**3. The identification of currency and banking crises**

The identification of currency and banking crises can be divided into three groups. In currency crises, the Exchange Market Pressure Index is arguably the most popular approach to identify the crises. In the banking crises, there is a growing interest to employ the Money Market Pressure Index to identify the crises. While the above indexes gain popularity in the currency and banking crises literature, there may be a benefit to investigating the crises as twin currency and banking crises due to interconnection in the financial market. Thus, the Financial Market Pressure model arguably provides better insight into the overall pressure on the financial market.

However, economists should employ the market pressure-based approach with caution due to the absence of consensus on how to weigh the variables and how to define the thresholds. As different weights and thresholds may lead to different crisis databases, economists may be tempted to adjust the models to fit their preferences.

#### **3.1 Identification of currency crises**

In general, there are two methods to identify currency crises. Early studies of currency crises generally use the depreciation of the exchange rate at a certain level as a basis to identify the crisis. There is no consensus about the threshold of currency depreciation to identify currency crises. For example, some economists define a currency crisis as when a currency depreciates more than 25% and there is an increase of 10% in the rate of depreciation [30].

However, using exchange rate depreciation to identify the currency crises may be biased when the central bank intervenes in order that the exchange rate does not depreciate despite considerable pressure on the currency. Even though central banks announce that they are employing an information targeting framework or a free float exchange rate regime, it is commonly acknowledged that central banks do intervene

in the foreign exchange market to smooth exchange rate volatility or to maintain the exchange rate in a certain band due to the fear of floating [31].

For that reason, most recent studies use Exchange Market Pressure Index (EMPI) as the basis to identify currency crises. This model is originally developed as a monetary model to calculate the amount of foreign exchange intervention to meet a desired exchange rate target [32].

EMPI illustrates that the pressure on the exchange rate is not only reflected in the depreciation (Δe*t*) but also on the amount of central bank intervention through the spot market (Δ*Rt*) and sometimes through the interest rate. In the event of an intervention by central banks to slow the depreciation rate, EMPI shows higher pressure in the exchange market despite there being only limited depreciation in the exchange rate.

As the variables included in the EMPI have different volatility, careful consideration of the weight associated with each variable is therefore required, so that no particular variable can distort the EMPI. Currently, there are three different popular weighting methods in the market pressure-based approaches [33–35], all of which use the standard deviation to weight the variables.

$$\mathbf{EMPTI}\_{\mathbf{f}} = \Delta \mathbf{e}\_{\mathbf{f}} - \frac{\sigma\_{\mathbf{e}}}{\sigma\_{\mathbf{R}}} \Delta R\_{\mathbf{f}} \tag{6}$$

$$\text{EMPI}\_{t} = \frac{1}{\sigma\_{\varepsilon}} \Delta \mathbf{e}\_{t} - \frac{1}{\sigma\_{R}} \Delta R\_{t} \tag{7}$$

$$EMPI\_t = \frac{\frac{1}{\sigma\_t}}{\left(\frac{1}{\sigma\_t} + \frac{1}{\sigma\_R}\right)} \Delta \mathbf{e}\_t - \frac{\frac{1}{\sigma\_R}}{\left(\frac{1}{\sigma\_t} + \frac{1}{\sigma\_R}\right)} \Delta R\_t \tag{8}$$

where σ<sup>e</sup> is the standard deviation of the exchange rate and σ<sup>R</sup> is the standard deviation of foreign reserve.

There is no consensus on the threshold, for example, some economists define currency crises as EMPI exceeding three standard deviations or more above the mean.

#### **3.2 Identification of banking crises**

There are two popular methods to identify banking crisis episodes. The first method is based on events, such as bank performance, government bailout, widespread bank failures, the extent of bank runs, and professional analysis to specify bank crises [36, 37].

Despite its popularity, it is difficult to identify the start date of banking crises using this event method. For example, the government's bailout normally occurs at the peak of a crisis, sometimes it involves a political process that delays the bailout.

To address the drawback of the event methods, some economists develop a Money Market Pressure Index (MMPI) as a quantitative approach to identify banking crises. The new method argues that pressure in the banking system should be reflected by the change in the interest rate. However, the central bank may conduct a monetary operation to manage the interest rate. Thus, the pressure in the banking system cannot be shown by the interest rate alone. To address this issue, the interest rate should be offset by the monetary operation [38].

MMPI can be formulated as:

$$\text{MMPI}\_{t} = a\mathbf{o}\_{1}\Delta\mathbf{y}\_{t} + a\mathbf{o}\_{2}\Delta\dot{\mathbf{i}}\_{t} \tag{9}$$

Where Δ*γ<sup>t</sup>* is changes in reserves to bank deposits ratio, Δ*it* is changes in shortterm real interest rate, and *ω* is the weight between variables.

Although the MMPI was introduced before the Global Financial Crisis of 2007– 2008, it gained popularity as an approach to identifying banking crises in the aftermath of the Global Financial Crisis due to its reliability and simplicity. The index shows that while it is based on only two variables, the MMPI can identify banking crises in both developed and emerging markets [39]. In addition, the MMPI provides a clear indication of the start and end dates of banking crises - a feature that is not available in the 'so-called' event approach.

