IMPLICATIONS OF LOW PRODUCTIVITY

GROWTH FOR DEBT SUSTAINABILITY

Neil R. Mehrotra

Brown University

Peterson Institute for International EconomicsNovember 9th, 2017

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PUBLIC DEBT AND PRODUCTIVITY GROWTH

OECD ECONOMIES

0 50 100 150 200

Switzerland Korea

Denmark Sweden

Australia Germany

Canada New Zealand

Finland Netherlands

Ireland Austria

United States France Spain

United Kingdom Belgium Portugal

Italy Japan

Debt to GDP

2015

2000

0.00 1.00 2.00 3.00 4.00 5.00

Italy United Kingdom

New Zealand Belgium

United States Switzerland

Finland Netherlands

Austria Portugal

France Canada

Germany Spain

Denmark Japan

Sweden Australia

Korea Ireland

Labor productivity growth

2010-2016

1990-1999

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DEBT SERVICING COSTS

OECD ECONOMIES

-4.0 -2.0 0.0 2.0 4.0 Ireland

Japan United Kingdom

United States Austria

Norway Belgium

Latvia Canada

Germany Iceland

Netherlands Slovak Republic Czech Republic

Sweden Australia

Korea Israel

Denmark Luxembourg

Chile Switzerland

Mexico France

New Zealand Finland Poland

Hungary Slovenia

Spain Italy

Portugal

Unit fiscal cost: r - g

-4.00 -2.00 0.00 2.00 4.00 Ireland

Japan United Kingdom

United States Austria

Norway Belgium

Latvia Canada

Germany Iceland

Netherlands Slovak Republic Czech Republic

Sweden Australia

Korea Israel

Denmark Luxembourg

Chile Switzerland

Mexico France

New Zealand Finland Poland

Hungary Slovenia

Spain Italy

Portugal

Debt servicing cost

US fiscal cost

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RESEARCH QUESTION AND APPROACH:

Key tradeoff:I Persistent r < g implies the increases in debt raise revenues

I With a large stock of public debt, interest rate reversals imposesizable fiscal costs

Approach:I Empirical evidence on level and variability of debt servicing

costs

I Interest rate and debt servicing cost projections for the G7

I Employ a quantitative model to study implications for debtservicing cost of low productivity growth

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HISTORICAL DEBT SERVICING COST

Servicing the public debt:

Tt + Bgt+1 = Gt + (1 + rt)Bg

t

⇒ T̃ = G̃ + (r− g) B̃g

Fiscal Cost Measure

1870-2013 1946-2013 1870-2013 1946-2013Net fiscal cost: r - (g+n)

25th percentile -2.64 -2.80 -3.23 -3.13Median 0.13 -0.35 -0.52 -0.3775th percentile 2.82 1.85 1.99 1.26

Fraction < 0 48.8% 55.3% 56.5% 59.7%Fraction < -2% 29.7% 31.7% 34.4% 32.8%

No. of observations 2107 1068 131 67

Using five-year averages - winsorized at +- 10%

1870-2013 1946-2013 1870-2013 1946-2013Net fiscal cost: r - (g+n)

25th percentile -2.64 -2.74 -2.15 -1.72Median 0.08 -0.38 -0.16 -1.3575th percentile 2.28 1.55 1.09 0.57

Fraction < 0 49.3% 54.3% 55.2% 69.2%Fraction < -2% 31.4% 32.6% 31.0% 23.1%

No. of observations 493 221 29 13

17 Advanced Countries United States

Real interest rate is the long-term nominal interest rate less a three-year moving average of inflation rates. Fraction < 0 is the percentage of years with negative net fiscal cost. Fraction < -2% is the percentage of years with net fiscal cost of less than -2%. Statistics based on data set after observations with net fiscal cost > 10% or less than -10% are winsorized at thresholds.

17 Advanced Countries United States

Real interest rate is the long-term nominal interest rate less a three-year moving average of inflation rates. Fraction < 0 is the percentage of years with negative net fiscal cost. Fraction < -2% is the percentage of years with net fiscal cost of less than -2%. Statistics based on data set after observations with net fiscal cost > 10% or less than -10% are dropped.

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DEBT SERVICING COST AND PRODUCTIVITY

GROWTH

ADVANCED ECONOMIES: 1870-2013-.1

-.05

0.0

5.1

-.2 -.1 0 .1 .2Real GDP per capita growth (5-year averages)

Fiscal cost (5-year averages) Fitted values

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REVERSION SCENARIOS

CURRENT G7 COVARIATES

Probit specification:

P(fisci,t+j > 0 | X

)= Φ

(c + βf fisci,t + βppopgrwthi,t + βddgdpi,t + εi,t

)Reversion Scenarios

Countries 5-year forward10-year forward

Debt to GDP ratio

Current unit cost

Current fiscal cost

Fiscal cost if r-g = 1.55%

Canada 41.2% 47.9% 67 -1.54% -1.03 1.01France 52.8% 54.8% 96 -0.14% -0.14 1.44Germany 49.0% 57.3% 68 -1.62% -1.10 1.02Italy 83.5% 71.7% 133 2.43% 3.23 2.00Japan 24.9% 38.1% 198 -1.51% -2.98 2.97United Kingdom 38.2% 48.1% 90 -1.84% -1.65 1.35United States 41.1% 47.9% 76 -1.42% -1.08 1.14

