Causal and Stochastic Elements in Business Cycles: An Essential Extension of Macroeconomics Leading to Improved Predictions of Data (Lecture Notes in Economics and Mathematical Systems)

A critical examination of The prevailing orthodoxy according to which all macroeconomic theory should be reducible to microeconomics. The book provides a mathematical extension of the Lucas theory to allow for the effects of creation of knowledge upon economic development so as to improve the prediction of business cycle data.

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 Are real business cycle theories outdated?.- 9.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.