Consumption Smoothing and the Current Account
Evidence for France, 1970-1994
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 2 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 3 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

This paper estimates a simple consumption-smoothing model of the French current account, and examines its capacity to predict recent developments in France’s external performance. The model views the current account as a buffer through which private agents can smooth consumption over time in response to temporary disturbances to output, investment, and government expenditure. The empirical results indicate that the model performs well overall, and predicts correctly the sharp turnaround in France’s external accounts observed in the past three years—a feature of the data that conventional models of trade flows, based on income and relative price variables, appear unable to explain.

Abstract

This paper estimates a simple consumption-smoothing model of the French current account, and examines its capacity to predict recent developments in France’s external performance. The model views the current account as a buffer through which private agents can smooth consumption over time in response to temporary disturbances to output, investment, and government expenditure. The empirical results indicate that the model performs well overall, and predicts correctly the sharp turnaround in France’s external accounts observed in the past three years—a feature of the data that conventional models of trade flows, based on income and relative price variables, appear unable to explain.

I. Introduction

France’s external accounts improved markedly in 1992, and continued to improve in 1993 and 1994. The trade balance recorded a surplus equivalent to 0.5 percent of GDP in 1992 and 1.3 percent in 1993 (compared to a deficit of 0.4 percent in 1991), whereas the current account balance recorded a surplus of 0.3 percent in 1992 and 0.9 percent in 1993-94. However, conventional models of trade flows based on income and relative price variables appear to be unable to account for these developments. Movements in competitiveness recorded since the late 1980s and the 1992-93 recession apparently explain only a small fraction of the improvement in France’s external accounts between 1992-94. 1/

This paper attempts to interpret France’s recent external performance on the basis of the consumption-smoothing (or intertemporal) approach to the current account. This approach, which has gained in popularity in recent years, focuses on the impact of current and future values of households’ long-run expected income on saving and investment. 2/ The consumption-smoothing model has also featured prominently in the debate launched by Feldstein and Horioka (1980) on the degree of capital mobility across countries. As observed by Ghosh (1995), a formal comparison of the variance of the current account derived from the intertemporal model with the variance of the actual current account provides a natural procedure for assessing the extent to which a country can borrow freely (subject to a no-Ponzi game condition) at world interest rates.

In the present paper, a simple intertemporal model of the current account is estimated and used as a benchmark for assessing the behavior of France’s external accounts. Section II presents the model. Section III provides estimates of the model parameters. Estimation results indicate that the model tracks remarkably well the historical data over the period 1970 to 1994--despite the fact that France experienced large external shocks during the 1970s and that the period prior to the mid-1980s was characterized by capital controls. The existence of such controls could have been expected to distort lending and borrowing operations of French residents, and thus prevent them from effectively smoothing consumption spending over time. A comparison of the actual and simulated paths indicates that the model also accounts for the current account surpluses registered between 1992 and 1994. This result suggests that the surpluses may have reflected a downward revision in households’ long-run expected resources, rather than a significant improvement in external price competitiveness.

II. The Model

The intertemporal approach to the current account is derived from the permanent-income theory of consumption and saving. In the context of a small open economy with access to world capital markets, the permanent-income theory implies that temporary shocks (which by definition have larger effects on current resources than lifetime resources) may lead to large fluctuations in national saving and the current account.

The model tested in this paper is based on a simple one-good framework, which can be described as follows. 1/ Suppose that the only traded asset is a consumption-indexed bond with fixed face value that pays net interest at the rate p between two periods. The representative consumer’s preferences are separable intertemporally. The expected value of the discounted utility flow of the consumer is given by

t=0αtu(ct),0<α<1(1)

where α is a discount factor, ct consumption, E0 the expectations operator (conditional on information available at t = 0), u() the instantaneous utility function, which possesses all familiar properties (namely, u′ > 0 and u″ < 0). The consumer’s budget constraint is

Δbt+1=ρbt+yt-It-ct-τt,(2)

where bt denotes holdings of indexed bonds (which are freely traded across countries) at the beginning of period t, ρ the world interest rate (assumed fixed), yt output, It investment, τt lump-sum taxes, and Δ the first-difference operator. The government maintains a balanced budget, so that

gt=τt,(3)

where gt denotes government spending.

