This document discusses the mathematics behind the Phillips curve and different monetary policy approaches. It summarizes an initial model of the Phillips curve that assumes expected inflation equals actual inflation and a constant monetary policy by the central bank. This initial model results in periodic behavior of unemployment and inflation. The document then introduces the idea of a variable monetary policy where the central bank adapts its policy based on unemployment and inflation levels. This makes the relationship between monetary policy and the Phillips curve nonlinear.
Workhour haircut an instrument in times of economic crisisRam Madhavan
The document discusses using a "workhour haircut" policy during economic crises to reduce unemployment. This involves governments capping total employee work hours, requiring employers to cut hours and pay by a small percentage. This would encourage hiring more employees to make up lost hours. The paper uses economic models and dynamic systems analysis to study the effects on inflation, unemployment, and money supply. It incorporates the workhour haircut idea into existing Phillips curve and IS-LM models. Analyzing the models numerically with different work hour reductions, it finds the economy takes fewer spirals to reach equilibrium when hours are cut, implying faster recovery from recession.
This document provides an introduction to macroeconomics. It defines macroeconomics as the study of factors that determine aggregate production, employment, prices and their changes over time in an economy. Key aspects covered include the classical and Keynesian views of macroeconomics, macroeconomic variables, models and approaches used in analysis. Important macroeconomic issues discussed are achieving economic growth, preventing business cycles, controlling inflation, unemployment, budget deficits, and managing international economic issues.
This document summarizes key concepts from Chapter 12 of Prof. Cunningham's Intermediate Macroeconomics class on New Classical Economics. It discusses the rational expectations hypothesis and how it differs from adaptive expectations. It then outlines several implications of the rational expectations approach, including the policy ineffectiveness proposition, the Phillips curve under rational expectations, criticisms of fiscal and monetary policy, Lucas' critique of econometric models, and the time inconsistency problem. The document concludes by summarizing the New Classical view of Keynesian economics and the New Keynesian response.
This document presents a new FIR filter method for dating US recessions in real time using unemployment rate and employment trend index data. The filter, called the M-Coppock curve, is a modified version of the Coppock curve commonly used in equity markets. It is shown to peak near economic troughs of post-WWII recessions, allowing recessions to be called in real time. While current models from the Federal Reserve banks forecast low recession probabilities, the author's M-Coppock curve has been trending upward since 2014, indicating weakening labor market strength despite falling unemployment levels. The simple and intuitive M-Coppock curve approach aims to address issues with instability in other predictive models.
This document summarizes key concepts relating to output, inflation, and unemployment from chapters in an intermediate macroeconomics textbook. It discusses the original Phillips curve developed by A.W. Phillips showing the relationship between wage inflation and unemployment. It then covers Milton Friedman's natural rate theory which argues that in the long run, real variables like employment are determined by real factors, not monetary factors. The document also discusses how expectations of future inflation can shift the short-run Phillips curve and the policy implications of these concepts.
The document provides an overview of monetarism and Milton Friedman's restatement of the quantity theory of money. It discusses four key aspects of monetarism: (1) that fluctuations in the money supply are the dominant cause of fluctuations in real output; (2) monetarism's use of an expectations-augmented Phillips curve; (3) a monetary approach to exchange rates; and (4) support for monetary policy rules over discretionary policies. It also summarizes Friedman's restatement of the quantity theory and three arguments for adopting a rule-based monetary policy of steady money supply growth.
This document introduces the basic overlapping generations model of economic growth for a closed world economy. It consists of two generations that overlap - a young working generation and an old retired generation. Households maximize utility from consumption when young and old. Firms produce output using capital and labor according to a Cobb-Douglas production function. Capital accumulates through investment and depreciates over time. Labor and productivity grow at exogenous rates. The model aims to endogenously explain capital accumulation, output growth, and other macroeconomic variables over time based on intertemporal optimization by households and firms.
This document provides an overview of key macroeconomic concepts including Gross Domestic Product (GDP) and the business cycle. It defines GDP as the total value of final goods and services produced within a country in a given year, which can be measured using either the expenditure approach or the income approach. It also explains how to use price indices to adjust nominal GDP values for inflation and obtain real GDP in order to make accurate comparisons over time. Finally, it outlines the four phases of the typical business cycle: peak, trough, recession, and expansion.
Workhour haircut an instrument in times of economic crisisRam Madhavan
The document discusses using a "workhour haircut" policy during economic crises to reduce unemployment. This involves governments capping total employee work hours, requiring employers to cut hours and pay by a small percentage. This would encourage hiring more employees to make up lost hours. The paper uses economic models and dynamic systems analysis to study the effects on inflation, unemployment, and money supply. It incorporates the workhour haircut idea into existing Phillips curve and IS-LM models. Analyzing the models numerically with different work hour reductions, it finds the economy takes fewer spirals to reach equilibrium when hours are cut, implying faster recovery from recession.
This document provides an introduction to macroeconomics. It defines macroeconomics as the study of factors that determine aggregate production, employment, prices and their changes over time in an economy. Key aspects covered include the classical and Keynesian views of macroeconomics, macroeconomic variables, models and approaches used in analysis. Important macroeconomic issues discussed are achieving economic growth, preventing business cycles, controlling inflation, unemployment, budget deficits, and managing international economic issues.
This document summarizes key concepts from Chapter 12 of Prof. Cunningham's Intermediate Macroeconomics class on New Classical Economics. It discusses the rational expectations hypothesis and how it differs from adaptive expectations. It then outlines several implications of the rational expectations approach, including the policy ineffectiveness proposition, the Phillips curve under rational expectations, criticisms of fiscal and monetary policy, Lucas' critique of econometric models, and the time inconsistency problem. The document concludes by summarizing the New Classical view of Keynesian economics and the New Keynesian response.
This document presents a new FIR filter method for dating US recessions in real time using unemployment rate and employment trend index data. The filter, called the M-Coppock curve, is a modified version of the Coppock curve commonly used in equity markets. It is shown to peak near economic troughs of post-WWII recessions, allowing recessions to be called in real time. While current models from the Federal Reserve banks forecast low recession probabilities, the author's M-Coppock curve has been trending upward since 2014, indicating weakening labor market strength despite falling unemployment levels. The simple and intuitive M-Coppock curve approach aims to address issues with instability in other predictive models.
This document summarizes key concepts relating to output, inflation, and unemployment from chapters in an intermediate macroeconomics textbook. It discusses the original Phillips curve developed by A.W. Phillips showing the relationship between wage inflation and unemployment. It then covers Milton Friedman's natural rate theory which argues that in the long run, real variables like employment are determined by real factors, not monetary factors. The document also discusses how expectations of future inflation can shift the short-run Phillips curve and the policy implications of these concepts.
The document provides an overview of monetarism and Milton Friedman's restatement of the quantity theory of money. It discusses four key aspects of monetarism: (1) that fluctuations in the money supply are the dominant cause of fluctuations in real output; (2) monetarism's use of an expectations-augmented Phillips curve; (3) a monetary approach to exchange rates; and (4) support for monetary policy rules over discretionary policies. It also summarizes Friedman's restatement of the quantity theory and three arguments for adopting a rule-based monetary policy of steady money supply growth.
This document introduces the basic overlapping generations model of economic growth for a closed world economy. It consists of two generations that overlap - a young working generation and an old retired generation. Households maximize utility from consumption when young and old. Firms produce output using capital and labor according to a Cobb-Douglas production function. Capital accumulates through investment and depreciates over time. Labor and productivity grow at exogenous rates. The model aims to endogenously explain capital accumulation, output growth, and other macroeconomic variables over time based on intertemporal optimization by households and firms.
This document provides an overview of key macroeconomic concepts including Gross Domestic Product (GDP) and the business cycle. It defines GDP as the total value of final goods and services produced within a country in a given year, which can be measured using either the expenditure approach or the income approach. It also explains how to use price indices to adjust nominal GDP values for inflation and obtain real GDP in order to make accurate comparisons over time. Finally, it outlines the four phases of the typical business cycle: peak, trough, recession, and expansion.
