Fiscal and Monetary Policies: Background

Fiscal and Monetary Policies: Background Behzad Diba University of Bern April 2012 (Institute) Fiscal and Monetary Policies: Background April 2012 1 / 19

Research Areas Research on fiscal policy typically abstracts from monetary conditions (focuses on real models and data for real variables), with two major exceptions: (Institute) Fiscal and Monetary Policies: Background April 2012 2 / 19

Research Areas Research on fiscal policy typically abstracts from monetary conditions (focuses on real models and data for real variables), with two major exceptions: 1 research on the inflation tax and seigniorage 2 research on fiscal multipliers particularly in the context of Dynamic Stochastic General Equilibrium (DSGE) models and how their size depends on the conduct of monetary policy Monetary Theory mostly abstracts from fiscal policy, except for research (over the last two decades) on the Fiscal Theory of the Price Level (FTPL) (Institute) Fiscal and Monetary Policies: Background April 2012 2 / 19

Research Areas Research on fiscal policy typically abstracts from monetary conditions (focuses on real models and data for real variables), with two major exceptions: 1 research on the inflation tax and seigniorage 2 research on fiscal multipliers particularly in the context of Dynamic Stochastic General Equilibrium (DSGE) models and how their size depends on the conduct of monetary policy Monetary Theory mostly abstracts from fiscal policy, except for research (over the last two decades) on the Fiscal Theory of the Price Level (FTPL) The public debt does not play a major role in standard quantitative models used for policy analysis [e.g., debt does not, typically, appear in DSGE models developed at central banks] (Institute) Fiscal and Monetary Policies: Background April 2012 2 / 19

Research Areas Research on fiscal policy typically abstracts from monetary conditions (focuses on real models and data for real variables), with two major exceptions: 1 research on the inflation tax and seigniorage 2 research on fiscal multipliers particularly in the context of Dynamic Stochastic General Equilibrium (DSGE) models and how their size depends on the conduct of monetary policy Monetary Theory mostly abstracts from fiscal policy, except for research (over the last two decades) on the Fiscal Theory of the Price Level (FTPL) The public debt does not play a major role in standard quantitative models used for policy analysis [e.g., debt does not, typically, appear in DSGE models developed at central banks] these models typically exhibit Ricardian Equivalence (Institute) Fiscal and Monetary Policies: Background April 2012 2 / 19

DSGE Models The IS-LM model (with a fixed price level) incorporated the Keynesian consumption function, linking consumption to current disposable income (Institute) Fiscal and Monetary Policies: Background April 2012 3 / 19

DSGE Models The IS-LM model (with a fixed price level) incorporated the Keynesian consumption function, linking consumption to current disposable income this is why the multiplier for government purchases is larger than one according to the old Keynesian view the same consumption function is behind Keynesian tax multipliers DSGE models do not support the old Keynesian view because they postulate utility maximizing consumers A benchmark case is Barro s debt neutrality (Ricardian Equivalence) proposition: given the path of government purchases, the financing decision (debt versus taxes) has no effect on consumption, employment, output, the real interest rate, and the current-account balance (Institute) Fiscal and Monetary Policies: Background April 2012 3 / 19

DSGE Models The IS-LM model (with a fixed price level) incorporated the Keynesian consumption function, linking consumption to current disposable income this is why the multiplier for government purchases is larger than one according to the old Keynesian view the same consumption function is behind Keynesian tax multipliers DSGE models do not support the old Keynesian view because they postulate utility maximizing consumers A benchmark case is Barro s debt neutrality (Ricardian Equivalence) proposition: given the path of government purchases, the financing decision (debt versus taxes) has no effect on consumption, employment, output, the real interest rate, and the current-account balance In these models, the effects of fiscal policy reflect incentives (e.g., income and substitution effects on labor supply) and distortions (Institute) Fiscal and Monetary Policies: Background April 2012 3 / 19

