2. THE INTERTEMPORAL MODEL OF THE CURRENT ACCOUNT

The starting point of an optimal consumption model [see, e.g. Ghosh (Reference Ghosh1995) or, for a broader view, Obstfeld and Rogoff (Reference Obstfeld and Rogoff1996)] is an infinitely lived representative agent whose optimisation problem is:

$$\matrix{ {\max \mathop \sum \limits_{t = 0}^\infty \beta ^tE[ {U( {c_t} ) } ] } \hfill & {0 < \beta < 1} \hfill \cr} $$

subjected to her budget constraint:

$$b_{t + 1} = \; ( {1 + r} ) b_t + q_t-c_t-i_t-g_t$$

and the no-Ponzi condition:

$$\mathop {\lim} \limits_{t\to \infty} b_{t + 1} = 0$$

where β, discount factor; E, expectations operator; U, utility; b, net foreign assets owned by the representative agent; r, world interest rate; q, level of output or GDP; c, private consumption; i, investment and g, government consumption.

For simplicity, we will henceforth assume that the subjective discount rate equals the world interest rate, which rules out the possibility of consumption tilting. Solving the above problem, we obtain the value of optimal consumption c*:

(1)$$c_t^{^\ast} = r\left\{ {b_t + \displaystyle{1 \over {1 + r}}E_t\left[ {\mathop \sum \limits_{i = 0}^\infty \displaystyle{{( {q_{t + i}-i_{t + i}-g_{t + i}} ) } \over {{( {1 + r} ) }^i}}} \right]} \right\} \ \eqno [1]}$$

or, alternatively:

$$c_t^{^\ast} = rW_t$$

where

$$W_t = b_t + \displaystyle{1 \over {1 + r}}E_t\left[ {\mathop \sum \limits_{i = 0}^\infty \displaystyle{{( {q_{t + i}-i_{t + i}-g_{t + i}} ) } \over {{( {1 + r} ) }^i}}} \right]$$

is the level of wealth.

On the other hand, the current account balance that smooths consumption is defined as:

(2)$$ca_t = y_t-i_t-g_t-c_t^{^\ast} \eqno [2]$$

where y _t = q _t + rb _t is the national income or GNP (i.e. GDP plus net factor payments); which, replacing the value of c*, becomes:

(3)$$ca_t = -E_t\mathop \sum \limits_{i = 1}^\infty \displaystyle{{\Delta z_{t + i}} \over {{( {1 + r} ) }^i}}\eqno [3]$$

where z _t ≡ q _t − i _t − g _t denotes the so-called national cash flow.

The above equation is the open economy version of Campbell's (Reference Campbell and Shiller1987) «saving for a rainy day» equation and shows the current account as the present discounted value of expected future changes in output, investment and government consumption. As can be seen, if the shocks to the national cash flow (i.e. output, investment or government consumption) are permanent, they will not affect ca, since their expected variation is zero; however, if the shocks are transitory, they will affect ca, which will adjust to keep the present consumption unchanged. Specifically, if agents expect that the national cash flow is going to increase in the future, they will increase their present consumption, which will lead to a current account deficit. In contrast, if agents anticipate a future fall in the national cash flow, the current account will move to a surplus. In addition, it should be noticed that, according to the most recent literature, the «trade channel» stressed by the intertemporal approach to the current account (i.e. adjustment to an external disequilibrium through future trade surpluses), should be complemented by a «valuation channel» (i.e. changes in the returns on domestic assets held by foreigners relative to the return on foreign assets held by domestic residents through a depreciation of the domestic currency); see Gourinchas and Rey (Reference Gourinchas and Rey2007).

