Lecture 10 Optimal Growth Endogenous Growth. Noah Williams
|
|
- Shonda McDonald
- 5 years ago
- Views:
Transcription
1 Lecture 10 Optimal Growth Endogenous Growth Noah Williams University of Wisconsin - Madison Economics 702 Spring 2018
2 Optimal Growth Path Recall we assume exogenous growth in population and productivity: A t N t = (1 + n)(1 + g)a t 1 N t 1 (1 + η)a t 1 N t 1 So now let s consider the optimal allocation: max β t U (C t ) {C t,k t+1 } t=0 subject to: C t = F(K t, N t ) K t+1 + (1 δ)k t, t, K 0 given This can be re-written as: max [β(1 + η) 1 σ ] t c1 σ t { c t, k t+1 } 1 σ t=0 subject to: c t = k α t (1 + η) k t+1 + (1 δ) k t
3 Characterizing the Optimal Growth Path Form the Lagrangian with β = β(1 + η) 1 σ : L = max ( { c t, k t+1 } t=0 ) β t c1 σ t 1 σ + λ t[ k t α (1 + η) k t+1 + (1 δ) k t c t ] First order conditions for any c t, and for k t+1, t > 0: (1 + η)λ t + λ t+1 [α k α 1 t+1 These imply the Euler equation: σ β t c t = λ t + 1 δ] = 0. (1 + η) c σ t = σ α 1 β c t+1 [α k t δ]
4 Optimal Balanced Growth Look for a steady state of the transformed optimal allocation. (1 + η)( c ) σ = β( c ) σ [α( k ) α δ] (1 + η) = β[α( k ) α δ] Or, recalling that β = 1/(1 + θ): f ( k ) = = 1 + η β(1 + η) 1 σ + δ 1 (1 + θ) (1 + η) σ + δ 1 δ + θ + ση δ + θ + σ(n + g)
5 Optimal Balanced Growth Therefore we have capital per unit of effective labor in the balanced growth path: k = ( α δ 1 + (1 + θ)(1 + η) σ ( ) 1 α 1 α δ + θ + σ(n + g) ) 1 1 α This generalizes the solution we had for the optimal allocation without growth. As in the Solow model, along a balanced growth path all level variables are growing at rate η n + g. Unlike the Solow model, the steady state depends on the household preferences, as the savings rates are determined optimally.
6 Qualitative Dynamics We can analyze the qualitative dynamics just as we did without productivity growth. The key equations of the model are now: (1 + η)u ( c t ) = β(1 + η) 1 σ U ( c t+1 )[f ( k t+1 ) + 1 δ] (1 + η) k t+1 = (1 δ) k t + f ( k t ) c t The dynamics work in much the same way, only now they depend on η. So we can analyze the effects of a change in n or g which lead to a change in η. In steady state, c t+1 = 0, and f ( k ) δ + θ + ση Also in steady state k t+1 = 0, so: c = f ( k) (δ + η) k
7 Phase Diagram of Optimal Growth Model c c=0: f (k*)=δ+θ+ση c* k=0: f(k)-(δ+η)k k* Phase diagram of the optimal growth model k
8 Effect of an Increase in n or g c c* c0 c f (k )=δ +θ+ση f (k*)=δ +θ+ση f(k)-(δ+η)k f(k)-(δ+η )k k k* Phase diagram: An increase in the growth rate η to η. As before, initial effect depends on the slope of the saddle path. k
9 Endogenous Growth Models Now briefly discuss some models which try to explain sources of growth endogenous growth models. An active research topic initiated in late 1980s. Romer (1986, 1990), Lucas (1988) most influential: models of R & D, human capital. More recently Acemoglu et al: role of institutions in growth.
10 What s in TFP? Institutions & Geography Aside from innovations (which we ll turn to next), infrastructure, institutions, and geography are also important. Interesting comparison: experiences of former colonies. Acemoglu, Johnson and Robinson (2001). Small initial differences in income. Differences in settlers mortality influenced whether colony was run for extraction or whether colonists developed institutions. Those colonies where institutions took hold developed faster. Large differences in outcomes still today!
11
12 What s in TFP? Ideas and Human Capital Relatively new branch of economic theory: endogenous growth theory seeks to explain how technical change happens. Simple endogenous growth model (AK model): aggregate production function Y = AK. (Ignore labor and population growth, could think of this as per capita production.) Not subject to diminishing returns: MPK is constant F K = Y K = A. Idea: Aggregate capital K captures not just increases in physical capital but changes in the makeup of that capital.
13 Human Capital as a Source of Growth Human capital: knowledge, skills, and training of individuals. As economies become richer they invest in human capital in the same proportion, offsetting the diminishing marginal product of physical capital alone. Explicitly: production depends on human capital H, physical capital K: Y = zh θ K 1 θ Say H = hk, so that human capital is constant fraction of physical, then letting A = zh θ : [ Y = z(hk) θ K 1 θ = zh θ] K = AK
14 Other Interpretations Research and development programs are part of capital investment. They increase the stock of knowledge, which offsets diminishing marginal products of capital accumulation. Learning by doing: as economies produce more they learn better how to produce.
