prices and limiting debt accumulation in normal times. Onaverage, thepolicyraiseswelfare, thoughwealthierandmoreleveragedhouseholds experience welfare losses due to declines in asset values and tighter (cid:28)nancial conditions. In summary, the model suggests that economies with lower inequality, whether due to reduced idiosyncratic risk (as seen in advanced versus emerging economy calibrations) or wealth redistribution across agents (with identical idiosyncratic risk but di(cid:27)erent initial conditions), experience less severe Sudden Stop crises, (cid:28)ndings that align with empirical observations. References Aiyagari,SRaoandMarkGertler.1991. (cid:16)Assetreturnswithtransactionscostsanduninsured individual risk.(cid:17) Journal of Monetary Economics 27 (3):311(cid:21)331. (cid:22)(cid:22)(cid:22). 1999. (cid:16)Overreaction of asset prices in general equilibrium.(cid:17) Review of Economic Dynamics 2 (1):3(cid:21)35. Angeletos, George-Marios. 2007. (cid:16)Uninsured idiosyncratic investment risk and aggregate saving.(cid:17) Review of Economic Dynamics 10 (1):1(cid:21)30. Auclert, Adrien, Matthew Rognlie, Martin Souchier, and Ludwig Straub. 2021. (cid:16)Exchange 36

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For Online Publication Appendix to (cid:16)Inequality and Asset Prices during Sudden Stops(cid:17) Sergio Villalvazo This Online Appendix consists of the following sections: A. Microdata for Mexico B. The 2009 Mexican Sudden Stop at the Aggregate Level C. Model Details D. Solution Algorithm E. Model Nonlinearities F. Aggregate Risk Model: Event Studies G. Aggregate Risk Model: Impulse Responses A-1

Appendix A. Microdata for Mexico In this Appendix we show the distribution of houeholds by deciles according to the Mexican Family Life Survey (MxFLS) for 2005. Table A-1 shows the mean net wealth, portfolio composition, and leverage ratio in 2005, ordered by deciles of the net wealth distribution. The leverage ratio is de(cid:28)ned as the household’s total debt over the sum of the household’s total assets. As the second and third rows show, Mexican households’ wealth is mostly in physical assets (real estate and other durable goods). Although the proportion of debt decreases as households amass higher net wealth, as we can see from the last two rows of the table, there are leveraged and non-leveraged households in each of the deciles. Table A-1: Mean net wealth and its composition by deciles in 2005 I II III IV V VI VII VIII IX X Netwealth($) -507 761 2,564 5,368 9,184 14,451 20,524 29,512 45,067 204,855 Assets Realestate(%) -103.6 24.2 46.9 69.6 76.9 80.9 82.5 82.8 82.1 75.1 Other(%) -68.5 88.3 49.5 30.7 23.4 19.8 15.8 14.2 14.2 9.3 Financial(%) -10.7 9.7 12 7.5 4.5 4.9 3.4 5.3 6.3 16.8 Debt(%) 282.8 -22.2 -8.3 -7.7 -4.9 -5.6 -1.7 -2.3 -2.6 -1.2 Leverageratio Mean 0.77 0.10 0.05 0.05 0.04 0.04 0.02 0.02 0.02 0.02 p90 1.69 0.38 0.17 0.16 0.12 0.09 0.04 0.05 0.06 0.04 p10 0 0 0 0 0 0 0 0 0 0 Note: Ordered by deciles of net wealth in 2005 dollars. Source: MxFLS. Table A-2 and Figure A-1 present the evolution of the household leverage ratio distribution before and during the crisis. We classify households as (cid:28)nancial savers if they report positive holdings of (cid:28)nancial assets, as indebted but unconstrained if their leverage ratio falls below the 90th percentile (0.168 in 2005), and as (cid:28)nancially constrained if their leverage ratio exceeds this threshold. Between 2002 and 2005, prior to the crisis, the share of (cid:28)nancial savers rose by 1.7 percentage points, while the share of (cid:28)nancially constrained households declined by 2.3 percentage points. However, from 2005 to 2009, as the crisis unfolded and aggregate liquidity contracted, the share of (cid:28)nancial savers dropped signi(cid:28)cantly by 5 percentage points likely re(cid:29)ecting the need to draw down savings to smooth consumption. Over the same period, the share of (cid:28)nancially constrained households increased by 1.7 percentage points, consistent with tightening (cid:28)nancial conditions. Additionally, Table A-3 shows descriptive evidence of the di(cid:27)erentiated individual e(cid:27)ects duringaperiodoftimeoutsideofaSuddenStop. Speci(cid:28)cally,itshowstheannualizedmedian A-2