Likelihood of r > g Fiscal consolidation

Reversion probabilities obtained as fitted values from regression specifications (2) - (3), and (5) - (6) with r - g - n = 0.0054, g = 0.007, n = 0.007, and debt to GDP ratio of 0.7. Optimistic and pessimistic scenarios consider alternatives with g = 0.015 and g = 0 respectively. Fiscal cost (% of GDP) is r - g - n multiplied by debt to GDP ratio of 70%. Probit estimates

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DEBT SERVICING COST PROJECTIONSScenario Summary

Canada France Germany Japan Italy UK USAReal interest rates

Current: 2012-2017 0.41 0.70 -0.25 -0.28 2.10 0.26 0.74Projection: 2018-2025 1.38 1.76 -0.25 -1.01 1.13 1.71 1.00

GDP per capita growthCurrent: 2012-2017 0.95 0.27 1.34 1.21 -0.49 1.62 1.30Downside (PIIE estimates) 0.70 0.50 0.50 0.10 0.10 0.50 0.70

Cost of servicing the debt (% of GDP)Current: 2012-2017 -1.00 -0.10 -1.12 -2.93 3.19 -1.66 -1.08Projection: 2018-2025 -0.35 0.92 -1.12 -4.38 1.90 -0.35 -0.88Downside (PIIE estimates) -0.18 0.70 -0.55 -2.18 1.12 0.66 -0.43

Countries

Real interest rates are averages from 2012-2017 of nominal rates on 10-year government debt less the average inflation rate as measured by a consumer price index (data from OECD). Interest rate projection are obtained from the bilateral VECM model for the G6 and 2-variable VECM for the US. GDP per capita growth rates and population growth are 5-year averages from the OECD and Jorda, Schularick and Taylor databases respectively. The debt to GDP ratio is obtained from national sources. The unit cost of servicing the debt is simply r - g where g is the sum of population growth and GDP per capita growth. The fiscal cost of servicing the debt is the unit cost multiplied by the stock of debt.

I Real interest rate projections obtained from 3-variable VECM

I Uncertainty bands quite large for real interest rate projections

VECM estimates

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INTEREST RATE DETERMINATION IN A

LIFECYCLE MODEL

Debt servicing cost:((1 + r

(g, n, B̃g

))− (1 + g) (1 + n)

)B̃g

I Quantitative 56-period lifecycle model

I Households face lifecycle profile of income, save for retirement,and face mortality risk

I Calibrate to US labor share, I/Y, real interest rate r, risk premia

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EFFECT OF PRODUCTIVITY GROWTH ON USFISCAL COST

MODEL INTEREST RATE ELASTICITIES

0.0%

0.5%

1.0%

1.5%

2.0%

0.0% 0.5% 1.0% 1.5% 2.0%

Rea

l Int

eres

t Rat

e

Productivity Growth

IES = 0.5

IES = 1

IES = 2

45 degree line

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EFFECT OF DEBT TO GDP RATIO ON US FISCAL

COST

18.0%

18.2%

18.4%

18.6%

18.8%

19.0%

19.2%

19.4%

19.6%

19.8%

20.0%

0.4 0.6 0.8 1 1.2

Taxe

s (%

of G

DP)

Debt to GDP Ratio

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DEBT SUSTAINABILITY IN SMALL OPEN

ECONOMIESDebt servicing cost:

((1 + r (g∗, n∗))− (1 + g) (1 + n)) B̃g

I Evidence of a stronger common component in rates than growth

I Key determinant: deviation of g from global prod. growth g∗

I Indirect channels: real exchange rate and financial stability

I Evidence that when US real rates are low, RER appreciates, loangrowth increases, house prices increase

Int’l spillovers

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KEY TAKEAWAYSLessons:

I On average, cost of servicing the debt is frequently negative

I Nevertheless, servicing cost shows substantial variability and amoderate likelihood of reversion in medium term

I Slower productivity growth may benefit debt sustainability bylowering real interest rate

I Even with r < g, revenue-maximizing level of debt is lower

Limitations:I r− g not a sufficient statistic for optimal level of debt

I Abstracted from any constraints on real rates due to the ZLB

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Additional Slides

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COST OF SERVICING THE US PUBLIC DEBT

-30%

-20%

-10%

0%

10%

20%

30%

1872 1882 1892 1902 1912 1922 1932 1942 1952 1962 1972 1982 1992 2002 2012

Fiscal cost: r-g-n

Fiscal cost, 5-yr MA

Back

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REVERSION LIKELIHOODS

Probit specification:

P(

fisci,t+j > 0 | X)= Φ

(c + βf fisci,t + βppopgrwthi,t + βddgdpi,t + εi,t

)Probit RegressionsUsing five-year averages - winsorized at +- 10%

Variable (2) (3) (5) (6)Current value: r - (g+n) 12.483*** 25.869*** 5.707*** 12.895***

