by: Jonathan Matthew Gresham

July 4, 2024

Inflation can be managed by asset pricing rather than the Taylor Rule while uncertainty provides Phillips curve behavior in an exchange framework. Recently, the topic of managing inflation with mathematics or statistics has forced us to consider some puzzling questions, including whether we should fear the Taylor interest rate rule and whether we should adjust Phillips curves. Historically, the answers to these questions were simpler because NPR had not aired “Could an Equation Do a Better Job at Setting a Target Interest Rate than the Fed?” yet (“Could an Equation Do a Better Job at Setting a Target Interest Rate than the Fed?”). However, since the advent of the remarks of Darian Woods and Mary Childs regarding the Taylor rule we have seen changes in inflation theory which have forced scholars to grapple with the mathematical management of inflation.

The economy could have mathematical uncertainty if wages were increasing because of reduced unemployment. This is an exponential function with elements that alleviate reduced unemployment and increase wages. Asset pricing may be used to manage inflation rather than the Taylor interest rate rule. Audiences of the management of inflation by using this model include readers of Bloomberg News, followers of finance data and activists that traditionally cooperate with social gatherings. The Taylor rule is a subject of mathematical and economic relationships. Emotional reactions to the mathematical management of inflation and globalization are statistical. Uncertainty is modeled as a Phillips curve in an exchange framework. Formulas provide theory for practical use like the Taylor interest rate rule, yet asset pricing may be used as an alternative (Gillman 2). Asset pricing provides an alternative to Taylor interest rate rule (Gillman 2) while uncertainty provides Phillips curve behavior in an exchange framework (Gillman 2).

One way the management of inflation with mathematics could alleviate reduced unemployment and increase wages is with asset pricing. "Okay but explain." Robert Lucas's pioneering neutrality paper determined inflation by the money supply growth rate with random fluctuations due to public finance needs such as wartime spending or bank crises. Lucas completes it within a framework restricted to a single optimization problem without additional equations added on such as a policy rule of how the market interest rate depends on endogenous variables within the model. Instead, Lucas created the economic consumption-based capital asset pricing model (CCAPM) that derives the interest rate behavior by using a general equilibrium utility maximization ‘microfounded’ framework. This behavior is known today as the asset pricing equation. It forms the bridge to ‘macro-finance’ by encompassing in general equilibrium the partial equilibrium ‘capital asset pricing model’ that is typically viewed as the core of finance theory. Extensions to the consumption-based capital asset pricing model continue today as an endogenous rate relation that serves as an alternative to deploying the Taylor rule is determined by the market (Gillman 33).

"But can't you use the Taylor rule?" Robert Lucas's pioneering neutrality paper "thus provides Phillips curves that are temporary rather than permanent. Not only is the L72 [Lucas's pioneering neutrality paper] theory rigorous, but it also builds methodological foundations for long-lasting differences on setting up general equilibrium models and how the Federal Reserve interest rate policy should be conducted today. New Keynesians add on equilibrium conditions to those of the representative agent optimization problem, as in Galí (2015). They assume rigid prices and allow relative price increases to be determined by increases in monopoly power that are then called ‘inflation’. This combination yields an ever-present type of Phillips relation that links inflation positively to output growth. And since they only have the Fisher equation to determine market interest rates, while leaving out the money supply growth that should be included as part of the government budget constraint within the consumer optimization model, they assume a ‘policy rule’ to determine interest rates that is known as the Taylor equation. This assumption is made despite the Federal Reserve policy ignoring the Taylor rule, as in the policy of fixing the interest rate on reserves by setting it to near zero for most years since 2009" (Gillman 33).

Bibliography

“Could an Equation Do a Better Job at Setting a Target Interest Rate than the Fed?” All Things Considered, Nov. 2022. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&db=edsgit&AN=edsgit.A726268903&site=eds-live&scope=site. The following is from "Could an equation do a better job at setting a target interest rate than the Fed?" which was an NPR news report from the show "All Things Considered" (“Could an Equation Do a Better Job at Setting a Target Interest Rate than the Fed?”). Darian Woods said "And when the Fed had deviated from the Taylor Rule, that was the 1970s, when inflation got so high that the Fed had to crash the economy in the early '80s to stamp it out. It was also in the early 2000s, when low interest rates contributed to massive housing price growth, fueling the speculative bubble that led to the Great Recession in 2008" ("Could an equation do a better job at setting a target interest rate than the Fed?"). Mary Childs is another reporter from that source, and Mary does not seem to like mathematics managing globalization or the economy, but specifically inflation. I am not sure what sort of background that Mary Childs specifically comes from that would lead her with such an emotional reaction to the Taylor Rule, but Darian Woods unfortunately describes something related: he said that John Taylor's version of the world is a world without human beings. Mary Childs is another reporter from that source, and Mary does not seem to like mathematics managing globalization or the economy, but specifically inflation. I am not sure what sort of background that Mary Childs specifically comes from that would lead her to develop such an emotional reaction to the Taylor Rule, but if I may repeat once that Darian Woods unfortunately said that John Taylor's version of the world is a world without human beings. This indicates bias.

Gillman, Max. “Lucas’s Methodological Divide in Inflation Theory: A Student’s Journey.” Journal of Economic Methodology, vol. 29, no. 1, Mar. 2022, pp. 30–47. EBSCOhost, https://doi-org.ezproxy.snhu.edu/10.108 ... 21.2019818. Asset pricing provides an alternative to Taylor interest rate rule (Gillman 2) while uncertainty provides Phillips curve behavior in an exchange framework (Gillman 2). Lucas’s Methodological Divide in Inflation Theory: A Student’s Journey is about Robert E. Lucas, Jr. towards the beginning of the text where it says that he a was professor at the University of Chicago. He was involved with specific topics according to the writer of Lucas’s Methodological Divide in Inflation Theory: A Student’s Journey. Topics like asset pricing, and "price-theoretic foundations of aggregate supply and demand for output." Gillman, author of Lucas’s Methodological Divide in Inflation Theory: A Student’s Journey, says Lucas was wrong in his paper he wrote in 1976: "Econometric policy evaluation: A critique" (Gillman 2). Gillman says that with the evidence of Phillips curves. Gillman describes the consumer or firm in Lucas' critique when he says the following statement. "The consumer or firm is posited to make decisions given fundamental parameters including policy parameters (such as the money supply growth rate)" (Gillman 2). Gillman then says that the behavioral parameters may change and there could be a policy change or even a regime change which will change things. “The alternative hypothesis of a long-run negatively sloped Phillips curve has long been a key issue dividing neoclassical and New Keynesian economics, with the latter using ‘secular stagnation’ theories based for example on the estimation of a 60-year long-term Phillips curve” (Gillman 2).