Expectations, Credibility, and the Persistence of Currency Substitution

Abstract

This study examines why currency substitution proves so difficult to reverse, even after countries succeed in stabilizing inflation. Focusing on Bolivia, Brazil, Mexico, and Turkey—economies that endured severe inflationary episodes before implementing stabilization programs—the paper asks a simple but important question: why does reliance on foreign currency persist long after inflation has been brought down? To answer this, the analysis adopts a structural time-series state-space framework that allows behavioral parameters to evolve gradually over time. Rather than assuming persistence, the model lets it emerge from the data and, crucially, compares alternative ways in which agents might form expectations about exchange rate movements. The evidence reveals a consistent pattern. By the end of the sample period, currency substitution remains statistically and economically significant in all four countries. The dominant expectation mechanism is extrapolative: agents tend to look at recent depreciation and assume it will continue. This tendency creates a reinforcing loop—when currencies depreciate, expectations of further depreciation strengthen, and the incentive to hold foreign currency intensifies. What makes these findings particularly striking is that this dynamic does not vanish once inflation is stabilized. Even in periods of relative macroeconomic calm, substitution persists. Past instability leaves a lasting imprint on expectations, and concerns about the durability of policy reforms continue to shape monetary behavior. In several cases, ongoing depreciation against the U.S. dollar further validates these cautious beliefs. As a result, the findings suggest that currency substitution is not merely a mechanical residue of past inflation. It is sustained by the way people form and update expectations in environments marked by credibility challenges. Stabilizing inflation is therefore a necessary step, but it is not enough on its own. Durable confidence in the domestic currency requires rebuilding credibility in a way that gradually reshapes expectations and restores trust over time.

1. Introduction

This paper examines why currency substitution often persists even after inflation has been brought under control. The analysis focuses on Bolivia, Brazil, Mexico, and Turkey not simply as illustrative cases, but because they offer a particularly informative setting for studying post-stabilization dynamics. Each of these countries experienced severe inflationary episodes followed by formal stabilization efforts, yet currency substitution remained present well beyond the stabilization phase. At the same time, their institutional trajectories, exchange-rate arrangements, and credibility-building paths differ in meaningful ways. This combination of shared inflationary histories and heterogeneous policy experiences provides a natural laboratory for examining whether persistence reflects historical scars or ongoing expectation dynamics.

The contribution of the study lies in moving beyond mechanical explanations of persistence. Rather than relying on ratchet variables tied to past inflation peaks, the paper allows the substitution elasticity itself to evolve gradually within a stochastic trend state-space framework. This makes persistence an empirical outcome rather than an imposed assumption. In addition, the study evaluates extrapolative, adaptive, and regressive expectation mechanisms within a unified structure, enabling a direct comparison of how beliefs are formed after stabilization. By concentrating explicitly on post-stabilization regimes, the analysis sheds light on the process of credibility rebuilding and clarifies whether continued substitution reflects inherited memory or forward-looking expectation formation.

High inflation rarely leaves economies untouched once price stability is restored. A substantial body of research shows that one of its most durable legacies is currency substitution—the continued reliance on foreign currency for transactions and savings even after inflation declines (Calvo & Végh, 1992; Mongardini & Mueller, 2000). This behavior poses a meaningful challenge to monetary sovereignty and weakens the effectiveness of domestic monetary policy, particularly in emerging and post-crisis economies (Végh, 2013).

The persistence of substitution suggests that the issue extends beyond contemporaneous inflation rates. Episodes of severe inflation or exchange rate instability can erode trust in the domestic currency in ways that are not easily reversed. Even when stabilization programs succeed in lowering inflation, confidence may recover only gradually. While this intuition is widely acknowledged (Calvo & Végh, 1992), much of the empirical literature captures persistence using ratchet variables constructed from historical inflation or depreciation peaks. Although informative, this approach risks attributing persistence to historical maxima rather than to evolving expectations.

This study approaches the problem differently. Instead of imposing persistence through historical benchmarks, it allows the substitution elasticity to evolve within a stochastic trend state-space model. This framework makes it possible to observe whether agents continue to react strongly to expected depreciation after stabilization. In addition, the paper compares extrapolative, adaptive, and regressive expectation mechanisms within a unified empirical structure. By focusing on post-stabilization regimes beginning in the mid-1990s, the analysis isolates credibility rebuilding from the measurement distortions typical of hyperinflationary breakdowns, consistent with discussions of stabilization dynamics in developing economies (Calvo & Végh, 1999).

