[PPT] - Monetary Policy Uncertainty Credit Risk and Chinas Macroeconomic PowerPoint Presentation

SLIDE 1

Monetary Policy Uncertainty，Credit Risk and China’s Macroeconomic Fluctuations

Li Li Guanghua School of Management, Peking University 2018.10

SLIDE 2

Road map

Institution background
Literature review
Model
Bayesian VAR evidence
Conclusion

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Background

In 2017, Zhou Xiaochuan,former chief of China’s central bank, warns of

‘Minsky moment’.

Economic policy makers led by President Xi made preventing financial

risk an economic priority for the next three years after annual Central Economic Work Conference in 2017.

Chinese Prime Minister Li Keqiang said preventing financial risks was
ne of the country's "three fundamental battles" along with fighting

poverty and pollution.

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Why China’s leaderships are so serious about financial risks?
The International Monetary Fund has repeatedly warned of risks stemming from

China's high debt-to-GDP ratio and called for speedy deleveraging.

In 2017, Moody’s downgrades China’s sovereign credit rating since 1989, which raises

the worry about the alarming risk of financial instability in China.

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When it comes to China’s Financial risks

Downgrade of GDP growth
Massive shadow banking
High corporate debt and household indebtedness
Local government Debt
Housing sector
Huge Financial market fluctuations
Capital outflows

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Why should study Chinese government's policy uncertainty?

100 200 300 400 500 600 700 800

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

China News-Based EPU(Baker et al.,2016)

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Policy uncertainty (also called policy risk) is a class of economic risk where the

future path of government policy is uncertain, policy uncertainty may refer to uncertainty about monetary or fiscal policy.

China offers an excellent place to study policy uncertainty
Dual track or gradualist approach
Crossing the river by feeling the stone
Launching the circuit breaker in the China stock market is a vivid example of how

to depict policy uncertainty.

This hurried implementation and with-drawal of the circuit breaker revealed that the

government still has a long way to go in improving scientificity in policy making.

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Why China’s monetary policy uncertainty?

Multiple tools, intensively intervention and various work all lead to the increase of

China’s monetary policy uncertainty.

1. Multiple tools
Open Market Operations (OMO)
Reserve Requirement Ratio (RRR)
Interest rates
Rediscount
Window guidance
SLF、MLF、SLO、PSL 、 TLF…
Individuals may feel ambiguous about the orientation, effect size and persistence
f those tools.

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2.Intensively intervention and various targets
changing benchmark interest rates to regulate funding cost
changing required reserve ratio
developing macroprudential framework
managing the stock market and real estate sector
RMB exchange rate intervention
...
The intensive intervention and dominant role of Chinese Central bank in

financial system indicate that slight changes in monetary policies could produce significant uncertainty shock.

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Monetary policy uncertainty index of US(Sun Bo et al.,2016)

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Link the credit risks with monetary policy uncertainty

Song and Xiong(2017)—Risks in China’s Financial System
Debt Crisis Risk
Housing Risk
Capital Outflow Risk
Stock Market Risk
Policy Risk
Active government interventions have profound impacts on the financial system.

Policies and regulations can deliver unintended consequences, some of which may be entirely counterproductive. This may eventually reduce the efficiency of the financial system and exacerbate the systemic risk.

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Main contribution

Provided the first direct evidence that China’s monetary policy uncertainty exacerbate

its financial risks.

Developed a specific proxy for China’s monetary policy uncertainty.
Measured China’s credit risks by using large-scale factor models

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Literature review

Uncertainty shocks in business cycles
Bloom (2009), Bloom et al.(2012),Villaverde et al. (2011)
Empirical evidence for uncertainty shocks
Baker et al. (2016) ,Ng et al. (2015)
Policy uncertainty
Villaverde et al. (2015), Born and Pfeifer (2014),Bianchi and Melosi(2017)

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Transmission mechanism from uncertainty to real economy

Real option channel
Bloom (2009),Bloom et al. (2012),Bachmann and Bayer (2013)
Precautional saving channel
Gourio (2012),Basu and Bundick (2012)
Financial friction channel
Gilchrist (2012),Alfaro et al. (2016)
Labor market friction(Leduc and Liu, 2016)
Imperfect information and uncertainty(Wang et al.,2018)

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China’s policy uncertainty

Hachem and Song (2017)
stricter liquidity standards and unintended credit booms
Cai et al. (2017)
tripling of stamp tax and speculative bubble in warrant market
Xiong and Song (2017)
active government interventions and financial risks
Xiong et al. (2017)
gradualist approach and misallocation

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We constructed the DSGE model with credit risks based on Bernanke et al.(1999) and

Christiano et al. (2014), and introduced monetary policy uncertainty shock by augmenting the Taylor rule with stochastic volatilities.

We estimated the uncertainty of monetary policy in China by using the Bayesian

MCMC method, and applied the time-varying dynamic factor model to measure financial risks in China’s bond market, stock market and credit market respectively, based on a large macro and financial dataset of China.

We further provided some empirical evidences of the impact of China’s monetary

policy uncertainty documented in the theoretical model by using Bayesian VAR model.

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Main findings

the increase of China’s monetary policy uncertainty could bring about

negative effects on economic activity and exacerbate the credit risks.

Credit risks could spill over to the real economy and amplify negative

impact of the monetary policy uncertainty on the output.

Credit risks currently make the greatest contribution to China’s whole

financial risks.

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This paper is linked with different streams of literature in macroeconomic concerning

uncertainty shocks and frictions.

The model can well duplicate the traditional channels documented in the literature through which the

uncertainty shock can tighten the economic activities. eg. Precautional saving channel (Gourio,2012), Real-option channel (Bloom et al. ,2012),and financials friction channel (Gilchrist ,2012).

