Political constraints and currency crises in emerging markets and less developed economies

Abstract

Political institutions may directly affect the likelihood of currency crises by influencing market confidence. They may indirectly affect the likelihood of currency crises by influencing economic fundamentals. This study uses econometric mediation to estimate both direct and indirect causal pathways for veto player theory—a common framework for analyzing political institutional constraints—and finds this approach improves upon the standard econometric approach in the extant literature, which only estimates the direct causal pathway. This new mediated approach shows that political constraints also indirectly reduce the likelihood of crises through strengthening key economic fundamentals. Additionally, the analysis finds that when global conditions are stable, more constraints are shown to directly reduce the risk of crises. When global conditions are volatile, more constraints are shown to directly increase the risk of crises. Global volatility is more likely to cause crises in countries with relatively constrained political systems, and vice versa.

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Data availability

The data that support the findings of this study are available from the author upon reasonable request.

Notes

  1. 1.

    See Claessens and Kose (2013) for an overview of the literature on currency crises.

  2. 2.

    See Breuer (2004) for an early overview of the this topic.

  3. 3.

    In perhaps the most related paper in the extant literature, Acemoglu et al. (2003) considers these indirect causal pathways, with results suggesting institutional factors may dominate, or be the underlying determinants of, the standard economic correlates of crises.

  4. 4.

    Meyer (2020) estimates these indirect causal pathways in an analysis of banking crises.

  5. 5.

    However, if the observation level effect is not independent across stages, there may be a bias in the estimated mediated effect (Glynn 2011). To attempt to evaluate whether this bias is present, the mediated effect is estimated and calculated conditional upon other variables, known as moderators (Hayes 2013). A difference in the estimated mediated effect when including moderators indicates bias in the estimated mediated effect.

  6. 6.

    The predictive value of the econometric analysis is exclusively linked to the second stage of the mediation estimation. Therefore, the addition of the first stage estimations—which do not affect the second stage of the estimation—used to calculate the full mediated effect lead to no change in the predicted values of the second stage model. In this context the value of mediation is to offer additional insight into institutions as a cause of vulnerability to crises through their effect on economic factors associated with crises—not improving predictive value.

  7. 7.

    This section first analyzes the effect of political constraints on both levels of inflation, foreign exchange reserve coverage, and economic growth, and the inertia in them. It next reports estimates of the conditional effects of veto players on the probability of currency crises while controlling for the mediator variables and other covariates.

  8. 8.

    See Breuer (2004) for an overview of early research on the political economy of crises.

  9. 9.

    Ganghof (2003) or Hallerberg (2010) give an overview of veto player theory.

  10. 10.

    For a more in-depth discussion of currency crashes and crises, see Kaminsky (2006).

  11. 11.

    Global risk is proxied by the VIX. The VIX is the Chicago Board Options Exchange volatility index. This is a measure of implied volatility of the S&P 500 options over the following thirty days, calculated using a weighted average of option prices, and is often used as a global risk proxy.

  12. 12.

    E.g. Treisman (2000), Henisz (2000), Duttagupta and Cashin (2011).

  13. 13.

    This econometric analysis of veto players and currency crises implements the same methodology used by Meyer (2020) to estimate the relationship between veto players and banking crises.

  14. 14.

    Individual equations comprising the different stages of mediation, and the aggregation of these equations into mediation effects, are reported (respectively) in “Appendix A” and Sect. 4.

  15. 15.

    The mediator variable(s) is/are the variable(s) on the causal pathway indirectly linking veto players to crisis. E.g. if more veto players increase economic growth, and economic growth reduces the likelihood of crises, then economic growth is the mediator variable.

  16. 16.

    Motivated by the tendency crises to be triggered markets “reacting” to economic/political vulnerabilities with sell-offs and/or speculative attacks.

  17. 17.

    E.g., estimations of the effect of veto players on inflation, and of inflation on the probability of crisis, must each be significant for there to be a mediated effect of veto players on the probability of crises by influencing inflation.

  18. 18.

    For a detailed discussion of multiple mediation and mediation using a logit model in the second stage, see (respectively) Preacher et al. (2007); Preacher and Hayes (2008).

  19. 19.

    The indirect effects—representing only the effects of veto players on the likelihood of currency crises through their effect on economic fundamentals—is reported in “Appendix B”.

  20. 20.

    The figures throughout this section will display SGMM coefficients for the imbalance estimation parameters, and the outputs for the Laeven and Valencia currency crash measure for the Reactions estimation parameters.

  21. 21.

    Breen et al. (2013) gives a detailed explanation of this process.

  22. 22.

    It should be noted the highest observed value of the Veto Player index is approximately .9, while the maximum of the axes and the veto player index is one.

  23. 23.

    These estimations are reported in “Appendix A.1”.

  24. 24.
    $$\begin{aligned} \sigma _{ME}^2 = \bigtriangledown f(l) \cdot \Omega \cdot \bigtriangledown f(l)'\quad (8) \end{aligned}$$

    Where the elements of the gradient are calculated as follows:

    $$\begin{aligned} \bigtriangledown f(l)&= \Bigg [\frac{1}{n}\sum _{i=1}^n\left(\frac{\partial ^2f}{\partial \gamma _j ~ \partial z}\right)_i + \frac{1}{n}\sum _{i=1}^n\left(\frac{\partial f}{\partial \gamma _j}\right)_i,\ldots , \frac{1}{n}\sum _{i=1}^n\left(\frac{\partial ^2 f}{\partial \pi _j ~ \partial z}\right)_i~\\&\quad +\frac{1}{n}\sum _{i=1}^n\left(\frac{\partial f}{\partial \pi _j}\right)_i,\ldots ,\frac{1}{n}\sum _{i=1}^n\left(\frac{\partial ^2 f}{\partial \beta _j ~ \partial z}\right)_i,\ldots , \frac{1}{n}\sum _{i=1}^n\left(\frac{\partial f}{\partial \chi _j}\right)_i,\ldots \Bigg ]. \quad (9) \end{aligned}$$

    This is a vector of partial derivatives with respect to each model parameter comprised of cross-partial derivatives:

    $$\begin{aligned} \begin{aligned} \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial ^2f}{\partial \beta _w ~ \partial z}\right) _i = \frac{1}{n}\sum _{i=1}^n \bigg [ \big [({\hat{p}}_{i}(1-{\hat{p}}_{i})(1-{\hat{p}}_{i}))-((1-{\hat{p}}_{i}){\hat{p}}_{i}{\hat{p}}_{i})\big ] \cdot z \cdot w_i \bigg ], \quad (10) \end{aligned} \end{aligned}$$

    with respect to each model parameter and the derivative of each coefficient in \(\pi\):

    $$\begin{aligned} \begin{aligned} \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial f}{\partial \pi _j}\right) _i = \frac{1}{n}\sum _{i=1}^n \big [ {\hat{p}}_{i}(1-{\hat{p}}_{i}) \cdot e_i^{m} \big ], \quad (11) \end{aligned} \end{aligned}$$

    and the derivative of each coefficient in \(\gamma\):

    $$\begin{aligned} \begin{aligned} \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial f}{\partial \gamma _j}\right) _i = \frac{1}{n}\sum _{i=1}^n \big [ {\hat{p}}_{i}(1-{\hat{p}}_{i}) \cdot e_i^{d} \big ], \quad (12) \end{aligned} \end{aligned}$$

    where \(\beta _w\) is the coefficient of variable w, and \(e_j^m\) and \(e_j^d\) are the elements of vector \(J_{\text {f}}\) corresponding with variable j at representative values of v and x. \(\Omega\) is the logit model cluster-robust variance-covariance matrix, extended by incorporating first-stage variances of veto player terms on the diagonal and covariances of the first-stage veto player coefficients from the joint estimations. Elements of \(J_f\) representing mediator variables are rescaled by \(\frac{1}{(1~-~\lambda _{1j})}\) when estimating long-run marginal effects.

