Properties of the fundamental equilibrium exchange rate in the Treasury model.

Church, Keith B.

1. Introduction On 1 January 1999 the inhabitants of eleven member states of the European Union commenced the buying and selling of goods and services using the European single currency. The UK has opted not to participate for the time being, but retains the option to do so at a later date. One feature of the single currency is the joining together of currencies at the nominal parities that previously prevailed in the Exchange Rate Mechanism (ERM). However, this fixing of nominal rates does not mean that exchange rates between members ceased to be important from the start of 1999, because the existence of different inflation rates across countries ensures that real exchange rates between member states still vary.

Any country experiencing higher inflation than its fellow participants, perhaps following a shock felt only in the domestic market, finds its goods and services becoming less attractive with the appreciation of the real exchange rate. Outside of a currency union this loss of competitiveness might be eliminated by a fall in the nominal exchange rate, a reduction in domestic inflation or a combination of both. For the member of the single currency the first option is ruled out and so the domestic inflation rate must fall below levels elsewhere until the loss of competitiveness is reversed Given the rigidity in European labour markets, achieving adjustment through lower price rises is likely to be costly in terms of jobs and output in the medium term.

If it is decided that the costs of membership are outweighed by the benefits and the UK elects to join the single currency then the question arises of the appropriate entry rate for sterling. This choice should reflect the fact that any adjustment of the real exchange rate to an appropriate level will be harder to achieve once the nominal exchange rate is fixed. This article uses the model of Her Majesty's Treasury (HMT) to calculate the value of the real exchange rate for the UK that is compatible with medium-term macroeconomic equilibrium. This is known as the fundamental equilibrium exchange rate (FEER) and is the rate consistent with an economy growing at its 'natural' rate with unemployment at the NAIRU, and where any deviation of the current account from balance is sustainable through inflows or outflows of capital over the medium term. The long-run relationships which form the supply side and trading sectors of the HMT model are solved to give this equilibrium rate.

The consequences of entering a fixed exchange rate regime at the wrong nominal rate were demonstrated in September 1992 when sterling left the ERM. Several studies were published at that time, including Wren-Lewis et al. (1991) and Church (1992), showing that the actual real exchange rate was well above the FEER. Convergence while sterling was fixed around a band centred on DM2.95 might have been achieved through a prolonged period where UK inflation was lower than that in the rest of Europe but one interpretation of the events of September 1992 is that the markets saw this as unrealistic and so forced the convergence to occur through a large depreciation in the nominal exchange rate instead.

If the single currency is a success for the eleven countries participating from the start then it seems likely that the current government would want sterling to join. If the model of Her Majesty's Treasury (HMT) in some sense represents the government's view of how the UK economy works then it should give some insight into the decision of the appropriate level of the exchange rate to enter at. This article uses the HMT model to estimate the FEER so that the extent of any real exchange rate disequilibrium can be evaluated.

The article proceeds as follows. In Section 2 the theoretical framework underlying the FEER is outlined. The extent to which the HMT model conforms to this framework is examined in Section 3, while in Section 4 the core results together with the outcome of various sensitivity exercises are presented. Section 5 contains concluding comments.

2. The FEER framework

The fundamental equilibrium exchange rate (FEER) as developed by Williamson (1983) is that value of the real exchange rate which is consistent with medium-term macroeconomic equilibrium and is achieved when domestic activity is at its 'normal' rate and the trading position with the rest of the world is sustainable. The FEER calculations presented here give estimates of the value of the real exchange rate that we might expect the economy to converge towards, but we do not suggest how the convergence to this equilibrium might take place. Indeed the FEER itself is dependent on the path the actual real exchange rate takes to reach equilibrium, a point noted by Wren-Lewis (1992). When the real exchange rate moves very slowly to the FEER, large differences in current account imbalance persist which flow onto asset stocks. This is not the case when adjustment is rapid. The size of asset stocks determines the magnitude of debt interest payments which are themselves a part of the FEER calculation. Hence if the UK takes a long time to eliminate any deficit exceeding 'normal' capital inflows then a lower than otherwise level of the FEER is required to counter the higher debt interest payments heading abroad.

