The document summarizes a research paper that evaluates the welfare and distributional effects of fiscal volatility using a quantitative model. The paper uses a standard Krusell-Smith model with government spending and tax shocks, calibrated to match wealth inequality. It finds that eliminating government spending shocks increases welfare by 0.029%, with effects increasing for wealthier households. The key transmission is volatility in marginal tax rates affecting returns for wealthy agents. The summarized paper is praised for its clear execution and potential for further research on portfolio choice and longer-term fiscal shocks.

1. Discussion of The Welfare and Distributional Effects of
Fiscal Volatility: a Quantitative Evaluation
by R¨udiger Bachmann, Jinhui H. Bai, Minjoon Lee and
FudongZhang
Jochen Mankart1
Deutsche Bundesbank
19 March 2018
1The views expressed in this presentation represent the authors’ personal opinions
and do not necessarily reflect those of the Deutsche Bundesbank.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 1 / 12

2. Paper: Welfare in HAFP Heterogenous Agents Fiscal Policy
Research question: What are the effects of fiscal volatility in the presence
of inequality?
Strategy:
Use a standard Krusell-Smith model.
Add G & G shocks and a realistic tax scheme, calibrate it.
Counterfactual: eliminate G shocks.
Compute welfare gains, including stochastic transition (!).
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 2 / 12

3. Paper: Welfare in HAFP Heterogenous Agents Fiscal Policy
Research question: What are the effects of fiscal volatility in the presence
of inequality?
Strategy:
Use a standard Krusell-Smith model.
Add G & G shocks and a realistic tax scheme, calibrate it.
Counterfactual: eliminate G shocks.
Compute welfare gains, including stochastic transition (!).
Key results:
1 Welfare effects small.
2 Welfare effects increasing in wealth.
Very clear, very mature paper.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 2 / 12

4. Model
Aggregate TFP and G shocks.
G volatility transmits to tax volatility.
Exogenous discount factor shocks: β = {βL, βM, βH }.
Exogenous income shocks: households are E earn wage, or U get
benefits. No labor supply decision.
Self insurance through savings in asset a.
As in KS, TFP and U rate (perfectly correlated) 2-states only:
Ug = 4%, Ub = 10%.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 3 / 12

5. Fiscal side
Acyclical AR(1) shocks to government spending.
UI transfers countercyclical.
Estimated (aggregate) tax rule. T = T(Yt, Bt, Gt )
Tax system
Linear consumption tax τc
Progressive income tax (Castaneda et al, 2003; Gouveia & Strauss,
1994)
τy
(yt ) = τ1 yt − y−τ2
t + τ3
− 1
τ2
+ τ0yt (1)
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 4 / 12

6. Calibration and results
Lot of work to show which of the tax parameters does the cyclical
adjustment.
It’s τ1 since tax share of rich pro-cyclical and top marginal tax rate is
τ0 + τ1.
Discount factor heterogeneity process (values and transitions)
calibrated to match capital-output ratio, wealth Gini and wealth share
of top 1%
Very careful description of initial stoachastic (2 agg shock) steady
state, new (1 shock) stochastic steady state, and transitional
dynamics.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 5 / 12

7. A deeper look into results
Eliminating G shocks, increases welfare by 0.029%.
0.021% is the direct utility effect of risk-averse preferences over G.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 6 / 12

8. A deeper look into results
Eliminating G shocks, increases welfare by 0.029%.
0.021% is the direct utility effect of risk-averse preferences over G.
Remaining 0.008% distributed (roughly):
flat for < 95% of wealth distribution,
increasing in top 5%.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 6 / 12

9. A deeper look into results
Eliminating G shocks, increases welfare by 0.029%.
0.021% is the direct utility effect of risk-averse preferences over G.
Remaining 0.008% distributed (roughly):
flat for < 95% of wealth distribution,
increasing in top 5%.
Behind this are 3 effects:
1 Vola bad because hampers insurance function of savings.
2 Taxation shocks are effectively shocks to top marginal tax rate: rate of
return shocks.
3 Factor prices change due to changes in capital stock.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 6 / 12

