Taylor Rule

Examples of Taylor Rule in the following topics:

• The Taylor Rule

  • Taylor's rule was designed to provide monetary policy guidance for how a central bank should set short-term interest rates.
  • The Taylor rule is a formula developed by Stanford economist John Taylor.
  • The Taylor rule doesn't always provide an easy answer.
  • However, the Taylor rule can still provide a handy "rule of thumb" to policy makers on how to balance these conflicting issues when setting the interest rates.
  • However, the Federal Reserve does not follow the Taylor rule as an explicit policy.

• Macroeconomic Factors Influencing the Interest Rate

  • Taylor explained the rule of determining interest rates using three variables: inflation rate, GDP growth, and the real interest rate.
  • In economics, a Taylor rule is a monetary-policy rule that stipulates how much the Central Bank should change the nominal interest rate in response to changes in inflation, output, or other economic conditions.
  • According to Taylor's original version of the rule, the nominal interest rate should respond to divergences of actual inflation rates from target inflation rates and of actual Gross Domestic Product (GDP) from potential GDP:
  • In this equation, both απ and αy should be positive (as a rough rule of thumb, Taylor's 1993 paper proposed setting απ =αy = 0.5).
  • Taylor explained the rule in simple terms using three variables: inflation rate, GDP growth, and the equilibrium real interest rate.

• The Natural Logarithmic Function: Differentiation and Integration

  • This leads to the Taylor series for $\ln(1 + x)$ around $0$:
  • This is the case because of the chain rule and the following fact:
  • The Taylor polynomials for $\ln(1 + x)$ only provide accurate approximations in the range $-1 < x \leq 1$.
  • Note that, for $x>1$, the Taylor polynomials of higher degree are worse approximations.

• Taylor Polynomials

  • A Taylor series is a representation of a function as an infinite sum of terms calculated from the values of the function's derivatives.
  • Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.
  • To evaluate the integral $I = \int_{a}^{b} f(x) \, dx$, we can Taylor-expand $f(x)$ and perform integration on individual terms of the series.
  • Therefore, as long as Taylor expansion is possible and the infinite sum converges, the definite integral ($I$) can be evaluated.
  • The exponential function (in blue) and the sum of the first 9 terms of its Taylor series at 0 (in red).

• Taylor and Maclaurin Series

  • The concept of a Taylor series was formally introduced by the English mathematician Brook Taylor in 1715.
  • Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.
  • The Taylor series of a function is the limit of that function's Taylor polynomials, provided that the limit exists.
  • A function may not be equal to its Taylor series, even if its Taylor series converges at every point.
  • Identify a Maclaurin series as a special case of a Taylor series

• Applications of Taylor Series

  • Taylor series expansion can help approximating values of functions and evaluating definite integrals.
  • The partial sums (the Taylor polynomials) of the series can be used as approximations of the entire function.
  • Taylor series is especially useful in evaluating definite integrals.
  • $e^{ix}$ can be found from the Taylor expansion of $\cos(x)$ and $\sin(x)$:
  • As more terms are added to the Taylor polynomial, it approaches the correct function.

• Frederick Taylor

  • Scientific management, also called Taylorism, concerns the analysis and synthesis of workflows to improve productivity.
  • Scientific management, also called Taylorism, is a theory of management that analyzed and synthesized workflows.
  • Its development began with Frederick Winslow Taylor in the 1880s and 1890s within the manufacturing industries.
  • Taylor proposed a "neat, understandable world in the factory, an organization of men whose acts would be planned, coordinated, and controlled under continuous expert direction. " Factory production was to become a matter of efficient and scientific management—the planning and administration of workers and machines alike as components of one big machine.
  • Scientific management, also called Taylorism, is a theory of management that analyzed and synthesized workflows.

• Scheduling Work

  • Kelly Johnson, later famous for Kelly's 14 rules of intrapreneurship, was the director of this group. (2) Another example could be 3M, who encourage many projects within the company.
  • Frederick Taylor developed a theory in an effort to establish a science for every job within an organization (Taylorism or Scientific Management) .
  • The principles of Taylorism are as follows:
  • Frederick Winslow Taylor lived from 1856 to 1915.
  • Taylorism was named after him.

• Scientific Management: Taylor and the Gilbreths

  • While the terms "scientific management" and "Taylorism" are often treated as synonymous, an alternative view considers Taylorism to be the first form of scientific management.
  • A significant part of Taylorism was time studies.
  • Taylor was concerned with reducing process time and worked with factory managers on scientific time studies.
  • By counting and calculating, Taylor sought to transform management into a set of calculated and written techniques.
  • This difference led to a personal rift between Taylor and the Gilbreths, which, after Taylor's death, turned into a feud between the Gilbreths and Taylor's followers.

• Classical Versus Behavioral Perspectives

  • Scientific management theory, which was first introduced by Frederick Winslow Taylor, focused on production efficiency and productivity of employees.
  • By managing production efficiency as a science, Taylor thought that worker productivity could be completely controlled.
  • Another leader in the classical perspective of management, Max Weber, created the bureaucracy theory of management, which focuses on the theme of rationalization, rules, and expertise for an organization as a whole.
  • The classical perspective of management theory pulls largely from these three theorists (Taylor, Weber, and Fayol) and focuses on the efficiency of employees and on improving an organization's productivity through quantitative (i.e., measurable, data-driven) methods.