Fiscal Policy and the Slowdown in Trend Growth Mariano Kulish , - - PowerPoint PPT Presentation

Fiscal Policy and the Slowdown in Trend Growth

Mariano Kulish∗, Nadine Yamout∗ and Alex Beames⋆

∗University of Sydney ⋆

Aug 2019 New Zealand Treasury

Average GDP growth per capita over the past decade:

% per year

2000 2002 2004 2006 2008 2010 2012 2014 2016

• 0.5%

0% 0.5% 1% 1.5% 2% 2.5% 3% 3.5% Canada New Zealand Norway Sweden United Kingdom United States Australia

• Slow pace of recovery following GFC suggests long-term

growth may have slowed down.

• Is there evidence of a permanent slowdown in trend growth?
• If so, what are the implications for fiscal policy ?

Related Literature

• Strand that assesses empirically the slowdown in trend growth:

Antolin-Diaz et al. (2016); McCririck and Rees (2016); Eo and Morley (2018).

• Strand that revisits secular stagnation hypothesis of Hansen

(1939): Summers (2015); Cowen (2011) and Gordon (2015); Jones (2018); Eggertsson and Mehrotra (2014).

• Strand that estimates fiscal policy rules to measure the effects
• f fiscal policy with fully-specified structural models: Straub

and Coenen (2005); Forni et al. (2009); Leeper et al. (2010); Ratto et al. (2009)

This paper ...

• Estimates, with Australian aggregate data and a structural

model, the magnitude and timing of the slowdown in trend growth.

• The sole cause of a permanent slowdown in our model is a

permanent fall of the growth rate of labour-augmenting technology.

• Then uses the method of Kulish and Pagan (2017) to allow,

but not to impose, in estimation a break in the growth rate of labour-augmenting productivity; likelihood function is free to choose what change in trend growth, if any, best fits the data.

• We find that trend growth is estimated to have fallen from just
• ver to 2 per cent to just below 0.2 per cent per year.
• Then study the implications for government debt, government

spending and tax revenues.

Slowdown driven by slowing TFP.

• 2
• 1

1 2 3 4 5

• 2
• 1

1 2 3 4 5 1976-77 1981-82 1986-87 1991-92 1996-97 2001-02 2006-07 2011-12 2016-17 Per cent Per cent

Growth Accounting - 5-yr rolling average

Real GDP per capita growth MFP contribution Capital per capita contribution

Next steps

• First, understand changes in trend growth in the standard

Ramsey model.

• Then set up an open economy stochastic growth model with

fiscal policy.

• Set parameter values – calibrated/estimated on Australian

aggregate data

• Quantify for Australia the fiscal implications for government

debt, government spending and tax revenues of the estimated permanent fall of the growth rate of TFP, z.

Trend Growth in the Ramsey Model

Time, t, is continous. The production function is: Y = K α (ZL)1−α (1) where Z is labour augmenting TFP which grows according to ˙ Z Z = z and L is population which we normalise to 1. Equation (1) can be written in intensive form as y = k α (2) where y = Y /Z and k = K/Z

Trend Growth in the Ramsey Model (cont’d)

Preferences are U = ∞ e−ρtu (C) dt where C is consumption at time t, ρ is the subjective discount rate, and u(C) is the instantaneous utility function which is given by: u (C) =

• C 1−σ−1

1−σ

if σ = 1 and σ ≥ 0 ln (C) if σ = 1

Trend Growth in the Ramsey Model (cont’d)

In units of effective labour, preferences are U = ∞ e−(ρ−(1−σ)z)tu (c) dt (3) where c = C/Z and ρ − (1 − σ)z > 0 holds. The budget constraint in units of effective labour units is: ˙ k = k α − (z + δ)k − c (4)

Trend Growth in the Ramsey Model (cont’d)

In equilibrium: ˙ c c = 1 σ

• αk α−1 − ρ − δ − σz
• (5)

˙ k = k α − (z + δ)k − c (6) Along the balanced growth path, ˙ k = ˙ c = 0 which implies ¯ k =

