by Michael Debabrata Patra, Harendra Behera, Dhirendra Gajbhiye, Sujata Kundu and Rajas Saroy^{^}

A comprehensive examination of India’s equilibrium exchange rate through various approaches, namely the BEER, PEER and FEER, highlights the role of relative productivity differentials, net terms of trade, net foreign assets position and the fiscal balance in determining the Indian rupee’s equilibrium value. The suite of models offers policymakers a guiding framework to assess exchange rate movements while being cognisant of model limitations and country-specific circumstances.

Introduction

What is the appropriate level of the nominal exchange rate is a central policy question, irrespective of the type of exchange rate regime. It can be argued that it is the actual market rate as long as the foreign market is continuously clearing. Yet, policymakers are acutely sensitive to the fact that a variety of factors impinge on market behaviour to often produce idiosyncratic outcomes. Besides the high noise-to-signal ratios embedded in the market’s pricing in of news in real time, other factors that can generate destabilising movements are real shocks such as commodity price fluctuations, shifts in capital flows, and nominal shocks such as changes in monetary policy (Krugman, 1990). As a result, the foreign exchange market may initially overreact, and the dissipation of this overreaction can take long – the seminal overshooting hypothesis (Dornbusch, 1976). Accordingly, if policymakers have some sense of “equilibrium”, they can facilitate adjustment by allowing or inducing nominal rates to move in that direction since getting nominal rates wrong can be costly in terms of real economy effects like loss of export competitiveness, misallocation of resources or even asset price fluctuations, and surges, sudden stops and withdrawals of capital.

The equilibrium exchange rate is a concept that has generated a proliferation of theoretical and empirical research. It has its roots in seminal work that defines it as the exchange rate that is consistent with the simultaneous achievement of internal and external balance (Artus, 1977; Williamson, 1985). Internal balance is that level of economic activity that keeps inflation low and stable or at target. External balance is related to a sustainable¹ level of the current account balance that reflects a desired level of saving and investment. Both involve normative choices and hence methodological and measurement issues emerge. For the opportunistic policymaker, therefore, the equilibrium exchange rate is an empirical issue and it has to be estimated under heroic assumptions about these underlying fundamentals.

Surveys of the literature reveal a number of approaches to modelling the equilibrium exchange rate (Driver and Westaway, 2004; IMF 2007; Bussière et al. (2010). In view of the absence of any consensus on the correct approach to estimating equilibrium exchange rate, the pragmatic approach has been to estimate a suite of available models that take into account a broad range of indicators and other analytical tools to make a forthright assessment of the exchange rate level (IMF, 2005).

In this article, we adopt the pragmatic approach and attempt to empirically estimate equilibrium exchange rate models for India as guideposts for assessing the appropriate levels of the exchange rate of the Indian rupee (INR) that are consistent with the attainment of internal and external balance². In this category are the fundamental equilibrium exchange rate (FEER) model (Williamson, 1994) and the desired equilibrium exchange rate (DEER) model (Bayoumi, et al, 1994). We also estimate equilibrium exchange rate models by applying to Indian data an exogenous set of factors that are identified that capture the policy preference for the representation of internal and external balance. A reduced form is then constructed that links the exchange rate to these fundamental factors (Edwards, 1994). Thus, there is no need to determine what the sustainable level of the current account balance should be as it becomes endogenous to the system (Feyzioglu, 1997). In this class of models belong the behavioural equilibrium exchange rate (BEER) model (MacDonald and Clark, 1998), the permanent equilibrium exchange rate (PEER) model (Maeso-Fernandes, et al, 2001) and the natural real equilibrium exchange rate (NATREX) model (Allen, 1995). Underlying this approach is the view that each model attempts to respond to one particular policy question and all of them taken together provide a range with which to assess the equilibrium exchange rate for India.

In this article, we begin this quest by estimating purchasing power parity (PPP) as the most basic principle underlying equilibrium exchange rates in terms of a common basket of goods and services valued in the currency of each country; the fundamental equilibrium exchange rate (FEER), which embodies consistency with macroeconomic balances; the behavioural equilibrium exchange rate (BEER), which considers long-term macro-fundamentals and short-term cyclical influences; and the permanent equilibrium exchange rate (PEER) which considers long run fundamentals only and is an extension of the BEER.

