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Macroeconomic uncertainty, precautionary saving, and the current account
JOURNALOF
Monetary
ELSEVIER
Journal of Monetary Economics 40 (1997) 121-139
ECA)NOMICS
Macroeconomic uncertainty, precautionary saving, and the current account Atish R. Ghosh, Jonathan D. Ostry* International Monetary Fund, Washington, DC 20431, USA Received January 1995; final version received January 1997
Abstract The relationship between current account developments and changes in the macroeconomic environment is a key issue in open economy macroeconomics. This paper extends the standard intertemporal model of the current account to incorporate the effects of macroeconomic uncertainty on external saving behavior. It is shown that the greater the uncertainty in national cash flow, defined as output less investment less government consumption, the greater will be the incentive for precautionary saving and, ceteris paribus, the larger the current account surplus. Empirical support for the model is found using post-war quarterly data for the United States, Japan, and the United Kingdom, as well as a long time series (1919-90) for the United States.
Keywords: Current account; Precautionary saving JEL classification: C32; E21; F32
1. Introduction
The relationship between the current account and the macroeconomic environment remains a key issue in open economy macroeconomics. Modem theories of the current account [see, for example, Sachs (1982), Frenkel and Razin (1987)]
* Corresponding author. Tel.: 202-623-7405; fax: 202-623-6336; e-mail: [email protected]. We are grateful to John Campbell, Ricardo Caballero, an anonymous referee, and seminar participants at Princeton, NYU, the Board of Governors of the Federal Reserve, and the Econometric Society Meetings for useful comments and suggestions. 0304-3932/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved, Pll S 0 3 0 4 - 3 9 3 2 ( 9 7 ) 0 0 0 3 1-7
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emphasize its consumption-smoothing role in the face o f shocks to national cash flow, defined as output less investment less government consumption. The expected time profile o f national cash flow serves as a sufficient statistic for the determination o f the current account in these models. Thus, a country should dissave externally whenever individuals in the economy believe that current national cash flow is temporarily below its permanent level, regardless o f the source o f the shock to national cash flow. Typically, these models assume perfect foresight. But this leads to a logical inconsistency, i.e., the models are specifically designed to examine the behavior o f optimizing agents in the face o f various stochastic shocks, but those agents are assumed to have assigned a zero probability to these shocks ever occurring (or, alternatively, certainty equivalence is imposed). Not surprisingly, if instead agents are assumed to know that they live in a stochastic environment, the implied behavior o f the current account becomes rather different. In this paper we examine current account dynamics in an explicitly stochastic macroeconomic environment. Our starting point is the closed-economy work on the behavior o f individual saving when agents are subject to uninsurable labor income variability. In that literature it is well-known that an increase in income uncertainty will result in greater saving, 1 because o f a precautionary motive (see, e.g. Caballero, 1990). 2 While there is a growing body o f literature that examines the empirical evidence for precautionary saving at the level o f the individual in a closed economy setting, surprisingly little attention has been paid to the open economy implications. Yet, i f precautionary savings represent a significant portion o f aggregate savings, as Zeldes (1989) and Caballero (1990) among others contend, then it should be reflected in data on the current account which, after all, measures the country's aggregate external saving. To examine the effect o f precautionary saving on the current account, this paper relates aggregate income uncertainty (or, more precisely, uncertainty about national cash flow) to the level o f external savings. I f incomes are perfectly pooled across individuals - as a representative agent model assumes - then it
1This result depends on the technical assumption that the utility function has a positive third derivative. Kimball (1990) establishes a measure of the strength of the precautionary saving motive that is isomorphic to the measures of risk-aversion familiar from the work of Pratt (1964) and Arrow (1965); see Kimball (1991). On the interaction between risk-aversion and intertemporal substitution, see Kimball and Weil (1992). 2 The early literature on precautionary saving helped explain the empirical findings of Fisher (1956) and Friedman (1957) about differences in saving rates across groups whose earnings have different risk characteristics. Using two-period models, Leland (1968), Sandmo (1970), and Dreze and Modigliani (1972) showed that there would be a precautionary motive for saving as long as marginal utility is convex. Miller (1976) confirmed these results in a multi-period setting. More recently, Skinner (1988) has argued that precautionary savings account for a significant proportion of total savings in the United States. Zeldes (1989), Caballero (1990), and Carroll (1992) have exploited the notion of a precautionary demand for savings to explain several 'puzzles' in the consumption literature.
A.R. Ghosh, J.D. Ostry/Journal of Monetary Economics 40 (1997) 121-139
123
is only that component of income which cannot be diversified at the national level which affects precautionary saving. Since individuals typically do not share risks perfectly, aggregate income uncertainty is only a proxy for (unobservable) individual income uncertainty, and its importance for external saving depends upon the extent to which these measures are correlated. Conversely, since there is at least some risk sharing within a country, the magnitude of national income uncertainty will be proportionately smaller than individual uncertainty. This is sometimes interpreted as implying that a precautionary motive proxied by aggregate income uncertainty cannot be important for aggregate saving. But it does not imply that precautionary motives cannot be an important component of external saving. Simply put, while aggregate income uncertainty may be as much as an order of magnitude smaller than individual uncertainty, external saving is typically two orders of magnitude smaller than national saving. Thus uncertainty about the evolution of cash flow could indeed be an important determinant of the current account. 3 We begin, in Section 2, by deriving the current account in a fully optimizing model of an open economy in which agents are assumed to take explicit account of the stochastic environment. The optimal current account is shown to consist of two components. The first, which is also present in models which assume certainty equivalence, is equal to the present discounted value of expected declines in national cash flow. If national cash flow is, on average, expected to grow over time; this term is negative, and the current account will be in deficit, as agents dissave against resources they expect to earn in the future. The second component, which is present only when uncertainty is explicitly incorporated, is proportional to the variance of life-time innovations to national cash flow. This term reflects the role of precautionary saving in the current account. Ceteris paribus, an increase in this variance will lead to greater precautionary saving and to a larger current account surplus. Section 3 turns to the empirical evidence using quarterly data from 1955 to 1990 for five of the G-7 industrialized countries. 4 In addition, for the United States, we use a separate data set spanning the period 1919-90. This is a very long-time series by any account and provides a rich setting in which to examine whether precautionary effects may be present in the determination of the current account. Before discussing the econometric results, we first establish whether, for plausible values of the parameters of the utility function, the precautionary saving component could represent an appreciable fraction of observed current account surpluses. Our results are largely encouraging. Assuming a risk-aversion
3 Another issue is whether international portfolio diversification makes the variability of NCF an overestimate of the uncertainty faced by individuals. Empirically, however, most portfolios exhibit a strong 'home bias', so diversification is likely to be limited in practice (see, for example, Baxter et al.. 1995). 4 France and Italy were omitted because they lack the necessary quarterly national accounts data.