DSGE Models The IS-LM model (with a fixed price level) incorporated the Keynesian consumption function, linking consumption to current disposable income this is why the multiplier for government purchases is larger than one according to the old Keynesian view the same consumption function is behind Keynesian tax multipliers DSGE models do not support the old Keynesian view because they postulate utility maximizing consumers A benchmark case is Barro s debt neutrality (Ricardian Equivalence) proposition: given the path of government purchases, the financing decision (debt versus taxes) has no effect on consumption, employment, output, the real interest rate, and the current-account balance In these models, the effects of fiscal policy reflect incentives (e.g., income and substitution effects on labor supply) and distortions On these fronts, the implications of standard New Keynesian models are closer to those of the Real Business Cycle model, than they are to traditional Keynesian views (Institute) Fiscal and Monetary Policies: Background April 2012 3 / 19

Public Debt and Inflation? Monetarist doctrine and evidence for advanced economies support the conventional wisdom that major central banks can control inflation, and fiscal policy does not matter much for inflation Monetarist doctrine makes a sharp distinction between the monetary base and other nominal liabilities of the public sector In standard monetary models, fiscal policy does not play a major role in inflation determination, unless the central bank monetizes the debt There is not much evidence linking the public debt to inflation in advanced economies (although the connection seems clear for broad cross sections of countries and historical episodes) (Institute) Fiscal and Monetary Policies: Background April 2012 4 / 19

Public Debt and Inflation? Monetarist doctrine and evidence for advanced economies support the conventional wisdom that major central banks can control inflation, and fiscal policy does not matter much for inflation Monetarist doctrine makes a sharp distinction between the monetary base and other nominal liabilities of the public sector In standard monetary models, fiscal policy does not play a major role in inflation determination, unless the central bank monetizes the debt There is not much evidence linking the public debt to inflation in advanced economies (although the connection seems clear for broad cross sections of countries and historical episodes) But the fiscal outlook in many advanced economies has led to policy concerns that the conventional wisdom may be misleading, as we will discuss, and new lines of research have emerged (Institute) Fiscal and Monetary Policies: Background April 2012 4 / 19

Public Debt and Output (Growth)? Growth models with an ad hoc consumption function (following the Solow-Swan model) link national saving to the budget deficit (Institute) Fiscal and Monetary Policies: Background April 2012 5 / 19

Public Debt and Output (Growth)? Growth models with an ad hoc consumption function (following the Solow-Swan model) link national saving to the budget deficit fiscal policy can affect the steady-state equilibrium (or the balanced growth path) through this channel But our more modern growth models share the strong implications of DSGE models about debt neutrality (Ricardian Equivalence) because all these models incorporate optimizing households although the models do not always imply strict Ricardian Equivalence [e.g., they may incorporate finite horizons], their departures from Ricardian Equivalence, are often quantitatively small The empirical literature on growth does not establish a clear role for the public debt once we control for other factors (although there is more convincing evidence on the adverse growth effects of external debt in emerging-market economies) (Institute) Fiscal and Monetary Policies: Background April 2012 5 / 19

Public Debt and Output (Growth)? Growth models with an ad hoc consumption function (following the Solow-Swan model) link national saving to the budget deficit fiscal policy can affect the steady-state equilibrium (or the balanced growth path) through this channel But our more modern growth models share the strong implications of DSGE models about debt neutrality (Ricardian Equivalence) because all these models incorporate optimizing households although the models do not always imply strict Ricardian Equivalence [e.g., they may incorporate finite horizons], their departures from Ricardian Equivalence, are often quantitatively small The empirical literature on growth does not establish a clear role for the public debt once we control for other factors (although there is more convincing evidence on the adverse growth effects of external debt in emerging-market economies) Again, the current fiscal outlook has led to concerns that these conventional views may be misleading (Institute) Fiscal and Monetary Policies: Background April 2012 5 / 19

Non-Quantitative Models Policy analysis may also draw on smaller (non-quantitative models) that highlight specific frictions in a stylized setting (Institute) Fiscal and Monetary Policies: Background April 2012 6 / 19