The main conclusion is also in line with the literature focus on credit risks and business cycles.(Gilchriste t

al.,2012;Miao and Wang,2010)

This paper is also associated with the growing literature on China’s policy issues provides the findings
ffer direct evidence to support the analysis of Song and Xiong (2018).

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Model outline

New keysian DSGE model based on BGG model and Christiano et al. (2014)
Habit formation, investment adjustment cost, price stickness,financial friction
We depart from them by introducing monetary policy uncertainty shock

Household Banks Entrepreneur Capital producer Retailor Government

Deposit Loan Labor Wage Capital Wholesale goods Final goods Government purchasing Consumption Tax Interest

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1.Household

𝑛𝑏𝑦𝐹𝑢 ෍

𝑢=0 ∞

𝛾𝑢 𝐷𝑢 − 𝑐𝐷𝑢−1 − ൗ 𝜔𝑂𝑢

1+𝜃 1 + 𝜃 1−𝜏 − 1

1 − 𝜏 𝑡. 𝑢 𝑄𝑢𝐷𝑢 + 𝐶𝑢+1 = 𝑋

𝑢𝑂𝑢 + 𝑆𝑢𝐶𝑢 + 𝛲𝑢 − 𝑈𝑢

𝜇𝑢 = 𝐷𝑢 − 𝑐𝐷𝑢−1 − 𝜔 𝑂𝑢

1+𝜃

1 + 𝜃

−𝜏

− 𝛾𝑐 𝐷𝑢+1 − 𝑐𝐷𝑢 − 𝜔 𝑂𝑢+1

1+𝜃

1 + 𝜃

−𝜏

𝜇𝑢 = 𝛾𝐹𝑢 ቊ ቋ 𝜇𝑢+1𝑆𝑢+1 𝑄𝑢 𝑄𝑢+1 𝜇𝑢 𝑋

𝑢

𝑄𝑢 = 𝐷𝑢 − 𝑐𝐷𝑢−1 − 𝜔 𝑂𝑢

1+𝜃

1 + 𝜃

−𝜏

𝜔𝑂𝑢

𝜃

Representative household choose consumption and labor to maximize its lifetime expected utility function: We can get the following first-order condition:

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2.Entrepreneur

𝑍

𝑢 = 𝐵𝑢𝐿𝑢 𝛽𝑂𝑢 1−𝛽

𝐶𝑢+1

𝑑

= 𝑅𝑢𝐿𝑢+1 − 𝑊

𝑢

According to Bernanke et al. (1999), entrepreneurs manage the production sector that produces wholesale goods and sell it to the retailor firms .Entrepreneurs purchase capital from the capital producer and employ labor force from the household: At the end of period of 𝑢,Entrepreneurs issue debt contracts with financial institution to fund for new capital purchasing :

Period 𝒖 Period 𝒖 + 𝟐 End of period 𝑢,entrepreneurs use the net worth 𝑊

𝑢 and sign debt contracts

with bank to get 𝐶𝑢+1

𝑑

for their new capital purchasing 𝐿𝑢+1 Entrepreneurs decide default or non-default thus determine their net worth Entrepreneurs begin production and observe idiosyncratic productivity shock 𝜕𝑢+1 Period 𝒖 + 𝟑 End of period t+1,a fraction of γ entrepreneurs can survive, they use net worth 𝑊

𝑢+1 and sign new debt contract to

get 𝐶𝑢+2

𝑑

for purchasing 𝐿𝑢+2

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2.Entrepreneur

Assume that the entrepreneur’s production activity suffer from idiosyncratic productivity shock 𝜕𝑢,thus their capital return becomes 𝝏𝒖𝑺𝒖

𝒍.Assume 𝜕𝑢 is i.i.d and log normal with cumulative density function

ሻ 𝐺(𝜕𝑢 and density function ሻ 𝑔(𝜕𝑢 , 𝐹(𝜕𝑢ሻ =1.Due to the information asymmetry in the credit market, entrepreneur can observe 𝜕𝑢 while financial institutions have to pay extra cost to detect 𝜕𝑢, which is monitoring cost. Monitoring cost is propositional to the capital return 𝝂𝝏𝒖+𝟐𝑺𝒖+𝟐

𝒍

𝑹𝒖𝑳𝒖+𝟐.Define entrepreneur’s default threshold value 𝜜𝑢+1： 𝜜𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1 = 𝑆𝑢+1

𝑐

𝐶𝑢+1

𝑑

Where 𝑆𝑢+1

𝑐

is non default loan interest rate. Costly State Verification (CSV) framework of Townsend (1979). A debt contract specify the loan amount 𝐶𝑢+1

𝑑

and loan interest rate 𝑆𝑢+1

𝑐

Optimal Allocation is a standard debt contract : If 𝜕𝑢+1 ≥ 𝜜𝑢+1，no bankruptcy, entrepreneur pay fixed interests 𝑆t+1

𝑐

𝐶t+1

𝑑

； If 𝜕𝑢+1 < 𝜜𝑢+1 ，bankruptcy, entrepreneur’s pay full returen 𝜕𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1 ,net income of financial institution (minus monitor cost) is (1 − 𝜈ሻ𝜕𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1

𝐹𝑢𝑆𝑢+1

𝑙

= 𝐹𝑢 ቐ ቑ ൰ 1 𝑌𝑢+1 𝛽𝑍

𝑢+1

𝐿𝑢+1 + 𝑅𝑢+1(1 − 𝜀 𝑅𝑢

The expected marginal return of the capital is

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3.Financial intermediation

Arrow-Lind Theorem tells that financial intermediation can be seen as risk neutral and achieve zero profit in equilibrium:

1 − 𝐺 𝜜𝑢+1 𝑆𝑢+1

𝑐

𝐶𝑢+1

𝑑

+ 1 − 𝜈 න

𝜜𝑢+1

𝜕𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1𝑒 𝐺 𝜕𝑢+1 = 𝑆𝑢𝐶𝑢+1

𝑑

The optimal debt contract is equivalent to choose 𝜜𝑢+1 and 𝑀𝑢 to maximize entrepreneur’s utility function subject to zero profit conditions.

max𝑉

ሼ ሽ 𝜜𝑢+1,𝑀𝑢 =

ධ

𝜜𝑢+1 ∞

𝜕𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1 − 𝑆𝑢+1

𝑐

𝐶𝑢+1

𝑑

𝑒𝐺 𝜕𝑢+1 𝑊

𝑢𝑆𝑢

= ׬

𝜜𝑢+1 ∞

𝜕𝑢+1 − 𝜜𝑢+1 𝑒𝐺 𝜕𝑢+1

𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1 𝑆𝑢𝑊

𝑢

= ׬

𝜜𝑢+1 ∞

𝜕𝑢+1 − 𝜜𝑢+1 𝑒𝐺 𝜕𝑢+1

𝑆𝑢+1

𝑙

𝑆𝑢 𝑀𝑢

The entrepreneur maximize his utility function ,which can be defined as the expected return and

pportunity cost:

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We define the credit risk of this economy as the default probability of entrepreneur

𝐶𝑏𝑜𝑙𝑠𝑣𝑞𝑢𝑢 = න

𝜜𝑢+1

𝑒𝐺 𝜕𝑢+1 = 𝐺 𝜜𝑢+1 𝐺 𝜕𝑢 = log𝑜𝑑𝑒𝑔 𝜕𝑢, 𝜈𝑢, 𝜏𝑢

2

𝑚𝑝𝑕 𝜏𝑢 𝜏 = 𝜍𝜏𝑚𝑝𝑕 𝜏𝑢−1 𝜏 + 𝜁𝜏𝑢

Since 𝜕𝑢 reflect the idiosyncratic risk in actual business activities of entrepreneur, 𝜏𝑢 characterizes the extent of cross-sectional dispersion in, 𝜏𝑢 was interpreted as the risk shocks according to Christiano et al. (2014).

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4.Capital producers

𝑛𝑏𝑦

𝐽𝑢 𝐹𝑢 𝑅𝑢𝐿𝑢+1 − 𝐽𝑢 − 𝜓

2 𝐽𝑢 𝐿𝑢 − 𝜀

2

𝑡. 𝑢. 𝐿𝑢+1 = 𝑣𝑢𝐽𝑢 + 1 − 𝜀 𝐿𝑢 FOC: 𝑅𝑢 = 1 𝑣𝑢 1 + 𝜓 𝐽𝑢 𝐿𝑢 − 𝜀

Capital producers purchase the final goods from retailer firms and use them to produce the capital for next period with a linear technology. The optimization problem of capital producer is:

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5.Retailer

𝐹𝑢 ෍

𝑙=0 ∞

𝜚𝑞

𝑙𝛭𝑢,𝑢+𝑙

ത 𝑄𝑢 𝑗 𝑄𝑢+𝑙 − 𝑄𝑢+𝑙

𝑋

𝑄𝑢+𝑙 𝑍

𝑢+𝑙 𝑗

𝑡. 𝑢. 𝑍

𝑢 𝑗 =

𝑄𝑢 𝑗 𝑄𝑢

−𝜁𝑞

𝑍

𝑢

All the retailer pricing strategy according to Calvo(1983), only 1 − 𝜚𝑞 of them can adjust price each period.

𝑄𝑢 = 𝑄𝑢−1

𝜚𝑞 ത

𝑄𝑢

1−𝜚𝑞

Inflation transition equation:

𝑄𝑢 𝑄𝑢−1 = 𝜆 𝑄𝑢

𝑋

𝑄𝑢

𝜚𝑞

𝐹𝑢 𝑄𝑢+1 𝑄𝑢

𝛾

𝜚 = ൗ 1 − 𝜚𝑞 1 − 𝛾𝜚𝑞 𝜚𝑞

Retailers are introduced to produce price stickiness. The optimal pricing strategy of retailers is to choose optimal price to maximize their expected profits:

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6.Central bank and government

𝑗𝑢 = 𝑗0 + 𝛿0𝑗𝑢−1 + 𝛿1𝜌𝑢 + 𝛿2𝑧𝑢 + ℎ𝑢𝜊𝑢 𝜊𝑢 ∼ 𝑂 0, 𝜏1

2

𝑚𝑜ℎ𝑢 = 𝛽0 + 𝜍1𝑚𝑜ℎ𝑢−1 + 𝑤𝑢 𝑤𝑢 ∼ 𝑂 0, 𝜏2

2

A related literature has emphasized the importance of time-varying volatility in macroeconomic time series models, where the heteroskedastic errors are typically modeled by introducing the stochastic volatility (see, e.g., Cogley and Sargent, 2005; Primiceri, 2005;Sims and Zha,2006) 𝜊𝑢 is first moment shock, level shock， 𝑤𝑢 is second moment shock ,uncertainty shock Assume the ration of fiscal expense to GDP is fixed at 𝜕𝑢

𝑕:

𝐻𝑢 = 𝜕𝑢

𝑕𝑍 𝑢

𝐻𝑢 = 𝑈𝑢

Following Villaverde et al.(2011),we introduce the following Taylor rule: A myriad of literature show that there exists uncertainty in central bank’s monetary policy (Davig and Leeper ,2007;Mumtaz and Zanetti,2013;Born and Pfeifer,2014;Bianchi and Melosi,2017).

