Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Ragnar Nurkse's balanced growth theory wikipedia , lookup
Virtual economy wikipedia , lookup
Long Depression wikipedia , lookup
Monetary policy wikipedia , lookup
Interest rate wikipedia , lookup
Fractional-reserve banking wikipedia , lookup
Quantitative easing wikipedia , lookup
Modern Monetary Theory wikipedia , lookup
Real bills doctrine wikipedia , lookup
Monetary Business cycles – Lesson 1 Introducing money in the neoclassical model 1- The money-in-the-utility model (MIU) 2- The cash-in-advance model (CIA) Introduction - Objective We incorporate money in a standard RBC model What is the effect of money on the economy? Can we generate a procyclical behavior for labor? Introduction - Objective But first, we need to introduce a demand and supply for money Supply of money Budget constraint of the public sector In nominal terms: Where does this equation come from? How does the Central Bank issue money? What are the underlying assumptions? Monetary aggregates Supply of money: How is money created? How to increase the supply of money Increase the direct monetary transfers to households Open market operations: sell government bonds ? Supply of money A short digression on monetary aggregates to understand the underlying assumption(s) Monetary aggregates Notes and coins in circulation Currency Notes and coins in bank vaults Central bank credit Demand deposits Savings and time deposits Monetary base (MB) Monetary aggregates – from narrow to broad Notes and coins in circulation Notes and coins in bank vaults Central bank credit Demand deposits Savings and time deposits M0 Bank reserves R (minimum reserves + excess reserves) MB Monetary aggregates – from narrow to broad More Liquid Notes and coins in circulation Notes and coins in bank vaults Central bank credit Demand deposits Savings and time deposits M0 M1 M2 Monetary aggregates – from outside to inside money Some elements of MB (bank reserves) are not in M0, M1, M2 Why? M0, M1, M2: liabilities of the banking sector visà-vis the private economy (households, firms…) Exclusion of liabilities of the banking sector (central bank+commercial banks) to itself Avoid double counting Monetary aggregates – from outside to inside money Notes and coins in circulation Central bank money Notes and coins in bank vaults (« outside money ») Central bank credit (minimum =MB reserves+excess reserves) Demand deposits Savings and time deposits Commercial bank money (« inside money ») =M1-M0, M2-M0 Monetary aggregates – from outside to inside money Outside money (MB): liabilities of the central bank, controlled by the central bank =policy instrument. Outside + inside money (M1 or M2 ): liabilities of the banking system (Central Bank+commercial banks) vis-à-vis the private economy = actual supply of money to the private economy How does the Central Bank control the actual money supply through its policy instrument? Monetary aggregates Monetary aggregates - US 9000.0 8000.0 6000.0 M0 M1 M2 MB 5000.0 4000.0 3000.0 2000.0 1000.0 Source: Federal Reseve Bank of Saint-Louis 2009 2007 2005 2003 2001 1999 1997 1995 1993 1991 1989 1987 1985 1983 1981 1979 1977 1975 1973 1971 1969 1967 1965 1963 1961 0.0 1959 Billions of US$ 7000.0 Monetary aggregates – from outside to inside money: the money multiplier Monetary multiplier m=M1/MB>1: Money is created endogeneously by the banking system « Fractional-reserve banking »: one unit of deposits is backed by less than one unit of reserves: the banks lend part of the deposits Supply of money Underlying assumption(s)? Supply of money Budget constraint of the public sector In real terms: Demand for money Why is there a demand for money? Motive to hold money? Demand for money Two main approaches: Money in the utility function: money provides transaction services holding money affects directly the utility of agents (Sidrauski 1967) Cash-in-advance constraint: money is held to finance purchases affects indirectly the utility of agents (through the utility of goods it helps purchasing) (Lucas 1982, Svensson 1985, Cooley and Hansen 1989) Money-in-the-utility (MIU) We first ignore uncertainty and labor-leisure choice Three types of assets (stores of value): capital k: , f increasing and strictly concave nominal bonds B: return it, nominal interest rate and money M, no nominal return but flow of services MIU - Utility Representative household with utility function: where is the stock of real money balances at the end of the period u is increasing in c and m, strictly concave and continuously differentiable U is separable in c and m: same utility out of money whatever the level of consumption Intertemporal utility: MIU – Household’s budget constraint Nominal budget constraint: In real terms: Inflation tax Inflation Distortion on the demand