  25. 25.

    These calculations use 1st stage parameters from the SGMM first-stage estimations as reported in “Appendix B”.

  26. 26.

    This evaluation uses the calculation of the long-run—rather than short run—effect of veto players on GDP growth, inflation, and foreign exchange reserve coverage.

  27. 27.

    The inclusion of indirect effects does not change the role of veto players conditioning the effect of the VIX on the likelihood of currency crises.

  28. 28.

    This is a standard approach in the literature on financial crises.

  29. 29.

    A change of this magnitude is rare within a country, indicating substantial political reforms or a move from single party rule to a large coalition. Cross-country differences of this size are more common, and are comparable, for instance, to the difference between the US (~.4 typically) and the U.K. with a coalition government (~.7). The standard deviation of the difference between the value of the variable and the panel mean is ~.18. The standard deviation of the panel means is ~.25.

  30. 30.

    For a full explanation of the estimator see Roodman (2009).

  31. 31.

    This is done using Windmeijer (2000) correction procedure for standard errors with the two-step SGMM estimator. Both specifications pass all standard postestimation tests. Instrumentation is discussed in “Appendix E”.

  32. 32.

    For the Imbalance stage of moderated mediation the basic model is as follows:

    $$\begin{aligned} m_{it} = \lambda _{2}m_{it-1} + \phi _{1}d_{it}\cdot {v_{it}}+\phi _{2}d_{it} + \phi _{3}{v_{it}} + a_i + \epsilon _{it}. \quad (13) \end{aligned}$$

    Where \(d_{it}\) is the moderating variable. The remainder of the estimation remains fundamentally unchanged, but the marginal effect of veto players is no longer \(\chi _j\), but

    $$\begin{aligned} \frac{\partial m}{\partial v} = (\phi _3 + \phi _1{d_{it}}). \quad (14) \end{aligned}$$

    Showing the marginal effect of veto players on the mediator is now conditional upon the moderator. These sets of estimations will take place with six moderators for each mediator. Estimation results are not reported, but the moderated mediated marginal effects are reported in “Appendix C.2”.

  33. 33.

    Economic fundamentals the reactions estimations find influence the likelihood of currency crises.

  34. 34.

    A full data description can be found in “Appendix D”.

  35. 35.

    In the econometric model this implies the veto player coefficient for inflation, \(~\chi _{inf}\), is statistically significant and negative. The veto player coefficients for GDP growth, the real exchange rate overvaluation, and foreign exchange reserve coverage (\(\chi _{gdp}\), \(~\chi _{rxr}\), and \(~\chi _{res}\)) are statistically significant and positive.

  36. 36.

    In the econometric model this implies the veto player coefficient for inflation, \(~\chi _{inf}\), is statistically significant and positive. The veto player coefficients for GDP growth, the real exchange rate overvaluation, and foreign exchange reserve coverage (\(\chi _{gdp}\), \(~\chi _{rxr}\), and \(~\chi _{res}\)) are statistically significant and negative.

  37. 37.

    It may be unreasonable to assume output and trade are predetermined in the relevant period. As such, they are lagged to reduce the “bad control” problem associated with the potential causal link between veto players and output, and veto players and trade openness. These concerns are reduced with respect to central bank independence and exchange rate regime.

  38. 38.

    Bias associated with this reverse causality is reduced through the dynamic restrictions associated with the panel approach—any causal link from output to veto players likely operates after a lag.

  39. 39.

    Note this is percent, not percentage points. One standard deviation more veto players would be associated with inflation falling from 10% to 8.5%, for example.

  40. 40.

    In the econometric model this implies \(\alpha _{1j}\) will be statistically significant and positive. \(\alpha _1 > 0\) indicates the marginal effect of \(m_{it-1}\) on \(m_{it}\) (i.e., inertia) is larger with more veto players, as \((\lambda _3 + \alpha _1v)\) is increasing in v. The positive coefficient means there is greater inertia in the mediator variable when there are more veto players. The null and the research hypotheses are as follows:

    $$H_0: \alpha _{1} \le 0$$
    (18)
    $$H_1: \alpha _{1} > 0$$
    (19)

    When the null is rejected there is evidence that inertia in the mediator variable is higher with more veto players.

  41. 41.

    E.g.Kruger et al. (2000).

  42. 42.

    Fixed Effects are not used in this model as all panels without a crisis observation will be omitted, producing a biased sample.

  43. 43.

    These variables are specified as outlined in prior sections.

  44. 44.

    In the econometric model this implies the linear veto player term (\(\gamma _{\text {vp}}\)) will be statistically significant and positive.

  45. 45.

    In the econometric model this implies the linear veto player term (\(\gamma _{\text {vp}}\)) will be statistically significant and negative.

  46. 46.

    In the econometric model, this implies veto player interaction term (\(\gamma _{\text {vp} \cdot \text {vix}}\)) will be statistically significant and positive.

  47. 47.

    This measure has better coverage, containing more crisis observations, relative to the alternative crash measures.

  48. 48.

    Preliminary estimations and BIC tests find the inclusion of the current account weakens the model, while having little effect on the results. Specifications adding the current account as a control are reported in Table 8.

  49. 49.

    A statistically significant effect at each stage is required for mediation to occur. Therefore, growth will not be treated as a mediator for crises.

  50. 50.

    The marginal effect of a variable included in an interaction term is given by the coefficient of the linear term plus the coefficient of the interaction term multiplied by a representative value of the variable it is interacted with. Formally, in the simple linear model:

    $$\begin{aligned} y = \alpha + \beta _1 x_1 + \beta _2 x_2 + \beta _3 (x_1 \cdot x_2) + u \end{aligned}$$
    (23)

    The marginal effect of \(x_1\) is given by:

    $$\begin{aligned} = \beta _1 + \beta _3 x_2 \end{aligned}$$
    (24)

    This implies that in the logit model reported in this section, the marginal effect of the veto player variable is conditional upon the value of the VIX (and vice versa). Given the negative coefficient of the linear veto player term and positive coefficient of the interaction term, this implies that when the VIX is lower more veto players will relatively lower the likelihood of crises, and when the VIX is higher more veto players will relatively raise the likelihood of crises. These marginal effects are reported in Sect. 4.1. It should be noted for the sake of interpreting these coefficients that the veto player variable has a mean and standard deviation of approximately .35 and .3, and the VIX has a mean and standard deviation of approximately 20 and 7 (respectively).

  51. 51.

    The figures will display the outputs for the SGMM specifications for the imbalance estimation parameters, and the outputs for the Laeven and Valencia currency crash measure for the Reactions estimation parameters.

  52. 52.

    The calculation of this standard error is substantively similar to the calculation of the standard error of the full marginal effect. The only difference in the process of calculating the standard error is in the gradient:

    $$\begin{aligned} \bigtriangledown f(l)&= \left[ \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial ^2f}{\partial \gamma _j ~ \partial z}\right) _i,\ldots , \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial ^2 f}{\partial \pi _j ~ \partial z}\right) _i~\right. \\&\left. \quad +\frac{1}{n}\sum _{i=1}^n\left( \frac{\partial f}{\partial \pi _j}\right) _i,\ldots ,\frac{1}{n}\sum _{i=1}^n\left( \frac{\partial ^2 f}{\partial \beta _j ~ \partial z}\right) _i,\ldots , \frac{1}{n}\sum _{i=1}^n\left( \frac{\partial f}{\partial \chi _j}\right) _i,\ldots \right] \quad (28) \end{aligned}$$

    Which no longer includes the terms \(\frac{1}{n}\sum _{i=1}^n(\frac{\partial f}{\partial \gamma _j})_i\), accounting for the direct effect of the \(\gamma _j\) coefficients.

  53. 53.

