Public Debt Sustainability Under Uncertainty:

A Vector Autoregression Approach, applied to Brazil, Mexico, and Turkey.

January 2007

Evan Tanner, International Monetary Fund (INS)

Issouf Samake, International Monetary Fund, (AFR)

NOTE: The views expressed in this presentation are those of the author and should not be attributed tothe International Monetary Fund, its Executive Board, or its management.

I Introduction

• Sustainable fiscal policy: one that can be continued indefinitely without modification;– No adjustment to primary surplus, no default (by inflation or

otherwise). – At minimum: satisfy intertemporal solvency– More often: stabilize the debt stock (ratio to GDP).

• Defined thusly, sustainability is difficult to achieve:– Despite good intentions, adverse shocks to interest rates, exchange

rates, output, etc, may cause persistent debt increases.

• More ambitious objective: preempt future fiscal adjustments for all but most unfavorable circumstances– Surplus exceeds that required to merely stabilize the debt; such a

policy will on average reduce the debt.

I Introduction

• Sustainability of fiscal policy under uncertainty: Brazil, Mexico, and Turkey.

Retrospectively: “If historical policies were to be continued into the future, would fiscal policy be sustainable – or will a modification of policies be required?”

Prospectively: “What policies should be undertaken today in order to prevent the need for further adjustments in the future?”

I Introduction

• Previous work (detailed review in paper): – Retrospectively:

• Some accounting “naked eye” (i.e. Blanchard et. al (1990) fiscal gap),

• Many econometric studies - ‘present value tests’ (started by Hamilton and Flavin (1986)).

– Prospectively: • Typically accounting (IMF Template, stress tests);

• Recent development: stochastic simulations and ‘fan chart’ (i.e. Celasun, Debrun, Ostry (2005) – some based in econometrics.

I Introduction

• Our work: – Retrospectively: debt accumulation attributed to (i)

baseline policy, (ii) policy-shocks (discretion), (iii) non-policy shocks (luck); (“shocking facts”)

• Adverse (beneficial) shocks to non-(fiscal)-policy variables boosts (reduces) debt, country deemed ‘unlucky’ (‘lucky’).

• Historical decompositions from simple (near) vector autoregression (VAR).

• More than previous work, ours highlights the role of unanticipated shocks in debt increases or decreases.

I Introduction

• Our work: – Prospectively: Monte-Carlo simulation of model

• Assume current fiscal policy (similar to Garcia and Rigobon,2004, Celasun, Debrun, and Ostry,2005);

– They summarize debt forecasts with “fan charts” -- mean value and with upper- and lower- confidence intervals that increase with time.

• Normative emphasis: Calculate hypothetical primary surpluses that would prevent debt from rising for all but worst 50%, 20%, 10% of outcomes over a given horizon (1 to 5 years).

• A menu of options: how much insurance to preempt future adjustments?

• Clear precautionary objective to justify debt reduction; • Simple, easily understood rule a la Kydland and Prescott (1977)

I Introduction

• Organization of rest of the paper:– In Part II: review previous work on fiscal

sustainability “roots in literature from 80s, 90s”

• In Part III: overview of our methodology. – Part IV Brazil

– Part V Mexico

– Part VI Turkey

– Part VII concludes.

III Overview of Our ApproachLike other recent papers we highlight uncertainty policy and luck. Near-vector autoregression (VAR) model, endogenous variables X:

Xt = [ipt,deft,t, rt]

ip = industrial production index,def = some measure of the deficit (primary (ps), operational def (b)) = real depreciation (bilaterally vs.US dollar) r = real interest rate

Exogenous variables: oil price growth, dummy (i.e. crisis periods).

Retrospective Sustainability: Historical decomposition well-known representation of VAR model (less widely used than variance decomposition).

Each element of X composed of: (i) Baseline projection of that variable, conditional on all information available in the base period M; (ii) impacts of shocks from all variables, accumulated from M+1 forward

Alternative presentation: observed value, what would have happened if a certain shock had not occurred (counterfactual).

