Debt burdens and the interest rate response to fiscal stimulus, theory and cr...ADEMU_Project
This document presents research on the relationship between government spending and interest rates across countries. It finds that while theory predicts government spending should raise interest rates, the data show interest rates fall in response to spending in over half of OECD countries. The paper develops a theory that this is due to "debt-burdened households" whose consumption is constrained by minimum levels. Empirical analysis finds cross-country variation in interest rate responses is related to proxies for household debt burdens, supporting the theory. Microdata from the U.S. also shows low-wealth households consume more in response to income increases, as the theory predicts.
Optimal Austerity - by Juan Carlos Conesa, Timothy J. Kehoe, Kim J.RuhlADEMU_Project
The document summarizes a research paper that extends a model of self-fulfilling debt crises to allow governments to optimally choose tax rates. It finds that when governments can commit to tax rates before lenders choose to lend, they may optimally implement "austerity" by raising taxes and reducing debt, even outside of crisis periods, in order to deter panics and support more sustainable debt levels. However, models without government commitment find austerity is never optimal outside of crisis periods. The ability of governments to commit to fiscal policies can influence welfare outcomes depending on inherited debt levels.
When Fiscal consolidation meets private deleveragingADEMU_Project
This document summarizes a model that analyzes the interaction between public and private deleveraging in a small open economy. The model shows that larger and front-loaded fiscal consolidations entail larger output and welfare losses by postponing the end of the private deleveraging process. The model finds that deleveraging-friendly fiscal consolidations that are more gradual in nature minimize these losses.
This document provides an overview of key concepts in international macroeconomics and the open economy model. It introduces accounting identities that apply to an open economy, where spending does not necessarily equal output and saving does not necessarily equal investment due to trade flows. It then presents the small open economy model, where the domestic economy is too small to affect global interest rates. In this model, the trade balance and exchange rate are determined by the interaction of domestic saving and investment with the exogenous world interest rate. Fiscal and monetary policies can influence the trade balance and exchange rate through their impact on saving and investment.
Debt burdens and the interest rate response to fiscal stimulus, theory and cr...ADEMU_Project
This document presents research on the relationship between government spending and interest rates across countries. It finds that while theory predicts government spending should raise interest rates, the data show interest rates fall in response to spending in over half of OECD countries. The paper develops a theory that this is due to "debt-burdened households" whose consumption is constrained by minimum levels. Empirical analysis finds cross-country variation in interest rate responses is related to proxies for household debt burdens, supporting the theory. Microdata from the U.S. also shows low-wealth households consume more in response to income increases, as the theory predicts.
Optimal Austerity - by Juan Carlos Conesa, Timothy J. Kehoe, Kim J.RuhlADEMU_Project
The document summarizes a research paper that extends a model of self-fulfilling debt crises to allow governments to optimally choose tax rates. It finds that when governments can commit to tax rates before lenders choose to lend, they may optimally implement "austerity" by raising taxes and reducing debt, even outside of crisis periods, in order to deter panics and support more sustainable debt levels. However, models without government commitment find austerity is never optimal outside of crisis periods. The ability of governments to commit to fiscal policies can influence welfare outcomes depending on inherited debt levels.
When Fiscal consolidation meets private deleveragingADEMU_Project
This document summarizes a model that analyzes the interaction between public and private deleveraging in a small open economy. The model shows that larger and front-loaded fiscal consolidations entail larger output and welfare losses by postponing the end of the private deleveraging process. The model finds that deleveraging-friendly fiscal consolidations that are more gradual in nature minimize these losses.
This document provides an overview of key concepts in international macroeconomics and the open economy model. It introduces accounting identities that apply to an open economy, where spending does not necessarily equal output and saving does not necessarily equal investment due to trade flows. It then presents the small open economy model, where the domestic economy is too small to affect global interest rates. In this model, the trade balance and exchange rate are determined by the interaction of domestic saving and investment with the exogenous world interest rate. Fiscal and monetary policies can influence the trade balance and exchange rate through their impact on saving and investment.
This document provides an overview of classical theories of inflation and the quantity theory of money. It defines key concepts like money, inflation, the money supply, and velocity. The quantity theory of money posits that inflation is primarily caused by increases in the money supply that outpace economic growth. It predicts a direct relationship between money growth and inflation. The document uses graphs and international data to show this relationship generally holds in practice and discusses implications for interest rates.
Fiat value in the theory of value, by Edward C Prescott (Arizona State Univer...ADEMU_Project
Technology is rapidly advancing in the information processing area, which is changing the monetary/payment system. It's now technically feasible to have a currency–less monetary system; Professor Prescott explores such a system.
This chapter discusses two modern theories of business cycles:
1) Real Business Cycle theory assumes flexible prices and that fluctuations result from optimal responses to productivity shocks.
2) New Keynesian theory explains why prices and wages are sticky in the short-run, causing recessions as coordination failures when firms do not lower prices together. It incorporates insights from both schools to better understand economic fluctuations.
This chapter introduces the Solow growth model, which examines how capital accumulation and population growth impact economic growth and living standards over the long run. The key aspects covered include:
- The Solow model framework of production, consumption, investment, and capital accumulation over time.
- How economies converge to a steady state level of capital per worker and output per worker.
- How factors like the saving rate can impact the steady state level and long-run growth.
- The "Golden Rule" concept of finding the optimal saving rate and capital stock that maximizes long-run consumption per person.
This chapter introduces key concepts in macroeconomics including:
1. Facts about the business cycle such as GDP growth averaging 3-3.5% per year with large short-run fluctuations and unemployment rising during recessions.
2. The model of aggregate demand and aggregate supply which shows how the price level and output are determined in the short-run and long-run.
3. How shocks such as changes in money supply, oil prices, or velocity can temporarily push the economy away from full employment and affect inflation and output. Stabilization policies like monetary policy can be used to counteract shocks.