• α

ρ + δ + σz

• 1

1−α

(7) ¯ c = ¯ k α − (z + δ)¯ k (8)

Trend Growth in the Ramsey Model (cont’d)

In equilibrium: ˙ c c = 1 σ

• αk α−1 − (z + δ) − (ρ − (1 − σ)z
• (9)

˙ k = k α − (z + δ)k − c (10)

Steady state

k c ˙ c(t) = 0 ˙ k(t) = 0 A kA cA

A permanent decrease in z

k c ˙ c(t) = 0 ˙ c(t) = 0 ˙ k(t) = 0 ˙ k(t) = 0 A E B kA kB cA cB

A permanent decrease in z

• ↑ k, ↑ y = f (k) and ↑ c
• changes composition of output (i.e c/y and i/y)

c y = k α − (z + δ)k k α = 1 − (z + δ)k 1−α i y = (z + δ)k k α = (z + δ)k 1−α Can show that ∂ (c/y) ∂z = −∂ (i/y) ∂z = −α (ρ + (1 − σ)δ) (z + δ + ρ)2 < 0 for 0 < σ < 1 + ρ/δ. So, ↓ z →↑ (c/y)

Trend Growth in Ramsey with Fiscal Policy

The government maintains a balanced budget so the budget constraint is: g = τ (11) where g = G/Z is government spending and τ = T/Z are lump-sum taxes both in units of effective labour.

Trend Growth in Ramsey with Fiscal Policy

Under these assumptions we now have the system

˙ c c = 1 σ

• αk α−1 − ρ − δ − σz
• (12)

˙ k = k α − (z + δ)k − c − g (13)

Note: (12) which is unchanged determines k which in turn determines y = f (k); so g crowds out c.

Trend Growth in Ramsey with Fiscal Policy

Must specify how government spending is determined. Consider two cases

1 Case 1:

g = γy

constant fraction γ of output.

2 Case 2:

g = ¯ g

constant level of government spending per effective labour unit.

Two assumptions for g

k c ˙ c(t) = 0 ˙ k(t) = 0 (g = ¯ g) ˙ k(t) = 0 (g = γf(k)) A kA cA

Fall in z with g = γy

k c ˙ c(t) = 0 ˙ c(t) = 0 ˙ k(t) = 0 (g = γf(k)) ˙ k(t) = 0 (g = γf(k)) A E1 B1 kA kB cA cB1

Fall in z with g = ¯ g

k c ˙ c(t) = 0 ˙ c(t) = 0 ˙ k(t) = 0 (g = ¯ g) ˙ k(t) = 0 (g = ¯ g) A E2 B2 kA kB cA cB2

Fall in z: g = γy vs. g = ¯ g

k c ˙ c(t) = 0 ˙ c(t) = 0 ˙ k(t) = 0 (g = ¯ g) ˙ k(t) = 0 (g = γf(k)) ˙ k(t) = 0 (g = γf(k)) ˙ k(t) = 0 (g = ¯ g) A E2 E1 B1 B2 kA kB cA cB1 cB2

Trend growth, z, and government spending, g

• When g = ¯

g, a fall in z means increases y and as result ¯ g/y is lower in the new steady state.

• As a result relatively less taxes are needed to finance ¯

g, so consumption is higher than under the g = γy rule.

• How the steady state level of g is pinned down is important

when z changes. With a fiscal policy rule like: ln gt = (1 − ρg)g + ρg ln gt−1 + εg,t under g = ¯ g we have that ¯ g/y will be less than γ = g/y after z falls. More on this later.