15 Implications of the Endogenous Growth Model Again savings constant fraction s of output. So: K = sak δk Since Y = AK, Ẏ Y = K K = sa δ Growth of output depends on the saving rate, even in the long run. No steady state. Higher savings more human capital, R&D, learning by doing. So higher savings leads to productivity improvements and higher growth. Important implication, some evidence that measured TFP does depend on savings, human capital.
16 A More Explicit Model of Human Capital Cobb-Douglas aggregate production function: Y = K α H β (AN ) 1 α β Again we have constant returns to scale now in (K, H, N ). Human capital and labor enter with different coefficients. Society accumulates human capital according to: Ḣ = s h Y δh Capital accumulation equation: Technological progress: K = s k Y δk Ȧ A = g > 0. Labor force grows at constant rate: Ṅ N = n > 0.
17 Analyzing the Model Dividing the production function by AN : ỹ = k α hβ Decreasing returns to scale in per efficiency units. The evolution of inputs is determined by: k = s k kα hβ (n + g + δ) k h = s h kα hβ (n + g + δ) h System of two differential equations determining k, h.
18 Balanced Growth Path To find the BGP equate both equations to zero: From first equation: s k k α h β (n + g + δ) k = 0 s h k α h β (n + g + δ) h = 0 ( (n + g + δ) h = s k Plugging it in the second equation k 1 α ) 1 β ( (n + g + δ) n + g + δ s h k α s k 1 α (n + g + δ) k s k ( ) 1 s h n + g + δ s k = k 1 α β k s k k 1 α ) 1 β = 0
19 Finding the Balanced Growth Path 1 α 1 k β s h s k k = = ( n + g + δ 1 α β k β s k = s k s h k 1 α ) 1 β ( (n + g + δ s k ) 1 β ( k = ( h = s 1 β k s β h n+g+δ s α k s1 α h n+g+δ ) 1 1 α β ) 1 1 α β
20 The Balanced Growth Path Using the production function: ỹ = Y AN = k α hβ = ( s 1 β k s β ) α ( 1 α β h sk αs1 α h n + g + δ n + g + δ ) β 1 α β y = Y ( s 1 β N = k s β ) α ( 1 α β h s α ) β k s1 α 1 α β h A n + g + δ n + g + δ Given some initial value of technology A 0 we have: y = ( s 1 β k s β ) α ( 1 α β h s α ) β k s1 α 1 α β h A 0 e gt n + g + δ n + g + δ
21 Evaluating the Model Taking logs: log y = log A 0 + gt α + β log (n + g + δ) + 1 α β α + 1 α β log s β k + 1 α β log s h What if we have a lot of countries i = 1,..., n? We can assume that log A 0 = a + ε i Also assume that g and δ are constant across countries.
22
23 TFP growth rate, (Labor share=0.65, no returns to education) IDN IRL PRT MUS TUN CHL BWACOG MYS ZWE ITA ISR IND KEN COL URY BRA BEL SWESP NLD AUS GRC AUT DNK PAK PRY MAR USAGBR FRA ECU EGY GHA GTMLKA UGA BGD DOM SYRTUR CAN TTO ZAF DZA PAN MLI PHL ARG PER JAMEX BFA BOL NZL CHE ETH SLV CIV NPL HND MWI VEN SEN JOR CRI RWA BDI TZA BENCMR PNG MDG CAF MRT TGO NGA NER ZMB AGO MOZ ZAR NIC HKG KOR THA JPN FIN NOR Saving rate, Figure 1: Relation of TFP growth to saving rate SGP TFP growth rate, (Labor share=0.65, no returns to education) THA IDN PRT NOR TUN MUS ZWE BWA ITAMYS CHL COG JPNISR KEN BRAIND COL URYGRCAUT SWE PAK MAR PRY ECU GBR FRA ESP BEL FIN AUSDNK NLD USA GTM UGA BGD GHA DOM TUR LKA SYR EGY CAN DZA PAN ZAF ARGMEX PER TTO BFA MLI PHL JAM MWI CIV NPL HND BOL CHE NZL BDI TZA ETH SLV VEN SEN CRI RWA BEN PNG CMR MDG CAF MRT NGA NER ZMB TGO AGO MOZ ZAR NIC Human capital investment rate, Figure 2: Relation of TFP growth to schooling rate HKG SGP KOR IRL JOR 45