Looking at the components of overall equilibrium we first consider 'internal balance'. The domestic economy is in equilibrium when inflation is stable and the prevailing rate of unemployment is the equilibrium rate. There are a variety of methods we might use to arrive at an estimate for the equilibrium path for output in the economy. The benefit of using a large-scale macroeconometric model is that it provides consistent estimates of all the relationships that form the supply side of the economy and from these relationships it is possible to derive the steady-state growth path for output. This equilibrium path is an important determinant of the FEER because changes in domestic activity feed directly into the import equations and hence change the level of the current account. However, there are differing views on whether the real exchange rate itself influences the equilibrium level of activity in the long run. Earlier vintages of several UK models described in Church et al. (1993) have this property because of the way the real exchange rate influences wage bargaining, while in the UK models described in Church et al. (1997) this feature is confined to the HMT model. Where this effect is present there is a positive relationship between the level of the real exchange rate and the equilibrium level of activity. This is illustrated by considering the impact of a devaluation and the associated increase in real import prices. This increase puts downward pressure on real wage rates. On one side of the wage bargain, workers or their representatives resist this reduction while on the other side firms wish to limit the fall in their profitability caused by this resistance. The equilibrium level of activity changes to balance the objectives of both sides. In this case equilibrium employment and output fall to ensure inflation stability.

Wren-Lewis and Driver (1998) outline two further mechanisms through which the real exchange rate might influence internal balance. The first is closely related to the bargaining issue discussed above. Real labour costs are linked to the price of domestic output while real incomes are measured in terms of consumer prices which have an import price component. Therefore an appreciation in the real exchange rate increases real incomes and hence (assuming a positively-sloped labour supply curve) the supply of labour and trend output. This effect is present in the manufacturing sector of the HMT model. The second channel is through the cost of capital. Where capital goods are imported an appreciation in the real exchange rate reduces the relative price of investment goods and hence the cost of capital. This increases investment and hence the productive capacity of the country. This effect does not appear in the FEER calculations presented in Section 4.

The second part of overall equilibrium is 'external balance'. Because the FEER is a medium-term concept it is not necessary for the current account balance to be zero in equilibrium. The UK economy has in the recent past usually run a current account deficit and there are various reasons why this might be sustainable over the medium term. Some structural capital inflows reflect long-term investment in the UK and cannot be quickly reversed. This type of substantial structural capital flows persisting into the medium term is typified by the flow of investment into the UK by large car manufacturers, rather than 'hot' money which seeks a short-term home based on fluctuating overnight interest rates. The size of these effects are difficult to quantify and deciding the proportion of the current account disequilibrium that can be justified as 'structural' is perhaps the most fragile part of the FEER calculation.

To help decide what the 'normal' current account balance might be, Williamson (1991) reproduces the standard textbook identity, namely

(X - M) = (S - I)- (G - T)

or, in words,

current account = net savings of private sector - public sector deficit.

Therefore the equilibrium current account balance depends on the nature of the asset equilibrium of the private sector and also on the public sector deficit position. Implicit in the calculation of internal balance outlined above is the existence of an asset flow equilibrium for the private sector, but the presence of equilibrium in the goods market does not preclude the possibility that asset stocks are changing because invariably private sector investment differs from saving and the government fiscal stance is not neutral. If, in the medium term, asset stocks are changing and a country is in a position where it needs to import or export capital then the sustainable current account need not be in balance. Evaluating the normal private and government sector position automatically informs us of the equilibrium current account position.

Any change in the attitude of the government to fiscal policy in light of the Maastricht conditions has important implications for the asset flow equilibrium. Barrell and Sefton (1998) look at the effects on the real exchange rate of the fiscal policy required to deliver the conditions on debt and deficits that the European countries agreed as part of monetary union. They calibrate a modified Mundell-Fleming model reflecting the properties of the National Institute of Economic and Social Research (NIESR) large-scale world model and show the consequences of an increase in the domestic debt target. Private sector assets return to base in the long run as there is little Ricardian equivalence in the model and virtually all the new debt is held overseas. The real exchange rate must depreciate to ensure that a trade surplus is generated to match exactly the increased outflow of debt interest payments going abroad. The policy implication from this is that the equilibrium real exchange rate changes with the level of debt target. If the UK is to hit a debt target of 40 per cent of GDP as outlined by the Chancellor in his 1998 Mansion House speech, then this implies a higher level of the FEER than that associated with a looser fiscal policy. The belief expressed by Barrell and Sefton (1998) that the public sector structural deficit for the UK is falling is matched by a target current account that shows a trend from large deficit to small surplus over the 1990s.