3. EMPIRICAL MODEL

We will proceed to estimate equation [3] following the approach in Otto (Reference Otto2003), which is based in turn on the work of Campbell (Reference Campbell1987) and Campbell and Shiller (Reference Campbell and Shiller1987); see also Agénor et al. (Reference Agénor, Bismut, Cashin and McDermott1999) for a similar methodology. More specifically, our estimation will proceed in two steps:

1. (i) First, we will test whether the actual current account balance incorporates agents' expectations on the future movements of the national cash flow. This can be done by estimating the following equation:

   $$\Delta z_t = \pi + \theta \Delta z_{t-1} + \alpha ca_{t-1} + \varepsilon _t$$

and then test whether the coefficient α is negative and statistically significant. From a technical point of view, we would be testing whether the current account Granger-causes variations in the national cash flow. The Granger-causality test, however, does not test all the restrictions that the present-value model imposes on the data; a formal test of the present-value model can be obtained as follows (see Otto, Reference Otto2003, for details). Starting from the t + 1 term of equation [3], taking expectations on both sides, assuming rational expectations and operating, we obtain:

$$ca_{t + 1}-\Delta z_{t + 1}-( {1 + r} ) ca_t = \omega _{t + 1}$$

where ω is an error term. Under the present-value model, the left-hand side of this equation should be uncorrelated with any variable dated at t or earlier. Accordingly, the model can be tested through the estimation of:

(4)$$x_t = \pi + \theta _1\Delta z_{t-1} + \theta _2ca_{t-1} + \nu _t\eqno [4]$$

where x _t ≡ ca _t+1 − Δz _t+1 − (1 + r)ca _t, and then testing θ ₁ = θ ₂ = 0.

1. (ii) Second, we will estimate the optimal current account balance, using a first-order VAR model for the variables Δz _t and ca _t:

   $$\left[ {\matrix{ {\Delta z_{t + 1}} \cr {ca_{t + 1}} \cr}} \right] = \left[ {\matrix{ {a_{11}} & {a_{12}} \cr {a_{21}} & {a_{22}} \cr}} \right]\left[ {\matrix{ {\Delta z_t} \cr {ca_t} \cr}} \right] + \left[ {\matrix{ {\nu_{1t + 1}} \cr {\nu_{2t + 1}} \cr}} \right]$$

so that, iterating the model forward, taking expectations and using the vector $\left[ {\matrix{ 1 & 0 \cr}} \right]$ to collect the forecast of Δz _t, we can write the infinite sum in the present-value model [3] as:

$$ca_t^{^\ast} = -\phi \left[ {\matrix{ 1 & 0 \cr}} \right]\left[ {\matrix{ {{\tilde{a}}_{11}} & {{\tilde{a}}_{12}} \cr {{\tilde{a}}_{21}} & {{\tilde{a}}_{22}} \cr}} \right]\; \left[ {\matrix{ {\Delta z_t} \cr {ca_t} \cr}} \right]$$

or, more simply:

(5)$$ca_t^{^\ast} = -\phi (\tilde{a}_{11}\Delta z_t + \tilde{a}_{12}ca_t)\eqno [5]$$

where ϕ = (1 + r)⁻¹ and $\left[ {\matrix{ {{\tilde{a}}_{11}} & {{\tilde{a}}_{12}} \cr {{\tilde{a}}_{21}} & {{\tilde{a}}_{22}} \cr}} \right] = \left[ {\matrix{ {a_{11}} & {a_{12}} \cr {a_{21}} & {a_{22}} \cr}} \right]\left( {I-\phi \left[ {\matrix{ {a_{11}} & {a_{12}} \cr {a_{21}} & {a_{22}} \cr}} \right]} \right)^{-1}$, being I the 2 × 2 identity matrix.

The variable $ca_t^* $ is the optimal current account balance, that is, an estimate of the current account, consistent with the VAR [1] model and with the constraints derived from the intertemporal model. In the end, a graphical comparison of the actual current account balance, ca _t, and its optimal value, $ca_t^* $, will allow us to assess the validity of equation [3]. Notice, finally, that, for the optimal current account to equal the actual current account, two constraints from [5] must hold:

$$w_{\Delta z}\equiv -\phi\, \tilde{a}_{11} = 0$$

$$w_{ca}\equiv -\phi \, \tilde{a}_{12} = 1$$

4. DATA AND EMPIRICAL RESULTS

Our data source is the new set of historical national accounts provided by Prados de la Escosura (Reference Prados de la Escosura2017). In particular, our two variables of interest, z and ca, are computed, respectively, as:

• • GDP minus gross fixed capital formation, minus changes in inventories, minus government consumption.

