Methodological issues in the estimation of current account imbalances 1

2.1 The CA balance from an accounting perspective

According to the IMF’s Balance of Payments Manual 6 (BPM6) definition, the CA balance records the difference between the sum of exports and income receipts on domestically-owned factors of production (capital and labour) that are employed abroad and the sum of imports and income payments to foreign-owned factors of production employed at home. In formal terms:

C ⁢ A = X - M ⏟ Trade balance + 𝐵𝑃𝐼 + 𝐵𝑆𝐼(1)

Exports (X) and imports (M) refer to trade in both goods and services and their balance is commonly known as the trade balance. Income refers to both primary (BPI) and secondary income (BSI). The primary income balance accounts for income inflows and outflows of an economy’s residents vis-à-vis non-residents, decomposed into labour income (i.e. compensation of employees), investment income, in turn related to the income generated on international financial assets and liabilities, and other income (rents on natural resources abroad, taxes and subsidies on products and production, etc.). The secondary income balance captures international unreciprocated payments and receipts, for example transfers between governments and international organisations, such as emergency aid, technical assistance and migrants’ remittances.

The CA balance is equal to the difference between national saving and investment on the basis of national accounts (NA) identities. Gross national disposable income (GNDY) is the total income earned by the residents of an economy, including that which is generated abroad and is given by the sum of the gross domestic product (GDP) and net income from abroad:

𝐺𝑁𝐷𝑌 = 𝐺𝐷𝑃 + 𝐵𝑃𝐼 + 𝐵𝑆𝐼(2)

where GDP can be rewritten according to the expenditure approach, leading to the following equation:

𝐺𝑁𝐷𝑌 = C + G + I + X - M ⏟ 𝐺𝐷𝑃 + 𝐵𝑃𝐼 + 𝐵𝑆𝐼(3)

where C is household consumption, G is government consumption and I is gross fixed capital formation. By reshuffling its components, Eq. (3) can be rewritten as:

𝐺𝑁𝐷𝑌 - C - G ⏟ S := gross savings - I = X - M + 𝐵𝑃𝐼 + 𝐵𝑆𝐼 ⏟ C ⁢ A := Current account balance(4)

The CA balance can be hence represented as the excess of saving over investment:

C ⁢ A = S - I .(5)

Clearly and as mentioned in the introduction, a CA deficit (surplus) does not per se necessarily imply an imbalance, as it can make sense, for example, for an emerging (advanced) economy to borrow (to lend) vis-à-vis the rest of the world against future income.

Two main alternative approaches are currently used in surveillance to measure CA imbalances, often employed as cross-consistency checks, for example in the case of the IMF’s annual External Balance Assessment (EBA).

The first approach (“External Sustainability Approach”), put forward in [10], consists in estimating the CA balance that allows reaching or maintaining a target level for the Net International Investment Position (NIIP). As discussed in [4], the resulting CA benchmarks are commonly interpreted as prudential thresholds for external sustainability, that is as a lower limit that the CA needs to reach to stabilise an NIIP position that would otherwise be deteriorating or an upper limit if the NIIP is growing. A key assumption concerns the level at which the NIIP is to be stabilised, often viewed as its current level, a minimum requirement in case of large CA deficits and large stocks of net foreign liabilities, such that the country’s NIIP does not deteriorate any further.6 Moreover, these CA benchmarks rely on partial equilibrium equations representing NIIP dynamics, in which all other variables are assumed to be exogenous.

The second approach, inaugurated by [11], is based on the estimation of country-specific and time-varying CA norms. It implies the estimation of a reduced-form equation, which leads to the computation of a CA norm that is consistent with economic fundamentals, against which actual CA balances are appraised. This methodology aims at detecting past systematic empirical regularities between the CA and its medium-term determinants, and is hence not able nor set up to tackle causality, which only a structural approach would allow.7 In this article we will focus on these reduced-form models, loosely defined hereon as “CA models”.

In formal terms, for each country i at time t a simple CA model estimates the reduced-form relationship between the CA balance (in percentage of GDP; CA) and a set of “fundamentals” ( X F ) and non-fundamental variables, in turn including both cyclical factors ( X C ) and policy variables ( X P ):

C ⁢ A i , t = α + β ′ ⁢ X i , t F + ψ ′ ⁢ X i , t C + γ ′ ⁢ X i , t P + ϵ i , t(6)

where ϵ i , t is the error term.

Many studies, amongst which [12, 13, 14, 15], remove cyclical factors from the model by using non-overlapping averages of data over fixed (e.g. five or ten-year) time-spans. However, this procedure, as well as arbitrarily imposing a fixed duration of business cycles to all countries, significantly restricts the estimation sample, thereby reducing the information content of the data. More refined models (e.g. [3, 4]) are estimated on annual data and explicitly account for cyclical factors, as in Eq. (6), which we hence consider as the workhorse model.

In order to ensure multilateral consistency, since CA balances depend not only on domestic but also on foreign developments, and whenever is meaningful, explanatory variables are constructed relative to world averages (for example, GDP-weighted, as in [16, 3], or trade-weighted, as in [7, 13, 14]). This transformation also applies to policy variables, allowing for a decomposition of their effect on a given country’s CA into its domestic and foreign components.