This document discusses the natural rate of unemployment and its causes. It begins by defining the natural rate of unemployment as the average rate around which the actual unemployment rate fluctuates over the business cycle. It then presents a model showing how the natural rate is determined by the rates of job separation and job finding. Frictional unemployment results from the time it takes to search for and transition between jobs, while structural unemployment stems from wage rigidities that prevent wages from adjusting downward to clear the labor market. The document explores factors like minimum wages, unions, efficiency wages, and sectoral shifts that contribute to real wage rigidity and the natural rate of unemployment.
Policymakers debate whether monetary and fiscal policy should be active or passive in response to economic fluctuations, and whether policy should be set by rule or at the discretion of officials. Arguments for active policy include reducing economic hardship during recessions, while critics argue policies have long and variable lags. Policy rules aim to increase credibility and reduce time inconsistency problems, like central banks targeting an inflation rate or following the Taylor rule. The optimal approach remains an open debate among economists.
This document summarizes key concepts from Chapter 12 of Mankiw's Macroeconomics textbook on open economy macroeconomics. It introduces the Mundell-Fleming model, which uses the IS-LM framework to analyze the effects of fiscal and monetary policy in a small open economy. It discusses the implications of floating versus fixed exchange rates and how this determines the effectiveness of different policies. It also examines the impacts of interest rate differentials and trade policies. The summary slides provide a concise overview of the model and the main policy conclusions.
This document provides an overview of the Solow growth model, which examines how economic growth and standards of living are determined in the long run. It introduces key concepts such as the production function, saving rate, depreciation rate, capital accumulation, and steady state. The steady state is the level of capital where investment just offsets depreciation and capital remains constant. The model predicts that countries with higher saving and investment rates will have higher levels of capital and income per worker in the long run. It also discusses finding the optimal saving rate and capital stock, known as the Golden Rule, which maximizes consumption.
This document summarizes key concepts from Chapter 8 of an economics textbook on economic growth. It discusses how to incorporate technological progress into the Solow growth model by including a variable for labor efficiency that grows exogenously over time. It then reviews empirical evidence on growth, including balanced growth, conditional convergence between countries, and the relationship between factor accumulation and production efficiency. Finally, it examines policy issues such as evaluating a country's saving rate and how to increase savings and allocate investment between different types of capital.
The document provides an overview of key concepts in macroeconomics, including:
1. The IS-LM model which determines income and interest rates in the short-run when prices are fixed. It combines the IS curve, representing goods market equilibrium, and the LM curve, representing money market equilibrium.
2. The IS curve shows combinations of interest rates and income where planned expenditure equals actual expenditure. It slopes downward because lower interest rates increase investment and expenditure.
3. The LM curve shows combinations of interest rates and income where money demand equals supply. It slopes upward because higher income increases money demand, requiring higher interest rates to balance the money market.
4. The intersection of the IS and LM curves
This document provides an overview of aggregate supply and the short-run tradeoff between inflation and unemployment known as the Phillips curve. It discusses three models of aggregate supply - the sticky-wage model, imperfect-information model, and sticky-price model - and how they each imply a positive relationship between output and the price level in the short run. The Phillips curve relationship is then derived from the aggregate supply relationship. The document also discusses concepts like adaptive expectations, inflation inertia, cost-push vs demand-pull inflation, and the sacrifice ratio.
This document provides an overview of key concepts relating to money supply and money demand from Chapter 18 of Mankiw's Macroeconomics textbook. It discusses how fractional-reserve banking allows banks to create money by lending out deposits. It also examines the three tools the Federal Reserve uses to control the money supply and explains why the Fed cannot precisely control the money supply. Finally, it summarizes theories of money demand, including a portfolio theory and the Baumol-Tobin transactions model.
This document provides an overview of several prominent theories of consumption, including:
1) John Maynard Keynes' theory that current consumption depends on current income. Later theories found problems with Keynes' prediction that consumption would grow more slowly than income over time.
2) Irving Fisher's intertemporal choice theory, which assumes consumers maximize lifetime satisfaction subject to an intertemporal budget constraint. This theory formed the basis for later work on consumption.
3) Franco Modigliani's life-cycle hypothesis, which proposes consumption depends on lifetime resources and income varies systematically over a consumer's life cycle, allowing saving to achieve smooth consumption. This theory helped solve the "consumption puzzle."
4)
This document provides an overview of Chapter 17 from an economics textbook on investment. It discusses three types of investment - business fixed investment, residential investment, and inventory investment. It then covers theories to explain business fixed investment, including the neoclassical model showing how investment depends on marginal product of capital and interest rates. The document discusses factors that affect the rental price of capital and rental firms' investment decisions. It also addresses how taxes impact investment and Tobin's q theory of investment.
Macroeconomics is the study of the economy as a whole, including issues like growth, inflation, and unemployment. Economists use models to help explain and address these issues. Models make simplifying assumptions, like whether prices are flexible or sticky in the short-run. The chapter introduces concepts like endogenous and exogenous variables. It provides an example model of supply and demand for cars and how it can be used to analyze changes. The chapter outlines the topics that will be covered in the macroeconomics textbook, including classical theory, growth theory, and business cycle theory.
1) The chapter uses the IS-LM model to analyze the effects of fiscal and monetary policy shocks on aggregate output and the interest rate in the short run.
2) Fiscal policy like increases in government spending or tax cuts shift the IS curve right, raising output. Monetary policy like increases in the money supply shift the LM curve down, lowering interest rates and raising output.
3) Shocks like increases in wealth from a stock market boom shift the IS curve right, raising output, while shocks that increase money demand like credit card fraud shift the LM curve left, lowering output.