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coefficient of 3, for example, precautionary motives could account for 2 - 7 % of observed current account surpluses. We then examine the role of precautionary saving directly by measuring the response of the current account to the timevarying component of our measure of macroeconomic uncertainty. In two of our data sets the time-variation of uncertainty is too small to enable us to reliably estimate its effect on the current account. It bears emphasizing that this does not imply that a precautionary saving motive is not important in these cases, but merely that our methodology cannot identify it. In the remaining four cases we do find evidence in favor of a precautionary saving component of the current account, the evidence being strongest in the two US datasets. Section 4 offers some brief concluding remarks.
2. The model We use the standard, infinite horizon, small open economy model of international borrowing and lending as the basis of our theoretical framework. While the assumption of a small open economy may appear suspect when considering current account movements of countries as large as the United States, ultimately the adequacy of the model is an empirical issue. The results reported below, and the findings of Ghosh (1995), Sheffrin and Woo (1990) and Otto (1992), suggest that the model is capable of explaining developments in the current accounts of the major countries. These empirical results suggest that even for large industrialized countries, general equilibrium effects, operating through changes in an endogenous world interest rate, are not large. The economy is assumed to be populated by a single, infinitely-lived, representative agent whose preferences are given by 5
1
t=O
(1 +r)~
EU(c,),
(1)
where U(.) is the instantaneous utility function, r is the world interest rate, and ct denotes consumption of the single good. With a view to empirical implementation, we assume
U(ct) = (1/ct)e -~c',
(2)
where e > 0 is the Arrow-Pratt measure of (absolute) risk-aversion. Although this utility function does not bound consumption away from zero, it is chosen because it yields a closed-form solution for the consumption function in the presence of time-varying uncertainty. It is simplest to work in terms of the social
5 The derivation here assumes that the subjective discount rate equals the world interest rate. When they differ, there will be a linear trend in the current account; we allow for such a trend in our empirical work below.
A.R. Ghosh, J.D. OstrylJournal o f Monetary Economics 40 (1997) 121-139
125
planner's problem, although the competitive equilibrium yields equivalent results. The planner maximizes (1) subject to the economy's dynamic budget constraint: bt=(1
(3)
+r)bt_l +qt-ct-it-gt,
where b is the net level o f foreign assets owned by the country, q is the level of output (GDP), i is the level o f investment, and 9 is the level o f government consumption. We assume that uncovered real interest rate parity holds at all times. Therefore, the assumption that the country is small in the world capital markets means that Fisherian separability will hold here. This implies that investment and output may be treated as given when choosing the optimal path for consumption. 6 Maximizing (1) subject to (3) yields the first-order condition:
(4)
e - ~ c, = E ( e - ~ c,+, [ (2t),
where f2t is the agent's information set at time t. At this point, it is easiest to postulate a process for consumption that satisfies the first-order condition (4) and use it to derive the consumption function. The appendix provides a full derivation. Under certainty equivalence, Hall (1978) shows that consumption follows a process such that its first difference equals the life-time innovation in income. 7 In the model developed here, however, the behavior of the change in consumption reflects a precautionary demand for external saving, which depends upon the variance o f shocks to life-time cash flow. One way to capture the effects o f uncertainty is to consider a comparative statics exercise in which the current account responds to exogenous changes in the variance of life-time cash flow. The problem with such an approach is that even though it tries to identify agents' systematic response to changes in uncertainty within the model, agents are assumed to have assigned a zero probability to such changes. Therefore, in this paper, we assume instead that agents make their consumption decisions taking explicit account o f the stochastic properties of the variance process. 8 Empirically, for our data sets, we find that the variance is either constant, or it follows a stochastic process with an AR(1 ) structure (and parameter p). Our guess for the consumption process is then ct - ct-1 = ~t + A t - 1
St
r+(1
-p)
(5)
6 Notice that the separability between the consumption and investment decisions allow us to write output as exogenous to the consumption decision, but not (necessarily) to the investment decision. 7 Hall (1978) showed that marginal utility follows a random walk; this translates into a random walk for consumption when, as is discussed below, innovations to national cash flow are normally distributed. 8 Caballero (1990) pioneers this approach in the context of a single household facing a labor income process with stochastic higher moments.
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A.I~ Ghosh, ,I.D. OstrylJournal of Monetary Economics 40 (1997) 121-139
where ~t is the life-time innovation in national cash flow, i.e., r oo 1 ~t -- 1 + r i_-~0(1 + r)J E(qt+j -- it+j - gt+j [ (2t) r
1 T- F
~ 1 j=~0(1 + r)J E(qt+j - it+j - Yt+j 1~2,_, ).