Let X P * denote values of policy variables that are deemed desirable, which may or may not coincide with actual values X P . Then, the predicted CA can be decomposed into three components: the (cyclically-adjusted) CA norm, the cyclical component and the policy gap:

C ⁢ A i , t ^ = α ^ + β ′ ^ ⁢ X i , t F + γ ^ ⁢ X P * ⏟ CA norm + ψ ′ ^ ⁢ X i , t C ⏟ Cyclical component + γ ^ ⁢ ( X P - X P * ) ⏟ Policy gap(7)

As seen in Eq. (7), the CA norm ( C ⁢ A i , t 𝑁𝑜𝑟𝑚 ) is computed on the basis of the contributions solely of economic fundamentals and of desirable policy levels. In order to define the desirable policy levels for a given country, a normative assessment is necessary [3]. Note that if policy variables are specified as deviations from world averages, policy gaps appear only if a country’s policy distortion is different from their corresponding world average.

An alternative approach, adopted by the EC, is to interpret world averages for policy variables as desirable levels and to assume that country-specific policy variables are in line with world averages: hence, the policy gap for all countries is zero. As a result, X P drops out from Eq. (6) and the norm in this case is defined more simply as follows:

C ⁢ A i , t 𝑁𝑜𝑟𝑚 = α ^ F + β ′ ^ ⁢ X i , t F(8)

where α ^ F is given by C ⁢ A ¯ - β ′ ^ ⁢ X F ¯ and the bars denote averages.

However defined, the CA norm is then used as a benchmark value not for the headline CA balance but for the CA balance adjusted for business-cycle effects, the so-called cyclically-adjusted CA balance, generally defined as follows:

CACA i , t = C ⁢ A i , t + η i , t ⏟ Cyclical adjustment(9)

Finally, a “CA imbalance” is then derived as the percentage-point difference between the cyclically-adjusted CA and the CA norm:

CAimb i , t = CACA i , t - C ⁢ A i , t 𝑁𝑜𝑟𝑚(10)

In general, as defined in Eq. (9), the cyclically-adjusted CA balance is obtained as the headline CA balance with a correction due to the cyclical component. In all existing methodologies to our knowledge, the effect of the business cycle on the CA is assumed to be reflected solely in the trade balance, while it could be the case that the primary and secondary income balances also vary with output fluctuations. However, the relation between CA components other than the trade balance and the business cycle does not lend itself to an intuitive modelling and therefore this channel is generally neglected.

The IMF follows a straightforward approach to cyclical adjustment as it simply subtracts from the headline CA balance the predicted value obtained using the cyclical variables drawn from Eq. (7), such that the cyclical adjustment term is defined as follows:

η i , t = - ψ ′ ^ ⁢ X i , t C(11)

In particular, the cyclical variables considered in [3] are the country’s relative output gap (with respect to the GDP-weighted world output gap average) and its commodity terms-of-trade gap (relative to the country-specific trend), interacted with the country’s degree of trade openness. The first variable aims at capturing the impact on the CA balance of the relative position in the business cycle of a country relative to its main trading partners, in particular via the trade balance: a booming domestic economy usually results in high imports, lowering the CA balance on a temporary basis, while a favourable global cycle implies that foreign demand will likely stimulate exports, boosting the CA balance in the short run. The second variable measures the effect of deviations of a country’s commodity terms-of-trade index from its country-specific trend, given that improvements in terms of trade usually determine a higher trade balance, and is interacted with trade openness, since a larger impact on the CA balance is expected for more open economies.8

The EC instead interprets the cyclically-adjusted CA balance of a given country as the CA balance that would prevail if the output gaps of the country and of its trade partners were zero, i.e. if both domestic and foreign demand9 were at their potential [4] and exports and imports responded proportionately. This leads to measuring the cyclical adjustment term in the following manner:

η i , t = 1 Y t ⁢ [ θ M ⁢ M t ⁢ Y t - Y t * Y t * ⏟ Domestic output gap - θ X ⁢ X t ⁢ Y t F - Y t * F Y t * F ⏟ Foreign output gap ](12)

where Y t ⁢ ( Y t F ) defines actual nominal domestic (foreign) GDP at time t , the asterisks denote nominal potential levels, M t ⁢ ( X t ) captures the country’s imports (exports), θ M ⁢ ( θ X ) the corresponding trade elasticity to GDP. In this formulation it is assumed that the activation of imports (exports) associated with domestic (foreign) output is constant and independent of output movements; therefore, the amount of imports (exports) that stems from closing the current home (foreign) output gap is simply given by the product of elasticity of imports (exports), of current imports (exports) and of the current (foreign) output gap. Moreover, both import and export elasticities to GDP are set by the EC to 1.5 for all countries, although the empirical literature points to a relatively large dispersion in these elasticities across countries and periods. By assuming a fixed import elasticity in particular, the EC methodology neglects composition effects in aggregate demand, i.e. the fact that the latter’s different components activate imports with different intensities (e.g. [17]). It also does not take into account the fact that the evolution of exports, driven by the foreign output gap, feeds back into the domestic output gap and that treating these variables as independent is not entirely correct.

The Bank of Italy [18] overcomes this last issue by developing a model that posits that real imports are isoelastic (i.e. present a constant elasticity relative) to a reduced-form import-intensity-adjusted demand (IAD) variable, in turn a convex combination of both exports and domestic demand.