Open Economy Model: Households

The representative household maximises its expected lifetime utility: I E0

∞

• t=0

βtζt

• ln(Ct − hCt−1) − γζL

t

L1+ν

t

1 + ν

• subject to the budget constraint:

(1 + τc

t )Ct + It + Bt + B F t

≤ Rt−1Bt−1 + RF

t−1B F t−1 + (1 − τw t )WtLt

+ (1 − τK

t )r K t Kt−1 + TRt

and the capital accumulation equation: Kt = (1 − δ) Kt−1 + ζI

t

• 1 − Υ

It It−1

• It

where ζt follows: ln ζt = ρζ ln ζt−1 + εζ,t ζL

t folows:

ln ζL

t = ρL ln ζL t−1 + εL,t

and ζI

t follows:

ln ζI

t = ρI ln ζI t−1 + εI ,t

Open Economy Model: Firms

Firms produce using the Cobb-Douglas production function: Yt = K α

t−1 (ZtLt)1−α

where Zt is a labour-augmenting technology whose growth rate, zt = Zt/Zt−1, follows: ln zt = (1 − ρz ) ln z + ρz ln zt−1 + εz,t and so z governs labour-augmenting growth, which is the rate of trend growth.

Open Economy Model: Fiscal Policy

The government budget constraint is: Bt + τc

t Ct + τw t WtLt + τK t r K t Kt−1 + TRt = Rt−1Bt−1 + Gt

And follows fiscal rules given by: ln gt = (1 − ρg) ln g + ρg ln gt−1 − (1 − ρg)γgb bt−1 yt−1 − b y

• + εg,t

τc

t = (1 − ρc)τc + ρcτc t−1 + (1 − ρc)γcb

bt−1 yt−1 − b y

• + εc,t

τw

t = (1 − ρw)τw + ρwτw t−1 + (1 − ρw)γwb

bt−1 yt−1 − b y

• + εw,t

τK

t = (1 − ρK)τK + ρKτK t−1 + (1 − ρK)γKb

bt−1 yt−1 − b y

• + εK,t

τt = (1 − ρτ)τ + ρττt−1 + (1 − ρτ)γτb bt−1 yt−1 − b y

• + ετ,t

where bt

yt − b y stands for the deviation of the debt to output ratio

from its steady state value. Here yt = Yt

Zt , gt = Gt Zt , and bt = Bt Zt .

Open Economy Model: Net Foreign Assets

We close the small open economy model assuming that the interest rate that the household receives on foreign bonds depends on the economy’s net foreign asset position according to: RF

t = R∗ t exp

• −ψb

bF

t

yt − bF y

• where bF

y is the steady-state ratio of net foreign asset to GDP, R∗ t

follows the exogenous process below: ln R∗

t = (1 − ρR∗) ln R∗ + ρR∗ ln R∗ t−1 + εR∗,t

In steady state, R∗ = z/β. Assumes when z falls that the slowdown happens abroad and at home.

Open Economy Model: Real interest rate differentials

• In steady state, R∗ = z/β, so a change in z changes R∗
• R∗

t will converge gradually, governed by ρR∗, to its lower

steady state.

• A differential between R∗

t and Rt will give rise to capital

inflows or outflows.

• Imagine R∗

t falls quickly but Rt takes longer to fall (maybe

because of a commodity price boom or because of adjustments costs)

• In this case, R∗

t < Rt =

⇒ capital inflows, a trade deficit and a deterioration of the NFA.

• Eventually, trade surpluses during the transition restore NFA

position.

Open Economy Model: Trade Balance and the Current Account

The trade balance is given by: NXt = Yt − Ct − It − Gt and the current account is given by: CAt = NXt + (RF

t−1 − 1)BF t−1

In equilibrium the evolution of the net foreign debt position of the economy is given by: BF

t = RF t−1BF t−1 + NXt

The Government Budget Constraint in the Steady State

Eexpressed in terms of shares of output the GBC becomes: g y + 1 β − 1 b y = τc c y + τw(1 − α) + τKα + τ y Following a permanent decrease in z to a lower value z ′:

• Baseline assumption: Fiscal authority does not adjust g

the government spending-to-output ratio gradually decreases in the transition towards the lower value of g/y ′

• Alternative assumption: Target g/y ratio

government spending increases to g ′ so that in the new balanced growth path g/y = g ′/y ′.