III Overview of Our ApproachIII.a Retrospective Sustainability

Absent shocks, fiscal policy is sustainable over the period M+1 through M+j if:

(10) b(base)M+j/GDPM+j ≤ bM/GDPM.

Baseline policy is “unsustainable” if the debt rises under baseline projection (no innovations); otherwise, policy is “sustainable”.

(11a) b(omit i)M+j= bM+j - z*

bij

(11b) b(omit i)M+j = b(omit i)M+j-1 + bM+j - z*

bij

Retrospective sustainability:

Counterfactual: what would have debt been if some specific shock had not taken place?

Informal taxonomy for non-policy shocks: Lucky vs. Unlucky

III Overview of Our ApproachIII.b Prospective Sustainability

 

Monte-Carlo simulations of VAR system (randomly generated shocks).

•Similar work: Garcia and Rigobon (2004), Celasun, Debrun, and Ostry (2005).

• Positive emphasis::debt projections whose forecast variance increases with horizon length – “fan charts.” Similar to adverse scenarios in Fund Sustainability Template.

Normative emphasis: Upper bands of fan charts (or adverse scenarios) represent undesirable outcomes.

Implicit objective: to preempt precisely these bad outcomes for all but some low probability (50% or less); otherwise fan charts / Fund template stress test are uninteresting. *

For prob less than 50%, primary surplus more than debt stabilizing value (ps > rb).

*See Tanner and Carey (2005) “The Perils of Tax Smoothing: Sustainable Fiscal Policy with Random Shocks to Permanent Output,” IMF WP 05/207.

III Overview of Our ApproachIII.b Prospective Sustainability

“Value-at-risk”-like approach: government aims for primary surplus in order to prevent an increase in debt for all but worst w-percent of cases (w =insurance level chosen by authority).

Baseline scenario: simulated means, standard deviations, and fractiles (median, 75 th, and 90th percentiles) of simulated debt/GDP ratios.

Menu of policy options: alternative primary surplus required to keep the debt ratio constant for all but the worst w-percent of cases (w = 50%, 75%, 90%) – over a given horizon.

Clearer than current approaches?

Doesn’t just show bad outcomes – shows how to avoid them.

IV Brazil

 

Estimated model January 1995 - May, 2005); dummies for exchange rate regimes.Baseline period for policy mid-2000 (M = 2000:5).

Figure 2. Brazil: Real Public Debt Purged of Exchange Rate and Interest Rate Shocks(b(omit ,r); Units are Millions of Constant Reais (1995=100))

350000

370000

390000

410000

430000

450000

470000

490000

510000

530000

550000

b (actual)b (base)b (omit e,r)

Exchange rate/interest rates explain 97% of debt variation; 1999 crisis “dummied out”

IV Brazil

 

Table A.5. Brazil: Summary of Alternative Estimates (Versions (i)–(v))

Version

Sample Crisis Dummy

98:11–99:3 Flex Regime

Dummy 99:4–05:6

Time Trend

(i)* 95:5–05:6 Yes Yes Yes (ii) 95:5–05:6 Yes Yes No (iii) 95:5–05:6 No Yes No (iv) 99:4–05:6 NA NA Yes (v) 99:4–05:6 NA NA No

Figure A.1. Brazil: Observed and Baseline Debt, Alternative Estimates

(Versions (i)–(v))

350000

370000

390000

410000

430000

450000

470000

490000

510000

530000

550000

Observed Ver (i)

Ver (ii) Ver (iii)

Ver (iv) Ver (v)

IV Brazil

Table 4b(i). Brazil: Prospective Sustainability from 2005:6 Onward; Higher Interest Rate