Table A-2: Distribution of households (percent) 2002 2005 2009 Financial savers 12.5 14.2 9.2 Unconstrained (leverage ratio ∈ [0,0.168)) 75.2 75.8 79.1 Financially constrained (leverage ratio ≥ 0.168) 12.3 10.0 11.7 Source: MxFLS. Figure A-1: Leverage Ratio Histogram noitcarF 6. 4. 2. 0 0 .05 .1 .15 .2 Leverage Ratio (solid gray: 2005, red: 2002, blue: 2009) Note: The distribution is truncated at 0.168, which is the 90th percentile of the leverage ratio distribution in 2005. Source: MxFLS. percent change in the real value of real estate (de(cid:29)ated with an aggregate house price index) owned by households from 2002 to 2005 relative to the average and sorted according to their net wealth and leverage ratio in 2005. Wealthy households correspond to the top decile of net wealth, and the (cid:28)nancially constrained households correspond to the top decile of the leverage ratio. As shown in the table, the real estate held by wealthy households increases in large magnitudes for all leverage ratio deciles. Suggesting that prior to the crisis, the wealthy households were accumulating more assets and that the dynamics during the crisis are not necessarily driven by a mean reversion mechanism. A-3

Table A-3: Median annualized percent change in real value of real estate by deciles, 2002(cid:21)05 Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII 0.0 38.1 VIII 0.5 27.2 IX 0.0 35.5 X -0.8 56.7 Source: MxFLS. Appendix B. The 2009 Mexican Sudden Stop at the Aggregate Level A Sudden Stop is a fast and large out(cid:29)ow of international capital. Hence, these types of episodes are characterized by large current account (CA) movements.24 In this Appendix, we use aggregate data to show the Sudden Stop that the Mexican economy experienced in 2009. In Figure A-2, we can see that the CA de(cid:28)cit reversed around 1.5 percentage points of GDP. Also, GDP and consumption declined, and there was a drop in consumer con(cid:28)dence and a decline in consumption credit, while (cid:28)rm and housing credit was not a(cid:27)ected. Onthepricesside, inFigureA-3, weseethattherewasalargedeclineinthestockmarket, house prices decelerated and remained constant for about four years after the crisis burst, the J.P. Morgan EMBI+ spread that measures the Mexican sovereign bond risk increased about 2 percentage points, and there was a large depreciation of the Mexican peso against the dollar. The aggregate dynamics shown in this Appendix are not particular to Mexico. See Bianchi and Mendoza (2020) for a recent survey of Sudden Stop episodes among both advanced and emerging economies. Appendix C. Model Details In this Appendix we (cid:28)rst provide a micro-foundation for the collateral constraint and then de(cid:28)ne the recursive competitive equilibrium. 24 Some Sudden Stop episodes have even registered CA reversals, meaning that the economy transitions from having a negative CA (foreign capital entering the economy) to having positive CA surpluses (capital leaving the economy). A-4

Figure A-2: Quantities and Consumption Determinants (a) CA/GDP % (b) Consumption and GDP Index (2007 = 100) (c) Consumer Con(cid:28)dence Index (d) Credit Index (2007 = 100) (2007 = 100) Note: The gray area corresponds to the crisis. Source: INEGI, World Bank, Banxico. The micro-foundations of the collateral constraint are similar to the ones presented by Bianchi and Mendoza (2018) extended for an economy with non-insurable idiosyncratic risk. Speci(cid:28)cally,theLtVconstraintcanbederivedfromanincentivecompatibilityconstraintthat arises due to a limited enforcement problem, in an economy where debt contracts are signed with competitive creditors, and households can switch to another creditor at any given point in time. At the beginning of the period, credit and asset markets open, production happens, and households choose bi with price R−1 and ai with price q . Then markets close, t+1 t t+1 t and households decide to divert resources from the credit and default. Local competitive (cid:28)nancial intermediaries monitor costlessly who diverts resources and seize a fraction κ of the household asset holdings, which are q ai . After defaulting, the household regains access t t+1 to credit markets instantaneously and repurchases the assets that investors sell in open markets at a price q . In this environment, a household that borrows −R−1bi and engages t t t+1 A-5

