Model Description
General Discussion
Monetary and fiscal policies are two of the main tools for pursuing and achieving macroeconomic stability. Coordination between such policies is relevant as both can have an impact on two of the most important relative prices in an economy: the real interest rate and the real exchange rate. The magnitude and temporality of such an impact depend on several factors: the level of inflation, the deviation of inflation from the central bank's target, the nature of financial frictions, the credibility of the monetary and fiscal authorities, the level of government debt, the dynamics of the fiscal deficit and the balance of external accounts, among others.
The government has to satisfy its inter-temporal budget restriction. In particular, in each period, expenditures minus revenues equals the deficit. Part of these revenues could come from the inflation tax. Thus, if the government cannot access financial markets to issue more debt, a rise in the inflation tax would decrease the real value of the nominal debt (denominated in local currency), thus, satisfying the budget constraint. This would subordinate monetary policy to fiscal policy (fiscal dominance).
The choice of which policy to use to address macroeconomic and/or financial shocks, or in some cases which combination of these, depends on their nature.
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Thus, it is essential to have both policies prepared within the toolbox of economic policy makers. A necessary condition for this to happen is the absence of fiscal dominance (Sargent and Wallace, 1981). In recent history, particularly in the 1980s and 1990s, several Latin American economies faced situations of fiscal dominance (e.g., Esquivel, C. et al. 2019).
However, the real value of foreign debt is not affected by inflationary shocks. In general, in order to service foreign debt, it is necessary to generate surpluses in the external accounts. To this end, the real exchange rate tends to depreciate, which in turn tends to increase exports and reduce imports. To the extent that the depreciation of the real exchange rate is a market phenomenon, reflecting an adjustment in the relative prices of the economy, this should not have a significant impact on inflation. Nonetheless, if monetary policy is used to try to generate a continuous depreciation of the nominal exchange rate (and therefore of the real exchange rate), this would result in a sustained increase in prices and inflation. Obviously, the risk is that it would initiate an inflationary spiral from the exchange rate to prices to the exchange rate. In this case, the inflationary tax would be operating on holders of debt denominated in local currency, and the resources collected would be directed to serve the foreign currency debt. Of course, this brings a redistribution of resources, from the holders of domestic debt to those of foreign debt. For all the above reasons, in many cases, to bring the economy out of a situation of fiscal dominance, several countries not only had to implement considerable structural improvements in their fiscal position, but also renegotiate their foreign debts. They also had to implement other types of reforms that would give greater credibility to their macroeconomic management. One of them was to provide autonomy or independence to their central banks with the explicit purpose, in most cases, of avoiding financing public spending with the inflation tax, and another was for central banks to operate with an inflation targeting scheme.
However, as is well known, and in light of the use of unconventional monetary policies in the major advanced economies, both in the aftermath of the global financial crisis and more recently in the COVID-19 crisis, the line between monetary and fiscal policies has become somewhat blurred. This has not been a problem for the advanced economies; however, it has generated a debate on the implications it may have on the emerging economies.
This shows the importance of closely monitoring inflation in the context of the prudent management of public finances.
1/ When an economy faces a shock, it is necessary to evaluate its nature. Also, it is necessary to consider that when responding to a shock using monetary policy there is a bias towards interest rates absorbing a larger portion of the shock. In responding to a shock using fiscal policy, there is a bias towards the real exchange rate absorbing a larger share of the shock. Thus, it is necessary to have both policies in place to be ready to respond.
Model
Motivation
Fiscal and monetary policies are intrinsically linked through various channels. Moreover, the intensity of this link changes under different macroeconomic conditions and/or contingencies. A general approach considers the budget constraints of the government and the central bank as one. Thus, for example, when a government has fiscal problems, it may be forced to obtain resources from the central bank. Additionally, the relationship between fiscal and monetary policies may be subject to structural changes. Indeed, a favorable structural fiscal change may contribute to stabilizing inflation expectations or to reinforcing previously achieved stability.
The economic history of the region in the last decades of the previous century, and in some cases until more recently, was characterized by periods of instability and contrasts in policy implementation. While one might think that the causes of the crises are different in each case, the subsequent evolution of the main macroeconomic indicators followed similar patterns. In most of the crises, the underlying cause has been a fiscal one.