First year primary surplus/GDP ps = 4.5 %

Time Horizon

Statistics 1 Year 2 Years 3 Years 4 Years 5 Years Mean 52.19 52.51 53.05 53.65 54.72 Standard Deviation 6.64 9.95 13.39 16.08 19.35 Median 51.82 51.93 51.41 51.28 51.73 75th Percent 56.63 58.55 61.29 62.30 64.18 90th Percent 60.79 65.98 70.38 74.87 79.31 Time Horizon 1 Year 2 Years 3 Years 4 Years 5 Years Stabilizing debt (b) with probability: 50 %; Requires initial ps of: 5.44 5.17 5.14 5.14 5.20 ► average debt ratio, end of horizon 51.40 51.40 51.40 51.40 51.40 75 % Requires initial ps of;: 9.31 7.78 7.41 6.85 6.66 ► average debt ratio, end of horizon 47.30 45.75 43.85 43.57 42.79 90 %; Requires initial ps of : 12.92 10.55 8.75 8.92 8.60 ► average debt ratio, end of horizon 43.52 39.79 39.41 34.13 31.38

Scenario 1: Real interest rate ≈12.8% (recent history); GDP growth just under 4 percent (optimistic assessment - Deutsche Bank (2006)).

Baseline ps = 4.5%

Modest debt increase

More precaution requires more adjustment.

IV BrazilScenario 2: Lower real interest factor ≈8.5% (market expectations data); GDP growth ≈3.5% (IMF, authorities)

Baseline ps = 4.5%

Debt decreases on average

Table 4b(ii). Brazil: Prospective Sustainability from 2005:6 Onward; Lower Interest Rate

First year primary surplus/GDP ps = 4.5 %

Time Horizon

Statistics 1 Year 2 Years 3 Years 4 Years 5 Years Mean 48.5 46.3 44.1 41.7 39.5 Standard Deviation 3.8 5.3 6.7 7.5 8.4 Median 48.4 45.9 43.6 41.3 38.9 75th Percent 51.0 49.6 48.6 46.1 44.5 90th Percent 53.5 53.7 53.1 51.7 50.2 Time Horizon

1 Year 2 Years 3 Years 4 Years 5 Years Stabilizing debt (b) with probability: 90 %; Requires initial primary surplus of: 6.6 5.5 5.0 4.6 ... ► average debt ratio, end of horizon 46.4 44.2 42.5 41.6 ...

Somewhat more precaution

IV Brazil

 

4D: Counterfactual Prospective Sustainability: Brazil, 2000:5 - onward First year pri sur/GDP = 3.1% Time Horizon

Statistics: 1 Year 2 Years 3 Years 4 Years 5 Years

Mean 49.47 50.63 52.03 53.68 55.80 Std. Dev 4.28 6.30 8.37 9.94 12.06 Median 49.26 50.53 51.90 53.21 54.90 75th Pct 52.44 54.58 57.42 59.53 62.50 90th Pct 55.22 58.90 63.07 66.83 71.25 Time Horizon Stabilizing debt with probability 1 Year 2 Years 3 Years 4 Years 5 Years

50% requires primary surplus of: 3.40 3.77 3.94 4.07 4.21 -- average debt ratio, end of horizon 49.22 49.22 49.22 49.22 49.22 75% requires primary surplus of: 6.00 5.45 5.42 5.24 5.21 -- average debt ratio, end of horizon 46.44 45.58 44.34 43.96 43.37 90% requires primary surplus of: 8.44 7.21 6.80 6.45 6.33 -- average debt ratio, end of horizon 43.89 41.79 39.77 38.44 36.82

“Baseline scenario”: GDP growth ≈ 4%,real interest rate ≈ 12.8%.

Mean debt increases.

With hindsight, these numbers not extraordinarily high.

“Menu of policy options”: primary surplus is initial year; average debt is end of year in column.

Note: Debt stabilization (50%) would have required somewhat higher primary surplus than initial target --- but close to later values.

Counterfacutal prospective: A “rear view mirror” for policy makers.

V Mexico

 

Two components to Mexican public debt:

•“Traditional” ≈ 18% percent of GDP in 2005; available monthly, used for retrospective.

•“Augmentation” includes liabilities associated with bank bailouts and development borrowing, became important after 1994-5 crisis.

•“Augmented” (sum) ≈ 45.3% of GDP in 2005 – Used for prspective.

Monthly data from mid-1997 to mid-2005. (omits 1994 crisis and aftermath.).

(13) X(Mexico)t = [ipt, pst,t, b, rt], 6 lags;

Discrepancies between overall balance (‘above the line’) and change in government debt (‘below the line’); require that operational deficit bt be included in X.;

VAR filters out effects of ps and r contained therein.