#### **3.3 Identification of twin currency and banking crises**

While there are many techniques for identifying currency and banking crises, those techniques mainly examine the crises as isolated crises. However, as the financial system is interconnected, identifying a crisis as an isolated crisis may lead to incomplete information about overall pressure in the financial system. For example, high pressures in the exchange market can be distributed to the money market, or vice versa, and create a mild pressure in both markets. Thus, the exchange market and the money market may seem stable amid high pressures on the overall financial market, which creates hidden crises [40]. Understanding these hidden crises will be the key to future mitigation policy. Therefore, there are significant benefits in considering currency and banking crises as a twin crises, rather than isolated crises.

To understand the model, let us start with the monetary equilibrium as follows:

$$\mathcal{M}^{\circ} = \mathcal{M}^{d} \tag{10}$$

where:

*Ms* = total money supply issued by the Central Bank.

*M<sup>d</sup>* = total demand for money.

On the one hand, money is supplied by the central bank, which creates money by buying foreign reserves (*Ft*) and domestic assets (*Dt*). On the other hand, the demand for money can be represented as a function of price (*Pt*), income (*Yt*) and interest rate (*Rt*). Thus, eq. (10) can be rewritten as:

$$F\_t + D\_t = P\_t Y\_t^{\beta\_t} \exp\left(-a\_t R\_t\right) \tag{11}$$

where:

*βt*= income elasticity >0 at time *t.*

*αt*= interest rate coefficient > 0 at time *t.*

As the money created by buying foreign reserves can be measured by multiplying foreign reserves by the exchange rate (*ERt*), eq. (11) can be represented as follows:

$$P(F\_t.ER\_t) + D\_t = P\_t Y\_t^{\beta\_t} \exp\left(-a\_t R\_t\right) \tag{12}$$

The real measure of monetary equilibrium can be obtained by deflating the changes in the money supply by the total money supply created by the Central Bank.

$$f\_t + d\_t = \pi\_t + \beta\_t y\_t - a\_t r\_t \tag{13}$$

$$\begin{array}{l}\text{where:}\\f\_{\mathfrak{f}} = FR\_{\mathfrak{f}} \ \mathit{ER}\_{\mathfrak{f}} \ / \mathcal{M}\_{\mathfrak{f}^\*}\\d\_{\mathfrak{f}} = \Delta D\_{\mathfrak{f}} \ / M\_{\mathfrak{r}}\\\pi\_{\mathfrak{r}} = \Delta P\_{\mathfrak{r}} / P\_{\mathfrak{r}^\*}\\\mathcal{Y}\_{\mathfrak{f}} = \Delta Y\_{\mathfrak{t}} / Y\_{\mathfrak{t}^\*}\\r\_{\mathfrak{i}}\left(t\right) = \Delta R\_{\mathfrak{t}} / d\_{\mathfrak{t}^\*}\\\Gamma \quad (12) \quad \frac{1}{\mathfrak{r}^\*}\end{array}$$

Eq. (13) can be re-arranged to separate financial system and macroeconomic indicators as follow:

$$f\_t + d\_t + a\_t r\_t = \pi\_t + \beta\_t \mathbf{y}\_t \tag{14}$$

In an open economy, the monetary equilibrium is affected by other countries. Thus, the interaction between country *a* and country *b* can be determined by employing the International Fisher Effect to the monetary equilibrium:

$$\left(f\_a - f\_b\right) + \left(d\_a - d\_b\right) + a(r\_a - r\_b) = \left(\beta\_a \mathcal{y}\_a - \beta\_b \mathcal{y}\_b\right) + \left(\pi\_a - \pi\_b\right) \tag{15}$$

By adjusting the change of foreign reserves and the change of price by the rate of appreciation of currency *a* in terms of currency *b* (*eab*), eq. (15) can be rewritten as:

$$\left(f\_{\;\;a} + e\_{ab} + d\_a + ar\_a = \left(\beta\_a \underline{y}\_a + \pi\_a\right) + \left(f\_{\;\;b} + d\_b + ar\_b - \beta\_b \underline{y}\_b - \pi\_b + e\_{ab}\right)\right) \tag{16}$$

The (*f <sup>a</sup>* þ *eab* þ *da* þ *αra*) is referred to as the Financial Market Pressure, *βaya* þ *π<sup>a</sup>* as the Macroeconomic Pressure, and *<sup>f</sup> <sup>b</sup>* <sup>þ</sup> *db* � *<sup>β</sup>byb* � *<sup>π</sup><sup>b</sup>* <sup>þ</sup> *eab* <sup>þ</sup> *<sup>α</sup>rb* as the External Pressure. Thus, in the final form, eq. (16) can be represented as:

*Financial Market Pressure* ¼ *Macroeconomic Pressure* þ *External Pressure*

The above model shows that, in a close economy, the relationship between the financial market pressure and the macroeconomic pressure should be one-on-one. However, external pressure may force the relationship to break apart.

The financial market pressure model suggests that the twin currency and banking crisis is characterised by a sharp depreciation of the exchange rate and the rise of the interest rate. To address the issues, central banks may sell their foreign reserve to stabilise the exchange rate and expand the base money. Thus, the exchange rate and the interest rate may seem stable amid high pressure in the financial system. In order to measure the total pressure in the financial market, the change in the exchange rate and the interest rate should be offset by the central bank's intervention in the exchange market and domestic money market.
