Behavioural Equilibrium Exchange Rate (BEER) model

Abstract: In this article, we will introduce another method for evaluating the ‘fair’ value of a currency: the Behavioural Equilibrium Exchange Rate (BEER), a model which is widely used in practice. The BEER model was developed by Clark and MacDonald (1999) and estimates the fair value of currencies according to short, medium and long-run determinants. An important concept is that there is no prior theory for the choice of economic variables; hence, the choice of variables is based on economic intuition and data simplicity and availability.

We will also do an application of the BEER and run a Fixed-Effect panel regression on the G10 currencies, using the US Dollar as the base currency, and three widely used macroeconomic variables – inflation, terms-of-trade and interest rates – for our regression. We will conclude by commenting the results and making a brief analysis on the Euro (Spot rate versus BEER value).

 LINK ===> BEER_Models

BIS Nominal and Real Effective Exchange Rates (EER): NEER and REER

As we mentioned it in our previous lecture on Real Exchange Rate (RER), a more interesting measure would be the Real Effective Exchange Rate (REER), which gives a bilateral RERs average between the domestic country and each of its trading partners, weighted by the trade shares of each business partner.

  1. Computing the Nominal Effective Exchange Rate (NEER)

The first step to compute the REER of a specific home country i (currency) would require to determine the Nominal Effective Exchange Rate (NEER) of that specific country i. For instance, the NEER of the Japanese Yen is a summary measure of the Japanese Yen (JPY) vis-à-vis the currencies of Japan’s most important trading partners.

The NEER of a specific currency i is calculated as the geometric weighted average of a basket of bilateral nominal exchange rates (M. Schmitz et al., 2012):NEEREq.JPG

Where N stands for the number of competitor countries in the reference group of trading partners. According to the FX literature, it is common to use geometric averages rather than arithmetic averages to compute effective exchange rates.

There are several to compute the weight associate with each economy, but we will use the weighting scheme presented in Turner and Van’t dack (1993). Details on the trade-based weighting methodology can be seen on the appendix.

With information and fundamentals becoming more and more transparent for every country, the Bank of International Settlements is now releasing monthly (and daily) data on Effective Exchange Rates (Nominal and Real). There are two monthly indices: the Broad Index comprising 61 economies with data from 1994 and the Narrow Index comprising 26 economies with data from 1964. The reason why the BIS EER (Effective Exchange Rates) has been broadened to 61 economies was to reflect the rising importance of the emerging economies in Asia, Central and Eastern Europe and Latin America. In addition, the BIS adopted a time-varying weights in the EER calculations in order to match the rapidly changing patterns between countries; they assign a three-year average trade weights and then construct and indices. For today EER calculations, the most recent weights are based on trade in the 2011-2013 period, with 2010 as the indices’ base year. The 2011-2013 period will be used until the next set of three-year data (i.e. 2014-2016) becomes fully available. This time-varying weights method gives accurate picture of medium to long-term exchange rate movements by taking into account the importance of all trading partners in different periods of time.

Chart 1 represents the historical monthly BIS CNY NEER index since 1995 (as I wrote in my article on the Chinese Yuan History, the CNY became an international  currency in 1995 when it was pegged to the US Dollar at an exchange rate of 8.28 Yuan per US Dollar.

Chart 1. Historical data of BIS CNY NEER (1995  – 2016)


(Source: BIS)

We can see that over the past 20 years, the Chinese Currency has been appreciating against its broad basket of trading partners; the index rose from 75 to 117 (August 2016) and hit a high of 127.4 in July 2015. As you can see, the last ‘sharp’ appreciation of the Chinese Yuan occurred between summer of 2014 and the summer of 2015, which matches the Obama Dollar Rise (The US Dollar appreciated by 25% overall during that period). Therefore, as the Chinese Yuan is loosely pegged to the US Dollar, the Chinese currency followed the Dollar move. The previous appreciation of the Renminbi wasn’t a problem as China was experiencing a double-digit growth and was a huge player in international trade in the 2000s; however, with shrinking global demand (i.e. end of the super-cycle, downward revisions of global growth forecasts) and deteriorating trade conditions, the post-2012 ‘area’ was more concerning for China Officials. As a consequence, the PBoC allosed the Yuan to depreciate by nearly 4% against the USD in August 2015 (two-day depreciation, 11th and 12th). Since then, the NEER CNY index has constantly been decreasing according to BIS calculations.