24 TFP growth rate, (Labor share=0.65, no returns to education) PRT NOR IRL THA IDN ITA JPN MUS CHL COG ISR TUN MYS ZWE BWA BEL FIN URY AUT GRC SWE DNK GBR FRA ESPNLD AUS IND BRA COL KEN USA MAR PAK ECU PRY CAN LKA EGY ARG CHE NZL TTO BGD GHA GTM TUR PAN DOM SYR JAM ZAF UGA PER BFA MLI PHL MEX DZA BOL NPL MWI HND SLV VENCIV ETH SEN CRI BDI TZA RWA PNG CMRBEN MDG CAF MRT NGA TGO AGO NER ZMB MOZ HKG KOR Labor force growth rate, Figure 3: Relation of TFP growth to labor force growth rate SGP ZAR NIC JOR TFP growth rate, (Labor share=0.65, 7% return to education) IRL IDN COG PRT MUSCHL ITA IND KEN TUN MYS COL URY BWA BRA BEL ZWEAUS DNK AUT ISR GTMLKA PAK PRY USAGBR SWESPGRC NLD FRA ECU UGA GHA BGDDOM CAN MLI EGY BOL TTO ZAF SYRTUR DZA ARGJAM PAN MWIPHL PERNZL MEX CHE SEN SLV NPL HND TZA CRI VEN RWA BENCMR PNG JOR MOZ CAF TGO NER ZAR NIC ZMB HKG KOR THA Saving rate, Figure 4: Relation of TFP growth to saving rate JPN FIN NOR SGP 46
Lecture 9 Endogenous Growth Consumption and Savings. Noah Williams
Lecture 9 Endogenous Growth Consumption and Savings Noah Williams University of Wisconsin - Madison Economics 702/312 Optimal Balanced Growth Therefore we have capital per unit of effective labor in the
More informationEconomic Growth: Lecture 1, Questions and Evidence
14.452 Economic Growth: Lecture 1, Questions and Evidence Daron Acemoglu MIT October 23, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 1 October 23, 2018 1 / 38 Cross-Country Income Differences Cross-Country
More informationECON 581. The Solow Growth Model, Continued. Instructor: Dmytro Hryshko
ECON 581. The Solow Growth Model, Continued Instructor: Dmytro Hryshko 1 / 38 The Solow model in continuous time Consider the following (difference) equation x(t + 1) x(t) = g(x(t)), where g( ) is some
More informationLecture Note 13 The Gains from International Trade: Empirical Evidence Using the Method of Instrumental Variables
Lecture Note 13 The Gains from International Trade: Empirical Evidence Using the Method of Instrumental Variables David Autor, MIT and NBER 14.03/14.003 Microeconomic Theory and Public Policy, Fall 2016
More informationInferring Latent Preferences from Network Data
Inferring Latent Preferences from Network John S. Ahlquist 1 Arturas 2 1 UC San Diego GPS 2 NYU 14 November 2015 very early stages Methodological extend latent space models (Hoff et al 2002) to partial
More informationENDOGENOUS GROWTH. Carl-Johan Dalgaard Department of Economics University of Copenhagen
ENDOGENOUS GROWTH Carl-Johan Dalgaard Department of Economics University of Copenhagen MOTIVATION AND SETTING THE SCENE How to sustain growth? Under standard assumptions (e.g., diminishing returns and
More informationAgriculture, Transportation and the Timing of Urbanization
Agriculture, Transportation and the Timing of Urbanization Global Analysis at the Grid Cell Level Mesbah Motamed Raymond Florax William Masters Department of Agricultural Economics Purdue University SHaPE
More information!" #$$% & ' ' () ) * ) )) ' + ( ) + ) +( ), - ). & " '" ) / ) ' ' (' + 0 ) ' " ' ) () ( ( ' ) ' 1)
!" #$$% & ' ' () ) * ) )) ' + ( ) + ) +( ), - ). & " '" ) () -)( / ) ' ' (' + 0 ) ' " ' ) () ( ( ' ) ' 1) )) ) 2') 3 45$" 467" 8" 4 %" 96$ & ' 4 )" 3)" ::" ( & ) ;: < ( ) ) =)+ ( " " " $8> " ') +? @ ::
More informationA re examination of the Columbian exchange: Agriculture and Economic Development in the Long Run
Are examinationofthecolumbianexchange: AgricultureandEconomicDevelopmentintheLongRun AlfonsoDíezMinguela MªDoloresAñónHigón UniversitatdeValéncia UniversitatdeValéncia May2012 [PRELIMINARYRESEARCH,PLEASEDONOTCITE]
More informationINSTITUTIONS AND THE LONG-RUN IMPACT OF EARLY DEVELOPMENT
DEPARTMENT OF ECONOMICS ISSN 1441-5429 DISCUSSION PAPER 49/12 INSTITUTIONS AND THE LONG-RUN IMPACT OF EARLY DEVELOPMENT James B. Ang * Abstract We study the role of institutional development as a causal
More informationLandlocked or Policy Locked?