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Why 𝒊𝒖 can represent the monetary policy uncertainty?

Since it’s in line with Ng et al.(2015)’s definition about the uncertainty:
define h -period ahead uncertainty in the variable 𝑧𝑘𝑢 ∈ 𝑍

𝑢 = (𝑧1𝑢, 𝑧1𝑢,… 𝑧1𝑢)′, denoted by 𝑉 𝑘𝑢 𝑧 ℎ :

𝑉

𝑘𝑢 𝑧 ℎ = 𝐹

𝑧𝑘𝑢+ℎ − 𝐹 𝑧𝑘𝑢+ℎห𝐽𝑢

2ห𝐽𝑢

𝑉𝑢

𝑧 ℎ

= 𝑞lim

𝑂𝑧→∞

෍

𝑘=1 𝑂𝑧

𝜕𝑘𝑉𝑘𝑢

𝑧 ℎ

Ng et al.(2015)’s Econometrics framework:

𝑧𝑘𝑢 = 𝑑

𝑘 + ෍ 𝑞=1 𝑄

𝜍𝑗,𝑞𝑧𝑘,𝑢−𝑞 + ෍

𝑟=1 𝑅

𝑐𝑗,𝑟𝑎𝑢−𝑟 + 𝜏𝑗,𝑢𝑓𝑗,𝑢, 𝑓𝑗,𝑢~𝑂 0,1 𝑎𝑢 = 𝐷 + ෍

𝑚=1 𝐼

𝑒𝑚𝑎𝑢−𝑚 + ℎ𝑢𝑤𝑢, 𝑤𝑢 ~𝑂 0,1 It can be written as a VAR model with stochastic volatility: 𝑧𝑘𝑢 𝑎𝑢 = 𝑑

𝑘

𝐷 + 𝜍 𝑀 𝑐 𝑀 𝑒 𝑀 𝑧𝑘𝑢 𝑎𝑢 + 𝜏𝑗,𝑢𝑓𝑗,𝑢 ℎ𝑢𝑤𝑢

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7.Equilibrium

Given the model setup and fiscal policyሼ ሽ 𝐻𝑢, 𝑈

𝑢 𝑢=0 ∞

chose by government and monetary policyሼ ሽ 𝑆𝑢 𝑢=0

∞

set by central bank, we can define the equilibrium of this model as： Allocation sequnce 𝛰 can maximize the utility of household and entrepreneur and solve the profit maximization problem of capital producer and retailer, price sequence 𝛦 can clear the product market and bond market: 𝑍

𝑢 = 𝐷𝑢 + 𝐽𝑢 + 𝐻𝑢 + 𝜈 න 𝜜𝑢+1

𝜕𝑢+1𝑆𝑢+1

𝑙

𝑅𝑢𝐿𝑢+1𝑒 𝐺 𝜕𝑢 Price sequence 𝛦 ≡ ൛ ൟ 𝑄𝑢, 𝑄𝑢

𝑋, 𝑆𝑢 𝑙, 𝑆𝑢 𝑐, 𝑋 𝑢, 𝑅𝑢, 𝜇𝑢, 𝜌𝑢 𝑢=0 ∞

Allocation sequence 𝛰 ≡ ሼ ሽ 𝐷𝑢, 𝑂𝑢, 𝑍

𝑢, 𝐿𝑢, 𝐶𝑢, 𝐽𝑢, 𝑊 𝑢, 𝑀𝑢, 𝜜𝑢 𝑢=0 ∞

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Calibration

𝑗𝑢 = 𝑗0 + 𝛿0𝑗𝑢−1 + 𝛿1𝜌𝑢 + 𝛿2𝑧𝑢 + ℎ𝑢𝜊𝑢 𝜊𝑢 ∼ 𝑂 0, 𝜏1

2

𝑚𝑜ℎ𝑢 = 𝛽0 + 𝜍1𝑚𝑜ℎ𝑢−1 + 𝑤𝑢 𝑤𝑢 ∼ 𝑂 0, 𝜏2

2

parameter value parameter value



Subjective discount rate 0.993

b

Habit formation parameter 0.7



Deprecation rate 0.025



Elasticity of labor supply 2

p



Price stickiness 0.75

p



Elasticity of substitution 10



Capital-output share 0.5



Risk-aversion coefficient 2



Monitoring cost 0.2

g



Government expenditure ratio 0.178

N

Steady state labor supply 0.33

( )

F 

Steady state default rate 0.004

 b  

p

 p

    g  N( )

F 

SLIDE 31

𝑗𝑢 = 𝑗0 + 𝛿0𝑗𝑢−1 + 𝛿1𝜌𝑢 + 𝛿2𝑧𝑢 + ℎ𝑢𝜊𝑢 𝜊𝑢 ∼ 𝑂 0, 𝜏1

2

𝑚𝑜ℎ𝑢 = 𝛽0 + 𝜍1𝑚𝑜ℎ𝑢−1 + 𝑤𝑢 𝑤𝑢 ∼ 𝑂 0, 𝜏2

2

Divide the parameter five groups:𝐶1 = 𝑗0, 𝛿0, 𝛿1, 𝛿2 , 𝐶2 = 𝛽0, 𝜍1 , 𝜏1

2, 𝜏2 2, ሼ

ሽ ℎ𝑢 (1)Set prior: 𝐶1∼ 𝑂 ഫ 𝐶1, ഫ 𝛵1 , 𝐶2 ∼ 𝑂 ഫ 𝐶2, ഫ 𝛵2 , 𝜏1 ∼ 𝐽𝐻

𝑈

1

2 , 𝜑1 2 , 𝜏2 ∼ 𝐽𝐻 𝑈

2

2 , 𝜑2 2

Get the initial value of 𝑪𝟐, 𝑪𝟑, 𝝉𝟐, 𝝉𝟑 through OLS estimation and set initial value of 𝒊𝒖equal to ො 𝜻𝒖