In the next section, we describe the underlying factors that have a bearing on the behaviour of the exchange rate of the Indian rupee (INR) in order to draw out the rationale for the selection of variables. Section III lays out the distinctive features for each of the models and their shortcomings. Section IV presents the results and inferences therefrom. Section V concludes the article with some policy perspectives.

II. Stylised Facts

India’s exchange rate has evolved across several regimes spanning over 130 years. These regimes, i.e., formal frameworks with objectives and instruments mapped to them cover the gold exchange standard (1893-1946), the Bretton Woods par value system (1947-1971), the pegged basket-of-currencies regime (1975-1990), a transitional dual exchange rate regime (1991-1992) and finally a market-driven exchange rate system from March 1993.

Since the early 2000s, India’s 40-currency trade-weighted real effective exchange rate (REER) has appreciated on average by 1 per cent on an annual basis, while the nominal effective exchange rate (NEER) has depreciated by around 2 per cent per year, the wedge constituting inflation differentials between India and its trading partners. Since the REER is calculated with a broad basket of currencies and adjusted for price levels, it tends to show a steadier trend than bilateral nominal exchange rates. Both real and nominal shocks impinge on the evolution of the REER, with its long-term trends adjusted for cyclical forces reflecting deep, structural changes within the economy.

A shift in the REER’s trend can occur due to technological changes, shifts in the composition of trade, productivity dynamics, net foreign asset positions and long-term interest rate differentials, terms of trade changes and the current account balance to GDP ratio. In India, rising productivity in the tradable goods sector has contributed to a sustained trend of REER appreciation, consistent with the Balassa-Samuelson effect³ (Chart 1).

In the short run, the REER can be affected by commodity price shocks – for instance, prices of crude oil in the case of India – imparting terms of trade changes. In the Indian experience, an improvement in net terms of trade (ToT) is generally found to be positively associated with REER appreciation with a lag of one quarter (Chart 2).

Higher current account deficits entail depreciation of the INR, while a rise in India’s net foreign assets appreciates the REER (Chart 3).⁴

Real interest rate differentials are a crucial determinant of the REER through the uncovered interest rate parity (UIP) condition – when India’s long-term interest rate exceeds those of its trading partners, it attracts foreign capital, driving up demand for the local currency and pushing up the REER (Chart 4a). This relationship serves as a bridge between short-term and medium-term exchange rate dynamics. Actual experience negates the theoretical proposition that interest rate differentials should converge across countries in the long run.

Trade openness leads to an increase in the overall volume of trade. If the current account deteriorates as a result, the REER typically depreciates to restore balance. Conversely, if the current account improves, the REER appreciates in response (Chart 4b).

III. Model Descriptions

The PPP framework (Rogoff, 1996; De Broeck and Sløk, 2001) consists of a cross-sectional regression of relative price levels on the ratio of PPP-adjusted per capita GDPs of trading partners – a proxy for relative productivity differentials. The slope of the regression line indicates the expected real exchange rate appreciation associated with a 1 per cent increase in GDP per capita relative to that of the United States (Chart 5).

The regression results obtained are as follows:

where P represents the domestic price level, P^US denotes the foreign price level proxied by US prices, and GDP and GDP^US are the GDP per capita on PPP basis of various countries and the US, respectively⁵.

In this simplistic framework, the predicted values from the regression serve as a reference exchange rate that accounts for the Balassa-Samuelson effect. Countries positioned above the regression line such as India have higher price levels relative to their standards of living, indicating that exchange rates are higher than equilibrium levels. Conversely, countries that are below the line exhibit relatively lower price levels, implying an undervalued exchange rate.

The BEER approach is an extension of the real UIP and can be identified through historical data (Macdonald, 1997; 1999). Using cointegration methods, BEER considers short-term deviations in the real exchange rate as misalignments due to speculative pressures, temporary shocks or policy interventions. This approach aligns the equilibrium exchange rate with current economic fundamentals, offering flexibility. BEER’s reliability depends, however, on stable data and variables approaching steady state, making it more suitable for mature economies.

