Causal and Stochastic Elements in Business Cycles: An Essential Extension of Macroeconomics Leading to Improved Predictions of Data

Causal and Stochastic Elements in Business Cycles: An Essential Extension of Macroeconomics Leading to Improved Predictions of Data

by Arvid Aulin

Paperback(Softcover reprint of the original 1st ed. 1996)

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Product Details

ISBN-13: 9783540605935
Publisher: Springer Berlin Heidelberg
Publication date: 02/19/1996
Series: Lecture Notes in Economics and Mathematical Systems , #431
Edition description: Softcover reprint of the original 1st ed. 1996
Pages: 116
Product dimensions: 6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

I. The Mathematical Tools.- 1. The Hamilton-Jacobi Theory.- 1. The Hamiltonian function.- 2. The Lagrangian function.- 3. The action principle.- 4. The Legendre function.- 5 Transversality conditions.- 6. The “principle of the largest action”.- 2. Maximization of Accumulating Utility.- 1. Canonical equations for discounted utilities.- 2. The Solow growth model revisited.- 3. The parameter conditions of transversality in the Solow model.- 4. The Arrow-Kurz generalization.- II. The Lucas Growth Theory and Its Generalization to Business Cycles.- 3. The Lucas Growth Theory.- 1. The reaction of the market to common knowledge.- 2. The market clearing.- 4. Generalization to Include Business Cycles.- 1. The first axiom of generalization.- 2. The fundamental equations.- 3. The second axiom of generalization.- 4. The derivation of a general solution algorithm.- 5. The natural boundary conditions.- 7. The Legendre condition.- 8. Transversality conditions.- III. The General Theory of Economic Growth and Business Cycles.- 5. The Basic Growth Paths.- 1. The balanced-growth path: Growth Type 1.- 2. The path of logistically rising productivity of capital: Growth Type 2.- 3. Verification by the Solow (1957) material.- 6. The Basic Business Cycles.- 1. The state-plane and the cycle center.- 2. The decreasing relative size of the cycles.- 3. The existence of well-behaving general solutions.- 4. The invariance group and the time scale.- 5. The cycle functions.- IV. The Basic Business Cycles as the Causal Part of Business Cycles.- 7. The Predictive Power of the Basic Cycles Compared With That of the Stochastic Models: Ordinary Business Cycles.- 1. The linear approximation of the Basic Business Cycles.- 2. Comparisons with empirical correlations and variances.- 3. Comparisons with empirical autocorrelations.- 8. Conclusions and Challenges.- 1. Is the Lucas-Bellman formalism too narrow?.- 2. Economic stability.- 3. Are real business cycle theories outdated?.- 9. The Dynamics of Anomalous Basic Business Cycles and Its Quantitative Verification.- 1. Fundamental theory vs model construction in economics.- 2. The method of calculation.- 3. The fall in procyclicality of consumption and investment.- 4. The retained high procyclicality of employment.- 5. An appraisal of the results.- V. The Effects of Nonmaterial Values and Other Ignored Factors Upon Economic Growth.- 10. Primary Causal Factors of Economic Growth.- 1. The reduction to human capital.- 2. The freedom factor.- 3. The three ultimate determinants of the level of national economy.- 4. The form of the function b($$\xi ,\dot \xi ,\ddot \xi$$).- 11. The Growth Effects of Savings Rate.- 1. Which is the causal order of parameters?.- 2. The existence of the growth effects of savings rate.- 3. An empirical test.- VI. An Alternative Vision of the Stochastic Element in Business Cycles.- 12. Stochastic Shocks as Perturbations Superposed Upon the Basic Business Cycles.- 1. Are the business cycles purely stochastic processes?.- 2. The production of random series with a definite mean and standard deviation.- 3. How technological shocks affect each economic variable?.- 13. Final Result: Both the Stochastic and Nonstochastic BBC Versions Predict Better Than Any of the Models Based On Stochastic Optimization.- 1. Correlations and variances of stochastic cycle functions over a cycle: the formulae.- 2. Preliminary steps of calculation.- 3. Calibration.- 4. The small but not negligible effect of shocks.- 5. The final result in numbers: Table 12.- 6. The final result illustrated: Figures 9 and 10.- 7. Final comments.- References.- Appendix 1: The Dependence of the Predicted Anomalous Correlations on Savings Rate.- Appendix 2: Numerical Tables.

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