Non-Quantitative Models Policy analysis may also draw on smaller (non-quantitative models) that highlight specific frictions in a stylized setting for example, the models reviewed in Alesina and Perotti (1996) that involve some "expectations view of fiscal policy" or "credibility effects" of fiscal adjustment belong to this class non-quantitative models (by definition) do not have to take a stand on the magnitude of departures from Ricardian Equivalence (they may, for example, model households who only live two periods) (Institute) Fiscal and Monetary Policies: Background April 2012 6 / 19

Non-Quantitative Models Policy analysis may also draw on smaller (non-quantitative models) that highlight specific frictions in a stylized setting for example, the models reviewed in Alesina and Perotti (1996) that involve some "expectations view of fiscal policy" or "credibility effects" of fiscal adjustment belong to this class non-quantitative models (by definition) do not have to take a stand on the magnitude of departures from Ricardian Equivalence (they may, for example, model households who only live two periods) Non-quantitative models are also useful in motivating empirical research (albeit with a looser connection than what quantitative models aspire to achieve) (Institute) Fiscal and Monetary Policies: Background April 2012 6 / 19

Fiscal Stance Alternative measures of the fiscal balance are useful in various applications: 1 The wording "budget deficit" (or surplus) usually refers to the actual deficit (surplus) inclusive of interest payments on the national debt 2 The "primary" deficit (surplus) excludes interest payments on the national debt 3 The "structural" (full-employment) and "cyclical" components of the deficit (surplus) are useful for medium-term projections (Institute) Fiscal and Monetary Policies: Background April 2012 7 / 19

primary surplus = tax revenues - government expenditures other than interest payments budget surplus inclusive of interest payments = tax revenues - government expenditures inclusive of interest payments increase in the national debt = budget deficit inclusive of interest payments structural (full-employment) budget surplus: estimate based on potential output (rather than actual real GDP) cyclical budget surplus = actual surplus - structural surplus the role of progressive tax code and entitlement programs leading to cyclical deficits during recessions

Fiscal Stance Alternative measures of the fiscal balance are useful in various applications: 1 The wording "budget deficit" (or surplus) usually refers to the actual deficit (surplus) inclusive of interest payments on the national debt 2 The "primary" deficit (surplus) excludes interest payments on the national debt 3 The "structural" (full-employment) and "cyclical" components of the deficit (surplus) are useful for medium-term projections Although "fiscal sustainability" is not a precise concept, a pragmatic definition is based on the time path of the debt-to-gdp ratio (Institute) Fiscal and Monetary Policies: Background April 2012 7 / 19

Dynamics of Debt/GDP Letting b t denote the real stock of government bonds, with a net real interest rate r t, debt dynamics are governed by and the debt-to-gdp ratio follows b t = (1 + r t 1 )b t 1 + G t T t, b t Y t = (1 + r t 1 ) ( Yt 1 Y t ) bt 1 Y t 1 + G t T t Y t, 1 In a growing economy, the government can consistently have a deficit inclusive if interest payments (r t 1 b t 1 + G t T t > 0) without causing an explosion of the debt-to-gdp ratio (as long as these deficits are suitably small) (Institute) Fiscal and Monetary Policies: Background April 2012 8 / 19

Dynamics of Debt/GDP Letting b t denote the real stock of government bonds, with a net real interest rate r t, debt dynamics are governed by and the debt-to-gdp ratio follows b t = (1 + r t 1 )b t 1 + G t T t, b t Y t = (1 + r t 1 ) ( Yt 1 Y t ) bt 1 Y t 1 + G t T t Y t, 1 In a growing economy, the government can consistently have a deficit inclusive if interest payments (r t 1 b t 1 + G t T t > 0) without causing an explosion of the debt-to-gdp ratio (as long as these deficits are suitably small) 2 But a primary deficit (G t T t > 0) leads to growth of the debt-to-gdp ratio (as long as the real interest rate on debt exceeds the growth rate of real GDP (Institute) Fiscal and Monetary Policies: Background April 2012 8 / 19

Fiscal Sustainability Most economists consider a long-run structural surplus a necessary condition for fiscal sustainability (Institute) Fiscal and Monetary Policies: Background April 2012 9 / 19

