# Peru

The states chosen for Peru have, like Sargent et al. (2009), a configuration for the process that follows the deficit of 3 states for the mean (low, intermediate, and high) and 2 for the variance (low and high). The estimates use as input the month-by-month, seasonally adjusted inflation in the period from January 1957 to July 2021.

#### Inflation and Seasonally Adjusted Inflation

Three periods can be identified for inflation in Peru. In the first, which began in the mid-1950s and ended in the mid-1980s, there was a relative calm with occasional episodes of price rises. Subsequently, between the mid-1980s and the mid-1990s, there were periods of hyperinflation. Finally, in relation to a series of fiscal reforms and the granting of independence to the Central Bank, it can be considered that inflation has remained stable since the mid-1990s.

Notes: Month-to-month percentage changes of the Consumer Price Index. ”a.e”, refers to seasonally adjusted data.
Sample: January 1957 to July 2021. Source: With data from the Central Reserve Bank of Peru.

#### Estimated parameters for the model

The following table shows the parameters resulting from the numerical solution of the optimization problem for the likelihood function associated with the SWZ model. Refer to the model description for a discussion on the intuition behind the model. In addition, the interested reader is referred to Sargent, Williams and Zha (2009), and Ramos-Francia, García-Verdú and Sánchez-Martínez (2018) for further details.

Below is a brief description of the model parameters.

• The model assumes an adaptive inflation expectation mechanism with constant gain. This means that agents form their inflation expectation for the next period based on their expectation of the present period and the observed inflation. The parameter ν determines the weight that the agents give to the observed inflation to generate their expectation. Thus, a parameter ν close to 0 indicates that the agents take into account only their past inflation expectation. In contrast, a parameter ν close to 1 indicates that the agents only take into account the observed inflation. It is called constant because the ν parameter is fixed.

• The parameter λ measures the sensitivity of the demand for money to changes in expected inflation and can take values between 0 and 1. In this model, such demand for money (in real terms) depends linearly and with a negative sign on the expected price level. In this model, such demand for money (in real terms) depends linearly and negatively on the expected price level.

• It is assumed that the parameters of the deficit distribution follow two independent Markov processes. In these processes each state has an associated set of values that indicate the probability of remaining in the same state or of moving to a neighboring state in the next period. In the table, the probability of remaining in the same state is presented. If there is only one possible neighbor state, the probability of transiting to it is the unit minus the probability of remaining in the original state. On the other hand, if you are in a state with two possible neighboring states, it is assumed that there is the same probability of transiting to any of them.

• The parameter σ(π) measures the standard deviation of the process that determines the adjustment of inflation and inflation expectations in the case of a cosmetic reform. In such a case, inflation and its expectations are readjusted to the value of the balance for the state of the average associated with the low level (which is stable) plus some noise.

• Notes: The standard errors of the parameters are estimated using the Crámer-Rao bound. The point in the case of the ν parameter represents that it is not possible to obtain a proper estimate for its standard error.

#### Discussion

Peru starts from a benign situation at the end of the 1950s. Estimates of the probabilities of being in the states with low or intermediate average and high variance predominate. By the late 1970s and during the 1980s, estimates of the probabilities of being in the state with a high mean and low variance increase. By the mid-1990s, this situation is reversed, with a transition period between states so that the estimate of the probability of the state with low mean and low variance maintains a probability close to 0.9.

On the other hand, the probability of escape has remained close to zero throughout the entire sample, except for three occasions in the late 1980s and early 1990s. This seems to have led to a positive cosmetic reform. Remarkably, the estimate of the probability of escape has remained essentially equal to zero in recent years; including major episodes of global economic and financial stress, such as the crisis that began in 2008. The exceptions are some of the episodes in the late 1990s, which although the estimate only increased to 0.01. In recent periods, the estimate of the escape probability has been zero.

Moreover, in the particular case of Peru, the probability of having an escape event becomes relevant between 1988 and mid-1990. This period can be associated with some episodes of hyperinflation and the programs implemented to control it in 1990.

The estimates of the probabilities of the different states and of escape coincide with some of the main historical events in Peru. They also seem to be in line with the narrative of Martinelli and Vega (2018) and Pastor (2012).

##### Estimation of the probability of being in one of the states of the model (mean, variance)

Note: To consider any state for the mean deficit, it is necessary to add the probabilities of the low and high states for the variance. For example, to consider the probability of being in the low state for the mean deficit it is necessary to add the probabilities of the states ( low , low) and ( low , high).
To view a subset of the states in the model, please click on the legends in the graph to show or hide the corresponding state.
Sample: January 1957 to July 2021. Source: With data from the Central Reserve Bank of Peru.

##### Self-Confirmed Equilibrium (SCE) and Inflation Expectations

The solutions of the differential equation that determines the equilibrium levels for expected inflation are shown. When the probabilities of remaining in each of the states of the mean are close to 1, these equilibrium levels are considered to be good approximations.

Specifically, the crosses of each curve with the vertical axis, represented by horizontal lines, determine the stable (those with lower levels) and unstable (those with higher levels) levels of equilibrium.

Source: With data from the Central Reserve Bank of Peru.

The closer inflation expectations are to the unstable equilibrium level associated with the state in which they are most likely to be, the greater the probability of escape. An escape event would trigger the need for reform to bring the level of inflation and its expectations back to stable levels.

Sample: January 1957 to July 2021. Source: With data from the Central Reserve Bank of Peru.

##### Estimation of the probability of escape

Sample: January 1957 to July 2021. Source: With data from the Central Reserve Bank of Peru.

#### References

• Martinelli, C., & Vega, M. (2018). "Monetary and Fiscal History of Peru 1960-2017: Radical Policy Experiments, Inflation, and Stabilization". University of Chicago, Becker Friedman Institute for Economics Working Paper, (2018-63).

• Pastor, G. C. (2012). "Peru: Monetary and Exchange Rate Policies, 1930-1980." IMF Working Paper No. 12/166.