Figure A-3: Asset Prices (a) House Price Index (2007 = 100) (b) Stock Market Value Index (2007 = 100) (c) J.P. Morgan EMBI Spread for (d) Mexican Peso Exchange Rate for Mexico in % USD Note: The gray area corresponds to the crisis. Source: Sociedad Hipotecaria Federal, Moody’s Analytics, INEGI, World Bank. in diversion activities gains −R−1bi and loses κq ai . Hence, households repay if and only t t+1 t t+1 if −R−1bi ≤ κq ai . t t+1 t t+1 Now we are ready to de(cid:28)ne a recursive competitive equilibrium. Let the individual bond ¯ and asset holdings be elements (b,a) ∈ [b,b]×[0,a¯] ≡ S, and let the individual productivities ¯ be elements (ϵw,ϵd) ∈ {ϵw,...,ϵw } × {ϵd,...,ϵd } ≡ EInd. In addition, let M be the set of 1 Nw 1 N d probability measures of the set S×EInd, and let the aggregate shocks be elements (ϵR,ϵA) ∈ {ϵR,...,ϵR }×{ϵA,...,ϵA } ≡ EAgg. Finally, let the function π(ϵ′|ϵ) be the exogenous Markov 1 NR 1 NA transition probability that the next-period shock takes the value ϵ′ conditional on the shock in the current period being ϵ, where ϵ = (ϵw,ϵd,ϵR,ϵA) ∈ EInd ×EAgg = E. De(cid:28)nition 1. A recursive competitive equilibrium in this economy is given by a value function v : S × E × M → R; policy functions for the household c : S × E × M → R, b′ : S × E × M → R, and a′ : S × E × M → R; a domestic asset-pricing function A-6

q : M×EAgg → R; and an aggregate law of motion HΩ : M×EAgg → M such that 1. Given the asset-pricing function and the aggregate law of motion, the value function v satis(cid:28)es the household’s Bellman equation 4, and c, a′, and b′ are the associated policy functions. 2. For all Ω ∈ M and all (ϵR,ϵA) ∈ EAgg , the asset market clears: (cid:82) adΩ = (cid:82) a′(b,a,ϵw,ϵd,ϵR,ϵA,Ω)dΩ = K ¯ . S×EInd S×EInd 3. For all Ω ∈ M and (ϵR,ϵA) ∈ EAgg, the aggregate resource constraint is satis(cid:28)ed: (cid:82) c(b,a,ϵw,ϵd,ϵR,ϵA,Ω)dΩ +(ϵRR ¯ )−1 (cid:82) b′(b,a,ϵw,ϵd,ϵR,ϵA,Ω)dΩ S×EInd S×EInd (cid:82) +q(Ω,ϵR,ϵA) Φ(a′(b,a,ϵw,ϵd,ϵR,ϵA,Ω),a)dΩ S×EInd = ϵAA ¯ w¯ + (cid:82) aϵAA ¯ ϵ¯dd ¯ dΩ+ (cid:82) bdΩ. S×EInd S×EInd 4. The aggregate law of motion is generated by the exogenous Markov process π and the policy functions b′ and a′ as described below: Let (ϵw,ϵd) = ϵInd and (ϵR,ϵA) = ϵAgg and de(cid:28)ne the transition function Q : Ω,ϵAgg S ×EInd ×B(S)×B(EInd) → [0,1], where B(·) is the corresponding Borel set, by Q (b,a,ϵInd,S,EInd) = Ω,ϵAgg    (cid:80) π(ϵInd′,ϵAgg′|ϵInd,ϵAgg), if (b′(·),a′(·)) ∈ S.  ϵInd′∈EInd,ϵAgg′∈EAgg   0, otherwise. Then, for any S ∈ B(S) and any EInd ∈ B(EInd) the aggregate law of motion is given by (cid:90) Ω′(S,EInd) = (HΩ(Ω,ϵAgg))(S,EInd) = Q (b,a,ϵInd,S,EInd)dΩ. Ω,ϵAgg S×EInd Appendix D. Solution Algorithm In this Appendix, we describe the solution method. Building from Krusell and Smith (1997) we adapt their nontrivial market clearing algorithm to a small open economy framework. In particular, instead of solving problem 4, we solve A-7