It is important to emphasize that fiscal problems arise not only because of the size of the expenditure, but also because of the capacity to collect taxes as a function of government spending (Esquivel, C. et al. 2019). This is determined by present tax collection and debt issuance capacity (i.e., future tax collection). The accumulation of fiscal deficits is what may generate inflationary pressures, given the possible need to finance part of such deficits with money issuance (inflation). To the extent that economies are perceived to have sufficient future revenue capacity (i.e., that they can continue to issue debt), such pressures should not be generated. However, the existence of high fiscal deficits and inflation may lead to a crisis. Under this scenario, implementing changes in the management of public finances would have to issue sufficient credibility that the government will recover its tax collection capacity in relation to its spending.
On the other hand, agents' inflation expectations depend, among other factors, on budget restrictions being met and on debt paths and fiscal deficits being sustainable. These expectations are formulated given the information that the agents have. For example, agents could formulate their expectations depending on their estimation error of the previous period. If their expectation was higher (lower) than the realized inflation, it is likely that they correct downwards (upwards). Also, if they believe that the discrepancy between their expectation and actual inflation was due to an unlikely state, they may not consider it relevant to make a correction. More generally, the formation of inflation expectations influences, to a large extent, the observed inflation.
Background
The following are some of the seminal works that have studied the interrelationship of fiscal and monetary policies.
Cagan's classic model (1956) involves a demand for money and an expectation-formation mechanism. In this model, in general, for a level of tax collection per seigniorage there are two inflationary equilibriums: one associated with a low level of inflation and another associated with a high level of inflation. Under certain conditions (which are considered reasonable), the first would be stable and the second unstable. This suggests that the transition from a high to a low inflation equilibrium implies numerous challenges and will require the implementation of various economic policies. Among these, the government's commitment to clean up public finances could be highlighted, as well as the coordination of the different agents to anchor their inflation expectations at low and stable levels.
A seminal article in this literature is Sargent and Wallace (1981). Under their model, nominal government debt is expressed in real terms as a function of expected fiscal flows and seigniorage. Under the assumption that, at the end of time, the public debt is indeed repaid, the authors add the budget constraints of the government and the central bank. If there were an expectation that fiscal flows might not be sufficient to support the real value of the nominal debt, then the inflation tax would have to increase, which would imply a raise in inflation. ^{2/}
Bruno and Fischer (1990) study the stability of dual inflation equilibrium under fiscal deficits financed by the inflation tax. The authors emphasize that the stability of the two inflation balances, one with high inflation and the other with low inflation, depends on the speed with which the demand for money and inflation expectations adjust to changes in inflation. ^{3/}
Intuitively, the authority's ability to obtain resources through the inflation tax depends on how quickly agents in the economy adjust their demand and inflation expectations. On one hand, the adjustments can be slow. In this case, agents can adjust their demand for money slowly in the face of rising inflation. Likewise, they can adjust their inflation expectations slowly. Under this scenario, the real value of resources that can be obtained by the authority through the inflation tax is greater than if both adjustments were relatively faster. Thus, a slow response by agents allows the authority to have more resources available via the inflation tax. On the other hand, adjustments can be fast. In this case, agents can adjust their demand for money quickly in the face of an increase in inflation, decreasing their money holdings. Likewise, they can adjust their inflation expectations quickly. Under this scenario, the real value of the resources the government can obtain through such a tax is lower. In sum, the relative magnitudes of the responses determine the properties of the equilibrium in question.
In Bruno and Fischer’s model, under a high inflation equilibrium, if the demand for money responds slowly to the expected inflation and the inflation expectations adapt slowly to changes in inflation, the agent is not able to adapt when changes in said inflation level are important, so the referred equilibrium is unstable. Under a low inflation equilibrium, the sluggishness of the responses corresponds to small changes in low inflation levels, so the low balance is stable. Conversely, if the demand for money responds quickly to expected inflation and inflation expectations adapt quickly to changes in inflation, the agent can adapt to important changes in inflation, so the high inflation equilibrium is stable. Similarly, by responding quickly to changes in low inflation levels, the agent responds disproportionately, making the low inflation equilibrium unstable.
Bruno and Fischer, like Cagan, use a semi-logarithmic demand for money and an adaptive mechanism of expectations formation, but, in their case, they include the government's budget restriction. In their model, the economy could be trapped in a high inflation equilibrium, even though the low inflation equilibrium is feasible, given the same public financing needs. It should be noted that, if the demand for money has a semi-logarithmic shape, then a given tax collection for the inflationary tax can be congruent with two different levels of inflation: one high, and one low (in fact, you have a "Laffer curve" for the inflation tax). In such a model, there is a unique equilibrium under certain conditions. For example, when financing deficits through bonds is allowed, keeping the nominal growth of money fixed. Intuitively, by allowing bond financing, the government gains flexibility, and by fixing the nominal growth of money, it gains credibility. This only works if the bonds finance temporary deviations from net government expenditures.