𝟑

(2)Sampling ℎ𝑢|𝐶1, 𝐶2, 𝜏1, 𝜏2 Step1: when t=2 to T-1,sampling from the candidate density: 𝑟 𝛸𝐻+1 = ℎ𝑢

−1𝑓𝑦𝑞

Τ − 𝑚𝑜ℎ𝑢 − 𝜈 2 2𝜏ℎ 𝜈 = Τ 𝛽0 1 − 𝜍1 + 𝜍1 lnℎ𝑢+1 + lnℎ𝑢−1 1 + 𝜍1

2 , 𝜏ℎ =

Τ 𝜏2 1 + 𝜍1

2

Calculate the accept ratio: 𝛽 = min ൘ ℎ𝑢,𝑜𝑓𝑥

−1

𝑓𝑦𝑞

−𝑛𝑢

2

2ℎ𝑢,𝑜𝑓𝑥

ℎ𝑢,𝑝𝑚𝑒

−1 𝑓𝑦𝑞 −𝑛𝑢

2

2ℎ𝑢,𝑝𝑚𝑒 , 1

𝑛𝑢 = 𝑗𝑢 − 𝑗0 − 𝛿0𝑗𝑢−1 − 𝛿1𝜌𝑢 − 𝛿2𝑧𝑢 Sampling 𝒗 ∼ 𝑽 𝟏, 𝟐 𝒋𝒈 𝒗 < 𝜷 then 𝒊𝒖 = 𝒊𝒖,𝒐𝒇𝒙 otherwise retain 𝒊𝒖,𝒑𝒎𝒆 Step 2:When t=T,sampling ℎ𝑈 from 𝑟 𝛸𝐻+1 = ℎ𝑢

−1𝑓𝑦𝑞

Τ − 𝑚𝑜ℎ𝑢 − 𝜈 2 2𝜏ℎ , 𝜈 = 𝑚𝑜ℎ𝑢−1, 𝜏ℎ = 𝜏2 Step 3: When t=0, sampling 𝑤𝑢 ∼ 𝑂 0, 𝜏2

2 and set ℎ0= exp 𝛽0 + 𝜍1𝑚𝑜ℎ1 + 𝑤𝑢

Bayesian MCMC Method

SLIDE 32

(5) Repeat the step (2) to (4) 10000 times，the last 5000 draws provide an approximation to the marginal posterior distributions. 𝐶2 ∼ 𝑂 𝐶2

∗, 𝛵2 ∗

𝐶2

∗ =

ഫ 𝛵2

−1 + 1

ො 𝜏1

2 𝑌′𝑢𝑌𝑢 −1

ഫ 𝛵2

−1ഫ

𝐶2 + 1 ො 𝜏1

2 𝑌′𝑢𝑍 𝑢

𝛵2

∗ =

ഫ 𝛵2

−1 + 1

ො 𝜏1

2 𝑌′𝑢𝑌𝑢 −1

Sampling 𝝉𝟑

𝟑 from

𝜏2

2 ∼ 𝐽𝐻 𝑈2 ∗

2 , 𝜑2

∗

2 𝑈2

∗ = 𝑈2 + 𝑈

𝜑2

∗ = 𝜑2+ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢

′ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢 (4)Sampling 𝑪𝟐, 𝝉𝟐|𝒊𝒖, 𝑪𝟑, 𝝉𝟑, WLS estimate of 𝒁𝒖 = ൛ ൟ Τ 𝒋𝒖 𝒊𝒖 to 𝒀𝒖= ቄ Τ 𝟐 𝒊𝒖 ൟ , Τ 𝒋𝒖−𝟐 𝒊𝒖 , Τ 𝒛𝒖 𝒊𝒖 , Τ 𝝆𝒖 𝒊𝒖 𝐶1 ∼ 𝑂 𝐶1

∗, 𝛵1 ∗

𝐶1

∗ =

ഫ 𝛵1

−1 + 1

ො 𝜏1

2 𝑌′𝑢𝑌𝑢 −1

ഫ 𝛵1

−1ഫ

𝐶1 + 1 ො 𝜏1

2 𝑌′𝑢𝑍 𝑢

𝛵2

∗ =

ഫ 𝛵2

−1 + 1

ො 𝜏1

2 𝑌′𝑢𝑌𝑢 −1

𝜏1

2 ∼ 𝐽𝐻 𝑈 1 ∗

2 , 𝜑1

∗

2 𝑈

1 ∗ = 𝑈 1 + 𝑈

𝜑1

∗ = 𝜑1+ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢

′ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢 (3)Sampling , OLS estimate of 𝒁𝒖= ሼ ሽ 𝐦𝐨𝒊𝒖 to 𝒀𝒖 = ሼ𝟐 ሽ , 𝐦𝐨𝒊𝒖−𝟐 𝐶2, 𝜏2|ℎ𝑢, 𝐶1, 𝜏1 Sampling 𝝉𝟐

𝟑 from

෠ 𝐶1 = ൛ Ƹ 𝑗0, ሽ ො 𝛿0, ො 𝛿1, ො 𝛿2 ො 𝜏1

2 = 𝑍 𝑢 − ෠

𝐶2𝑌𝑢

′ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢 ෠ 𝐶2 = ሼ ሽ ො 𝛽0, ො 𝜍1 ො 𝜏2

