Numerical methods for analyzing nonstationary dynamic economic models and their applications

149 Pages·2015·1.72 MB·English

by  Inna Tsener

Numerical methods for analyzing
nonstationary dynamic economic models
and their applications

Inna Tsener
Departamento de Fundamentos del Ana´lisis Econo´mico
Facultad de Ciencias Econ´omicas y Empresariales
Numerical methods for analyzing
nonstationary dynamic economic models
and their applications
Inna Tsener
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Memoria presentada para aspirar al grado de
DOCTORA POR LA UNIVERSIDAD DE ALICANTE
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Mencio´n Doctora Internacional
Doctorado en Econom´ıa Cuantitativa
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Dirigida por: Prof. Lilia Maliar, Prof. Serguei Maliar

To my parents
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Acknowledgements
I would like to express my deep gratitude to my thesis supervisors Lilia Maliar and
SergueiMaliarforthesupportandguidanceduringthedevelopmentofthisthesis. Their
constructive suggestions and useful critiques improved this research work significantly.
I would like to thank the members of the Department of Economics and the partici-
pants of its seminars for creating an optimal research environment. My grateful thanks
are intended to former and present directors of the department Juan Mora and Lola
Collado. I would also like to thank Jose Agullo, Pedro Albarran, Vadym Lepetyuk,
Adam Sanjurjo and Francesco Turino for the advices and help provided during the last
year of my doctoral studies.
I owe my deepest thanks to colleagues Nathan Carroll and Rafael Valero and friends
AnnaGrigoriyeva, ElenaOgnivtseva, OlesyaZarubegnova, EkaterinaTkachenko, Dmit-
riy Solodkiy and Andrey Trutnev who have always given me great help during these
years.
I am deeply grateful to Fernando Garcia for encouragement and moral support at
times when it was needed. Finally, I am infinitely indebted to my parents and thank
them for being so patient.
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It is in our nature to explore,
to reach out into the unknown.
The only true failure would be
not to explore at all.
“Shackleton’s Journey”
8
Contents
Resumen iii
Introduction xiii
1 ATractableFrameworkforAnalyzingaClassofNonstationary Markov
Models 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 A class of nonstationary Markov economies . . . . . . . . . . . . . . . . 6
1.2.1 The stochastic environment . . . . . . . . . . . . . . . . . . . . 7
1.2.2 A nonstationary optimization problem . . . . . . . . . . . . . . 7
1.2.3 Assumptions about exogenous variable . . . . . . . . . . . . . . 8
1.2.4 Assumptions about the utility and production functions . . . . . 10
1.2.5 Optimal program . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Extended function path framework . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Introducing extended function path framework . . . . . . . . . . 12
1.3.2 Theoretical foundations of EFP framework . . . . . . . . . . . . 16
1.4 Relation of EFP to the literature . . . . . . . . . . . . . . . . . . . . . 19
1.4.1 Early literature on stochastic growth models . . . . . . . . . . . 19
1.4.2 Methods constructing Markov decision functions . . . . . . . . . 19
1.4.3 Methods constructing a path for variables . . . . . . . . . . . . 21
1.5 Assessing EFP accuracy in a test model with balanced growth . . . . . 23
1.5.1 Implementation details of EFP . . . . . . . . . . . . . . . . . . 23
1.5.2 A comparison of four solution methods . . . . . . . . . . . . . . 24
1.6 Numerical analysis of nonstationary and unbalanced growth applications 30
1.6.1 Application 1: An unbalanced growth model with a CES produc-
tion function and capital-augmenting technological progress . . 30
1.6.2 Application 2: A nonstationary model with a parameter shift . . 33
1.6.3 Application 3: A nonstationary model with a parameter drift . . 37
1.6.4 Application4: Calibratingagrowthmodelwithaparameterdrift
to unbalanced U.S. data . . . . . . . . . . . . . . . . . . . . . . 40
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
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