Genuine%20 %2008%20-%20 inflation%20and%20unemploymentDaniseck Adam
The document discusses inflation and unemployment. It defines inflation as a sustained rise in the general price level and outlines several key causes of inflation including cost-push, demand-pull, and monetary explanations. Cost-push inflation results from increases in production costs, while demand-pull inflation occurs when aggregate demand exceeds output. The quantity theory of money suggests that inflation is primarily a monetary phenomenon caused by excessive growth of the money supply. International data and studies of Tanzania support the role of monetary factors in driving inflation.
This study examines the impact of conflict on economic growth using a production function model. The authors regress GDP growth against capital growth, labor growth, and several conflict variables (terrorism, displacement, violent episodes) for 126 countries. While capital and labor growth are expected to positively impact GDP growth, the conflict variables are expected to have a negative impact by reducing productivity. This cross-country analysis aims to provide a macro-level understanding of how conflict generally affects economic growth, building on prior micro-level case studies of specific countries. The authors acknowledge limitations of their cross-sectional approach compared to prior time-series analyses of individual countries.
This study aims to analyze the impact of conflict on economic growth across 126 countries from 2004 to 2009. It uses a production function model where GDP growth is regressed against capital growth, labor growth, and various measures of conflict, including terrorism, displacement, and violent episodes. This expands upon previous micro-level studies of specific countries by taking a macro-level, cross-country approach. The study predicts conflict will negatively impact GDP growth. However, the conflict variables are not significant in the model, suggesting the model may not adequately capture the effects of conflict on economic growth.
This document provides an acknowledgements section for the author Mannig J. Simidian and an introduction to the topics that will be covered in the macroeconomics textbook and course. It thanks various individuals who influenced the author and provided guidance. It also outlines some of the key macroeconomic concepts that will be discussed, including real GDP, inflation, unemployment, models, endogenous and exogenous variables, market clearing, and the relationship between microeconomics and macroeconomics.
This document provides an overview of different types of microeconomics analysis:
1) Micro statics refers to the equilibrium between economic variables at a single point in time. It shows the relationship between price and quantity at a moment when supply and demand curves intersect.
2) Micro dynamics analyzes how an initial equilibrium breaks down and a new equilibrium is established over time as prices and quantities change. It shows the disequilibrium process.
3) Comparative micro statics compares different equilibriums at different points in time as conditions change, but does not analyze the process of moving between equilibriums. It is concerned with explaining different equilibrium states rather than the transition between them.
This document provides an overview of key concepts in macroeconomics, including:
1) Macroeconomics deals with the performance and decision-making of the entire economy, including factors like GDP, unemployment, and inflation.
2) The document outlines different macroeconomic schools of thought including Keynesian, neoclassical, monetarist traditions.
3) It also summarizes tools and models used in macroeconomics like fiscal/monetary policy, aggregate supply/demand, and circular flow analysis.
The Causal Analysis of the Relationship between Inflation and Output Gap in T...inventionjournals
The purpose of the paper is to study dynamic relationships between the inflation and output gap by using Granger causality, Impulse response and variance decompositions analysis within VECM framework for the quarterly data over the first period of 2003 and second period of 2016. The results of the study indicate that the output gap Granger cause the inflation in Turkey both in short-and long-runs. Also, sign of the causality is negative and same causal relationships between two variables hold beyond the sample period. The results should be taken as an evidence of the conclusion that the output gap has important implications for the CBRT's monetary policy.
1) The document discusses the classical theory of inflation, including its causes, effects, and macroeconomic costs.
2) It explains the quantity theory of money, which links inflation to the growth of money supply. If money supply grows faster than real GDP, inflation will result.
3) In the long run, changes in money supply growth determine inflation, while inflation expectations and real GDP growth are stable. Higher money growth causes proportionally higher inflation.
1) Zimbabwe experienced hyperinflation from 1998-2008, with inflation reaching 66,200% by 2007, the second highest recorded rate in history.
2) The hyperinflation was caused by the central bank excessively printing money and lending it to state-owned enterprises and private entities, effectively hiding the large fiscal deficit.
3) Some groups, like those with connections to state enterprises, benefited from arbitraging the dual exchange rates, but most Zimbabweans suffered from the hyperinflation.
The document compares the monetary and Keynesian approaches to economic stability. The monetary (or monetarist) approach is based on the role of money in stabilizing aggregate demand, and believes that limiting government intervention and controlling the money supply are key. The Keynesian approach focuses on the role of government spending in stabilizing aggregate demand, and does not restrict government intervention. It believes fiscal policy tools like tax rates and government spending are most important for achieving economic stability, especially during downturns when suggested solutions include increasing various types of spending.
Macroeconomics analyzes aggregate economic indicators like unemployment, growth, GDP and inflation. It studies how the overall economy behaves. Governments and businesses use macroeconomic models and analysis to inform economic policymaking and strategic planning. Three major concerns of macroeconomics discussed are inflation, output growth, and unemployment. Inflation refers to a general increase in the price level of goods and services in an economy over time.
The Heterogenous Effects of Government Spending - by Axelle Ferriere and Gast...ADEMU_Project
- The paper examines how tax progressivity affects government spending multipliers using US data from 1913-2012.
- It finds that spending multipliers are positive only when spending is financed by more progressive taxes that place relatively more of the burden on high-income households. However, multipliers are negative when the tax burden falls more on low-income households.
- At the micro-level, spending has heterogeneous effects - it expands output for low-income households only when accompanied by more progressive taxes, but has no effect on high-income households.
Don Patinkin criticized the neoclassical assumptions of homogeneity and dichotomization. He proposed the real balance effect to reconcile goods and money markets. The real balance effect posits that changes in the price level affect real purchasing power, which impacts demand for goods. When prices rise, real balances and goods demand fall, pushing prices back down. This feedback loop between prices, real balances, and goods demand is represented using the IS-LM model, where a fall in prices shifts the LM curve right, raising output and employment until full employment is reached. Patinkin argues this real balance effect denies the homogeneity assumption and integrates goods and money markets.
The document summarizes three models of aggregate supply and the relationship between inflation and unemployment known as the Phillips curve. The models are the sticky-wage, imperfect-information, and sticky-price models. It also discusses how expectations are formed, the short-run tradeoff in the Phillips curve, and the costs of reducing inflation through contractionary policy.
1) The document discusses the classical theory of inflation and the costs of inflation. It provides historical examples of inflation rates over time including hyperinflation events.
2) Hyperinflation is defined as inflation exceeding 50% per month and examples are given from Austria, Hungary, Germany and Poland in the early 1920s where prices increased dramatically as money supplies rose rapidly.
3) The costs of inflation discussed include shoe leather costs from having to visit banks more often, menu costs to update prices, tax distortions from not adjusting for inflation, and effects on savings from the reduction of purchasing power over time.
How inflation and unemployment are relatedAlok upadhayay
The document discusses the relationship between inflation and unemployment. It begins by explaining the inverse correlation between inflation and unemployment based on principles of supply and demand. When demand for labor exceeds supply, wage inflation rises and vice versa. The Phillips Curve, developed by A.W. Phillips, showed this inverse relationship, though it was nonlinear. While the Phillips Curve could be used by policymakers to balance inflation and unemployment in the short run, monetarists like Milton Friedman argued it did not apply in the long run. The relationship between inflation and unemployment only works temporarily, not as a permanent policy tool.
Chapter 5 the challenge of new classical macroeconomics (Scarth)Abdul Hadi Ilman
1) The document discusses the New Classical approach to macroeconomics, which explains business cycles through real shocks like technology changes rather than nominal rigidities.
2) It examines extensions to the original real business cycle model, including variations to the utility function, indivisible labor, non-market activity, and changes to government spending, to better match empirical observations.
3) It also discusses optimal inflation policy using New Classical models, finding that even 2% inflation reduces steady-state consumption substantially, implying inflation should be kept very low.
This document provides an overview of macroeconomics and the debate between free-market and Keynesian schools of thought. It discusses how Adam Smith developed ideas of free markets but John Maynard Keynes advocated government intervention to boost demand in response to the Great Depression. In the 1970s, Milton Friedman led a counter-revolution arguing excessive money supply and unions caused stagflation. Margaret Thatcher embraced free-market policies, but the 2007 crisis saw a return of Keynesian responses as the UK faced its worst recession since the 1930s.
