| The 2008 financial crisis once again triggered people's reflection on the existing macroeconomic model.Although the macroeconomic model based on the DSGE framework before the crisis had better adaptability and scalability,it also successfully fitted the macroeconomic fluctuations of the past few decades.However,it cannot explain the reality that output and investment continue to decline after the crisis in industrialized countries.Even with the inclusion of banking and other financial frictions,the common linearized DSGE model cannot describe sudden,large and persistent changes in asset prices,output,and investment during the crisis period,including the 2008 financial crisis,and does not properly reflect asset prices and non-linear features that are widespread in the financial sector.Moreover,Cochrane(2017)proposes that we need to integrate the two long-term splitting areas of asset pricing and macroeconomics under the general equilibrium framework in which with time-varying risk premium and time-varying risk tolerance as the core.This paper constructs a stochastic general equilibrium model that integrates traditional asset pricing model,financial intermediary asset pricing model and macroeconomic model in continuous time.Compared with the previous discrete time models and macroeconomic models(such as DSGE models),the continuous-time stochastic model has the characteristics of high nonlinearity,endogenous risk,time-varying risk premium and random steady states.Furthermore,there is great advantages and conveniences in the construction and derivation of models.However,when it comes to solve the continuous time.models,it faces the "dimension curse".Therefore,there is a problcm in the selection of state variables in related research.Fortunately,the development of artificial intelligence and machine learning in recent years has provided a new way to solve this kind of macro financial model.This paper takes surplus consumption ratio,wealth share of financial institutions and central bank's normal interest rate as the state variables to measure the investor's risk tolerance.This paper constructed three continuous-lime stochastic general equilibrium macro-financial models with time-varying risk premium as the core,and those models were solved using machine learning.Under the general equilibrium framework of the models,not only can we better discuss how state variables affect financial market risk premiums,asset prices and their volatility,but also more easily explore the relationship between these variables and macro factors such as consumption volatility,investment and output.Compared with the existing literature,this model can describe the relationship between fund supply side(family),capital demand side(financial institution)and policy department(central bank)in different situations and decision-making and economic fluctuations.Furthermore,it is possible to evaluate the effect of monetary policy through the hedging and change of risk premium under the multi-risk sources.Specifically,this paper expands on the following three aspects of the existed literatures:First,the utility function has been modified and one new state variable was added which represents the risk tolerance of the fund provider,especially the family investor.This is missing from the existing financial intermediation literature,and this is also a promotion of Campbell and Cochrane(1999)in terms of continuous time and general equilibrium.Second,after the financing shock,the redemption ratio of household funds is related to the surplus consumption ratio of the state variable.After the expansion,the optimal choice of financial institutions has the situation of incomplete provision financing,which is closer to the reality of financial institutions,rather than the assumption that financial institutions hold enough liquidity assets as in Drechsler et al.(2018).Therefore,our expanded models are closer to the actual operation of financial institutions.Third,the value range of the nominal interest rate representing the monetary policy has been reset.We have changed the nominal interest rate from[0,5%]in Drechsler et al.(2018)to[0,10%].Such improvements not only make the nominal interest rate closer to the real value of the nominal interest rates between China and the Un ited States,but also help us to explore the situation in which financial institutions are not fully prepared for financing shocks.The results of the model show that,firstly,the surplus consumption ratio,as a state variable to measure the risk tolerance of representative investors,not only shows a nonlinear relationships between itself and consumption fluctuations,risk premiums,asset prices and their fluctuations,which is similar to Campbell and Cochrane(1999).Moreover,it also causes investment and output to reach a new stochastic steady state when it suffers from negative shocks.Second,in the heterogeneous investor model,when the surplus consumption ratio is different,the financial institution will actively expose some of the financing shocks instead of holding enough liquid assets to fully cover the financing shock.Relatively full covering,when financial institutions are not fully prepared for financing shocks,they will reduce the holding leverage of risk assets in the portfolio.At this time,the negative impact of state variables such as the surplus consumption ratio and the wealth ratio of financial institutions has relatively little impact on consumption volatility,investment and economic output.In the case of partly cover the financing shock,the negative impact of the financial institution's wealth ratio will not only trigger the "financial accelerator" effect similar to the BGG model and Brunnermeier and Sannikov(2014),but also trigger the self-feedback mechanism with"reverse effect".Third,in the model of coexistence of production capital shocks and monetary policy shocks,the increase in nominal interest rates affects the proportion of risky assets held by financial institutions by increasing the cost of holding liquid assets and increasing the risk premium of risky assets.In the case of full provision,the impact of the holding cost of liquid assets is dominant,while in the case of non-complete provision,the impact of risk premium is dominant.Fourth,when both risk sources of production capital and monetary policy exist simultaneously,the implementation of appropriate monetary policy reverse shocks based on the impact of production capital can hedge some of the risk premium changes and economic fluctuations. |
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