Optimal Simple Fiscal Rules for CommodityExporters

Arthur Mendes Steven PenningsPUC-Rio World Bank

9 September 2016

Motivation

I Fiscal policy of commodity exporters often characterized asbeing needlessly pro-cyclical:

I spend in booms and cut in busts (balanced budget rule, BBR)

I Chile “poster child” of good fiscal policy: follows structuralsurplus rule (SSR) – save temporary copper revenues in a SWF

I Kumhof and Laxton (2013) (and others) find large welfaregains from SSR

I mostly because smooth consumption of Hand-to-Mouth HHs

Q: What is the optimal simple fiscal rule (OSR) for commodityexporters?

Motivation

I Fiscal policy of commodity exporters often characterized asbeing needlessly pro-cyclical:

I spend in booms and cut in busts (balanced budget rule, BBR)

I Chile “poster child” of good fiscal policy: follows structuralsurplus rule (SSR) – save temporary copper revenues in a SWF

I Kumhof and Laxton (2013) (and others) find large welfaregains from SSR

I mostly because smooth consumption of Hand-to-Mouth HHs

Q: What is the optimal simple fiscal rule (OSR) for commodityexporters?

This Paper

I Revisit this question in a model some key ingredients:

I Ricardian Households who can borrow/saveI Hand-to-Mouth (HtM) cannot borrow/saveI Government receives commodity revenues (and taxes) and

transfer them to HHs

I Main Result: The OSR is for commodity revenues is(surprisingly) procyclical.

I BBRs are often better than SSR for commodity revenues.

I Examine this question:

1. Analytically in a simple model with only HtM HHs2. Quantitatively in a model with both HtM HH & Ricardian

HHs and exogenous income (RBC results are similar)

Intuition: two observations

1. Permanent Income Hypothesis: HHs should consume out ofpermanent income

1.1 Spend permanent shocks and save temporary shocks

2. Commodity prices are highly persistent (close to random walk)

2.1 Oil/copper ρ =0.9-0.96 (annual); Half life of 7-17 years.

I Highly persistent commodity shocks don’t need smoothing.

I Just spend/transfer current income

I New: Few recent quantitative papers consider response tohighly persistent shocks (mostly calibrate to temporary shocks)

Other findings

1. Shock type is important:Non-commodity revenues are moretemporary and so should be saved

2. Reduce SWF volatility: govts should spend more thaninterest on SWF, otherwise SWF explode with persistentshocks

3. Share the burden: Entirely smoothing incomes of HtM HH ispossible but not optimal: big costs for Ricardian HHs

4. Same rule for all HHs: the optimal transfer rule forRicardians very similar to that for HtM HHs.

1. Analytical Model (linear quadratic case)

Model Overview

I Small open economy (exogenous world interest rate - annual)

I Exogenous non-resource income accrues to households (Y ).

I Exogenous resource income accrues to the govt (Q × P).

I Government able to save/borrow internationally (A)

I Fiscal policy aims to stabilize cons. over the business cycle.

I Find simple rules, where transfers are a function of Y , P , or A

Analytical Model (linear quadratic case)

I Assume only HtM HHs. Benevolent government’s problem:

max{Tr ′′} − E0

∞∑t=0

βt(c ′′t − γ)2 s.t.

such that :

[HH’s budget constraint] c ′′t = (1− τ)Yt + Tr ′′t

[Government’s budget constraint]At = (1 + r)At−1 + τYt + PtQ − Tr ′′t

[Exogenous shocks]Pt − P = ρP(Pt−1 − P) + ePtYt − Y = ρY (Yt−1 − Y ) + eYt

Optimal simple rule

Fiscal Rule : Tr ′′t = Tr ′′+θA(At−1−A)+θY(Yt − Y

)+θPQ(Pt−P)

I Response to oil price: θP =r

1 + r − ρPI As ρP → 0 then θP → r/(1 + r) ≈ 4% (SSR)I As ρP → 1 then θP → 1 (BBR)

I Response to SWF Assets: θA = r ≈ 4%

I Response to non-Res GDP θY = −[1− τ − r

1 + r − ρY

]

Some calculations

Fiscal Rule : Tr ′′t = Tr ′′+θA(At−1−A)+θY(Yt − Y

)+θPQ(Pt−P)

I Response to oil price: e.g . ρP = 0.96 and r = 0.04 then:

I Spend around half of movements in oil prices.

θP =r

1 + r − ρP= 0.5

I Response to non-Res GDP ρY = 0 and τ = 0.15 then

I Strongly counter cyclical rule for non-resource shocks.