for money MIU – FOC Lagrangian: FOC: (1) (2) (3) (4) MIU – FOC Intertemporal arbitrage: Since resources must be divided between consumption, capital, bonds and money balances, each use must yield the same marginal benefit MIU – Intertemporal arbitrage These equivalences imply two relations that are relevant for money and inflation: No-arbitrage between nominal bonds and capital (between nominal and real assets in general): Notation for real return on capital: Fisher relationship: Nominal interest rate Return on real asset Approximation: Inflation rate MIU – Intertemporal arbitrage No-arbitrage between money and consumption: Demand for money: User cost of money (price of money) Marginal rate of substitution between money and consumption =inflation tax/(1+rt) Inflation affects the demand for money through the inflation tax MIU – Closing the model Money supply: the government sets the growth rate of money Zero supply of bonds: Aggregate budget constraint of the economy: MIU – Dynamic system Euler equation Budget constraint Fisher relationship Growth of real money balances Demand for money Endogenous variables: m, k, c, i, п MIU – Neutrality of money Now that we have the dynamic system, we ask: Is money neutral? real variables (capital, output and consumption) are independent of the level of money supply M? Is money superneutral? real variables are independent of the inflation rate п and the rate of growth of nominal money θ? MIU – Superneutrality of money Take the Euler equation and the budget constraint separately: Ramsey model in discrete time Superneutrality? MIU – Steady-state equilibrium – Real variables Steady state defined by: Money grows at rate θ c, m and k are constant Long-run superneutrality: steady-state real variables (capital and consumption) are independent of the rate of inflation θ: MIU – Steady-state equilibrium – Nominal variables m is constant Prices grow at the same rate as money Nominal interest rate defined by the Fisher relationship: Approximation: MIU – Steady-state equilibrium – Effects of inflation The fact that inflation has no real effect does not mean that it doesn’t affect households! Then what is the effect of inflation on the economy? It affects the demand for money It affects utility MIU – Steady-state equilibrium – Demand for money Steady-state real money holdings are determined by the steady-state user cost of money: Fisher relationship: inflation increases the user cost of money How does inflation affect real money balances m? MIU – Steady-state equilibrium – Utility How can the government increase welfare? MIU – Superneutrality – More on intuition Why doesn’t money growth θ have any effect on the real economy? Increase in money growth rate θ leads to an increase in the cost of money (inflation tax) Analysis in terms of wealth and intertemporal substitution effects MIU – Superneutrality – More on intuition Wealth effect: the inflation tax weighs on households’ budget This should impair HH consumption (negative wealth effect) Is it the case? Why? MIU – Superneutrality – More on intuition Intertemporal substitution effect: Intertemporal substitution of consumption: Intertemporal substitution of money: They are independent Classical « dichotomy » MIU – Taking stock So far: Important concepts: Inflation tax Fisher relationship: i=r+ п Effect of money on the economy Money has an effect on utility and on the demand for money However, money is both neutral and superneutral: absolutely no effect on real variables! Is that realistic? Which assumption should we relax? MIU – Superneutrality and the separability of utility function Superneutrality relies on separability between consumption and money: It means that having more money does not affect the marginal utility of consumption However, the utility of money (eg. facilitating transactions) is not independent of the amount of goods we would like to buy (non-separability): MIU – Non-separability – Dynamic system General case (non-separability): Euler equation Budget constraint Fisher relationship Growth of real money balances Demand for money MIU – Non-separability – Superneutrality? Importantly, the Euler equation is affected by money holdings: Money affects intertemporal substitution of cons. Example: money and consumption are Edgeworth complements: How does money affect consumption? What about wealth effects? MIU – Non-separability – Superneutrality? Real effect of money in the short run What happens in the long run? MIU – Introducing shocks Analysis of the impact of monetary shocks Uncertain environment: Monetary shocks: Productivity shocks: Expected intertemporal utility: MIU – Shocks – FOC Lagrangian: FOC: (1) (2) (3) (4) MIU – Shocks – Intertemporal arbitrage Intertemporal choices are affected by uncertainty Euler equation: MIU – Shocks – Intertemporal