In formal terms, let Δ ⁢ M t * ⁢ ( Δ ⁢ X t * ) be the difference between “potential” imports (exports) and current imports (exports) at time t . Since exports are assumed to be isoelastic to overall foreign demand as in [4],10 Δ ⁢ X t * is equivalent to the second term inside the square brackets of Eq. (12):

Δ ⁢ X t * = - θ X ⁢ X t ⁢ Y t F - Y t * F Y t * F(13)

The key difference with the EC methodology lies instead on the import side:

Δ ⁢ M t * = M t ⁢ θ M 𝐼𝐴𝐷 ⁢ ω x ⁢ M t X t ⁢ Δ ⁢ X * + θ M 𝐼𝐴𝐷 ⁢ ( 1 - ω x ) ⁢ M t D ⁢ D t ⁢ Δ ⁢ D ⁢ D t *(14)

where θ M 𝐼𝐴𝐷 is the constant long-run elasticity of imports to IAD, in turn a geometric weighted average of the demand components, with weights reflecting their relative imports contents; ω x is the weight of exports in constructing the IAD variable and ( 1 - ω x ) is the weight of domestic demand D ⁢ D t ; Δ ⁢ D ⁢ D t * is the difference between the potential domestic demand and the current domestic demand.

The model can be solved by imposing the NA identity for GDP (applied to the potential level of all variables):

Y t * = D ⁢ D t * + X t * - M t *(15)

and substituting out M * using Eq. (14), then solving for Y t * , X t * and finally D ⁢ D t * . This provides an equation for Δ ⁢ M * expressed in terms solely of given parameters, which can thus be brought to the data (actual trade flows from NA and exogenous potential domestic, foreign output gap and potential exports as obtained by Eq. (13)). It also solves the inconsistency issue underlying the EC methodology.

The cyclical adjustment term is then given by:

η i , t = 1 Y t ⁢ [ Δ ⁢ M t * - Δ ⁢ X t * ](16)

This more refined computation of potential imports has a non-negligible impact on the cyclically-adjusted CA balance, also due to the different calibration of the trade elasticities.11 The impact is exemplified in Fig. 2 referred to Italy, which compares estimates based on the EC and the Bank of Italy’s models, respectively. Since 2012 the Bank of Italy’s cyclical adjustment has indeed been slightly larger than the EC’s correction, implying a lower cyclically-adjusted CA balance.

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However measured (IMF, EC or Bank of Italy methods), the cyclical adjustment term of the CA is highly sensitive to the set of output gap estimates employed in the computations. It is known that the latter figures vary significantly across institutions, given the high uncertainty surrounding these measures, and the resulting cyclical adjustment terms of the CA can therefore turn out to be different. As an example, in the twenty years from 2000 to 2019 the domestic output gap estimated by the EC was on average half a percentage point (in GDP terms) lower than that estimated by the Bank of Italy (which are those used by [18]).12 If the EC had assumed the same domestic output gap as that of the Bank of Italy, the cyclical adjustment would have been 0.1 percentage points of GDP larger, ceteris paribus (i.e. keeping the methodology fixed as in Eq. (12)).

After having outlined the possible ways to measure the cyclically-adjusted CA balance, we now turn to five general modelling choices to be undertaken when setting up a CA model.

3.1 A review of the CA determinants suggested by the literature

An early framework for examining CA developments is the “elasticities approach”, put forward in [20]. Exports (imports) are modeled as a function of relative prices between the exporting (importing) country and the rest of the world (i.e. the real effective exchange rate, REER), as well as of foreign (domestic) income or demand. The trade balance is thus expected to respond positively to foreign demand and negatively to the REER. As discussed in [10, 21], the REER is considered as playing a key role as an equilibrating mechanism in the CA adjustment process, but only in the short run. This trade elasticity approach hence is inherently limited in its ability to explain “equilibrium” CA positions, since it mainly focuses on the proximate, as opposed to medium-to-long-run, drivers of CA balances.13

As illustrated in Section 2.1, the CA is also the outcome of national saving less domestic investment. This alternative viewpoint, which led to the so-called “absorption approach”, stresses how macroeconomic factors ultimately determine international borrowing or lending patterns [24]. The more modern “inter-temporal representative approach” ([25, 26]) extends the absorption approach through its recognition that the saving and investment decisions of representative agents – namely households, firms and governments – are the result of forward-looking optimization calculations based on expectations of future variables.

A third, alternative approach is to consider the aggregate trade balance, the key component of the CA balance, as the sum of all bilateral trade relations. This approach (e.g. [27]) implies investigating the possible determinants of bilateral trade balances, such as the role of highly specialized intermediate goods and of pairwise trade costs, in turn reflecting, for example, bilateral protectionist measures. However, the current dominant consensus among economists is that aggregate trade balances are linked to the evolution of macroeconomic factors that are relatively independent from a single trade relation ([28, 29, 30]), so that bilateral balances are not actually relevant to the conduct of macroeconomic policy.

The most recent CA models are hence commonly grounded on the “inter-temporal representative approach”. However, the precise empirical implications of this framework are not straightforward and there is no consensus about the correct model specification [31]. Indeed, under this general framework, specific theoretical models have different predictions about the macroeconomic drivers of the CA balance, as well as of their expected signs and magnitudes.

As mentioned in Section 2.2, one way of classifying the possible CA determinants is to group them into fundamental, cyclical and policy variables, although in practice the distinction across the three categories may not be clear-cut. We here attempt to adopt this classification in order to review the main drivers of the CA balance pinpointed by the existing literature.

In principle, it could be appealing to model the two accounting components of the CA (savings and investment) separately, since it allows for the fact that a given determinant may have a heterogeneous impact on savings supply and investment demand. In other terms, it could be intriguing not to consider the CA balance as the dependent variable of a CA model, but rather the savings and the investment rates, separately.

