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?:Influence of inequality on monetary policy. Estimated HANK model.
Sergey Ivashchenko
Dynamic stochastic general equilibrium (DSGE) models are one of the key instruments of macroeconomic analysis. It combines good forecasting quality and microeconomic foundation [Tovar 2009]. However, the most of them are representative agent new keynsian (RANK) models that suggests that each type of agents are homogenous. The minor exception is one dimensional one parameter distribution of agents that is used in Calvo pricing. There are some papers that divide households into two groups (usually ricardians and non-ricardians). These models call two agents new Keynsian (TANK) models. They may be extended to k-agents new Keynsian (KANK) models where agents differ by some parameters. All these types of DSGE models suggest that agents cant change their type. The perturbation technique can be used for approximation of their solution.
There is alternative approach that suggested infinite (continius) number of agents. They calls Heterogeneous agents new keynsian (HANK) models. This type of models allows agents to change their position in inequality space. They suggest some idiosyncratic shocks. Many HANK models are continuous time models and the solution technique is guess and verify. There are only two papers that suggest universal approaches for solution approximation of models with heterogeneous agents [Ahn et al (2018), Guil (2019)].
This paper suggests a new approach that allows to compute models with heterogeneous agents. The problem with approximation of models with heterogeneous agents is that there are infinite number of variables and equations. However, we are interesting in knowledge of moments of heterogeneous variables. The approach requires that heterogeneous equation can be transformed such that all heterogeneous expectation and state variables are in left hand side of equations while all lag of heterogeneous state variables and current values of expected variables are in right hand side of equation. It is possible to do for the equations that appear in the most models. The next step is computing of integrals of heterogeneous equation over heterogeneous dimensions. It requires to use some approximation. This approach suggests that all heterogeneous variables have normal distribution. Such approximation allows to compute integrals analytically. However, the number of moments is larger than number of types of heterogeneous equations. So, additional equations are squared equations and equations multiplied by expected idiosyncratic shocks. The specific parameterization prevent non-positive define covariance matrix.
The approach is tested on the model with heterogeneous households that face to idiosyncratic shocks (time preference and wages). They have aces to bond market. They make decision about amount of consumption and work. The model is estimated on Russian data (2000q1-2020q4 (full), 2015q1-2020q4 (short)). The 4 variables are observed: MIACR, GDP growth rate, private consumption deflator and ratio of consumption expenditures 90% quantile to 10% quantile. The model is estimated with first and second order approximations.
The HANK model allows to understand influence of inequality on monetary policy. The estimated linearized model allows to compare impulse response of estimated model with model that have alternative level of inequality. It may be achieved by decreasing variance of idiosyncratic shocks. The first case is 10% decrease of standard deviation of idiosyncratic shocks. If estimation corresponds to short sample used than influence on impulse response is small. However, if full sample is used than it leads to dramatic changes and creates price puzzle. It should be noted that full sample results can be affected by structural change of monetary policy in 2014 while model suggest the same policy during all years. The second case is small (5%) changes of inequality. It produces much smaller effect. It demonstrates that inequality have highly nonlinear effect on monetary policy response (even threshold type effect when changes until some level have small influence and change above this level have large influence).
Described above effect is comparison of two worlds with different inequality level. However, there are some fluctuations of inequality in real world. Linearized model impulse response is independent on the state of the economy. Such dependence appears in case of nonlinear approximation (second order approximation). It allows to compare response at steady-state and at alternative point with different level of inequality. The consumption is not state variable, so it is impossible to change only inequality of consumption. However, assets are state variable, so assets inequality is changed.
Important technical detail is that linearized IRFs are computing analytically (condition on model and parameters). Nonlinear IRFs are computing numerically by averaging over simulation of difference between 2 trajectories: the first one have larger shock at the first period while all other shocks are the same. The main computation uses 40000 draws.
The standard deviation of assets across households is changed by 10%. Such changes significantly increases magnitude of response. It means that inequality level different than steady-state makes economy more sensitive to shocks.
Literature
Ahn S., G. Kaplan, B. Moll, T. Winberry, C. Wolf (2018) // NBER Macroeconomics Annual, 2018, vol. 32, issue 1, 1 - 75
Guil H. G. (2019) Solving Heterogeneous-Agent Models around the Ergodic Steady-State // researchgate DOI:10.13140/RG.2.2.21235.17447
Tovar C. E.,(2009). DSGE models and central banks//Economics-The Open-Access, Open-Assessment E-Journal, 2009, ! 3(16), pages 1-31
NWMB Bank of Russia; The Institute of Regional Economy Studies (Russian Academy of Sciences); Financial Research Institute.
The views expressed in this paper are solely those of the authors and do not necessarily reflect the official position of the Bank of Russia. The Bank of Russia assumes no responsibility for the contents of the paper.
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