• • GDP minus private consumption, minus gross fixed capital formation, minus changes in inventories, minus government consumption, plus net primary income from the rest of the world, plus net current transfers from the rest of the world.

Notice that the series for all variables cover the period 1850-2017, except for the net primary income and net current transfers, which are only available until 2016. Accordingly, our period of analysis will be 1850-2016.

The two variables were converted into real terms using the GDP deflator (2010 = 100). Finally, since the model is based on a representative agent, both z and ca are computed in per capita terms dividing by total population. The GDP deflator and total population have been taken, respectively, from Table 7 and Table 3; net primary income and net current transfers from the rest of the world, from Table 3; and the rest of variables, from Table 2. All tables refer to the Electronic Appendix of Prados de la Escosura (Reference Prados de la Escosura2017), which can be accessed at http://espacioinvestiga.org/bbdd-chne/?lang=en. The final variables are measured in 2010 € per person.

To have a first glimpse of the data, we show the evolution of the Spanish current account as a share of GDP, over the period 1850-2016, in Figure 1.

FIGURE 1 CURRENT ACCOUNT AS A SHARE OF GDP: SPAIN, 1850-2016.

Source: Prados de la Escosura (Reference Prados de la Escosura2017) and see the text.

Once the Spanish economy had been able to leave behind all the disruptions brought about by the loss of the American colonies, through the second half of the 19^th century foreign trade began to grow at a faster pace than in France or Britain (Tortella Reference Tortella2000). Regarding the current account, Prados de la Escosura (Reference Prados de la Escosura2010) characterised two main periods in its evolution during the period before the First World War: one of persistent deficits between 1850 and 1890; and another where surpluses prevailed, between 1891 and 1913 (with the exception of the years 1899-1904). According to this author, economic growth at the end of the 19^th century was stimulated by high amounts of foreign capital inflows, which helped to finance current account deficits and complemented domestic savings. In turn, reversals of net capital inflows (in the form of «sudden stops», i.e. significantly and unexpectedly) after 1891 slowed down growth since investment had to rely solely on domestic savings.

The broad pattern detected by Prados de la Escosura (Reference Prados de la Escosura2010), that is, current account deficits in the periods of higher growth, and surpluses in the periods of lower growth, remains roughly valid in subsequent years. Current account deficits, then, reappeared throughout the booming 1920s, after the highest surplus of the whole series: 7.4 per cent of GDP in 1919, coinciding with the acute crisis after the end of the First World War. Next, the current account balance stayed at low levels during the turbulences of the central years of the 20^th century, that is, the sequels of the Great Depression in the 1930s, and the autarchic policy stance imposed by the Franco regime at the end of the Spanish Civil War and during the 1940s and 1950s. The increased openness of the economy following the Stabilisation Plan of 1959 paved the way for the high-growth period of the 1960s and early 1970s, which contemplated the re-emergence of large current account deficits, reaching a then maximum of 7 per cent of GDP in 1966. After some years of economic stagnation, growth and large current account deficits returned in the second half of the 1980s, following membership into the EU; and even more after joining EMU in 1999, reaching the highest current account deficit ever: 9.6 per cent of GDP in 2007. Finally, these huge deficits faded away, and even turned into surpluses, once the current crisis started. Overall, current account deficits, by making the arrival of foreign capital inflows possible, would have eased the possibility of higher economic growth; in this sense, the external sector does not seem to have worked as a constraint on the growth of the Spanish economy over the long run (Bajo-Rubio Reference Bajo-Rubio2012).

We now turn to the empirical results. We start by testing for the order of integration of the variables Δz _t and ca _t using the tests proposed by Ng and Perron (Reference Ng and Perron2001), and the results are shown in Table 1. Since the null hypothesis of a unit root (i.e. non-stationarity) is rejected for the tests $MZ_\alpha ^{GLS} $, $MZ_t^{GLS} $ and ADF ^GLS, and the null hypothesis of stationarity is not rejected for the tests MSB ^GLS and MPT ^GLS, we can conclude that the two variables are stationary.