    For a discussion of moderated mediation—AKA conditional indirect effects—see Preacher et al. (2007).

  54. 54.

    The exchange rate is not included as it was not found to mediate the effect of Veto Players in prior estimations. GDP growth was only found to mediate the effect of veto players for currency crises, and will not be included when testing for a moderated effect in the currency crisis estimations.

  55. 55.

    Notation is simplified from the more rigorous explanation in “Appendix A.3

  56. 56.

    The standard error of this marginal effect is calculated substantively as in prior sections.

  57. 57.

    “Appendix D” contains descriptions of all variables.

  58. 58.

    For example: in the currency crash estimations for economic growth with financial development as a potential moderator; the negative coefficient on the first-stage interaction term indicates the marginal effect of veto players on economic growth is smaller in more financially developed economies. The positive second stage coefficient on the interaction term shows the marginal effect of the mediator (growth) in reducing the likelihood of crises is smaller more financially developed economies. This indicates the effect of the first stage will be relatively small (large) when the effect of the second stage is relatively small (large), meaning (due to the multiplicative effect of mediation) the aggregate effect of mediation relative to the estimated mediate effect will rise once this moderation is accounted for.

  59. 59.

    Each estimation calculating the mediated effects without moderation includes the moderator as a control, to avoid both omitted variable bias, or changing estimations related to sample size.

  60. 60.

    Moderation was not assessed for economic growth and currency crises, because it was not found to be a mediator in the mediation analysis.

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Acknowledgements

I am thankful for the comments and critiques of committee members Eunyoung Ha and Yi Feng on the dissertation in which this analysis began. I appreciate Puspa Amri, Jayant Rao, and Roman Garagulagian for comments and proofreading, and Maxim Ananyev for excellent feedback at the SCPI conference as a discussant. Several anonymous reviewers provided invaluable feedback throughout the project. Dissertation committee chair Thomas Willett deserves a special thanks for his detailed feedback and guidance.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for profit sectors.

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Appendices

Appendices

Appendix A Estimation

This section first reports and briefly discusses the estimations of each stage of the econometric analysis. Full results of the mediation analysis and a detailed discussion of these results are reported in Sect. 4. The full data description and output tables of robustness checks are reported in “Appendix D”.

Potentially restrictive identification assumptions are required to draw causal inference from the following mediation analysis. In the second stage estimations, domestic economic and institutional variables are lagged one year to avoid endogeneity associated with the effect of crises on the control variablesFootnote 28— motivating the sequential ignorability assumption associated with the link between the mediator variables and the outcome variable required for causal identification of the indirect effect of the mediation analysis. The exception is the veto player variable (an index from Henisz 2005), which uses data available on January 1st of the given year and ranges from zero to one with higher values indicating more constraints, and global variables. This motivates the sequential ignorability assumption required for causal identification of the direct effect of the mediated analysis.

In the first-stage imbalance estimations, contemporaneous observations of the veto player variable are used, as this variable is constructed for the year observation using only data available on January 1st of that year, thus reducing concerns of endogeneity. These estimations use fixed effects in a dynamic panel framework to help the estimations to identify the effect of veto players. This focuses the estimations on how within-panel variation in political constraints across time influences the behavior of the dependent variables. This is motivated by the goal of disentangling causal effects related to political constraints from other correlated factors that may also influence the dependent variables. The causal effects of other underlying institutional factors (e.g., the “inclusive versus extractive” framework discussed by Acemoglu et al. 2014) are largely captured in the country-level fixed effects, as these underlying differences likely exhibit little variation over time. Bias associated with time-variant non-institutional factors that may influence both economic fundamentals and and veto players are addressed with the dynamic nature of the estimator, as the contemporaneous observation of the veto player variable is determined before that of the dependent variable (by the nature of the date of its measurement), while any reverse causality between economic fundamentals and veto players operates with reasonably large lags. This motivates the sequential ignorability assumption required for the causal identification of the indirect effect of the mediated analysis.

The effects are re-scaled to a one \(\sigma\) increase in veto players for the discussion of these results (a value of ~.3 for the political constraint variable).Footnote 29

Imbalances

The “imbalances” section estimates the effect of the independent variable (veto players) on the mediators (m). I use dynamic panel data estimations to identify both the long- and short-run effects of veto players on the mediator variables. The direct effects of veto players (estimated in “Appendix A.3”) likely operate only in the short-run, while the indirect effects (through influencing fundamentals) likely also operate in the long-term. To fully understand this topic, it is necessary to disentangle these effects. I first use fixed effects (country level—a) least squares to estimate the equations individually. I then estimate this system of equations jointly in a seemingly unrelated regression—a process utilizing cross-equation correlation of error terms in the estimation of parameters. The next set of estimations uses an Arellano-Bover/Blundell-Bond (System GMM)Footnote 30 estimatorFootnote 31 to address the Nickel Bias in panel estimations with lagged dependent variables. The final estimate adds controls to the individually estimated FELS models. I choose controls intending to both avoid controlling for variables on the causal pathway linking veto players to the mediators, and “bad controls” that may introduce other biases related to endogeneity, such as those which are potentially determined by veto players as well (Angrist and Pischke 2008). Throughout the paper figures display the outputs for the SGMM specifications as the imbalance estimation parameters.

Fig. 6
figure6

Imbalance path estimation

I calculate mediated effects using the System GMM first-stage regressions. The System GMM estimations reduce Nickell bias associated with the dynamic panel approach, though this estimator is potentially susceptible to problems related to instrumentation. The econometric model (without controls) for each equation in these first-stage estimationsFootnote 32 is

$$\begin{aligned} m_{it} = \lambda _{1}m_{it-1} + \chi {v_{it}} + a_{i} + \epsilon _{it}. \end{aligned}$$
(15)

This equation is estimated for each potential mediatorFootnote 33 (j): inflation (logged), foreign exchange reserve coverage (log of the ratio of foreign exchange reserves to the M2), real exchange rate undervaluation (log of the ratio of the exchange rate relative to PPP with the US dollar, adjusted for Balassa-Samuelson), and real GDP per capita growth.Footnote 34 The long-run marginal effects are calculated by multiplying each coefficient by \(\frac{1}{(1~-~\lambda _{1})}\). Figure 6 illustrates the paths (highlighted) and parameters estimated in this stage. Table 2 reports partial results.

Section 2 outlines the varied potential effects of veto players on these economic fundamentals. Under the Commitment Approach, many veto players may constrain governments from short-term expansionary policy, facilitating commitment to farther-sighted and higher-quality policy. If so, more veto players will reduce inflation, reserve vulnerability, and real exchange rate overvaluation while increasing GDP growth.

Hypothesis 1

(Commitment Approach) When there are more veto players, inflation will tend to be lower, GDP growth higher, the exchange rate relatively less overvalued, and foreign exchange reserve coverage strongerFootnote 35

The Collective Action approach outlines how more veto players may increase log-rolling, generating relatively expansionary policy, and thereby producing an expansionary bias. If so, more veto players will have the opposite effect.

Hypothesis 2

(Collective Action Approach) When there are more veto players, inflation will tend to be higher, GDP growth lower, the exchange rate relatively more overvalued, and foreign exchange reserve coverage weakerFootnote 36

The causal effect of veto players on the mediator variables is likely indirect (with mechanisms working through several policy factors). To avoid controlling for factors on the causal pathway linking veto players to the mediators, and to achieve identification as described in the prior section, estimates without controls are of interest, and will be used in mediation. I also report estimations with controls to evaluate whether the results substantively change. For these FELS estimations with controls, I attempt to select control variables by avoiding those that are not on the causal pathway between veto players and the mediators and those that may introduce biases associated with their potentially being an “outcome variable” of the veto player variable. The use of fixed effects in a dynamic panel framework attempts to allow the estimations to identify the effect of veto players. This is achieved by focusing on how within-panel changes in political constraints across time influences the behavior of the dependent variables, plausibly disentangling causal effects related to political constraints from other correlated underlying (institutional or otherwise) factors that may also influence the dependent variables – as described above. I use the same controls for each estimation, adding the global interest rate (proxied by the U.S. three-year treasury rate) for mediators that are external factors (foreign exchange reserves and the exchange rate).