(6)
At-1 is the stochastic slope of the consumption path between periods t - 1 and t, which depends on the variance ~t_l,denoted G~_1; and st is the innovation to At .9 Intuitively, under certainty equivalence, the first difference of consumption would just be equal to ~t. In our case, however, there are two additional terms, which reflect precautionary saving behavior. A high value of the variance last period raises At_l, which increases the growth rate of consumption (lowers ct-1), in line with the precautionary saving hypothesis. A positive innovation to the variance today - which implies a positive drawing for the shock st - lowers the growth rate of consumption (lowers ct). If p = 1, so that the innovation to today's variance is expected to be permanent, then agents revise their estimate of the future variance by the full amount of the shock and the effect on consumption growth is equal to the annuity value of the innovation stir. If p < 1, the shock gets reversed in the future, and the effect of the innovation is correspondingly smaller. Substituting (5) into (4) and evaluating the expectation in (4) under the assumption that the innovations are normally distributed yields an expression for At-1. Using this expression in (5) and the transversality condition that the present value of consumption must equal the present value of national cash flow, yields ct. Using the budget constraint (3) and the definition of the current account as the rate of accumulation of foreign assets, C A t = b t bt-l, yields (see Appendix) CAt=-~
j=l
1 (1 + r ) J { E A ( q t + j - i t + j - g t + J ) [ O t } +
c~pa~t 2(r + (1 p ) ) '
(7)
where A is the backward difference operator, A x t = x t - x t - 1 . Eq. (7) shows that the current account can be decomposed into a certainty equivalent term, equal to the expected present value of future declines in cash flow, and a precautionary term which depends on the degree of risk-aversion, ~, and the persistence, p, of the variance shocks. As noted above, the derivations ignore general equilibrium interest rate effects. To the extent that the changes in uncertainty are strongly correlated across countries (which does not appear to be the case empirically -
9 It is straightforward to verify that the innovation to the A process, st, is proportional to the innovation to the variance process; also, it is clear that if the variance process is an AR(1) with parameter, p, then the A process will also be an AR(1) with parameter, p. (See Appendix.)
A.R. Ghosh, ,I.D. O s t r y / J o u r n a l o f M o n e t a r y Economics 40 (1997) 121-139
127
see below), the incipient change in the current account would be absorbed by the world interest rate) ° Finally, if the variance process is constant a~ = 6¢2, then the optimal current account simplifies to ~c 1 0~ 2 CAt ----- ~--~ (1 + r)J { E A ( q t + j - it+j - gt+j) I f2t} + 2--rj=l
(8)
3. Empirical evidence
3.1. H o w i m p o r t a n t can p r e c a u t i o n a r y savin 9 be?
Before proceeding with the econometric analysis, it is worth pausing to ask how large precautionary saving effects could be, given plausible assumptions about the relevant parameters. Assume, for simplicity, that the variance of the innovation to national cash flow is constant, then the precautionary saving component of the current account is given by the second term of (8). Estimates of the degree of relative risk-aversion vary widely in the empirical literature; some of Hall's (1988) estimates would put this parameter well above 10, while estimates ranging between 2 and 5 are fairly common) 1 A reasonable range of values is therefore 1-10, with higher values possible, though less likely) 2 Now we need an estimate of the variance of the life-time innovation to national cash flow, (re2 . The simplest approach would be to estimate a univariate autoregression in national cash flow: A ( q t - it - y t ) = ~ l A ( q t - 1
- i t - l - g t - l ) + £t.
(9)
Then from (6) ~t - -
gt
1 - ~h/(1 + r ) '
(10)
so that an estimate of 5~ can be obtained from (10) directly. 13 The first two columns of Table l report the estimate of 5~ and the resulting precautionary
t0 The same logic applies to innovations to national cash flow in the context of the certaintyequivalent version of the model [see Ghosh (1995)]. ii Carroll (1992) notes that a consensus value of the coefficient of relative risk-aversion would be about 3; but he adds that empirical estimates frequently place its value well above 5. See also Mankiw and Zeldes (1990) for estimates from microeconomic data. On the interaction between risk-aversion and intertemporal substitution see Kimball and Weil (1992). t2 Note that the empirical literature typically identifies the coefficient of relative risk-aversion, ~ r while a is the degree of absolute risk-aversion. They are related by the formula a = cd/( where ~ is the mean level of consumption. 13 In all calculations below, 1/(1 + r ) - 0 . 9 5 .
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saving component under alternative assumptions about the degree of relative riskaversion, expressed both as a percentage o f the mean current account and of the mean absolute current account. 14 Note that the first term o f (7) or (8) - the present value o f expected changes in NCF - can be either positive or negative while the second term, corresponding to precautionary motives, is necessarily non-negative. The fractions reported in Table 1 therefore indicate the extent to which precautionary motives might be an important factor in explaining observed external saving. Since this may be zero on average, we also report the ratio to the mean absolute value o f the current account as well. For a risk-aversion coefficient equal to 3, the fraction o f external saving which could be explained by precautionary motives is substantial, ranging around 6 - 4 5 % o f the (absolute value o f ) the current account. Such estimates suggest that, for reasonable values o f the behavioral parameters, uncertainty about national cash flow could indeed be a significant determinant o f the current account. One problem with this univariate approach, however, is that agents will typically have more information about the future evolution o f national cash flow than is contained in its own past values. This implies that the innovation to lifetime cash flow, ~t, calculated using expectations conditional on the econometrician's information set Ot will not, in general, equal the true innovation calculated using expectations conditional on agents' information set, ~2t; because Ot will be a subset o f f2t. Since the variance o f an expectation conditional on an information set is a non-decreasing function o f the size o f that information set, this means that the estimate of 6¢2 using (10) will generally be smaller than the true 6~2 (where the latter is the variance o f the innovation to lifetime cash flow using expectations conditional on agents' entire information set f2t). Under the null hypothesis that the model is true, however, it is possible to include all the relevant data in the econometrician's data set, 6)t. As argued by Campbell and Shiller (1988) in a somewhat different context, the current account itself should incorporate any additional information that agents may have: from (8) the certainty-equivalent portion o f the current account is equal to the expected present value o f changes in national cash flow where the expectation is conditional on agents' entire information set, f2t. Formally, if agents have substantially more information about the evolution o f national cash flow than is contained in its own past values, then the current account should Granger-cause changes in national cash flow. This suggests that a more appropriate way to calculate 6¢2 would be
14For the United States the units are billions of dollars (base 1985). For the remaining countries, national currencies were converted into dollars using the average exchange rate for the entire sample. Data are from the International Financial Statistics of the IMF. Private consumption, c; government consumption, 9; investment, i; GNP, y; GDP, q; c a - y - c - i - 9. All data are converted into real terms by dividing by the implicit GDP deflator. To construct the long time-series for the United States we use two sources. For the period 1919-1983 we use the historical national accounts put together in Gordon (1983), while for the subsequent period we use the IFS.