TABLE 1 NG–PERRON TESTS FOR UNIT ROOTS

Note: *denotes significance at the 5% level. The critical values are taken from Ng and Perron (Reference Ng and Perron2001), Table 1. The autoregressive truncation lag has been selected using the modified Akaike information criterion, as proposed by Perron and Ng (Reference Perron and Ng1996).

Next, we present the estimation of a VAR for Δz _t and ca _t over the whole period 1850-2016 in Table 2. The number of lags in the VAR was identified using the Bayesian information criterion, and the optimal lag selected was one. The estimation method is ordinary least squares with the White correction of standard errors for heteroscedasticity (White Reference White1980). We can see that the current account would help to predict future changes in the national cash flow, as predicted by the present-value model. This is shown by the negative and statistically significant coefficient on ca _t−1 in the first column of the table, even though this coefficient is quantitatively very small.

TABLE 2 ESTIMATION OF A VAR [1] FOR Δz _t AND ca _t: SPAIN, 1850-2016

Note: t-statistics are given in parentheses, and 95% confidence intervals in square brackets.

Now, we proceed to test for the orthogonality condition, from the estimation of equation [4]; the results are shown in Table 3. The real interest rate used to compute the dependent variable x _t (see above) is 2 per cent (from an average over the period of 4.8 per cent for the UK bank rate and 2.9 per cent for the inflation rate; see Hills et al. Reference Hills, Thomas and Dimsdale2015). Since the p-value of an F-test on the joint significance of the lagged values of Δz and ca is 0.01, we can reject the null hypothesis that the latter are uncorrelated with the dependent variable x _t ≡ ca _t+1 − Δz _t+1 − (1 + r)ca _t. Hence, according to this test, the present-value model of the current account would be rejected by the data.

TABLE 3 ESTIMATION OF THE ORTHOGONALITY CONDITION: SPAIN, 1850-2016

Note: t-statistics are given in parentheses.

Finally, Figure 2 shows the optimal current account, as a share of GDP, computed from equation [5], and compares it with the actual values, shown in Figure 1. The values of the weights of Δz and ca used to compute the optimal current account according to equation [5] are −0.371 and 0.817, respectively; these values, together with 95 per cent confidence intervals, appear in Table 2 and have been computed from the estimation of the VAR. Notice that both values are not too close to the theoretical values 0 and 1, respectively, needed for the present-value model to be a valid characterisation of the path followed by the current account. As can be seen in the figure, the optimal current account does not fit perfectly the movements of the actual current account. More specifically, two broad periods can be detected, before and after the early 1960s (i.e. the years where a significant change took place in the performance of the Spanish external sector), so that in the first period the optimal current account overpredicts the actual current account; unlike the second period, where it underpredicts it. In fact, after 1960 Spanish foreign trade becomes «mature» in the terminology of Serrano-Sanz et al. (Reference Serrano-Sanz, Sabaté-Sort and Gadea-Rivas2008), that is, characterised by the predominance of manufactures and services, unlike the period before the 1930s which was characterised by the predominance of primary products. Finally, we have computed the variances of the two series at 7.52 and 8.92, for the actual and optimal current account, respectively, which would not be significantly different according to an F-test of equality of variances.

FIGURE 2 ACTUAL AND OPTIMAL CURRENT ACCOUNT AS A SHARE OF GDP: SPAIN, 1850-2016.

Source: Prados de la Escosura (Reference Prados de la Escosura2017) and see the text.

Due to the length of our sample period (i.e. 167 years), we have allowed for the possibility of a differentiated behaviour of the relevant variables across subperiods. To this end, we have applied a formal test of structural change to the current account series, ca _t. In particular, we use the approach of Qu and Perron (Reference Qu and Perron2007) to detect endogenously multiple structural breaks in a VAR system. These authors proposed several test statistics to identify the possible break points:

• • The WDmax test of the null hypothesis of no structural break vs. the alternative of an unknown number of breaks given some upper bound M.

• • The supLR _T test of the null hypothesis of no structural break (m = 0) vs. the alternative of a fixed (arbitrary) number of breaks (m = k).

• • The SEQ _T(l + 1|l) test of the null hypothesis of l breaks vs. the alternative of l + 1 breaks.