Table 2 Imbalances partial results

The controls are as follows: the log of lagged output, central bank independence, an exchange rate regime dummy variable, and lagged trade as a portion of GDP.Footnote 37 The veto players variable is correlated with output—with the causal linkage potentially operating in both directions—making output important to control for in order to minimize the potential resulting bias associated with the influence of the level of development on the mediator variables.Footnote 38 Central bank independence is also correlated with the veto players variable, and acts as an important influence upon different economic fundamentals. The exchange rate regime—tallied as a one if the country has a fixed exchange rate—can have significant influence on various economic fundamentals. Trade as a portion of GDP is the final control, as openness will influence many variables, in particular external factors. The coefficient on veto players tends to fall in absolute value after controls are added. However, signs of the veto player coefficient appear fairly consistent for variables used in mediation.

A one standard deviation increase in the veto player variable reduces inflation ~13%Footnote 39 with System GMM estimations. For foreign exchange reserve coverage, this is approximately 5%. The exchange rate weakens by approximately 12%—though this effect is not statistically different than zero. Economic growth is approximately one percentage point higher with a one standard deviation increase in the veto player variable. All economic fundamentals tested in this section exhibit changes characteristic of less vulnerability to currency crises with more veto players. This supports the Commitment Approach.

Table 3 Between effects: veto players and \(\sigma _{m}\)

Adjustment

More veto players make it more difficult to change policy. When this is the case, economic policy is more static, leading economic conditions to exhibit more inertia. Weak (or strong) economic fundamentals in a given period will have a larger effect on later periods if more veto players are present and increase policy inertia. If a shock or vulnerability in economic fundamentals affects the likelihood of a crisis in a given period, a shock or this state of economic conditions in the period in question will have a larger effect on the probability of a crisis in later periods with more veto players increasing inertia in these conditions.

I take a two-pronged approach to evaluating inertia in these economic fundamentals. The first set of estimations regress the panel standard deviation of each mediator on the panel mean of veto players. This estimates the effect of an increase in the panel mean of veto players on the standard deviation of the panel for the mediator. Table 3 reports the results of this estimation. Countries with more veto players tend to have a lower panel standard deviation for all variables, indicating more veto players increase inertia in the mediators. This effect is statistically different than zero for the real exchange rate, economic growth, and foreign exchange reserve coverage. These results show some support for the Inertia Approach.

However, many individual observations of the independent variable used in the calculation of the panel mean of veto players are observed after components used in the calculation of the panel standard deviation of the dependent variable, creating the potential for endogeneity bias. Therefore, a more robust estimation is necessary. I do this with a FELS joint dynamic panel data estimation that allows the autoregressive coefficient to vary conditional on the amount of veto players. I interact the veto player variable (v) with the lagged dependent variable (\(m_{it-1}\)). This estimates the autoregressive effect in each mediator conditional upon the amount of veto players. The regressions are specified as follows:

$$\begin{aligned} m_{it} = + \lambda _{3}m_{it-1} + \alpha _{1}m_{it-1}{v_{it}} + \alpha _{2}{v_{it}} + a_i + \epsilon _{it} \end{aligned}$$
(16)

A larger conditional autoregressive effect indicates a current state of the mediator variable is more dependent on prior states (i.e., there is greater inertia). The autoregressive effect is now

$$\begin{aligned} \frac{\partial m_{it}}{\partial m_{it-1}} = (\lambda _3 + \alpha _1v_{it}). \end{aligned}$$
(17)

If the Inertia Model is correct, there should be more inertia in economic fundamentals with more veto players. Formally I expect,

Hypothesis 3

(Inertia Model) The autoregressive effect will be stronger in countries with more veto players, with lagged values of variables having a larger effect on present values of the same variable.Footnote 40

Even if the empirical analysis supports this hypothesis the interpretation of the result is highly conditional upon the state of fundamentals this inertia is “locking-in.” If these fundamentals are vulnerable and require adjustment to avoid a crisis, more veto players will increase the likelihood of crises. If economic fundamentals are strong, more inertia will impede action by policymakers that may change these low-risk conditions, reducing the likelihood of these fundamentals weakening, and therefore reducing the likelihood of crises.

Table 4 Adjustment: conditional autoregressive effect

Table 4 reports selected results. For three mediator variables (inflation, foreign exchange reserve coverage, and real exchange rates) there is no significant change in the autoregressive coefficient conditional upon veto players. This does not support the inertia model. However, we do find some evidence that the autoregressive coefficient is conditional upon veto players for economic growth. The interaction term between the lagged dependent variable and the veto player variable for economic growth is statistically significant and shows a fairly large economic effect. Moving from the 20th percentile of the veto player variable (0) to the 80th percentile (.68), the autoregressive coefficient rises from .061 to .29.

Reactions

The set of control variables for the “Benchmark” specification is constructed based on prior literatureFootnote 41 and the theoretical analysis in Sect. 2, after which BIC tests were used to help remove unnecessary regressors and select a final model. As a robustness check five alternative specifications in which different sets of variables are added to the core model. One model adds additional financial variables, one model adds additional political variables, one variable adds additional external factors, one variable adds variables related to standing of the country’s fiscal conditions, and a final specification adds an interaction term of a democracy dummy variable as a covariate. While post estimation tests suggest the addition of each of these sets of controls weakens the fit of the model relative to the model reported as the benchmark specification (in part due to the reduction of the sample space due to missing observations of the new controls), they are reported in the “Appendix” to indicate the omission of these variables as controls does not substantively change the results of the estimation. The figures display the coefficients from the Laeven and Valencia currency crash measure for the Reactions estimation parameters. Figure 7 gives an illustration of the paths and parameters estimated. The relationship estimated in this stage is as follows:

$$\begin{aligned} c =g( x_{\text {v}}\gamma + x_{\text {m}}\pi + x_{\text {c}}\beta + u), \end{aligned}$$
(20)

with g indicating a link function converting values of independent variables into crisis/crash outcomes. \(x_{\text {v}}\) is a n x 2 matrix of veto player terms \([v_{\text {vp}},v_{\text {vp}}\cdot x_{vix}]\), \(x_{\text {m}}\) is a n x 4 matrix of mediator variables \([m_{\text {inf}},~ m_{\text {gdp}},m_{\text {res}},m_{\text {rxr}}]\), and \(x_{\text {c}}\) is a matrix containing observations of control variables. This implies a latent variable p(c) that gives the probability of a currency crisis:

$$\begin{aligned} p(c) = p\big (c~|~x_{\text {v}},~x_{\text {m}},~x_{\text {c}}\big ), \end{aligned}$$
(21)

which is estimated with a logit modelFootnote 42

$$\begin{aligned} p(c) =f_{\text {logit}}^{-1}( x_{\text {v}}\gamma + x_{\text {m}}\pi + x_{\text {c}}\beta + u) \end{aligned}$$
(22)

This fits the three vectors of the parameters. \(\gamma\) is a \(2 ~\text {x}~ 1\) vector of veto player coefficients (\(\gamma _j\)), \(\pi\) is a \(4 ~\text {x}~ 1\) vector of mediator coefficients, and \(\beta\) is a \(k ~\text {x}~ 1\) vector of control variable coefficients. The four mediators (\(m_j\)) are inflation, GDP growth, real exchange rate valuation, and foreign exchange reserve coverage.Footnote 43 The control interacted (\(v_{\text {vp}}\cdot x_{\text {vix}}\)) with veto players (\(v_{\text {vp}}\)) is the VIX (\(x_{\text {vix}}\)), an index of implied volatility proxying global risk. The interaction term allows the marginal effect of veto players to vary conditional upon global risk and volatility and the marginal effect of global risk to vary conditional upon veto players (i.e., how constrained policy reactions to the volatility are). Marginal effects are reported in Sect. 4 and use the benchmark specification, with the equal weights (“E.W.”) measure for currency crises, and the Laeven and Valencia (“L.V.”) measure for currency crashes.