Substituting equation (3) in equation (2) yields

bt+1=(1+ρ)bt+yt-It-ct-gt.(4)

The representative consumer maximizes (1) subject to (4). As for instance in Otto (1992) and Sheffrin and Woo (1990), Fisherian separability is assumed to hold so that the levels of output and investment are treated as exogenous in solving for the optimal consumption path. Approximating the instantaneous utility function by the quadratic function u(ct)=ct-αct2/2 (which requires that ct < 1/σ for the marginal utility of consumption to remain positive) and imposing the standard no-Ponzi game restriction yields: 1/

ct*=ρθ(1+ρ)Et{h=0(1+ρ)-hzt+h}+(ρ/θ)bt,(5)

where Et is the expectations operator, Θ ≡ αρ(1+ρ)/[α(1+ρ)2-1], and zt = yt - It - gt is output net of private investment and public spending, and is often referred to as net output (Sheffrin and Woo, 1990), net private noninterest cash flow (Obstfeld and Rogoff, 1994), or simply national cash flow (Ghosh, 1995). The parameter Θ ⋛ 1 reflects the consumption tilting dynamics of consumption, which results from divergences between the world interest rate and the domestic rate of time preference, (l-α)/α. When Θ > 1 (or Θ < 1), agents tilt consumption towards the future (the present), whereas if Θ = 1 there is no tilting effect (see Sachs, 1982). In general, the higher the elasticity of intertemporal substitution, the stronger will be the tilting effect (Obstfeld and Rogoff, 1994). Thus, along the optimal path, private consumption depends on the present value of the expected future stream of the cash flow, as well as the economy’s existing stock of net foreign assets. Equivalently, equation (5) shows that private optimal consumption is proportional to wealth, defined as the present discounted value of the cash flow plus interest payments on the existing stock of assets. As pointed out by Milbourne and Otto (1992, p. 372), gt in (5) could be interpreted as the present-value tax cost, using a Ricardian-equivalence argument. Thus, (5) may be viewed as expressing consumption as a function of the present-value of savings out of disposable income.

By definition, the current account is equal to gross national product qt (GDP plus interest income on the outstanding stock of foreign assets, yt+ρbt) minus private and public expenditure (ct+It+gt). The consumption-smoothing component of the current account, CAt*, can be defined as: 1/

CAt*=(qt-It-gt)-θct*.(6)

Noting that the current account is also equal to net foreign asset accumulation (bt+1-bt), simple manipulations using (5) and (6) yield

CAt*=Et{h=1(1+ρ)-hΔ(yt+h-It+h-gt+h)},(7)

which shows that the consumption-smoothing component of the current account is equal to minus the present discounted value of expected changes in the national cash flow variable. Equation (7) indicates that permanent shocks, which have no effect on expected changes in the cash flow variable, leave the current account unaffected--as their expected change is zero. A permanent increase in yt, for instance, induces a one-for-one increase in consumption and no change in the current account. 2/ Unfavorable temporary cash flow shocks—such as an unexpected increase in government expenditure or investment—cause the expression on the right-hand side of (7) to fall, that is, the current account to move into smaller surplus or greater deficit, and conversely in the case of favorable shocks. Thus, the current account acts as a buffer to smooth consumption in the presence of temporary disturbances. 3/

The main problem with implementing (7) empirically is the measurement of the expected changes in the cash flow variable. In line with most of the existing literature, here we will assume that the current account itself reflects all information about the future course of the cash flow variable. 1/ In other words, national saving (net of investment) should help predict subsequent movements in the national cash flow variable.

We begin therefore by estimating a first-order unrestricted bivariate vector autoregressive (VAR) model in the cash flow variable and the actual consumption-smoothing component of the current account, defined as CAt=(qtItgt)Θ˜ct:

[ΔztCAt]=[a1a2a3a4][Δzt-1CAt-1]+[1t2t],(8)

where ∊1t and ∊2t are disturbance terms and Θ˜ an estimated value of Θ (see below). We then make use of the implication that

Et[Δzt+hCAt+h]=[a1a2a3a4]h[ΔztCAt]=Ah[ΔztCAt],(9)

which can be substituted in (7) to give the estimate of the optimal current account:

CAt*=-[10][(1+ρ)-1A][I-(1+ρ)-1A]-1[ΔztCAt],(10)

where I is the identity matrix. Expression (9) is valid as long as the infinite sum in equation (7) converges. This requires that the variables appearing in the VAR system (8) be stationary. Assuming that zt is I(1), Δzt will be I(0). And since under the null the actual consumption-smoothing current account (which is then equal to CAt*) is a discounted sum of Δzt, it will also be I(0). 2/

The expression for the optimal current account derived from (10) can then be compared to the actual current account to determine, for instance, the extent to which the surplus recorded in the past three years in France can be explained by consumption smoothing behavior. A variety of additional tests are also reported below.