The policy relevance of this question is clear. In extreme cases, countries have resorted to full currency substitution as a response to monetary collapse. Zimbabwe, for example, abandoned its domestic currency in 2009, and similar debates have emerged in other high-inflation environments. Yet even in countries that avoid official dollarization, informal substitution may remain widespread long after stabilization. Understanding why this happens is central to evaluating the durability of monetary reforms.

The structure of the paper is as follows. The subsequent section surveys the relevant literature on expectation formation and currency substitution. This is followed by the specification of the model and the estimation approach, along with a description of the data and the practical findings. The final section concludes.

2. Literature Review

2.1. Theoretical Perspectives on Currency Substitution

Currency substitution sits at the heart of monetary economics because it forces us to confront a basic question: what ultimately sustains confidence in money? The value of money arises not only from its official or legal standing but also from collective belief in its stability. Classical monetary theory distinguishes between its functions as a means of payment, a store of purchasing power, and a unit used to measure prices. In practice, the shift toward foreign currency often begins quietly—typically as a defensive portfolio decision when inflation erodes purchasing power—but it can gradually extend into everyday transactions, at which point monetary sovereignty becomes visibly constrained (McKinnon, 1982; Giovannini & Turtelboom, 1992). For this reason, following Calvo and Végh (1992), the present study focuses on the medium-of-exchange dimension, where substitution directly affects policy effectiveness.

From a portfolio-choice perspective under exchange rate uncertainty (Miles, 1978), agents allocate wealth between domestic and foreign currencies based on expected returns and risks. When expected depreciation rises, holding domestic money becomes more costly relative to foreign currency. What may begin as a rational hedging strategy during inflationary turmoil can gradually solidify into persistent monetary behavior. Crucially, this shift depends less on past inflation itself and more on how agents interpret the future.

Severe inflation undermines trust in money’s store-of-value function. Yet the long-term consequences hinge on credibility. Stabilization programs can reduce inflation quickly, but rebuilding confidence often takes longer (Calvo & Végh, 1992; Végh, 2013). If agents remain uncertain about the durability of reforms, they may continue to protect themselves against potential depreciation. In this way, expectations become the bridge between past instability and present monetary choices.

Two interpretations therefore compete. One attributes persistence to memory: once inflation reaches extreme levels, its legacy lingers mechanically. The other emphasizes ongoing belief formation: substitution persists because agents continue to project recent exchange-rate movements forward. Distinguishing between these views is not merely technical—it speaks directly to whether currency substitution is fundamentally backward-looking or driven by active, forward-looking expectations. This distinction provides the conceptual foundation for the empirical strategy adopted here.

2.2. Empirical Evidence and the Question of Persistence

Empirical studies typically analyze currency substitution within money demand frameworks where expected depreciation or inflation enters as a key opportunity-cost variable (Miles, 1978). When the local currency depreciates, foreign currency becomes relatively more attractive, leading to a reduction in the demand for domestic money. A substantial body of cross-country evidence confirms this negative relationship, particularly in economies marked by recurring macroeconomic instability (Bahmani-Oskooee & Tanku, 2006; Temperley, 2022; Ouattara & Kone, 2023).

To capture persistence, many studies incorporate ratchet variables based on historical inflation or depreciation peaks (Mongardini & Mueller, 2000). These variables formalize an intuitive idea: once economic agents experience extreme inflation, they do not easily revert to prior monetary habits. While this approach has been useful in documenting hysteresis, it also builds persistence into the specification itself. As a result, it becomes difficult to determine whether substitution continues because agents remain responsive to ongoing risks or simply because the model embeds historical maxima mechanically.

A growing strand of research highlights credibility and expectation formation as central drivers of post-stabilization dynamics. Yet relatively few contributions compare alternative expectation mechanisms within a common empirical structure. Without such comparison, it is challenging to assess whether agents extrapolate recent depreciation, adjust beliefs gradually through adaptive learning, or expect exchange rates to revert toward equilibrium. Understanding which of these mechanisms dominates is essential for interpreting persistence—not as a passive legacy of the past, but as an active reflection of how agents continue to process new information.

Addressing this issue requires an empirical framework that allows behavioral parameters to evolve over time rather than remain fixed. Only then can persistence be observed as it unfolds, instead of being imposed ex ante through historical thresholds.

2.3. Research Gap and Guiding Hypotheses

The discussion above suggests that the persistence of currency substitution cannot be understood solely by referring to past inflation peaks. Instead, it may depend on how expectations are formed and updated after stabilization.