This document discusses macroeconomics and macroeconomic policy debates from classical and Keynesian perspectives. It covers unemployment, price stability, and exchange rates. On unemployment, classical economists believe full employment is always achieved through flexible wages, while Keynesians believe unemployment is normal and government intervention is needed. On price stability, classical economists see prices adjusting to maintain full employment while Keynesians see stable prices with variable output. Exchange rates are influenced by demand and supply factors in both frameworks.
Inflation, Unemployment, and Stabilization Policies.pptmajidaghaei4
This document discusses fiscal and monetary policy and their effects on inflation, unemployment, and economic stabilization. It covers topics such as:
- How fiscal policy can be expansionary or contractionary through increasing or decreasing government spending and taxation.
- How fiscal policy affects aggregate demand and the budget balance.
- How monetary policy can be expansionary or contractionary through increasing or decreasing the money supply.
- The relationship between inflation, unemployment, and the output gap as depicted by the Phillips Curve.
- How expectations can cause shifts in the Phillips Curve in the long run.
This chapter discusses the relationship between money, inflation, and prices according to the quantity theory of money. It introduces key concepts such as the money supply, monetary policy, the quantity equation, velocity of money, and how the money supply and inflation are connected. The quantity theory predicts a direct relationship between the growth of the money supply and the inflation rate in the long run.
Genuine%20 %2008%20-%20 inflation%20and%20unemploymentDaniseck Adam
The document discusses inflation and unemployment. It defines inflation as a sustained rise in the general price level and outlines several key causes of inflation including cost-push, demand-pull, and monetary explanations. Cost-push inflation results from increases in production costs, while demand-pull inflation occurs when aggregate demand exceeds output. The quantity theory of money suggests that inflation is primarily a monetary phenomenon caused by excessive growth of the money supply. International data and studies of Tanzania support the role of monetary factors in driving inflation.
This study examines the impact of conflict on economic growth using a production function model. The authors regress GDP growth against capital growth, labor growth, and several conflict variables (terrorism, displacement, violent episodes) for 126 countries. While capital and labor growth are expected to positively impact GDP growth, the conflict variables are expected to have a negative impact by reducing productivity. This cross-country analysis aims to provide a macro-level understanding of how conflict generally affects economic growth, building on prior micro-level case studies of specific countries. The authors acknowledge limitations of their cross-sectional approach compared to prior time-series analyses of individual countries.
This study aims to analyze the impact of conflict on economic growth across 126 countries from 2004 to 2009. It uses a production function model where GDP growth is regressed against capital growth, labor growth, and various measures of conflict, including terrorism, displacement, and violent episodes. This expands upon previous micro-level studies of specific countries by taking a macro-level, cross-country approach. The study predicts conflict will negatively impact GDP growth. However, the conflict variables are not significant in the model, suggesting the model may not adequately capture the effects of conflict on economic growth.
This document provides an acknowledgements section for the author Mannig J. Simidian and an introduction to the topics that will be covered in the macroeconomics textbook and course. It thanks various individuals who influenced the author and provided guidance. It also outlines some of the key macroeconomic concepts that will be discussed, including real GDP, inflation, unemployment, models, endogenous and exogenous variables, market clearing, and the relationship between microeconomics and macroeconomics.
This document provides an overview of different types of microeconomics analysis:
1) Micro statics refers to the equilibrium between economic variables at a single point in time. It shows the relationship between price and quantity at a moment when supply and demand curves intersect.
2) Micro dynamics analyzes how an initial equilibrium breaks down and a new equilibrium is established over time as prices and quantities change. It shows the disequilibrium process.
3) Comparative micro statics compares different equilibriums at different points in time as conditions change, but does not analyze the process of moving between equilibriums. It is concerned with explaining different equilibrium states rather than the transition between them.
This document provides an overview of key concepts in macroeconomics, including:
1) Macroeconomics deals with the performance and decision-making of the entire economy, including factors like GDP, unemployment, and inflation.
2) The document outlines different macroeconomic schools of thought including Keynesian, neoclassical, monetarist traditions.
3) It also summarizes tools and models used in macroeconomics like fiscal/monetary policy, aggregate supply/demand, and circular flow analysis.
The Causal Analysis of the Relationship between Inflation and Output Gap in T...inventionjournals
The purpose of the paper is to study dynamic relationships between the inflation and output gap by using Granger causality, Impulse response and variance decompositions analysis within VECM framework for the quarterly data over the first period of 2003 and second period of 2016. The results of the study indicate that the output gap Granger cause the inflation in Turkey both in short-and long-runs. Also, sign of the causality is negative and same causal relationships between two variables hold beyond the sample period. The results should be taken as an evidence of the conclusion that the output gap has important implications for the CBRT's monetary policy.
1) The document discusses the classical theory of inflation, including its causes, effects, and macroeconomic costs.
2) It explains the quantity theory of money, which links inflation to the growth of money supply. If money supply grows faster than real GDP, inflation will result.
3) In the long run, changes in money supply growth determine inflation, while inflation expectations and real GDP growth are stable. Higher money growth causes proportionally higher inflation.
1) Zimbabwe experienced hyperinflation from 1998-2008, with inflation reaching 66,200% by 2007, the second highest recorded rate in history.
2) The hyperinflation was caused by the central bank excessively printing money and lending it to state-owned enterprises and private entities, effectively hiding the large fiscal deficit.
3) Some groups, like those with connections to state enterprises, benefited from arbitraging the dual exchange rates, but most Zimbabweans suffered from the hyperinflation.
The document compares the monetary and Keynesian approaches to economic stability. The monetary (or monetarist) approach is based on the role of money in stabilizing aggregate demand, and believes that limiting government intervention and controlling the money supply are key. The Keynesian approach focuses on the role of government spending in stabilizing aggregate demand, and does not restrict government intervention. It believes fiscal policy tools like tax rates and government spending are most important for achieving economic stability, especially during downturns when suggested solutions include increasing various types of spending.
Macroeconomics analyzes aggregate economic indicators like unemployment, growth, GDP and inflation. It studies how the overall economy behaves. Governments and businesses use macroeconomic models and analysis to inform economic policymaking and strategic planning. Three major concerns of macroeconomics discussed are inflation, output growth, and unemployment. Inflation refers to a general increase in the price level of goods and services in an economy over time.
The Heterogenous Effects of Government Spending - by Axelle Ferriere and Gast...ADEMU_Project
- The paper examines how tax progressivity affects government spending multipliers using US data from 1913-2012.
- It finds that spending multipliers are positive only when spending is financed by more progressive taxes that place relatively more of the burden on high-income households. However, multipliers are negative when the tax burden falls more on low-income households.
- At the micro-level, spending has heterogeneous effects - it expands output for low-income households only when accompanied by more progressive taxes, but has no effect on high-income households.
Don Patinkin criticized the neoclassical assumptions of homogeneity and dichotomization. He proposed the real balance effect to reconcile goods and money markets. The real balance effect posits that changes in the price level affect real purchasing power, which impacts demand for goods. When prices rise, real balances and goods demand fall, pushing prices back down. This feedback loop between prices, real balances, and goods demand is represented using the IS-LM model, where a fall in prices shifts the LM curve right, raising output and employment until full employment is reached. Patinkin argues this real balance effect denies the homogeneity assumption and integrates goods and money markets.
The document summarizes three models of aggregate supply and the relationship between inflation and unemployment known as the Phillips curve. The models are the sticky-wage, imperfect-information, and sticky-price models. It also discusses how expectations are formed, the short-run tradeoff in the Phillips curve, and the costs of reducing inflation through contractionary policy.
1) The document discusses the classical theory of inflation and the costs of inflation. It provides historical examples of inflation rates over time including hyperinflation events.
2) Hyperinflation is defined as inflation exceeding 50% per month and examples are given from Austria, Hungary, Germany and Poland in the early 1920s where prices increased dramatically as money supplies rose rapidly.
3) The costs of inflation discussed include shoe leather costs from having to visit banks more often, menu costs to update prices, tax distortions from not adjusting for inflation, and effects on savings from the reduction of purchasing power over time.
How inflation and unemployment are relatedAlok upadhayay
The document discusses the relationship between inflation and unemployment. It begins by explaining the inverse correlation between inflation and unemployment based on principles of supply and demand. When demand for labor exceeds supply, wage inflation rises and vice versa. The Phillips Curve, developed by A.W. Phillips, showed this inverse relationship, though it was nonlinear. While the Phillips Curve could be used by policymakers to balance inflation and unemployment in the short run, monetarists like Milton Friedman argued it did not apply in the long run. The relationship between inflation and unemployment only works temporarily, not as a permanent policy tool.