2 = 𝑍 𝑢 − ෠

𝐶2𝑌𝑢

′ 𝑍 𝑢 − ෠

𝐶2𝑌𝑢

SLIDE 33

SLIDE 34

Estimated monetary policy uncertainty

SLIDE 35

Comparing to Ng et al.(2015)’s method

0.1 0.2 0.3 0.4 0.5 0.6 0.7 mpu-h3-ng MPU

SLIDE 36

Impulse response matching with empirical VAR(Christiano et al.,2005)

𝐾 = min

𝛪

𝛺 𝛪 − ෡ 𝛺

′𝑊−1 𝛺 𝛪 − ෡

𝛺 𝛪=ሼ ሽ 𝛽0，𝜍1，σ2

SLIDE 37

Monetary policy uncertainty shock: third-order approximation

According Schmitt-Grohe & Uribe (2004) , a large set of DSGE models can be recast in the following form

𝐹𝑢 𝑔 𝑦𝑢+1, 𝑧𝑢+1, 𝑦𝑢, 𝑧𝑢 = 0

As shown in Schmitt-Grohe & Uribe (2004) ,a solution of the above equation takes the form:

𝑦𝑢+1 = ℎ 𝑦𝑢, 𝜏 + 𝜏𝜗𝑢+1 𝑧𝑢 = 𝑕 𝑦𝑢, 𝜏

Schmitt-Grohe & Uribe (2004) showed the second-order approximation of the policy functions:

𝑦𝑢+1 = ℎ𝑦𝑦𝑢+

1 2 ℎ𝜏𝜏𝜏2+ 1 2 ℎ𝑦𝑦 𝑦𝑢⨂𝑦𝑢 + 𝜏𝜗𝑢+1

𝑧𝑢 = 𝑕𝑦𝑦𝑢+1

2 𝑕𝜏𝜏𝜏2+ 1 2 𝑕𝑦𝑦 𝑦𝑢⨂𝑦𝑢

Andreasen (2017) showed the third-order approximation of the policy functions:

𝑦𝑢+1 = ℎ𝑦𝑦𝑢+

1 2 ℎ𝜏𝜏𝜏2+ 1 2 ℎ𝑦𝑦 𝑦𝑢⨂𝑦𝑢 + 1 6 ℎ𝜏𝜏𝜏𝜏3 + 3 6 ℎ𝜏𝜏𝑦𝜏2𝑦𝑢 + 1 6 ℎ𝑦𝑦𝑦 𝑦𝑢⨂𝑦𝑢⨂𝑦𝑢 + 𝜏𝜗𝑢+1

𝑧𝑢 = 𝑕𝑦𝑦𝑢+

1 2 𝑕𝜏𝜏𝜏2+ 1 2 𝑕𝑦𝑦 𝑦𝑢⨂𝑦𝑢 + 1 6 𝑕𝜏𝜏𝜏𝜏3+ 3 6 𝑕𝜏𝜏𝑦𝜏2𝑦𝑢 + 1 6 𝑕𝑦𝑦𝑦 𝑦𝑢⨂𝑦𝑢⨂𝑦𝑢

SLIDE 38

Impulse response function should be adjusted

According to Koop et al.(1996) the generalized impulse response function for nonlinear VAR model:
Dynare calculate the traditional impulse response function:
Problems arise if there are high-order terms in the equation when we do simulation, we have to

“pruning" out the unstable higher-order terms. Andreasen et al. (2017) provided the pruning algorithm and related MATLAB toolbox.

An example: 𝑧𝑢 = 𝜍𝑧𝑢−1 + 𝛽𝑧𝑢−1

2

+ 𝜁𝑢

The pruning solution is:
𝑧𝑢 = 𝜍𝑧𝑢−1 + 𝛽 ෤

𝑧𝑢−1

2

+ 𝜁𝑢

෤

𝑧𝑢−1 = 𝜍 ෤ 𝑧𝑢−2 + 𝜁𝑢−1

𝐽𝑆𝐺𝑢 𝑘 = 𝐹 𝑧𝑢+𝑘|Ω𝑢−1, 𝜁𝑢 ≠ 0, 𝜁𝑢+𝑘 = 0, 𝑘 > 1 − 𝐹 𝑧𝑢+𝑘หΩ𝑢−1, 𝜁𝑢 = 0, 𝜁𝑢+𝑘 = 0, 𝑘 > 1 𝐽𝑆𝐺𝑢 𝑘 = 𝐹 𝑧𝑢+𝑘|Ω𝑢−1, 𝜁𝑢 ≠ 0 − 𝐹 𝑧𝑢+𝑘|Ω𝑢−1, 𝜁𝑢 = 0 for j = 0,1,2 …

SLIDE 39

The algorithm to calculate IRF at ergodic mean

Suppose we have time 0, time 𝑢 and time 𝑈 where 𝑈 > 𝑢 and 𝑢 itself is large.
1. From a random number generator, draw H sets of shocks 𝜁𝑢 𝑢=0