To our knowledge, however, few studies pursue this avenue. An early example is [10]. This study examines the saving-investment balance within a system of separate equations for the CA, saving and investment (all as ratios of GDP), with cross-equation restrictions imposed in the estimation. In particular, each equation includes the lagged dependent variable, whose coefficient is imposed to be the same across the three equations. Moreover, the coefficients of all other fundamental explanatory variables in the CA equation are restricted to be equal to the difference between the corresponding coefficients in the saving and investment equations, while country fixed effects, which enter each equation, are estimated with no constraints. The results of this study point to changes in relative fiscal or demographic positions affecting the saving-investment balance primarily through their effect on domestic saving. Relative income per capita operates roughly equally through both saving and investment, while the effect of the output gap on the CA largely works through its effects on investment.27

Another, more recent study, [50], i.e. the methodological paper that underlies the old IMF EBA methodology, uses the same set of CA determinants to assess their relationship with savings and investment in two separate equations, but purely as a robustness check.28 The study concludes that the majority of the significant variables in the CA regressions appears to operate through the savings channel.29

Even more recently, [15] examines the determinants of saving, investment and the CA separately, but using the same set of explanatory variables. The main finding is again that the main channel via which the CA determinants operate is the savings channel.30

De facto, however, modelling the investment and savings channels separately in order to then yield a consistent CA norm is problematic. This is due to the observed statistical discrepancy between the official data on CA and S - I for several countries (Fig. 4), implying that Eq. (5) does not tightly hold in practice. Although the quality of statistics has significantly improved over time – as testified by the decreasing discrepancy, in absolute value terms, since the 1980s – for emerging economies the gap is currently still far from negligible.

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This statistical discrepancy could explain why the majority of existing studies targets the CA position directly and why the residual literature has either imposed coefficient restrictions, as in [10], in order to guarantee consistency, or has resorted to the estimation of savings and investments separately simply as a robustness check to assess the relative relevance of the two channels for a given determinant.

Measurement and data availability are key constraints in setting up a CA model, which condition the set of variables to be included in the specification. Several determinants cited in Section 3.1 are indeed hard to measure, especially those that attempt to capture less standard variables, which in turn reflect more recent, global trends. In this section we provide some examples of key CA drivers and the measurement issues affecting them, which often have no clear solution.

One prominent example is demography. Standard “static” measures of demographic factors (e.g. [13, 40, 50]), associated with the age composition of a country’s population, in turn recently driven by declining fertility rates, are: the old-age dependency ratio, constructed as the ratio of people older than 65 years to the working-age population aged between 14 and 65; the youth dependency ratio, constructed as the ratio of young people under 14 to the working-age population aged between 14 and 65;31 population growth, which partly proxies the share of young people.32[35] uses a low-order polynomial to represent 15 population age shares, a technique, introduced by [63], which has the advantage of capturing the information contained in the entire age distribution while maintaining a parsimonious parameterization. Instead, based on [64, 3] introduces a less common static demographic factor (the share of prime-aged savers, aged 45–64, as a proportion of the total working-age population), as well as variables aimed at capturing the dynamics of demography, which measure the role of increasing life expectancy, in turn driven by longevity or old age survival risk, via the following proxies: the life expectancy of prime-aged savers and its interaction with the future (i.e. 20-year ahead) old-age dependency ratio.33

Strictly related to demographics is migration, another variable that is hard to measure [15], even when abstracting from illegal migration. A migrant stock is defined as the total number of international migrants present in a given country at a particular point of time. A migration flow is defined as the number of persons arriving or leaving a given country over the course of a specific period of time. As documented in [65], international comparisons on migration flow data are difficult to conduct. Indeed, similarly to trade flow data, movements can be reported by sending or receiving countries; when data collection methods or measurements in countries differ, the reported mirror data do not match. Moreover, in many countries data collection systems for migration flow data do not exist or are partial. Conversely, stock data are more widely available, both across time and countries. For these reasons, to proxy for migration flows some studies (e.g. [66]) rely on the difference between two successive bilateral stock matrices. These measures are good estimates of the long-term flows of permanent migrants, but they understate the inflow of new migrants in that between the two periods some migrants present in the first period may die, return or migrate towards another country. To overcome this drawback, [65] puts forward a new method that estimates migrant transition flows between two sequential migrant stock tables, using data on population, i.e., the number of births and deaths. [15] employs this latter dataset to compute net immigration flow rates given by the difference between immigration and emigration flows per population of the host country. The study also considers net immigration stock rates, computed as the difference between immigration and emigration stocks as a percentage of the host country population. Indeed, since former migrants may continue to remit to their home country, relying on migration stocks rather than flows is more relevant to reflect the influence of such remittances on the CA, in that they imply the settlement of migrants in host countries over a relatively long period. The proxies employed in [15] may hence be the most appropriate to be included in a CA model. However, to our knowledge, these data are not publicly available.

By considering several databases – namely the IMF World Economic Outlook, the World Bank World Development Indicators and the United Nations World Population Prospects datasets –, coverage of the various demographic and migration proxies discussed thus far, for the years between 1980 and 2018 and for the 57 countries listed in Table A.1 in the Annex is almost complete, with the exception of Taiwan for a couple of proxies. However, the net migration rate is computed on data on net international migration flows and on the differences in overall population growth and the increase in its natural rate (i.e. the portion of population change determined exclusively by births and deaths), thereby suffering from the afore-mentioned drawbacks. Moreover, only few of these variables are currently available for 2019, implying lack of timeliness, but given that these measures vary little over time this is not a significant issue. Rather, it becomes important to select the most relevant demographic proxy or proxies, as they are highly correlated amongst themselves, and including the bunch of them together in a CA model may not be the most appropriate solution in the econometric sense, as later discussed.