Fiscal Sustainability Most economists consider a long-run structural surplus a necessary condition for fiscal sustainability But fiscal sustainability involves theoretical subtleties and practical considerations that we will discuss later In a monetary economy, the definition of tax revenues should also include central bank transfers (which reflect seigniorage and revenues from the inflation tax) Letting B t denote the stock of nominal government bonds with a net nominal interest rate i t, and M t the money stock, the public sector s nominal liabilities follow ( ) M t + B t = M t 1 + (1 + i t 1 )B t 1 + P t G t T t, where P t is the price level, and T t is tax revenues excluding central bank transfers (Institute) Fiscal and Monetary Policies: Background April 2012 9 / 19

Seigniorage and Central Bank Transfers In real terms (dividing by P t ), we get ( ) Pt 1 b t = (1 + i t 1 ) b t 1 + G t T t M t M t 1 P t P t and we can define T t T t + M t M t 1 P t as tax revenues inclusive of seigniorage Alternatively, we can write the public-sector budget constraint as ( ) ( ) M t + B t Pt 1 Mt 1 + B t 1 = (1 + i t 1 ) + G t T t i t 1M t 1 P t P t P t 1 P t where the last term represents real central bank transfers (Institute) Fiscal and Monetary Policies: Background April 2012 10 / 19

Seigniorage and Central Bank Transfers In real terms (dividing by P t ), we get ( ) Pt 1 b t = (1 + i t 1 ) b t 1 + G t T t M t M t 1 P t P t and we can define T t T t + M t M t 1 P t as tax revenues inclusive of seigniorage Alternatively, we can write the public-sector budget constraint as ( ) ( ) M t + B t Pt 1 Mt 1 + B t 1 = (1 + i t 1 ) + G t T t i t 1M t 1 P t P t P t 1 P t where the last term represents real central bank transfers Note that M + B has the interpretation of the total stock of government bonds including bonds held by the central bank (Institute) Fiscal and Monetary Policies: Background April 2012 10 / 19

Dynamic Analysis To analyze debt dynamics, we will need some mathematical background (Institute) Fiscal and Monetary Policies: Background April 2012 11 / 19

Dynamic Analysis To analyze debt dynamics, we will need some mathematical background simple (linear) stochastic processes (Institute) Fiscal and Monetary Policies: Background April 2012 11 / 19

Dynamic Analysis To analyze debt dynamics, we will need some mathematical background simple (linear) stochastic processes first-order linear difference equations (Institute) Fiscal and Monetary Policies: Background April 2012 11 / 19

Dynamic Analysis To analyze debt dynamics, we will need some mathematical background simple (linear) stochastic processes first-order linear difference equations Law of Iterated Expectations (Institute) Fiscal and Monetary Policies: Background April 2012 11 / 19

Dynamic Analysis To analyze debt dynamics, we will need some mathematical background simple (linear) stochastic processes first-order linear difference equations Law of Iterated Expectations This background will also serve us in our discussion of inflation dynamics (Institute) Fiscal and Monetary Policies: Background April 2012 11 / 19

The Random Walk Process The evolution of {Y t } is governed by Y t = Y t 1 + ε t where {ε t } is a "white noise" process: (Institute) Fiscal and Monetary Policies: Background April 2012 12 / 19

The Random Walk Process The evolution of {Y t } is governed by Y t = Y t 1 + ε t where {ε t } is a "white noise" process: E ε t = 0, for all t (Institute) Fiscal and Monetary Policies: Background April 2012 12 / 19

The Random Walk Process The evolution of {Y t } is governed by Y t = Y t 1 + ε t where {ε t } is a "white noise" process: E ε t = 0, for all t E (ε t ) 2 = σ 2, for all t (Institute) Fiscal and Monetary Policies: Background April 2012 12 / 19

The Random Walk Process The evolution of {Y t } is governed by Y t = Y t 1 + ε t where {ε t } is a "white noise" process: E ε t = 0, for all t E (ε t ) 2 = σ 2, for all t E ε t ε s = 0, for all s = t (Institute) Fiscal and Monetary Policies: Background April 2012 12 / 19