A.R. Ghosh, ,I.D. OstrylJournal of Monetary Economics 40 (1997) 121-139 Table 1 Potential magnitude of precautionary motive (univariate estimate of
Country United ~r ~r
_ _
=
a~
129
cry)
100 x - ~ / / C A
100
~2
__
States 1
215.5
18.2
3.3
3
215.5
54.7
9.9
215.5
182.3
32.9
c~r = 10 United States (1919-1990) c~r = 1
102.7
19.5
14.5
er = 3
102.7
58.4
43.6
~r = 10
102.7
194.8
145.4
Japan c~r = 1
27.7
8.0
6.4
c~r = 3
27.7
24.0
19.1
c~r = 10
27.7
80.2
63.8
Germany :~r = 1
9.6
2.1
2.1
c~r = 3
9.6
6.4
6.3
c~r - 10
9.6
21.3
21.1
~r = 1
23.6
30.9
7.1
cer -- 3
23.6
92.8
21.3
c~r = 10
23.6
309.3
71.0
United Kingdom
Canada cd = I
4.6
-5.3
c~r = 3
4.6
- 16.0
15.0
5.0
c~r = 10
4.6
-53.4
50.0
to first estimate the bivariate vector autoregression:
I
A(qt-it-gt) CAt
][ =
7[
~'11
~12
I//21
I//22 J
A(qt-l-it-l--g,-l) CAt-I
+
'st 2
,st
'
(11) and then use the relation
~,=[10][I-7t/(l+r)]-I
['S~] '$2
•
The first two columns of Table 2 report the variance of ff~ calculated using the VAR and the implied fraction of the current account surplus that could
130
A.1L Ghosh, J.D. O s t r y / J o u r n a l
of Monetary Economics 40 (1997) 121-139
Table 2 Potential magnitude of precautionary motive (VAR estimate of a ~ )
Country United States or = 1
8? -
100 X ~ 2t / - -
=r '/CA
100 X ~ 2t /
zr
--
/ICA[
I00× ~p~r~ / e ~ -
2<~+<,-v))/
100X~pa2t /
--
2 ,+ ,_L/IcAI
395.2
34,5
6.3
2.3
~r=3
395.2
103.5
18.7
6.9
0.4 1,0
~r = 10
395.2
345.0
62,5
19.0
3.4
(1919-1990) ~r = 1
104.9
26.9
19.7
1.5
1.1
c~r = 3 c~r = 10
104.9 104.9
80.7 270.0
59.2 197.4
4.6 15.3
3,4 11,4
~r = 1 0~r = 3
28.9 28.9
8.5 25.4
6.7 20.2
0.4 1.3
0,4 1.0
~r = 10
28.9
84.6
67.3
4.3
3.5
12.5 12.5 12.5
2.8 8.3 27,6
2.7 8.2 27.4
or = 1 ~r = 3
26.8 26.8
34.1 102.4
7.8 23.5
1.0 2.9
0.2 0.7
o r = 10
26.8
341.4
78.3
9.8
2.2
United States
Japan
Germany or = 1 c~r = 3 ~r = 10
United Kingdom
Canada c~r = 1 or = 3
5.1 5.1
--5.9 --17.6
5.4 16,4
c~r = 10
5.1
-58.6
54.3
be attributed to a precautionary motive; as expected, these are larger than the corresponding entries in Table 1 though the differences are modest. The major difference is for the two United States data sets; this is consistent with the results reported in Table 5 below where the evidence for Granger causality is strongest for the United States. The estimates reported in the second and third columns o f Table 2 are derived under the assumption that the variance of it is constant and, as such, represent the maximum precautionary saving effect. 15 When the variance is not constant, the precautionary saving effect is given by the second term in (7), where p is the persistence of the variance process. To obtain an estimate of p we estimate an
15 Notice from (7) that the precautionary saving term is at a maximum when p = 1.
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131
Table 3 ARCH Estimates of p Country United States United States (1919 Japan Germany United Kingdom Canada
1990)
p
SE
0.57 0.39 0.50 0.39 0.39 0.04
0.22** 0.08** 0.18"* 0.26 0.18"* 0.31
Note: ** indicates significance at the 5% level.
ARCH model for the process A ( q t - i t - gt). 16 We find strong evidence in favor of such a time-varying variance of the error term in four of the six data sets (both US data sets, the UK and Japan) though not for Canada and Germany. 17 Table 3 reports maximum likelihood estimates of the ARCH coefficient, p, together with its standard error. Allowing for time-varying variances lowers the estimate of the maximum precautionary saving motive considerably but it can still account for an appreciable portion of observed current account surpluses (see the fourth and fifth column of Table 2).