2. From NEER to REER (Real Effective Exchange Rate)

Now that we know the definition of the NEER, we can proceed to the calculation of the Real Effective Exchange Rate, which serves as an indicator of international price and costs competitiveness. The REER is also computed using a geometric weighted average, however we need to deflate nominal exchange rates using relative price or cost measures:


The BIS uses consumer price indexes (CPI) to deflate each exchange rate, which is the simplest measure of inflation as data are available everywhere. Other inflation measure that could be used are GDP deflator, PCE deflator, PPI…

For this case, we are going to study historical REER data for Japan (details on the history of the Japanese Yen here).

Chart 2. Historical data of BIS JPY REER (1995  – 2016)


(Source: BIS)

Since the Housing (and Equity) bubble burst in the early 90s, Japan plunged into a long deflationary period (some say a depression), and has always tried to rebuild its economy through fiscal and monetary stimulus. Despite the highest debt-to-GDP ratio in the world (230%, more than 10tr USD of public debt), a concerning declining population (see more here), and a massive QQME program launched in April 2013 after Abe regained ‘power’ in December 2012 (three arrows, Abenomics), the Japanese Yen has always been considered a safe-haven currency according to market participants:

  • It strengthened for several years after the Japanese Equity market popped (Nikkei 225 index almost reached 40,000 on December 29, 1989 before it collapsed) as you can see in the appendix (Bloomberg Chart, JPYUSD in candlestick, if it goes up, it means the JPY gains strength).
  • The JPY strengthen again during the Great Financial Crisis (massive carry unwinds, i.e. AUDJPY); the JPY REER index rose from 80 to 107 in 18 months.
  • Eventually, after a sharp depreciation due to the post-Kuroda effect (80tr of JGBs purchase to reach a target inflation of 2%) – the JPY REER went down from 97 to 67 in 2-and-half years – the Yen has been strengthening over the past year as a reflection of an equity sell-off (Nikkei 225 is down 20% since June 2015).

The big question today is: could the Yen still be perceived as a safe-haven currency based on Japanese fundamentals? As I wrote it in many articles, it seems that Japanese Officials are running out of options at the moment. The poor performance of the equity market, a negative yield curve up to 10Y and a ‘strong’ Yen is persistently hurting the Japanese economy (poor exports, sluggish growth, market is still  not pricing in inflation…), and today the BoJ doesn’t have many bullets to use. The ones we discussed were helicopter money and Reverse Operation Twist.

To conclude, I believe the EERs released by the BIS are important indexes to watch in addition to the historical spot rates as they reflect a more fair / accurate value of a specific currency. In the next lectures, we will study other approaches to examine if a country’s actual real effective exchange rate is consistent with fundamentals. The BEER (Behavioural Equilibrium Exchange Rate) approach, for instance, uses economic methods to establish a behavioural link between the real rate and relevant economic variables. Another more complex approach is the FEER (Fundamental Equilibrium Exchange Rate), one of the most popular of the underlying balance (UB) models.


M. Klau and S.S. Fund (2006), The new BIS Effective Exchange rate indices (BIS)

M. Schmitz (2012), Revisiting the Effective Exchange Rates of the Euro (ECB)

P. Turner and J. Van’t dack (19930, Measuring international price and cost competitiveness (BIS)

Appendix 1. Weights for NEER (and REER)


Appendix 2. JPYUSD (Candlestick) vs. Japan BIS REER (yellow line) since 1989 (Source : Bloomberg)


Eurostat-OECD PPP and the RER (Real exchange rate)

  1. PPP analysis with FX exchange rates

Last time, we gave an easy example of PPP – a simple model of exchange rate determination that defines relation between the exchange rates and the prices of goods in different countries – the Big Mac Index.

A more sophisticated one was developed by the Eurostat and OECD and its computation is described in their manual called Eurostat-OECD Methodologies Manual on Purchasing Power Parities. It gives a better approximation of the PPP, which is difficult to measure as countries can have different baskets of goods or different weights in their price level measures. We are not going to go further in the three-stage calculation of the PPPs, all we need to know here is that it gives a more accurate value of the PPP than the Big Mac Index, and therefore is used by many academics and practitioners.