Shocks to bt are orthogonal to all other variables; thus, they are additional (error)

component of primary deficit.

V Mexico

 

Figure 4Mexico: Real Public Debt purged of exchange rate and interest rate shocks.

b(omit ,r); Units are millions of 1995 Pesos.

900000

950000

1000000

1050000

1100000

1150000

1200000

1250000

1300000

1350000

1400000

Apr-99 Apr-00 Apr-01 Apr-02 Apr-03 Apr-04 Apr-05

Actual (b) b(base)

b(omit e+r)

Beneficial impacts of interest rate reductions and stronger Peso most important in Beneficial impacts of interest rate reductions and stronger Peso most important in 2001-02. 2001-02.

V Mexico

 

Figure 5Mexico: Real Public Debt purged of deficit shocks.

b(omit def); Units are millions of 1995 Pesos.

900000

950000

1000000

1050000

1100000

1150000

1200000

1250000

1300000

1350000

1400000

Apr-99 Apr-00 Apr-01 Apr-02 Apr-03 Apr-04 Apr-05

Actual (b) b(base)

b(omit def)

Discretionary expansions of fiscal policy 02 – 04;Discretionary expansions of fiscal policy 02 – 04;

End period – about ½% of GDP End period – about ½% of GDP

V Mexico

 

Not analyzed here (work in progress): preservation of oil wealth.

Primary surplus due to oil (non-oil primary surplus ≈ 4 – 5% of GDP. This may be “too high” to preserve net wealth (oil wealth minus debt); “Stay tuned”

Table 5b. Mexico: Prospective Sustainability from 2005:6 Onward Initial period primary surplus/GDP ps = 2.1%

Time Horizon

Statistics 1 Year 2 Years 3 Years 4 Years 5 Years Mean 45.0 43.5 41.9 40.2 38.7 Standard Deviation 2.1 3.4 4.2 4.9 5.6 Median 44.9 43.3 41.5 40.0 38.1 75th Percent 46.5 45.7 44.6 43.1 42.0 90th Percent 47.7 47.9 47.6 46.6 46.0 Time Horizon

1 Year 2 Years 3 Years 4 Years 5 Years Stabilizing debt with probability: 75 % requires primary surplus of: 3.2 2.3 1.9 1.6 1.5 ► average debt ratio, end of horizon 42.7 43.1 42.6 42.3 41.9 90 % requires primary surplus of: 4.4 3.2 2.8 2.4 2.3 ► average debt ratio, end of horizon 42.7 41.2 39.9 39.1 38.0

Modest fall in average debt

Like a “fan chart”; There are risks.

Somewhat more precaution

“Baseline scenario”: GDP growth ≈ 3%,real interest rate ≈ 5%; unlike staff report, PS stays at about 2.1% throughout scenario; Debt reduction close to staff report.

VI Turkey

2.E+07

3.E+07

4.E+07

5.E+07

6.E+07

7.E+07

8.E+07

9.E+07

1.E+08

1.E+08Actual (b) b(base)

b(omit def)

Expansionary fiscal policy increased debt in 98-2000, Expansionary fiscal policy increased debt in 98-2000, 01-0201-02

Figure 7. Turkey: Real Public Debt Purged of Deficit Shocks(b(omit ps,b); Units are millions of 2001 Turkish Lira)

VI Turkey

 

2.E+07

3.E+07

4.E+07

5.E+07

6.E+07

7.E+07

8.E+07

9.E+07

1.E+08

1.E+08Actual (b) b(base)

b(omit e, r)

Shocks to real interest rate (combined real exchange rate) Shocks to real interest rate (combined real exchange rate) increased debt; increased debt;

Figure 6. Turkey: Real Public Debt Purged of Exchange Rate and Interest Rate Shocks(b(omit ,r); Units are millions of 2001 Turkish Lira)

VI Turkey

 

6C: Prospective Sustainability, 2005:5 - onward First year pri sur/GDP = 6.6% Time Horizon