3.2. Direct evidence The results reported above indicate that precautionary saving could be important for the behavior of the current account, but do not, of course, provide any direct evidence that such effects have been present. To test for such effects, we use Eq. (7). Since we identify the effects of precautionary saving behavior by changes in uncertainty about the macroeconomic environment, our test cannot be applied to countries in which there is no time-varying component of azt (Canada and Germany). This does not imply that precautionary saving motives are unimportant for explaining the behavior of the current account of these countries but simply that our methodology cannot identify such effects. (In essence, the precautionary saving effect would be captured entirely by the constant term of the regression and therefore would not be easily distinguishable from any other effects that may be present.) We thus proceed for the remaining data sets in which national cash flow follows an ARCH process. As a preliminary step, Table 4 reports augmented Dickey-Fuller statistics for the current account (with deterministic trend removed) and the level of national cash flow for the four data
16Eq. (11) can be estimated by a multivariate ARCH model [see Kraft and Engle (1983), Bollerslev et al. (1988)] but in practice we find little evidence of a time-varying error variance in the current account process. We also experimented with more general processes for a~2t, but found the ARCH(I ) process to be adequate. 17 See note to Table 3.
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132
Table 4 t-statistics for ADF tests on CA and NCF Country
CA
(q - i - g)
United States United States (1919-1990) Japan United Kingdom
-3.90 -4.25 -3.67 -3.11
1.90 3.52 2.32 1.59
sets. For the relevant infinite sums to converge we require that the variables in the VAR estimated below be stationary, which they will be as long as (qt- it- 9t) is I ( 1 ) and CAt is I(0); as indicated in Table 4 these conditions are satisfied in each case. Since we use a maximum likelihood technique for estimating the ARCH models, we obtain the time-series for a~t directly. The coefficient on a~t is then a function of the coefficient of absolute risk-aversion, the interest rate, and the persistence of the variance process, as summarized by the second term of (7). To obtain the first term we follow Ghosh (1995) Sheffrin and Woo (1990) and Otto (1992) and project the vector autoregression (11) forwards:
Et [A(qt+k--it+k--gt+k)]
= [1~21 ~t22~q2]k[A(qt--it--Yt) CAt
so that 1
PDV
=- - ~
j=l - tl
(I + r)J {EA((qt+J - it+j - 9t+j))If2t}
0]~P/(1 + r ) [ I
(12)
- W/(1 q-r)] -1 [ A(qt - i t - 9 t ) ]
1
CAt
J
(13)
which is just a linear combination of the change in national cash flow and the current account; where the VAR parameters W are reported in Table 5. Substituting for the present discounted value of expected changes in national cash flow, PDV, from (13) into (7) then yields our regression test:
CAt = flo + flla~t + fl2PDVt + v,. We use lagged values of the current account and the change in national cash flow to instrument for PDV. In addition, as stressed by Pagan (1984), the standard error on the precautionary saving term will be incorrect unless it is estimated by an instrumental variable since our proxy of macroeconomic uncertainty, a~t, constitutes a 'constructed' regressor; we use lagged values of a~t as instruments. Table 6 reports the coefficients from this regression together with their heteroscedastic-consistent standard errors. For each of the four data sets we find
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Table 5 VAR parameters (row variables regressed on column variables) Country
A ( q t - 1 -- it-1 -- Or-1 )
SE
CAt_l
SE
--0.009 -0.194
0.083** 0.068**
--0.135 0.860
0.039** 0.036**
0.172 -0.019
0.059** 0.032
--0.097 0.931
0.040** 0.021"*
--0.003 -0.045
0.080 0.748
--0.03 0.903
0.048 0.051"*
--0.408 --0.088
0.083** 0.074
--0.051 0.874
0.055 0.005**
United States A ( q t -- il -- gt) CAt
United States (1919-1990) A ( q t -- it -- .qt) CAt
Japan A ( q t -- it -- Or) CAt
United Kingdom A ( q t -- it -- 9t) CAt
Note: ** indicates significance at the 5% level.
Table 6 Effect of precautionary saving on CA Country
~l
Se(~l )
~2
Se(~2 )
United States United States (1919-1990) Japan United Kingdom
0.004 0.019 0.001 0.180
0.002** 0.009** 0.0006"* 0.112"
1.12 0.93 3.23 2.97
0.006** 0.010"* 0.007"* 0.035**
Note: • and ** indicates significance levels at the 10% and 5% levels, respectively. evidence in favor o f a precautionary saving effect on the current account with the coefficient o n trot b e i n g positive and statistically significant as predicted by the t h e o r y ) 8 The results are particularly e n c o u r a g i n g for both U S data sets and for Japan, where the precautionary saving term is significant at the 5% level or better. U s i n g the point estimates o f p obtained above, moreover, the regression coefficients i m p l y degrees o f relative risk-aversion r a n g i n g from s o m e w h a t over unity for Japan to about 10 for the U n i t e d States. In turn, these imply that precautionary motives can account for about 1% o f the observed current account surplus o f Japan and about 5 - 1 9 % o f the US surplus (Table 7). For the U K , the results are more mixed. The statistical significance is lower and the implied degree o f relative risk-aversion seems i m p l a u s i b l y high
18If macroeconomic uncertainty moves together in different countries, the increase in uncertainty would be reflected in the interest rate rather than the current account. Empirically, however, the cross-country correlation of a~2tare extremely small, ranging between -0.02 and 0.13.