Fig. 7
figure7

Reactions estimation

Hypothesis 4

(Collective Action Approach) When there are more veto players, increased rent-seeking and political dysfunction will reduce market confidence in the country’s economy, increasing the likelihood of crisesFootnote 44

If relatively constrained political systems exhibit rent-seeking and dysfunction consistent with the Collective Action approach, more veto players will increase the likelihood of crises through direct mechanisms related to market confidence. Markets, observing this poor policy quality and dysfunction, will engage in speculative attacks sparking currency crises at lower thresholds of economic vulnerabilities and global/shocks (Table 5). However, if the Commitment Approach accurately explains the functioning of constrained political systems, then we should expect the opposite.

Hypothesis 5

(Commitment Approach) When there are more veto players, the expectation of higher quality and more stable economic policy will increase market confidence in the country’s economy, reducing the likelihood of crisesFootnote 45

Table 5 Exchange rate logit estimation: benchmark specification

If relatively constrained political systems improve the quality of economic policy (e.g., if requiring more policymakers support legislation for it to pass culls low-quality policy, or if commitment mechanisms reducing myopic policy perspectives), then more constrained political systems may improve market confidence, reducing the likelihood of speculative attacks and capital reversals. More constrained political systems may also lead to a reduced likelihood of political shocks that shift collateral values or long-run expectations of income, engendering stability. Further, if markets internalize lessons associated with the findings of prior sections (that more constrained systems lead to stronger and more stable economic fundamentals) more constrained political systems can reduce the risk of crises through the expectation of stronger future fundamentals. However, this effect may be conditional upon global conditions.

Hypothesis 6

(Inertia Model) More veto players will reduce the likelihood of crises when global economic/financial conditions are more stable, but increase the likelihood of crises when global economic/financial conditions are more volatile. Global volatility will have a larger effect on the likelihood of crises in systems where political constraints impede rapid policy responsesFootnote 46

If the effect of veto players on the probability of crises is conditional upon global risk/volatility—and vice versa—then the interaction term will be statistically significant and positive. A positive coefficient on the interaction term indicates veto players increase the likelihood of crises by more when global conditions are volatile. When global conditions are stable (i.e., the VIX is low) there may be little need for governments to engage in policy adjustment. However, when global volatility is high, governments may need flexibility to react to quickly shifting global conditions to avoid crises. Further, markets may have less faith that a political system can react to high global volatility when policymakers are relatively constrained, and then react to this global volatility with speculative attacks and capital reversals after smaller shocks and/or at lower levels of vulnerability.

Table 5 reports the results of this benchmark specification. Each column uses a different currency crisis/crash measure. The primary measures to be discussed are “E.W.,” a measure of exchange market pressure based on equal weighting of reserves and exchange rates across countries, and “L.V.,” the currency crash measure from Laeven and Valencia (2012).Footnote 47 “P.W.” is an exchange-market-pressure-based measure using precision weights, while the “Crash” measures are various thresholds (the number indicates which threshold is used). Alternative specifications, each adding two or three more controls of a specific type of factor, are reported after Table 6 reports a specification adding financial variables (credit growth and financial development), Table 7 reports a specification adding debt/deficit variables (the structural fiscal deficit to GDP, and the debt-to-GDP ratio), Table 8 reports a specification adding external variables (the current account to GDP and trade as a portion of GDP) and Table 9 reports a final general robustness check specification adding political variables (a dummy variable for democracy, and another for the presence of a left-wing government). Results are substantively unchanged. Considering the democracy variable is included in a linear term, it is plausible that the specification controlling for democracy does not account for the conditional effect of democracy (a variable that is correlated with veto players) being the real effect captured by the primary specification. However, results reported in Table 10 indicate this is not the case. The more parsimonious model reported in Table 5 is used for mediation to maintain the sample size (a particular issue using mediation with a nonlinear estimator) due to results of AIC/BIC tests indicating this parsimonious model is stronger than the more complex specifications. The other specifications are reported as robustness checks to show that the inclusion of the variables omitted from the benchmark model does not substantively alter the results.

Table 6 Exchange rate logit estimation: financial factors specification
Table 7 Exchange rate logit estimation: fiscal factors specification
Table 8 Exchange rate logit estimation: external factors specification
Table 9 Exchange rate logit estimation: political factors specification

The selection of the mediator and control variables is motivated by the discussion in Sect. 2. The U.S. interest rate is included as a proxy for the global risk-free interest rate, an important pull factor. With a higher risk free interest rate, there will tend to be capital outflows from emerging markets, putting pressure on these countries’ currencies, which can lead to currency crises/crashes. Further, the resulting domestic interest rate increases (or the expectation thereof) can weaken the financial system, generating outflows associated with the expectation of increased financial stress caused by high global interest rates. Results show support for this hypothesis, with higher U.S. interest rates associated with an increased risk of a crisis in most specifications. The next control is a dummy variable for fixed exchange rates. Fixed exchange rates can impose a discipline mechanism generating confidence that the rate will be maintained (reducing the likelihood of speculative attacks) and/or provide a discipline mechanism leading to higher quality economic policy, reducing the likelihood of crises through this mechanism. However, there is little evidence of this mechanism in these results, with the variable statistically significant in only one specification and the sign of the coefficient changing across specifications. Countries with more independent central banks are likely better able to quickly and effectively use monetary policy to raise interest rates when a currency is under pressure in order to defend the exchange (in addition to related market confidence mechanisms). However, the results only find evidence of this effect in currency crises, and relatively mild currency crashes, with more independent central banks associated with a higher likelihood of crises during large crashes. This is intriguing and deserves further investigation. The final control is output. The output of a country indicates more resources are available to defend the currency, market confidence associated with the strength of the economy, and stronger structural factors associated with the level of development. However, these estimations find little evidence that output has an effect on the likelihood of crises. The next set of variables are the mediator variables. These are the real exchange rate, foreign exchange reserve coverage, inflation, and economic growth.

The real exchange rate is specified as the log of the deviation from PPP with the USD, adjusted for the Balassa-Samuelson effect. Higher values indicate a weaker exchange rate. This variable was considered as a potential mediator in the prior sections, but was not found to be influenced by veto players. Hereafter, it is treated as a control. A stronger real exchange rate indicates disequilibrium that is difficult to maintain for long periods of time. This can generate market expectations for a future devaluation, leading to speculative attacks and currency crises/crashes. Overvalued exchange rates can also lead to current account imbalances, forcing capital inflows or reserve decumulation that is unsustainable.Footnote 48 Further, appreciated exchange rates can result from “hot-money” capital inflows, generating vulnerability to crises if these inflows reverse or stop. The estimations find strong evidence that weaker real exchange rates reduce the likelihood of crises, with this effect being rather weak for crises and relatively small crashes and very economically and statistically significant for large crashes. This finding is quite interesting and may merit a followup project of its own.

