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How Singularities Affect the Phillips Curve and Economic Policy
by Keynesian TechnologyDecember 6th, 2024
Too Long; Didn't Read
This paper critiques the Phillips curve using a new framework that highlights three key singularities—wall-crossing, statistical restrictions, and inter-temporal substitution by firms. It challenges existing macroeconomic theories and introduces a roadmap for understanding equilibrium existence, bifurcation theory, and policy implications.
‘a simple graph of a supply and demand curve. The graph should have labeled X and Y axes but no numerical values.’ Image created by HackerNoon AI Image Generator
Table of Links
4 Calvo Framework and 4.1 Household’s Problem
4.3 Household Equilibrium Conditions
4.5 Nominal Equilibrium Conditions
4.6 Real Equilibrium Conditions and 4.7 Shocks
5.2 Persistence and Policy Puzzles
6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems
7 General Linearized Phillips Curve
8 Existence Results and 8.1 Main Results
9.2 Algebraic Aspects (I) Singularities and Covers
9.3 Algebraic Aspects (II) Homology
9.4 Algebraic Aspects (III) Schemes
9.5 Wider Economic Interpretations
10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs
10.4 Microeconomic Interpretation
Appendices
A Proof of Theorem 2 and A.1 Proof of Part (i)
B Proofs from Section 4 and B.1 Individual Product Demand (4.2)
B.2 Flexible Price Equilibrium and ZINSS (4.4)
B.4 Cost Minimization (4.6) and (10.4)
C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence
D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium
D.2 Profits and Long-Run Growth
E Slopes and Eigenvalues and E.1 Slope Coefficients
E.4 Rouche’s Theorem Conditions
F Abstract Algebra and F.1 Homology Groups
F.4 Marginal Costs and Inflation
G Further Keynesian Models and G.1 Taylor Pricing
G.3 Unconventional Policy Settings
H Empirical Robustness and H.1 Parameter Selection
I Additional Evidence and I.1 Other Structural Parameters
I.3 Trend Inflation Volatility
3 Outline and Preview
This final introductory section has two parts: the first summarizes the Phillips curve argument, whilst the second sets out the structure of the rest of the paper.
3.1 Phillips Curve
A typical textbook New Keynesian Phillips curve currently looks like this
The reason why is that as we approach ZINSS the Phillips curve is punctured by the following system of three singularities.
The first is the wall of the crossing, which is necessary to the bifurcation. The second is a statistical restriction that destroys the error term. The third reflects the inter-temporal substitution incentive of the resetting firms. The crucial point is that substituting the singularities into the correct Phillips curve (2) simplifies to yield (1) the incorrect counterpart. The nature of the wall-crossing is that it is not possible to move in the other direction. This explains where macroeconomists went wrong for so many years.
The precise parametric form of all coefficients are detailed later in the paper. The output gap term vanishing is specific to the parametization choices, which is discussed in the Appendix H alongside robustness exercises. The only nonstandard selection was a lower value for the inflation response, in the policy rule, in line with the anti-Taylor principle.
3.2 Roadmap
The remainder of the paper is organized as follows. Section 4 sets out the New Keynesian framework. Section 5 focuses on existing solutions and details the Lucas critique. Section 6 lays out the stochastic equilibrium and a priori results. Section 7 derives the general Phillips curve. Section 8 proves the theoretical conditions governing existence and non-existence of equilibrium. Section 9 rigorously develops the bifurcation theory. Section 10 covers theoretical and econometric implications. Section 11 is devoted to the policy rule. Section 12 is for discussion.
Author:
(1) David Staines.
This paper is available on arxiv under CC 4.0 license.
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