Chapter 5 the challenge of new classical macroeconomics (Scarth)Abdul Hadi Ilman
1) The document discusses the New Classical approach to macroeconomics, which explains business cycles through real shocks like technology changes rather than nominal rigidities.
2) It examines extensions to the original real business cycle model, including variations to the utility function, indivisible labor, non-market activity, and changes to government spending, to better match empirical observations.
3) It also discusses optimal inflation policy using New Classical models, finding that even 2% inflation reduces steady-state consumption substantially, implying inflation should be kept very low.
This document provides an overview of macroeconomics and the debate between free-market and Keynesian schools of thought. It discusses how Adam Smith developed ideas of free markets but John Maynard Keynes advocated government intervention to boost demand in response to the Great Depression. In the 1970s, Milton Friedman led a counter-revolution arguing excessive money supply and unions caused stagflation. Margaret Thatcher embraced free-market policies, but the 2007 crisis saw a return of Keynesian responses as the UK faced its worst recession since the 1930s.
This document discusses macroeconomics and macroeconomic policy debates from classical and Keynesian perspectives. It covers unemployment, price stability, and exchange rates. On unemployment, classical economists believe full employment is always achieved through flexible wages, while Keynesians believe unemployment is normal and government intervention is needed. On price stability, classical economists see prices adjusting to maintain full employment while Keynesians see stable prices with variable output. Exchange rates are influenced by demand and supply factors in both frameworks.
Inflation, Unemployment, and Stabilization Policies.pptmajidaghaei4
This document discusses fiscal and monetary policy and their effects on inflation, unemployment, and economic stabilization. It covers topics such as:
- How fiscal policy can be expansionary or contractionary through increasing or decreasing government spending and taxation.
- How fiscal policy affects aggregate demand and the budget balance.
- How monetary policy can be expansionary or contractionary through increasing or decreasing the money supply.
- The relationship between inflation, unemployment, and the output gap as depicted by the Phillips Curve.
- How expectations can cause shifts in the Phillips Curve in the long run.
This chapter discusses the relationship between money, inflation, and prices according to the quantity theory of money. It introduces key concepts such as the money supply, monetary policy, the quantity equation, velocity of money, and how the money supply and inflation are connected. The quantity theory predicts a direct relationship between the growth of the money supply and the inflation rate in the long run.
This lecture note introduces classical macroeconomic theory, which examines the linkages between interest rates, money, output, and inflation. It will first cover classical monetary theory, which assumes money is neutral and its supply only determines prices. It then presents a basic classical model of the real economy with aggregate supply and demand. Equilibrium output and interest rates are determined by the intersection of these curves. Money enters by facilitating transactions but does not affect real variables. Money demand depends on nominal income and interest rates, determining equilibrium money holdings and the price level.
This document discusses different types of unemployment including frictional, seasonal, cyclical, structural, and disguised unemployment. It also discusses underemployment and defines unemployment rate, labor force participation rate, and discouraged workers. Additionally, it covers the relationship between unemployment and inflation including the short-run and long-run Phillips curves. Expected inflation rate is identified as a key factor that can shift the short-run Phillips curve. The natural rate hypothesis and need for disinflation policies if unemployment is kept below the natural rate for too long are also summarized.
This document provides an overview of a dynamic model of aggregate demand and aggregate supply (AD-AS). It introduces notation to represent variables over time and outlines the five key equations that make up the dynamic AD-AS model: the demand for goods and services equation, the Fisher equation, the Phillips curve, the assumption of adaptive expectations, and the monetary policy rule. It then discusses how these equations determine the model's endogenous variables and how the economy responds to various shocks.
This document discusses various theories of monetary policy and inflation. It begins by explaining that less developed countries often struggle with high inflation and unemployment due to low production and high population growth. It then discusses monetary theory, including the quantity theory of money formula MV=PQ. It notes that monetary theory is controlled by central governments in many developing economies. The document also discusses criticisms of monetary theory, definitions of inflation, causes of inflation according to Keynesian and monetarist theories, examples of hyperinflation and stagflation, negative inflation/deflation, and the objectives of monetary policies.
This document provides an overview of key concepts related to inflation and unemployment from a macroeconomics textbook. It includes:
1) Definitions of inflation as an increase in the average level of prices and explanations of the relationship between nominal interest rates, real interest rates, and inflation.
2) A model of labor force dynamics that shows unemployment is determined by the rates of job separation and job finding, and how this relates to the natural rate of unemployment.
3) Descriptions of different types of unemployment including frictional, structural, and others, as well as factors that can increase or decrease unemployment rates.
4) An introduction to aggregate supply and demand models and the short-run tradeoff between inflation
This document provides an introduction to macroeconomics. It discusses key macroeconomic concepts such as stocks and flows, equilibrium and disequilibrium, and the circular flow of income in closed and open economies. It also outlines macroeconomic goals like full employment and price stability. The development of macroeconomics from classical to Keynesian and monetarist theories is summarized. Finally, it discusses important macroeconomic indicators and policy tools like fiscal and monetary policy.
Chapter 7 - inflation ,unemployment and underemployment for BBAginish9841502661
This document defines various types of inflation including low inflation, galloping inflation, and hyperinflation. It also discusses different measures used to calculate inflation rates such as the Consumer Price Index (CPI) and Wholesale Price Index (WPI). Finally, it outlines several causes of inflation including demand-pull factors related to increases in the money supply according to the Quantity Theory of Money, and cost-push factors like increases in wages or costs of raw materials.
Munich Personal RePEc ArchiveShould a Government Fiscally .docxroushhsiu
Munich Personal RePEc Archive
Should a Government Fiscally Intervene
in a Recession and, If So, How?
Harashima, Taiji
Kanazawa Seiryo University
2 April 2017
Online at https://mpra.ub.uni-muenchen.de/78053/
MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC
Should a Government Fiscally Intervene in a Recession and, If So, How?
Taiji HARASHIMA*
April, 2017
Abstract
The validity of discretionary fiscal policy in a recession will differ according to the cause and
mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a
fundamental shock that changes the steady state downwards is examined. In such a recession,
households need to discontinuously increase consumption to a point on the saddle path to
maintain Pareto efficiency. However, they will not “jump” consumption in this manner and
instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike
unsmooth and discontinuous consumption and behave strategically. The paper concludes that
increasing government consumption until demand meets the present level of production and
maintaining this fiscal policy for a long period is the best option. Consequent government debts
can be sustainable even if they become extremely large.
JEL Classification code: E20, E32, E62, H20, H30, H63
Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government
debts; Pareto inefficiency; Time preference
*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,
Kanazawa-shi, Ishikawa, 920-8620, Japan.
Email: [email protected] or [email protected]
mailto:[email protected]
mailto:[email protected]
1
1 INTRODUCTION
Discretionary fiscal policy has been studied from many perspectives since the era of Keynes
(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;
Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in
a recession, and if so, how. The answer will differ according to the cause and mechanism of
recession. Particularly, it will be different depending on whether “disequilibrium” is generated.
The concept of disequilibrium is, however, controversial and therefore arguments continue even
now about the use of discretionary fiscal policy in a recession. In this paper, the concept of
disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient
path” is used.
Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;
Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).
Some fundamental shocks will change the steady state, and if the steady state is changed
downwards (i.e., to lower levels of production and consumption), households must change the
consumption path to one that d ...
Munich Personal RePEc ArchiveShould a Government Fiscally .docxjacmariek5
Munich Personal RePEc Archive
Should a Government Fiscally Intervene
in a Recession and, If So, How?
Harashima, Taiji
Kanazawa Seiryo University
2 April 2017
Online at https://mpra.ub.uni-muenchen.de/78053/
MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC
Should a Government Fiscally Intervene in a Recession and, If So, How?
Taiji HARASHIMA*
April, 2017
Abstract
The validity of discretionary fiscal policy in a recession will differ according to the cause and
mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a
fundamental shock that changes the steady state downwards is examined. In such a recession,
households need to discontinuously increase consumption to a point on the saddle path to
maintain Pareto efficiency. However, they will not “jump” consumption in this manner and
instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike
unsmooth and discontinuous consumption and behave strategically. The paper concludes that
increasing government consumption until demand meets the present level of production and
maintaining this fiscal policy for a long period is the best option. Consequent government debts
can be sustainable even if they become extremely large.