4) In the long run, price adjustments return output to potential as the price level falls to accommodate any short
The document summarizes key concepts from a chapter in a macroeconomics textbook. It discusses the gross domestic product (GDP) and how it measures the market value of all final goods and services produced in an economy over a period of time. It also describes the circular flow between households, firms, and the financial sector and how they exchange money, products, and resources. The chapter covers macroeconomic indicators like leading, coinciding, and lagging indicators used to predict and analyze economic fluctuations. It analyzes aggregate demand and supply curves and how they determine equilibrium output and price levels in the economy. The summary provides an overview of the US economic history, including the Great Depression, postwar growth, and stagflation in the
This document provides an overview of a macroeconomic model that examines national income. It discusses how total output is determined by factors of production like capital and labor. It then explains how factor prices, like wages and rental rates, are set through supply and demand in factor markets. The model shows how total national income is distributed to factor payments. It also outlines the components of aggregate demand, like consumption, investment, and government spending, and how their equilibrium in the goods market determines total output.
This document provides an overview of key macroeconomic statistics including Gross Domestic Product (GDP), the Consumer Price Index (CPI), and the unemployment rate. It discusses how GDP can be measured through expenditures, income, and value added. The components of GDP expenditures are defined as consumption, investment, government spending, and net exports. Real GDP is introduced to control for inflation. The GDP deflator and inflation rates are also explained.
Fiscal rules and the sovereign default premiumADEMU_Project
This document summarizes a research paper on using fiscal rules and sovereign bond spreads to anchor fiscal policy expectations. It finds that a fiscal rule targeting a ceiling on sovereign bond spreads, or "spread brake", outperforms a rule targeting a ceiling on debt levels, or "debt brake". A spread brake provides a more robust policy anchor that is better suited for heterogeneous economies. It allows borrowing levels to vary appropriately with debt intolerance. A common spread brake threshold maximizes welfare gains compared to a common debt ceiling. Future work is needed to determine optimal spread thresholds and implementation of spread brakes.
A framework to analyse the sovereign credit risk exposure of financial instit...Jide Lewis PhD, CFA, FRM
This paper develops an integrative dynamic framework to evaluate the exposure of banks to sovereign credit risk using stress tests. The framework is used to replicate the historical twin-crisis dynamics which ensues when stress tests are implemented on selected macro-financial variables, based on a perfect foresighting exercise for the case of Jamaica.
This document provides an overview of classical theories of inflation and the quantity theory of money. It defines key concepts like money, inflation, the money supply, and velocity. The quantity theory of money posits that inflation is primarily caused by increases in the money supply that outpace economic growth. It predicts a direct relationship between money growth and inflation. The document uses graphs and international data to show this relationship generally holds in practice and discusses implications for interest rates.
Fiat value in the theory of value, by Edward C Prescott (Arizona State Univer...ADEMU_Project
Technology is rapidly advancing in the information processing area, which is changing the monetary/payment system. It's now technically feasible to have a currency–less monetary system; Professor Prescott explores such a system.
This chapter discusses two modern theories of business cycles:
1) Real Business Cycle theory assumes flexible prices and that fluctuations result from optimal responses to productivity shocks.
2) New Keynesian theory explains why prices and wages are sticky in the short-run, causing recessions as coordination failures when firms do not lower prices together. It incorporates insights from both schools to better understand economic fluctuations.
This chapter introduces the Solow growth model, which examines how capital accumulation and population growth impact economic growth and living standards over the long run. The key aspects covered include:
- The Solow model framework of production, consumption, investment, and capital accumulation over time.
- How economies converge to a steady state level of capital per worker and output per worker.
- How factors like the saving rate can impact the steady state level and long-run growth.
- The "Golden Rule" concept of finding the optimal saving rate and capital stock that maximizes long-run consumption per person.
This chapter introduces key concepts in macroeconomics including:
1. Facts about the business cycle such as GDP growth averaging 3-3.5% per year with large short-run fluctuations and unemployment rising during recessions.
2. The model of aggregate demand and aggregate supply which shows how the price level and output are determined in the short-run and long-run.
3. How shocks such as changes in money supply, oil prices, or velocity can temporarily push the economy away from full employment and affect inflation and output. Stabilization policies like monetary policy can be used to counteract shocks.
This document discusses the natural rate of unemployment and its causes. It begins by defining the natural rate of unemployment as the average rate around which the actual unemployment rate fluctuates over the business cycle. It then presents a model showing how the natural rate is determined by the rates of job separation and job finding. Frictional unemployment results from the time it takes to search for and transition between jobs, while structural unemployment stems from wage rigidities that prevent wages from adjusting downward to clear the labor market. The document explores factors like minimum wages, unions, efficiency wages, and sectoral shifts that contribute to real wage rigidity and the natural rate of unemployment.
Policymakers debate whether monetary and fiscal policy should be active or passive in response to economic fluctuations, and whether policy should be set by rule or at the discretion of officials. Arguments for active policy include reducing economic hardship during recessions, while critics argue policies have long and variable lags. Policy rules aim to increase credibility and reduce time inconsistency problems, like central banks targeting an inflation rate or following the Taylor rule. The optimal approach remains an open debate among economists.
This document summarizes key concepts from Chapter 12 of Mankiw's Macroeconomics textbook on open economy macroeconomics. It introduces the Mundell-Fleming model, which uses the IS-LM framework to analyze the effects of fiscal and monetary policy in a small open economy. It discusses the implications of floating versus fixed exchange rates and how this determines the effectiveness of different policies. It also examines the impacts of interest rate differentials and trade policies. The summary slides provide a concise overview of the model and the main policy conclusions.
This document provides an overview of the Solow growth model, which examines how economic growth and standards of living are determined in the long run. It introduces key concepts such as the production function, saving rate, depreciation rate, capital accumulation, and steady state. The steady state is the level of capital where investment just offsets depreciation and capital remains constant. The model predicts that countries with higher saving and investment rates will have higher levels of capital and income per worker in the long run. It also discusses finding the optimal saving rate and capital stock, known as the Golden Rule, which maximizes consumption.
This document summarizes key concepts from Chapter 8 of an economics textbook on economic growth. It discusses how to incorporate technological progress into the Solow growth model by including a variable for labor efficiency that grows exogenously over time. It then reviews empirical evidence on growth, including balanced growth, conditional convergence between countries, and the relationship between factor accumulation and production efficiency. Finally, it examines policy issues such as evaluating a country's saving rate and how to increase savings and allocate investment between different types of capital.
