The Origins and Consequences of Inflation in Latin America

Abstract

Inflation in Brazil and other Latin American countries such as Argentina, Mexico, Bolivia, Chile and Peru, has been of an endemic nature. The question that normally arises among the economists who try to understand this situation is how to explain the difference between inflation in Latin America and other parts of the world, such as North America, Western Europe and Asia.

This is an edited version of a paper originally published in Pesquisa e Planejamento Econômico vol 19 (December 1989), pp. 505–523.

Appendix

• (a) Consider the following non-linear system of equations of finite differences:

  $$\displaystyle{\left \{\begin{array}{c} \left (1-\gamma \right )\pi _{t} -\pi _{t-1} =\gamma \left (r + \frac{\alpha }{\beta }\right ) - \frac{\gamma } {\beta h_{ t}}\\ \\ h_{t} = \frac{h_{t-1}} {1+\pi _{t}} + d\end{array} \right.}$$

  A linear approximation of this system around point (h, π) is given by:

  $$\displaystyle{\left [\begin{array}{c} \tilde{\pi }_{t}\\ \\ \tilde{h}_{t}\end{array} \right ] = \frac{\beta h\left (1+\pi \right )^{2}} {\left (1-\gamma \right )\beta h\left (1+\pi \right )^{2}+\gamma }\left [\begin{array}{cc} 1 & \frac{\gamma } {\beta h^{2 } \left (1+\pi \right )} \\ \\ - \frac{h} {\left (1+\pi \right )^{2}} & \frac{1-\gamma } {1+\pi }\end{array} \right ]\left [\begin{array}{c} \tilde{\pi }_{t-1}\\ \\ \tilde{h}_{t-1}\end{array} \right ]}$$

  Let D be the matrix that multiplies the vector $[\tilde{\pi }_{t-1}\tilde{h}_{t-1}]'$. The necessary and sufficient condition for the non-linear system of equations of finite differences to be locally stable at point (h, π), is that the auto-values of matrix D have a smaller module than 1, which is equivalent to the following conditions:

  $$\displaystyle\begin{array}{rcl} & \vert \vert D\vert \vert < 1 & {}\\ & \vert trD\vert < 1 + \vert D\vert & {}\\ \end{array}$$

  where | D | is the determinant of matrix D and the symbol tr stands for the matrix trace, and the two vertical bars stand for the absolute value of the variable. With a little algebra these inequalities imply the following restrictions:

  $$\displaystyle\begin{array}{rcl} & \gamma < \frac{\beta h\left (1+\pi \right )\pi } {h\left (1+\pi \right )^{2}-1}& {}\\ & \qquad h\left (1+\pi \right )\pi < 1 & {}\\ \end{array}$$

  Note that the equilibrium values of h and π are independent of γ. They depend on the other parameters of the model: β, d, r and α. Consequently the point of low inflation is locally stable for some values of γ, and locally unstable for others.

• (b) Consider the following non-linear system of equations of finite differences:

  $$\displaystyle{\left \{\begin{array}{c} \log b_{t} = k -\alpha \pi _{t-1}\\ \\ b_{t} = \frac{b_{t-1}} {1+\pi _{t}} + d\end{array} \right.}$$

  A linear approximation of this system around point (b, π), is given by:

  $$\displaystyle{\left [\begin{array}{c} \tilde{b}_{t}\\ \\ \tilde{\pi }_{t }\end{array} \right ] = D\left [\begin{array}{c} \tilde{b}_{t-1}\\ \\ \tilde{\pi }_{t-1 }\end{array} \right ]}$$

  where matrix D is equal to:

  $$\displaystyle{D = \frac{\left (1+\pi \right )^{2}} {b} \left [\begin{array}{cc} 0 & - \frac{\alpha b^{2}} {\left (1+\pi \right )^{2}}\\ \\ \frac{1} {1+\pi } & \alpha b\end{array} \right ]}$$

  By applying the necessary and sufficient condition for local stability of the system, the following restriction is reached:

  $$\displaystyle{\alpha <\min \left \{ \frac{1} {1+\pi }, \frac{1} {\left (1+\pi \right )\pi }\right \}}$$

  where min {, } indicates the smaller of the two numbers.

• (c) Consider the following non-linear system of equation of finite differences:

  $$\displaystyle{\left \{\begin{array}{c} b_{t} = \frac{b_{t-1}} {1+\pi _{t}} + d\\ \\ \pi _{t} = \frac{\pi _{t-1}+\delta k+\delta \alpha \log b_{t}+\delta \gamma f-\delta \bar{y}} {1-\delta \beta }\end{array} \right.}$$

  A linear approximation of this system around point (b, π), is given by:

  $$\displaystyle{\left [\begin{array}{c} \tilde{b}_{t}\\ \\ \tilde{\pi }_{t }\end{array} \right ] = D\left [\begin{array}{c} \tilde{b}_{t-1}\\ \\ \tilde{\pi }_{t-1 }\end{array} \right ]}$$

  where matrix D is equal to:

  $$\displaystyle{D = \frac{\left (1-\delta \beta \right )\left (1+\pi \right )^{2}} {\left (1-\delta \beta \right )\left (1+\pi \right )^{2}+\delta \alpha }\left [\begin{array}{cc} \frac{1} {1+\pi } & - \frac{b} {\left (1+\pi \right )^{2}\left (1-\delta \beta \right )}\\ \\ \frac{\delta \alpha } {\left (1-\delta \beta \right )b\left (1+\pi \right )} & \frac{1} {1-\delta \beta }\end{array} \right ]}$$

  By applying the necessary and sufficient condition for local stability of the system, the following restrictions are obtained:

  $$\displaystyle\begin{array}{rcl} & \delta \left [\beta \left (1+\pi \right )^{2}-\alpha \right ] < \left (1+\pi \right )\pi & {}\\ & \left [\left (2 -\delta \beta +\pi \right )\left (1-\delta \beta \right ) - 1\right ] < \left (1-\delta \beta \right )\left (1+\pi \right )^{2}+\delta \alpha & {}\\ \end{array}$$