Análisis de la estructura física de la edificación y del entorno

Models

Clark and MacDonald (1998) propose the estimation of a reduced-form equation in order to explain the behaviour of the real effective exchange rate both in the short and medium run—what they call the behavioural equilibrium exchange rate (BEER). As is the case for the FEER model above, the acronym BEER is often used to indicate, by extension, a whole family of models which follow similar methodologies.

The Standard BEER Model

The BEER model can be used to estimate what Clark and MacDonald (1998) call the current misalignment and the total misalignment of a currency. The current misalign- ment is defined as the difference between actual values of the exchange rate and the estimated level of the fair value given the current values of the fundamentals. The to- tal misalignment is instead the difference between actual values of the exchange rate and the estimated level of the fair value given a measure of the sustainable or long-run fundamentals.

The theoretical basis of the BEER model is the risk-adjusted uncovered interest parity condition in real terms. By definition, the log excess return on foreign exchange

3.4. Models/Taxonomy

is equal to the interest rate differential plus the appreciation rate of the foreign currency

zt+k =i∗t −it+ (st+k−st), (3.7)

where st is the natural logarithm of the exchange rate (defined as the domestic price of

foreign currency, so that an increase in st denotes appreciation of the foreign currency),

and it and i∗t are the continuously compounded k-period domestic and foreign riskless

interest rates, respectively. In terms of the log real exchange rate, defined as qt = st + p∗t − pt, where p∗t and pt are the logs of the foreign and domestic price levels,

Equation (3.7) can be rewritten as

zt+k =r∗t+k−rt+k+qt+k−qt, (3.8)

where rt+k and rt∗+k denote domestic and foreign real interest rates, respectively. In

general, the expected excess return,Etzt+k, will be equal to a time-varying risk premium, ρt, so that

qt=Et(qt+k) +Et(rt∗+k−rt+k)−ρt. (3.9)

That is, the equilibrium real exchange rate reflects expectations of future real exchange rates, expectations of future real interest rate differentials, and a time-varying risk premium.

To make their model empirically tractable, Clark and MacDonald make the further assumption that the unobservable expectations of the exchange rate are a function of long-run economic fundamentals, i.e. Et(qt+k) = β′Zt, where Zt denotes the vector

of fundamentals. They identify the latter as the terms of trade, the relative price of nontraded to traded goods (proxying for Harrod-Balassa-Samuelson effects), and net foreign assets. Moreover, they proxy the time-varying risk premium ρtwith the relative

supply of domestic and foreign debt, arguing that an increase in the relative supply of outstanding domestic debt relative to foreign debt will increase the domestic risk premium, thereby requiring a depreciation of the current equilibrium exchange rate (see e.g. Giorgianni, 1997).

3.4. Models/Taxonomy

Empirically, the BEER is generally estimated using the fitted values of a cointe- gration relationship between the real effective exchange rate and a set of fundamentals such as those estimated above. For example, Clark and MacDonald (1998) use theJo- hansen (1988) method which allows for the existence of multiple cointegrating vectors. Extensions of the BEER approach are among the most popular fair value models among policy institutions and in the financial industry. For example, see the IMF equilibrium real exchange rate (ERER) approach and Goldman Sachs’s GSDEER model discussed later in this chapter.

A related approach is the so-called capital enhanced equilibrium exchange rate (CHEER), introduced by Johansen and Juselius (1992) and MacDonald and Marsh (1997), and later extended by MacDonald and Marsh (2004). The starting point is the view that nominal exchange rates may be misaligned form their PPP-implied level because of non-zero interest rates differentials (whatMacDonald and Marsh (1997) call the “Casselian view” of PPP). A cointegration relation is therefore estimated between nominal exchange rates, domestic and foreign price levels, and domestic and foreign interest rates. In this approach, the estimated speed of convergence tends to be faster than the typical PPP adjustment based on univariate models, and the inferred nominal exchange rate forecasts have some degree of short-term predictive ability when compared to the random walk benchmark.

The Permanent Equilibrium Exchange Rate (PEER)

Even though the BEER model explicitly recognises the distinction between current and total misalignment (see above), most of the actual implementations of BEER models generally focus only on the former. As the current values of fundamentals may de- part substantially from sustainable or long-run levels, a number of researchers have been investigating the fair value of the real exchange rate consistent with its long-run fundamentals.

Huizinga (1987) and Cumby and Huizinga (1990) use respectively univariate and multivariate Beveridge-Nelson decompositions in order to decompose the real exchange

3.4. Models/Taxonomy

rate into the sum of permanent and transitory components. The permanent component is then considered to be the permanent equilibrium exchange rate.

More recently, the permanent equilibrium exchange rate (PEER) model of Clark and MacDonald(2004) is a direct extension of the BEER models outlined above. Clark and MacDonald use the method developed by Gonzalo and Granger (1995) in order to decompose the fundamentals in permanent and transitory components, where the former are used to identify the long-run value of the fundamentals necessary to estimate the total misalignment defined above. The fundamentals are the same as in the BEER approach, but the terms of trade and the government debts ratio are dropped in the empirical analysis.