arbitrage Fisher relationship: Approximation: with Any substantial change? MIU – Shocks – Dynamic system Euler equation Budget constraint Fisher relationship Growth of real money balances Demand for money Productivity shocks Monetary shocks MIU – Shocks – Specifications Functional forms: The effect of money on real variables depends on Ucm Ucm has the same sign as b-Φ What are b and Φ? MIU – Shocks – Specifications 1/Φ: elasticity of intertemporal substitution: 0.5-3 b: elasticity of substitution between goods and money Equation of demand for money: 1/b is the interest elasticity of money: 0.3-0.5 b=2-3.3 Benchmark: Φ=2 , b=2.56 Since b-Φ>0, then (c and m are complements) MIU – Shocks – Baseline calibration MIU – Shocks We consider two cases: 1) No autocorrelation in the monetary shock: γ=0 2) Positive autocorrelation in the monetary shock: γ>0 % deviation from SS Responses to a shock in money growth 1 inflation 0.5 0 -2 nominal rate 0 2 4 Years after shock 6 Responses to a shock in money growth 1 0.5 0 investment -0.5 -1 -2 0 2 4 Years after shock 6 8 Responses to a shock in money growth 1 0.5 0 real rate -0.5 -1 -2 8 % deviation from SS % deviation from SS % deviation from SS MIU: Responses to a money growth shock, γ =0 (no autocorrelation) 0 2 4 Years after shock 6 8 Responses to a shock in money growth 1 0.5 0 output -0.5 -1 -2 0 2 4 Years after shock 6 8 MIU: Responses to a money growth shock, γ =0.5 (autocorrelation) Responses to a shock in money growth 1 0.5 0 -2 0 2 4 Years after shock 6 8 0.04 0.02 0 -0.02 -2 0 2 4 Years after shock Responses to a shock in money growth 5E-3 0E-3 investment -5E-3 consumption -10E-3 -2 0 2 4 6 Years after shock 8 % deviation from SS % deviation from SS 1.5 nominal rate % deviation from SS 0.06 inflation % deviation from SS % deviation from SS Responses to a shock in money growth 2 6 Responses to a shock in money growth 0 -0.5E-5 -1E-5 -1.5E-5 8 -2E-5 -5 real rate 0 5 Years after shock Responses to a shock in money growth 4E-4 output 3E-4 2E-4 1E-4 0 -2 0 2 4 Years after shock 6 8 10 MIU: Responses to a money growth shock Only expected inflation has an impact Is money neutral? Is it superneutral? What is the channel? MIU – Introducing labor supply Elastic labor supply l: Equilibrium in the labor market: How does money affect labor supply? MIU – Introducing labor supply Functional forms: MIU: Responses to a money growth shock, φ=0.5, with elastic labor supply (baseline) 1 0.5 0 -2 0 2 4 Years after shock 6 8 nominal rate 0.04 0.02 0 -0.02 -2 0 Responses to a shock in money growth 5E-3 0 investment -5E-3 consumption -10E-3 -2 0 2 4 6 Years after shock 8 2 4 Years after shock % deviation from SS % deviation from SS 1.5 % deviation from SS % deviation from SS inflation 0.06 % deviation from SS Responses to a shock in money growth Responses to a shock in money growth 2 6 8 Responses to a shock in money growth 0 -1E-5 -2E-5 -3E-5 -2 real rate 0 2 4 6 Years after shock Responses to a shock in money growth 5E-4 0 -5E-4 output employment -10E-4 -2 0 2 4 6 Years after shock 8 8 MIU: Responses to a money growth shock – conclusion Real effect on output only if anticipated rise in money growth: money is neutral but not superneutral The effect on output is negative Channel: Positive effect on the nominal interest rate (Fisher equation), which increases the cost of money (inflation tax) Intertemporal substitution effects Intertemporal substitution of consumption (effect on capital) Intertemporal substitution of leisure (effect on labor supply) Small quantitative effects Non-neutrality comes from a supply effect ≠ keynesian view of fluctuations Cash-in-advance constraint (CIA) Same model as MIU Only differences: Utility does not depend directly on mt : Cash-in-advance constraint (households must hold cash in order to make transactions): We also start by ignoring uncertainty and laborleisure decisions CIA – Demand for money Cash-in-advance constraint: This constraint is binding (why?): Budget constraint of the government: CIA – Specifications We add stochastic productivity and monetary shocks We add labor Same functional forms as MIU, except: Same calibration % deviation from SS Responses to a shock in money growth 1.5 inflation 1 0.5 nominal rate 0 -0.5 -2 0 2 4 Years after shock 6 8 Responses to a shock in money growth 1 investment 0.5 0 consumption -0.5 -2 0 2 4 Years after shock 6 Responses to a shock in money growth 0 -0.5E-3 -1E-3 real rate -1.5E-3 -2 % deviation from SS % deviation from SS % deviation from SS CIA: Responses to a money growth shock 8 0 2 4 6 Years after shock 8 Responses to a shock in money growth 0.02 0 -0.02 -0.04 -2 output employment 0 2 4 Years after shock 6 8 CIA: Responses to a money growth shock Similar effects But stronger responses Why? Empirical validity? None! See next lesson