(1.174) (3.430) (1.421) (3.281)

Debt to GDP ratio -0.146 -0.142 -0.212 -0.204(0.183) (0.280) (0.189) (0.315)

Population growth -29.185** -24.618 -24.450** -28.148(11.762) (23.497) (10.973) (22.866)

Constant 0.363** 0.373* 0.300** 0.483**(0.145) (0.200) (0.143) (0.207)

McFadden pseudo R-squared 0.120 0.260 0.037 0.110No. of observations 448 204 431 187

Reversion likelihoodUS 0.480 0.472US optimistic (1.5% prod.) 0.440 0.454US pressimistic (0 prod.) 0.515 0.488

The dependent variable is a dummy variable that takes a value of 1 if the fiscal cost measure is positive (i.e. r > g+n) in next period (1-5 years forward) and in the subsequent period (6-10 years forward) respectively. Columns (1) and (4) do not include population growth; columns (3) and (6) limit the sample to the postwar period. Each column presents a separate regression. Standard errors are clustered at the country level. *** are coefficients significant at the 1% level, ** are coefficients significant at the 5% level, and * are coefficients

5-year forward: (r > g+n) 10-year forward (r > g+n)

Back

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EXTERNAL AND FINANCIAL SPILLOVERS TO

SMALL OPEN ECONOMIES

Fixed effects specification:

yi,t = ci + δ1t + δlag1t−1 + εi,t

Fixed Effect Regressions

Dependent variable Current accountReal exchange

rate Loan growthMortgage loan

growth House prices(1) (2) (3) (4) (5)

US real rate (< 1%) 0.000 -0.033*** 0.007 0.004 0.009(0.003) (0.004) (0.006) (0.008) (0.006)

US real rate (< 1%, 5 yr. lag) -0.012** 0.023*** 0.031*** 0.030*** 0.021*(0.005) (0.005) (0.007) (0.008) (0.010)

H0: Sum of current and one lag -0.012* -0.010* 0.038*** 0.034*** 0.030**(0.006) (0.005) (0.008) (0.010) (0.012)

Country fixed effects Yes Yes Yes Yes YesNo. of observations 208 208 208 208 190

External Financial

The dependent variable is described in the first row, the independent variable is a dummy variable that is equal to 1 when US real interest rates are below 1%. Each column presents a separate regression. Standard errors are clustered at the country level. *** are coefficients significant at the 1% level, ** are coefficients significant at the 5% level, and * are coefficients significant at the 10% level. Back

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COMMON COMPONENT IN RATES

AND GDP GROWTH

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

1950 1960 1970 1980 1990 2000 2010 -10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

1950 1960 1970 1980 1990 2000 2010

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VECM ESTIMATES OF REAL RATESVECM specification:

∆yt = γ + αβyt−1 +J

∑j=1

Πj∆yt−j + εt

VECM Estimates

Canada France Germany Japan Italy UK USACointegration coefficients

US real interest rate -0.96** -0.83** -0.76** -1.40** -1.58** -1.45** N/A(0.12) (0.14) (0.13) (0.28) (0.27) (0.35) N/A

Local GDP per capita growth 0.82** 0.01 -0.65** -0.06 0.26 2.62** -4.50**(0.13) (0.16) (0.11) (0.15) (0.23) (0.44) (0.89)

Error-correction coefficientsLocal real interest rate -0.22** -0.44** -0.11 -0.06 -0.21** -0.07** N/A

(0.07) (0.09) (0.08) (0.08) (0.07) (0.02) N/AUS real interest rate -0.10 -0.005 0.19** 0.19** 0.08 -0.04 0.01

(0.08) (0.08) (0.09) (0.05) (0.06) (0.03) (0.02)Johansen trace statistic

H0: No cointegrating relationship 65.93** 44.48** 40.98** 33.26* 27.81 63.40** 28.96**

Lag specificationCriterion AIC AIC AIC AIC AIC AIC AICLag length 2 2 2 2 4 2 3

No. of observations 64 64 64 64 62 64 63

Each column presents a separate estimation of a vector error correction model assuming 1 cointegration vector and consisting of the local long-term real interest rate, the long-term US real interest rate, and local GDP per capita growth. Data are from 1950-2015 and presents cointegration coefficients and error correction coefficients for local and US rates (error-correction term for GDP per capita and lag coefficients are suppressed). Estimates via maximum likelihood and Johansen trace statistic critical values are 29.68 and 35.65 at the 5% and 1% levels. ** are coefficients significant at the 1% level, and * are coefficients significant at the 5% level.

Countries

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REAL INTEREST RATE PROJECTIONS:US AND UK

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast VECM (4 country)

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast VECM (4 country)

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REAL INTEREST RATE PROJECTIONS:JAPAN AND GERMANY

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast VECM (4 country)

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast VECM (4 country)

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REAL INTEREST RATE PROJECTIONS:FRANCE AND ITALY

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025

Real interest rate VECM forecast

Back

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