JEL Classification code: E20, E32, E62, H20, H30, H63
Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government
debts; Pareto inefficiency; Time preference
*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,
Kanazawa-shi, Ishikawa, 920-8620, Japan.
Email: [email protected] or [email protected]
mailto:[email protected]
mailto:[email protected]
1
1 INTRODUCTION
Discretionary fiscal policy has been studied from many perspectives since the era of Keynes
(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;
Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in
a recession, and if so, how. The answer will differ according to the cause and mechanism of
recession. Particularly, it will be different depending on whether “disequilibrium” is generated.
The concept of disequilibrium is, however, controversial and therefore arguments continue even
now about the use of discretionary fiscal policy in a recession. In this paper, the concept of
disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient
path” is used.
Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;
Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).
Some fundamental shocks will change the steady state, and if the steady state is changed
downwards (i.e., to lower levels of production and consumption), households must change the
consumption path to one that d.
Munich Personal RePEc ArchiveShould a Government Fiscally .docxdohertyjoetta
Munich Personal RePEc Archive
Should a Government Fiscally Intervene
in a Recession and, If So, How?
Harashima, Taiji
Kanazawa Seiryo University
2 April 2017
Online at https://mpra.ub.uni-muenchen.de/78053/
MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC
Should a Government Fiscally Intervene in a Recession and, If So, How?
Taiji HARASHIMA*
April, 2017
Abstract
The validity of discretionary fiscal policy in a recession will differ according to the cause and
mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a
fundamental shock that changes the steady state downwards is examined. In such a recession,
households need to discontinuously increase consumption to a point on the saddle path to
maintain Pareto efficiency. However, they will not “jump” consumption in this manner and
instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike
unsmooth and discontinuous consumption and behave strategically. The paper concludes that
increasing government consumption until demand meets the present level of production and
maintaining this fiscal policy for a long period is the best option. Consequent government debts
can be sustainable even if they become extremely large.
JEL Classification code: E20, E32, E62, H20, H30, H63
Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government
debts; Pareto inefficiency; Time preference
*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,
Kanazawa-shi, Ishikawa, 920-8620, Japan.
Email: [email protected] or [email protected]
mailto:[email protected]
mailto:[email protected]
1
1 INTRODUCTION
Discretionary fiscal policy has been studied from many perspectives since the era of Keynes
(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;
Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in
a recession, and if so, how. The answer will differ according to the cause and mechanism of
recession. Particularly, it will be different depending on whether “disequilibrium” is generated.
The concept of disequilibrium is, however, controversial and therefore arguments continue even
now about the use of discretionary fiscal policy in a recession. In this paper, the concept of
disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient
path” is used.
Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;
Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).
Some fundamental shocks will change the steady state, and if the steady state is changed
downwards (i.e., to lower levels of production and consumption), households must change the
consumption path to one that d.
Munich Personal RePEc ArchiveShould a Government Fiscally .docxgriffinruthie22
Munich Personal RePEc Archive
Should a Government Fiscally Intervene
in a Recession and, If So, How?
Harashima, Taiji
Kanazawa Seiryo University
2 April 2017
Online at https://mpra.ub.uni-muenchen.de/78053/
MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC
Should a Government Fiscally Intervene in a Recession and, If So, How?
Taiji HARASHIMA*
April, 2017
Abstract
The validity of discretionary fiscal policy in a recession will differ according to the cause and
mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a
fundamental shock that changes the steady state downwards is examined. In such a recession,
households need to discontinuously increase consumption to a point on the saddle path to
maintain Pareto efficiency. However, they will not “jump” consumption in this manner and
instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike
unsmooth and discontinuous consumption and behave strategically. The paper concludes that
increasing government consumption until demand meets the present level of production and
maintaining this fiscal policy for a long period is the best option. Consequent government debts
can be sustainable even if they become extremely large.
JEL Classification code: E20, E32, E62, H20, H30, H63
Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government
debts; Pareto inefficiency; Time preference
*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,
Kanazawa-shi, Ishikawa, 920-8620, Japan.
Email: [email protected] or [email protected]
mailto:[email protected]
mailto:[email protected]
1
1 INTRODUCTION
Discretionary fiscal policy has been studied from many perspectives since the era of Keynes
(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;
Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in
a recession, and if so, how. The answer will differ according to the cause and mechanism of
recession. Particularly, it will be different depending on whether “disequilibrium” is generated.
The concept of disequilibrium is, however, controversial and therefore arguments continue even
now about the use of discretionary fiscal policy in a recession. In this paper, the concept of
disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient
path” is used.
Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;
Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).
Some fundamental shocks will change the steady state, and if the steady state is changed
downwards (i.e., to lower levels of production and consumption), households must change the
consumption path to one that d.
Munich Personal RePEc ArchiveShould a Government Fiscally .docxgemaherd
Munich Personal RePEc Archive
Should a Government Fiscally Intervene
in a Recession and, If So, How?
Harashima, Taiji
Kanazawa Seiryo University
2 April 2017
Online at https://mpra.ub.uni-muenchen.de/78053/
MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC
Should a Government Fiscally Intervene in a Recession and, If So, How?
Taiji HARASHIMA*
April, 2017
Abstract
The validity of discretionary fiscal policy in a recession will differ according to the cause and
mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a
fundamental shock that changes the steady state downwards is examined. In such a recession,
households need to discontinuously increase consumption to a point on the saddle path to
maintain Pareto efficiency. However, they will not “jump” consumption in this manner and
instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike
unsmooth and discontinuous consumption and behave strategically. The paper concludes that
increasing government consumption until demand meets the present level of production and
maintaining this fiscal policy for a long period is the best option. Consequent government debts
can be sustainable even if they become extremely large.
JEL Classification code: E20, E32, E62, H20, H30, H63
Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government
debts; Pareto inefficiency; Time preference
*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,
Kanazawa-shi, Ishikawa, 920-8620, Japan.
Email: [email protected] or [email protected]
mailto:[email protected]
mailto:[email protected]
1
1 INTRODUCTION
Discretionary fiscal policy has been studied from many perspectives since the era of Keynes
(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;
Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in
a recession, and if so, how. The answer will differ according to the cause and mechanism of
recession. Particularly, it will be different depending on whether “disequilibrium” is generated.
The concept of disequilibrium is, however, controversial and therefore arguments continue even
now about the use of discretionary fiscal policy in a recession. In this paper, the concept of
disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient
path” is used.
Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;
Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).
Some fundamental shocks will change the steady state, and if the steady state is changed
downwards (i.e., to lower levels of production and consumption), households must change the
consumption path to one that d.
Munich personal re p ec archiveshould a government fiscally MARRY7
- The document examines whether a government should intervene fiscally during a recession caused by an upward shift in the rate of time preference (RTP).
- When the RTP increases, the steady state of the economy shifts downward, requiring households to adjust their consumption path. However, households will not "jump" consumption to the new efficient path due to risk aversion and wanting smooth consumption over time.
- This results in households choosing a "Nash equilibrium of a Pareto inefficient path" rather than the efficient path, leading to increased unemployment during the recession. The document evaluates whether the government should intervene through increasing spending, cutting taxes, or not intervening at all.
Unemployment is measured as the number of people willing and able to work but unable to find employment. There are different types of unemployment including cyclical, frictional, and structural. Theories of unemployment include the Keynesian and classical theories. Keynesian theory states that aggregate demand determines employment while classical theory says real wages impact employment. Unemployment has costs like reduced income and increased dependence. The NAIRU is the lowest unemployment rate that avoids inflation increases. Factors like productivity and benefits influence the NAIRU, which is important for policymakers to consider.
This document provides an overview of macroeconomics and the circular flow of income through several models. It discusses key concepts such as:
1. Macroeconomics studies the economy as a whole by looking at aggregates like total output and income, whereas microeconomics looks at individual units.
2. Common macroeconomic policy objectives are full employment, price stability, economic growth, and balance of payments equilibrium.
3. The circular flow of income can be modeled in a two-sector closed economy with households and firms or a three-sector model that includes government. Savings and investment are incorporated through financial markets to achieve equilibrium.