The results of the Qu and Perron tests are shown in Table 4. We have allowed up to two breaks, and used a trimming ε of 0.20, so that each segment has at least thirty-three observations. All the test statistics are significant at the 5 per cent level; the critical values are taken from Bai and Perron (Reference Bai and Perron1998, Reference Bai and Perron2003). First, according to the WDmax test, at least one break is present. Next, the supLR _T(2) test is highly significant, which, together with the significance of supLR _T(1), means that there is at least one break. Finally, the SEQ _T(2|1) test is also significant and the sequential procedure selects two breaks. The dates of the breaks have been estimated at 1919 and 1959, with confidence intervals of [1914, 1924] and [1956, 1962], respectively.

TABLE 4 STABILITY OF THE CURRENT ACCOUNT: SPAIN, 1850-2016

The year 1919 marks the start of a deep crisis following the economic boom associated with the First World War. Indeed, the Spanish economy enjoyed a period of great prosperity during the war years; since the countries at war moved their economies mostly to satisfy military purposes, neutral countries such as Spain had to substitute imports from these countries, at the same time that the demand for exports rose dramatically. These favourable conditions did not only affect the manufacturing industry, but also service activities such as trade, sea transportation or banking; in fact, as can be seen in Figure 1, in 1919 the current account reached the highest surplus of the whole series, 7.4 per cent of GDP. However, a sharp crisis occurred at the end of the war, characterised by the massive closing of factories, bank failures, a generalised drop in prices, a rise in unemployment and a huge fall in industrial production (Carreras and Tafunell Reference Carreras and Tafunell2010). This situation resulted in growing social unrest that paved the way for the dictatorship of general Primo de Rivera 4 years later. On the other hand, the second break is justified by the approval of the Stabilisation Plan of 1959, which ended the policy of autarky implemented at the end of the Spanish Civil War, and made possible the very high growth rates of the next 15 years (the so-called Spanish miracle). It was only after the 1959 Stabilisation Plan that the timid liberalising measures implemented some years before were in fact able to operate (Tortella Reference Tortella2000)Footnote ¹.

Accordingly, we have re-estimated the model for the periods 1850-1918, 1919-1958 and 1959-2016. From the estimation of a VAR [1] (again validated by the Bayesian information criterion) for Δz _t and ca _t, we can see in Table 5 that now the current account does not help to predict future changes in the national cash flow in any of the three subperiods, unlike the prediction of the present-value model. In turn, from the results of the test on the orthogonality condition shown in Table 6, we cannot reject the null hypothesis that the lagged values of Δz and ca are uncorrelated with the dependent variable of equation [4]. In other words, for the three subperiods the present-value model of the current account would be rejected by the data according to the first test, but not according to the orthogonality test.

TABLE 5 ESTIMATION OF A VAR [1] FOR Δz _t AND ca _t: SUBPERIODS

Note: t-statistics are given in parentheses, and 95% confidence intervals in square brackets.

TABLE 6 ESTIMATION OF THE ORTHOGONALITY CONDITION: SUBPERIODS

Note: t-statistics are given in parentheses.

We have also computed the optimal current account from equation [5] for the three subperiods, and compared it with the actual values; the results are shown in Figure 3. Again, the fit between both series is anything but good and no clear pattern emerges, especially for the first subperiod. In the case of the second subperiod the optimal current account generally overpredicts the actual one, except for the first half of the 1940s (i.e. the core years of the Second World War). Finally, and unlike the results in Figure 2, for the third subperiod the optimal current account overpredicts the actual current account most of the time, especially on the eve of the current economic and financial crisis. When computing the variances of the actual and optimal current account we now obtain, unlike the case of the whole period, the most usual result of a higher variance for the former than for the latter, namely, 5.84 and 2.31, 3.07 and 0.53 and 7.64 and 5.11, for the first, second and third subperiods, respectively. The two variances are significantly different for the first and second subperiods, but not for the third, according to an F-test of equality of variances.

FIGURE 3 ACTUAL AND OPTIMAL CURRENT ACCOUNT AS A SHARE OF GDP: SUBPERIODS (A) 1850-1918, (B) 1919-1958 AND (C) 1959-2016.

Source: Prados de la Escosura (Reference Prados de la Escosura2017) and see the text.