Inflation (the first variable used in mediation—which was found to be lower with more veto players) is found to have a statistically significant and positive effect on the likelihood of crises/crashes in all specifications. High inflation can be a general sign of economic mismanagement (weakening confidence in the currency), can lead to a weakening of the nominal exchange rate in floating regimes (which can lead to hearing behavior and speculative attacks), and is often associated with strong fiscal deficits and/or absorption, each of which can culminate in crises/crashes. Foreign exchange reserve coverage (the second mediator—which is found to be stronger with more veto players) also has a statistically significant and negative association with the likelihood of crises across the majority of specifications. Stronger reserve coverage indicates an increased ability of policymakers to defend the exchange rate—thus reducing the likelihood of speculative attacks (which reduces the likelihood of crashes or crises) and reducing the likelihood that any speculative attacks that do occur will be successful (which further reduces the likelihood of crashes). The statistically significant effect for crises, and the finding the effect is much stronger for crashes, suggests both mechanisms are relevant. The final mediator is real GDP per capita growth. Higher growth can indicate general economic strength, reducing the risk of speculative attacks and crises, and/or lead to increased investment that can generate inflows supporting the currency. We do not find evidence of this effect for crises,Footnote 49 and only find evidence of this effect in the L.V. measure of crashes. Evaluating the effect of veto players working through these mediators requires the calculation of mediated marginal effects. These results are presented in Sect. B.

The veto player variable has a negative coefficient in the linear term and a positive coefficient in the interaction term for both the crisis and crash estimations.Footnote 50 These results are relatively stable across all crisis/crash measures and are relatively robust to alternative specifications. The positive coefficient indicates that more veto players, likely through introducing policy stability that facilitates long-term investment and reduces quick capital stops/reversals, reduce the likelihood of currency crises and crashes. However, the positive interaction term indicates that when the VIX is high, more veto players increase the likelihood of crises. This effect likely operates through reducing market confidence in policymakers’ ability to respond to changing global conditions—which becomes relatively more economically significant with high global volatility, when conditions require a policy response. The overall effect of veto players on the likelihood of crises is therefore conditional upon global conditions. Evaluating this conditional effect requires the calculation of marginal effects, which are reported in Sect. 4.1. This conditional effect, combined with the mediated effect, comprises the full effect. This is reported in Sect. 4.2.

A final result is the effect of the VIX on the likelihood of crises/crashes. When global volatility is high, “flight-to-quality” effects lead to exchange market stress for non-core economies, while generating financial stress through liquidity shocks and falling asset values and increasing the likelihood of quick shifts in capital flows/speculative attacks. All of these factors increase the likelihood of crises and crashes— and preliminary estimations support this effect. However, once an interaction term (with veto players) is included, we see that a higher VIX primarily increases the likelihood of crises in the presence of political constraints. This effect becomes larger when the political system is more constrained. The interpretation of this is as follows: in relatively less constrained political systems, markets maintain confidence that policymakers will be able to adjust to shocks generated by global volatility—and therefore don’t engage in the reversals/speculative attacks that generate crises. In relatively more constrained political systems, markets lose confidence that policymakers can respond to the exchange market stress generated by global volatility and do engage in the speculative attacks and capital reversals that cause currency crashes and crises when global risk/volatility is high.

Appendix B Mediated effects

This section calculates the effect of veto players on the likelihood of crises working through economic fundamentals, referred to as the “indirect effect.” Figure 8 shows the paths and parameter estimates used in the calculation of the mediated marginal effect.Footnote 51 The marginal effects are first calculated as average mediated marginal effects, then at representative values of the VIX—as crises are significantly more likely in times of global volatility, this allows for the estimation of these indirect marginal effects in situations that can be considered “edge cases”; in which countries are close to a crisis and small differences have the capacity to be the tipping point of a crisis, rather than during stable conditions in which crises are less likely. A statistically significant effect of the independent variable on the mediator and the mediator on the dependent variable is a necessary but insufficient condition for mediation to occur. Therefore, only variables meeting both conditions are calculated (inflation and foreign exchange reserves for crises, with real GDP per capita growth an additional mediator for crashes) will have mediated effects calculated for them. The mediated AMERV is therefore

$$\begin{aligned} \frac{\overline{\partial p(c)}}{\partial v}~ =\frac{1}{n}\sum _{i=1}^n {\hat{p}}_i(1-{\hat{p}}_i)\cdot (z_{m}), \end{aligned}$$
(25)

where \({\hat{p}}_i\) is estimated in Equation 11, and is calculated using either observed or representative values for the VIX (specified in \(x_{\text {v}}\)), observed values for \(x_m\) and \(x_{\text {c}}\), and the coefficient vectors from both the “E.W.” and “L.V.” currency crisis/crash measures. Table 11 reports these estimations. \(z_m\) is,

$$\begin{aligned} z_{m}=(j_{m}\cdot {\hat{\pi }}), \end{aligned}$$
(26)

where \({\hat{\pi }}\) is a vector of the mediator variable coefficients from Eq. 20. The gradient of the mediator variables with respect to veto players on the interior of the logistic function is,

$$\begin{aligned} j_{m} = [{\hat{\chi }}_{\text {inf}}, ~ {\hat{\chi }}_{\text {gdp}},~{\hat{\chi }}_{\text {res}}], \end{aligned}$$
(27)

where \({\hat{\chi }}_j\) is the first-stage coefficient of the veto player variable from Eq. 15. Rescaling each element of \(j_{m}\) by \(\frac{1}{(1~-~{\hat{\lambda }}_{1j})}\) gives the long-run marginal effect. The delta method gives the standard error of this marginal effect.Footnote 52

Fig. 8
figure8

Mediated marginal effects

Table 11 reports the results from the calculation of these indirect effects. The results for currency crises shows that a one-standard-deviation increase in veto players reduces the probability of currency crises indirectly by approximately .9 (.2) and .6 (.1) percentage points in the long-run (short-run) by reducing inflation and strengthening foreign exchange reserves (respectively). Given an unconditional probability of approximately 9 percent for currency crises, the combined reduction in the likelihood of crises realized by strengthening in these factors (1.6 percentage points in the long-run) is fairly large. As expected, these marginal effects are relatively higher when global conditions are risky (i.e., when the VIX is high), reflecting borderline conditions in which currency crises are relatively more likely.

We see relatively larger effects for currency crashes. Results of these indirect effects show that in the long-run (short-run), veto players reduce the likelihood of currency crashes through inflation by .5 (.1) percentage points, foreign exchange reserves by .8 (.1) percentage points, and economic growth by .6 (.5) percentage points. The combined effect is .7 percentage points in the short-run, and 1.6 percentage points in the long-run—substantial effects relative to the 3.5 percent unconditional probability of currency crashes. By strengthening these economic fundamentals, veto players indirectly reduce the likelihood of both currency crises and crashes.

Table 10 Exchange rate logit estimation: including democracy interaction specification
Table 11 Mediated marginal effects in percentage points

Appendix C Moderated mediated marginal effects

Estimation methodology

If the assumption of cross-stage independence in the regression coefficients does not hold, the indirect effect described in Sect. 3 will be biased. Rather the estimated indirect effect (in a linear function) being the product of the coefficients:

$$\begin{aligned} \beta _x\beta _{m} \end{aligned}$$
(29)

it instead is:

$$\begin{aligned} \beta _x\beta _{m} + \text {Cov}(\beta _{x,i},\beta _{m,i}), \end{aligned}$$
(30)

The additional term represents the cross-stage covariance in individual effects that may bias the estimated effects. The estimator used in the second stage of mediation in this paper is nonlinear, but the effect of this unobserved heterogeneity is substantively unchanged. This bias occurs only in the indirect pathway (indicated with bold lines). To test for this bias in the indirect pathway the coefficient giving the effect of the independent variable on the mediator—and the mediator on the dependent variable (the onset of a crisis)—is allowed to vary conditional upon variables known as moderators (d). In the Imbalance regressions the moderator interacts with the independent variable (veto players).Footnote 53 In the Reactions regressions the moderator interacts with the mediators (Hayes 2013).

