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Author: pmichaillat

content/courses/c1.md

@@ -55,7 +55,7 @@ author: "Pascal Michaillat"
 description: "This course presents a matching model of unemployment and uses it to study unemployment fluctuations, job rationing, and labor market policies." 
 summary: "This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance." 
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-    image: "/c1.png"
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     alt: "Rationing and frictional unemployment in the United States, 1964–2009"
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content/courses/c2.md

@@ -35,7 +35,7 @@ author: "Pascal Michaillat"
 description: "This graduate course presents matching models of economic slack and uses them to study business-cycle fluctuations, monetary policy, and fiscal policy." 
 summary: "This graduate course presents various matching models of economic slack. It uses them to study business-cycle fluctuations; Keynesian, classical, and frictional unemployment; optimal monetary policy and the zero lower bound; and optimal government spending." 
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-    image: "/c2.png"
+    image: "/c2s.png"
     alt: "Optimal monetary policy and optimal government spending in the dynamic model of slack"
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content/courses/c3.md

@@ -14,7 +14,7 @@ author: "Pascal Michaillat"
 description: "This graduate course covers basic mathematical methods for macroeconomics: dynamic programming, optimal control, and differential equations." 
 summary: "This graduate course covers basic mathematical methods for macroeconomics: dynamic programming, optimal control, and differential equations." 
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-    image: "/c3.png"
+    image: "/c3s.png"
     alt: "Phase diagram depicting a saddle path"
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content/courses/c4.md

@@ -24,7 +24,7 @@ author: "Pascal Michaillat"
 description: "This undergraduate course covers IS-LM model of business cycles, matching model of unemployment, inflation, and Malthusian and Solowian models of growth."
 summary: "This undergraduate course introduces macroeconomic concepts—such as GDP and inflation—and covers the IS-LM model of business cycles, matching model of unemployment, Phillips curve, Malthusian model of growth, and Solowian model of growth."
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-    image: "/c4.png"
+    image: "/c4s.png"
     alt: "Comparative statics in a matching model of unemployment"
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content/courses/c5.md

@@ -8,7 +8,7 @@ author: "Pascal Michaillat"
 description: "This minicourse describes business cycles, develops a matching model to explain them, and discusses how monetary and fiscal policy can tame them."
 summary: "This minicourse presents basic facts about business cycles. It then develops a matching model to explain these business-cycle facts. Finally, it explains how monetary policy and government spending should be designed to tame business cycles." 
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-    image: "/c5.png"
+    image: "/c5s.png"
     alt: "Unemployment and GDP over the business cycle"
     relative: false
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content/design/d1.md

@@ -7,7 +7,7 @@ author: "Pascal Michaillat"
 description: "This template produces an academic presentation with LaTeX and Beamer. The presentation follows typographical best practices and has a minimalist design."
 summary: "This template produces an academic presentation with LaTeX and the Beamer class. The presentation follows typographical best practices and has a minimalist design."
 cover:
-    image: "/d1.png"
+    image: "/d1s.png"
     alt: "Presentation slide produced with template"
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content/design/d2.md

@@ -7,7 +7,7 @@ author: "Pascal Michaillat"
 description: "This template produces an academic paper with LaTeX. The paper follows typographical best practices and has a minimalist design."
 summary: "This template produces an academic paper with LaTeX. The paper follows typographical best practices and has a minimalist design." 
 cover:
-    image: "/d2.png"
+    image: "/d2s.png"
     alt: "Paper page produced with template"
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content/design/d3.md

@@ -7,7 +7,7 @@ author: "Pascal Michaillat"
 description: "This collection of commands makes it easy to write mathematical expressions with LaTeX while automatically respecting the rules of mathematical typography." 
 summary: "This collection of commands makes it easy to write mathematical expressions with LaTeX while automatically respecting the rules of mathematical typography." 
 cover:
-    image: "/d3.png"
+    image: "/d3s.png"
     alt: "Mathematical expressions produced with commands"
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content/design/d4.md

@@ -6,7 +6,7 @@ author: "Pascal Michaillat"
 description: "This script produces a set of scientific figures with MATLAB. The figures adhere to best practices for the visual display of quantitative information."
 summary: "This script produces a set of scientific figures with MATLAB. The figures adhere to best practices for the visual display of quantitative information."
 cover:
-    image: "/d4.png"
+    image: "/d4s.png"
     alt: "Figure produced with script"
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content/design/d5.md