To examine this issue more directly, the empirical analysis is guided by three testable propositions. First, if substitution truly persists beyond stabilization, the substitution elasticity should remain statistically significant and negative. Second, if agents form expectations by projecting recent exchange rate movements into the future, extrapolative mechanisms should provide the strongest empirical support. Third, if agents expect exchange rates to revert toward equilibrium, regressive expectation models should not be consistent with sustained substitution behavior. These propositions are evaluated within a stochastic trend state-space framework that allows substitution elasticity to evolve gradually over time. In doing so, the analysis connects theoretical intuition about credibility and expectations with a flexible empirical structure capable of capturing post-stabilization dynamics.

3. Model Specification and Estimation

This section presents the empirical framework used to estimate currency substitution dynamics. The empirical framework is expressed in a linear Gaussian state-space representation, allowing key behavioral parameters to evolve over time. This approach is particularly suitable in post-stabilization environments, where credibility and expectation formation may adjust gradually rather than discretely.

3.1. Observation Equation

Real money balances are expressed as follows:

$$m_t={\mu }_t+{\beta }_t{E}_t\left(∆s_{t+1}\right)+{\epsilon }_t$$

(1)

where $m_t$ is logarithm of real domestic money balances, $E_t\left(∆s_{t+1}\right)$ is the anticipated exchange rate depreciation, ${\mu }_t$ denotes the intercept that evolves over time and captures structural factors. ${\beta }_t$ is time-varying substitution elasticity, and ${\epsilon }_t$ is the disturbance term, assumed normally distributed with zero mean; ${\epsilon }_t ~ N(0,{\sigma }_{\epsilon }^2)$.

A negative value of ${\beta }_t$ indicates currency substitution: higher expected depreciation reduces demand for domestic money. Allowing both ${\mu }_t$ and ${\beta }_t$ to vary over time ensures that persistence is not imposed mechanically, but instead emerges from evolving expectations and credibility conditions.

3.2. Stochastic Trend Representation

To clarify the structure of parameter evolution, the state equations are written in compact matrix form as a local linear trend model:

$$\left[\begin{array}{c}{\mu }_t\\ {\beta }_t\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]\left[\begin{array}{c}{\mu }_{t-1}\\ {\beta }_{t-1}\end{array}\right]+\left[\begin{array}{c}{\eta }_t\\ {\zeta }_t\end{array}\right]$$

(2)

where ${\zeta }_t ~ NID(0,{\sigma }_{\zeta }^2)$ and ${\eta }_t ~ NID(0,{\sigma }_{\eta }^2)$. ${\mu }_t$ represents the level component of the series, and ${\beta }_t$ captures the slope. These correspond, respectively, to the intercept and the time-trend coefficient.

In scalar form, it implies:

$${\mu }_t={\mu }_{t-1}+{\beta }_{t-1}+{\eta }_t$$

(3)

$${\beta }_t={\beta }_{t-1}+{\mathsf{\zeta }}_t$$

(4)

Here, ${\mu }_t$ represents the evolving level of money demand and ${\beta }_t$ represents the evolving slope (substitution elasticity). In this formulation, the level represents the intercept, while the slope captures the coefficient associated with the time trend in a standard regression specification. This formulation makes explicit that the intercept follows a stochastic trend whose growth rate is governed by the evolving slope component. The previously used random-walk specification is therefore a special case of this more general stochastic trend structure.

3.3. Why a Stochastic Trend Instead of a Ratchet Variable?

Much of the currency substitution literature captures persistence using a ratchet variable constructed from past inflation or exchange rate maxima. While informative, such an approach imposes persistence mechanically through historical benchmarks. In contrast, the stochastic trend specification allows persistence to arise endogenously through gradual parameter evolution. If agents continue to react strongly to expected depreciation after stabilization, this will be reflected in a persistently negative final-state estimate of ${\beta }_t$. Persistence therefore becomes an empirical outcome rather than an imposed assumption.

3.4. Estimation Strategy

Parameter estimation relies on a Kalman filtering procedure in which the likelihood function is maximized (Harvey, 1989; Durbin & Koopman, 2012). The estimation proceeds recursively: Prediction step: the current state is predicted using information available up to time t−1. Updating step: the prediction is revised using the observed value of $m_t$. Likelihood construction: prediction errors are used to construct and maximize the log-likelihood function.

Diffuse initial conditions are used for the state vector to minimize the influence of arbitrary starting values. The variance parameters ${\sigma }_{\epsilon }^2$, ${\sigma }_{\eta }^2$ and ${\sigma }_{\mathsf{\zeta }}^2$ are estimated jointly with the state variables. If the estimated state variances were equal to zero, the model would collapse to a fixed-coefficient regression. Their statistical significance therefore confirms genuine time variation in the parameters. For inference, smoothed state estimates are used rather than only filtered estimates. The smoothed estimates incorporate information from the entire sample, providing more efficient and stable measures of the final substitution elasticity.