Based on the model of Bruno and Fischer, Bruno (1989) tackles the design of economic reforms. He conceives a reform as a transition from a balance characterized by high inflation, to one with low and stable inflation, which is Pareto-superior, based on some economic program. Bruno applies this logic to a program implemented in Israel to stabilize inflation. This program involved corrections in the government budget and external accounts, and the implementation of agreed price and wage increases among the different sectors in the economy. The latter with the aim of coordinating the inflation expectations of economic agents in a low and stable inflation.
It is worth mentioning that the nature of dual inflationary equilibriums of models such as those presented in Bruno (1989) and Bruno and Fischer (1990) is different from that of dual inflationary equilibriums of models such as those of Sargent al. (2009). The first difference is the characterization of the stability of the equilibriums. While in Bruno (1989) and Bruno and Fischer (1990) the stability of each equilibrium depends on the estimated values of certain parameters, in the model of Sargent et al. (2009), in general, the stable equilibrium is the one with the lowest level, and the unstable equilibrium is the one with the highest level, if they exist. Also, the comparison is not straightforward because the dual equilibriums in Sargent et al. (2009) are defined in terms of expected inflation in a framework that includes several stochastic elements in the model.
Model by Sargent, Williams and Zha (2009)
This section intuitively explains the model proposed by Sargent et al. (2009, SWZ). This is the model that is estimated and used to explore the relationship between three fundamental variables in the interaction between fiscal and monetary policies: inflation, its expectations and the fiscal deficits financed by the inflation tax. In particular, this model is estimated for some Latin American economies. Also, the results are briefly discussed based on the narrative of some of the main events in each economy.
SWZ propose a model that attempts to capture the financing of fiscal deficits through seigniorage using inflation time series as the only input. This is a nice feature of the model as there is usually less access to fiscal data. In contrast, many economies present their inflation data in a timely manner and it is reasonable to assume that, at least in relative terms, their measurement is better than that of the fiscal variables associated with the model.
The SWZ model consists of four main components: a demand for money based on expected inflation, a government budget constraint, and a process of formation of agents' inflation expectations. Likewise, fiscal deficits follow a probability distribution that depends on two parameters: their mean and their variance.
These two parameters follow, in turn, two Markov processes: one determines the value of the mean, and the other the value of the variance. The two processes are assumed to be independent. The use of Markov processes implies that the probability that a parameter changes in value depends only on the value it has in the period in question. In particular, the probability does not depend on the history of the values the parameter has had, only on the value it has. The magnitudes of the possible values that the mean and variance can take provide valuable information about the dynamics of the deficits. It is worth mentioning that the model allows to estimate the probability that a certain parameter has a specific value in a given period. In practice, it is assumed that the parameter actually has the value whose probability is the highest (with respect to the probabilities of the other parameters) in a given period. The dynamics of these probabilities are very important for the interpretation of the results. Naturally, they are reported.
Although this type of model estimates the value of each of the parameters, the total number of parameters must be determined before the final estimation. Thus, there are several options. First, assume the number of values for each parameter of the model, which is usually done based on previous knowledge of the data or the model. Second, estimate the model with different numbers of parameters and implement tests to determine the best fit between them. In any case, the main interest is that the estimates are economically reasonable and have some congruence with major economic events.
In general, for each value of the average deficit, the model has two balances, which are associated with two levels of inflation expectations, one high and one low. In these equilibriums, the inflation expectations of the agents are a good approximation to the expected inflation, conditional on a value of the average of the deficit. These balances are called Self-Confirming Equilibriums (SCE).
This approach is better to the extent that the probability that the mean value is maintained is close to one. In practice, this probability is usually close to one. ^{4/} The SCEs are the equilibriums equivalent to the equilibriums in Cagan's classical model (1956). The SCEs can be interpreted as more general equilibriums.
Similar to the referred model, the equilibrium associated with the high level of inflation is unstable. Conversely, the equilibrium associated with the low level of inflation is stable. More specifically, the stable interval of the equilibrium associated with the low level of inflation is found between zero and the equilibrium associated with the high level of inflation. On the contrary, if expected inflation is higher than the equilibrium associated with the high level, then the expected inflation would grow without limit. In other words, the fact that expected inflation is above the high inflation equilibrium implies that it would become unstable.
