The number of states chosen for Mexico has a configuration for the process that follows the deficit of 3 states for the mean and 2 for the variance. The estimates use as input the inflation, month by month, adjusted for seasonality in the period from February 1969 to July 2021.
Inflation and Seasonally Adjusted Inflation
Notes: Month-to-month percentage changes of the Consumer Price Index. ”a.e”, refers to seasonally adjusted data. Sample: February 1969 to July 2021. Source: With data from the National Institute of Statistics and Geography (INEGI).
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
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 high-mean 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. More specifically, it is the maximum value of the deficit for the constraints in the model to be satisfied. The point in the standard error of the parameter σ(π) is due to the fact that the likelihood function of the model is very flat in the direction of such a parameter.
Prior to 1970, fiscal and monetary policies were successful in maintaining price stability for several years. It is plausible that estimates of the probability of being in states with a low mean and low variance close to one in the early 1970s are a reflection of this.
That said, as the 1970s progressed, estimates of the probabilities of being in a state with an intermediate mean increased. Throughout the 1980s, estimates of the probabilities of the state with a high mean and high variance increased, peaking in the early 1980s. For the 2000s, the estimate of the probability of being in the state with low mean and low variance remained close to one, with some positive probability estimated for the upper-middle state until the end of the sample.
With respect to the escape probability, its estimate remained close to one during the 1980s, with some ups and downs during that period. The estimate of this probability goes down in the 1990s. It presents a peak in December 1994, which coincides with the beginning of the well-known Tequila Crisis. That said, the estimate remains on the decline to practically zero in 1998. From the years 2000 onwards, its estimate remains essentially at zero until the end of the sample. As mentioned in the description of the model, the reforms may be cosmetic or fundamental.
The estimates of the dynamics of the probabilities of the different states seem to be largely in line with the narrative of several economic events relevant to Mexico such as those described in Ramos-Francia et al. (2018) and Meza (2018).
Estimation of the probability of being in one of the states of the model (mean, variance)
To consider any state for 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
state for the mean of the deficit it is necessary to add the probabilities of the states
, low) and (
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: February 1969 to July 2021. Source: With data from INEGI.
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 INEGI.
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: February 1969 to July 2021. Source: With data from INEGI .
Estimation of the probability of escape
Sample: February 1969 to July 2021. Source: With data from INEGI
Meza, F. (2018) . The Monetary and Fiscal History of Mexico: 1960-2017. University of Chicago, Becker Friedman Institute for Economics Working Paper, (2018-64) .
Ramos-Francia, M., S. García-Verdú, & M. Sánchez-Martínez (2018). Inflation Dynamics under Fiscal Deficit Regime Switching in Mexico. Bank of Mexico, Working Paper 2018-21. URL