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 3.5% 3% 2.5% 2% 1.5% 1% 0.5% 0% -0.5% 2000 2002 2004 2006 2008 2010 2012 2014 2016 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 of 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 over 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. Growth Accounting - 5-yr rolling average Per cent Per cent 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 1976-77 1981-82 1986-87 1991-92 1996-97 2001-02 2006-07 2011-12 2016-17 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 � ∞ e − ρ t u ( C ) dt U = 0 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: � C 1 − σ − 1 if σ � = 1 and σ ≥ 0 1 − σ u ( C ) = ln ( C ) if σ = 1

Trend Growth in the Ramsey Model (cont’d) In units of effective labour, preferences are � ∞ e −( ρ −( 1 − σ ) z ) t u ( c ) dt U = (3) 0 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 ˙ α k α − 1 − ρ − δ − σ z � � (5) σ k = k α − ( z + δ ) k − c ˙ (6) Along the balanced growth path, ˙ k = ˙ c = 0 which implies 1 � � α 1 − α ¯ k = (7) ρ + δ + σ z k α − ( z + δ ) ¯ c = ¯ ¯ k (8)

Trend Growth in the Ramsey Model (cont’d) In equilibrium: c = 1 ˙ c α k α − 1 − ( z + δ ) − ( ρ − ( 1 − σ ) z � � (9) σ k = k α − ( z + δ ) k − c ˙ (10)

Steady state c c ( t ) = 0 ˙ A c A ˙ k ( t ) = 0 k k A

A permanent decrease in z c c ( t ) = 0 ˙ c ( t ) = 0 ˙ B c B A c A ˙ k ( t ) = 0 E ˙ k ( t ) = 0 k k A k B

A permanent decrease in z • ↑ k , ↑ y = f ( k ) and ↑ c • changes composition of output (i.e c / y and i / y ) y = k α − ( z + δ ) k c = 1 − ( z + δ ) k 1 − α k α y = ( z + δ ) k i = ( z + δ ) k 1 − α k α Can show that ∂ ( c / y ) = − ∂ ( i / y ) = − α ( ρ + ( 1 − σ ) δ ) < 0 ∂ z ∂ z ( z + δ + ρ ) 2 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: (11) g = τ 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 = 1 ˙ c α k α − 1 − ρ − δ − σ z � � (12) σ 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 = γ y constant fraction γ of output. 2 Case 2: g = ¯ g constant level of government spending per effective labour unit.

Two assumptions for g c c ( t ) = 0 ˙ A c A ˙ k ( t ) = 0 ( g = ¯ g ) ˙ k ( t ) = 0 ( g = γf ( k )) k k A

Fall in z with g = γ y c c ( t ) = 0 ˙ c ( t ) = 0 ˙ c B 1 B 1 A c A ˙ k ( t ) = 0 ( g = γf ( k )) E 1 ˙ k ( t ) = 0 ( g = γf ( k )) k k A k B

Fall in z with g = ¯ g c c ( t ) = 0 ˙ c ( t ) = 0 ˙ c B 2 B 2 ˙ k ( t ) = 0 ( g = ¯ g ) A c A E 2 ˙ k ( t ) = 0 ( g = ¯ g ) k k A k B

Fall in z : g = γ y vs. g = ¯ g c c ( t ) = 0 ˙ c ( t ) = 0 ˙ c B 2 B 2 c B 1 B 1 ˙ k ( t ) = 0 ( g = ¯ g ) A c A E 2 ˙ k ( t ) = 0 ( g = γf ( k )) ˙ E 1 k ( t ) = 0 ( g = ¯ g ) ˙ k ( t ) = 0 ( g = γf ( k )) k k A k B

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 = γ y rule. • How the steady state level of g is pinned down is important when z changes. With a fiscal policy rule like: ln g t = ( 1 − ρ g ) g + ρ g ln g t − 1 + ε g , 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: ∞ L 1 + ν � � � β t ζ t ln ( C t − hC t − 1 ) − γζ L t I E 0 t 1 + ν t = 0 subject to the budget constraint: ( 1 + τ c t ) C t + I t + B t + B F R t − 1 B t − 1 + R F t − 1 B F t − 1 + ( 1 − τ w ≤ t ) W t L t t ( 1 − τ K t ) r K + t K t − 1 + TR t and the capital accumulation equation: � I t � �� K t = ( 1 − δ ) K t − 1 + ζ I 1 − Υ I t t I t − 1 where ζ t follows: ln ζ t = ρ ζ ln ζ t − 1 + ε ζ, t ζ L t folows: ln ζ L t = ρ L ln ζ L t − 1 + ε L , t and ζ I t follows: ln ζ I t = ρ I ln ζ I t − 1 + ε I , t

Open Economy Model: Firms Firms produce using the Cobb-Douglas production function: Y t = K α t − 1 ( Z t L t ) 1 − α where Z t is a labour-augmenting technology whose growth rate, z t = Z t / Z t − 1 , follows: ln z t = ( 1 − ρ z ) ln z + ρ z ln z t − 1 + ε z , 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: B t + τ c t C t + τ w t W t L t + τ K t r K t K t − 1 + TR t = R t − 1 B t − 1 + G t And follows fiscal rules given by: � b t − 1 � − b ln g t = ( 1 − ρ g ) ln g + ρ g ln g t − 1 − ( 1 − ρ g ) γ gb + ε g , t y t − 1 y � b t − 1 � − b τ c t = ( 1 − ρ c ) τ c + ρ c τ c t − 1 + ( 1 − ρ c ) γ cb + ε c , t y t − 1 y � b t − 1 � − b τ w t = ( 1 − ρ w ) τ w + ρ w τ w t − 1 + ( 1 − ρ w ) γ wb + ε w , t y t − 1 y � b t − 1 � − b τ K t = ( 1 − ρ K ) τ K + ρ K τ K t − 1 + ( 1 − ρ K ) γ Kb + ε K , t y t − 1 y � b t − 1 − b � τ t = ( 1 − ρ τ ) τ + ρ τ τ t − 1 + ( 1 − ρ τ ) γ τ b + ε τ, t y t − 1 y where b t y t − b y stands for the deviation of the debt to output ratio from its steady state value. Here y t = Y t Z t , g t = G t Z t , and b t = B t Z t .

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: � b F − b F � �� R F t t = R ∗ t exp − ψ b y t y where b F y is the steady-state ratio of net foreign asset to GDP, R ∗ t follows the exogenous process below: t = ( 1 − ρ R ∗ ) ln R ∗ + ρ R ∗ ln R ∗ ln R ∗ t − 1 + ε R ∗ , t In steady state, R ∗ = z /β . Assumes when z falls that the slowdown happens abroad and at home.