Real exchange rate indicators

1. The CPI-based measure is widely available, facilitating comparisons with other countries. It is also a broad-based indicator, including both goods and services. The main drawbacks are that such indices include a large number of nontraded goods and services, and exclude intermediate goods, which are an important component of traded goods; and the representative basket will vary across countries. In transition countries, the CPI can also be significantly affected by price liberalization and adjustments of administered prices.

2. The PPI-based measure retains the disadvantage that the basket varies across countries. However, the items in each basket are typically more representative of traded goods, including traded intermediate goods. But the PPI-based measure may not be a good measure of competitiveness as companies can price to market by squeezing profits in the short run.

3. The ULC-based measure is often thought to be the most appropriate for use as a competitiveness measure, because labor costs are an important component of production costs. But the measure misses some important aspects of actual production costs; a fall in unit labor costs that results from the substitution of capital for labor, for example, need not necessarily signal an improvement in underlying competitiveness. The measurement of productivity that underlies the ULC-based measure is difficult in practice, especially when used as a basis for cross-country comparisons, and typically highly sensitive to variations in the economic cycle.

4. The main difference between price- and ULC-based REERs stems from the Balassa-Samuelson effects, which should produce steady but sustainable increases in CPI-based REERs, but affect ULC-based REERs for manufacturing, where traded goods weigh heavily, relatively little. The usefulness of REER measures is can be according to their ability to explain actual trade flows. Marsh and Tokarick (1994), for example, find that for a range of advanced countries, trade flows are most closely correlated with ULC-based REER measures.

Profit share indicators

5. A measure of relative profit shares in the tradable-intensive sector of the economy is given by the ratio of wage costs per employee to value added (in current prices) per person in manufacturing. As opposed to the ULC-based REER, this indicator takes into account variations across countries in the price of tradable output (Lipschitz and McDonanld, 1991). However, this measures has some drawbacks. First, relative profit shares in manufacturing are not a good guide to differences in the rate of return on capital if there are significant differences in production technology. Comparison of profit shares between countries at roughly similar stages of development should be more meaningful, although different product mixes can distort level comparisons. Second, the aggregate indicators could hide large differences in profit shares within manufacturing industry.

6. Macro model-based and/or econometric estimates of equilibrium exchange rates. These techniques attempt to estimate time-varying equilibrium exchange rates as a function of economic fundamentals. The results from their application to transition countries need to be interpreted with particular caution due to structural changes in the relationships and the limited availability of long data series.

The Theoretical Framework and the Empirical Model

4. The model used follows that developed by Alberola and et al. (2002) and is based on the decomposition of the exchange rate into two different relative prices, the price of domestic relative to foreign tradable goods, and the relative prices of nontradable goods relative to tradable goods within each country. The first component captures the competitiveness of the economy and determines the evolution of the net foreign assets position, and it is therefore associated with the external equilibrium of the economy. The second component incorporates the concept of productivity differentials as in the Balassa-Samuelson hypothesis, and since these prices determine the allocation of resources within the economy, it is associated with the internal equilibrium of the economy. The long-run solution of the model represents an equilibrium value for the real exchange rate consistent with the internal and the external equilibria of the economy.

5. Assuming that there are two countries in the world, each producing a tradable good (T) and a nontradable good (N), the REER (q) in logarithm terms can be defined as

where p and p^* are the domestic and the foreign consumer price indices (CPI), respectively, and s is the nominal exchange rate. For each country, the CPI, which is formed by prices of domestic and foreign tradable goods and nontradable goods, can be expressed as follows

where the as determine the share of each good in the consumer price index. Substituting these expression in (1), we obtain

where the weights of nontradable goods for the two countries are assumed to be the same, and the lack of perfect substitution between tradable goods between different countries is also considered. The latter expression indicates that the exchange rate is determined by two different components: the evolution of relative prices of domestic to foreign tradable goods, $q_x=(p_T+s-p_T^{*})$, which reflects the external dimension of the economy; and the behavior of nontradable goods relative to tradable goods across countries, $q_1=[(p_N-p_T)-(p_N^{*}-p_T^{*})]$, which relates the internal dimension of the economy. Thus, the equilibrium exchange rate ($\overline{q}$) implies both external and internal equilibrium.

6. The external equilibrium. The external balance clears the tradable goods market, and is characterized by the achievement of a desired stock of net foreign assets. The evolution of the current account balance, which determines adjustments to the equilibrium, leads to an accumulation of net foreign assets. The current account balance (ca) is defined as the trade balance (x) plus the net income received or paid by residents (r^*) on foreign asset holdings (nfa):

ca=x+r^*nfa expressed in real terms. The trade balance depends on the evolution of the external real exchange rate,¹⁴ namely x=-γq_x, and the current account adjusts to the difference between the current and the desired level of net foreign assets (Mussa (1984)), so that a current account surplus would reflect a net foreign asset position below the desired level

In the long run, and the equilibrium external exchange rate can be defined as follows

where the bars over the variables indicate long-run equilibrium values.