134
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Table 7 Average contributionof uncertaintyto current account (absolute values) Country
~¢2t
United States United States (1919-1990) Japan United Kingdom
420 98 30 23
100 × fl%~
ICAI
5 19 1 45
(around 100). It should be emphasized, however, that these implied risk-aversion coefficients are only approximate, being predicated on (and rather sensitive to), inter alia, the estimated degree of persistence, p. Another way to understand these results is to undertake the same exercise reported in Zeldes (1989). Suppose that a¢2., were one (of its own) standard deviations higher; what would be the effect on the (absolute value) of the current account? Using these estimates, we find that the (absolute value) of the US current account would have been 2.7% higher (and 13.4% higher for the long sample); the Japanese current account would have been 0.5% higher; and the UK current account some 35% higher. 19 Turning to the P D V term, it is positive and highly significant, suggesting that the intertemporal model performs reasonably in its other implications as well. Consistent with the findings of Ghosh (1995) (who examines the US, Japan, Germany, the UK, and Canada) and Otto (1992) (who examines the US and Canada), this coefficient is greater than unity for countries other than the United States. It bears emphasis that this effect is quite independent of any precautionary saving motives of external saving; Ghosh (1995) discusses this finding in terms of excess volatility of the current account in response to speculative capital flows. The P D V term captures much of the high-frequency movement of the current account. If precautionary saving is to explain the remainder, then (CA - P D V ) should be positive. Fig. 1 provides a graphical presentation of the regression results, with the solid line representing our measure of uncertainty, and the dashed line the current account controlling for its certainty-equivalent component. As required by the model, the residual of (CA - P D V ) is generally positive and, particularly for the United States, well correlated with uncertainty. The oil shocks (1974 and 1979) appear to be the only periods in which the uncertainty measure is correlated across our three countries. Both the United States and Japan responded by sharp increases in their current accounts (controlling for the P D V term); in the United Kingdom an increase in the current account is only seen one year later. During the second oil shock, the United States and the United Kingdom show improvements in the current account, but not Japan (again, controlling for the 19The effect on the average current account (as opposed to the average of the absolute value of the current account) is of course larger.
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136
A.K Ghosh, J.D. OstrylJournal of Monetary Economics 40 (1997) 121-139
P D V term). Finally, for the United States, there are various spikes of heightened uncertainty during the 1980s, generally matched by increases in external savings.
4. Conclusions This paper develops a simple optimizing model of an open economy in order to examine the role of macroeconomic uncertainty in determining the current account. The current account may be decomposed into two additive terms: (i) a component which is equal to the present value of expected declines in national cash flow; and (ii) a component which depends upon the degree of macroeconomic uncertainty. The second component, corresponding to the individual's precautionary saving motive, depends upon the degree of risk-aversion, the variance of the life-time innovations to national cash flow, and the degree of persistence of such innovations. The variance of the life-time innovation to national cash flow, in turn, is increasing in the degree of persistence of the underlying stochastic process for national cash flow. Under plausible assumptions about preferences, and the degree of risk aversion, precautionary motives can account for quantitatively important fractions of observed external saving in each of the six data sets considered here. Our results suggest that, at times of heightened macroeconomic uncertainty, agents will seek to increase their external saving and this should be reflected in current account surpluses. To the extent that all of the major industrialized countries attempt to increase their surpluses, of course, the net effect would be a change in world interest rates. Typically, however, our measure of uncertainty is not highly correlated across countries, presumably because even common shocks (such as oil price changes) affect the major industrialized countries differently. Thus, macroeconomic uncertainty may indeed be an important determinant of current account dynamics.
Appendix In this appendix we derive the expression for the current account, given in Eq. (7) of the text. We proceed in three steps. First we show that our guess for the consumption process satisfies the Euler equation (5). Substituting (6) into (5) yields: e-~C, = Ete-~[c,+~,+~-s,+d(r+O-p))+Ad.
(A. 1)
Since ct and At are in the information set at time t, we can solve for the slope of the consumption process, At
1
¢rrt+ I
At = - [ l n E t e - ~ ¢ ' + ' + l n E t e ~ ] . O~
(A.2)
A.R. Ghosh, ,I.D. OstrylJournal o f Monetary Economics 40 (1997) 121-139
137
Under the assumption that ~t+l is normally distributed with mean zero and variance ~r~t+l, the expectation in (A.2) can be evaluated to yield: At=
(A.3)
2Etff~t+l + const.
If ¢r~ follows an AR(1) process with parameter p, then the expression for At simplifies to: 2° ~P 2 At = --f tr~t+ const.
(A.4)
Clearly, with At so defined, our guess for the consumption process satisfies the Euler equation. Second, we show that the consumption function is ct = yP
At r+(1 -p)
(A.5)
where yP, 'permanent cash-flow', is given by ytp = rbt + ~
OO
Y~j=0 (7@+~)JE,(qt+j
-- it+j -- gt+j).
To verify the consumption function, we need to show that (A.5) satisfies (6), which, as shown above, satisfies the Euler equation with At given by (A.4). Substituting (A.5) into the consumption process, (6) gives Ct - - C t - - I
A t -- A t - I
r + ( 1 - p)'
=YP - Y : - I
but from the budget constraint, YP -- Y Pt--I = ~t +
rAt-1
21
r+(1 -p)"
2o Notice At will also follow an AR(I ) with parameter p since: ~P
2
Et nat = ~Et-lcr~t = ~ p a ~ t _ t = p A t - l .
y: - yL~ = y f - (l + r ) y L , +ryf_, -- 1 + r
~
~
Et(qt+j - it+j -- Ot+j) --Et-l(qt+j -- it+j -- Yt+j)
j=0 (1 + r ) ( q t - I -- it-I -- Yt-1) / + r[bt -- (1 +r)bt_l + YP-I]" Using (3) and (A.5): bt--(1 + r ) b t - l - - ( q t - l - - i t - i --gt 1)=c~-t, Ct-l = Y t Q I - - A t _ l / [ r + ( 1 --p)]. Therefore, yf - ytP_l = ~t + (rAt_l/r + (1 - p)).