Fig. 9
figure9

Moderated mediated estimation

If there are statistically significant differences between estimations that involve moderation and those that do not, then it can be inferred that heterogeneity is present and that the indirect effect is biased (Preacher et al. 2007). Five moderators are tested: Financial Development, Central Bank Independence, Democracy, Exchange Rate Regime, and Level of Economic Development. While no list of moderators can be exhaustive, this work focuses primarily on institutional factors that may influence the relationship between veto players and the mediators, and/or between the mediators and the likelihood of crises. As no significant evidence of moderation was found, these results are reported in “Appendix C.2” and further analysis is reported under the assumption of cross-stage independence.

Results

Observation level effects in individual stage effects must be independent for the mediation estimates—and therefore estimates of the full effect—reported in Sect. 4 to be unbiased. To test this, estimates are run to evaluate if the mediated effect is moderated by any other variables—with a statistically different mediated effect in estimations with and without a moderator taken to indicate this unobserved heterogeneity is present. This is done by interacting a potential moderator with the independent variable (veto players) in the first stage, and the moderator with the mediator variable(s) in the second stage (inflation, reserve coverage, and economic growth) (Preacher et al. 2007). Two methods test for moderation to evaluate whether this assumption of cross stage independence holds. The first method considers moderation effects at individual stages. A statistically significant coefficient on the interaction term at both stages indicates a moderation effect (Fairchild and MacKinnon 2009). The second method evaluates whether there are differences in the entire mediated effect when accounting for moderation (Preacher et al. 2007). The former analyzes each mediator and stage separately to evaluate if there is a moderated effect—but has been shown to still be a powerful test of moderation. The latter tests for moderation in the whole mediated effect, interacting a moderator with the independent variable in each estimation in the first stage, and the moderator with each mediator variable in the second stage. In theory this second test is robust. However, this test may struggle to identify moderation that is only present in specific variables if coefficients for other variables/stages have large standard errors, leading to a large standard error of the whole mediated effect. Therefore both methodologies are considered.

For these tests of moderation, a fixed effects least squares estimator is used in the Imbalance regressions. This avoids instrumentation difficulties related to the use of the System GMM when including interaction terms between instrumented variables. As the relevant metric is the mediated marginal effects with and without moderation—indicated by a statistically significant interaction term at each stage—instead of the estimated mediated effect, Nickell bias is a less important concern. A visual representation of the estimated paths is shown in Fig. 9. Pathways where mediation is tested for are indicated in bold.Footnote 54 As this effect is tested for five potential moderators, parameter values are not reported for the sake of parsimony. Once a moderator variable is included in the Reactions regressions the specificationFootnote 55 is:

$$\begin{aligned} p(\text {crisis}) =f( x_{\text {v}}\gamma + x_{d}\psi + x_{\text {c}}\beta + u), \end{aligned}$$
(31)

Where \(x_{\text {v}}=[v_{\text {vp}},~v_{\text {vp}}^{2}~,v_{\text {vp}}\cdot x_{\Delta \text {VIX}}]\) is a vector of veto player terms, \(x_d =[m_{\text {inf}},~m_{\text {inf}}\cdot d, ~ m_{\text {gdp}}, ~ m_{\text {gdp}}\cdot d, ~ m_{\text {cdt}}, ~ m_{\text {cdt}}\cdot d]\) is a vector of the variables involved in the moderated mediation, and \(x_{\text {c}}\) is the control variables. d is the moderator variable. \(\gamma\) contains the veto player coefficients, \(\psi\) the moderated mediator coefficients, and \(\beta\) the control coefficients.

To calculate the moderated mediated marginal effect the equation used is:

$$\begin{aligned} \frac{\overline{\partial p(c)}}{\partial v}~ =\frac{1}{n}\sum _{i=1}^n {\hat{p}}_{i}(1-{\hat{p}}_{i})\cdot (z_o), \end{aligned}$$
(32)

Where z is:

$$\begin{aligned} z_o=(j_o\cdot {\hat{\psi }}). \end{aligned}$$
(33)

However, the calculation of \(j_o\) is more complex than the equivalent vector in mediation. This gradient on the interior of the logistic function is now:

$$\begin{aligned} \begin{aligned} j_o = [{\hat{\phi }}_{3,\text {inf}} + {\hat{\phi }}_{1,\text {inf}}\cdot {d_{i}},~({\hat{\phi }}_{3,\text {inf}} + {\hat{\phi }}_{1,\text {inf}}\cdot {d_{i}})\cdot d_{i},\\ ~{\hat{\phi }}_{3,\text {gdp}} + {\hat{\phi }}_{1,\text {gdp}}\cdot {d_{i}},~ ({\hat{\phi }}_{3,\text {gdp}} + {\hat{\phi }}_{1,\text {gdp}}\cdot {d_{i}})\cdot d_{i},\\ ~{\hat{\phi }}_{3,\text {cdt}} + {\hat{\phi }}_{1,\text {cdt}}\cdot {d_{i}},~ ({\hat{\phi }}_{3,\text {cdt}} + {\hat{\phi }}_{1,\text {cdt}}\cdot {d_{i}})\cdot d_{i}]. \end{aligned} \end{aligned}$$
(34)

This term uses the estimated values of \({\hat{\phi }}_{3j}\), \({\hat{\phi }}_{1j}\), and the observed value of d, from Eq. (13). The term \({\hat{\phi }}_{3,\text {inf}} + {\hat{\phi }}_{1,\text {inf}}\cdot {d_{i}}\) contains the marginal effect of more veto players on each mediator in the first-stage estimations—with the coefficient of the interaction term multiplied by the observed value of the moderator variable. This term alone is in the element of the vector multiplied by the coefficients of the linear terms of the mediators in the 2nd stage, and is multiplied by the observed value of the moderator d in the elements of the vectors that are being multiplied by the coefficient of the interaction terms in the second stage. This gives the marginal effect of an increase in veto players (conditional on the moderator) for each mediator variable, with the marginal effect of that term on this function conditional on the moderator. If this moderated mediated marginal effect is statistically different than the mediated marginal effect while controlling for the moderator variable in both stages, then d is said to moderate the mediated effect.Footnote 56 This indicates unobserved heterogeneity in the individual level effects across stages conditional upon the moderator, indicating there is bias in our estimated mediated effect. If there is no evidence of this moderation, then it is safe to proceed assuming cross-stage independence in the individual level coefficients.

The first test for moderation follows the method of Fairchild and MacKinnon (2009). This individually tests if the interaction term between veto players and the potential moderator in the first stage, and the mediator and the potential moderator in the second stage, are each statistically significant. Table 12 reports the results of this estimation for five variables that may potentially moderate the indirect effect of veto players on the likelihood of crises through their effect on economic fundamentals.Footnote 57 Results are reported by moderator. Each of the first two rows for each moderator show whether the interaction term at that stage increases or decreases (in absolute value) the marginal effect of veto players on the mediator, and the mediator on the likelihood of crises, at that stage. These effects are listed “N/A” if they cannot statistically be distinguished from zero. The final row for each moderator reports if moderation has occurred, and if it has, whether these moderation effects indicate the real mediated effect is larger or smaller than the estimated mediated effect.Footnote 58 The direction of this effect is indicated by \(| \Delta | < 0\), or \(| \Delta | > 0\). The same (opposite) signs across the two stages indicates the real mediated effect of that variable is larger (smaller) than what was reported in Sect. 4.2 and “Appendix B”, after estimation includes this moderator. Only one potential moderator (financial development) is found to moderate a variable; economic growth in the currency crash estimations. However, these estimations indicate the real mediated effect may be even larger (in absolute value) than the estimated mediated effect from Sect. 4.2 and “Appendix B”.

Table 12 Testing for moderation: individual stages and mediators

Preacher et al offer a different method to test for moderation (2007). This test assess whether there is a statistically significant difference between the mediated effect and the mediated effect after accounting for moderation.Footnote 59 Table 13 reports these results.Footnote 60 The mediated effect while accounting moderation is reported in the first column. The mediated effect without moderation is reported in the second column. The third column reports whether or not these mediated values are statistically different—with a statistically significant difference in mediated effects giving evidence of this cross-stage heterogeneity that biases the mediated effects. The fourth column gives the ratio of these estimations, which can be considered a multiplier of estimated mediated effects from “Appendix B” yielding an estimate of the true indirect effect. A lack of significance of this effect is signified by an “N/A.”