7. The internal equilibrium. The evolution of the internal real exchange rate is determined by the different behavior of sectoral relative prices between countries, which in turn are related to the evolution of sector productivity. Starting from the productivity

hypothesis, it can be shown that ${\overline{p}}_N-{\overline{p}}_T=\mu +(pro{d}_T-pro{d}_N)$

where the prod’s are the average sectoral productivities. Neglecting constant terms, it follows that the equilibrium internal exchange rate can be expressed as follows

8. Putting together the external and internal equilibria concepts produces the equation for the equilibrium REER:

where v is speed of adjustment of net foreign assets to changes in relative prices, (k-k^*) is the difference between measures of relative sector productivity at home and abroad ($(\text{where }k=pro{d}_T-pro{d}_N\text{and }{k}^{*}=pro{d}_T^{*}-pro{d}_N^{*}),\text{and}$ (z-z^*) = demand shocks

9. The empirical model. The theoretical model has identified two main determinants of the real exchange rate (q) in the long-run: the stock of net foreign assets (nfa) and the relative sectoral productivities between countries (prod) and could be rewritten in the following form by factoring nfa:

10. In this form the equilibrium real effective exchange rate is a function of three variables, nfa, the difference between measures of relative sector productivity at home and abroad, and demand shocks. Abstracting from demand shocks we obtain our empirical model:

11. Since the main objective is to compute the equilibrium exchange rate as a function of its fundamentals, first the existence of a long-run relationship among the variables has to be established, and second the equilibrium levels of the determinants nfa and prod must be estimated. In order to determine the existence of a long-run relationship among variables (i.e. to test for cointegration), the Johansen procedure for cointegration is applied. To establish the equilibrium level of the REER, q_t is assumed to fluctuate around its long-term value, but it is not permanently at that value. Moreover, in order to derive the equilibrium exchange rate, nfa_t and n_t are allowed to deviate from their long-run values. From an empirical point of view, the three variables in the system are decomposed into transitory $[{\widehat{q}}_t,n\widehat{f}{a}_t,pr\widehat{o}{d}_t]$ and permanent components $[{\overline{q}}_t,n\overline{f}{a}_t,pr\overline{o}{d}_t]$, with the latter capturing the equilibrium of the system:

12. Bearing in mind that a unique decomposition between permanent and transitory components does not exist (see among other Maravall (1993) and Quah (1992)), the decomposition by Gonzalo and Granger (1995) is considered. The latter is based on the assumption that shocks to the transitory component (i.e., misalignments) do not affect the permanent component (i.e., the equilibrium).

13. Gonzalo and Granger (1995) derive a decomposition where the transitory component does not Granger-cause the permanent component in the long run and where the permanent component is a linear combination of contemporaneous observed variables. In other words, the first restriction implies that a change in the transitory component today will not affect the long-run values of the variables. The second restriction makes the permanent component observable and assumes that the contemporaneous observations contain all the necessary information to extract the permanent component. The decomposition is done using the identification implicit in the cointegration of the series. In particular, if cointegration exists amongst a number of variables, then the vector will have a common, or factor, decomposition (Stock and Watson (1988)). Gonzalo and Granger demonstrate that the common factor can be estimated if it is assumed to be a linear combination of the series under analysis and if it is further assumed that the residuals from this model do not have a permanent effect on the original series. The former assumption makes the common factor observable, while the second permits identification.

14. Analytically, consider a 3×1 vector x_t=[q_t, nfa_t, prod_t]^’, which under the null hypothesis of one cointegration vector admits the following representation:

where e_t is a vector white noise process with zero mean and variance Σ and Π is a 3×3 matrix, whose rank will determine the number of cointegration vectors. If cointegration exists, ∏ is not full rank (r<3, with r=1 in our case) and can be written as the product of two rectangular matrices, ∏= αβ^’, where β is the matrix whose columns are the linearly independent cointegrating vectors and α is the factor-loading matrix, indicating the speed with which the system responds to last period’s deviation from the equilibrium level of the exchange rate. Next, one can always define the orthogonal complements α_⊥ and β_⊥ as the eigenvectors associated with the unit eigenvalues of the matrices (I-α(α^’α)^-1 α^’) and (I-β(β^’β)^-1β^’), respectively. The matrix α_⊥ is formed by the vectors defining the space of the common stochastic trends, and therefore should be informative about the key “driving” variable(s) in each of the systems, while β_⊥ gives the loadings associated with, i.e., the series which are driven by the common trends. Notice that α^’⊥α=0 and β^’⊥β=0. If the vector x is of reduced rank, r, Gonzalo and Granger have demonstrated that the elements of x can be explained in terms of a smaller number of (3- r) of I(1) variables called common factors, f_t, plus some I(0) components, the transitory elements, $\widehat{{\displaystyle x_t}}$:

15. The identification of the common factors may be achieved in the following way. If it is assumed that the common factors are linear combinations of the variables x_t:

and if A¹f_t and ${\widehat{x}}_t$ form a permanent-transitory decomposition of x_t, then from the representation in (1), the only linear combination of x_t such that ${\widehat{x}}_t$ has no long-run impact on x_t is:

16. This identification of the common factors allows to obtain the following permanenttransitory decomposition of x_t

where the permanent and the transitory components are captured by the terms ${\beta }_{\perp }({\alpha }_{\perp }^{\prime }{\beta }_{\perp }{)}^{-1}{\alpha }_{\perp }{x}_t$ and $\alpha ({\beta }^{\prime }\alpha {)}^{-1}{\beta }^{\prime }{x}_t$, respectively. Gonzalo and Granger (1995) show that the transitory components defined in this way will not have any effect on the long-run values of the variables captured by the permanent components. The identification of the permanent component with the equilibrium implies that

and

from where the estimation of the equilibrium exchange rate and its deviation directly follow.

The Data

17. The time period under consideration is 1995Q1-2003Q3 and data are quarterly (seasonally adjusted). The three following variables have been used in the analysis:

Real effective exchange rate (qt): CPI-based real effective exchange rate of the forint relative to a group of trading partners that represents the vast majority of Hungarian trade. The group comprises Austria, Belgium, Denmark, France, Germany, Italy, The Netherlands, Poland, Spain, and The United Kingdom.¹⁵ The variable is expressed in logarithms.

Net foreign assets (nfa_t) position is calculated by adding up the current account balances. The initial stock of net foreign assets is 1997Q1, as provided by the international investment position published by the MNB. The net foreign assets position is normalized by the GDP.

Relative sectoral productivities (tradable to nontradable goods) (prod_t) are defined as the ratio of the labor productivity index of total industry without construction relative to the productivity index for the rest of the economy relative to the corresponding weighted average of partner country ratios, using the same weights as the ones applied to qt.¹⁶ The data source is Eurostat. The variable is expressed in logarithms.

Econometric results

18. The econometrics results are illustrated in Figure 10. The top panel reports the historic series of the real effective exchange rate and its equilibrium. The bottom panel displays the deviations from the equilibrium exchange rate along with the computed 95 percent standard error bands.¹⁷

19. On the basis of the cointegration results (Table), there is evidence of one significant cointegration vector for the system regarding the real effective exchange rate, the net foreign assets position and the relative productivity differentials. It must be noticed that the coefficient of the relationship are positive as expected.

Table.

Hungary. Cointegration Analysis Results

Table.

Hungary. Cointegration Analysis Results

Ho: r<=	Eigenvalues	Trace	λ -max	Critical Value 10%
				Trace	λ -max
2	0.05	1.73	1.73	6.50	6.50
1	0.20	9.17	7.44	15.66	12.91
0	0.45	28.94	19.77	28.71	18.90
Cointegration Relationship:		qt= 0.17 nfat+1.1 prodt
Loading vector:	-0.05	0.42	-0.19
Half-life estimate	13.5
Residual analysis
Stationary test (c.v. 5.99)		36.07	10.29	31.72
Exclusion test (c.v. 3.84)		9.85	2.58	9.67
Homogeneity test (c.v. 3.84)			6.51

View Table

Table.

Hungary. Cointegration Analysis Results

Ho: r<=	Eigenvalues	Trace	λ -max	Critical Value 10%
				Trace	λ -max
2	0.05	1.73	1.73	6.50	6.50
1	0.20	9.17	7.44	15.66	12.91
0	0.45	28.94	19.77	28.71	18.90
Cointegration Relationship:		qt= 0.17 nfat+1.1 prodt
Loading vector:	-0.05	0.42	-0.19
Half-life estimate	13.5
Residual analysis
Stationary test (c.v. 5.99)		36.07	10.29	31.72
Exclusion test (c.v. 3.84)		9.85	2.58	9.67
Homogeneity test (c.v. 3.84)			6.51

20. The adjustment (or loading vector) associated to the cointegration vector is also reported in Table 1. The negative α coefficient in the exchange rate equation indicates that the exchange rate moves to close the gap of a disequilibrium by approximately 50 percent every approximately 14 quarters, or that most of the adjustment to a shock to the real exchange rate will be offset after almost seven years.