138
A.R Ghosh,J.D. OstrylJournalof Monetary Economics40 (1997) 121-139
Therefore, ct - c t - 1 = it + A t - 1 - ( st/r q- ( 1 - p ) ) since A t = p A t - 1 -'If-St. Thus the consumption function (A.5) satisfies the Euler equation. Finally, substituting (A.5) into (3): cat=bt-bt-l=(qt+rbt-it-gt)-
=qt--it--gt r
--
yP
r+(1---p)
r ~ ( 1 )j A, l~r.j~_o ~ Et(qt+j-it+j-gt+J)+r+(l_p )
° ° ( 1 )
j
l~_r.j~=l ~
which, upon substitution of At,
At EtA(qt+j-it+J--gt+J)+r+(1-p) is
Eq. (7) of the text.
References Arrow, K.J., 1965. Aspects of the Theory of Risk Bearing. Yrjo Jahnsson Lectures, Helsinki. Baxter, M., Jermann, U., King, R., 1995. Nontraded Goods, Nontraded Factors, and International Non-Diversification, NBER Working Paper 5175. Bollerslev, T., Engle, R., Wooldridge, J., 1988. A capital asset pricing model with time-varying covariances. Journal of Political Economy 96, 116-131. Caballero, R.J., 1990. Consumption puzzles and precautionary savings. Journal of Monetary Economics 25, 113-136. Campbell, J., Shiller, R., 1988. Stock prices, earnings, and expected dividends. Journal of Finance 43, 661-676. Carroll, C., 1992. The buffer-stock theory of saving. Some macroeconomic evidence. Brookings Papers on Economic Activity 2, 661-135. Dreze, J., Modigliani, F., 1972. Consumption decisions under uncertainty. Journal of Economic Theory 5, 308-335. Fisher, M., 1956. Exploration in savings behavior. Oxford University Institute of Economics and Statistics Bulletin XVIII, 201-278. Frenkel, J., Razin, A., 1987. Fiscal Policies and the World Economy: An Intertempoml Approach, MIT Press. Friedman, M., 1957. A Theory of the Consumption Function. Princeton University Press. Ghosh, A., 1995. International capital mobility amongst the major industrialised countries: Too little or too much? Economic Journal 105, 107-128. Gordon, R., (Ed.), 1986. The American Business Cycle: Continuity and Change. University of Chicago Press. Hall, R., 1978. Stochastic implications of the life-cycle-permanent income hypothesis. Journal of Political Economy 86, 971-988. Hall, R., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96, 339-357. Kimball, M., 1990. Precautionary saving in the small and in the large. Econometrica 58, 53-73. Kimball, M., Weil, P., 1992. Precautionary saving and consumption smoothing across time and possibilities. NBER Working Paper No. 3976. Kraft, D., Engle, R., 1983. Autoregressive Conditional Heteroscedasticity in Multiple Time-Series. Mimeo, UC, San Diego. Leland, H., 1968. Saving and uncertainty: the precautionary demand for saving. Quarterly Journal of Economics 82, 465-473.
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139
Miller, B., 1976. The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case. Journal of Economic Theory 13, 154 167. Otto, G., 1992. Testing a present value model of the current account: Evidence from US and Canadian time-series. Journal of International Money and Finance 11, 414-430. Pagan, A., 1984. Econometric issues in the analysis of regressions with generated regressors. International Economic Review 25, 221-247. Pratt, J., 1964. Risk aversion in the small and in the large. Econometrica 32, 122 136. Sachs, J., 1982. The current account and the macroeconomic adjustment process. Scandinavian Journal of Economics 84, 147 159. Sandmo, A., 1970. The effect of uncertainty on savings decisions. Review of Economic Studies 37, 353 -360. Sheffrin, S., Woo, W.T., 1990. Present value tests of an intertemporal model of the current account. Journal of International Economics 29, 237-253. Skinner, J., 1988. Risky income, life-cycle consumption, and precautionary savings. Journal of Monetary Economics 22, 237-255. Zeldes, S., 1989. Optimal consumption with stochastic income: Deviations from certainty equivalence. Quarterly Journal of Economics 104, 275-298.
Monetary
ELSEVIER
Journal of Monetary Economics 40 (1997) 121-139
ECA)NOMICS
Macroeconomic uncertainty, precautionary saving, and the current account Atish R. Ghosh, Jonathan D. Ostry* International Monetary Fund, Washington, DC 20431, USA Received January 1995; final version received January 1997
Abstract The relationship between current account developments and changes in the macroeconomic environment is a key issue in open economy macroeconomics. This paper extends the standard intertemporal model of the current account to incorporate the effects of macroeconomic uncertainty on external saving behavior. It is shown that the greater the uncertainty in national cash flow, defined as output less investment less government consumption, the greater will be the incentive for precautionary saving and, ceteris paribus, the larger the current account surplus. Empirical support for the model is found using post-war quarterly data for the United States, Japan, and the United Kingdom, as well as a long time series (1919-90) for the United States.