10. Income process
2 states (E and U) implies counterfactual earnings distribution.
Why is earnings distribution less relevant than wealth distribution?
You have 2 ∗ 3 = 6 discrete states anyway, why not use a process that
gets the earnings and wealth distribution (including the joint
distribution)?
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 7 / 12

11. Income process
2 states (E and U) implies counterfactual earnings distribution.
Why is earnings distribution less relevant than wealth distribution?
You have 2 ∗ 3 = 6 discrete states anyway, why not use a process that
gets the earnings and wealth distribution (including the joint
distribution)?
UI replacement rate set to 10%, why?
Replacement rate in data 40%, overstates income risk.
Explanation in paper,
U duration is 2 quarters in the model while in data it is less than 1
quarter, therefore divide 40% by 2, and
in data only 60% are eligible and take-up rate only 75%
First is a bug in the model, second is all outside your model (e.g.
family insurance or stigma). This matters because welfare implications
are different.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 7 / 12

12. Income process
2 states (E and U) implies counterfactual earnings distribution.
Why is earnings distribution less relevant than wealth distribution?
You have 2 ∗ 3 = 6 discrete states anyway, why not use a process that
gets the earnings and wealth distribution (including the joint
distribution)?
UI replacement rate set to 10%, why?
Replacement rate in data 40%, overstates income risk.
Explanation in paper,
U duration is 2 quarters in the model while in data it is less than 1
quarter, therefore divide 40% by 2, and
in data only 60% are eligible and take-up rate only 75%
First is a bug in the model, second is all outside your model (e.g.
family insurance or stigma). This matters because welfare implications
are different.
In robustness exercise with a somewhat richer income process, welfare
gains 0.005% instead of 0.008%.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 7 / 12

13. Assets
For computational reasons, assume same (stochastic) payoff for bonds
as for capital.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 8 / 12

14. Assets
For computational reasons, assume same (stochastic) payoff for bonds
as for capital.
This forces the poor to hold a risky asset, which they don’t like. If
welfare cost of risk are convex, then your results will be biased
upwards.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 8 / 12

15. Assets
For computational reasons, assume same (stochastic) payoff for bonds
as for capital.
This forces the poor to hold a risky asset, which they don’t like. If
welfare cost of risk are convex, then your results will be biased
upwards.
Rich in reality hold stocks, probably a lot more volatile than the MPK
in the model. Why not stochastic depreciation?
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 8 / 12

16. Assets
For computational reasons, assume same (stochastic) payoff for bonds
as for capital.
This forces the poor to hold a risky asset, which they don’t like. If
welfare cost of risk are convex, then your results will be biased
upwards.
Rich in reality hold stocks, probably a lot more volatile than the MPK
in the model. Why not stochastic depreciation?
Too many PIH households?
Recent HA literature focuses a lot on MPC distribution.
Assets here are all pretty liquid.
More rich hand-to-mouth might lead to different results.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 8 / 12

17. Uncertainty or volatility
Welfare effects for rich come from shocks to top marginal tax rate
τ0 + τ1.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 9 / 12

18. Uncertainty or volatility
Welfare effects for rich come from shocks to top marginal tax rate
τ0 + τ1.
Do these shocks exist at a quarterly horizon?
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 9 / 12

19. Uncertainty or volatility
Welfare effects for rich come from shocks to top marginal tax rate
τ0 + τ1.
Do these shocks exist at a quarterly horizon?
How does the corresponding graph look in the paper?
A nominal model with inflation shocks yields volatility at quarterly
frequency.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 9 / 12

20. What is is fiscal risk?
σG , στ
or
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 10 / 12

21. What is is fiscal risk?
σG , στ
or
Modeling debt limit hard, beyond the scope of the paper but ...
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 10 / 12

22. Minor comments (1):
1 Don’t emphasize that model matches expecially the top 1% well. You
target it.
2 Luttmer & Samwick has been published AER, 2018.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 11 / 12

23. Conclusion
Very clear paper, incredibly well-executed and well-documented
model.
Will be the standard for HAFP
Lots of potential for follow up research.
A proper portfolio choice might be interesting, still one state net worth
but two controls.
Another interesting extension would be to look at longer maturities and
inflation shocks.
Jochen Mankart (Deutsche Bundesbank) HAFP 19 March 2018 12 / 12