𝑈

,but no need to draw 𝜁𝑢 : 𝜁0

1, 𝜁1 1, … 𝜁𝑢−1 1

, 𝜁𝑢+1

1

, 𝜁𝑢+2

1

, 𝜁𝑢+𝑈

1

…. 𝜁0

𝐼, 𝜁1 𝐼, … 𝜁𝑢−1 𝐼 , 𝜁𝑢+1 𝐼 , 𝜁𝑢+2 𝐼 , 𝜁𝑢+𝑈 𝐼

2.Using 𝜁𝑢 = 𝜏𝜁 together with above H sets of shocks to compute(with pruning) 𝑧0

1,1, 𝑧 1 1,1, … 𝑧𝑢−1 1,1 , 𝑧𝑢+1 1,1 , 𝑧𝑢+2 1,1 , 𝑧𝑢+𝑈 1,1

…. 𝑧0

𝐼,1, 𝑧 1 𝐼,1, … 𝑧𝑢−1 𝐼,1, 𝑧𝑢+1 𝐼,1, 𝑧𝑢+2 𝐼,1, 𝑧𝑢+𝑈 𝐼,1

3.Using 𝜁𝑢 = 0 together with above H sets of shocks to compute(with pruning) 𝑧0

1,0, 𝑧 1 1,0, … 𝑧𝑢−1 1,0 , 𝑧𝑢+1 1,0 , 𝑧𝑢+2 1,0 , 𝑧𝑢+𝑈 1,0

…. 𝑧0

𝐼,0, 𝑧 1 𝐼,0, … 𝑧𝑢−1 𝐼,0, 𝑧𝑢+1 𝐼,0, 𝑧𝑢+2 𝐼,0, 𝑧𝑢+𝑈 𝐼,0

4.The first 𝑢 periods is dropped in each replication (Burn in).Then, 𝐽𝑆𝐺 = 1 𝐼 ෍

𝑗=1 𝐼

𝑧𝑢+𝑘

𝑗,1 − 𝑧𝑢+𝑘 𝑗,0

SLIDE 40

Risk shock

SLIDE 41

Monetary policy uncertainty shock

SLIDE 42

SLIDE 43

Monetary policy uncertainty rise Credit risk increase Output decline

SLIDE 44

Dissecting other channels of monetary policy uncertainty on real economy

Precautional saving channel
Gourio(2012) ,Basu and Bundick (2017)
Real Option Value channel
Bloom (2009) ,Born and Pfeifer(2014)
Financial frictions channel
Gilchrist(2014), Lin xiaoji et al.(2016)

SLIDE 45

SLIDE 46

SLIDE 47

SLIDE 48

Time-varying Dynamic Factor Model

We build the p-lag time-varying DFM (dynamic factor model) to construct the

financial risk factors, written as:

Set
The time varying coefficients are assumed to follow random walk:
The TVP-DFM are estimated by the Bayesian MCMC method proposed by Koop

and Korobilis(2014).

𝑔

𝑢

𝑧𝑢 = 𝑑𝑢 + 𝐶1𝑢 𝑔

𝑢−1

𝑧𝑢−1 + ⋯ + 𝐶𝑞𝑢 𝑔

𝑢−𝑞

𝑧𝑢−𝑞 + 𝑤𝑢 𝑦𝑢 = 𝛭𝑢

𝑔𝑔 𝑢 + 𝛭𝑢 𝑧𝑧𝑢 + 𝑓𝑢

𝑏𝑢 = 𝑑𝑢

′, 𝑤𝑓𝑑 𝐶1𝑢 ′, … , 𝑤𝑓𝑑 𝐶𝑞𝑢 ′ ′

𝑐𝑢 = 𝛭𝑢

𝑔 ′, 𝛭𝑢 𝑧 ′ ′

𝑏𝑢=𝑏𝑢−1 + 𝜈𝑢

𝑏

𝑐𝑢=𝑐𝑢−1 + 𝜈𝑢

𝑐

𝜈𝑢

𝑏 ∼ 𝑂(0, ෍ 𝑢 𝑏

ሻ 𝜈𝑢

𝑐 ∼ 𝑂(0, ෍ 𝑢 𝑐

ሻ

SLIDE 49

# Abbreviation Description Unit 1 3mTED 3m SHIBOR/3m Household Savings Deposits Rate Spread % 2 6mTED 6m SHIBOR/6m Household Savings Deposits Rate Spread % 3 3mTED 1y SHIBOR/1y Household Savings Deposits Rate Spread % 4 1-5yHRate Individual Housing Provident Fund loan rate: 5 Year or Less % 5 O5yHRate Individual Housing Provident Fund loan rate: Over 5 Year % 6 CLoan_s Consume Loan: Local & Foreign Currency: Short Term/VAI % 7 CLoan_l Consume Loan: Local & Foreign Currency: Medium & Long Term/VAI % 8 Loan_s Financial Inst: Use: Loan: Domestic: Short Term/VAI % 9 Loan_l Financial Inst: Use: Loan: Domestic: Medium & Long Term/VAI % 10 B_beta CAPM Beta Value of Banks Stock Level Value 11 1y3mTS 1y Treasury Bond Yield/ 3m Treasury Bond Yield Spread % 12 3y3mTS 3y Treasury Bond Yield/ 3m Treasury Bond Yield Spread % 13 5y3mTS 5y Treasury Bond Yield/ 3m Treasury Bond Yield Spread % 14 7y3mTS 7y Treasury Bond Yield/ 3m Treasury Bond Yield Spread % 15 10y3mTS 10y Treasury Bond Yield/ 3m Treasury Bond Yield Spread % 16 1y3mCS 1y Enterprise Bond (AAA) Yield / 3m Treasury Bond Yield Spread % 17 3y3mCS 3y Enterprise Bond (AAA) Yield / 3m Treasury Bond Yield Spread % 18 5y3mCS 5y Enterprise Bond (AAA) Yield / 3m Treasury Bond Yield Spread % 19 7y3mCS 7y Enterprise Bond (AAA) Yield / 3m Treasury Bond Yield Spread % 20 10y3mCS 10y Enterprise Bond (AAA) Yield / 3m Treasury Bond Yield Spread % 21 SVOL_SH Volatility of Shanghai Stock Exchange Composite Index Return % 22 SVOL_SZ Volatility of Shenzhen Stock Exchange Composite Index Return % 23 TO_SH Turnover Rate of Shanghai Stock Exchange Composite Index % 24 TO_SZ Turnover Rate of Shenzhen Stock Exchange Composite Index % 25 VIX CBOT Volatility Index Index Value 26 M2VAI M2/VAI % 27 FAIVAI Fixed Asset Investment/VAI % 28 RSVAI Retail Sales of Consumer Goods /VAI % 29 PMI Purchasing Managers’ Index Index Value 30 ECI Economic Climate Indicator: Coincident Index Index Value