- A liquidity trap is a situation where the short-term nominal interest rate is zero, meaning that increasing the money supply has no effect on output or prices according to traditional Keynesian theory.
- Modern theory argues that monetary policy can still be effective even at zero interest rates by managing expectations about future money supply levels when interest rates rise above zero again.
- For monetary policy to be effective in a liquidity trap, central banks must commit to maintaining lower future interest rates once deflationary shocks subside in order to stimulate expectations about future money supply levels and interest rates.
1. The Mathematics Behind Monetary Policy
and the Phillips Curve
Christopher Braden Vernet
Fall 2015
1
2. 1 Introduction
In economics there is this idea called creative destruction. A new technol-
ogy challenges an entire industry by creating a better and cheaper product.
This forces competition to either adapt the new technology or perish. Sim-
ilarly economics goes through a similar cycle. A certain economic theory or
idea will reign supreme until a massive economic downturn happens then a
new theory will rise from the ashes of the old. For example the Great De-
pression saw Adam Smith’s classicalism change to Keynesianism which was
replaced with Milton Friedman’s Monetarism, which was ditched during the
Great Recession in 2008 with the implementation of Quantitative Easing.
One of the ideas that has adapted and survived was known as the Phillips
curve. The basic idea is that in the short run inflation and unemployment
are negatively related. Higher inflation leads to lower unemployment and
vice versa. Tamara Todorova explored the mathematics behind the Phillips
Curve in her paper The Economic Dynamics of Inflation and Unemployment.
In her paper she discusses the stability of critical points in the Phillips Curve
model depending on different linear economic theories and models. In this
paper I want to expand that analysis with an emphasis on different mone-
tary policies. Instead of a constant monetary policy, the central bank adapts
a monetary policy based on unemployment and inflation levels, which can
become a nonlinear relationship.
2 Methods
For each of these models we will start with the mathematics to hypothesize
about the long term behavior of the solution. Then we will populate these
models with real and artificial variables. Artificial variables are used to
illustrate the behavior and don’t have any basis in the real world. On the
other hand real variables will be based on the behavior of the US dollar
between January 1990 and December 2007. This period was chosen because
it was a relatively calm time for US Economics. It was some time after the
early 1980s energy crisis and ends right before the Great Recession. The
data was obtained from the St. Louis Federal Reserve and the US Bureau of
Labor Statistics. All the data can be accessed at the url [9]. All models will
be graphed using Matlab’s ODE45 or ODE15s if the behavior of the solutions
are intractable.
2
3. 3 Initial Model
Our initial model of the Phillips curve is based off the Todorova’s Extended
model [Todorova, 135]. It assumes that expected inflation is equal to the
actual inflation. This may not necessarily be true in the short run and will
be discussed later. Her model is based off four factors: The unemployment
rate (U), the natural rate of unemployment (UN ), the inflation rate (q) and
the change in the money supply (m).
Unemployment is a function of aggregate demand. Aggregate demand is
the sum of a nation’s consumption, investment, government spending, and
net exports. When aggregate demand goes up, more goods and services are
demanded from the economy, meaning employers need to hire more staff
decreasing unemployment. Therefore, aggregate demand is a function of the
nominal money supply (M) divided by the price level (p). The nominal
money supply is how many dollars exist in the economy. On the other hand
the price level is how much stuff that money can buy. This level is calculated
via goods baskets. Every month the Bureau of Labor Statistics sends agents
around the country collecting prices on different goods. The average of these
prices is called the Consumer Price Index. When aggregate demand goes
rises, demand for labor also rises which decreases unemployment. However
because of diminishing returns, this relationship is logarithmic as opposed to
linear.
U = γ − β ln
M
p
β, γ > 0 [Todorova, 135] (1)
Take the derivative by time and we get
dU
dt
= −β(
d ln(M)
dt
−
d ln(p)
dt
) = −β(
M
M
−
p
p
) = −β(m − q) (2)
where U is the rate of unemployment, m = M
M
is the percent change in the
money supply and q = p
p
is the change in the price level divided by the price
level which is the definition of inflation.
In modern economies m (the percentage change in the money supply) is
based on the policy of a country’s central bank. If the central bank increases
the money supply then m is positive, on the other hand if the central bank
decreases the money supply then m is negative. There are many schemes
that a central bank can use to determine monetary policy and no two coun-
tries have the exact same monetary scheme. In this paper we are going to
3
4. examine three general schemes: constant, free floating, and inflation target-
ing. Free floating schemes are where the central bank is given free reign on
monetary policy. However they will almost always expand the monetary base
when unemployment is high, and reduce it when inflation is high. Inflation
targeting is when the central bank tries to bring inflation into a certain range
[Truman 5]. Constant monetary policy is when the central bank will expand
the monetary base at a constant rate without regard to unemployment or
the inflation rate.
For now we will assume that the central bank will have a constant mone-
tary policy. The change in unemployment is related to the difference between
the inflation rate and the monetary policy. If inflation is lower than the mon-
etary expansion, this will encourage spending, investment and exports which
will bring unemployment down. In essence the central bank is “tricking”
the economy into lower unemployment. In effect the central bank convinces
people that they have more purchasing power then they actually do. This
“overheats” the economy. On the other hand when inflation outstrips the
monetary policy, the average person loses purchasing power so consumption
decreases which increases unemployment.
In the long run the unemployment rate will reach an equilibrium which
Milton Friedman called the natural rate of unemployment (UN ) [Friedman,8].
It is “the level of unemployment that occurs in long term overall equilibrium
if market imperfections exist on the labour and commodity markets [Bofinger
101].” This rate can be different between countries and can even change over
time. However changes in the natural unemployment rate are usually due
to government policies or shifting demographics [Blanchard 176]. In other
words, the natural rate of unemployment cannot be changed by monetary
policy. However, in the short run it is possible for the unemployment rate to
deviate from the natural rate of unemployment by manipulating the interest
rate. From this we get the equation
dq
dt
= −α(U − UN ) α, UN > 0 (3)
When the unemployment level is lower than the natural rate of unemploy-
ment then people are spending and investing more and thus demand for all
goods and services go up. This causes prices to rise which increases inflation.
If unemployment is higher than the natural rate then people are spending
and investing less so inflation goes down. Therefore we now have a system
of linear equations that can be solved.
4
5. From (2) and (3) we get the following system of equations.
dq
dt
= −α(U − UN )
dU
dt
= −β(m − q)
(4)
The main assumptions in Todorova’s paper is that all the parameters are con-
stant. The central bank has a constant monetary policy, the natural rate of
unemployment doesn’t change, and the relation between inflation and unem-
ployment doesn’t change. Immediately we can see that the nonhomogenous
linear system has a steady state solution (m, UN ). The linear part of (7) is
represented by the matrix
0 −α
β 0
We find that the eigenvectors for this matrix ±
√
−βα
2
= ±i
√
βα
2
. Because β and
α are positive, the real part of the eigenvalues are zero. The solution to this
system form a family of periodic orbits with the critical point as their center.
3.1 Sample Model
To illustrate the system’s stability, we can populate the model with vari-
ables. Using the variables UN = 5, m = 2, β = .08 and α = .23. UN is based
off the US natural unemployment rate which is considered to be between 5%
and 6%. m is based off the Federal Reserve’s target inflation of 2% [2]. α and
β are based off a linear regressions taken from annual data taken between
1990 and 2007. [Cite data dropbox]. Starting with the initial condition of
2.1% inflation and an unemployment rate of ranging from 5% to 5.4%. and
letting t go from 0 to 40 we get Figure 1.
According to this model the economy is periodic. This makes sense math-
ematically because the eigenvalues of this matrix are purely imaginary. Also
the solution moves in a counterclockwise direction. This means that when
unemployment is low, inflation is increasing, because the economy is heating
up. When unemployment gets too high, then the economy starts to cool
down and inflation decreases. This simulates the business cycle, where un-
employment increases for a while, then decreases. Furthermore, Hoesk and
Zhan hypothesize that the economy would move in this direction in their
unemployment-inflation cycle [Hosek and Zahn 248]. However in real life the
economy does not fluctuate this regularly.
5
6. Figure 1: Red dot is the critical point. Black points are the initial conditions.
Notice that the solutions move in a clockwise direction.