The Random Walk Process The evolution of {Y t } is governed by Y t = Y t 1 + ε t where {ε t } is a "white noise" process: E ε t = 0, for all t E (ε t ) 2 = σ 2, for all t E ε t ε s = 0, for all s = t Note that and Y t+1 = Y t + ε t+1 E t Y t+1 = Y t (Institute) Fiscal and Monetary Policies: Background April 2012 12 / 19

Calculating Expectations Similarly for any j 1, we have E t Y t+j = Y t (Institute) Fiscal and Monetary Policies: Background April 2012 13 / 19

Calculating Expectations Similarly for any j 1, we have E t Y t+j = Y t Application: suppose the logarithm of the price level (p t ) is related to the expected path of the logarithm of the money supply (m t ) by p t = (1 β)e t β j m t+j j=0 with (0 < β < 1). Then, if {m t } takes a random walk, we get: p t = (1 β) j=0 β j E t m t+j = (1 β) j=0 β j m t = m t (Institute) Fiscal and Monetary Policies: Background April 2012 13 / 19

The AR(1) Process The first-order autoregressive process {Y t } is generated by Y t = ρy t 1 + ε t where {ε t } is a "white noise" process. (Institute) Fiscal and Monetary Policies: Background April 2012 14 / 19

The AR(1) Process The first-order autoregressive process {Y t } is generated by Y t = ρy t 1 + ε t where {ε t } is a "white noise" process. for any j 1, we get E t Y t+j = ρ j Y t (Institute) Fiscal and Monetary Policies: Background April 2012 14 / 19

The AR(1) Process The first-order autoregressive process {Y t } is generated by Y t = ρy t 1 + ε t where {ε t } is a "white noise" process. for any j 1, we get E t Y t+j = ρ j Y t The process is explosive if ρ > 1. We often use the stationary process with positive autocorrelation: 0 < ρ < 1 (Institute) Fiscal and Monetary Policies: Background April 2012 14 / 19

The AR(1) Process The first-order autoregressive process {Y t } is generated by Y t = ρy t 1 + ε t where {ε t } is a "white noise" process. for any j 1, we get E t Y t+j = ρ j Y t The process is explosive if ρ > 1. We often use the stationary process with positive autocorrelation: 0 < ρ < 1 Note that with ρβ < 1 E t β j Y t+j = Y t j=0 (ρβ) j = j=0 Y t 1 ρβ where the last step follows from summation of a geometric series (Institute) Fiscal and Monetary Policies: Background April 2012 14 / 19

Difference Equations Suppose we know the sequence {X t }, and want to find the sequence {Y t } satisfying Y t = λy t 1 + X t (Institute) Fiscal and Monetary Policies: Background April 2012 15 / 19

Difference Equations Suppose we know the sequence {X t }, and want to find the sequence {Y t } satisfying Y t = λy t 1 + X t This is a first-order linear difference equation with constant coeffi cient λ and variable term X t The difference equation is "stable" if λ < 1 and "unstable" (explosive) if λ > 1 (Institute) Fiscal and Monetary Policies: Background April 2012 15 / 19

Difference Equations Suppose we know the sequence {X t }, and want to find the sequence {Y t } satisfying Y t = λy t 1 + X t This is a first-order linear difference equation with constant coeffi cient λ and variable term X t The difference equation is "stable" if λ < 1 and "unstable" (explosive) if λ > 1 We can iterate the equation backward or forward (Institute) Fiscal and Monetary Policies: Background April 2012 15 / 19

Backward Iteration Use and to get Y t = λy t 1 + X t Y t 1 = λy t 2 + X t 1 Y t = λ 2 Y t 2 + λx t 1 + X t (Institute) Fiscal and Monetary Policies: Background April 2012 16 / 19

Backward Iteration Use and to get Keep iterating to get Y t = λy t 1 + X t Y t 1 = λy t 2 + X t 1 Y t = λ 2 Y t 2 + λx t 1 + X t Y t = λ t t 1 Y 0 + j=0 λ j X t j (Institute) Fiscal and Monetary Policies: Background April 2012 16 / 19