v˜(b,a,ϵw,ϵd,ϵR,ϵA,B,q) = max u(c)+βE[v(b′,a′,ϵw′,ϵd′,,ϵR′,ϵA′.B′)] s.t. {c,b′,a′≥0} c+(ϵRR ¯ )−1b′ +q(a′ +Φ(a′,a)) = ϵAA ¯ ϵww¯ +a(q +ϵAA ¯ ϵdd ¯ )+b, (ϵRR ¯ )−1b′ ≥ −κqa′, ϕ Φ(a′,a) = (a′ −a)2, 2 B′ = γ0 +γ1B +γ2D , B B B R q = γ0 +γ1B +γ2D +γ3q , (A.1) q q q R q −1 where we replaced the full household distribution Ω with the aggregate bond position B = (cid:82) bdΩ and market clearing in the asset holdings is achieved using a (cid:28)xed-point iteration on q such that K ¯ = (cid:82) a′(·)dΩ. Then the solution algorithm follows the simulation method described in Krusell and Smith (1997). Appendix E. Model Nonlinearities To better understand the mechanism and the risk-wealth tradeo(cid:27), Figures A-4 through A-7 show the policy functions and the nonlinearities generated in the stationary model. In the upper row of Figure A-4, the solid lines correspond to the bond policy for the high- (low-) dividend shock in blue (red) and the average labor income shock as a function of the current asset holdings for three di(cid:27)erent values of the current bond holding b#. Additionally, the dashed lines represent the corresponding debt limits, and the black dashed lines correspond to the bottom 1 and top 99 percentiles of bond and asset holdings obtained from the model’s simulated cross-section. The (cid:28)gure shows that for low-dividend shocks (red lines), a household lowers its bond holdings (or gets more debt) as it increases its asset holdings. This e(cid:27)ect is stronger for constrained households, as shown in panels (b) and (c). As described in Section 5.1, the risk-wealth tradeo(cid:27) generates the convex form of the bond policy for high-dividend shocks (blue lines). For asset-poor households, as they increase their assets, they also lower their bond holdings (or get more debt if the holdings are negative), and there is a certain level for which the dividend risk exposure overcomes the bene(cid:28)t from more debt A-8

capacity that makes households increase their bond holdings. Regarding the bottom row of the (cid:28)gure, we can see the asset policy function that is highly linear and behaves as expected: for high-dividend shocks, households accumulate more assets, and for low-dividend shocks, households decumulate assets. Figure A-4: Stationary Bond and Asset Policies as a Function of Current Asset Holdings 0.1 0.1 0.1 0 0 0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.3 -0.3 -0.3 -0.4 -0.4 -0.4 -0.5 -0.5 -0.5 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 (a) p99 Current Bond Holding (b) p50 Current Bond Holding (c) p01 Current Bond Holding 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 (d) p99 Current Bond Holding (e) p50 Current Bond Holding (f) p01 Current Bond Holding Note: For a current bond holding b# and mean labor shock ϵ¯w, the upper (lower) row corresponds to the bond (asset) policies, the solid blue (red) line corresponds to the policy function with the high- (low-) dividend shock, and the dashed blue (red) line corresponds to the debt limit with the high- (low-) dividend shock. Dashed black lines correspond to the bottom 1% and top 99% of bond and asset holdings obtained from the model’s simulated cross-section. Dotted black lines correspond to the 45-degree line. The missing values across the state space correspond to the infeasible individual states that would imply a negative consumption. Moreover, in Figure A-5, we show similar bond and asset policies but now as a function of the current bond holdings. In the upper row, we can see the standard bond policies under a binding debt limit. Panel (a) shows the policy for a high-asset holder. Here we can see that the debt limit is not binding for the states within the 1st and 99th percentiles. However, as we move to lower asset holdings, in panels (b) and (c), we can see that the LtV becomes binding when households accumulate enough debt. With respect to the cross-sectional (cid:28)resales in the model, in the bottom row of the (cid:28)gure, we can see that households accumulate less assets as they increase their debt holdings. However, this relation is highly strengthened A-9