If the ratio of the moderated mediated effect to the mediated marginal effect is \(>1\) then there is evidence the real indirect effect of veto players on the likelihood of crises is greater than the estimated mediated effect (and vice versa). This method used to check for a moderation effect is conceptually similar to the method reported above—except the estimates evaluate the full mediated effects relative to the full mediated effect while accounting for moderation, rather than checking for moderation for each variable at each stage.

Table 13 Average moderated mediated marginal effects: crises

Point estimates of the mediated effect are different when controlling for moderation. There is no moderator for which results show a statistically significant difference between the mediated effect and the moderated mediated effect. It is then not appropriate to infer cross stage heterogeneity from these results using this method of Preacher (2009), while the method of Fairchild and MacKinnon (2009) indicates one of the five potential moderators may moderate the effect of economic growth exclusively in currency crashes. Given the limited evidence of cross-stage heterogeneity in individual level effects found in these estimates of a potential moderated effect, results in the body of the paper are conducted under the assumption of cross-stage independence.

Appendix D Data sources and description

Panels run from 1990 to 2012, and include all countries in the IMF’s systemic crisis database—though they are unbalanced due to missing observations. Summary statistics for the observations used in each specification are reported in the relevant table. Data from 111 countries are included in the data used in the regressions. Summary statistics are reported in Tables 14, 15 and 16.

The crash variable is from the IMF’s systemic crisis database, coded by Laevan and Valencia as a 1 if an exchange rate depreciates by at least 30%, given this depreciation is at least 10% more than the previous year’s depreciation. The data used in the reactions specifications of probability model regressions contains 45 crisis instances. The crisis variable weights movements in exchange rates and foreign exchange reserve coverage to generate an index of exchange market pressure. If this index rises more than 1.5 standard deviations above the mean for the country, the event is tallied as a crisis. The measure (E.W.) uses equal weights across countries, with weights calculated excluding high inflation episodes. The data used in the model for this measure contains 100 observation of crises. The variable of interest (Veto Players) is political constraints from Heinzs (2006). It is constructed as an index ranging from zero to one, and is coded based on data available on January 1st of the given year. The index is constructed such that higher values correspond to more institutional or partisan constraints. This measure accounts for both the number of institutional actors (whether individuals or governing bodies) that have the ability to directly influence policy, and the alignment of the preferences of those actors. When there are more actors with veto power, and/or those actors exhibit greater differences in policy preferences, the political constraints variable will take on a higher value.

The first variable tested through the mediation analysis is the (logged) foreign exchange reserve ratio, from the World Bank’s World Development Indicators (World Development Indicators 2016). This is constructed as the log of FX reserves divided by the M2, with higher values indicating stronger reserve coverage. The next is inflation, also logged and from the WDI. The final variable tested in the mediation analysis is a three-year rolling average of real GDP per capita growth, calculated from the Penn World Tables (Summers and Heston 2016).

The first set of control variables are global pull factors; the VIX (a measure of risk and implied volatility from the CBOI—constructed as an annual average) is used a proxy for global risk, and the U.S. three year treasury rate (a measure of the global risk-free interest free interest rate from the St. Louis Federal Reserve) (BOE 2017).

First of the variables considered economic fundamentals as controls in the full model is a measure of de jure Central Bank independence, constructed by Garriga (2016), with higher values indicating a central bank that is less able to be influenced by other policymakers. The next variable is a measure of the real exchange rate undervaluation, constructed using data from the Penn World Tables. This measure applies a Balassa-Samuelson GDP per capita adjustment to a real exchange rate variable, with higher values indicating a relatively undervalued exchange rate. Logged Real GDP Per Capita is generated from the Penn World Tables, to account for the effect of levels of development on crisis probability. This same data source is used to generate a three year rolling average of Real GDP Per Capita Growth an additional control. The final control variable in the primary specification is a dummy variable for if the country has a fixed exchange rate regime, calculated using the dataset of Reinhart and Rogoff (2017).

Four alternative specifications each add two variables from a given category as robustness checks; political variables, fiscal variables, external variables, and financial variables. The political variables are a dummy variable tallied if a one if the country has a left wing government (from the WDI’s DPI), and a dummy variable tallied as one if the country is a democracy (calculated from the POLITY IV index) (2000) (Polity 2017). The fiscal variables are debt as a portion of GDP (also from the WDI), and the structural deficit. The structural deficit is calculated using the methodology of Hamilton (2017) to separate GDP into a trend and cyclical component. Using the methodology of the IMF’s Fedelino et al. (2009), this is then used to calculate the structural fiscal deficit as a percentage of GDP. The external variables are the current account balance as a portion of GDP, and trade (imports plus exports) as a portion of GDP, each from the WDI. The financial variables are credit growth (from the WDI), specified as the log-difference of credit to the private sector as a portion of GDP, and an index of financial development from Svirydzenka (2016) at the IMF.

For the Imbalance and Adjustment sections, summary statistics are listed in Table 15. All variables described above are under the same label and are constructed using the same methodology—only with more observations now that this table is the full dataset rather than just what was used in the Currency Crisis regressions (some may be included as a level rather than a difference). Due to missing observations for certain variables, panels are unbalanced.

New variables included are M2 Growth (M2Growth), also from the World Bank, measured as a the percent change in the M2 from the previous year (2016). The next variables added are manufacturing value added (Manu VA/GDP), and the logged real interest rate, also from the World Bank’s WDI. The final control variable is the deficit as a portion of the M2, included (and specified in this rather unorthodox way in order to account for inflationary pressure due to the fiscal policy), again from the WDI.

Table 14 Summary statistics: equal weighted currency crises
Table 15 Summary statistics: Laeven and Valencia currency crashes
Table 16 Summary statistics: imbalance/adjustment estimations

Appendix E Instrumentation

With the exception of the exchange rate undervaluation measure, both the full set and each individual instrument pass all standard postestimation tests indicating exogeneity and first order (but not second) serial correlation. The two step estimation process, robust standard errors, and orthogonal transformation are used. All GMM instruments are collapsed.

Inflation—Lags 2 through 5 of logged inflation are specified as GMM instruments. Lags 2 and 3, M2 growth, and the logged real interest rate are specified as collapsed GMM instruments. The change in the ratio of claims on the central government to the M2, manufacturing value added, and logged real GDP per capita are specified as standard instrumental variables. First lags did not pass tests of exogeneity. Total instrument count is 12.

Foreign Exchange Reserve Ratio—The dependent variable and political constraints are specified as GMM instruments for lags 1 through 6 with the instrument matrix collapsed, M2 Growth is specified as a GMM instrument in the first and second lag also with the instrument matrix collapsed. Polcon is specified as a GMM instrument in lags 1 through 5. The differenced logged real interest rate is specified as a standard instrument. Total instrument count is 16.

Economic Growth—The dependent variable is specified as a a GMM limit using lags 2 through 6. The lag of logged GDP per capita is specified as a standard instrument.

Exchange Rate Undervaluation—The dependent variable is specified as a GMM instrument using lags 2 through 10 (Table 10). Post-estimation tests do not suggest instrumentation is valid, and the GMM estimations for exchange rate undervaluation is not utilized in the mediation analysis.

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Meyer, J.M. Political constraints and currency crises in emerging markets and less developed economies. Rev World Econ (2021). https://doi.org/10.1007/s10290-021-00407-4

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Keywords

  • Empirical international finance
  • Currency crises
  • Global political economy
  • Econometric mediation
  • Veto player theory

JEL Classification

  • F4
  • F5
  • C3
  • E3