4 Variable Monetary Policy
Holding m to be constant is a legitimate hypothesis. “The Federal Open
Market Committee judges that inflation at the rate of 2 percent ...is most
consistent over the longer run with the Federal Reserve’s mandate for price
stability and maximum employment.”[2] So taking a constant monetary pol-
icy would be a reasonable assumption. And during normal economic times
this tends to be true. This hypothesis breaks down during difficult economic
times. Looking at Figure 2 we can see that before 2008 that the growth of
the money supply was constant and stable. During these periods the un-
employment rate and inflation rates were relatively normal. However during
the Great Recession that started in August 2008 we can notice that the
monetary policy expanded drastically a few times. During this period the
Fed increased the money supply to bring down unemployment in a program
called Quantitative Easing.
The Fed should behave according to a few rules The monetary policy is
a function of unemployment and inflation: m = f(q, U). We assume that m
has the following properties
1. m( ¯m, UN ) = ¯m
2. mU ≥ 0
6
7. Figure 2: US Adjusted Monetary Base Feb 1984-Sept 2015[3]
3. mq ≤ 0
It is assumed that the Fed has a target monetary policy that it won’t deviate
from when the economy is doing well. This goal is denoted as ¯m and defined
as m( ¯m, UN ) = ¯m. When the economy is stable then the central bank does
not need to deviate from their stated goals. From our quote above we can see
that the value of ¯m is 2. If unemployment gets too high, then the Fed will
increase the monetary base in order to stimulate the economy. Therefore
mU ≥ 0. Lastly, if inflation gets too high then the Fed will decrease the
money supply in order to bring prices back down. Therefore mq ≤ 0.
Under these assumptions our linear system (4) becomes
dq
dt
= −α(U − UN )
dU
dt
= −β(m(q, U) − q)
(5)
Notice that ( ¯m, UN ) is still an equilibrium solution by property 1 of m. Using
these assumptions we can update our linearization matrix to include variable
monetary policy.
0 −α
−βmq( ¯m, UN ) + β −βmU ( ¯m, UN )
7
8. If we assume that the monetary policy is constant then mU = mq = 0. This
would give our original linearization matrix. Furthermore we can update our
eigenvalues.
−βmU ± (βmU )2 − 4αβ(1 − mq)
2
(6)
We know that α, β and 1 − mq are positive (property 3) therefore the eigen-
valuses real parts are negative whenever mU (UN , ¯m) < 0. This means that
solutions initially near the critical point will will always converge to the
critical point. How the solution converges depends on the relation between
(a)= (βmU )2
− 4αβ(1 − mq) and zero. If (a) is greater than zero then the
solution converges along one of the eigenvectors of the matrix. On the other
hand if (a) is less than zero then the solution spirals towards the critical
point.
4.1 m(U, q) = ¯m + ec1(U−UN )
− ec2(q− ¯m)
This is a simplistic model that a central bank could use to determine its
monetary policy. When the unemployment level is above the natural rate
the ec1(U−UN )
gets large and will start to dominate. This is equivalent to the
central bank expanding the money supply to decrease unemployment. On
the other hand when inflation exceeds the central bank’s target, −ec2(q− ¯m)
will dominate. The central bank is constricting the money supply to reduce
inflation. c1 and c2 are positive real numbers that represent the central bank’s
approach to monetary policy. A relatively high c1 represents an activist
central bank who are willing to reduce unemployment at the expense of
higher inflation. A relatively high c2 represents a stability-oriented central
bank that tries to maintain a low inflation rate[Bofinger 113]. In order to
maintain the three properties, c1 and c2 are both positive. At the critical
point (UN , ¯m), m(UN , ¯m) = ¯m+1−1 = ¯m, mU = c1 > 0 and mq = −c2 < 0.
Thus m fits our profile.
This equation has a few properties that make it ideal to study the three
rules effects on the system. First it is easy to calculate and adjust mU and
mq. Second, higher deviations lead to disproportionately larger reactions.
For example with
m = ¯m + c1(U − UN ) − c2(q − ¯m)
the increase in money supply is the same if unemployment goes from 5%
to 6% as it would if it went from 6% to 7%. This isn’t realistic. A 6%
8
9. unemployment rate is relatively benign while a 7% unemployment rate is
considered problematic. The following equation would also have increasing
responses.
m = ¯m + c1(U − UN )k1
− c2(q − ¯m)k2
where k1 and k2 are odd integers (even integers violate assumptions 2 and
3). The problem with this is that this complicates the modeling. Instead of
having to determine two variables, we would have to look over four. There
is nothing wrong with this equation, however the original m is simpler.
Replacing m into the original equations we get the system
dq
dt
= −α(U − UN )
dU
dt
= −β( ¯m + ec1(U−UN )
− ec2(q− ¯m)
− q)
(7)
giving us the coefficient matrix
0 −α
c2β + β −c1β
From this we can get the eigenvalues of
−c1β±
√
(c1β)2−4αβ(c2+1)
2
. If (c1)2
β >
4α(c2 + 1) then the solution will converge directly along some vector to the
fixed point. On the other hand if (c1)2
β < 4α(c2 + 1) then the solution will
spiral in towards the fixed point. The central bank’s approach to monetary
policy will affect the movement of the economy. The long term solution
remains constant.
4.2 An Illustration on Different policies
We will be reusing the numbers from section 3 in our updated model. This
gives us the following system.
U = −.08(2 + ec1(U−5)
− ec2(q−2)
− q)
q = −.28(U − 5)
(8)
From our analysis above, if c1 <
c2
2−14
14
then we have a stable node, however
if c1 >
c2
2−14
14
then we have a stable focus (See Figure 3).
Let’s assume that the central bank holds deviations from equilibrium
equally. In other words, a 6% unemployment is just as bad as a 3% inflation.
9
10. Figure 3: Bifurcation diagram for c1 and c2 between 0 and 10
If for c1 = c2 then for any real number h, m(UN + h, ¯m + h) = ¯m. Starting
simply c1 = c2 = 1, we get negative complex eigenvalues (−.08±
√
.992i
2
) so the
critical point is a stable focus. This is true for all c’s less than 14.93. What
Figure 4: c1 = c2 = 1 Figure 5: c1 = c2 = 14.94
happens if the central bank handles deviations more harshly? As you can
see in Figure 5, the solution converges directly when c1 = c2 = 14.94. Next,
we want to study other values that would produce a stable node. By taking
c1 = 7 and c2 = 1 our chart in Figure 6 that the critical point should be as
10
11. stable node. All the initial conditions arrived along the same vector.
Figure 6: c1 = 7 c2 = 1
4.2.1 Inflation Targeting
So far the examples have supposed that the central bank will try to
influence the economic output. This is not always the case. In Inflation
targeting the central bank attempts to achieve price stability by attempting
to bring inflation to a certain level [Truman 6]. In other words the central
bank ignores the unemployment rate and achieves long term stability by
keeping the inflation rate low. This policy means that that c1 = 0, m =
3 − ec2(q−2)
and our model becomes.
dq
dt
= −α(U − 5)
dU
dt
= −β(3 − ec2(q−2)
− q)
(9)
Because the eigenvalues are now purely imaginary, we need to see use other
methods to determine the long term behavior. However se see that (9) is a
Hamiltonian system with Hamilton
V =
(U − 5)2
β
+
1
α
q
2
ec2(s−2)
+ s − 3 ds (10)
11
12. ec2(s−2)
+ s − 3 is positive when s > 2 and negative when s < 2. Therefore
V (q, U) → ∞ as ||(q, U)|| → ∞.
V =
(U − 5)2
2β
+
1
α
q
2
ec2(s−2)
+ s − 3ds
˙V =
2U (U − 5)
β
+
2(ec2(q−2)
+ q − 3)q
α
˙V =
2(U − 5)(−β)(−ec2(q−2)
− q + 3)
β
+
2(ec2(q−2)
+ q − 3)(−α)(U − 5)
α
˙V = 2(ec2(q−2)
+ q − 3)(U − 5)) − 2(ec2(q−2)
+ q − 3)(U − 5)) = 0
(11)
It can be shown that this equation forms a closed shape that is symmetric
around U=5. If we are given δ > 0 determined by V (q0, U0), we can get
δ =
(U − 5)2
2β
+
2
c
ec(q−2)
+ q2
− 6q + 8 − 2
c
α
(U − 5)2
= 2β(δ −
2
c
ec(q−2)
+ q2
− 6q + 8 − 2
c
α
)
(12)
Because δ is constant and the integral
q
2
ec(s−2)
+s−3ds → +∞ as |q| → ∞
we can see that V is a closed path that is symmetric around U=5. That
means that the solution cannot diverge off to infinity nor can it converge to
the critical point. Thus the solution is periodic with a stable closed orbit
around the critical point.