(households incur (cid:28)re-sales) when the debt limit becomes binding, which can be seen using panels (b) and (e) and also panels (c) and (f). There are strong declines in asset holdings (panels (e) and (f)) in the states where bond holdings reach the debt limit (panels (b) and (c)). Figure A-5: Stationary Bond and Asset Policies as a Function of Current Bond Holdings 0.1 0.1 0.1 0 0 0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.3 -0.3 -0.3 -0.4 -0.4 -0.4 -0.5 -0.5 -0.5 -0.4 -0.2 0 -0.4 -0.2 0 -0.4 -0.2 0 (a) p99 Current Asset Holding (b) p50 Current Asset Holding (c) p01 Current Asset Holding 8.5 1 0.1 0.08 0.8 0.06 8 0.04 0.6 0.02 7.5 0.4 0 -0.4 -0.2 0 -0.4 -0.2 0 -0.4 -0.2 0 (d) p99 Current Asset Holding (e) p50 Current Asset Holding (f) p01 Current Asset Holding Note: For a current bond holding b# and mean labor shock ϵ¯w, the upper (lower) row corresponds to the bond (asset) policies, the solid blue (red) line corresponds to the policy function with the high- (low-) dividend shock, and the dashed blue (red) line corresponds to the debt limit with the high- (low-) dividend shock. Dashed black lines correspond to the bottom 1% and top 99% of bond and asset holdings obtained from the model’s simulated cross-section. Dotted black lines correspond to the 45-degree line. The missing values across the state space correspond to the infeasible individual states that would imply a negative consumption. Additionally, in Figure A-6, we show the di(cid:27)erence in the bond policy function for a high- and a low-dividend shock in panel (a) and a labor income shock in panel (b). We can see a positive and increasing di(cid:27)erence in the next-period bond holdings between the highand low-dividend productivities as we move to higher current asset holdings (Figure A-6(a)). This result means that when the idiosyncratic dividend realization is high, the household optimally chooses larger bond holdings for the next period. Moreover, this di(cid:27)erence is kept almost constant (only increases close to the debt limit) across the current bond holdings. In contrast, in Figure A-6(b), we can see that the di(cid:27)erence in the bond policy function A-10

between the high and low idiosyncratic labor productivity realization is positive but close to zero and constant throughout all the feasible state-space. Figure A-6: E(cid:27)ect of Non-insurable Individual Shocks in the Bond Policy (a) Di(cid:27)erence in Dividend Shock (b) Di(cid:27)erence in Labor Shock Note: ϵ¯w and ϵ ¯d correspond to the mean shock values. The missing values across the state space correspond to the infeasible individual states that would imply a negative consumption. Figure A-7: E(cid:27)ect of Non-insurable Individual Shocks in the Asset Policy (a) Di(cid:27)erence in Dividend Shock (b) Di(cid:27)erence in Labor Shock Note: ϵ¯w and ϵ ¯d correspond to the mean shock values. The missing values across the state space correspond to the infeasible individual states that would imply a negative consumption. Similarly, in Figure A-7, we show the di(cid:27)erence in the asset policy function for a highand a low-dividend shock in panel (a) and a labor income shock in panel (b). We can see a positive and increasing di(cid:27)erence in the next-period asset holdings between the high- and low-dividend productivities as we move to higher current asset holdings (Figure A-7(a)). However, for high enough asset values, this positive di(cid:27)erence becomes relatively constant. Moreover, this di(cid:27)erence is kept almost constant (only increases close to the debt limit) across the current bond holdings. Finally, similarly to the bond policy function, in Figure A-11