@@ -6,7 +6,7 @@ author: "Pascal Michaillat"
 description: "This template produces a personal academic website with Hugo. The website has a minimalist design and is hosted on GitHub Pages."
 summary: "This template produces a personal academic website with Hugo. The website has a minimalist design based on the PaperMod theme and is hosted on GitHub Pages." 
 cover:
-    image: "/d5.png"
+    image: "/d5s.png"
     alt: "Webpage produced with template"
     relative: false
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public/c1/index.html

@@ -30,12 +30,12 @@
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 <meta name="twitter:title" content="Mathematics for Macroeconomics"/>
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@@ -73,7 +73,7 @@
   "articleBody": "Introduction This course covers basic mathematical methods to study dynamical systems, in discrete time and in continuous time. Dynamical systems are systems that involve more than one time-period; they are prevalent in macroeconomics. We first discuss dynamic programming, which is a method to solve dynamic optimization problems in discrete time. We then turn to optimal control, which is a method to solve dynamic optimization problems in continuous time. Finally, we show how to solve differential equations, which are used to describe continuous-time dynamical systems.\nDynamic programming This section covers dynamic programming, which is a method to solve dynamic optimization problems in discrete time. The key concepts of dynamic programming are introduced in a simple, deterministic consumption-saving problem. Then randomness is introduced into the consumption-saving problem, and the stochastic problem is solved with dynamic programming. As a further application, a Real Business-Cycle model is solved with dynamic programming. Finally, we discuss how to solve general problems with dynamic programming.\nThis section also shows that optimizing via dynamic programming yields the same results as optimizing via the Lagrangian approach. There is a certain obsession with dynamic programming in macroeconomics, but sometimes you will find that it is easier and more intuitive to use the Lagrangian method.\nLecture notes Problem set Reference: Acemoglu (2008, chapter 6) Optimal control This section studies optimal control, which is a method to solve dynamic optimization problems in continuous time. We start by formulating the consumption-saving problem in continuous time. The continuous-time problem is solved first with a present-value Hamiltonian, then with a current-value Hamiltonian. (Both approaches are equivalent.) Then we discuss the optimality conditions for general optimization problems solved by optimal control. We also establish the connection between these optimality conditions and the optimality conditions obtained via dynamic programming. To conclude, we derive and discuss the Hamilton-Jacobi-Bellman equation.\nLecture notes Problem set Reference: Acemoglu (2008, chapter 7) Differential equations This third section introduces differential equations, which are used to describe continuous-time dynamical systems. We first solve linear first-order differential equations. We then move to linear systems of first-order differential equations. Next, we show how to derive the properties of a linear system of first-order differential equations by drawing its phase diagram. Finally, we turn to nonlinear systems of first-order differential equations—which are common in macroeconomics. Although such system cannot be solved explicitly, its properties can be characterized by constructing its phase diagram.\nLecture notes Problem set Reference: Hirsch, Smale, Devaney (2013, chapters 1–6) Conclusion To conclude, a little more practice and an application. The problem set below brings together all the material from the course. And the paper below applies the course’s techniques to analyze the New Keynesian model in normal times and at the zero lower bound. Outside of growth theory, optimal control and differential equations are not used very much. Yet they are powerful tools to obtain theoretical results not only in long-run macroeconomics but also in short-run macroeconomics. For instance, as the paper shows, you can use them to analyze the New Keynesian model. It is easy to set up the model in continuous time, solve the household’s problem with optimal control, and study the model’s properties in normal times and at the zero lower bound using phase diagrams. The analysis is short and simple, and it offers many insights that are difficult to obtain in discrete time. For instance, with the phase diagrams, it is easy to understand where the anomalies of the New Keynesian model at the zero lower bound come from—the collapse of output and inflation collapse to implausibly low levels, and the implausibly large effects of government spending and forward guidance. It is also easy to understand how to resolve these anomalies.\nCumulative problem set Application of optimal control and differential equations to New Keynesian model ",
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   "dateModified": "2024-07-01T00:00:00Z",
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static/c1.png renamed to public/c1s.png