The document provides an overview of key concepts in macroeconomics, including:
1. The IS-LM model which determines income and interest rates in the short-run when prices are fixed. It combines the IS curve, representing goods market equilibrium, and the LM curve, representing money market equilibrium.
2. The IS curve shows combinations of interest rates and income where planned expenditure equals actual expenditure. It slopes downward because lower interest rates increase investment and expenditure.
3. The LM curve shows combinations of interest rates and income where money demand equals supply. It slopes upward because higher income increases money demand, requiring higher interest rates to balance the money market.
4. The intersection of the IS and LM curves
This document provides an overview of aggregate supply and the short-run tradeoff between inflation and unemployment known as the Phillips curve. It discusses three models of aggregate supply - the sticky-wage model, imperfect-information model, and sticky-price model - and how they each imply a positive relationship between output and the price level in the short run. The Phillips curve relationship is then derived from the aggregate supply relationship. The document also discusses concepts like adaptive expectations, inflation inertia, cost-push vs demand-pull inflation, and the sacrifice ratio.
This document provides an overview of key concepts relating to money supply and money demand from Chapter 18 of Mankiw's Macroeconomics textbook. It discusses how fractional-reserve banking allows banks to create money by lending out deposits. It also examines the three tools the Federal Reserve uses to control the money supply and explains why the Fed cannot precisely control the money supply. Finally, it summarizes theories of money demand, including a portfolio theory and the Baumol-Tobin transactions model.
This document provides an overview of several prominent theories of consumption, including:
1) John Maynard Keynes' theory that current consumption depends on current income. Later theories found problems with Keynes' prediction that consumption would grow more slowly than income over time.
2) Irving Fisher's intertemporal choice theory, which assumes consumers maximize lifetime satisfaction subject to an intertemporal budget constraint. This theory formed the basis for later work on consumption.
3) Franco Modigliani's life-cycle hypothesis, which proposes consumption depends on lifetime resources and income varies systematically over a consumer's life cycle, allowing saving to achieve smooth consumption. This theory helped solve the "consumption puzzle."
4)
This document provides an overview of Chapter 17 from an economics textbook on investment. It discusses three types of investment - business fixed investment, residential investment, and inventory investment. It then covers theories to explain business fixed investment, including the neoclassical model showing how investment depends on marginal product of capital and interest rates. The document discusses factors that affect the rental price of capital and rental firms' investment decisions. It also addresses how taxes impact investment and Tobin's q theory of investment.
Macroeconomics is the study of the economy as a whole, including issues like growth, inflation, and unemployment. Economists use models to help explain and address these issues. Models make simplifying assumptions, like whether prices are flexible or sticky in the short-run. The chapter introduces concepts like endogenous and exogenous variables. It provides an example model of supply and demand for cars and how it can be used to analyze changes. The chapter outlines the topics that will be covered in the macroeconomics textbook, including classical theory, growth theory, and business cycle theory.
1) The chapter uses the IS-LM model to analyze the effects of fiscal and monetary policy shocks on aggregate output and the interest rate in the short run.
2) Fiscal policy like increases in government spending or tax cuts shift the IS curve right, raising output. Monetary policy like increases in the money supply shift the LM curve down, lowering interest rates and raising output.
3) Shocks like increases in wealth from a stock market boom shift the IS curve right, raising output, while shocks that increase money demand like credit card fraud shift the LM curve left, lowering output.
4) In the long run, price adjustments return output to potential as the price level falls to accommodate any short
The document summarizes key concepts from a chapter in a macroeconomics textbook. It discusses the gross domestic product (GDP) and how it measures the market value of all final goods and services produced in an economy over a period of time. It also describes the circular flow between households, firms, and the financial sector and how they exchange money, products, and resources. The chapter covers macroeconomic indicators like leading, coinciding, and lagging indicators used to predict and analyze economic fluctuations. It analyzes aggregate demand and supply curves and how they determine equilibrium output and price levels in the economy. The summary provides an overview of the US economic history, including the Great Depression, postwar growth, and stagflation in the
This document provides an overview of a macroeconomic model that examines national income. It discusses how total output is determined by factors of production like capital and labor. It then explains how factor prices, like wages and rental rates, are set through supply and demand in factor markets. The model shows how total national income is distributed to factor payments. It also outlines the components of aggregate demand, like consumption, investment, and government spending, and how their equilibrium in the goods market determines total output.
This document provides an overview of key macroeconomic statistics including Gross Domestic Product (GDP), the Consumer Price Index (CPI), and the unemployment rate. It discusses how GDP can be measured through expenditures, income, and value added. The components of GDP expenditures are defined as consumption, investment, government spending, and net exports. Real GDP is introduced to control for inflation. The GDP deflator and inflation rates are also explained.
Fiscal rules and the sovereign default premiumADEMU_Project
This document summarizes a research paper on using fiscal rules and sovereign bond spreads to anchor fiscal policy expectations. It finds that a fiscal rule targeting a ceiling on sovereign bond spreads, or "spread brake", outperforms a rule targeting a ceiling on debt levels, or "debt brake". A spread brake provides a more robust policy anchor that is better suited for heterogeneous economies. It allows borrowing levels to vary appropriately with debt intolerance. A common spread brake threshold maximizes welfare gains compared to a common debt ceiling. Future work is needed to determine optimal spread thresholds and implementation of spread brakes.
A framework to analyse the sovereign credit risk exposure of financial instit...Jide Lewis PhD, CFA, FRM
This paper develops an integrative dynamic framework to evaluate the exposure of banks to sovereign credit risk using stress tests. The framework is used to replicate the historical twin-crisis dynamics which ensues when stress tests are implemented on selected macro-financial variables, based on a perfect foresighting exercise for the case of Jamaica.
Agents gradually learn the structure of the economy.