Below, we are going to provide three different analyses of FX spot rates (GBP, JPY and CAD) against the PPP values since the collapse of the Bretton Woods system in 1971.

GBPUSD: In the early 1970s, Cable was way undervalued compare to its PPP value, which converged slowly to the FX spot rate around 2.10 in 1979. Then, for the next three and half decades, we can say that the Exchange Rate has oscillated around its fundamental PPP value (Chart 1). The only big divergence we saw was in the 1980s as a consequence of the Federal Reserve increasing its interest rate up to 18% to fight inflation coming from the second oil shock (Shah Revolution in Iran). This sudden tightening cycle gave birth to the Dollar Reagan Rally between 1980 and 1985, which could explain the reason why Cable diverged sharply from its fundamental value. This rally was halted after the Plaza Agreements in September 1985 (in which the major central banks pledged to work towards a weaker US Dollar and a reduction of US Current Account Deficit) and the FX spot rate converged back toward its PPP level. Since 1990, the spot rate has more or less traded around its fundamental value.

The recent drop that pushed Cable below its fair value are the consequences of Brexit (more details here) as the pound was clearly hurt from investments outflows (i.e. property funds) and new easing measures announced by the Bank of England (25bps rate cut in addition to 60bn GBP QE expansion within the next 18 months). We could see more divergence [from the fundamental value] as the UK is clearly on its way to reach a ZIRP policy in the near future, which would add pressure to the British pound.

Chart 1. GBPUSD spot rate (red line) versus PPP (black line)


(Source: OECD)

USDJPY: In 1970, the fundamental value (PPP, black line) was estimated at around 225 while the FX spot rate was fixed at 360 JPY per USD. The Japanese currency was fairly undervalued (against the USD) for a long time according to economists, which could explain the large current account surpluses mainly driven by exports due to a cheap currency (click here for more details about The History of the Japanese Yen). After Bretton Woods ended, the Yen experienced two decades of appreciation against the greenback and constantly traded below its fundamental value between 1985 and 2013.

Then, the new measures launch by the trio Abe/Kuroda/Aso in 2012-2013 led to a massive Yen weakening period and the exchange rate eventually crossed over its fair value [according to Eurostat-OECD PPP] in 2014. The results of Abenomics levitated USDJPY from the mid-70s level in Q3 2012 to a high of 125 in June 2015, while the PPP index remained quite steady at around 105.

However, the weak global macro environment (lower global growth, Brexit and the European Banks, Fed delaying its tightening cycle…) in addition to no further BoJ stimulus (more details here) has played in favor of the Yen over the past year; USDJPY declined sharply below its fundamental value and is currently flirting with the psychological 100 support. The real now question now is how far will the Japanese Government [and the BoJ] let the currency pair diverge from its fundamental value on the downside before intervening in the market?

Chart 2. USDJPY spot rate (red line) versus PPP (black line)


(Source: OECD)

USDCAD: For our last PPP analysis, I chose a commodity currency: the Canadian Dollar also called the Loonie (Chart 3). It is pretty clear that all of the three charts show us that over a long period of time, the FX spot rate tend to mean-revert towards its fundamental value if it diverges too far away from it. I think that it is interesting to look at how commodity currency exchange rates (i.e. the Loonie) react vis-à-vis their fair PPP value. As opposed to the British pound (Chart 1), we can see that USDCAD FX spot rate is much more volatile [relative to its PPP value], and therefore USDCAD tends to divergence much more from its fundamental value and for a longer period of time. For instance, we first had an important divergence during the Reagan Rally where USDCAD rose from 1.15 to 1.40 (which means strong Canadian Dollar depreciation against the USD), but more importantly during the 1990s Clinton Rally when the Fed started a tightening cycle. The divergence is also explained by the sharp decline of the Canadian Dollar in the 1990s. The 90-91 recession that followed a significant interest rate increase, fiscal and political uncertainty during the mid-1990s in addition to the Quebec referendum of 1995 led to a progressive weakening of the Loonie (M. Devereux, 2008). On the top of that, the Asian financial crisis in 1997 led to a fall in commodity prices, which obviously accelerated the Canadian Dollar meltdown. USDCAD reached an annual average high of 1.5700 in 2002 [according to OECD data] and the market was speculating on a Fall of the Loonie.

