宏观冲击下的非线性微观收益过程（英）

MartínAlmuzara|ManuelArellano|RichardBlundellStéphaneBonhomme Nonlinear Micro Income Processeswith Macro ShocksMartínAlmuzara,ManuelArellano,RichardBlundell,andStéphaneBonhomme FederalReserve Bank of New York Staff Reports, no.1162August2025https://doi.org/10.59576/sr.1162 Abstract We propose a nonlinear framework to study the dynamic transmission of aggregateand idiosyncraticshocks to household income that exploits both macro and micro data.Our approach allows us to examineempirically the following questions: (a) How dobusiness-cycle fluctuations modulate the persistence ofheterogeneous individual historiesand the risk faced by households? (b) How do aggregate andidiosyncraticshocks propagate over time for households in different macro and micro states? (c)How dothese shocks shape the cost of business-cycle risk? We develop new identificationand estimationtechniquesand provide a detailed empirical analysis combiningmacro time series for the U.S. and a timeseries of household panels from the PSID. JEL classification:C23Keywords:income processes, business cycle, persistence, exposure to aggregate shocks This paper presents preliminary findings and is being distributed to economists and other interestedreaders solely to stimulate discussion and elicit comments. The views expressed in this paper are those ofthe author(s) and do not necessarily reflect theposition of the Federal Reserve Bank of New York or theFederal Reserve System. Any errors or omissions are the responsibility of the author(s). To view the authors’ disclosure statements, visithttps://www.newyorkfed.org/research/staff_reports/sr1162.html. 1Introduction In this paper, we propose a nonlinear framework to study the dynamic transmission ofaggregate and idiosyncratic shocks to income by leveraging both macro and micro data.Our approach makes it possible to empirically examine how business-cycle fluctuationsmodulate the persistence of heterogeneous individual histories and the risk faced byhouseholds. We also consider questions such as how aggregate and idiosyncratic shockspropagate over time for units in different macro and micro states, and how these shockscontribute to the cost of business-cycle risk. Answering these questions is important. Theyare essential to documenting the dynamics of income inequality over the business cycle.Furthermore, how the incomes of heterogeneous agents respond to macro and microshocks is key for consumer and firm behavior, and for the design of optimal monetaryand fiscal policies (Bhandari, Evans, Golosov, and Sargent, 2021). The literature on income risk has uncovered significant nonlinearities in the dynam-ics of individual incomes (Arellano, Blundell, and Bonhomme, 2017; Guvenen, Karahan,Özkan, and Song, 2021) and in their variation over the business cycle (Guvenen, Ozkan,and Song, 2014). Moreover, a growing recent literature investigates the heterogeneous ef-fects of monetary policy shocks on individual-level outcomes (Holm, Paul, and Tischbirek,2021; Andersen, Johannesen, Jørgensen, and Peydró, 2023; Amberg, Jansson, Klein, andRogantini Picco, 2022). Yet, a methodology for modeling the interaction between microand macro shocks capable of integrating non-linearities in the life-cycle and business-cycledynamics of income is still lacking. This is our main contribution. We consider a nonlinear Markovian micro income process with a macro state variableof the following form: whereuitandVtare micro and macro shocks, andηitandZtare potentially unobserved.A measurement system connects these two latent variables to observed micro and macrodata, specifically, a flexible persistent-transitory model for the micro states and a dynamicfactor model for the macro states.Our triangular formulation has the potential to al-low for feedback from the micro to the macro level, asZtcan incorporate distributionalcharacteristics of the micro data. The assumption underlying the triangular structure is atomicity, meaning that no single individual unit influences the aggregate state. Based on our income process we will highlight two key quantities. The first one is theelasticity of individual persistent earnings to the aggregate business-cycle stateZt: In our setup,βitis a measure of a household’s exposure to shocks to the aggregate statethat is heterogeneous along both the income distribution and business-cycle conditions.In addition,βitmay vary with the idiosyncratic shockuit, and so the impact of an aggregateshock may differ depending on idiosyncratic events (such as a job loss or a promotion).1 The second quantity is income persistence: Here,ρitis a measure of nonlinear persistence (Arellano et al., 2017, ABB) that may varydepending on the position in the income distribution and the idiosyncratic shocks hittingthe household. Moreover, unlike in ABB, our model allows for the aggregate state to affectincome and, thus, for the shape of persistence to be different in good or bad times. Documenting howβits andρits vary acr