@@ -30,12 +30,12 @@
 <meta property="og:description" content="This undergraduate course covers IS-LM model of business cycles, matching model of unemployment, inflation, and Malthusian and Solowian models of growth." />
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-<meta name="twitter:image" content="https://pascalmichaillat.org/c4.png" />
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 <meta name="twitter:title" content="Intermediate Macroeconomics"/>
 <meta name="twitter:description" content="This undergraduate course covers IS-LM model of business cycles, matching model of unemployment, inflation, and Malthusian and Solowian models of growth."/>
 
@@ -73,7 +73,7 @@
   "articleBody": "Introduction This course explores core topics in macroeconomics, including national statistics, consumption and saving, unemployment, inflation, business cycles, monetary and fiscal policy, economic growth, and population dynamics. The course discusses short-run and long-run economic fluctuations in the United States and abroad. It also presents models describing such fluctuations: the IS-LM model of business cycles, the matching model of unemployment, models of inflation, the Malthusian model of pre-industrial growth, and the Solowian model of modern growth.\nIntroductory slides Overview of macroeconomics Introductory reference Akerlof (2002) – This essay discusses macroeconomic models and their assumptions, and it isolates six macroeconomic phenomena that macroeconomic models should be able to explain. Macroeconomic concepts This section introduces key macroeconomic concepts: gross domestic product (GDP), inflation, and unemployment.\nLecture slides The world Defining GDP GDP over Time Composition of GDP Inflation Unemployment References Kuznets (1934) – This report produces the first estimates of GDP in the United States. Kuznets (1952) – This paper measures GDP in the United States between 1869 and 1948. Homework Quiz on macroeconomic concepts Problem set on macroeconomic concepts IS-LM model of business cycles This section presents the IS-LM model. Its goal is to explain the fluctuations of GDP observed over the business cycle. The model is also useful to understand the effects of monetary and fiscal policy.\nLecture slides Expenditure function IS submodel LM submodel OMO, ZLB, and money multiplier IS and LM curves Recessions Monetary and fiscal policy References Hicks (1937) – This paper builds the IS-LM model from Keynes’s General Theory. Krugman (2018) – This essay argues that the IS-LM is still good enough for policy work. Homework Quiz on IS-LM model of business cycles Problem set on IS-LM model of business cycles Matching model of unemployment The IS-LM model does not feature unemployment, which is problematic because high unemployment is the most costly consequence of recessions. To explain the existence of unemployment and the fluctuations of unemployment over the business cycle, this section develops a matching model of unemployment.\nLecture slides Matching function Labor supply Labor demand Wages Equilibrium of the matching model Labor-market policies Unemployment types References Michaillat (2012) – This paper shows how to introduce job rationing into a matching model of unemployment. It also shows that a mild amount of wage rigidity is sufficient to generate realistic fluctuations in unemployment over the business cycle. Landais, Michaillat, Saez (2018) – This paper develops a static matching model of unemployment. It represents its equilibrium with labor demand and supply curves in an employment-tightness plane. Homework Quiz on matching model of unemployment Problem set on matching model of unemployment Models of inflation This section introduces the Phillips curve and discusses fluctuations in inflation over the business cycle. It also briefly presents the quantity theory of inflation and discusses episodes of hyperinflation.\nLecture slides Phillips curve and quantity theory References Phillips (1958) – This paper discovers a negative relation between unemployment and wage inflation in the United Kingdom. Samuelson, Solow (1960) – This paper discovers a negative relation between unemployment and price inflation in the United States. (It also finds a negative relation between unemployment and wage inflation in the United States.) Homework Quiz on models of inflation Malthusian model of growth Moving away from short-run, business-cycle fluctuations, this section turns to long-run macroeconomic fluctuations. It describes long-run fluctuations in the pre-industrial period using the Malthusian model of growth.\nLecture slides Overview of the Malthusian model Population Output per worker in the Malthusian model Reference Ashraf, Galor (2011) – This paper describes fluctuations in population and output per worker in the pre-industrial era. It then develops the Malthusian model of growth to explain these observations. Homework Quiz on Malthusian model of growth Problem set on Malthusian model of growth Solowian model of growth This final section describes long-run fluctuations in the modern, industrial era using the Solowian model of growth.\nLecture slides Production and saving Output per worker in the Solowian model Golden rule Technological progress Balanced growth Reference Solow (1956) – This paper develops the basic Solowian model of growth. Solow (1957) – This paper adds technical progress to the Solowian model of growth. Homework Quiz on Solowian model of growth Problem set on Solowian model of growth ",
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