Landlocked or Policy Locked? How Services Trade Protection Deepens Economic Isolation Ingo Borchert University of Sussex Based on research with Batshur Gootiiz, Arti Grover and Aaditya Mattoo FERDI ITC
More informationInternational Investment Positions and Exchange Rate Dynamics: A Dynamic Panel Analysis
International Investment Positions and Exchange Rate Dynamics: A Dynamic Panel Analysis Michael Binder 1 Christian J. Offermanns 2 1 Frankfurt and Center for Financial Studies 2 Frankfurt Motivation Empirical
More informationGrowth and Comparative Development - An Overview
Growth and Comparative Development - An Overview Department of Economics Brown University August 16, 2013 Evidence Fundamental Puzzles Regional Variations in Income Per Capita: 2000 Evidence Fundamental
More informationFor Adam Smith, the secret to the wealth of nations was related
The building blocks of economic complexity César A. Hidalgo 1 and Ricardo Hausmann a Center for International Development and Harvard Kennedy School, Harvard University, Cambridge, MA 02138 Edited by Partha
More informationGrowth: Facts and Theories
Notes on Growth: Facts and Theories Intermediate Macroeconomics Spring 2006 Guido Menzio University of Pennsylvania Growth In the last part of the course we are going to study economic growth, i.e. the
More informationWP/18/117 Sharp Instrument: A Stab at Identifying the Causes of Economic Growth
WP/18/117 Sharp Instrument: A Stab at Identifying the Causes of Economic Growth By Reda Cherif, Fuad Hasanov, and Lichen Wang 2 2018 International Monetary Fund WP/18/117 IMF Working Paper Institute for
More informationGrowth and Comparative Development
Growth and Comparative Development Oded Galor AEA Continuing Education Program Lecture I AEA 2014 Oded Galor Growth and Comparative Development Lecture I AEA 2014 1 / 61 Introduction Comparative Development
More informationLandlocked or Policy Locked?
Landlocked or Policy Locked? How Services Trade Protection Deepens Economic Isolation Ingo Borchert joint work with Batshur Gootiiz, Arti Grover and Aaditya Mattoo Development Research Group The World
More informationCompetition, Innovation and Growth with Limited Commitment
Competition, Innovation and Growth with Limited Commitment Ramon Marimon Universitat Pompeu Fabra, CREi and CREA Vincenzo Quadrini University of Southern California December 22, 2005 Abstract We study
More informationConsumption-led Growth
1 / 31 Consumption-led Growth Markus Brunnermeier markus@princeton.edu Pierre-Olivier Gourinchas pog@berkeley.edu Oleg Itskhoki itskhoki@princeton.edu University of Helsinki Helsinki, November 2018 Introduction
More informationIDENTIFYING MULTILATERAL DEPENDENCIES IN THE WORLD TRADE NETWORK
IDENTIFYING MULTILATERAL DEPENDENCIES IN THE WORLD TRADE NETWORK PETER R. HERMAN Abstract. When studying the formation of trade between two countries, traditional modeling has described this decision as
More informationGrowth and Comparative Development: An Overview
Growth and Comparative Development: An Overview Oded Galor Oded Galor Growth and Comparative Development 1 / 62 Introduction Comparative Development Income per Capita across the Globe in 2010 0-1000 1000-3000
More informationLecture 5 Dynamics of the Growth Model. Noah Williams
Lecture 5 Dynamics of the Growth Model Noah Williams University of Wisconsin - Madison Economics 702/312 Spring 2016 An Example Now work out a parametric example, using standard functional forms. Cobb-Douglas
More informationThe Out of Africa Hypothesis of Comparative Development Reflected by Nighttime Light Intensity
The Out of Africa Hypothesis of Comparative Development Reflected by Nighttime Light Intensity Quamrul Ashraf Oded Galor Marc Klemp April 26, 2014 Abstract This research establishes that migratory distance
More informationThe Diffusion of Development: Along Genetic or Geographic Lines?
MPRA Munich Personal RePEc Archive The Diffusion of Development: Along Genetic or Geographic Lines? Douglas L. Campbell and Ju Hyun Pyun August 2014 Online at https://mpra.ub.uni-muenchen.de/57933/ MPRA
More informationLecture notes on modern growth theory
Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic
More informationIntermediate Macroeconomics, EC2201. L2: Economic growth II
Intermediate Macroeconomics, EC2201 L2: Economic growth II Anna Seim Department of Economics, Stockholm University Spring 2017 1 / 64 Contents and literature The Solow model. Human capital. The Romer model.
More informationTrade Structure and Growth **
Trade Structure and Growth ** Daniel Lederman William F. Maloney Office of the Chief Economist for Latin America and the Caribbean The World Bank Washington, DC November 2003 Abstract: This paper examines
More informationCurse or Blessing? Natural Resources and Human Development
Curse or Blessing? Natural Resources and Human Development José Pineda and Francisco Rodríguez 1 Human Development Report Office Abstract This paper argues against a natural resource curse for human development.
More informationAssumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t )
6. Economic growth Let us recall the main facts on growth examined in the first chapter and add some additional ones. (1) Real output (per-worker) roughly grows at a constant rate (i.e. labor productivity
More informationSUPPLEMENTARY MATERIAL FOR:
SUPPLEMENTARY MATERIAL FOR: THE BUILDING BLOCKS OF ECONOMIC COMPLEXITY Cesar A. Hidalgo, Ricardo Hausmann Center for International Development and Harvard Kennedy School, Harvard University TABLE OF CONTENTS
More informationThe Solow Growth Model
The Solow Growth Model Lectures 5, 6 & 7 Topics in Macroeconomics Topic 2 October 20, 21 & 27, 2008 Lectures 5, 6 & 7 1/37 Topics in Macroeconomics From Growth Accounting to the Solow Model Goal 1: Stylized
More informationPTV Africa City Map (Standardmap)
PTV Africa City Map 2018.2 (Standardmap) Map version name (Core) Map version name (Logistic) Release date (Logistics) Map version name (Logistics) (new) PTV_Africa_City_Map_2018.2 Data provider(s) Technology
More informationLecture 15 Real Business Cycle Model. Noah Williams
Lecture 15 Real Business Cycle Model Noah Williams University of Wisconsin - Madison Economics 702/312 Real Business Cycle Model We will have a shock: change in technology. Then we will have a propagation
More informationRoots of Autocracy. January 26, 2017
Roots of Autocracy Oded Galor Marc Klemp January 26, 2017 Abstract This research explores the origins of the variation in the prevalence and nature of political institutions across the globe. It advances
More informationEndogenous Growth. Lecture 17 & 18. Topics in Macroeconomics. December 8 & 9, 2008
Review: Solow Model Review: Ramsey Model Endogenous Growth Lecture 17 & 18 Topics in Macroeconomics December 8 & 9, 2008 Lectures 17 & 18 1/29 Topics in Macroeconomics Outline Review: Solow Model Review:
More informationPTV Africa City Map 2017 (Standardmap)
PTV Africa City Map 2017 (Standardmap) Map version name (Core) Map version name (Logistic) Release date (Logistics) Map version name (Logistics) (new) PTV_Africa_City_Map_2017 Data provider(s) Technology
More informationThe Solow Model. Prof. Lutz Hendricks. January 26, Econ520
The Solow Model Prof. Lutz Hendricks Econ520 January 26, 2017 1 / 28 Issues The production model measures the proximate causes of income gaps. Now we start to look at deep causes. The Solow model answers
More informationEconomic Growth: Lecture 9, Neoclassical Endogenous Growth
14.452 Economic Growth: Lecture 9, Neoclassical Endogenous Growth Daron Acemoglu MIT November 28, 2017. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 28, 2017. 1 / 41 First-Generation Models
More informationMean and covariance models for relational arrays
Mean and covariance models for relational arrays Peter Hoff Statistics, Biostatistics and the CSSS University of Washington Outline Introduction and examples Models for multiway mean structure Models for
More information14.05: Section Handout #1 Solow Model
14.05: Section Handout #1 Solow Model TA: Jose Tessada September 16, 2005 Today we will review the basic elements of the Solow model. Be prepared to ask any questions you may have about the derivation
More informationExternal Economies of Scale and Industrial Policy: A View from Trade
External Economies of Scale and Industrial Policy: A View from Trade Dominick Bartelme (Michigan) Arnaud Costinot (MIT) Dave Donaldson (MIT) Andrés Rodríguez-Clare (Berkeley) External Economies of Scale
More informationA. Cuñat 1 R. Zymek 2
1 2 1 University of Vienna and CESifo, alejandro.cunat@univie.ac.at 2 University of Edinburgh and CESifo, robert.zymek@ed.ac.uk and Outline accounting: quantitative assessment of the contribution of measurable
More informationSolow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4
Solow Growth Model Michael Bar February 28, 208 Contents Introduction 2. Some facts about modern growth........................ 3.2 Questions..................................... 4 2 The Solow Model 5
More informationPolitical Economy of Institutions and Development. Lecture 7: The Role of the State and Different Political Regimes
14.773 Political Economy of Institutions and Development. Lecture 7: The Role of the State and Different Political Regimes Daron Acemoglu MIT February 28, 2013. Daron Acemoglu (MIT) Political Economy Lecture
More informationOne-Sector Models of Endogenous Growth. Instructor: Dmytro Hryshko
One-Sector Models of Endogenous Growth Instructor: Dmytro Hryshko 1 Mid-1980s: dissatisfaction with exogenously driven explanations of long-run productivity growth. 2 It led to construction of models in
More informationIs the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-oecd countries
Is the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-oecd countries Mario Cerrato Department of Economics University of Glasgow Christian
More informationUniversity of Groningen. Corruption and governance around the world Seldadyo, H.