The situation reversed then and between 2002 and 2011, we saw a dramatic appreciation of the Loonie. It looks to me that the more a currency diverges from its fundamental value, the sharper the reversal is. This long period of Loonie strength could be summarize by the Super-Commodity cycle led by the elevated growth coming from Emerging Markets (the famous BRICs).

We can observe another important reversal in 2012, which has mainly been explained by the end of the super-cycle. Since 2012, commodity currencies (i.e. AUD, NZD, CAD or ZAR) suffered dramatic losses due to a decreasing global demand (slowing growth coming from China, the fall of Russia then Brazil, Fragile Fives…) which impacted the commodity market. The Loonie is once again undervalued according to the PPP Fair Value and the situation is not going to get better anytime soon I believe. Therefore, we could see further divergence from the fair value in the medium term (12-18 months) and LT mean reversal shorts should wait for the exchange rate [USDCAD] to reach higher levels.

Chart 3. USDCAD spot rate (red line) versus PPP (black line)


(Source: OECD)

  1. Real Exchange Rates

The real exchange rate (RER) seeks to measure the value of a country’s goods relative to those of another country at the prevailing nominal exchange rate. It is defined by the following formula:

Qt = St * P’t / Pt

Where P’t represents the price of foreign goods,Pt represents the price of domestic goods and St the nominal exchange rate.

If [absolute] PPP holds, therefore the real exchange rate Qt =1 as the price of goods would cost the same in the domestic country (i.e. United States) as in the foreign country (Great Britain) when the price is expressed in a common currency. However, we saw in our three cases that PPP doesn’t hold as FX spot rates tend to be usually overvalued or undervalued compare to their fundamental value.

From the formula above, we know that the competitiveness of the foreign country improves when Qt < 1as the foreign currency is undervalued according to the PPP model that we used. On the contrary, if Qt > 1 , the foreign currency is overvalued and the competitiveness of the foreign country deteriorates.

In our examples, we have the following results:

GBPUSD: Qt = 1.325 / 1.40 = 0.9464 < 1, which means that British Pound is undervalued vis-à-vis the US Dollar.

USDJPY:  Qt = (1/100) / (1/104) = 104/100= 1.04 > 1, the Japanese Yen is currently overvalued against the US Dollar according to PPP.

USDCAD: Qt = (1/1.2850) / (1/1.2150) = 1.2150/11.2850= 0.9420 < 1, i.e. the Canadian Dollar is undervalued against the greenback.

Even though the RER indexes between two countries, a more interesting measure would be the Real Effective Exchange Rate (REER) which gives a bilateral RERs average between the domestic country and each of its trading partners, weighted by the trade shares of each business partner. Therefore, our next lecture will be on how to calculate a REER series for a specific country and see if that country has an undervalued or overvalued exchange rate respective to its trading partners.


Devereux, Michael (2008), The Rise of the Canadian Dollar, 2002 2008

OECD (2012), Eurostat|OECD Methodological Manual on Purchasing Power Parities

Catao, Luis (2007), Why Real Exchange Rates?

Purchasing Power Parity: A quick introduction

After the familiar introduction on PPP (Big Mac Index), we can start by introducing Rudiger Dornbusch’s NBER Paper on PPP published in March 1985. In his working paper, Professor Dornbusch states that the PPP theory of exchange rate has ‘the same status in the history of economic thought and in economic policy as the Quantity Theory of Money (QT)’. The QT version most commonly used is the Fisher Identity (Economist Irving Fisher in his book The Purchasing Power of Money) defined by:

M.V = P.T, where

M = Money supply, or stock of money in coins, notes and bank deposits

V = Velocity of circulation

P = Some measure of the Price level (i.e. CPI)

T = Volume of Transactions in the economy

1. Historical context
The notion of purchasing power parity PPP can be traced to the 16-century Spanish Salamanca school, but the protagonist of the theory is the Swedish Economist Gustav Cassel. During and after WWI, he observed that countries like Germany or Hungary a sharp depreciation of the purchasing power of their currencies in addition to hyperinflation. Therefore, he proposed a model of PPP that became a benchmark for long run nominal exchange rate determination.

2. Statement of the PPP theory:
Let Pi and Pi* be the price of the ith commodity at home and abroad respectively (both in local currencies) and e the exchange rate. Let P and P* represent the price level at home and abroad.