The current account target used by Wren-Lewis and Driver (1998) is provided by an appendix to their paper by Williamson and Madar. Their approach is to examine the actual data and then to adjust in response to various factors. The current account target is determined by OECD projections of savings and investment rates, and amongst the various factors considered are demographics, initial levels of debt stock, the impact of inflation bias, the global current account discrepancy and revaluation effects on asset stocks. They finally decide that the appropriate target level for the UK current account is a deficit equal to 0.2 per cent of GDP. Again, this is only a target in the sense that the equilibrium level is automatically given when the normal level of capital flows is calculated.

3. The HMT model

The version of the HMT model used in this exercise was released in September 1996 and its properties, along with those of four other models, are evaluated by Church et al. (1997). The data used are from the version of the model released a year later. This model has been chosen because it is an 'official' model and therefore is presumably an important part of the decision-making process on whether or not the UK should enter a monetary union and if so the exchange rate at which this might happen.

The HMT model contains a large degree of detail describing the UK economy. This is an advantage in situations where aggregation implies a loss of information. For example, export and import volumes are separated into four sectors with the relevant activity and competitiveness measures varying across these sectors. If the volumes in each sector evolve differently in response to diverse factors then aggregation leads to a misspecified model. Competitiveness is typically measured by the relationship

R = PPIO.RX/WP,

where R is a measure of the real exchange rate and PPIO, RX and WP are domestic producer output prices, the sterling effective exchange rate index and world prices in dollars respectively. In the HMT model there are actually eight different real exchange rate measures, obtained by defining world prices in this expression as in turn, manufacturing exports prices, consumer prices, unit labour costs, commodity prices, oil prices, agricultural prices in the EU, food prices and basic material prices. Clearly if all these measures behave in exactly the same way then it is possible to aggregate without loss of information. The extent to which this is the case is demonstrated by the plots in Chart I which shows the first three versions of R, these having most weight in the model. They all share the sudden fall in 1992 caused by the exit of sterling from the ERM but subsequent behaviour differs slightly. The key measure defined in terms of manufacturing export prices immediately appreciated sharply for a year before declining again while the other two measures did not. Each measure is driven higher from the middle of 1996 onwards, reflecting the strength of sterling during this period.

Internal balance The HMT model is alone among the current vintage of UK macroeconomic models deposited at the ESRC Macroeconomic Modelling Bureau in having an estimate of the NAIRU which depends on the real exchange rate. The real exchange rate is one component of the wedge between employers' real wage costs and workers' real consumption wages. Bean (1994) argues that the impact of any permanent change in this wedge and hence the equilibrium level of activity has an offsetting effect on the workers' permanent income and subsequently their reservation wage. In other words, real wage resistance does not persist in the long run. However Chan et al. (1995) argue that there is empirical support for this type of long-run effect, hence its appearance in the HMT model. The estimate of the natural rate is obtained from the long-run solution to the supply side of the model. A stylised version of the supply side of the HMT model which assumes capacity utilisation is at equilibrium and ignores constant terms in the equations is given below. All variables are in natural logs and all coefficients defined to be positive. The wage rate is given by

w = pgdp + [pr.sup.*] - [[Alpha].sub.2]u + [[Alpha].sub.3](prx - pgdp), (1)

where u is the log of the unemployment rate, [pr.sup.*] is trend productivity and pgdp is the GDP deflator and is assumed to be simply determined by unit labour costs

pgdp = (w-[pr.sup.*]), (2)

while retail prices excluding mortgage interest payments (prx) are given by

prx = [[Beta]sub.1] (w - [pr.sup.*]) + [[Beta].sub.2]ppio + (1 - [[Beta].sub.1] - [[Beta].sub.2]) pm (3)

where pm is import prices and ppio is producer prices whose equation is represented by

ppio = [[Theta].sub.1]pm + (1 - [[Theta].sub.1])(w - [pr.sup.*]). (4)

Combining equations (1)-(4) and rearranging gives an expression for the NAIRU, namely

[u.sup.*] = -[[Alpha].sub.3]/[[Alpha].sub.2] ([[Theta].sub.1](1 - [[Beta].sub.1])/(1 - [[Theta].sub.1]) + (1 - [[Beta].sub.1] - [[Beta].sub.2])(ppio - pm).