3.5. Identification and Interpretation

Identification relies on sufficient variation in expected depreciation over time. The signal-to-noise ratio between state disturbances and the observation disturbance governs the degree of parameter flexibility:

Low state variance implies near-constant parameters.

Higher state variance implies greater behavioral adaptation.

A statistically significant and negative final smoothed estimate of β_t indicates that currency substitution persists at the end of the sample period.

This framework ensures that persistence is inferred from the data rather than mechanically imposed through historical variables, while maintaining full statistical coherence within a state-space structure.

4. Modelling Expectations

A central challenge in modeling currency substitution lies in capturing how agents form expectations about future exchange rate movements. Since expected depreciation is not directly observable, the empirical analysis relies on alternative expectation formation mechanisms that translate observable exchange rate behavior into beliefs about future depreciation. Before introducing the formal equations, it is useful to provide simple intuition for each mechanism.

Extrapolative expectations reflect the idea that agents project recent exchange rate movements into the future. When the domestic currency depreciates today, agents expect further depreciation tomorrow. This mechanism is particularly plausible in high-inflation environments where past instability shapes pessimistic beliefs.

Adaptive expectations assume that agents revise expectations gradually. New information affects beliefs, but only partially, implying inertia and slow adjustment.

Regressive expectations are based on mean reversion. Agents expect the exchange rate to return toward a perceived long-run equilibrium level, implying that current depreciation is expected to be reversed.

With this intuition in mind, the empirical specifications are introduced as follows.

4.1. Extrapolative Expectations

The simplest extrapolative mechanism assumes that expected depreciation is proportional to the most recent observed depreciation:

$$\Delta s_{t+1}^e=\delta \Delta s_t$$

(5)

The persistence in currency substitution can be interpreted as the outcome of slowly adjusting expectations and beliefs, rather than as the mechanical result of a fixed ratchet mechanism. The corresponding model takes the following form:

$${(m-p)}_t={\mu }_t+{\gamma }_t\Delta s_{t+1}^e+{\epsilon }_t$$

(6)

Here, ${(m-p)}_t$ is defined as the log of real money balances and $\Delta s_{t+1}^e$ is anticipation formed at time t + 1 regarding the exchange rate variation in period t. The coefficient $\gamma$ measures substitution elasticity with respect to $\Delta s_{t+1}^e$. Combining Equations (5) and (6) produces the following relationship:

$${(m-p)}_t={\mu }_t+\varphi \Delta s_t+{\epsilon }_t$$

(7)

where $\varphi =\gamma \delta$. The currency substitution condition $\varphi <0$ requires that $\delta >0$, which implies a destabilizing expectation, meaning an increase in the exchange rate is anticipated to continue in the same direction. On the other hand, if $\delta <0$, indicating a stabilizing expectation, it follows that $\varphi >0$. Since the condition $\delta <0$ indicates that domestic currency depreciation is expected to be reversed, it means that reverse currency substitution takes place. Consequently, the $\Delta s_t$ coefficient identifies whether expectations exhibit stabilizing or destabilizing behavior.

4.2. Generalized Extrapolative Expectations

A more flexible extrapolative mechanism allows agents to use more than one lag of exchange rate changes:

$$\Delta s_{t+1}^e=(1-\phi )\Delta s_t+\phi \Delta s_{t-1}$$

(8)

The corresponding money demand equation becomes:

$${(m-p)}_t={\mu }_t+\gamma (1-\phi )\Delta s_t+\gamma \phi \Delta s_{t-1}+{\epsilon }_t$$

(9)

In Equation (9), currency substitution is indicated by significantly negative coefficients on $\Delta s_t$ and $\Delta s_{t-1}$, or at least one of them. If the coefficient on $\Delta s_t$ is significant, while the coefficient on $\Delta s_{t-1}$ is insignificant, this means that expectation is formed based on the latest observed exchange rate variation at time t, while disregarding changes occurring in previous periods. In this case, $\phi =0$, so Equation (9) reduces to Equation (7).