Backward Iteration Use and to get Keep iterating to get Y t = λy t 1 + X t Y t 1 = λy t 2 + X t 1 Y t = λ 2 Y t 2 + λx t 1 + X t Y t = λ t t 1 Y 0 + j=0 λ j X t j This is useful if we have an initial condition that pins down Y 0 (Institute) Fiscal and Monetary Policies: Background April 2012 16 / 19

Backward Iteration Use and to get Keep iterating to get Y t = λy t 1 + X t Y t 1 = λy t 2 + X t 1 Y t = λ 2 Y t 2 + λx t 1 + X t Y t = λ t t 1 Y 0 + j=0 λ j X t j This is useful if we have an initial condition that pins down Y 0 Compare the dynamics of stable and unstable cases (Institute) Fiscal and Monetary Policies: Background April 2012 16 / 19

Forward Iteration Start with and iterate forward on Y t+1 = λy t + X t+1 Y t = λ 1 (Y t+1 X t+1 ) = λ 2 (Y t+2 X t+2 ) λ 1 X t+1 to get Y t = λ n Y t+n n j=1 λ j X t+j (Institute) Fiscal and Monetary Policies: Background April 2012 17 / 19

Forward Iteration Start with and iterate forward on Y t+1 = λy t + X t+1 to get Y t = λ 1 (Y t+1 X t+1 ) = λ 2 (Y t+2 X t+2 ) λ 1 X t+1 Y t = λ n Y t+n n j=1 λ j X t+j This is often useful if the difference equation is unstable ( λ > 1), and we let n go to infinity (Institute) Fiscal and Monetary Policies: Background April 2012 17 / 19

Infinite Forward Iteration For the case with λ > 1, assume {X t } is suitably bounded and consider Y t = λ n Y t+n n j=1 λ j X t+j (Institute) Fiscal and Monetary Policies: Background April 2012 18 / 19

Infinite Forward Iteration For the case with λ > 1, assume {X t } is suitably bounded and consider Y t = λ n Y t+n We often impose the restriction n j=1 lim n + λ n Y t+n = 0 λ j X t+j (Institute) Fiscal and Monetary Policies: Background April 2012 18 / 19

Infinite Forward Iteration For the case with λ > 1, assume {X t } is suitably bounded and consider Y t = λ n Y t+n We often impose the restriction n j=1 lim n + λ n Y t+n = 0 λ j X t+j This may be justified if we want a non-explosive solution (Institute) Fiscal and Monetary Policies: Background April 2012 18 / 19

Infinite Forward Iteration For the case with λ > 1, assume {X t } is suitably bounded and consider Y t = λ n Y t+n We often impose the restriction n j=1 lim n + λ n Y t+n = 0 λ j X t+j This may be justified if we want a non-explosive solution We get a unique bounded solution Y t = j=1 λ j X t+j (Institute) Fiscal and Monetary Policies: Background April 2012 18 / 19

Iterated Expectations Some Rational Expectations models lead to equations of the form E t Y t+1 = λy t + X t+1 and we need to iterate forward using E t+1 Y t+2 = λy t+1 + X t+2 (Institute) Fiscal and Monetary Policies: Background April 2012 19 / 19

Iterated Expectations Some Rational Expectations models lead to equations of the form E t Y t+1 = λy t + X t+1 and we need to iterate forward using E t+1 Y t+2 = λy t+1 + X t+2 The Law of Iterated Expectations implies E t (E t+1 Y t+2 ) = E t Y t+2 and E t Y t+2 = λe t Y t+1 + E t X t+2 (Institute) Fiscal and Monetary Policies: Background April 2012 19 / 19

Iterated Expectations Some Rational Expectations models lead to equations of the form E t Y t+1 = λy t + X t+1 and we need to iterate forward using E t+1 Y t+2 = λy t+1 + X t+2 The Law of Iterated Expectations implies and E t (E t+1 Y t+2 ) = E t Y t+2 E t Y t+2 = λe t Y t+1 + E t X t+2 This allows us to iterate forward when λ > 1 and get Y t = E t as the unique non-explosive solution λ j X t+j j=1 (Institute) Fiscal and Monetary Policies: Background April 2012 19 / 19