By setting c2 to 0, 1, 2, 4 we can see how the central bank’s policy will
affect the economy. In figure 7 the blue path was the shows our original
model when m = ¯m = 2. By increasing c we can show that the range
of inflation’s will decrease while the range of unemployments will remain
relatively constant. From this we can see that by increasing c1 the solution
will converge faster than if we increase c2.
5 Expected inflation
One of the first major hurdles of the Phillips Curve was Stagflation in the
1970s. In an attempt to bring unemployment down, the FED increased the
money supply. The problem was people started to expect higher inflation,
so the effect of expanded monetary policy was reduced. In other words, to
12
13. Figure 7: Blue-c2 = 0, Black-c2 = 1, Red-c2 = 2, Cyan-c2 = 4
reduce the unemployment by the same amount, the FED needed to increase
inflation to higher levels. This phenomenon is called expected inflation(π).
We are going to first see how the model works with a constant monetary
policy, then we will create a experiment with the pseudo-monetary policy
discussed in section 4.
Our expectation inflation equation is based on the idea of adapted ex-
pectations. People will update their expectations when new information is
presented. In this context people have their idea of what inflation is going
to be based on past experiences. Thus the expected inflation will look like
π = j(q − π) j ∈ (0, 1] [Todorova, 134] (13)
If j=1 then people will base their expectations on the last period’s infla-
tion. The higher j is, the faster people will change their expectations. Lower
j’s lead to more stable expectations The expected inflation will have an effect
on both inflation and the unemployment rate. Up until now we have been
assuming that q = π. If the central bank is honest and consistent then as
time goes on, then q should approach π. Todorova simplifies the inflation to
a linear function of unemployment and expected inflation.
q = c − αU + hπ h ∈ (0, 1] [Todorova, 134]
π = j(c − αU + (h − 1)π) j ∈ (0, 1]
(14)
13
14. Figure 8: Expected inflation over time. Notice it starts to converge to somewhere
between 1% and 2%
What this means is that if we can show that U and π converge, then q
will also converge. In Todorova’s original model, U’ was a function of the
monetary policy and inflation. “When inflation is high for too long, this may
discourage people from saving, consequently reduce aggregate investment
and increase the the rate of unemployment [Todorova, 134].” However, this
sounds more like expected inflation than actual inflation. When we were
assuming expected inflation equaled actual inflation this was fine. However
now we need to update our unemployment function.
U = −β(m − π) (15)
The monetary policy should still be the same. In real life it is easier to
calculate actual inflation than expected inflation. The government has many
incentives to maintain data on inflation. Therefore there tends to be more
up to date data on actual inflation than expected inflation. Thus it is easier
to obtain inflation data than expected inflation data. However, because
we are looking in terms of U and π, we need to update our function from
m = f(q, U) to m = g(U, π) we get m = f(U, c − αU + hπ) where f holds the
same properties as m. This gives us the equations
mU = fU − αfq ≥ 0
mπ = h · fq ≤ 0
(16)
14
15. Therefore even though m now must be in terms of π and U, it still holds its
original traits. We can therefore check the stability of our system.
−j(1 − h) −jα
−βhfq + β −βmU
We get the eigenvalues of
−(j(1−h)+βmU )±
√
(j(1−h)+β ˙mU )2−4[β ˙mU j(1−h)−jβ2(hfq−1)]
2
.
Because all the variables except fq are positive and h < 1, we can conclude
that U, π, and, by extension, q, converge. The method of convergence de-
pends on the sign of (j(1 − h) + βmU )2
− 4(jβ2
(hfq − 1)). If this is greater
than or equal to zero then the series converges linearly, however if it is less
then zero the solution spirals in towards the center.
5.1 Examples
Up until this point we have defined the natural unemployment rate as
the rate of unemployment when the economy is steady. However there are
many ways to determine the natural unemployment: “the natural rate of
unemployment is the unemployment such that the actual inflation rate is
equal to the expected inflation rate.” [Blanchard 170] Using data from 1990
to 2007 I estimated h to be equal to .84. If we want to keep the natural rate
of unemployment we simply need to find c such that
q = c − (.23 · 5) + .84q
This is satisfied with c=1.47. Lastly, we will take a j=.5. j in this case
is an artificial variable because the actual variable was very small. In our
scenario, the expected inflation will change based on 1/2 of the difference
between expected and actual inflation. we get the following system.
q = 1.47 − .23U + .84qπ
U = −.08(2 + ec1(U−5)
− ec2(−.53−.23U+.84π)
− q)
π = .5(1.47 − .23U − .16π)
(17)
Thus our eigenvalues are equal to
−.08 − .08mU ± (.08 + .08mU )2 − 4(.0064mU − .0032(−.84c2 − 1))
2
15
16. Convergence will depend on wether 4(.0064mU −.0032(.84fq −1)) is greater or
less than (.08 + .08mU )2
.Starting with a constant monetary policy we know
that mU = 0 and fq = 0 so .0064 − 4 · .0032 < 0 so the series will spiral
towards the critical point (Figure 9).
Figure 9: Convergence when m = 2
Bringing in the previous function for variable monetary policy we can
see that fu = c1 and fq = c2 converges directly to the fixed point. We
can see that the traits of the free floating bankng policies the path’s con-
vergence didn’t change. However, the inflation targeting model (Figure 13),
actually converged. By factoring in the expected inflation we have actually
increased the convergence of the model. Before a constant monetary policy
was periodic. Furthermore inflation targeting is convergent not periodic.
6 Conclusion
When accounting for expected inflation, the monetary policy will converge
to the critical point. Furthermore more aggressive policies will lead to faster
convergence. However there are a few assumptions that must be taken into
account. First this is still a simple model, there are many things that it
doesn’t take into account, such as energy prices, foreign prices, interest rates
16
17. Figure 10: c1 = c2 = 1 Figure 11: c1 = c2 = 14.94
Figure 12: c1 = 7, c2 = 1 Figure 13: c1 = 0, c2 = 4
economic bubbles and busts etc. All of these can affect the inflation and
unemployment rate. Nowhere in this model does it show that a country’s
main export suddenly dropped in value, causing a spike in unemployment
and inflation. Second, this assumes that the central bank knows and targets
the natural rate of unemployment which might not always be the case. Also
the natural rate of unemployment might change over the long run. Lastly,
central banks tend not to use a formula to determine economic policy. If that
was the case, then most central banks would be run by a computer.
References
[1] Blanchard, Oliver. Macroeconomics. 5th ed. New York City: Prentice
Hall, 2011. 164-204.
17
18. [2] Board of Govoners of the Federal Reserve. Federal Reserve, Web. 30 Nov.
2015. http://www.federalreserve.gov/faqs/economy_14400.htm.
[3] Federal Reserve Bank of St. Louis, St. Louis Adjusted Monetary
Base, retrieved from FRED, Federal Reserve Bank of St. Louis
https://research.stlouisfed.org/fred2/series/BASE/, November 3, 2015.
[4] Friedman, Milton. ”The Role of Monetary Policy.” The American Eco-
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[5] Hosek, William R., and Frank Zahn. Monetary Theory, Policy and Fi-
nancial Markets. New York City: McGraw-Hill Book Company, 1977.
[6] Perko, Lawrence. Differential Equations and Dynamical Systems. 3rd ed.
New York City: Springer, 2001.
[7] Todorova, Tamara. ”The Economic Dynamics of Inflation and Unemploy-
ment,” Theoretical Economics Letters, Vol. 2 No. 2, 2012, pp. 133-140.
[8] Truman, Edwin M. Inflation Targeting in the World Economy. Washing-
ton, DC: Institute for International Economics, 2003.
[9] https://drive.google.com/folderview?id=
0ByXZyPgM4REnUWUweGhCRUs4MFU&usp=sharing
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