Linked to demographic trends is a policy variable that measures the type or degree of generosity of a given country’s pension system. In order to calibrate social security systems, [36] innovatively collects information on pay-as-you-go systems across many countries.34 For each country, the authors construct a schedule of replacement rates for an average income earner, as a function of the number of years of contribution. Taking the difference between country-specific ages of retirement and labour market entry to proxy for the number of years of contribution, they thus obtain an official replacement rate. However, one also needs to account for the actual coverage of social security programmes, which varies cross countries.35 Lower coverage translates into lower contribution and replacement rates. For this reason the scholars adjust for (the mean of) two different proxies of coverage: the percentage of retired receiving benefits and the percentage of the working age population contributing to pensions.36 Although very original, the final measure of replacement rates is time-invariant, when it is known that since the 1980s many countries amongst those listed in Table A.1 underwent significant pension reforms and more may be in the pipeline.

As regards other potential CA determinants, in order to measure (household) credit constraints, [36] uses information on aggregate gross household debt. An issue with this proxy is that credit aggregates do not allow disentangling supply and demand [67]. The recent literature has therefore tried to improve identification using micro data, in particular direct, survey-based information on the limits of credit availability.37 Credit access conditions refer to the entire pool of possible borrowers and therefore these data are not subject to sample bias on granted loans as is the case for aggregate debt data. However, cross-country survey data on financial constraints are limited in terms of time and country coverage, which implies either: (i) resorting to a time average, losing out, however, on significant fluctuations over time, for example during the global financial crisis or the sovereign debt crisis; or (ii) complementing the missing countries and years with aggregate debt data.

Another non-standard variable is found in [14], which employs publicly available data sourced from [72] in order to capture financial regulation. In particular, the latter database covers seven dimensions of financial policy reform for 91 economies over the period 1973–2005: credit controls; interest rate controls; entry barriers; State ownership in the banking sector; financial account restrictions; prudential regulation and supervision of the banking sector; securities market policy. Along each dimension, a country is given a score on a graded scale from zero to three, with zero corresponding to the highest degree of repression and three indicating full liberalization. [14] shows that the different dimensions of financial regulation can have opposing effects on the CA, as already discussed in Section 3.1, such that it makes sense to consider them all jointly. Relative to the more standard indicators of financial development, such as credit gaps, which are likely to be endogenous to savings and investment decisions, these measures of regulatory settings are less likely to suffer from this bias. Furthermore, regulation is under the direct control of policy-makers and can be hence considered strictly as a policy variable. However, like all codings that convert qualitative information into a quantitative proxy, this measure suffers from a large judgement bias.

Finally, as mentioned in Section 3.1, financial centre dummies are sometimes included in CA models in order to capture measurement biases for a few economies with large gross foreign investment positions. However, these measurement biases may change in sign and size over time, since they vary with many factors, including net equity and debt positions, inflation differentials, differences in dividend policies, etc. For this reason the EBA methodology, which initially included financial centre dummies [50], then dropped them in the later update [3], in favour of “structural” outside-of-model adjustors for specific economies.38 This solution too, however, is not ideal, as it requires judgement and introduces the need to impose ex-post consistency across all countries’ estimates. In Section 4 we will return to connected mismeasurement issues.

In conclusion, the researcher faces a measurement trade-off: whereas for standard variables country-specific and time-varying measures are available for a large number of countries, in order to take into account the most recent developments of the CA literature, a feature which is desirable in setting up state-of-the-art CA models, data are, however, far less comprehensive. Moreover, providing there is a theoretical justification to including a given variable in a CA model and providing the data are available, which proxy should one use? Should one include all measures in the same regression, which is the IMF EBA approach, or should one select only the statistically significant proxies, also to avoid multicollinearity? The next section discusses possible model selection methods in this respect.

3.4 The selection of the core explanatory variables

As discussed thus far, there is no unambiguous prior theory for the selection of the explanatory variables to be included in a CA model; those proposed as CA drivers in previous studies cannot be excluded a priori. Yet, it is not necessarily optimal to include all possible variables as there is indeed a trade-off between using potentially redundant variables, which result in less precise coefficient estimates, and a potential omitted variable bias, which could distort estimates if the omitted variable is correlated with the other regressors. Hence, model uncertainty hampers consensus on the CA determinants to be included in the X vectors of Eq. (6).

This model uncertainty may be handled econometrically, for example by using Bayesian model averaging (BMA) techniques.39 To our knowledge, the studies applying this formal “horse-race” method to appropriately specify a CA model are only a handful, namely [13, 14, 75]. This methodology aims at detecting systematic empirical regularities, whereas precisely identifying causal relationships would require a more structural approach that cannot handle this amount of data, and which anyhow goes well beyond the scope of CA modelling for policy purposes. In particular, BMA involves the estimation of all possible sets of variables, assigning to each set a posterior model probability of being “true” based on Bayesian inference, and then the computation of a weighted average of all the estimates for a given coefficient in a statistically optimal way. Inference can then be based on the whole universe of candidate models, by considering not only the uncertainty associated to the coefficient estimate conditional on a given model, but also the uncertainty of the coefficient estimate across different models. In practice, via BMA different subsets of so-called “auxiliary” regressors (i.e. the potential determinants of the CA in our case) can be excluded from the model to improve, in the mean squared error sense, the efficiency of the “focus” parameter estimates (i.e. the coefficients attached to the variables that necessarily one wants to include in the model). As is standard in BMA applications ([73, 76, 9]), a variable can then be deemed to be a relevant CA driver when its posterior inclusion probability exceeds the threshold value of 0.5 across most specifications.

