Uruguay

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The number of states for Uruguay has a configuration for the deficit process of 2 states for the mean (low 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 1949 to October 2022.

Inflation and Seasonally Adjusted Inflation

Uruguay's economic history, between 1949 and the end of the sample, could be divided into four periods. In the first one, between 1949 and 1960, growth was achieved based on the import substitution model, with volatile monthly inflation however at single digit levels. The second period, between 1960 and 1973, was characterized by rising inflation, a period of some recovery and a rebound of inflation to levels above 20% per month. The third period, between 1974 and 1990, was characterized by the opening, liberalization and subsequent crisis in the balance of payments; in this period, inflation presented lower levels than before, but with important increases in some specific episodes. Finally, the period beginning in 1991 is considered the "golden years of Uruguay". In the latter, there was a second trade opening, a price stabilization plan and macroeconomic stability.

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 of Uruguay.

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.

Discussion

In the Uruguay model there are two states for each parameter. This means that, for the mean: low and high; and for the variance: high and low; for a total of four states. Considering the dynamics of the estimates of the states' probabilities, we have some comments.

At the beginning of the sample, the estimation of the probability of being in a state with a low mean and low or high variance, predominates. It was towards the end of the 1950s that these probabilities decreased. In the mid-1960s, the probability estimate was the one associated with a state with a high mean and low variance, which increased over a period of several lustrums. With exceptions in the early 1970s and 1980s, where there appears to be greater volatility in that probability estimates fluctuated sharply.

By mid-1997, estimates of the probability of the state with a low mean and low variance resume an upward path. There is a brief period in which the estimate decreases but returns quickly to remain above 0.9. This could reflect a good fiscal performance.

In the case of Uruguay, the estimate of the probability of escape fluctuates between 0 and 0.6 throughout the sample. The maximum is reached in the early 1970s. It is noteworthy that, from 1990 onwards, the trend of this probability is downhill, although with some slight peaks in some episodes in the 2000s. In recent periods, the estimate of the escape probability has increased from 0 to 0.01. This level is low in absolute and historical terms.

As mentioned in the description of the model, reforms can be cosmetic or fundamental. While this is indicative of the lack of pressure to implement any reforms, episodes where this probability increases could be associated with the implementation of stabilization programs and reforms in Uruguay. It is possible to think that, without the implementation of such measures, the probability of escape would have continued to grow, making the implementation of some reform imminent.

More specifically, the estimate of the probability of having an escape event peaks around 1967-1968. These could be associated with the consequences of the 1965 crisis and the reforms formulated as a result of it, as the creation of the Central Bank of Uruguay as a separate entity from the government. Similarly, this probability captures the economic instability associated with external shocks. Likewise, the probability of escape presents a local maximum at the end of 1990.

More generally, the model's estimates of probabilities reflect several of Uruguay's major economic events and largely coincide with the narrative of economic events in Oddone and Marandino (2020) and Banda, De Brun, and Oddone (2017).

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

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 National Institute of Statistics of Uruguay.

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 of Uruguay.

Estimation of the probability of escape