The model allows for the estimation of the probability that the expected inflation is higher than the high equilibrium level, which would become unstable, as already indicated. This probability is called the escape probability. To avoid an escape event, authorities can implement some kind of reform.
Intuitively, a reform involves making the level of expected inflation stable. Also, it can be interpreted to involve preventing expected inflation from becoming unstable. This can be achieved in two ways in this model.
First, if you change the expected inflation directly to a stable interval. In SWZ, it is reset to a sufficiently low (random) level.
Second, if the average of the deficit changes from one value to another in such a way that the expected inflation remains in the stable interval. This is because a transition of the average deficit from one value to another modifies the equilibriums of expected inflation and, notably, the stability interval of expected inflation. A decrease in the deficit average makes the stability interval larger.
In the model, when a reform occurs without a transition for the mean parameter to a smaller value, it is called a cosmetic reform. On other hand, if the reform involves a transition from the mean parameter to a lower value so that expected inflation is in a stable interval, it is called a fundamental reform. In principle, it is not ruled out that the two types of reform could take place at the same time. However, this would be unusual. Also, based on the estimates, the interpretation is that a fundamental reform is more difficult to achieve.
2/ More generally, seigniorage is understood as the sum of the monopoly income, since the state is the only issuer of the currency in a given district, and of the inflation tax.
3/ Analytically, it depends on the product of the semi elasticity of the demand for money with respect to the expected inflation (𝜆) by the weight (𝜈) that the agent gives to the observed inflation, in the formation of the expected inflation. The weight (1-𝜈) is assigned to the previous period's expected inflation. Specifically, if your product is less than one (𝜆𝜈 < 1), the balance of low-level inflation is stable and the balance of high-level inflation is unstable. On the other hand, if your product is larger than one (𝜆𝜈 > 1), the low-level inflation balance is unstable and the high-level inflation balance is stable.
4/ The estimation of the SCE involves solving a set of differential equations. For further details on the determination of such equations please refer to Sargent et al. (2009) or Ramos-Francia et al.
General considerations
About the estimates for each country
We assume that the number of regimes for the mean and the variance of the process that the deficit follows is 2 and 3, respectively. This, to make a direct comparison with SWZ, who determine that these are the optimal numbers for such regimes, according to the sample they use. It should be noted that this number of regimens could change when considering different samples.
We assume that the number of regimes for the mean and the variance of the process that the deficit follows is 2 and 3, respectively. This, to make a direct comparison with SWZ, who determine that these are the optimal numbers for such regimes, according to the sample they use. It should be noted that this number of regimens could change when considering different samples.
We assume that the number of regimes for the mean and the variance of the process that the deficit follows is 3 and 2, respectively. This allows us to have estimates consistent with the relevant economic events for the Mexican economy. As mentioned, the number of regimes must be determined using some information criteria.
We assume that the number of regimes for the mean and the variance of the process that the deficit follows is 3 and 2, respectively. This, to make a direct comparison with SWZ, who determine that these are the optimal numbers for such regimes, according to the sample they use. It should be noted that this number of regimens could change when considering different samples.
We assume that the number of regimes for the mean and the variance of the process that the deficit follows is 2 and 2, respectively. This allows us to have estimates consistent with the relevant economic events for the Uruguayan economy. As mentioned, the number of regimes must be determined using some information criteria.
References
- Bruno, M. (1989). Econometrics and the Design of Economic Reform. Econometrica , 57(2), pp. 275-306.
- Bruno, M., & S. Fischer (1990). Seigniorage, operating rules, and the high inflation trap. The Quarterly Journal of Economics , 105(2), pp. 353-374.
- Cagan, P. (1956). The monetary dynamics of hyperinflation. In Studies in the Quantity Theory of Money, edited by Milton Friedman. University of Chicago Press.
- Esquivel, C., T. J. Kehoe & J. P. Nicolini (2019). Lessons from the Monetary and Fiscal History of Latin America. University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2019-47.
- 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
- Sargent, T. and N. Wallace (1981). Some unpleasant monetarist arithmetic. Federal Reserve Bank of Minneapolis Quarterly Review , 5(3), pp. 1-17.
- Sargent T., N. Williams and T. Zha (2009). The Conquest of South American Inflation. Journal of Political Economy , University of Chicago Press, 117(2), pp. 211-256.