An alternative method that is capable of dealing with a very large number of predictors is the least absolute shrinkage selection operator (LASSO), put forward in [77]. This method provides a systematic, data-driven approach to variable selection, where a penalty on the absolute size of coefficient estimates is imposed and some coefficients are set to zero as a result, hence excluding the corresponding variables from the model. When applying this method, a choice however must be made concerning the level of penalisation. There are several possibilities, for instance based on the application of standard information criteria (Akaike, Bayesian, etc.) or on a process called “cross-validation”, which repeatedly subdivides the sample into smaller “training” and “validation” datasets, selecting the penalisation parameter that shows the best performance (a function of prediction errors) on the latter set. A drawback of LASSO is that the penalization procedure shrinks the size of the estimated coefficients attached to the variables that remain in the active set [78, 79]. This feature, acceptable for prediction purposes, is instead unpalatable for models with important normative implications, as it reduces the economic significance of the included explanatory variables. Moreover, conducting standard statistical inference, such as hypothesis testing, is complicated in the context of LASSO techniques. In sum, the LASSO procedure is best suited for prediction purposes, when a very large number of possible predictors must be considered, and less so for the estimation of a CA norm, where the set of potential explanatory variables, in turn guided by economic theory, is high but still manageable.

Finally, once the CA drivers are appropriately selected and the CA model is set up, the model needs to be accurately estimated, as discussed in the next section.

3.5 The econometric estimation of a CA model

Using a panel dataset on a wide sample of economies, as opposed to single country regressions, is now standard practice when estimating CA models. Exploiting both the time and the cross-section dimensions indeed increases sample size and raises the power of statistical tests, as well as achieving more robust estimates.

However, using a unique panel equation for calculating CA norms hinges on the very strong assumption that the same behaviour of economic fundamentals applies to all countries, which often include both advanced and emerging economies. To some extent, this is a desirable property: the economic fundamentals that drive CA balances in the long term should be the same across countries, if, looking forward, emerging economies should behave more like advanced economies. In other terms, estimating a single equation for all countries allows smoothing the impact of individual countries’ transitional dynamics [80]. However, the exact relation between the dependent variable and each of its drivers may differ across countries.

Moreover, the variables in the model are not necessarily stationary in the long time-spans usually considered. The construction of the explanatory variables as deviations from world averages can induce stationarity, but this is not always the case. Standard Ordinary Least Squares (OLS) is hence not the correct setting in the presence of non-stationary variables.

Another technical issue that a panel setting raises is that of cross-section dependence (CSD; e.g. [7]). Indeed, when both the number of countries and time periods are large, cross correlation of errors may emerge, due to omitted, unobserved common effects to all countries, such as global demand and supply shocks. In the specific CA model setting, the case for CSD is especially compelling, given the fact that most explanatory variables are expressed relative to a weighted average of partner countries. Conventional panel estimators such as fixed or random effects can result in misleading inference and even inconsistent estimators, depending on the extent of CSD and on whether the source generating the CSD (such as an unobserved common shock) is correlated with the regressors [81].

Allowing for various forms of country heterogeneity in the panel estimation procedure even in the presence of non-stationary variables is however possible owing to the latest-generation panel cointegration techniques. Moreover, these recently developed techniques can also correct for the potential CSD bias. Indeed, one possible solution is to adopt the common correlated effects mean group (CCEMG) estimation procedure [82], already employed in the context of equilibrium REER estimation, for example, in [5, 6]. The appropriateness of this estimation technique is due to the fact that: (i) it accommodates for both stationary and non-stationary cointegrated variables; (ii) it allows for heterogeneous slopes, which is of paramount importance given the vast country heterogeneity in the panels underlying CA models; (iii) it includes cross-section averages of the dependent and explanatory variables in order to tackle CSD. However, this procedure generally includes country fixed effects, necessary in the case of REER misalignment estimation due to the general index number nature of the dependent variable [9], but which are not appealing in the case of CA model estimation, as discussed in Section 3.1.40

Another econometric issue is reverse causality. Generally, in a CA model feedback from CA developments to the regressors is not allowed. Despite its relevance, this issue is typically neglected in the literature mainly due to the lack of instrumental variables [12]. It is indeed difficult to find a set of variables related to the CA determinants but not directly related to the CA. Moreover, lagged levels of the regressors, as used for example in [4], are only weak instruments, given the persistence of most variables. One partial exception is [3], which employs instruments for two CA determinants, namely fiscal policy and foreign exchange intervention.41 However, first-stage estimation results are not provided and is hence not possible to assess the validity of the chosen instrumental variables; moreover, they only address two out of many explanatory variables, for which endogeneity may still be a concern. Reverse causality in CA regressions and precisely identifying causal relationships would indeed require a more structural approach that cannot handle the amount of data underlying the CA model estimation. This aim, hence, goes beyond CA modelling for policy purposes.

4.1 The impact of global firms on the trade and income balances

The growing role of MNEs has, among other things, a large impact on balance of payments statistics (see, for example, [41]). Given the topic of this paper, here we focus solely on the CA, although naturally the ever increasing presence of MNEs has also affected financial account statistics. MNEs’ activity can imply at least four different phenomena that directly affect the computation of the CA balance ([83]).

