Research on China’s Monetary Policy Objectives

Abstract

For a long time, New Keynesian and neoclassical economists have always disagreed on the effectiveness of the monetary policy. Both sides adhere to their basic positions and learn from each other’s analytical methods. Neoclassical economists such as Robert E. Lucas Jr. and Robert J. Barro have always questioned the effectiveness of Neo-Keynesian government intervention policies (including fiscal and monetary policies); however, in practice, the application of neo-Keynesian monetary policy has not reduced, but it has gradually become the most important policy basis in the financial macro-control system of various countries. In order to further consolidate the fundamental arguments for the effectiveness of the monetary policy, New Keynesian scholars have also accepted the “Lucas Critique” viewpoint (Lucas R., 1976) and constantly improved the micro-theoretical basis of the ultimate goal of monetary policy under open economic conditions.

Appendix 2

The following proof: when $\varphi_{t} > 0$ (for all t) and $i_{t} \ge 1$ (for all t), the sufficient and essential condition for the quantity of money to be strictly greater than zero is $\zeta \chi \le i_{t} n\xi$.

(Necessary condition) suppose that the essential condition is not true, $\zeta \chi \ >i_{t} n\xi$. According to the setting of growth rate of legal currency deposits and population growth, the following equation holds:

$$\begin{array}{*{20}c} {\frac{{\varphi_{t + 1} i_{t} }}{{\varphi_{t} }} = \frac{{\varphi_{t + 1} i_{t} M_{t + 1} N_{t} n}}{{\varphi_{t} M_{t} \zeta N_{t + 1} }} = \frac{{\varphi_{t + 1} i_{t} m_{t + 1} n}}{{\varphi_{t} m_{t} \zeta }} = \frac{{q_{t + 1} i_{t} n}}{{q_{t} \zeta }}} \\ \end{array}$$

(A2.1)

where $q_{t} = \varphi_{t} m_{t}$. According to Eq. (4.12), it can be deduced from Eq. (4.15):

$$\begin{array}{*{20}c} {\frac{{q_{t + 1} i_{t} n}}{{q_{t} \zeta }} \ge \chi } \\ \end{array}$$

(A2.2)

Multiply both sides of equation (A2.2) by $\varsigma /n$ to get:

$$\begin{array}{*{20}c} {\frac{{q_{t + 1} i_{t} }}{{q_{t} }} \ge \frac{\chi \zeta }{n} > i_{t} \xi } \\ \end{array}$$

(A2.3)

The growth rate of endowment of each generation is $\xi$. If growth rate of $q_{t}$ is strictly greater than $\xi$, it will eventually break through the endowment value of young people of each generation. Any bounded sequence $\left\{ {q_{t} } \right\}$ cannot satisfy the income constraint.

(Sufficient condition) so we want to prove that as long as $\chi \zeta \le i_{t} \xi n,$ and exists $m_{t} = m_{1} \xi^{t - 1}$ For this purpose, a positive sequence $q_{t}$ needs to be found to satisfy:

$$\begin{array}{*{20}c} {v\left( { \cdot , \cdot } \right) = \frac{{\partial u/\partial c_{1t} }}{{\partial u/\partial c_{2t + 1} }} = \frac{{q_{t + 1} i_{t} n}}{{q_{t} \zeta }} \ge \chi } \\ \end{array}$$

(A2.4)

If there is a sequence $q_{t} = q_{1} \xi^{t - 1}$ that satisfies the part of Eq. (4.18), then $\chi \zeta \leq i_{t} \xi n$. Meanwhile, the existence (uniquely) of the above sequence is obvious, because as $q_{t}$ varies from 0 to $y_{1} \xi^{t - 1}$, $v\left( { \cdot , \cdot } \right)$ is continuously evaluated between 0 and $\infty$.