Calibration

Parameter Description Value β discount factor 0.996 δ depreciation rate 0.016 ν Inverse Frisch 2 z Steady-state TFP growth 1.0055 α Capital share 0.29 bF Steady-state net foreign assets g/y Steady-state government spending-to-output 0.23 b/y Steady-state debt-to-output 0.56 τc Steady-state consumption tax rate 0.06 τw Steady-state labour income tax rate 0.17 τK Steady-state capital income tax rate 0.13

Calibration: First Moments

Target Average 1983-2008 Model Macro Aggregates (annual per cent) Per capita output growth 2.2 2.2 Domestic real interest rate 4.2 4.2 Expenditure (per cent of GDP) Consumption 57.2 56.1 Investment 20.4 20.3 Government spending 23.6 23.6 Net exports

• 1.3

0.0 Tax Revenues (per cent of GDP) Consumption tax 3.7 3.7 Labour income tax 12.3 12.3 Capital income tax 4.1 4.1 Borrowing (per cent of annual GDP) Public Debt 13.4 13.4

Note: Model ratios calculated at initial regime where z = 1.0055.

Estimation – Observable variables

1983 1988 1993 1998 2003 2008 2013 2018

• 4
• 2

2 4 % Output growth 1983 1988 1993 1998 2003 2008 2013 2018

• 18
• 9

9 18 % Investment growth 1983 1988 1993 1998 2003 2008 2013 2018

• 3
• 1.5

1.5 3 % Net exports-to-GDP ratio 1983 1988 1993 1998 2003 2008 2013 2018 19 22 25 28 % Government spending-to-GDP ratio 1983 1988 1993 1998 2003 2008 2013 2018 10 20 30 % Public debt-to-GDP ratio 1983 1988 1993 1998 2003 2008 2013 2018 2 4 6 8 10 % Real interest rate 1983 1988 1993 1998 2003 2008 2013 2018

• 4
• 2

2 4 % Wage Growth 1983 1988 1993 1998 2003 2008 2013 2018 3 3.4 3.8 4.2 % Consumption tax revenues-to-GDP ratio 1983 1988 1993 1998 2003 2008 2013 2018 9 11 13 15 % Labour income tax revenues-to-GDP ratio 1983 1988 1993 1998 2003 2008 2013 2018 2 4 6 8 % Capital income tax revenues-to-GDP ratio

Technical steps

• Find steady state of non-linear system, linearise and solve

around it.

• we calibrate some parameters and estimate others, ϑ
• construct log-likelihood under structural change following

Kulish and Pagan (2017)

• put priors and construct posterior,

P(θ, T|Y) ∝ L(Y|θ, T)p(θ, T), (14)

• to estimate θ and T = (Tz , Tσ) by MCMC methods (Similar

to Kulish and Pagan (2017) and Kulish and Rees (2017)).

Estimation

In the sample t = 1, 2, · · · , T, the economy can be in one of three possible regimes:

1 First regime t = 1, 2, · · · , Tσ − 1: high trend growth, z and

high variance of shocks µΩ. A0yt = C0 + A1yt−1 + B0I Etyt+1 + D0εt

2 Second regime: For t = Tσ, · · · , Tz − 1, the variances of the

shocks change to Ω. A0yt = C0 + A1yt−1 + B0I Etyt+1 + D∗

0εt 3 Third regime: For t = Tz , · · · , T, trend growth changes to z ′.

A∗

0yt = C ∗ 0 + A∗ 1yt−1 + B∗ 0I

Etyt+1 + D∗

0εt

Results: Estimated Parameters

Prior distribution Posterior distribution Parameter Distribution Mean S.d. Mean Mode 5% 95% Structural Parameters h Beta 0.5 0.25 0.12 0.11 0.05 0.21 Υ

′′

Normal 5.0 2.0 3.39 2.99 2.19 4.92 ∆z Uniform [-0.01, 0.01]