III. Estimation Results

The data used in our empirical investigation are annual series on national accounts for the period 1970 to 1994, obtained directly from the French National Statistical Office, INSEE. yt is gross domestic product, qt gross national product, It gross private and public investment (defined as including inventory accumulation), and gt current government expenditure. All nominal series were deflated by the implicit GDP deflator to ensure consistency. 1/ The world interest rate was set at 4 percent in all calculations reported below. 2/

The first step in the procedure is to obtain an estimate of Θ, in order to construct the (stationary) consumption-smoothing component of the current account by removing the nonstationary component of the actual series (or, more specifically, the stochastic trend) associated with consumption tilting. This estimate can be obtained from a cointegrating regression which examines the relationship between private consumption ct and qt-It-gt. 3/ This relationship was estimated using the Phillips-Hansen FM method, which yields an asymptotically correct variance-covariance estimator when estimating cointegrating vectors in the presence of serial correlation and endogeneity (Phillips and Hansen, 1990). In our cointegrating regression of qt-It-gt on ct we obtained an estimate Θ˜ of 0.9757, with a long-run standard error (as derived from the FM method) of 0.005. A t-test (with the standard variance estimator replaced by the standard error derived from the FM method) indicates that the estimated value is significantly different from unity. This estimate therefore indicates that France has consumed more than its permanent cash flow and has foregone future consumption in favor of present consumption. By definition, as indicated above, the residual series from the cointegrating regression of qt-It-gt on ct is equal to CAt, the actual consumption-smoothing component of the current account.

The hypothesis of cointegration between the cash flow variable zt and private consumption ct was tested using the LC test of Hansen (1992), and the stability of the relationship between them was examined using Hansen’s (1992) mean-F and sup-F tests. 1/ The LC test of the null hypothesis of a cointegrated relationship between zt and ct does not reject the hypothesis: a value of 0.41 is the result; the 5 percent critical value (in the presence of a constant term) is 0.58. Furthermore, the Hansen stability tests indicate that the relationship between zt and ct is stable—the null hypothesis of constant parameters in the FM cointegrating regression is not rejected. The mean-F and sup-F tests have values of 4.07 and 5.51; the corresponding critical values at the 5 percent significance level are 4.57 and 12.40, respectively.

One of the testable implications of the consumption smoothing model is that the current account should Granger-cause subsequent changes in the cash flow variable (Obstfeld and Rogoff, 1994). A current account deficit today, for instance, should signal an expected increase in future cash flows—associated, say, with an expected reduction in future government expenditure. A standard F-test of the null hypothesis of the absence of Granger causality from CAt to zt is indeed rejected—it has a value of 5.87 and a p-value of 0.025.

We then estimated the VAR system in terms of Δzt and CAt, including constant terms. The intertemporal model described previously implies two restrictions on the parameter estimates derived from the VAR system under the null, namely, that the coefficient on Δzt be equal to zero and that the coefficient on CAt be equal to one in equation (10). Formally, let Γ denote the matrix multiplying the vector [Δzt CAt]’ in equation (10). Let Γ = [Γz ΓCA] be a conformable partition of the matrix Γ. The model therefore requires that Γz = 0, and ΓCA = 1. Acceptance of these restrictions implies that movements of the actual consumption-smoothing current account CAt reflect those of the optimal consumption-smoothing current account CAt*, constructed as in equation (10).

These joint restrictions were tested using a Wald test. The value of the test statistic (which is distributed has a x2 with 2 degrees of freedom) was Wald = 0.872 (with a p-value = 0.647), indicating strong acceptance of the restrictions. This suggests France had little difficulty in smoothing consumption through foreign borrowing and lending in the face of exogenous shocks. This is somewhat surprising, since during most of the estimation period (from the early 1970s to the mid-1980s) capital controls were in place—which in principle should have limited the ability of domestic residents to engage in international borrowing and lending. 1/ Actual and predicted values of the current consumption-smoothing current account are shown in Figure 1. The figure shows indeed that the two series move closely together. Changes in national cash flows explain fairly well movements in the actual consumption-smoothing current account balance.