θY = −[0.85− 0.04

1 + 0.04− 0

]≈ −0.8

2. Quantitative Model

Changes in the Quantitative ModelI Hand to Mouth Household. Same as in the analytical model with

population share 0.5 C ′′t = (1− τ)Yt + Tr ′′t

I The Ricardian household chooses foreign savings Bt and (perRicHH) consumption C ′

t to solve

max{Bt ,C ′t }

∞∑t=0

βtC ′1−σt

1− σs.t C ′t = Rt−1Bt−1 + (1− τ)Yt + Tr ′t − Bt

I Debt-elastic interest spread

I Government maximizes household welfare, which is equivalentto minimizing loss function: L = 0.5 {Var(c ′t) + Var(c ′′t )}

I Calibrate to Algeria (or Trinidad and Tobago)

Main result: BBR does surprisingly well

0.18 0.38 0.66 0.88 0.98persistence of oil-price shock (annual)

0

1

2

3

4

% o

f Css

Welfare Loss

BBRSSR

0.18 0.38 0.88 0.98persistence of oil-price shock (annual)

0

0.2

0.4

0.6

0.8

1

annu

al s

td d

evia

tion

Ric HH consumption

0.18 0.38 0.78 0.88 0.98persistence of oil-price shock (annual)

0

0.2

0.4

0.6

0.8

1

annu

al s

td d

evia

tion

HtM HH consumption

0.18 0.38 0.88 0.98persistence of oil-price shock (annual)

0

1

2

3

4

annu

al s

td d

evia

tion

Public Assets

Fiscal Rules

1. Full HtM Stabilization - govt completely smooths HtM’s cons

2. Balanced Budget Rule (BBR) - spend all income each period

3. Structural Surplus Rule (SSR) - only spend interest (save rest)

4. Hybrid BBR-CCY - Like BBR, but countercyclical w.r.t non-res Y

5. Hybrid SSR-CCY- Like SSR, but countercyclical w.r.t non-res Y

6. Optimal Simple Rule (OSR) chooses all parameters optimally minwelfare loss

7. OSR-Equal like OSR but where we must transfer the same to bothHHs

Large welfare loss from stabilizing HtM Cons

ψ = 0.01 (1) (2) (3) (4) (5) (6) (7)

ρP = 0.94 HtMHH BBR SSR BBR CCY SSR CCY OSR OSR Equal

θ′a 0.16 0.10 0.10 0.10 0.10 0.10 0.09

θ′y 0.02 0.16 0.00 -0.84 -0.84 -1.00 -0.71

θ′p 1.31 1.00 0.00 1.00 0.00 0.59 0.73

θ′′a 0.00 0.10 0.10 0.10 0.10 0.06 0.09

θ′′y -0.84 0.16 0.00 -0.84 -0.84 -0.75 -0.71

θ′′p 0.00 1.00 0.00 1.00 0.00 0.78 0.73

sd(c ′) 0.37 0.19 0.19 0.19 0.19 0.18 0.18

sd(c ′′) 0.00 0.19 0.22 0.19 0.22 0.19 0.18

sd(a) 1.37 0.04 3.00 0.13 3.00 1.21 0.95

sd(b) 0.69 1.78 3.13 1.77 3.13 0.47 0.24

Loss (% of Css) 6.96 3.59 4.26 3.54 4.23 3.38 3.38

I Full HtM Stabilization - govt completely smooths HtM’sconsumption

BBR performs better than SSR

ψ = 0.01 (1) (2) (3) (4) (5) (6) (7)

ρP = 0.94 HtMHH BBR SSR BBR CCY SSR CCY OSR OSR Equal

θ′a 0.16 0.10 0.10 0.10 0.10 0.10 0.09

θ′y 0.02 0.16 0.00 -0.84 -0.84 -1.00 -0.71

θ′p 1.31 1.00 0.00 1.00 0.00 0.59 0.73

θ′′a 0.00 0.10 0.10 0.10 0.10 0.06 0.09

θ′′y -0.84 0.16 0.00 -0.84 -0.84 -0.75 -0.71

θ′′p 0.00 1.00 0.00 1.00 0.00 0.78 0.73

sd(c ′) 0.37 0.19 0.19 0.19 0.19 0.18 0.18

sd(c ′′) 0.00 0.19 0.22 0.19 0.22 0.19 0.18

sd(a) 1.37 0.04 3.00 0.13 3.00 1.21 0.95

sd(b) 0.69 1.78 3.13 1.77 3.13 0.47 0.24

Loss (% of Css) 6.96 3.59 4.26 3.54 4.23 3.38 3.38

I Balanced Budget Rule (BBR) - spend all income each period;Structural Surplus Rule (SSR) - only spend interest (save rest)