From this we can see that the NAIRU decreases as the equilibrium level of the real exchange rate (ppio-pm) increases. Given this knowledge of how the unemployment rate changes in response to the real exchange rate, the (exogenous) level of working population gives the change in the number employed and this is allocated between manufacturing and non-manufacturing proportionally given the size of the two sectors. The equilibrium level of output in the economy is then obtained by finding the values consistent with the employment equations in the model. This demonstrates how, although the real exchange rate directly influences output, the HMT model is also consistent with the standard result from the neoclassical growth model because the equilibrium level of output in the economy depends on the growth rate of the working population and the rate of labour-augmenting technical progress, the latter being represented by time trends in the labour demand functions. External balance

The HMT model disaggregates exports and imports into four categories: manufactures, non-manufactures, services and oil.

Export volumes depend on the appropriate measure of competitiveness for that sector and WT a measure of the level of world trade.

X = W[T.sup.[[Theta].sub.1] [R.sup.-[[Omega].sub.2].

Import volumes depend on domestic activity Y rather than world trade

M = [Y.sup.[[Omega].sub.1] [R.sup.[[Omega].sub.2].

The trade balance part of the current account is obtained by the identity

CB = PX.X - PM.M,

where PX and PM are the prices of export and import goods and are given by

PX = PPI[O[[Sigma].sub.1] P[M.sup.(1 - [[Sigma].sub.1]

and

PM = (WP/RX).

The volume and price equations over the four different sectors of the economy are reparameterised in terms of the eight different measures of competitiveness described earlier. For a complete description for the current account the model of trade outlined above is insufficient as we also need to incorporate interest, profit and dividend (IPD) flows, net government payments to the EU and personal sector net transfers. IPD flows depend on the level of overseas assets held by domestic residents and by the level of domestic assets held by those abroad. As the FEER is consistent with an asset accumulation equilibrium a fully specified macroeconomic model would give the values of these flows. However, in this partial equilibrium approach it is assumed that IPD flows are in equilibrium, and they are not modelled explicitly, although the fact that the movement of the actual real exchange rate to the FEER changes the value of assets denominated in foreign currency is recognised and this revaluation effect is present for IPD credits. EU payments and transfers are not modelled but are smoothed to eliminate erratic behaviour and to give some idea of equilibrium behaviour. The real exchange rate can now be used to target the current account balance to whatever are regarded as 'normal' capital flows.

4. Results

The initial results here assume that 0.2 per cent of GDP represents a 'normal' level of the current account to GDP ratio. The sensitivity of the results to this choice is examined in the final simulation. The eight different measures of competitiveness are linked together in a way that the movements in the key measure of the real exchange rate defined in terms of the world price of manufactures are fully reflected in each of the other definitions.

Chart 2 shows the actual and fundamental rate from the start of 1990 to the middle of 1997. A useful appraisal of the model is achieved by examining the outcomes from around the time that sterling departed from the ERM. The model suggests that sterling was 19.5 per cent overvalued in the second quarter of 1992. The large fall in sterling during the third quarter of that year ensured that the difference between actual and fundamental closed to 10 per cent immediately after the UK left the ERM. For some time afterwards a small overvaluation persisted but during 1995 the actual was below the fundamental rate. This period is characterised by a fall in the actual rate but also by an improvement in the FEER. This improvement can be traced through to the performance of the manufacturing exports equation which substantially overpredicts the actual volume of exports during this period. This overprediction is associated with a sustained fall in the actual real exchange rate. The result is an improved underlying current account and hence the FEER has to depreciate by less in order to hit the target deficit of 0.2 percentage points. By the second quarter of 1997 the overvaluation had risen again to 18 per cent.