4.3. Adaptive Expectations

Under adaptive expectations, agents revise beliefs gradually according to past forecast errors:

$$\Delta s_{t+1}^e=\Delta s_t^e+\kappa (\Delta s_t-\Delta s_t^e)$$

(10)

where $0<\kappa \le 1$. By solving Equation (1) for $\Delta s_{t+1}^e$ and applying the lag operator, we obtain

$$\Delta s_t^e=-{\displaystyle \frac{{\mu }_{t-1}}{\gamma }}+{\displaystyle \frac{1}{\gamma }}{(m-p)}_{t-1}-{\displaystyle \frac{1}{\gamma }}{\epsilon }_{t-1}$$

(11)

By substituting and re-arranging, we obtain

$${(m-p)}_t={\mu }_t^{\prime }+\kappa \gamma \Delta s_t+(1-\kappa ){(m-p)}_{t-1}+{\epsilon }_t^{\prime }$$

(12)

where ${\mu }_t^{\prime }$ and ${\epsilon }_t^{\prime }$ are the modified trend and random components, which are defined as ${\mu }_t^{\prime }={\mu }_t-(1-\kappa ){\mu }_{t-1}$ and ${\epsilon }_t^{\prime }={\epsilon }_t-(1-\kappa ){\epsilon }_{t-1}$. If $\kappa =1$, Equation (10) collapses to a representation of static expectations. This would be the case if the variable ${(m-p)}_{t-1}$ fails to reach statistical significance.

4.4. Regressive Expectations

The regressive expectations hypothesis can be represented by the equation

$$\Delta s_{t+1}^e=-\theta (s_t-{\overline{s}}_t)$$

(13)

where the right-hand-side variable represents deviation from the equilibrium exchange rate ${\overline{s}}_t$, such that $\theta >0$. If $s_t>{\overline{s}}_t$, then $\Delta s_{t+1}^e<0$, and vice versa. This leads to the following representation of the money demand function:

$${(m-p)}_t={\mu }_t-\theta \gamma (s_t-{\overline{s}}_t)+{\epsilon }_t$$

(14)

which yields the following representation

$${(m-p)}_t={\mu }_t^{\prime }-\theta \gamma s_t+{\epsilon }_t$$

(15)

where ${\mu }_t^{\prime }={\mu }_t+\theta \gamma {\overline{s}}_t$. Currency substitution in this model is indicated by a significantly positive $\theta$. A high value of $s_t$ signals an expectation that the foreign currency will lose value, which strengthens the preference for holding domestic money.

4.5. Inflation Expectations and Depreciation: A Robustness Consideration

Using expected exchange rate depreciation together with expected inflation in a single model specification raises methodological concerns because the two variables are closely linked through purchasing power parity, particularly during high inflation. Empirically, this manifests as severe multicollinearity.

As a robustness check, the model was re-estimated including both expected inflation and expected depreciation. The results show unstable coefficients and inflated standard errors, with neither variable remaining consistently significant. This confirms that jointly including both expectations obscures identification rather than improving explanatory power. Accordingly, the baseline specification relies on expected depreciation as the single summary measure of inflationary expectations.

5. Data and Empirical Results

The analysis utilizes monthly observations for Bolivia, Brazil, Mexico, and Turkey sourced from the International Financial Statistics (IFS). The study is based on three primary variables: nominal exchange rate, which represents the domestic-currency value of one U.S. dollar, quantity of money, and consumer price index (CPI). Quantity of money in real terms is constructed via deflating money by CPI, and all variables are expressed in logarithms. The depreciation measure is obtained by taking the first difference in the exchange rate expressed in logarithmic form.

The data are organized according to widely accepted empirical conventions used in research on currency substitution and money demand, where logarithmic transformations and first differences are employed to capture proportional changes and mitigate non-stationarity (Cagan, 1956; Miles, 1978; Calvo & Végh, 1992). By aligning variable definitions with earlier studies, the results are directly comparable to existing empirical evidence on exchange-rate-driven money demand behavior.

The sample begins in January 1995–January 2024. The starting date is chosen intentionally to balance data availability and economic relevance. For all four countries, the mid-1990s mark the transition from episodes of very high inflation toward stabilization efforts, while also ensuring reasonably consistent monetary definitions across time. Starting the sample earlier would require combining periods of extreme hyperinflation with less reliable monetary aggregates, potentially obscuring post-stabilization dynamics that are central to the research question.

This sample design is consistent with earlier studies emphasizing the importance of focusing on post-stabilization regimes when analyzing expectation formation and money demand behavior (Calvo & Végh, 1999). Restricting the sample in this manner allows the analysis to isolate persistent behavioral mechanisms rather than conflating them with measurement issues typical of hyperinflationary breakdowns.

Major regime changes and stabilization episodes are accommodated through the stochastic trend structure of the model. Rather than imposing discrete structural breaks, the joint evolution of the level and slope components allows gradual adjustment in response to changing credibility conditions. This approach captures smooth transitions in behavioral responses without requiring exogenous break dates. This approach is well suited to capturing credibility rebuilding and expectation adjustment, which typically unfold slowly rather than at a single identifiable moment. In this sense, regime changes are reflected in the evolution of the estimated parameters rather than treated as exogenous structural breaks.