A-7(b), we can see that the next-period asset holdings di(cid:27)erence between the high and low idiosyncratic labor productivity realization is positive but close to zero and constant throughout all the feasible state-space. Appendix F. Aggregate Risk Model: Event Studies In Figure A-8 , we show the event study analysis for the same history of individual and aggregate shocks for the (cid:28)ve calibrations: (1) the baseline emerging economy (in solid lines), (2) the advanced economy with the same calibration but with zero variance in the dividend risk (in dotted lines), (3) the benchmark economy with a redistributive dividend tax (in solid lines with cross marker), (4) the representative agent economy with a lower LtV limit such that the average leverage ratio is the same as in the baseline model (in dash-dotted lines), and (5) the representative agent economy with a dividend tax (in solid lines with circle marker). Additionally, we compute the asset holding dynamics for the economy without dividend risk in Table A-4 and for the economy with a redistributive dividend tax in Table A-5. In the former, we can see that without the risk-wealth tradeo(cid:27), while the decumulation of assets during a Sudden Stop still happens for the wealthy leveraged households, this e(cid:27)ect becomes highly muted. For the latter, the (cid:28)re-selling of assets is still strong with a dividend tax but the aggregate e(cid:27)ects are less severe, due to the general equilibrium e(cid:27)ects and redistribution described in Section 6.2.5. Table A-4: Median asset holdings percent change in a crisis in economy with zero dividend risk Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII 1.5 1.1 VIII -2.4 1.2 IX -0.9 -2.3 X -1.0 -2.1 Appendix G. Aggregate Risk Model: Impulse Responses Lastly, in this Appendix we present two additional exercises that illustrate how to generate a more pronounced response in asset prices. The (cid:28)rst introduces a permanent shock, A-12

Figure A-8: Event Study of a Sudden Stop 1 3 0 2 -1 1 -2 0 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (a) Current Account / GDP (b) Consumption 2 2 1 1 0 0 -1 -1 -2 -2 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (c) Asset Price (d) Interest Rate Shock Note: Panels (a) and (d) correspond to the level di(cid:27)erence from the long-run mean in percent. Panels (b) and (c) correspond to percentage point deviations from the long-run average. while the second combines a permanent shock with an ad-hoc tightening of the LtV limit and an exogenous increase in asset supply, motivated by foreign investors selling o(cid:27) their asset holdings. In the latter case, the LtV limit (κ) is reduced by 2 percent to 0.1646 and the (cid:28)x supply of the asset is increased by 2 percent to 1.02. In the blue solid lines of Figure A-9 we can see that introducing only a permanent shock increases the persistence of the shock and has permanent e(cid:27)ect on consumption and the asset price of around 0.5 percent. Furthermore, the introduction of a permanent ad-hoc LtV limit tightening together with an increase in the asset supply (red dashed lines), double the size of the e(cid:27)ect on impact on consumption and asset prices, while the long run e(cid:27)ects are similar. However, an increase in the supply of the asset has a counterfactual e(cid:27)ect on the current account since now more assets are available to domestic households and this increases their debt limits. For this reason we also introduced the ad-hoc LtV limit tightening to induce a current account reversal. A-13

Table A-5: Median asset holdings percent change in a crisis in economy with dividend tax Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII -0.6 6.4 VIII 1.7 6.0 IX 1.1 2.2 X 1.3 -14.0 Figure A-9: Impulse responses to a permanent aggregate shock 0 1.5 -2 1 -4 0.5 -6 0 -8 0 5 10 15 20 0 5 10 15 20 (a) Current Account / GDP (b) Consumption 0 6 -0.5 5 -1 4 -1.5 3 -2 2 -2.5 1 0 0 5 10 15 20 0 5 10 15 20 (c) Asset Price (d) Interest Rate Shock Note: Impulse response functions after a permanent interest rate (and simultaneous TFP) shock of two standard deviations. The responses are obtained by conditioning the economy to start at the stationary ergodic distribution and at the long-run mean interest rate. The blue solid line corresponds to the permanent shock, while the red dashed line combines a permanent shock with an ad-hoc tightening of the LtV limit and an increase in asset supply. Lastly, Tables A-6 and A-7 show the asset holding dynamics on impact following the permanent negative shocks. The introduction of an ad-hoc tightening of the LtV constraint combined with an increase in asset supply (Table A-7), ampli(cid:28)es asset accumulation among wealthy, low-leverage households(cid:22)consistent with the empirical evidence. However, in the main paper, we follow the debt-de(cid:29)ation literature and assume that domestic assets remain closed to foreign ownership. A-14

Table A-6: Median asset holdings percent change on impact after a permanent shock Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII -1.6 5.8 VIII 5.8 4.1 IX 3.0 -10.4 X 2.4 -14.5 TableA-7: Medianassetholdingspercentchangeonimpactafterapermanentshockwithad-hoctightening of LtV and increase in asset supply Net Wealth Leverage Ratio I(cid:21)IX: Non-Wealthy X: Wealthy I(cid:21)VII -0.6 10.0 VIII 8.0 6.7 IX 8.1 6.2 X 4.6 -12.9 A-15