Learning model delivers a sizeable recession in 2008-2010,
...whereas RE model predicts a counterfactual expansion.
In a medium scale model learning still matters.
Advanced macroeconomics, 4th edition. Romer.
Chapter12.
12.1. The stability of fiscal policy. (Blinder and Solow, 1973.) By definition, the budget deficit equals the rate of change of the amount of debt outstanding: δ(t) ≡ D ̇(t). Define d(t) to be the ratio of debt to output: d(t) = D(t)/Y(t). Assume that Y(t) grows at a constant rate g > 0.
(a) Suppose that the deficit-to-output ratio is constant: δ(t)/Y(t) = a, where a > 0.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). Is this system stable?
(b) Suppose that the ratio of the primary deficit to output is constant and equal to a > 0. Thus the total deficit at t, δ(t), is given by δ(t) = aY(t) + r(t)D(t), where r(t) is the interest rate at t. Assume that r is an increasing function of the debt-to-output ratio: r(t) = r(d(t)), where r′(•) > 0, r′′(•) > 0, limd→−∞ r(d) < g, limd→∞ r(d) > g.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). In the case where a is sufficiently small that d ̇ is negative for some values of d, what are the stability properties of the system? What about the case where a is sufficiently large that d ̇ is positive for all values of d ?
12.2. Precautionary saving, non-lump-sum taxation, and Ricardian equivalence.
(Leland, 1968, and Barsky, Mankiw, and Zeldes, 1986.) Consider an individual who lives for two periods. The individual has no initial wealth and earns labor incomes of amounts Y1 and Y2 in the two periods. Y1 is known, but Y2 is random; assume for simplicity that E[Y2] = Y1. The government taxes income at rate τ1 in period 1 and τ2 in period 2. The individual can borrow and lend at a fixed interest rate, which for simplicity is assumed to be zero. Thus second-period consumption is C2 = (1 − τ1)Y1 − C1 + (1 − τ2)Y2. The individualchoosesC1 tomaximizeexpectedlifetimeutility,U(C1)+E[U(C2)].
(a) Find the first-order condition for C1.
(b) Show that E[C2] = C1 if Y2 is not random or if utility is quadratic.
(c) Show that if U ′′′(•) > 0 and Y2 is random, E[C2] > C1.
(d) Suppose that the government marginally lowers τ1 and raises τ2 by the same amount, so that its expected total revenue, τ1Y1 + τ2E[Y2], is un- changed. Implicitly differentiate the first-order condition in part (a) to find an expression for how C1 responds to this change.
(e) Show that C1 is unaffected by this change if Y2 is not random or if utility is quadratic.
(f) Show that C1 increases in response to this change if U ′′′(•) > 0 and Y2 is random.
12.3
Consider the Barro tax-smoothing model. Suppose that output, Y, and the real interest rate, r, are constant, and that the level of government debt out- standing at time 0 is zero. Suppose that there will be a temporary war from time 0 to time τ. Thus G(t) equals GH for 0 ≤ t ≤ τ, and equals GL there- after,whereGH >GL.Whatarethepathsoftaxes,T(t),andgovernmentdebt outstanding, D(t)?
12.4
Consider the Barro tax-smoothing model. Supp.
"Correlated Volatility Shocks" by Dr. Xiao Qiao, Researcher at SummerHaven In...Quantopian
Commonality in idiosyncratic volatility cannot be completely explained by time-varying volatility. After removing the effects of time-varying volatility, idiosyncratic volatility innovations are still positively correlated. This result suggests correlated volatility shocks contribute to the comovement in idiosyncratic volatility.
Motivated by this fact, we propose the Dynamic Factor Correlation (DFC) model, which fits the data well and captures the cross-sectional correlations in idiosyncratic volatility innovations. We decompose the common factor in idiosyncratic volatility (CIV) of Herskovic et al. (2016) into the volatility innovation factor (VIN) and time-varying volatility factor (TVV). Whereas VIN is associated with strong variation in average returns, TVV is only weakly priced in the cross section
A strategy that takes a long position in the portfolio with the lowest VIN and TVV betas, and a short position in the portfolio with the highest VIN and TVV betas earns average returns of 8.0% per year.
The dangers of policy experiments Initial beliefs under adaptive learningGRAPE
The paper studies the implication of initial beliefs and associated confidence on the system’s
dynamics under adaptive learning. We first illustrate how prior beliefs determine learning dynamics
and the evolution of endogenous variables in a small DSGE model with credit-constrained agents,
in which rational expectations are replaced by constant-gain adaptive learning. We then examine
how discretionary experimenting with new macroeconomic policies is affected by expectations that
agents have in relation to these policies. More specifically, we show that a newly introduced macroprudential policy that aims at making leverage counter-cyclical can lead to substantial increase in
fluctuations under learning, when the economy is hit by financial shocks, if beliefs reflect imperfect
information about the policy experiment. This is in the stark contrast to the effects of such policy
under rational expectations.
Hierarchical Applied General Equilibrium (HAGE) ModelsVictor Zhorin
New techniques for uncertainty quantification (Chernoff entropy-based) in highly non-linear stochastic models; Tensor computing
Purpose: address the changing nature of service industries as providers of multi-dimensional contracts rather than simple price-based bundles of goods; models based on large data sets, consisting of country-wide surveys of
household data from Thailand, Mexico, Brazil, Spain
in combination with variety of geophysical and socioeconomic data. Innovative methods to represent complex data (Analytics/Visualization)
Purpose: evaluate household microfinance initiatives and credit expansion under different policies.
Hanging off a cliff: fiscal consolidations and default riskADEMU_Project
Fiscal consolidations through tax increases may have a limited effect on reducing default risk. While tax increases improve the budget balance, they also induce economic distortions by lowering returns in the formal sector and increasing tax evasion. This impacts the government's future ability to raise revenues, which investors incorporate into debt prices. The model shows fiscal consolidations may only marginally reduce default risk when revenue raising ability is imperfect.