To verify the stability of the results, the estimation was repeated using an alternative monetary aggregate. Specifically, broad money was replaced with a narrower monetary aggregate where available. The key findings remain unchanged: the final sample estimates show a negative and statistically significant substitution elasticity, and extrapolative expectations continue to dominate across specifications. This confirms that the persistence of currency substitution is not driven by a particular choice of monetary aggregate.

The results of the maximum likelihood estimation for the currency substitution model, evaluated under several expectation formation mechanisms, are presented in Table 1, Table 2, Table 3 and Table 4. Each table reports the final smoothed estimates for the time-varying slope component ${\beta }_t$ from the stochastic trend model. Within the local linear trend framework presented in Section 3, the parameter ${\beta }_t$ measures the changing substitution elasticity that characterizes the reaction of demand of real money to anticipated exchange rate depreciation. If the final smoothed estimate is statistically significant with a negative sign, this indicates that currency substitution remains active at the end of the sample. Because the slope evolves jointly with the level component under the stochastic trend specification, persistence reflects gradual structural adjustment rather than a mechanically imposed historical effect.

Table 1. Maximum Likelihood Estimate Extrapolative Expectations 1.

	Bolivia	Brazil	Mexico	Turkey
${\mu }_t$	5.947	7.735	10.053	7.898
	(39.86)	(50.04)	(25.83)	(34.17)
${\beta }_t$	0.002	0.006	0.005	0.009
	(0.17)	(3.35)	(0.19)	(3.13)
$\Delta s_t$	−2.964	−5.475	−3.494	−7.084
	(−47.89)	(−46.14)	(−25.54)	(32.53)
$R_d^2$	0.78	0.34	0.94	0.44
Q	10.10	3.50	10.34	10.95
H	0.09	0.91	0.67	0.57

Notes: The empirical evidence points to a significant role for currency substitution in the context of extrapolative expectations. The estimated substitution elasticity is negative and highly significant for all four countries, indicating that expected depreciation based on recent exchange rate movements substantially reduces domestic money demand. Diagnostic statistics suggest no residual misspecification.

Table 2. Maximum Likelihood Estimate Extrapolative Expectations 2.

	Bolivia	Brazil	Mexico	Turkey
${\mu }_t$	6.022	7.736	10.034	6.926
	(88.96)	(49.99)	(24.33)	(14.55)
${\beta }_t$	0.005	0.007	0.004	0.004
	(0.72)	(3.35)	(0.15)	(0.24)
$\Delta s_t$	−2.976	−5.443	−3.634	−4.698
	(−98.31)	(−38.69)	(−22.58)	(−15.17)
$\Delta s_{t-1}$	−0.024	−0.032	0.149	−1.459
	(−0.76)	(−0.41)	(2.01)	(−4.71)
$R_d^2$	0.98	0.24	0.95	0.49
Q	13.20	17.34	14.33	11.07
H	0.89	0.11	0.92	0.44

Notes: Allowing expectations to depend on multiple lags of exchange rate changes confirms the dominance of extrapolative behavior. In most cases, currency substitution is driven primarily by the most recent depreciation episode, while additional lags play a limited role. The magnitude and significance of the substitution elasticity remain robust across countries.

Table 3. Maximum Likelihood Estimate Adaptive Expectations.

	Bolivia	Brazil	Mexico	Turkey
${\mu }_t$	5.947	7.804	10.053	5.634
	(39.82)	(71.96)	(25.81)	(7.84)
${\beta }_t$	0.002	0.007	0.005	−0.002
	(0.16)	(9.86)	(0.19)	(−0.16)
$\Delta s_t$	−2.963	−5.504	−3.494	−4.670
	(−47.89)	(−55.63)	(−25.54)	(−14.61)
${(m-p)}_{t-1}$	0.000	0.028	0.000	−0.306
	(0.00)	(−0.24)	(0.00)	(−0.45)
$R_d^2$	0.78	0.36	0.95	0.44
Q	14.81	3.22	11.34	10.58
H	0.09	0.52	0.71	0.50

Notes: The adaptive expectations model receives little empirical support. The coefficient on the lagged dependent variable is statistically insignificant across countries, suggesting that expectations are not revised gradually over time. These results indicate that adaptive mechanisms fail to explain the observed persistence of currency substitution.

Table 4. Maximum Likelihood Estimate Regressive Expectations.