• 0.0051
• 0.0051
• 0.0063
• 0.0040

µ Uniform [0, 3] 2.28 2.22 2.00 2.60 γgb Uniform [0, 0.5] 0.07 0.02 0.01 0.18 γcb Uniform [0, 0.5] 0.00 0.00 0.00 0.01 γwb Uniform [0, 0.5] 0.04 0.02 0.01 0.08 γKb Uniform [0, 0.5] 0.05 0.01 0.00 0.11 γτb Uniform [0, 0.5] 0.06 0.06 0.01 0.11 AR Coefficients ρz Beta 0.50 0.19 0.24 0.27 0.14 0.34 ρR∗ Beta 0.71 0.16 0.62 0.62 0.56 0.69 ρζ Beta 0.71 0.16 0.96 0.98 0.92 0.99 ρL Beta 0.71 0.16 0.99 0.99 0.99 0.99 ρI Beta 0.50 0.19 0.18 0.17 0.07 0.31 ρg Beta 0.71 0.16 0.94 0.95 0.89 0.97 ρc Beta 0.71 0.16 0.86 0.87 0.78 0.94 ρw Beta 0.71 0.16 0.87 0.89 0.81 0.92 ρK Beta 0.71 0.16 0.92 0.93 0.88 0.95 ρτ Beta 0.50 0.19 0.23 0.21 0.11 0.35

Results: Estimated Parameters

Prior distribution Posterior distribution Parameter Distribution Mean S.d. Mean Mode 5% 95% Standard Deviations σz

• Inv. Gamma

0.01 0.30 0.009 0.009 0.008 0.010 σR∗

• Inv. Gamma

0.01 0.30 0.002 0.002 0.002 0.002 σζ

• Inv. Gamma

0.10 0.30 0.029 0.023 0.018 0.045 σL

• Inv. Gamma

0.10 0.30 0.028 0.028 0.025 0.032 σI

• Inv. Gamma

0.10 0.30 0.088 0.079 0.058 0.125 σg

• Inv. Gamma

0.10 0.30 0.023 0.023 0.021 0.026 σc

• Inv. Gamma

0.01 0.30 0.001 0.001 0.001 0.002 σw

• Inv. Gamma

0.01 0.30 0.007 0.006 0.006 0.007 σK

• Inv. Gamma

0.01 0.30 0.009 0.009 0.008 0.011 στ

• Inv. Gamma

0.10 0.30 0.063 0.064 0.057 0.071 Log marginal density: 4703.3

Results: Trend Growth

Figure: Posterior Distribution of Trend Growth

• 1
• 0.5

0.5 1 1.5 2 2.5 % Posterior Distribution of Final Trend Growth Rate z′ Initial Trend Growth Rate z

Results: Date Breaks

Figure: Cumulative Posterior Distributions of Date Breaks

1983 1988 1993 1998 2003 2008 2013 2018 0.2 0.4 0.6 0.8 1 probability Date Break in Mean of Trend Growth 1983 1988 1993 1998 2003 2008 2013 2018 0.2 0.4 0.6 0.8 1 probability Date Break in Variance of Shocks

Estimated Transitional Dynamics

Figure: Data and Estimated Transitional Dynamics

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

• 4
• 2

2 4 %

Output growth

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

• 18
• 9

9 18 %

Investment growth

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

• 3
• 1.5

1.5 3 %

Net exports-to-GDP ratio

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 19 22 25 28 %

Government spending-to-GDP ratio

Non-stochastic Actual

Estimated Transitional Dynamics

Figure: Data and Estimated Transitional Dynamics

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 10 20 30 %

Public debt-to-GDP ratio

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2 4 6 8 10 %

Real interest rate

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

• 4
• 2

2 4 %

Wage Growth

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 3 3.4 3.8 4.2 %

Consumption tax revenues-to-GDP ratio

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 9 11 13 15 %

Labour income tax revenues-to-GDP ratio

Non-stochastic Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2 4 6 8 %

Capital income tax revenues-to-GDP ratio

Non-stochastic Actual

Sensitivity Analysis: g = γy

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 20 22 24 26 28 % Non-stochastic path with fixed government spending level in steady-state Non-stochastic path with fixed government spending-to-output ratio in steady-state Actual governemt spending-to-GDP ratio