University of Groningen Corruption and governance around the world Seldadyo, H. IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please
More informationResearch Article Diagnosing and Predicting the Earth s Health via Ecological Network Analysis
Discrete Dynamics in Nature and Society Volume 2013, Article ID 741318, 10 pages http://dx.doi.org/10.1155/2013/741318 Research Article Diagnosing and Predicting the Earth s Health via Ecological Network
More informationChapter 9 Solow. O. Afonso, P. B. Vasconcelos. Computational Economics: a concise introduction
Chapter 9 Solow O. Afonso, P. B. Vasconcelos Computational Economics: a concise introduction O. Afonso, P. B. Vasconcelos Computational Economics 1 / 27 Overview 1 Introduction 2 Economic model 3 Computational
More informationEcon 204A: Section 3
Econ 204A: Section 3 Ryan Sherrard University of California, Santa Barbara 18 October 2016 Sherrard (UCSB) Section 3 18 October 2016 1 / 19 Notes on Problem Set 2 Total Derivative Review sf (k ) = (δ +
More information004: Macroeconomic Theory
004: Macroeconomic Theory Lecture 22 Mausumi Das Lecture Notes, DSE November 11, 2014 Das (Lecture Notes, DSE) Macro November 11, 2014 1 / 12 AK Production Technology: First Step Towards Endogenous Growth?
More informationComparative advantage in routine production
Comparative advantage in routine production Liza Archanskaia, Jo Van Biesebroeck, Gerald Willmann KU Leuven Universität Bielefeld September 19, 2017 Motivation Our starting point We want to understand
More informationThe Solow Growth Model
The Solow Growth Model 1. Set-Up 2. Dynamics, Simulations and Steady-States 3. Comparative Dynamics 4. Golden Rule 5. Convergence 1 Set-Up Closed economy, single good produced each period, Yt. Discrete
More informationClimate Change and Food Security: Do Spatial Spillovers Matter?
Climate Change and Food Security: Do Spatial Spillovers Matter? Eric Nazindigouba Kere, Somlanare Romuald Kinda To cite this version: Eric Nazindigouba Kere, Somlanare Romuald Kinda. Climate Change and
More informationGrowth. Growth Theory. Mark Huggett 1. 1 Georgetown. January 26, 2018
Growth Theory Mark Huggett 1 1 Georgetown January 26, 2018 Growth Theory: The Agenda 1. Facts motivating theory 2. Basic Solow model 3. Model properties 4. How to use the model 5. Full Solow model 6. Use
More informationRamsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path
Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ryoji Ohdoi Dept. of Industrial Engineering and Economics, Tokyo Tech This lecture note is mainly based on Ch. 8 of Acemoglu
More informationAdvanced Economic Growth: Lecture 8, Technology Di usion, Trade and Interdependencies: Di usion of Technology
Advanced Economic Growth: Lecture 8, Technology Di usion, Trade and Interdependencies: Di usion of Technology Daron Acemoglu MIT October 3, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 8 October 3,
More informationMacroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PS 5, preliminary version
Macroeconomics I, UPF Professor ntonio Ciccone SOUTIONS PS 5, preliminary version 1 The Solow K model with transitional dynamics Consider the following Solow economy: production is determined by Y F (K,
More informationLectures 7: Growth Model and the Data
Lectures 7: Growth Model and the Data ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 2014 1/21 Plan of Lecture The growth model and the data 1 steady states and the data 2 choosing
More informationECON 402: Advanced Macroeconomics 1. Advanced Macroeconomics, ECON 402. New Growth Theories
ECON 402: Advanced Macroeconomics 1 Advanced Macroeconomics, ECON 402 New Growth Theories The conclusions derived from the growth theories we have considered thus far assumes that economic growth is tied
More informationDynamic Macroeconomics: Problem Set 4
Dynamic Macroeconomics: Problem Set 4 Universität Siegen Dynamic Macroeconomics 1 / 28 1 Computing growth rates 2 Golden rule saving rate 3 Simulation of the Solow Model 4 Growth accounting Dynamic Macroeconomics
More informationEndogenous Growth: AK Model
Endogenous Growth: AK Model Prof. Lutz Hendricks Econ720 October 24, 2017 1 / 35 Endogenous Growth Why do countries grow? A question with large welfare consequences. We need models where growth is endogenous.