	Bolivia	Brazil	Mexico	Turkey
${\mu }_t$	17.647	9.825	17.183	9.958
	(40.11)	(34.19)	(54.11)	(25.31)
${\beta }_t$	0.016	0.029	0.057	0.046
	(0.95)	(2.56)	(3.36)	(2.39)
$s_t$	−6.007	−2.216	−2.463	−2.100
	(−40.92)	(−32.93)	(−53.76)	(−24.43)
$R_d^2$	0.75	0.86	0.96	0.80
Q	18.67	9.97	17.54	6.93
H	0.27	0.60	0.62	1.04

Notes: The regressive expectations specification performs poorly relative to alternatives. The estimated coefficients imply mean-reverting behavior that is inconsistent with observed currency substitution dynamics. Overall, the results reject regressive expectations in favor of extrapolative mechanisms.

This interpretation is standard in the currency substitution literature and closely mirrors the theoretical predictions of portfolio choice models under exchange rate uncertainty (Miles, 1978; Giovannini & Turtelboom, 1992). The magnitude and significance of ${\beta }_t$ therefore provide a direct link between the empirical results and established theoretical mechanisms.

Statistical inference is based on the final smoothed state estimates obtained from the Kalman smoother. The reported t-statistics are computed using the smoothed coefficient and its associated standard error derived from the state covariance matrix. Model adequacy is evaluated using standardized prediction errors from the state-space model. Serial correlation is assessed using the Box–Pierce statistic, and heteroskedasticity is examined using the H test. In addition, likelihood ratio tests are conducted to evaluate whether the estimated state variances are statistically distinguishable from zero. When the null hypothesis is rejected, this confirms the time-varying specification is empirically justified and not reducible to a fixed-coefficient model.

A comparison across Table 1, Table 2, Table 3 and Table 4 reveals that extrapolative expectations consistently provide the strongest empirical support. Under these specifications, the substitution elasticity is not only statistically significant in all four countries, but also economically meaningful and larger in magnitude than under alternative mechanisms. Importantly, this conclusion is reached within a common stochastic trend framework, ensuring that differences across models reflect genuine behavioral variation rather than changes in specification.

The dominance of extrapolative expectations suggests that agents tend to project recent exchange-rate movements into the future, even after stabilization. This forward projection helps explain why currency substitution remains resilient. Rather than adjusting beliefs gradually or anticipating mean reversion, agents appear to respond quickly and directly to observed depreciation. In this sense, persistence is rooted less in mechanical memory and more in the way expectations continue to be formed in environments shaped by past instability.

The lack of statistical significance for the lagged dependent variable in these models suggests that expectations are not formed through a gradual adjustment process but instead react immediately to observed depreciation. Regressive expectations perform weakest. The implied sign and magnitude of the key coefficient suggest mean reversion toward equilibrium exchange rates, a pattern that is inconsistent with observed behavior in economies characterized by persistent currency substitution.

The empirical results convey a clear and consistent message. In all four countries, the final smoothed substitution elasticity remains negative and statistically significant, indicating that currency substitution does not fade automatically once inflation declines. Earlier studies have documented hysteresis using ratchet variables based on historical inflation peaks. What distinguishes the present findings is that persistence emerges even when no such mechanical structure is imposed. Because the substitution elasticity is allowed to evolve endogenously over time, its continued significance reflects sustained behavioral responses rather than inherited historical thresholds.

In practical terms, restoring price stability appears to be a necessary condition for rebuilding monetary credibility, but it is not sufficient on its own. The results suggest that expectations continue to shape monetary behavior long after stabilization, extending the credibility literature by showing that forward-looking belief formation remains central to understanding post-inflation dynamics.

When turning to expectation formation, the differences across mechanisms become clearer. Extrapolative specifications provide the most coherent explanation of the observed dynamics. The estimated elasticity remains economically meaningful even after allowing for gradual parameter evolution, and its trajectory suggests that agents continue to react strongly to expected depreciation. Similar patterns have been documented in studies linking exchange rate instability to persistent substitution behavior (Bahmani-Oskooee & Tanku, 2006; Yazgan & Zer-Toker, 2010). By contrast, adaptive and regressive formulations struggle to produce stable or intuitively consistent dynamics. Overall, the evidence points toward expectation persistence—rather than simple mechanical memory—as the key driver of post-stabilization substitution.

During episodes of high inflation, expectations often become self-reinforcing. Once depreciation accelerates, agents may begin to anticipate further losses in value, a mechanism consistent with extrapolative expectation models originally discussed in the monetary literature (Cagan, 1956; Miles, 1978). Such forward projection naturally strengthens the incentive to shift toward foreign currency holdings, a pattern widely observed in developing and emerging economies (Bahmani-Oskooee & Tanku, 2006).