The PEER represents the exchange rate that would prevail when all economic variables are at their steady state values, unaffected by temporary shocks or cyclical fluctuations. The PEER approach aims to isolate the underlying stable component of the real exchange rate by filtering out short-term factors such as speculative activity and policy-driven influences (Gonzalo and Granger, 1995; Clark and MacDonald, 2000). The PEER can be computed by replacing actual levels of fundamentals with their estimated trend levels in the BEER model (Égert, 2003). This extension of the BEER model provides an estimate of the equilibrium REER closer to the FEER.

The FEER approach seeks to estimate an exchange rate level that would bring the economy’s current account to a sustainable balance corresponding to the full employment or equilibrium level of output. It is normative as it requires determining the exchange rate consistent with a targeted balance of payments outcome over the medium term (often reflecting structural adjustments in the current account). This approach yields an equilibrium REER that is consistent with the economy’s macroeconomic balance (Williamson, 1994), as interpreted earlier. Estimating the equilibrium REER by this approach requires assumptions about the sustainable current account balance, making it less data-driven and more theoretical than the BEER. While BEER would provide the estimated equilibrium REER both in the short run and long run, PEER and FEER would provide the equilibrium REER that should prevail in the medium to long run.

PPP, FEER and BEER can be grouped together as they focus on observable economic fundamentals, which is of practical utility for short- to medium-term exchange rate assessments. These models rely on straightforward assumptions such as price levels (PPP), balance of payments sustainability (FEER), and the UPI condition (BEER). Compared to models like DEER, PEER and NATREX, which emphasise longer-term equilibrium or policy-driven targets, PPP, FEER and BEER are easier to operationalise. This grouping offers a cohesive framework for understanding exchange rate dynamics, complementing the strategic, long-term perspectives of alternative models.

IV. Empirical Methodology and Results

The following equation is used to estimate the equilibrium REER through the BEER approach:

While the NFA to GDP ratio (NFA_GDP) is expressed in per cent, relative GDP per capita (RELGDPPC)⁶ and net TOT (TOT)⁷ are transformed into their logarithmic forms to stabilise variances (Annex Table A1). All variables are de-seasonalised using the standard X-13 ARIMA procedure.

Based on equation (1), the equilibrium REER can be estimated in (2), with the hat symbol signifying the fitted series:

The fundamental determinants of BEER are then decomposed into permanent and transitory components by using the HP filter technique (Hodrick and Prescott, 1997) to obtain the PEER. The superscript p indicates permanent or long-term trends of the series.

For the FEER approach, a target current account balance/GDP ratio is assumed (CAB). This target should be consistent with a level that India can sustain over the long-term, avoiding excessive external imbalances or excessive foreign debt accumulation. CAB is expressed as a function of REER and key fundamentals.

where β captures the sensitivity of the current account to changes in the REER (in log form), γ_i are coefficients representing the relationship between the current account and other economic fundamentals (productivity differentials; terms of trade; net foreign assets; fiscal balance (FISC_t) and ϵ_t is an error term.

In order to estimate the equilibrium REER under the FEER approach, the REER should achieve a current account level equal to the target (CAB*).

This yields the following equilibrium condition:

A suite of cointegrating regressions are used on quarterly data from 2004-05:Q1 to 2023-24:Q4 (Annex table A1 provides details of the variables/indicators that have been used for the empirical analysis). In order to check the time series properties of the variables, standard unit root tests are conducted. While the REER is found to be integrated of order 1, the net terms of trade is stationary (Annex Table A2). Therefore, an autoregressive distributed lag model (ARDL) is used to estimate the equilibrium REER under the BEER approach. Fully modified ordinary least squares (FMOLS) and dynamic ordinary least squares (DOLS) methodologies are also used in order to check the robustness of the results.

The regression coefficients corresponding to the fundamental determinants of REER turn out to be statistically significant with the expected signs (Table 1). The results indicate that in the long run, productivity proxied by relative GDP per capita is a key determining factor of the equilibrium REER, followed by net terms of trade and net foreign assets to GDP ratio. The bounds test confirms the existence of a long-term relationship between the variables. The long-run coefficients obtained can hence be used to estimate the equilibrium REER.