Figure 1
Figure 1

France: Actual and Predicted Consumption Smoothing Component of the Current Account World Interest Rate = 0.04

(constant 1980 billion FFr)

Citation: IMF Working Papers 1995, 119; 10.5089/9781451940237.001.A001

A further testable implication of the model is that the variance of CAt and CAt* should be equal. Such a comparison provides a joint test of the assumption of a high degree of capital mobility and the validity of the intertemporal model of the current account (Ghosh, 1995). We found the variance of CAt to be significantly larger than that of CAt*--by more than 40 percent in relative terms—indicating “excess volatility” in the actual consumption-smoothing component of the current account. This result is similar to those obtained by Sheffrin and Woo (1990) and by Ghosh (1995) for Canada, Germany, Japan, and the United Kingdom. It suggests that capital flows between France and the rest of the world may have been more volatile than would be justified by expected changes in fundamentals.

IV. Summary and Conclusions

The purpose of this paper has been to estimate a simple intertemporal model of France’s current account over the period 1970-94, and to examine the extent to which it predicts recent developments. The key prediction of the model is that a country’s current account will be in deficit (surplus) whenever national cash flow, defined as gross domestic product less investment and government spending, is expected to rise (fall) over time. Intuitively, if the cash flow is expected to grow over time, the country will find it optimal to borrow against future resources (that is, to increase its external debt) by running a current account deficit. If, by contrast, national cash flow is expected to fall over time—as might be the case if government spending were expected to increase in the future—the country would run a current account surplus (increase its savings, or reduce external indebtedness) today in order to maintain consumption in the future at a level consistent with permanent income.

Estimation results suggested that, despite its simplicity, the basic consumption-smoothing model explains fairly well fluctuations of the current account balance since the early 1970s, which is suggestive of a high degree of capital mobility between France and the rest of the world. This is consistent with recent evidence for other industrial countries. Our results are particularly remarkable in view of the fact that estimation was performed in part over a period during which France experienced large external shocks, and restrictions on overseas capital transactions (which should have limited, in principle, international borrowing and lending activities by domestic residents) were in place. In addition, the model predicts correctly the sharp turnaround in France’s external accounts observed in 1992—a feature of the data that “traditional” models of trade flows, based on income and relative price variables, appear to be unable to explain. 1/ The improvement in the current account (or, equivalently, in net saving) appears to reflect a more pessimistic assessment by consumers of their future income prospects. In turn, the expected deterioration in income may have been related to the 1992-93 recession (the largest in France since the end of the second World War) and the associated increase in unemployment.

Appendix: Unit Root Tests

This Appendix examines the time series properties of consumption (ct), national disposable income (yt), and national cash flow (zt) series. The Phillips-Perron Z(α) and Z(t) unit root tests are used to determine the order of integration of the series. 1/ The Fejer kernel is used, as is the prewhitening technique of Andrews and Monahan (1992) to aid in estimating the long-run variance of the error term in the unit root regression. Andrews’ (1991) data-dependent automatic bandwidth selector is also invoked to determine the optimal lag truncation order.

The tests were sequenced from a maximum of two unit roots down to one unit root. At each stage an ordinary least squares regession of the form xt = μ + βt + αxt-1 + εt was run, where xt (which is equal to ct, zt or yt) is in first-difference form in the first stage, and in levels in the second stage.

The results indicate that all of the series are nonstationary (Table A1). Both statistics testing for one unit root versus no unit roots are insignificant, indicating that we cannot reject the null hypothesis of a unit root. Conversely, both statistics testing for two unit roots versus at most one unit root are significant, which indicates we can reject the hypothesis of two unit roots—the three series are integrated of order one, or I(1). 2/ Accordingly, both variables appearing in the VAR of equation (8) are stationary.

Table A1

Univariate Unit Root Tests, 1970-94

article image

The Phillips-Perron tests are based on the following model for any series x: xt = μ + βt + αxt-1 + εt. The tests rely on rejecting the null hypothesis of a unit root (a=1) in favor of stationarity. This hypothesis is tests by the Z(α) and Z(t) tests. If the null cannot be rejected (the test statistics are not significant), then the series has a unit root.

All series are in logarithms.

