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El. knyga: Dynamic Linear Economic Models

(University of Pittsburgh, USA)
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Originally published in 1974. This book provides a rigorous and detailed introductory treatment of the theory of difference equations and their applications in the construction and analysis of dynamic economic models. It explains the theory of linear difference equations and various types of dynamic economic models are then analysed. Including plenty of examples of application throughout the text, it will be of use to those working in macroeconomics and econometrics.

Chapter 1 Mathematical Preliminaries
1(71)
1.1 Complex Numbers
1(18)
1.2 Sequences
19(6)
1.3 The Algebra of Operators
25(6)
1.4 Introduction to Linear Algebra
31(24)
1.5 Characteristic Roots
55(17)
Chapter 2 Introduction To Difference Equations
72(22)
2.1 Applications of Difference Equations in Economics
73(9)
2.2 The Concept of a Solution of a Difference Equation
82(5)
2.3 The Solution of the Equation y(t+l) - ay(t) = b
87(2)
2.4 Limiting Behavior of the Solution
89(5)
Chapter 3 General Theory Of Linear Difference Equations
94(15)
3.1 Introduction
94(4)
3.2 The Homogeneous Linear Difference Equation
98(10)
3.3 Summary
108(1)
Chapter 4 Linear Homogeneous Difference Equations With Constant Coefficients
109(29)
4.1 Introduction
109(3)
4.2 The Second Order Case
112(7)
4.3 The n-th Order Case
119(13)
4.4 Limiting Behavior of Solutions of Linear Homogeneous Difference Equations Having Constant Coefficients
132(2)
4.5 Summary
134(4)
Chapter 5 Particular Solutions
138(15)
5.1 Introduction
138(2)
5.2 Particular Solution when f(t) is Constant
140(4)
5.3 The Method of Undetermined Coefficients
144(5)
5.4 Summary
149(4)
Chapter 6 Solving Linear Difference Equations Using Operators
153(16)
Chapter 7 Equilibrium And Stability
169(18)
7.1 Introduction
169(5)
7.2 The Routhian Conditions to Check Stability
174(10)
7.3 Summary
184(3)
Chapter 8 Systems Of Difference Equations
187(22)
Chapter 9 Distributed Lags
209(32)
9.1 Introduction
209(4)
9.2 The Koyck Distributed Lag Model
213(3)
9.3 The Lag Polynomial Operator
216(4)
9.4 The General Distributed Lag Model
220(11)
9.5 Some Frequently Used Lag Distributions
231(5)
9.6 Summary and Conclusions
236(5)
Chapter 10 Analysis Of Accelerator Models
241(42)
10.1 Introduction
241(18)
10.2 Analysis Using Matrices and Shift Operators
259(2)
10.3 Capital Stock Adjustment Models
261(8)
10.4 Various Criticisms
269(2)
10.5 Moving Equilibrium
271(12)
Chapter 11 Linear Dynamic Economic Models
283(40)
11.1 Introduction
283(4)
11.2 Klein's Model 1
287(4)
11.3 Impact and Delay Multipliers
291(4)
11.4 The First Order Model
295(9)
11.5 The Total Multipliers
304(7)
11.6 Analysis using Operators
311(7)
11.7 Summary
318(5)
Appendix
319(4)
Chapter 12 The Cyclic Properties Of The Linear Model
323(16)
12.1 Introduction
323(2)
12.2 The Effect of At(0)
325(2)
12.3 The Effect of DX(t) + ADX(t-1) +...+ At-1 DX(1)
327(4)
12.4 The Effect of V(t) + AV(t-1) +...+ At-1v(1)
331(8)
Appendix: The Expectation Notation
336(3)
Chapter 13 Introduction To Optimal Control
339(12)
13.1 Introduction
339(3)
13.2 The Single Period Optimal Control Problem
342(2)
13.3 A Generalization
344(1)
13.4 The Multi-Period Optimal Control Problem
345(6)
Chapter 14 Forecasting With Autoregressive Models
351(23)
14.1 Introduction
351(2)
14.2 Stationary Stochastic Processes
353(4)
14.3 Introduction to Autoregressive Models
357(5)
14.4 The Autocorrelation Function of an Autoregressive Process
362(2)
14.5 The Partial Autocorrelation Function of an Autoregressive Process
364(2)
14.6 Moving Average Processes
366(1)
14.7 Mixed Autoregressive-Moving Average Models
367(3)
14.8 Identification
370(4)
Bibliography 374(4)
Index 378
Kenkel, James L.
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