SLIDE 50

Variables Factor loading before rotation Factor loading after rotation Factor 1 Factor 2 Factor 3 Factor 1 Factor 2 Factor 3 TED

0.67
0.25

0.08

0.62

0.17

0.32

1-5yHRate 0.52

1.31

0.45

0.33
1.43
0.18

O5yHRate 0.55

1.31

0.44

0.30
1.45
0.17

CLoan_s

0.98

0.77

0.58
0.12

1.31

0.38

CLoan_l

1.20

0.93

1.11

0.09 1.71

0.78

Loan_s

0.95

0.93

0.03
0.36

1.27 0.14 Loan_l

0.95

0.89

1.28

0.36 1.58

0.83

B_beta 0.92

1.03

0.23 0.19

1.39
0.05

1y3mTS 0.37 0.38

0.60

0.75 0.24

0.12

3y3mTS 0.87 1.08

0.90

1.54 0.57 0.21 5y3mTS 1.14 1.05

0.65

1.58 0.32 0.48 7y3mTS 1.18 1.06

0.60

1.58 0.30 0.54 10y3mTS 1.17 0.91

0.51

1.47 0.16 0.52 1y3mCS 0.52

1.60
0.64

0.22

1.35
1.16

3y3mCS 1.15

0.72
1.23

1.32

0.88
0.91

5y3mCS 1.31

0.26
1.19

1.57

0.63
0.58

7y3mCS 1.42

0.13
1.07

1.63

0.63
0.37

10y3mCS 1.48

0.08
0.94

1.61

0.66
0.23

SVOL_SH 1.19 0.87 1.54 0.26

0.44

2.07 SVOL_SZ 1.10 0.94 1.13 0.46

0.22

1.76 TO_SH 0.63 0.69 1.44

0.15
0.22

1.69 TO_SZ 0.75 1.19 1.32 0.18 0.13 1.91 VIX 1.32

0.28

0.22 0.74

1.04

0.49

SLIDE 51

SLIDE 52

Bayesian VAR evidence

Considering the following VAR model with lag p :

𝑍

𝑢 = 𝑑 + 𝐶1𝑍 𝑢−1 + 𝐶2𝑍 𝑢−2 + ⋯ + 𝐶𝑞𝑍 𝑢−𝑞 + 𝑤𝑢

Where 𝐹 𝑤𝑢 = 0, 𝐹 𝑤𝑢

′𝑤𝑡 ′ = 0 𝑗𝑔 𝑢 ≠ 𝑡 and 𝐹 𝑤𝑢 ′𝑤𝑡 ′ = Σ 𝑗𝑔 𝑢 = 𝑡

Define 𝑌𝑢 = 𝑑𝑗, 𝑍

𝑗,𝑢−1, 𝑍 𝑗,𝑢−2,…𝑍 𝑗,𝑢−𝑞 then VAR can be written as:

𝑍

𝑢 = 𝑌𝑢𝐶 + 𝑤𝑢

Take the Vec Operator: 𝑧 = 𝐽𝑂⨂𝑌 𝑐 + 𝑊 Where 𝑧 = 𝑤𝑓𝑑 𝑍

𝑢 , 𝑐 = 𝑤𝑓𝑑 𝐶 and V = 𝑤𝑓𝑑 𝑤𝑢 .

Following Bańbura et al. (2010), produce the artificial data 𝑍

𝐸, 𝑌𝐸,run on OLS of 𝑍 𝐸 𝑝𝑜 𝑌𝐸

𝑐0 = 𝑌𝐸

′ 𝑌𝐸 −1 𝑌𝐸 ′ 𝑍 𝐸

𝑇 = 𝑍

𝐸 − 𝑌𝐸𝑐0 ′ 𝑍 𝐸 − 𝑌𝐸𝑐0

The prior of coefficient and covariance matrix are set to normal and Inverse Wishart distribution respectively: 𝑞 𝑐|Σ ∼ 𝑂 ෨ 𝑐0, Σ⨂ 𝑌𝐸

′ 𝑌𝐸 −1

𝑞 Σ ~𝐽𝑋 𝑇, 𝑈𝐸 − 𝐿 Where ෨ 𝑐0 = 𝑤𝑓𝑑 𝑐0 , 𝑈𝐸 is the length of artificial data and 𝐿 is the number of regressors in each equation.

SLIDE 53

Model’s fit

SLIDE 54

Bayesian VAR evidence: monetary policy uncertainty shock

SLIDE 55

Bayesian VAR evidence: Bond market risk shock

SLIDE 56

Bayesian VAR evidence: Credit risk shock

SLIDE 57

Bayesian VAR evidence: Stock market risk shock

SLIDE 58

Variance decomposition

SLIDE 59

Historical decomposition

SLIDE 60

Forecast

SLIDE 61

Conclusion

The increase of the uncertainty of monetary policy will lead to the rise of credit risks

and the decline of output.

The rise of credit risks in bank sector will have a significant tightening effect on real

economic activities and will further aggravate the negative impact of monetary policy uncertainty shock.

The policy implications for Chinese government to prevent financial risks:
1.Reduce the policy uncertainty and enhance the communication with public
2.Focus on the credit risks

SLIDE 62

Future improvement

1.Including Fiscal uncertainty shock and other uncertainty shock
2.Estimation of the full model to examine relative importance of different uncertainty shocks

Particle Filter

3.Other method to introduce uncertainty like regime switching
4.More micro-level empirical evidences

SLIDE 63