The critical values for the Z(α) and Z(t) tests at the 5 percent significance level are -7.3 and -1.95 for no deterministic components (μ=β=0), -12.5 and -3.0 for the constant term only (μ≠0, and (β=0), and (-17.9 and -3.60) for both deterministic components (μ≠0, and β≠0).

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*

This paper was prepared while Claude Bismut was a Senior Economist in the European I Department and Paul Cashin an Economist in the Research Department. We would like to thank, without implication, Ulrich Baumgartner, Benoit Coeuré, and Jean-Luc Tavernier for helpful discussions and comments on an earlier draft.

1/

Developments in competitiveness of the French manufacturing industry since the early 1980s are reviewed by Agénor (1995). A “conventional” model of trade flows (based on an an error-correction framework) is estimated by Agénor and Bismut (1995).

2/

See Obstfeld and Rogoff (1994) and Razin (1995) for recent surveys of the literature.

1/

This basic framework has been used by a number of authors, including Milbourne and Otto (1992), Otto (1992), Sheffrin and Woo (1992) and Ghosh (1995). The presentation here follows more closely the last two papers. Obstfeld and Rogoff (1994) and Razin (1995) discuss various extensions of the basic framework.

1/

The quadratic approximation is such that u‴() = 0, and implies that the optimal path of consumption does not depend on uncertainty over future consumption or the degree of variability of income.

1/

Removing the consumption-tilting component of the current account (which is nonstationary) is necessary to ensure validity of standard inference techniques, as discussed below.

2/

However, permanent positive shocks to investment, to the extent that they raise future output, will lead to a deterioration of the current account (see Obstfeld and Rogoff, 1994).

3/

Equation (7) also implies that a country will experience a persistent current account imbalance if the expected change in national cash flow has a non-zero mean. Suppose, for instance, that agents expect national cash flow to fall over time by an average of FF. 10 million. The steady-state current account surplus would be given by FF. (10/ρ) million—or, assuming a world interest rate equal to 4 percent, a surplus of about FF. 250 million.

1/

See for instance Ghosh (1995) and Sheffrin and Woo (1990). This approach rests on the idea of Campbell and Shiller (1987), according to which an asset price reflects all the available information that is useful in predicting future earnings.

2/

Trehan and Walsh (1991) examine the conditions under which the assumption of stationarity of the current account is necessary for intertemporal budget balance.

1/

Current account estimates based on national accounts data do not fully reflect nominal capital gains and losses on net foreign assets. In addition, our deflation procedure does not allow us to correct for the inflationary erosion of the real value of foreign assets. These limitations are common to most studies in this area.

2/

An annual world interest rate of 4 percent was used by Sheffrin and Woo (1990), and by Ostry and Levy (1995) in their analysis of the role of financial deregulation and intertemporal factors in the behavior of saving in France. We also estimated the model with a world interest rate equal to 2, 3, 5, and 6 percent. The results differed only marginally from those reported below. In particular, the ratio of the variance of the actual to the predicted current account tends to decrease as ρ increases.

3/

The Appendix reports the results of unit root tests showing that the two series are I(1).

1/

The Appendix presents the results of unit root tests on zt and ct.

1/

For a discussion of the structure of capital restrictions prior to the mid-1980s, see Ministry of Finance (1986). The dismantling of capital controls began in 1984 (within the context of a general movement towards capital market integration in Europe), and was completed in 1990. For an overview of the liberalization process in recent years, see the annual reports on Exchange Arrangements and Exchange Restrictions published by the Fund.

1/

The optimal current account predicted by the consumption-smoothing model for the period 1992-94 is lower than the actual current account balance—but the difference is not large.

1/

See Dickey and Rosanna (1994) for a discussion of Phillips-Perron tests of stationarity. These non-parametric tests have an advantage over the standard Dickey-Fuller tests in that nuisance parameters are (asymptotically) eliminated, even if disturbances are not independent and identically distributed.

2/

The Z(α) test for consumption (when β=0, and μ≠0) marginally fails to reject the null hypothesis of two unit roots at the 5 percent significance level. However, this hypothesis is rejected by the Z(t) test.

Consumption Smoothing and the Current Account: Evidence for France, 1970-1994
Author: Claude Bismut, Mr. Paul Cashin, Mr. C. John McDermott, and Pierre-Richard Agénor
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    France: Actual and Predicted Consumption Smoothing Component of the Current Account World Interest Rate = 0.04

    (constant 1980 billion FFr)