Notice that, in the end, since savings and investment decisions would be the result of agents' optimal decisions, a high current account deficit should not be a matter of concern according to the intertemporal approach to the current account; see for example Corden (Reference Corden2007)Footnote ². However, even if running a current account deficit is not bad in itself, it might be so when the deficit is very large or, more precisely, if it is «unsustainable». In Stanley Fischer's words, «if the current account deficit is ‘unsustainable’—that is to say, if it cannot be financed by drawing down reserves or through borrowing—or if reasonable forecasts show that it will be unsustainable in the future, devaluation will be necessary sooner or later» (Fischer Reference Fischer, Dornbusch and Helmers1988, p. 115).

Regarding the Spanish case, the current account balance was found to be sustainable over the long run in Bajo-Rubio (Reference Bajo-Rubio2012) (more specifically, in the periods 1850-1913 and 1940-2000), from the estimation of a long-run relationship between exports and imports of goods and services as ratios to GDP. One should be careful, however, to interpret these results as unambiguous evidence in favour of the intertemporal approach to the current account. Indeed, Edwards (Reference Edwards, Edwards and Frankel2002) shows that large current account deficits tend not to be persistent: «the typical pattern of current account deficits is that countries that experience large imbalances do so for a limited time; after a while, these imbalances are reduced, and a current account reversal is observed» (Edwards Reference Edwards, Edwards and Frankel2002, p. 66). Such reversals, in turn, have negative effects on economic performance. Therefore, for instance, when assessing the sustainability of current account deficits for a set of developed countries over the shorter and more recent period 1970-2007 in Bajo-Rubio et al. (Reference Bajo-Rubio, Díaz-Roldán and Esteve2014a), the results on current account sustainability were not clear-cut for several of those countries, Spain among them.

Turning to the role of the current account in the evolution of the Spanish economy over our period of analysis, we can see how from 1850 to the final years of the 19^th century, the current account showed an enduring deficit. However, rather than being used to smooth consumption in the presence of shocks, the resulting inflows of foreign capital enabled the Spanish economy to gain access to imported capital goods and raw materials above the amount allowed by export revenues. Accordingly, foreign capital inflows added to domestic savings, so increasing investment and fostering economic growth. In this way, foreign capital made a distinctive contribution to the investment boom in 19^th-century Spain (Prados de la Escosura Reference Prados de la Escosura2020). This situation reversed at the end of the 19^th century, when an inward-looking policy stance was adopted (Tena-Junguito Reference Tena-Junguito, Dormois and Lains2006; Carreras and Tafunell Reference Carreras and Tafunell2010). This policy can be described as a mix of protectionism, preservation of the domestic market to domestic production (through strong government interventionism) and economic nationalism (i.e. replacing foreign capital for domestic capital as the main driving force of growth). During these years, characterised by a low degree of external openness, the current account was in surplus most of the time, and growth rates were lower (with the exception of the 1920s). The pattern of the second half of the 19^th century, that is, current account deficits and foreign capital inflows, reappeared after 1960 when the Spanish economy enjoyed the highest growth rates in her history. Following a decade of stagnation between the mid-1970s and the mid-1980s, once again after Spain joined what is today known as the EU in 1986, a renewed opening of the economy was associated with a period of sustained growth in which foreign capital again played a leading role (Bajo-Rubio and Torres Reference Bajo-Rubio, Torres and Viñals1992).

Finally, once Spain joined EMU in 1999 borrowing in international markets became easier due to the disappearance of the exchange rate risk; as a result, the allowable external deficit would be higher in a monetary union (Blanchard and Giavazzi Reference Blanchard and Giavazzi2002). Accordingly, during this period and until the beginning of the financial crisis, the Spanish economy ran the highest current account deficits in her history; which again was far from being warranted on consumption smoothing grounds. However, as the most recent events have shown, current account imbalances, although possibly explained by fundamentals, can also be a sign of important macroeconomic and financial disequilibria (Obstfeld Reference Obstfeld2012). However, in a monetary union it is no longer possible to offset such disequilibria by way of a nominal exchange rate depreciation; but, in contrast, through lower growth of domestic prices that might harm future growth prospectsFootnote ³.