Affine cascade models for term structure dynamics of sovereign yield curvesLAURAMICHAELA
Rafael Serrano profesor de la Universidad del Rosario
Resumen:
In the first part of the talk, I will present an introduction to stochastic affine short rate models for term structure of yield curves In the second part, I will focus on a recursive affine cascade with persistent factors for which the number of parameters, under specifications, is invariant to the size of the state space and converges to a stochastic limit as the number of factors goes to infinity. The cascade construction thereby overcomes dimensionality difficulties associated with general affine models. We contrast two specfifications of the model using linear Kalman filter for a panel of Colombian sovereign yields.
1) This document examines optimal taxation and policy selection within a rational expectations framework using dynamic models with capital.
2) It finds that standard control theory techniques cannot be used to solve for the optimal taxation policy over time, as the optimal policy would be time inconsistent - what was optimal in the past would not be optimal now.
3) It develops a novel recursive method to overcome this difficulty by determining both the constraint set and value function recursively, even though there is doubt the optimal policy could actually be implemented due to its time inconsistency. The optimal policy still provides a benchmark to evaluate alternative time consistent policies.
The document discusses concepts related to consumption, saving, and investment. It summarizes that developing countries generally have higher gross domestic saving and investment rates than industrialized countries, with the highest rates in Asia. Saving and investment rates follow similar patterns across regions. The document then provides an overview of several economic theories for consumption and saving behaviors, including the Keynesian approach, permanent income hypothesis, and life-cycle model of consumption. It also discusses various determinants that can influence saving rates at both individual and aggregate levels.
The document summarizes key concepts around consumption, saving, and investment from economic theory. It discusses the Keynesian, permanent income hypothesis, and life-cycle models of consumption and saving behavior. It notes that developing countries generally have higher saving and investment rates than industrialized countries, with the highest rates in Asia. Gross domestic saving and investment rates are influenced by factors like income levels, demographic trends, financial development, and government policies.
Homework 51)a) the IS curve ln Yt= ln Y(t+1) – (1Ɵ)rtso th.docxadampcarr67227
Homework 5
1)
a) the IS curve: ln Yt= ln Y(t+1) – (1/Ɵ)rt
so the slope is: drt/dyt (is) = -Ɵ/Yt. That means that an increase in Ɵ will result in a steeper curve.
LM curve: Mt/Pt = Yt^(Ɵ/v) (1+rt / rt)^(1/v)
Ln(Mt/Pt) = (Ɵ/v) ln Yt +(1/v)ln(1+rt) – (1/v)ln rt.
0 = (Ɵ/v)(1/Yt)dYt + (1/v)(1/(1+rt)) drt – (1/v)(1/rt)drt.
The slope is: drt/dyt (LM) = (Ɵrt(1+rt))/Yt. That means that an increase in Ɵ will result in a steeper curve.
b) the curve IS is not affected by the value of V. while curve LM shifts upwards, since a decrease in v will result in an increase for the demand for real money.
c) IS is not affected byΓ(.)
optimal money holdings: BΓ’(Mt/Pt) = (it/(1+it)) U’(Ct)
B(Mt/Pt)^(-v) = (it/1+it) Yt^-Ɵ
Mt/Pt= B^(1/v) Yt^(Ɵ/v) (1+rt/rt)^(1/v)
So this means that the LM curve will shift downwards.
2)
a) AC= (PC/)+(αYP/2)i
AC/ = -(PC/^2) + (αYP/2)I = 0
C/^2 = αYi/2
So *=(2C/αYi)^(1/2)
b) average real money holdings:M/P= αY/2
M/P = (αY/2) (2C/αYi)^(1/2)
M/P= (αCY/2i)^(1/2)
Ln(m/p) = (1/2)(lnα+lnY+lnC-ln2-lni)
(1/(M/P))((M/P)/i) = -(1/2)(1/i)
Elasticity of real money with respect to i: ((M/P)/)(i/(M/P)) = -1/2
The elasticity with respect to Y : ((M/P)/Y)(Y/(M/P)) = ½
Average real money holdings increase in Y, and decrease in i.
4)
a)when p is at a level that generates maximum output, LS meets LD.
b) when p is above the level that generates maximum output, will cause unemployment.
7)
a)
b)i)
ii)
iii)
13)
a) the asset has an expected rate of return r. capital gain/loss plus dividends per unit time = rvp. There is no dividends per unit time while searching for the palm tree, and there is b probability per unit time of capital gain of (vc-vp)-c. the difference in the price of the asset is(vc-vp) and –c is what the asset pays, so at the end we have rvp=b(vc-vp-c)
b) there is probability aL that a person will find another person with a coconut and trade with that person and gain u̅. the difference in the price of the asset is (vp-vc). So we end up with
rvp=al(vp-vc+u̅).
c) vp=(rvc/aL)+vc-u̅.
r((rvc/aL )+vc-u̅)= b(vc-(rvc/aL)-vc+u̅-c)
vc(r(r+aL+b))/aL = u̅(r+b)-bc
the value of being in state C: vc= (aL(u̅(r+b)-bc)) / r(r+aL+b)
the value of being in state p: vp= ((u̅(r+b)-bc)/(r+aL+b)) + (aL(u̅(r+b)-bc)/r(r+aL+b)) - u̅
so finally
vc-vp = (bc+u̅aL)/(r+aL+b).
e) vc-vp ≥c
vc-vp = (bc+u̅a(b/a))/(r+a(b/a)+b) = (bc+bu̅)/(r+2b)
(bc+bu̅)/(r+2b) ≥ c
That means that
Bc+bu̅≥c and c(r+2b-b) ≤ bu̅
So finally we have
c≤ bu̅ / (r+b).
f) it is a steady-state equilibrium for no one who finds a tree to climb it for any value of c>0.
Yes there are values of c which there is more than one steady-state equilibrium for 0<c< bu̅/(r+b)
Yes, L = b/a has a higher welfare than L=0. When L=0 people don’t gain any utility since they don’t climb a tree and don’t have a chance to trade with other people and gain a coconut.