More informationAdvanced Macroeconomics
Advanced Macroeconomics Endogenous Growth Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 1 / 18 Introduction The Solow and Ramsey models are exogenous growth
More informationChapter 9.D Services Trade Data
Chapter 9.D Services Trade Data Arjan Lejour, Nico van Leeuwen and Robert A. McDougall 9.D.1 Introduction This paper has two aims. First of all, it presents CPB s contribution of bilateral services trade
More informationExploring the World of Growth and Development
Exploring the World of Growth and Development Ping Wang Department of Economics Washington University in St. Louis January 2018 1 Data source: Acemoglus (2009), Aghion-Howitt (2009), Jones (1998, 2015)
More informationLecture 5: The neoclassical growth model
THE UNIVERSITY OF SOUTHAMPTON Paul Klein Office: Murray Building, 3005 Email: p.klein@soton.ac.uk URL: http://paulklein.se Economics 3010 Topics in Macroeconomics 3 Autumn 2010 Lecture 5: The neoclassical
More information14.452: Introduction to Economic Growth Problem Set 4
14.452: Introduction to Economic Growth Problem Set 4 Daron Acemoglu Due date: December 5, 12pm noon Please only hand in Question 3, which will be graded. The rest will be reviewed in the recitation but
More informationDany Bahar. Ricardo Hausmann. Cesar A. Hidalgo. Harvard Kennedy School. Harvard Kennedy School MIT. August 2013 RWP
Neighbors and the Evolution of the Comparative Advantage of Nations: Evidence of International Knowledge Diffusion? Faculty Research Working Paper Series Dany Bahar Harvard Kennedy School Ricardo Hausmann
More informationGeneral motivation behind the augmented Solow model
General motivation behind the augmented Solow model Empirical analysis suggests that the elasticity of output Y with respect to capital implied by the Solow model (α 0.3) is too low to reconcile the model
More informationDEPARTMENT OF ECONOMICS Fall 2015 P. Gourinchas/D. Romer MIDTERM EXAM
UNIVERSITY OF CALIFORNIA Economics 202A DEPARTMENT OF ECONOMICS Fall 2015 P. Gourinchas/D. Romer MIDTERM EXAM The exam consists of two parts. There are 85 points total. Part I has 18 points and Part II
More informationEconomic Growth
MIT OpenCourseWare http://ocw.mit.edu 14.452 Economic Growth Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 14.452 Economic Growth: Lecture
More informationExploring the World of Growth and Development
Exploring the World of Growth and Development Ping Wang Department of Economics Washington University in St. Louis January 2018 1 A. The Big Picture 1. Long Term Development of the World Economy Five ancient
More informationLecture 3 - Solow Model
Lecture 3 - Solow Model EC308 Advanced Macroeconomics 16/02/2016 (EC308) Lecture 3 - Solow Model 16/02/2016 1 / 26 Introduction Solow Model Sometimes known as Solow-Swan Model: Solow (1956): General Production
More informationMaster 2 Macro I. Lecture 8 : Empirical studies of convergence
2012-2013 Master 2 Macro I Lecture 8 : Empirical studies of convergence Franck Portier (based on Gilles Saint-Paul lecture notes) franck.portier@tse-fr.eu Toulouse School of Economics Version 1.1 14/10/2012
More informationIntroduction to Economic Growth. Daron Acemoglu MIT Department of Economics
14.451 Introduction to Economic Growth Daron Acemoglu MIT Department of Economics January 2006 ii Contents I Introduction 1 1 StylizedFactsofEconomicGrowthandDevelopment 5 1.1 A Quick Look at the Facts...
More informationFrom Difference to Differential Equations I
From Difference to Differential Equations I Start with a simple difference equation x (t + 1) x (t) = g(x (t)). (30) Now consider the following approximation for any t [0, 1], x (t + t) x (t) t g(x (t)),
More informationGeneric Analysis of Endogenous Growth Models
c November 20, 2017, Christopher D. Carroll Endogenous Generic Analysis of Endogenous Growth Models The neoclassical theory of economic growth, as formulated by Solow (1956), and Cass (1965)-Koopmans (1965),
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1.1, Exogenous Growth Topics in Growth, Part 2 June 11, 2007 Lecture 1.1, Exogenous Growth 1/76 Topics in Growth, Part 2 Growth Accounting: Objective and Technical Framework
More informationNew Notes on the Solow Growth Model
New Notes on the Solow Growth Model Roberto Chang September 2009 1 The Model The firstingredientofadynamicmodelisthedescriptionofthetimehorizon. In the original Solow model, time is continuous and the
More informationEquilibrium in a Production Economy
Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in
More informationEconomics 202A Suggested Solutions to Problem Set 5
Economics 202A Suggested Solutions to Problem Set 5 David Romer/Galina Hale Spring 1999 1 Romer 3.1. Our R&D model without a capital is Y (t) = A(t)(1 a L )L(t) (1) Ȧ(t) = B[a L L(t)] A(t) θ θ