In an integrated, competitive market (no cost for transport and no barriers to international trade for the good), the concept is based on the Law of one Price where identical goods will have the same price in different markers when quoted in the same currency.

For unless Pi = e.Pi*        (1)

There will be an opportunity for profitable arbitrage.
Arbitrage:  Recall that arbitrage is the possibility to make a profit in financial market without risk and without net investment of capital. A portfolio π has an arbitrage opportunity if there exists T > 0 such that Xo = 0, Xt >= 0 (P – a.s.), P(Xt > 0) > 0.

For instance, if Pi < e.Pi*, then an arbitrageur will buy the good domestically for Pi, sell it abroad for Pi* and realize a risk-free profit as Pi*.e – Pi > 0. Such arbitrage, purchasing the cheap good and selling it where it is dear, would continue until the equality (1) held.

As we said, equation (1) states that the price of the ith commodity must be the same in both markets (i.e. two different countries, for instance US and UK). The Equation is known as Commodity Price Parity (CPP).

Example: Let’s say that the price of one ounce of gold sold in London is 846 GBP, whereas it is sold of for USD 1,290 in New York. If we apply equation (2), we can conclude that the implied rate for Cable (GBP/USD) is 1.5248 (as a result of 1,290 / 846).

Limits:  As we all know, in the real world, CPP may not hold for different reasons:
– Transactions costs (transportations costs, insurance fees)
– Non-traded Goods: items such as electricity, water supply, or goods with very high transportation costs such as gravel.
– Restraints of Trade
– Imperfect Competition

3. Purchasing Power
In an economy with a collection of commodities, ‘purchasing power’ is defined in terms of a representative bundle of goods. We evaluate purchasing power by constructing a price index based on a basket of (consumption) goods.

3.1. Absolute purchasing power parity
Let P = f(p1,…, pi,…,pn) and P* = g(p1*,…,pi*,…pn*) be domestic and foreign price indices.
Then, if the prices of each good (in dollars) are equalized across countries, and if the same goods enter each country’s market basket with the same weights, then Absolute PPP prevails.

e = P/P* = ($ price of a standard market basket of foods) / £ (price of the same standard basket)     (2)

If pi / pi* = k for i = 1,…,n , then

e = P/P* = k     (3)

There can be no objection to equation (2) as a theoretical statement. However, as we mentioned it earlier (limits), objections arise when equation (2) is interpreted as an empirical proposition (Tariffs, transportation costs make it difficult for the spot prices of a commodity i to be equal in different location at a given time).

Strong (Absolute) PPP implies that whatever monetary or real disturbances in the economy, the price of a common market of basket of goods will be the same, i.e. P/e.P*=1.

3.2. Relative Purchasing Power Parity
The relative version of PPP restates the theory in terms of changes in relative price levels and exchange rate: e = C. P/P*,

where C is a constant that reflect the trade obstacles. The difference in the rate of change in prices at home and abroad – difference in the inflation rate – is equal to the percentage depreciation or appreciation of the exchange rate:

ê = π – π*   (4)

where ^ denotes a percentage change, π – π* the inflation differences between two markets (i.e. countries) reflected in percentage changes in the exchange rate. For instance, if the inflation rate is π = 2% in the US and π* = 1% in the UK, then the British Pound (GBP) should appreciate by ê = π – π* = 1% against the USD.
Prices in the US are rising faster than in the UK, therefore UK exports are becoming more competitive (compare to US ones), raising importers’ interest. This should generate a higher demand for GBP (relative to USD), hence sending Cable (GBP/USD) higher.

Equation (4) was applied by Gustav Cassel to an analysis of exchange rate changes during World War, as according to PPP, the fair value of an  exchange rate between two countries is determined by the two countries’ relative price levels.

4. Opening
Since the early 1980s (after the collapse of Bretton Woods), advances in econometrics and longer time series covering the period of floating exchange rates were two important developments in the new generation of fair value models. The next article will focus on the two dominating families of currency fair values widely used today: the Behavioural Equilibrium Exchange Rate (BEER) models and Underlying Balance (UB) models adopted for flexible exchange rates.


Dornbusch, Rudiger (1985), “Purchasing Power Parity”. NBER Working Paper No. 1591.

Isaac, Alan G. Lecture in Purchasing Power Parity.

Jerry Coakley and Stuart Snaith (2004), “Testing for Long Run Purchasing Power Parity”.