0 1 2 3 4 5 -3 -2.2000000000000002 -1.8 -1.8 -2.2000000000000002 -3
0 1 2 3 4 5 7 6.5 5.5 3.5 1
0 1 2 3 4 -2 -2.5 -3.5 -5.5 -8
LD.
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1. Fiscal Rules and the Sovereign Default Premium
Juan Carlos Hatchondo Leonardo Martinez Francisco Roch
The views expressed herein are those of the authors and should not be attributed to
the IMF, its Executive Board, or its management.
1 / 83
3. FISCAL ANCHORS
Fiscal policy frameworks do not have an anchor to manage
expectations about future policies (unlike frameworks used for
monetary analysis; Leeper 2010).
This paper:
Having a fiscal anchor could be important.
The sovereign spread (and not the debt level) should be the anchor.
...1 Better common anchor (SGP).
...2 More robust anchor/policy advice (Spain?).
...3 Better ownership/more credible/easier to commit too.
3 / 83
4. FISCAL RULES COULD PROVIDE FISCAL ANCHORS
A large and increasing number of countries have fiscal rules with
numerical targets.
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
0
10
20
30
40
50
60
70
80
90
Numberofcountrieswithfiscalrules
4 / 83
5. MOST FISCAL RULES TARGET DEBT LEVELS
1985
1987
1989
1991
1993
1995
1999
2001
2003
2005
2007
2009
2010
2012
2014
Numberofcountrieswithfiscalrules
0
20
40
60
80
Debt rule
No debt rule and budget balance rule
No debt rule and no budget balance rule
5 / 83
6. WHAT IS THE OPTIMAL DEBT LEVEL?
Blanchard (IMFdirect 2011): “Are old rules of thumb, such as
trying to keep the debt-to-GDP ratio below 60 percent in
advanced countries, still reliable?”
The Fiscal Monitor (2013): “The optimal-debt concept has
remained at a fairly abstract level... adjustment needs scenario
has used benchmark debt ratios of 60 percent of GDP... But the
appropriate debt target need not be the same for all countries...”
Eberhardt and Presbitero (JIE 2015): impossibility of finding
common debt thresholds across countries for the relationship
between debt levels and long-run growth.
6 / 83
8. A COMMON, ROBUST, AND CREDIBLE ANCHOR
...1 Political constraints lead to common fiscal anchors for several
governments (e.g. SGP) that may face different levels of debt
intolerance.
...2 For one government, the level of debt intolerance changes over time
and is difficult to identify.
What is the debt level consistent with acceptable fiscal risk in
Greece? Brazil? Spain?
We would like policy advice to be robust to this uncertainty.
...3 The anchor should be credible: governments would not gain from
deviating from the fiscal rule.
8 / 83
9. SPREAD BRAKE VS. DEBT BRAKE
A spread (debt) brake imposes a limit on the fiscal balance when
the sovereign spread (debt) is above a threshold.
9 / 83
11. ENVIRONMENT
Government’s income in period t = yt. With t ∈ {1, 2, 3}.
y1 = y2 = 0, y3 > 0 and stochastic.
The government maximizes utility of a representative consumer.
A bond issued at t = 1 promises the payment sequence {δ, 1 − δ}.
A bond issued at t = 2 promises a payment of 1 at t = 3.
Foreign risk-neutral lenders’ discount factor = 1.
Lenders are atomistic and bond market is competitive.
Cost of defaulting: Lose fraction ϕ of y3 (no default in first two
periods)
11 / 83
12. OPTIMAL POLICIES
Ramsey policies: sequence of borrowing that maximizes the
government’s expected utility in period 1, given the default rule
of the period 3 government.
Markov policies: sequence of borrowing chosen sequentially by
the governments in periods 1 and 2.
12 / 83
13. (WITH LONG-TERM DEBT) WE NEED A FISCAL RULE
.
Proposition
..
......
Suppose δ < 1; i.e., the government issues long-term debt in period 1.
Then, only with a fiscal rule limiting the government’s choices in
period 2, Markov policies coincide with Ramsey policies.
13 / 83
15. IDIOSYNCRATIC DEBT BRAKE = IDIOSYNCRATIC
SPREAD BRAKE
Idiosyncratic debt brake imposes a ceiling on the debt level,
(1 − δ)b1 + b2 ≤ ¯b.
Idiosyncratic spread brake imposes a ceiling on the spread paid
by the government and thus a floor on the sovereign bond price,
q2(b1, b2) ≥ q.
.
Proposition
..
......
If the government’s choices in period 2 are limited with either a debt
brake with threshold ¯b∗ = (1 − δ)bR
1 + bR
2 or a spread brake with
threshold q∗ = q2(bR
1 , bR
2 ), Markov policies coincide with Ramsey
policies. 15 / 83
16. OPTIMAL “COMMON” FISCAL RULES
Consider a set of heterogenous economies indexed by the value of
the parameter θ ∈ {ϕ, σy, β}.
v(x; θ) = expected utility in period 1 of an economy with a fiscal
rule with threshold x.
h(θ) = density function for θ in the set.
The optimal common fiscal rule threshold X∗ maximizes
max
x
∫
v(x; θ)h(θ)dθ.
16 / 83
17. WHY A “COMMON AND ROBUST” FISCAL RULE?
X∗ would be chosen by a planner that maximizes the expected
utility in period 1 of
...1 a set of different economies while giving weight h(θ) to economies
with parameter value θ.
...2 a single economy when the planner is uncertain about the value of
the parameter θ and assigns the likelihood h(θ) to θ.
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19. COMMON SPREAD BRAKE ≻ COMMON DEBT BRAKE
.
Proposition
..
......