More informationValue added trade: A tale of two concepts
Value added trade: Robert Stehrer The Vienna Institute for International Economic Studies (wiiw) Version: 2012-12-09 December 10-11, 2012 - CompNet workshop ECB Frankfurt, Germany. Overview Two concepts
More informationThe Romer Model. Prof. Lutz Hendricks. February 7, Econ520
The Romer Model Prof. Lutz Hendricks Econ520 February 7, 2017 1 / 28 Issues We study models where intentional innovation drives productivity growth. Romer model: The standard model of R&D goes back to
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1, Endogenous Growth Economic Policy in Development 2, Part 2 March 2009 Lecture 1, Exogenous Growth 1/104 Economic Policy in Development 2, Part 2 Outline Growth Accounting
More informationEconomics 2: Growth (Growth in the Solow Model)
Economics 2: Growth (Growth in the Solow Model) Lecture 3, Week 7 Solow Model - I Definition (Solow Model I) The most basic Solow model with no population growth or technological progress. Solow Model
More informationLecture 2: Intermediate macroeconomics, autumn Lars Calmfors
Lecture 2: Intermediate macroeconomics, autumn 2008 Lars Calmfors 1 GDP per capita, percent of OECD average, PPP-adjusted Position 1970 Index Position 1980 Index 1 Switzerland 154 1 USA 140 2 USA 147 2
More informationIntroduction to Real Business Cycles: The Solow Model and Dynamic Optimization
Introduction to Real Business Cycles: The Solow Model and Dynamic Optimization Vivaldo Mendes a ISCTE IUL Department of Economics 24 September 2017 (Vivaldo M. Mendes ) Macroeconomics (M8674) 24 September
More informationproblem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves
More informationExam 1. Econ520. Fall 2013
Exam 1. Econ520. Fall 2013 Professor Lutz Hendricks UNC Instructions: Answer all questions. Clearly number your answers. Write legibly. Do not write your answers on the question sheets. Explain your answers
More informationOnline Appendix of the paper " How does sovereign bond market integration relate to fundamentals and CDS spreads?"
Online Appendix of the paper " How does sovereign bond market integration relate to fundamentals and CDS spreads?" Appendix A.1 - Summary statistics for sovereign bond returns Appendix A.2 - Correlations
More informationNeoclassical Models of Endogenous Growth
Neoclassical Models of Endogenous Growth October 2007 () Endogenous Growth October 2007 1 / 20 Motivation What are the determinants of long run growth? Growth in the "e ectiveness of labour" should depend
More informationEconometrics I KS. Module 1: Bivariate Linear Regression. Alexander Ahammer. This version: March 12, 2018
Econometrics I KS Module 1: Bivariate Linear Regression Alexander Ahammer Department of Economics Johannes Kepler University of Linz This version: March 12, 2018 Alexander Ahammer (JKU) Module 1: Bivariate
More informationNeoclassical Business Cycle Model
Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy
More informationThe Augmented Solow Model Revisited
The Augmented Solow Model Revisited Carl-Johan Dalgaard Institute of Economics University of Copenhagen February, 2005 Abstract This note briefly discusses some recent (re-)investigations of the (augmented)
More informationEquating output per worker to GDP per capita, the growth rate of GDP per capita
3 Homework 3 1. We have seen in class Kaldor s stylized facts of growth in developed countries. The Cobb-Douglas production function is used to replicate fact a. In this exercise, you are asked to show
More information1. Basic Neoclassical Model (Solow Model) (April 14, 2014)
Prof. Dr. Thomas Steger Advanced Macroeconomics I Lecture SS 14 1. Basic Neoclassical Model (Solow Model) (April 14, 2014) Introduction Model setup Intensive production function Capital accumulation The
More informationTHE SOLOW-SWAN MODEL WITH A NEGATIVE LABOR GROWTH RATE
Journal of Mathematical Sciences: Advances and Applications Volume 9, Number /,, Pages 9-38 THE SOLOW-SWAN MODEL WITH A NEGATIVE LABOR GROWTH RATE School of Economic Mathematics Southwestern University
More informationFIRST-TIME COLLEGE OTHER TOTAL FIRST GRAND GEOGRAPHIC ORIGIN UNDERGRADUATES UNDERGRADUATES GRADUATES PROFESSIONAL TOTAL
Report ID: USSR8071-IPED Page No. 1 Jurisdiction: ON-CAMPUS MISSOURI (BY COUNTY) 001 ADAIR 0 0 2 0 2 0 2 1 2 0 7 002 ANDREW 0 0 10 1 10 1 0 4 4 0 19 003 ATCHISON 0 0 2 1 2 1 0 0 1 0 4 004 AUDRAIN 0 0 3
More informationGLOBAL VS. GROUP-SPECIFIC BUSINESS CYCLES: THE IMPORTANCE OF DEFINING THE GROUPS
Number 334 January 2018 GLOBAL VS. GROUP-SPECIFIC BUSINESS CYCLES: THE IMPORTANCE OF DEFINING THE GROUPS Tino Berger and Marcus Wortmann ISSN: 1439-2305 Global vs. group-specific business cycles: The importance
More information