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# Behavioral Equilibrium Exchange Rate (BEER)

### Pablo Aznar

#### 08/02/2023

The equilibrium exchange rate (EER) can be defined as the rate which, in the absence of official intervention, balances the supply and demand of two currencies, (Williamson 1983).

Knowing this value of EER could be useful for several reasons:

• It can provide information about future currency pair movements.
• The movements of currency pairs can be due to macroeconomic causes. Therefore, the EER will give information on what policy measures can be taken. The same scenario takes place when there is an exchange rate peg.

There are different ways of measuring EER. The three most broadly known are the following:

• Purchasing Power Parity (PPP).
• Behavioral Equilibrium Exchange Rate (BEER).
• Macroeconomic Balance (MB).

Regarding predictive power, the PPP is the one that has the most in the long run. However, the distance between the PPP and the currency pair is often very large due to Harrod-Balassa-Samuelson effect and the PPP puzzle.

In addition, BEER and MB models relate the currency pairs to economic fundamentals. This added complexity in constructing the EER values does not result in greater predictive power [3]. BEER and PPP values are usually very close, so this means that BEER has a similar predictive power, being slightly lower. Moreover, the MB model is the least accurate of the three different values of equilibrium.

In previous posts, we have discussed Purchasing Power Parity. Therefore, in this post, we are going to talk about the Behavioral Equilibrium Exchange Rate.

## BEER

BEER states the possibility that the currency pairs are non-stationary and their movements are related to economic fundamentals. For that reason, let’s see how BEER is calculated.

On one hand, the actual exchange rate can be defined using the following formula:

$$q_t = \beta’_{1}Z_{1t} + \beta’_{2}Z_{2t} + \tau’T_t + \epsilon_t$$

Where:

• $$Z_1$$:  set of economic fundamentals that are expected to have persistent effects over the long-run.
• $$Z_2$$: set of economic fundamentals that affect the exchange rate over the medium term.
• $$\beta_1, \beta_2$$: vectors of reduced coefficients.
• $$T$$: set of transitory factors which affect the exchange rate in the short run.
• $$\tau$$: vector of reduced-form coefficients.
• $$\epsilon$$: random error term.

On the other hand, the equilibrium exchange rate $$q’_t$$, is defined with the transitory and random term as zero.

$$q’_t = \beta’_{1}Z_{1t} + \beta’_{2}Z_{2t}$$

Therefore, once both are defined, we can explain the current misalignment of a currency pair, cm. This can be defined as the difference between the actual exchange rate and the equilibrium exchange rate.

$$cm \equiv q_t – q’_t$$

$$= \beta’_{1}Z_{1t} + \beta’_{2}Z_{2t} + \tau’T_t + \epsilon_t – \beta’_{1}Z_{1t} – \beta’_{2}Z_{2t}$$

$$=\tau’T_t + \epsilon_t$$

As it can be seen, the current misalignment is the transitory and random error.

Besides the current misalignment, the total misalignment, tm, can also be defined. It is the difference between the actual exchange rate and the equilibrium exchange rate given by the long-run values of the economic fundamentals.

$$tm_t = q_t – \beta’_1\bar{Z}_{1t} – \beta’_2\bar{Z}_{2t}$$

Where $$\bar{Z}_{1t}$$ and $$\bar{Z}_{2t}$$ are the long-run values of the economic fundamentals. In addition, it can also be written as:

$$tm_t = (q_t – q’_t) + [\beta’_1(Z_{1t} – \bar{Z}_{1t}) + \beta’_2(Z_{2t} – \bar{Z}_{2t})]$$

So, the total misalignment can be decomposed into two components.

$$tm_t = \tau’T_t + \epsilon_t+ [\beta’_1(Z_{1t} – \bar{Z}_{1t}) + \beta’_2(Z_{2t} – \bar{Z}_{2t})]$$

One component is the effect of the transitory factors and random error, whereas the other indicates fundamentals’ distance from their long-run values.

### Summary

Therefore, summarizing the above, in order to calculate the BEER, we have to follow this steps:

1. Firstly, we have to estimate the relation between the real exchange rate and the fundamentals.
2. Then the current misalignment is calculated between the EER and the actual exchange rate.
3. Subsequently, we have to determine the long-run values for the used fundamentals.
4. Finally, the total misalignment is calculated.

## Macroeconomic variables

But, which macroeconomic variables are used to build the BEER?

The most common would be the following:

• Nominal interest rates: carry trade effect will cause the currency with higher interest rates to appreciate in the medium term.
• Inflation: when prices increase it is commonly followed by currency depreciation.
• Terms of trade: when this fundamental increases, the currency pair strengthens because it produces an increment in wealth. It shows how the price of import and exports evolve.
• Net Foreign Assets (nfa): an increase in this variable will deteriorate the trade balance, which will impact the currency pair.

Therefore, looking at the formula above we can identify the different components. $$Z_1$$ usually contains net foreign assets, a productivity term as GDP, and terms of trade. Whereas $$Z_2$$ contains interest rates.

The use of these macroeconomic variables allows us to use some that explain the HBS effect. Therefore, BEER can be used in emerging currency pairs.

## Conclusions

In this post, we have learnt what is the equilibrium exchange rate, which are the most broadly known, and described the BEER in depth. In addition, we have explained how it can be calculated and the different components that make it up.

Behavioral Equilibrium Exchange Rate has less predictive power than PPP, but allows us to use some macroeconomic variables that explains the HBS effect. This means that, it can be used as a measure of equilibrium in emerging currency pairs.

## Bibliography

[1] Clark P. and MacDonald R., Exchange rates and economic fundamentals: A
methodological comparison of BEERs and FEERs, IMF, 1998

[2] Driver, R. L., & Westaway, P. F. (2003). Concepts of equilibrium exchange rates. Exchange rates, capital flows and policy, 98-124.

[3] Ca’Zorzi, M., Cap, A., Mijakovic, A., & Rubaszek, M. (2020). The predictive power of equilibrium exchange rate models. Available at SSRN 3516749.

[4] MacDonald, R., & Dias, P. (2007). Behavioural equilibrium exchange rate estimates and implied exchange rate adjustments for ten countries. Peterson Institute of International Economics Working Paper, February.

[5] Zhang, Z. (2010). Understanding the behavioral equilibrium exchange rate model via its application to the valuation of Chinese renminbi. Available at SSRN 2120419.