Importantly, this behavior does not necessarily vanish with stabilization. Even after inflation declines, concerns about renewed instability may continue to influence monetary choices. This interpretation aligns with broader discussions of credibility rebuilding following disinflation episodes (Calvo & Végh, 1999; Végh, 2013). The experiences of Bolivia and Brazil—where inflationary pressures re-emerged after initial stabilization—illustrate how historical episodes can shape expectations in lasting ways, reinforcing substitution dynamics even in more stable periods.

The results reported in Table 1, Table 2, Table 3 and Table 4 further clarify the role of expectation formation. Under extrapolative specifications, the estimated coefficients consistently indicate destabilizing dynamics, meaning that recent depreciation feeds into expectations of further depreciation. This behavior is consistent with early theoretical insights into inflationary expectation processes (Cagan, 1956) and with empirical evidence linking exchange rate volatility to sustained currency substitution (Yazgan & Zer-Toker, 2010; Temperley, 2022). In contrast, adaptive expectation models receive limited support in the data, as the relevant parameters tend to be weak or statistically insignificant. This suggests that, in high-inflation contexts, expectations may adjust more rapidly than traditional adaptive frameworks imply. Regressive specifications, which assume mean reversion, also fail to align with the observed persistence of substitution. Taken together, these patterns reinforce the idea that expectation dynamics—rather than purely mechanical historical effects—play a central role in shaping post-stabilization monetary behavior (Mongardini & Mueller, 2000).

6. Conclusions

The empirical evidence presented here shows that the dynamics of de-dollarization are far more complicated than simply restoring macroeconomic stability. Currency substitution does not fade automatically once inflation declines. Instead, it often survives the very crisis that gave rise to it. The evidence indicates that when economies experience severe inflation, the impact extends beyond prices and into expectations. Even after stabilization, beliefs do not immediately adjust. Past instability leaves a lasting imprint, shaping how people interpret new information and how much confidence they place in the domestic currency. In this sense, what remains is not just inflation’s economic cost, but its psychological legacy—a credibility gap that policymakers must gradually rebuild.

A central reason for this persistence lies in the way expectations are formed. The results point clearly toward extrapolative behavior: when agents observe depreciation, they tend to assume that it will continue. This forward projection can create a reinforcing cycle. Depreciation feeds pessimistic expectations, and pessimistic expectations, in turn, strengthen the incentive to shift into foreign currency. In three of the four countries examined, domestic currencies continued to depreciate against the U.S. dollar even after inflation had been brought under control. In such an environment, continued reliance on foreign currency appears less like inertia and more like a cautious response to perceived risk.

The broader message is therefore straightforward but important: stabilizing inflation is a necessary achievement, yet it is not sufficient to reverse currency substitution. Persistence emerges from the interaction of two forces. First, exchange rate pressures often do not disappear entirely after stabilization. Second, expectations formed in turbulent periods may remain sensitive to any sign of renewed weakness. Together, these forces help explain why rebuilding confidence in the domestic currency takes time and why substitution proves so resilient.

At the same time, the results do not imply that expectations operate in isolation. Belief formation is closely tied to institutional credibility and policy consistency. When countries experience repeated stabilization attempts or shifting macroeconomic strategies, agents form judgments not only about inflation outcomes but also about fiscal discipline, exchange-rate management, and the durability of reforms. Persistence, therefore, reflects a broader credibility environment rather than simple behavioral rigidity.

The country experiences illustrate this interplay. In Bolivia, a fixed exchange rate helped contain depreciation, yet substitution remained widespread, suggesting that credibility cannot be restored overnight—even under a strong nominal anchor. Brazil and Turkey show how renewed depreciation pressures can quickly revive pessimistic expectations. Mexico presents a more gradual adjustment path, where improved macroeconomic management reduced substitution pressures without fully eliminating them. These contrasting trajectories underscore that persistence does not stem from a single uniform mechanism, but from the interaction between expectation dynamics and each country’s policy history.

Several limitations should be acknowledged. Expected depreciation is used as a proxy for inflation expectations, which may not capture belief formation as directly as survey-based measures. While the state-space framework allows behavioral parameters to evolve smoothly over time, it does not explicitly identify discrete structural breaks tied to particular policy events. In addition, the focus on four post-inflation economies means that the conclusions may not fully extend to low-inflation or fully dollarized contexts.

In conclusion, the findings highlight a broader lesson: credibility is rebuilt gradually, and expectations adjust slowly. Currency substitution is not merely a statistical artifact of past inflation, but a reflection of how economic agents process uncertainty and assess the durability of reforms. Reversing it requires not only macroeconomic stabilization, but sustained policy consistency capable of reshaping expectations over time.