# Chile

The number of states chosen for Chile has, like Sargent et al. (2009), a configuration for the process that follows the deficit of 2 states for the mean and 3 for the variance. The estimates use as inputs are the month-to-month, seasonally adjusted inflation in the period from January 1949 to October 2022.

#### Inflation and Seasonally Adjusted Inflation

Although Chile has not experienced any episode of hyperinflation since 1960, its monetary and fiscal policies have gone through several characteristic periods. The first one extends from the beginning of the sample to 1971, with inflation hovering around 1% to 5%, but with sustained economic growth. The second episode extends from 1972 to 1976 and was characterized by a period of certain instability in which inflation reached its peak at a level of almost 90%. This was followed by a period of slow stabilization between 1977 and 1994. Finally, the fourth period presents a stable inflation and covers from 1995 to the end of the sample.

**Notes:**
Month-to-month percentage changes of the Consumer Price Index. ”a.e”, refers to seasonally adjusted data.

**Sample:**
January 1949 to October 2022.
**Source:**
With data from the National Institute of Statistics.

##### Recent Inflation Data

#### 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 deficit parameter represents that it is not possible to obtain a proper estimate for the standard error because the parameter value is a corner solution of the problem
**.**

#### Discussion

The estimates of the probabilities of being in the different states for Chile reflect a trend of improvement of its fiscal position, although with some episodes where it is considered, there may have been transitions to states with intermediate and high mean deficits.

Since 1993, the estimation of the probability of the state with a low mean and low or intermediate volatility stands out. Except for a couple of episodes -the second one could be associated with the aftermath of the Global Financial Crisis- the estimate of the probability of the state with a low mean and low volatility is close to one. This can certainly be considered a positive result. Historically, the dynamics of such probabilities have been improving.

On the other hand, the estimate of the probability of escape, although it had a historical maximum in the mid-1970s close to one, has remained below the probability level of 0.15 since then. That said, it has had slight upturns in the late 1980s and a more recent one in 2009.

More specifically, from 1972, the probability of having an escape event presented a growing trend. It was not until 1976 that this probability was considerably reduced on a par with Chile's economic and inflation stabilization during that year.

In recent periods, it is notable that the estimate of the probability of the state with a low mean and low volatility has been essentially one. In line with this, the estimate of the probability of leakage remained basically at zero.

As a more general comment, the dynamics of the estimates of the probabilities of each state coincide with several of the main economic episodes in Chile's economic history. They also seem to be in line with much of the narrative for Chile in Caputo and Saravia (2018).

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

**Note:**
To consider any state for the
**mean of the**
deficit, it is necessary to add the probabilities of the low, intermediate and high states for the variance. For example, to consider the probability of being in the
**low**
state for the mean of the deficit it is necessary to add the probabilities of the
states (
**low,**
low),
(
**low**
, intermediate) and (
**low**
, high).

To look at 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 1949 to October 2022.
**Source:**
With data from the National Institute of Statistics.

##### 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 one, 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 National Institute of Statistics.

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 1949 to October 2022.
**Source:**
With data from the National Institute of Statistics.

##### Estimación de la probabilidad de escape

**Sample:**
January 1949 to October 2022.
**Source:**
With data from the National Institute of Statistics.

#### References

**Caputo, R., & Saravia, D. (2018).**"The Monetary and Fiscal History of Chile: 1960-2016". University of Chicago, Becker Friedman Institute for Economics Working Paper (2018-62).