The first refers to the relocation of production, which (a) can be shifted to a foreign subsidiary via offshoring or (b) can be outsourced to a company abroad that produces goods on the MNE’s behalf, according to a process known as “processing” or “contract manufacturing”, which has strongly increased in importance in key economic sectors in recent years.42 These cross-border manufacturing arrangements can affect the trade-in-goods component of the CA. Indeed, in case (a) the imports and exports of goods no longer show up in the MNE’s home country, but in that of the foreign subsidiary; the profit earned by the latter is then transferred to the former via the primary income component of the CA. As a result, the home country’s CA balance does not change relative to a pre-offshoring scenario, but its composition does. In case (b), according to the BPM6, during the production process the ownership of the inputs remains with the MNE and hence no trade flows are recorded in the contractor country’s balance of payments (with the exception of an import by the MNE of manufacturing services from the foreign company that is producing the good). The sale of the final products to third countries is recorded as the contractor country’s exports, thereby not affecting the CA balance of this country any differently relative to a situation in which the goods were exported directly.43

A second consequence for the CA balance arises as a result of the increased tendency of MNEs to move the location of their headquarters to financial centres or in general to countries according to tax and corporate governance considerations in a process called “redomiciliation” or “corporate inversion”. These operations do not generate any additional real economic activity in the new headquarters’ country, but change the attribution of income across countries. Redomiciliation, hence, does affect the size of CA balances, and not only their composition, because all unrepatriated earnings are allocated to a different country of corporate residence. This phenomenon can have large effects especially in those economies where MNE transactions and balance sheets are large relative to the size of the domestic economy. A prominent example is provided by Ireland where the relocation of foreign MNEs’ headquarters to the country in recent years brought on an increase in Ireland’s receipts of investment income, leading to an overstatement of this country’s net primary income balance and hence of the CA balance (e.g. [86]).

A third aspect is related to the employment and mobility of intellectual property (IP), an intangible asset including research and development, copyrights and computer software, which has markedly increased in importance in the context of the global diffusion of knowledge-based economies (e.g. [87]). IP products are non-rival goods, meaning that MNEs can freely use their IP anywhere they operate at zero marginal cost. According to the BPM6, the remuneration of intangible assets (i.e. license fees and royalties paid by a user of IP products to the foreign owner of these goods) is recorded as an import/export of services and the booking of these flows depends on the location of the economic ownership of IP. Whereas it takes time and significant disinvestment to relocate the physical production of goods in factories, IP products are far easier and cheaper to relocate and they are also harder to value at market prices. They can therefore be shifted around the world also in order to minimise tax expenditure and, more in general, foster profits (e.g. [88]). The relocation of IP across countries via MNEs can change the geographical location where exports and income are recorded. For example, the recent shift of IP to Ireland indeed affected the country’s net exports: in particular, the Irish resident companies started charging foreign companies fees to produce the patented products, leading to an increase in service exports and, since the Irish resident companies stopped paying fees for use of IP, a decrease in service imports was also recorded.

Linked to the impact of MNEs on CA statistics is also the increase in external financial openness since the mid-1990s, only partly interrupted by the 2008–09 global financial crisis (GFC; [89]), which has implied that primary income flows, and, in particular, investment income flows, a component of the CA balance as reported in Section 2.1, have also grown in size, leading to what has been defined as the “financialization of the CA”. Several CA models have attempted to capture this recent trend by introducing the FNA position as a regressor, but this solution is only rough and partial.

Moreover, the measurement of the investment income balance according to official BPM6 standards differs from the standard economic concept of accumulation of real net external wealth on an ultimate owner basis in at least two respects, as thoroughly discussed in [3]. First, the statistical treatment of retained earnings (i.e. profits retained in the foreign affiliate) is different for FDI and portfolio investment, the two main investment items, and is not always attributed to the ultimate owner.44 In particular, while for FDI equity both paid-out dividends (i.e. profits distributed to the direct investor) and retained earnings are recorded in the CA income balance, for portfolio equity only paid-out dividends are recorded.45 Second, although all forms of income in the balance of payments are recorded in nominal terms, the recording of interest income in this manner departs from the economic notion of real income and the income balance is therefore biased by inflation. The CA balance hence reflects these measurement issues concerning the investment income balance, in turn due to the existing statistical standards, and the accuracy of CA modelling is penalised as a result.

To sum up, MNEs can affect the recording of CA statistics in different directions, impacting either the trade balance or the primary income balance or both. To our knowledge no paper has ever attempted to model the trade balance and the income balance separately in an external balance assessment context, also due to the difficulty of gauging the cyclical vs. structural determinants of the latter, as discussed in Section 2.3. A very recent exception is [85], which conducts a panel analysis on the CA, the trade and the income balances separately.46 Two original aspects of this study stand out. First, the external balances are expressed in terms of gross national income, rather than of GDP. Second, the corporate income tax rate is employed, aside standard determinants of the CA, in order to capture the extent of profit shifting across MNEs. This innovative variable is found to be statistically significant in both the trade and income balance equations, but with opposite signs (negative for the former, positive for the latter); the overall effect on the CA balance is insignificant, because of these two offsetting forces. However, business-cycle effects are treated only via year fixed effects and it is not clear, therefore, if the analysed determinants are truly medium-term drivers of the CA.

More generally, the inclusion of dummies, such as financial centre dummies, in the CA model has partly attempted to tackle the MNE-induced measurement bias in those countries for which it is most relevant, but the recent literature has avoided this approach, as discussed in Section 3.3, as too broad-brush and even distorting. Even the IMF’s solution of including “structural” outside-of-model adjustors for specific economies, is not optimal. Hence, given the current official statistical framework, one rough way of accounting for all these phenomena could be to investigate the significance of a measure of the weight of foreign-owned firms, which may be done within, and not outside, a country’s CA model. Proxies for profit-shifting, such as the afore-mentioned corporate income tax, are also worth further exploring in a medium-run context.