Log marginal density = 4691.6 < 4703.3

Sensitivity Analysis: UC Model

The unobserved components trend-cycle decomposition model is given by yt = τt + ct (15) τt = z1(t < Tz ) + (z + ∆z)1(t ≥ Tz ) + τt−1 + ǫτ

t

(16) ct = ρ1ct−1 + ρ2ct−2 + ǫc

t

(17) where

ǫτ

t

ǫc

t

• = N
• 0,

µσ2

τ1(t < Tσ) + σ2 τ1(t ≥ Tσ)

µσ2

c1(t < Tσ) + σ2 c1(t ≥ Tσ)

UC Model Estimates

Prior distribution Posterior distribution Parameter Dist. Mean S.d. Mean Mode 5% 95% Parameters z ′ Uniform [0, 0.015] 0.0025 0.0029 0.0014 0.0036 ρ1 Beta 0.5 0.15 0.4145 0.4940 0.2159 0.6218 ρ2 Beta 0.5 0.15 0.4151 0.4926 0.2145 0.6204 στ Uniform [0, 0.2] 0.0079 0.0079 0.0079 0.0079 σc Uniform [0, 0.2] 0.0002 0.0002 0.0000 0.0003 µ Uniform [0, 3] 1.9206 1.8557 1.5915 2.3015 Break Dates Tz Flat [1997:Q4, 2015:Q2] 2006:Q2 2007:Q4 2000:Q4 2008:Q3 Tσ Flat [1997:Q4, 2015:Q2] 2002:Q3 2004:Q1 1998:Q2 2005:Q3

Estimates of trend growth – UC and RBC models

• 1
• 0.5

0.5 1 1.5 2 2.5 % Posterior Distribution of Final Trend Growth Rate z′ in Structural Model Posterior Distribution of Final Trend Growth Rate z′ in Unobserved Components Model Initial Trend Growth Rate z

Differences in estimates of trend growth

• The government spending to- output ratio, net

exports-to-GDP and the real interest rate all contribute to a lower estimate of z.

• Removing the real interest rate as an observable, increases the

estimate of trend growth from 0.16% to 0.31% per year.

• when the net exports to GDP series is removed, the estimate
• f trend growth increases further to 0.65%.

Real interest rates implied by UC model

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2 4 6 8 10 %

Structural model Unobserved Components model Observed real interest rate

Counterfactual

• What would be the path of output per capit had trend growth

stayed constant?

• To do this we draw from the posterior distribution and at each

draw compute the smoothed structural shocks.

• Use shocks to compute the evolution of the economy under

the assumption that ∆z = 0.

• By 2018:Q1 actual output per capita is $17, 574. At the mean
• f the posterior distribution of the counterfactual paths, by

2018:Q1, output per capita would have been 25% higher, around $21, 930.

• The cumulative loss of output over the whole sample at the

mean is $103, 528, one and a half times annual GDP per capita in Australia.

Counterfactual: Absence of Trend Growth Slowdown

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 0.8 1.1 1.4 1.7 2 2.3 2.6 $ ×104

Real GDP per capita

Counterfactual Mean of counterfactual distribution Actual 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

• 5

5 10 15 20 25 30 %

Public debt-to-GDP ratio

Counterfactual Mean of counterfactual distribution Actual

Conclusion

• We estimate the magnitude of the slowdown and assess

implications for a fiscal authority in a small open economy.

• We find strong evidence in favour of a permanent slowdown in

trend growth (from 2% to 0.16%) which leads to:

• an increase in k/y, an initial fall in c/y, a rise in i/y and an

initial fall in nx/y.

• a trade deficit to finance investment
• a transition in which the b/y ratio increases. Fiscal rules

determines this transition. For our estimated values, the slowdown initially deteriores the primary defict and increases debt.

• Structural model points to a more pronounced slowdown than

an UC model suggests. (general equilibrium inferences very different from reduced form statistical models!)

• r, nx/y, and g/y suggest that the slowdown is more

pronounced.