Statistics: 1 Year 2 Years 3 Years 4 Years 5 Years Mean 57.85 58.95 59.64 60.26 60.65 Std. Dev 7.44 11.81 15.43 19.77 23.28 Median 57.38 57.47 56.99 56.78 56.62 75th Pct 62.56 65.59 68.12 69.76 72.29 90th Pct 67.90 74.82 79.44 84.54 90.96 Time Horizon Stabilizing debt with probability 1 Year 2 Years 3 Years 4 Years 5 Years 75% requires primary surplus of: 10.48 9.79 9.38 8.83 8.69 -- average debt ratio, end of horizon 53.99 52.21 50.41 49.99 48.14 90% requires primary surplus of: 14.82 13.03 11.79 11.21 10.74 -- average debt ratio, end of horizon 49.66 45.32 42.34 38.91 35.75

Cautious optimism: modest rise in average debt

“Baseline scenario”: GDP growth ≈ 5%,real interest rate ≈ 12½%.

Like a “fan chart”; Risks appear substantial

“Menu of policy options”: primary surplus is initial year; average debt is end of year in column.

Note: Debt stabilization at 75%, 90% levels requires higher primary surplus than currently observed; Longer horizon implies less stringent initial fiscal policy – end period debt reflects cumulative effects of adjustment.

To be updated

VI Turkey 

Table 6b. Turkey: Prospective Sustainability from 2005:5 Onward Average primary surplus/GDP ps ≈ 6.5 Percent (Years 1 through 5)

Time Horizon

Statistics 1 Year 2 Years 3 Years 4 Years 5 Years No Shock Scenario 49.6 45.5 40.8 36.2 31.7 Mean 51.3 49.2 46.0 42.8 39.4 Standard Deviation 6.3 9.7 11.7 13.5 15.1 Median 50.9 48.0 44.8 40.4 37.3 75th Percent 55.3 55.0 52.9 50.9 47.2 90th Percent 59.9 61.9 61.3 60.8 58.9 Time Horizon

1 Year 2 Years 3 Years 4 Years 5 Years Stabilizing debt with probability: 90 %; Requires first year primary surplus of: 10.8 9.5 8.5 8.1 7.5 ► average primary surplus/GDP, years 1–5 10.3 9.1 8.0 7.6 7.1 ► average debt ratio, end of horizon 47.4 43.8 41.2 38.2 36.5

“No adjustment fatigue.” Sustained adjustment is critical.

Non linearities – less debt reduction under unertainty.

More precaution requires more adjustment.

VII Summary/Conclusions

 

This paper has examines the sustainability of fiscal policy under uncertainty in three emerging market economies: Brazil, Mexico, and Turkey.

Retrospective assessment -- decomposes effects of a baseline policy, luck, and discretionary policy on debt accumulation.

Prospective assessment incorporates uncertainty in way that differs from Fund template, but is similar to other recent papers cited herein.

Two advantages over currently used frameworks:

1. Econometric framework: permits us to combine prior beliefs/assumptions on mean (i.e.growth, interest rates, the primary surplus) with data’s own information on volatilities thereof; data thus informs policy process in richer, more sophisticated way than generally is the case.

VII Summary/Conclusions

 

2. Prospectively: framework clearly communicates a menu of options for policy makers.

Recognizes both costs and benefits to higher surpluses.

The optimal primary surplus -- and hence the optimal path of debt reduction -- will depend on the policy maker’s objective function – and ultimately will differ across countries according to specific circumstances in any country.

3. Our precautionary regimes will reduce the debt – not a novel policy. However, debt target per se is arbitrary, may be difficult to defend.

Clearly articulated safeguard against perm adverse shocks and future adjustments may foster clearer more understandable, more credible fiscal polices -- echoing Lucas (1976) and Kydland and Prescott (1977).

VII Summary/Conclusions

 

There is plenty of room for further work:

• Refinement of econometric modeling.

• Simulations of alternative fiscal rules within equilibrium model (see for example Hostland and Karam (2005)).

• Long-run interest rate response to changes in fiscal policy?

• Length of horizon – difficulty of commitment?