Further improvements when countercyclical

ψ = 0.01 (1) (2) (3) (4) (5) (6) (7)

ρP = 0.94 HtMHH BBR SSR BBR CCY SSR CCY OSR OSR Equal

θ′a 0.16 0.10 0.10 0.10 0.10 0.10 0.09

θ′y 0.02 0.16 0.00 -0.84 -0.84 -1.00 -0.71

θ′p 1.31 1.00 0.00 1.00 0.00 0.59 0.73

θ′′a 0.00 0.10 0.10 0.10 0.10 0.06 0.09

θ′′y -0.84 0.16 0.00 -0.84 -0.84 -0.75 -0.71

θ′′p 0.00 1.00 0.00 1.00 0.00 0.78 0.73

sd(c ′) 0.37 0.19 0.19 0.19 0.19 0.18 0.18

sd(c ′′) 0.00 0.19 0.22 0.19 0.22 0.19 0.18

sd(a) 1.37 0.04 3.00 0.13 3.00 1.21 0.95

sd(b) 0.69 1.78 3.13 1.77 3.13 0.47 0.24

Loss (% of Css) 6.96 3.59 4.26 3.54 4.23 3.38 3.38

I Hybrid BBR/SSR-CCY - Like BBR/SSR, but countercyclical withrespect to non-resource GDP

OSR very similar to BBR_CCY

ψ = 0.01 (1) (2) (3) (4) (5) (6) (7)

ρP = 0.94 HtMHH BBR SSR BBR CCY SSR CCY OSR OSR Equal

θ′a 0.16 0.10 0.10 0.10 0.10 0.10 0.09

θ′y 0.02 0.16 0.00 -0.84 -0.84 -1.00 -0.71

θ′p 1.31 1.00 0.00 1.00 0.00 0.59 0.73

θ′′a 0.00 0.10 0.10 0.10 0.10 0.06 0.09

θ′′y -0.84 0.16 0.00 -0.84 -0.84 -0.75 -0.71

θ′′p 0.00 1.00 0.00 1.00 0.00 0.78 0.73

sd(c ′) 0.37 0.19 0.19 0.19 0.19 0.18 0.18

sd(c ′′) 0.00 0.19 0.22 0.19 0.22 0.19 0.18

sd(a) 1.37 0.04 3.00 0.13 3.00 1.21 0.95

sd(b) 0.69 1.78 3.13 1.77 3.13 0.47 0.24

Loss (% of Css) 6.96 3.59 4.26 3.54 4.23 3.38 3.38

I Optimal Simple Rule (OSR) chooses all parameters optimally minwelfare loss

Same rule for all HHs just as good

ψ = 0.01 (1) (2) (3) (4) (5) (6) (7)

ρP = 0.94 HtMHH BBR SSR BBR CCY SSR CCY OSR OSR Equal

θ′a 0.16 0.10 0.10 0.10 0.10 0.10 0.09

θ′y 0.02 0.16 0.00 -0.84 -0.84 -1.00 -0.71

θ′p 1.31 1.00 0.00 1.00 0.00 0.59 0.73

θ′′a 0.00 0.10 0.10 0.10 0.10 0.06 0.09

θ′′y -0.84 0.16 0.00 -0.84 -0.84 -0.75 -0.71

θ′′p 0.00 1.00 0.00 1.00 0.00 0.78 0.73

sd(c ′) 0.37 0.19 0.19 0.19 0.19 0.18 0.18

sd(c ′′) 0.00 0.19 0.22 0.19 0.22 0.19 0.18

sd(a) 1.37 0.04 3.00 0.13 3.00 1.21 0.95

sd(b) 0.69 1.78 3.13 1.77 3.13 0.47 0.24

Loss (% of Css) 6.96 3.59 4.26 3.54 4.23 3.38 3.38

I OSR-Equal like OSR but where we must transfer the same to bothHHs

Conclusions and Caveats

I This paper: BBR do surprisingly well for commodity exporters,because commodity prices are highly persistent.

I But governments should respond differently to different shocks.

I Caveat 1 (Scope): Only look at cons. volatility. Results mightbe different results for public investment. Political constraints.

I Caveat 2 (Linearities): We ignore non-linearities fromborrowing constraints and ignore precautionary savings.

I Caveat 3 (Multipliers): Limited interactions between fiscalpolicy and other parts of the economy.