The path of the FEER slopes gently upwards over the 1990s at a rate of about 0.5 per cent per annum. This trend component of the FEER arises from the fitting of time trends to that part of the export and import volume data that is not explained by the activity and competitiveness terms. These trend terms suggest a generally improving current account position mainly through a reduced tendency to import as time goes by.

The actual level of unemployment for most of the 1990s has been much higher than the natural rate. Chart 3 plots the prevailing NAIRU and the actual unemployment rate. In equilibrium, when the economy achieves internal balance the actual rate of unemployment is equal to the NAIRU. Clearly this implies that all the previously unemployed workers are now in employment and producing output. The structure of the model is such that a 1 per cent increase in employment is matched by a I per cent increase in output. The consequence is that in equilibrium the levels of output and domestic GDP are much higher than the actual values of the mid-1990s. This increase in equilibrium domestic activity sucks in imports worsening the current account. The real exchange rate must then depreciate to make UK exports more attractive so that the extra output can be sold abroad, bringing the current account back to target. This decrease in the equilibrium real exchange rate also puts downward pressure on the natural rate of activity in the economy.

The model is silent on the nature of the extra output generated in equilibrium. If the workers removed from unemployment were assumed to be employed in industries producing goods and services in areas where the UK has a comparative advantage over its competitors and there is high demand, then off-loading the extra output abroad to offset the increase in imports and generate the equilibrium current account position might be achieved with a fairly small reduction in the real exchange rate. If, as seems more realistic, the extra employment was in low productivity sectors, then the decrease in the real exchange rate required to export the extra output would be much higher. Despite the actual current account showing a surplus in 1996-7, the FEER still lies below the actual real exchange rate during this period. If domestic activity had actually been in equilibrium, the higher level of demand implies more imports. The improvement in the current account observed in 1996-7 reflects import volumes being below trend. The overall underlying position for the UK economy appears to be a current account deficit that exceeds 1 per cent of GDP.

A partial simulation on the model indicates that a 1 per cent increase in the equilibrium real exchange rate delivers a fall in the NAIRU of about 0.2 percentage points. This feature of the model relies on the assumption that the level of the real exchange rate affects the wage bargain. This is not a feature of most large-scale macroeconomic models and the sensitivity of this link can be judged by simply setting [[Alpha].sub.3] = 0 in the wage equation and then recalculating the intercept term in the relationship. Because of this adjustment the NAIRU estimate in this variant is not directly comparable with the previous case. As Chart 4 confirms, the real exchange rate no longer influences the NAIRU and the estimate of the natural rate is now a constant 6.8 per cent. This change increases the gap between equilibrium and actual real exchange rate over the early part of the 1990s. The major difference that this change to the model makes is that previously the depreciation in the FEER put downward pressure on the equilibrium level of domestic utilisation and hence the response of imports.

Without this link the FEER must fall slightly more to generate the required improvement in the current account as shown in Chart 5.

The calculation of the NAIRU in this model is heavily dependent on the econometric estimates of parameters in the wage equation, particularly the intercept term and the coefficient on the log of the unemployment rate. As a degree of uncertainty surrounds these econometric estimates and because there are several other methods of calculating the NAIRU which give conflicting answers, it is important to examine the sensitivity of the FEER estimate to changes in the 'natural' rate. Chart 6 shows the FEER paths for NAIRUs that are 1 percentage point either side of the baseline case. When the NAIRU is 1 percentage point lower as shown by the line FEER-, employment, output and imports are higher and the FEER must depreciate in order to generate the extra exports required to give current account equilibrium. The fall in the FEER itself is around 1.9 per cent, increasing the gap between the actual real exchange rate and FEER in the second quarter of 1992 to 22.0 per cent and in the second quarter of 1997 to 20.7 per cent. If the NAIRU is actually 1 percentage point higher than our central estimate, the FEER is shown by line FEER+, and the overvaluation in the second quarters of 1992 and 1997 is reduced to 17.1 per cent and 16.4 per cent respectively.

Arguably the most important piece of sensitivity analysis revolves around the choice of target for the current account, which is possibly the most fragile part of the FEER calculation. The target in the previous experiments was a deficit of 0.2 per cent of nominal GDP, but given that the UK economy has routinely, over a period