Suppose δ = 0, u(c) = c, and Assumption 1 holds. Then, for any
economy with cost of defaulting ϕ, the optimal debt brake threshold is
¯b∗ = ηϕ and the optimal spread brake threshold is q∗ = 1 − F(η), with
η > 0. Therefore, for any set of economies that differ in the level of
debt intolerance (i.e., for economies with different values of ϕ), the
optimal common spread-brake threshold is Q∗
= 1 − F(η), and
generates larger welfare gains than any common debt-brake threshold
¯B.
19 / 83
20. NUMERICAL EXAMPLE
Assume:
u (c) = −c−1
β = 1,
log(y3) ∼ N
(
0, σy
)
,
δ = 0.
If σy = 0.1, debt levels between 25 and 169 percent of average
period 3 income, spreads between 1 and 12 percent.
20 / 83
21. WELFARE GAINS FROM IDIOSYNCRATIC RULE
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Same welfare gains with either optimal idiosyncratic debt brake or
optimal idiosyncratic spread brake
21 / 83
22. COMMON DEBT BRAKE DOESN’T WORK WELL
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
The optimal common debt brake does not impose an excessive
constraint in low-debt-intolerance economies and thus is not binding
in most economies.
22 / 83
23. COMMON SPREAD BRAKE IS BETTER
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
Common spread brake
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
Common spread brake
A relatively low spread threshold still does not impose an excessive
constraint in low-debt-intolerance economies but imposes a welfare
improving constraint in high-debt-intolerance economies.
23 / 83
27. EQUILIBRIUM CONCEPT
Markov Perfect Equilibrium.
Each period the government decides taking as given bond prices
and future defaulting, spending, taxing, and borrowing strategies.
Current optimal choices are consistent with future government
strategies.
Bond holders make zero expected profits.
Limit of finite-horizon economy.
27 / 83
30. IF THE GOVERNMENT PAYS ITS DEBT OBLIGATIONS
Issues long-term debt.
Bonds are perpetuities with geometrically decreasing coupon
obligations
Important for the quantitative performance of the model
(Hatchondo and Martinez 2009; Chatterjee and Eyigungor 2012).
Chooses provision of public good: g
Chooses labor tax: τ
30 / 83
31. DEFAULTS
Two costs of defaulting:
...1 Exclusion from credit market for a stochastic number of periods.
...2 Fall in TFP in every period in which the government is in default.
With constant probability, the government can exit the default by
exchanging α new bonds per bond in default (debt restructuring).
1 − α = haircut
Chooses g and labor tax τ while in default.
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33. SIMULATIONS MATCH TARGETS
Data No-rule benchmark
Mean debt-to-income ratio (in %) 61.8 61.5
Debt duration (years) 6.0 6.0
Annual spread (in %) 2.0 2.0
Mean g/c (in %) 36.5 36.5
σ(g)/σ(y) 0.9 0.9
σ(c)/σ(y) 1.1 1.1
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38. IDIOSYNCRATIC DEBT BRAKE ≃ IDIOSYNCRATIC
SPREAD BRAKE
Without rule Debt brake Spread brake
(52.5%) (0.45%)
Mean debt-to-income ratio 61.5 54.9 59.4
Annual spread (in %) 2.0 0.5 1.0
Mean g/c (in %) 36.5 37.1 36.9
σ(g)/σ(y) 0.9 0.9 1.0
σ(c)/σ(y) 1.1 1.1 1.1
Defaults per 100 years 2.9 0.8 1.1
Welfare gain (in %) 0.5 0.4
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39. BORROWING WITHOUT A FISCAL ANCHOR
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
0.5
1
1.5
2
2.5
3
Annualspread(in%)
Without rules
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%)
Without rules
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40. BORROWING WITH A FISCAL ANCHOR
The fiscal anchor allow for less debt (lower face value) but may allow
for more borrowing (because of the higher interest rate)
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
0.5
1
1.5
2
2.5
3
Annualspread(in%)
Without rules
With optimal spread brake
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%) Without rules
With optimal spread brake
40 / 83
41. NEGATIVE SHOCKS WITHOUT A FISCAL ANCHOR
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
41 / 83
42. NEGATIVE SHOCK WITH A FISCAL ANCHOR
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
Spread with optimal spread brake
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43. CONSUMPTION IS NOT MORE VOLATILE WITH THE
SPREAD BRAKE
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
Spread with optimal spread brake
0 10 20 30 40 50 60 70 80
Quarter
20
30
40
50
60
70
80
90
%
-5
0
5
10
15
%
Log private consumption without rule
Log private consumption with optimal spread brake
Log public consumption without rule
Log public consumption with optimal spread brake
Debt without rule
Debt with optimal spread brake
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44. COMMON RULES
Longer exclusion ⇒ ↑ cost of defaulting ⇒ more debt.
Higher recovery ⇒ ↓ benefit of defaulting ⇒ more debt.
More impatient borrower ⇒ ↑ benefit of borrowing ⇒ more debt.
We assume exclusions between 1 and 5 years (benchmark = 3), recovery
rates between 10% and 60% (benchmark = 35%), and discount factor
between 0.96 and 0.985 (benchmark = 0.97).
Thus, we study economies with average debt levels between 30% and
90%, and average spreads between 0.5% and 5.5%.
44 / 83
52. CONCLUSIONS
Maybe sovereign spreads should play a more prominent role in
anchoring discussions of fiscal policy
Economies that suffer less debt intolerance should be allowed to
issue more debt.
It may be much easier to enforce a spread brake than to enforce a
debt brake.
Also
a market-determined fiscal anchor could be less susceptible to
creative accounting
more comprehensive measure of fiscal risks (e.g., debt maturity,
currency composition, implicit or contingent liabilities) 52 / 83
53. NEED FOR FUTURE WORK?
What should the spread-brake threshold be? Should it be reduced
gradually (mimicking disinflation periods)?
Which interest rates should fiscal rules use?
The average spread over which period should be used to trigger
the spread brake?
How should a spread brake be complemented with other
numerical targets?
How fast should the fiscal adjustment triggered by the brake be?
Would the spread limit help with other shocks (bailout
probability, multiple equilibria, political shocks, debt shocks)?
53 / 83