4.2 The “corporate savings glut”

Another recent trend which has further complicated CA modelling is the so-called “corporate savings glut”. According to [91], whereas in the 1980s most of global investment was financed by household saving, nowadays nearly two-thirds of investment is funded by corporate saving, due to a widespread rise in the share of corporate profits that mirrors the global decline in the labour share. A similar recomposition has not been recorded for investment, implying that non-financial corporations have generally shifted from net borrower to net lender positions, hence contributing to a secular decline in domestic investment. [64] notes that the rise in corporate saving and net lending, in turn due to rising profitability, lower financing costs and reduced tax rates, has been most pronounced in countries with persistent CA surpluses, such as Germany and the Netherlands, but it has also affected some emerging economies. Theoretically, the standard model of intertemporally optimizing households with rational expectations predicts that the saving behaviour of the non-household sectors, i.e. the government and the private corporate sector, has no influence on total saving and on the CA [26]. To the extent that households own domestic corporations, household saving behaviour should offset differences in corporate saving. However, a rise (fall) in corporate saving leads to a higher (lower) CA if private households fail to see through the “corporate veil”, i.e. if higher (lower) corporate saving is not fully offset by lower (higher) household saving. This mechanism is conceptually similar to the non-Ricardian saving behaviour by households as a reaction to changes in the government budget discussed in Section 3.1. One possibility to take this trend into account is to include corporate saving in a CA model; to our knowledge this has only been done in [92], which finds statistically significant results, yet not for normative purposes.

4.3 The COVID-19 pandemic

At the time of writing this paper, the global economy was hit by the COVID-19 pandemic, which, amongst manifold effects, has marked large shifts in CA balances, driven by shocks to trade, oil prices, tourism and remittances. The pandemic, although global, has hit individual economies in a heterogeneous fashion, according to the composition of their trade flows, the degree of reliance on tourism, the relevance of immigration, amongst several factors. It has also triggered concerns over a possible dismantling of global supply chains and of the strengthening of protectionist measures and of anti-immigration policies.

It is far too early to predict the long-lasting economic effects of this pandemic since we lack sufficient relevant data (which is released with up to a two-year delay relative to the reference period),47 the health emergency is ongoing and uncertainty is high. However, in the short run, in order to be able to continue providing timely external position assessments, one-off adjustments to the medium-term CA norms could be made in order to take into account exceptional factors linked to the pandemic, such as the collapse of international tourism and the hike in COVID-19-related medical goods imports, providing they turn out to be temporary. These adjustments should be reported in a transparent manner. Moreover, even at this early stage some qualitative considerations on how the pandemic may affect CA model estimation in the medium term are useful.

The first issue concerns the uniqueness of the CA norm. Will it still be meaningful to estimate average coefficients over a time-span since 1980 as is commonly done now (e.g. [4, 3]) in order to derive one medium-term CA “equilibrium” value? Or will the post-2020 norm need to be estimated separately from the pre-2020 benchmark, as a reflection of a “new normal”? In other terms, will the COVID-19 outbreak lead to structural changes that will permanently affect CA norms, in turn leading to a new equilibrium? In particular, CA norms may be affected by such factors as changing global financial conditions, “scarring” effects of the pandemic, restructuring of global value chains, shifts in demographic trends, increase in health expenditure and changes in desirable fiscal positions. Given the high uncertainty, at the moment it is not possible to answer this question. However, robustness checks reported in [5], for example, concerning equilibrium REER estimation, provide evidence that the dramatic GFC in 2008–09, followed by the so-called Great Trade Collapse (GTC), did not represent a significant structural break (providing this crisis episode is correctly tackled econometrically).48 Similarly, the IMF’s CA model is estimated over the whole period since 1980, suggesting the absence of a structural break due to the GTC. This may, hence, be the case also for the COVID-19 pandemic, although the current crisis is already displaying significant differences relative to the GTC, for example as concerns to what extent services trade is affected, and the GTC therefore may not be an appropriate comparative benchmark.

The second issue concerns the changing importance of the CA drivers to be included in a CA model. It is reasonable to expect the economic relevance of several regressors, discussed in Section 3.1, to vary relative to pre-COVID19 times. This may be the case, for example, of oil or more in general commodity trade dependence, trade openness and the government budget, which may increase their contribution to the definition of the CA norm, and of migration flows, which may instead decrease. The outcome depends very much on how transitory or permanent current COVID-19 developments turn out to be. It may also be necessary to explicitly include new explanatory variables in the CA model, such as public and private health expenditure, the generosity and resilience of social security systems, the reliance on foreign intermediate and capital inputs in total production or corporate savings.49 Finally, it becomes even more important to disentangle cyclical from structural factors in the evolution of external imbalances in order to address sustainability issues, but this distinction, which was already challenging prior to the pandemic, may become even harder to undertake. For example, the uncertainty surrounding the output gap of a given economy, already high in normal times, is even larger at the current juncture.

Third, the measurement of certain key CA drivers may become more demanding. For instance, given the documented risk of rising protectionist measures introduced by some countries as a reaction to the pandemic, proxying tariff and non-tariff trade barriers with a given economy’s trade openness may not be satisfactory anymore. More direct, or even microfounded, measures of trade restrictions may be required, albeit posing country and time coverage issues. To a certain extent, [9] provides some reassuring evidence, contradicting this need. This study, focused on REER equilibrium estimation, employs the so-called “phi-ness” indicator of trade, put forward by [93], as a measure of the level of trade impediments for a given country, derived from bilateral trade flows according to a gravity equation. The correlation between the phi-ness indicator and trade openness is found to be high, hence suggesting that the trade openness variable may not be such a poor proxy of trade restrictions.

Whatever considerations may be made at the current stage, it is highly likely that taking into account the implications of increasing multinational activity and the COVID-19 outbreak in the context of CA models will become the new, major challenge for the measurement and assessment of external imbalances in the immediate future.