In the short run, however, own lags of REER turn out to be statistically significant.¹⁰ The error correction coefficient (ECM) is also found to be statistically significant with a magnitude of (-)0.4. The model satisfies post-estimation diagnostics and stability tests. The long-run coefficients obtained from the ARDL model are in line with the results obtained from the alternate FMOLS and DOLS models (Table 2). The fitted values of REER obtained from the model provide the short-run equilibrium REER based on the BEER approach, while the estimated long-run coefficients are used to derive the long-run equilibrium REER under this approach. Further, the long run coefficients from the BEER model, combined with the trends obtained from the underlying variables, are used to derive the equilibrium REER under the PEER approach.

In order to compute the equilibrium REER using the FEER approach, equation (4) is estimated by using an ARDL model. The results indicate that the current account deficit reduces with an improvement in net terms of trade, depreciation of the REER and reduction in the fiscal deficit. A rise in productivity differentials, however, could increase the current account deficit as productivity-led rise in income may raise the demand for imports (Table 3). Based on the estimated model parameters, we calculate the FEER as specified in equation (5).

As expected, the short-run BEER moves closely with the actual REER. The PEER is less volatile than the BEER. The FEER is found to be the most volatile estimate of the equilibrium REER. Both BEER and PEER approaches suggest that the REER is marginally below the level consistent with long-term fundamentals. On the other hand, the difference between the actual REER and the FEER is higher (Chart 6).

Overall, the results indicate that in 2023-24, India’s REER was somewhat below the level consistent with its long run fundamentals (Table 4). This is in contrast to the assessment in terms of short run approaches, including under the PPP approach – that is adjusted for Balassa-Samuelson effects – which suggests that the REER was above its equilibrium level during the same period, largely reflecting improvement in net terms of trade. This highlights the need to qualify short-term assessments of the level of the exchange rate with an evaluation that is consistent with long run fundamentals.

V. Concluding Remarks

The findings of this study underscore the relevance of a range of estimates of the equilibrium exchange rate, which is not observable. The alternative approaches estimated here are preferable to static indicators such as the REER or others that belong in the genre of the simple PPP framework. By allowing the equilibrium exchange rate to respond to changes in the underlying fundamentals, they allow policy makers to assess the level of the exchange rate in terms of misalignment or otherwise with respect to specific policy objectives. It is in this spirit that the sequel to this article will attempt to estimate the CHEER, DEER, and NATREX to complete a full suite of approaches for evaluating the equilibrium exchange rate of the INR.

While using these estimates for policy purposes, it is useful to be cognisant of their limitations. The FEER does not specify how the exchange rate will move to equilibrium or how to deal with hysteresis that typically effects exchange rate behaviour. The BEER assumes that stable long-run relationships can be estimated from historical data, which may be distorted by structural changes.

Accordingly, the pragmatic approach is to use multiple methods and to interpret each carefully by taking into account both underlying assumptions and their applicability to country-specific circumstances.

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Annex

^{^} The authors are from the Reserve Bank of India. The views expressed in this article are those of the authors and do not represent the views of the Reserve Bank of India.

¹ Consistent with a country’s intertemporal budget constraint.

² A few studies available in the Indian context have focused mainly on PPP or BEER approach (Annex Table A3).

³ The Balassa-Samuelson effect explains how higher productivity growth in the tradable sector, relative to the non-tradable sector, leads to rising wages across both sectors, increasing the relative price of non-tradables. This results in an appreciation of the real exchange rate in economies with faster-growing tradable sectors (Balassa,1964; Samuelson, 1964).

⁴ The other alternate variables that were considered in our analysis are net capital flows to GDP ratio and current account balance (CAB) to GDP ratio.

⁵ Both coefficients are statistically significant at the 1 per cent level; R2=0.16; Number of observations (countries) = 161.

⁶ Weighted sum of per capita GDP (constant prices) of 22 major trading partners, with weights same as the trade weights used in calculating the 40-country REER published by the RBI.

⁷ Weighted by net exports.

⁸ Null hypothesis: No serial correlation at up to 2 lags.

⁹ Null hypothesis: Homoskedasticity.

¹⁰ For brevity, results of the short-term representation of the model are not presented.