Keywords: Current account; Precautionary saving JEL classification: C32; E21; F32
1. Introduction
The relationship between the current account and the macroeconomic environment remains a key issue in open economy macroeconomics. Modem theories of the current account [see, for example, Sachs (1982), Frenkel and Razin (1987)]
* Corresponding author. Tel.: 202-623-7405; fax: 202-623-6336; e-mail: [email protected]. We are grateful to John Campbell, Ricardo Caballero, an anonymous referee, and seminar participants at Princeton, NYU, the Board of Governors of the Federal Reserve, and the Econometric Society Meetings for useful comments and suggestions. 0304-3932/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved, Pll S 0 3 0 4 - 3 9 3 2 ( 9 7 ) 0 0 0 3 1-7
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emphasize its consumption-smoothing role in the face o f shocks to national cash flow, defined as output less investment less government consumption. The expected time profile o f national cash flow serves as a sufficient statistic for the determination o f the current account in these models. Thus, a country should dissave externally whenever individuals in the economy believe that current national cash flow is temporarily below its permanent level, regardless o f the source o f the shock to national cash flow. Typically, these models assume perfect foresight. But this leads to a logical inconsistency, i.e., the models are specifically designed to examine the behavior o f optimizing agents in the face o f various stochastic shocks, but those agents are assumed to have assigned a zero probability to these shocks ever occurring (or, alternatively, certainty equivalence is imposed). Not surprisingly, if instead agents are assumed to know that they live in a stochastic environment, the implied behavior o f the current account becomes rather different. In this paper we examine current account dynamics in an explicitly stochastic macroeconomic environment. Our starting point is the closed-economy work on the behavior o f individual saving when agents are subject to uninsurable labor income variability. In that literature it is well-known that an increase in income uncertainty will result in greater saving, 1 because o f a precautionary motive (see, e.g. Caballero, 1990). 2 While there is a growing body o f literature that examines the empirical evidence for precautionary saving at the level o f the individual in a closed economy setting, surprisingly little attention has been paid to the open economy implications. Yet, i f precautionary savings represent a significant portion o f aggregate savings, as Zeldes (1989) and Caballero (1990) among others contend, then it should be reflected in data on the current account which, after all, measures the country's aggregate external saving. To examine the effect o f precautionary saving on the current account, this paper relates aggregate income uncertainty (or, more precisely, uncertainty about national cash flow) to the level o f external savings. I f incomes are perfectly pooled across individuals - as a representative agent model assumes - then it
1This result depends on the technical assumption that the utility function has a positive third derivative. Kimball (1990) establishes a measure of the strength of the precautionary saving motive that is isomorphic to the measures of risk-aversion familiar from the work of Pratt (1964) and Arrow (1965); see Kimball (1991). On the interaction between risk-aversion and intertemporal substitution, see Kimball and Weil (1992). 2 The early literature on precautionary saving helped explain the empirical findings of Fisher (1956) and Friedman (1957) about differences in saving rates across groups whose earnings have different risk characteristics. Using two-period models, Leland (1968), Sandmo (1970), and Dreze and Modigliani (1972) showed that there would be a precautionary motive for saving as long as marginal utility is convex. Miller (1976) confirmed these results in a multi-period setting. More recently, Skinner (1988) has argued that precautionary savings account for a significant proportion of total savings in the United States. Zeldes (1989), Caballero (1990), and Carroll (1992) have exploited the notion of a precautionary demand for savings to explain several 'puzzles' in the consumption literature.
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123
is only that component of income which cannot be diversified at the national level which affects precautionary saving. Since individuals typically do not share risks perfectly, aggregate income uncertainty is only a proxy for (unobservable) individual income uncertainty, and its importance for external saving depends upon the extent to which these measures are correlated. Conversely, since there is at least some risk sharing within a country, the magnitude of national income uncertainty will be proportionately smaller than individual uncertainty. This is sometimes interpreted as implying that a precautionary motive proxied by aggregate income uncertainty cannot be important for aggregate saving. But it does not imply that precautionary motives cannot be an important component of external saving. Simply put, while aggregate income uncertainty may be as much as an order of magnitude smaller than individual uncertainty, external saving is typically two orders of magnitude smaller than national saving. Thus uncertainty about the evolution of cash flow could indeed be an important determinant of the current account. 3 We begin, in Section 2, by deriving the current account in a fully optimizing model of an open economy in which agents are assumed to take explicit account of the stochastic environment. The optimal current account is shown to consist of two components. The first, which is also present in models which assume certainty equivalence, is equal to the present discounted value of expected declines in national cash flow. If national cash flow is, on average, expected to grow over time; this term is negative, and the current account will be in deficit, as agents dissave against resources they expect to earn in the future. The second component, which is present only when uncertainty is explicitly incorporated, is proportional to the variance of life-time innovations to national cash flow. This term reflects the role of precautionary saving in the current account. Ceteris paribus, an increase in this variance will lead to greater precautionary saving and to a larger current account surplus. Section 3 turns to the empirical evidence using quarterly data from 1955 to 1990 for five of the G-7 industrialized countries. 4 In addition, for the United States, we use a separate data set spanning the period 1919-90. This is a very long-time series by any account and provides a rich setting in which to examine whether precautionary effects may be present in the determination of the current account. Before discussing the econometric results, we first establish whether, for plausible values of the parameters of the utility function, the precautionary saving component could represent an appreciable fraction of observed current account surpluses. Our results are largely encouraging. Assuming a risk-aversion
3 Another issue is whether international portfolio diversification makes the variability of NCF an overestimate of the uncertainty faced by individuals. Empirically, however, most portfolios exhibit a strong 'home bias', so diversification is likely to be limited in practice (see, for example, Baxter et al.. 1995). 4 France and Italy were omitted because they lack the necessary quarterly national accounts data.
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124
coefficient of 3, for example, precautionary motives could account for 2 - 7 % of observed current account surpluses. We then examine the role of precautionary saving directly by measuring the response of the current account to the timevarying component of our measure of macroeconomic uncertainty. In two of our data sets the time-variation of uncertainty is too small to enable us to reliably estimate its effect on the current account. It bears emphasizing that this does not imply that a precautionary saving motive is not important in these cases, but merely that our methodology cannot identify it. In the remaining four cases we do find evidence in favor of a precautionary saving component of the current account, the evidence being strongest in the two US datasets. Section 4 offers some brief concluding remarks.
2. The model We use the standard, infinite horizon, small open economy model of international borrowing and lending as the basis of our theoretical framework. While the assumption of a small open economy may appear suspect when considering current account movements of countries as large as the United States, ultimately the adequacy of the model is an empirical issue. The results reported below, and the findings of Ghosh (1995), Sheffrin and Woo (1990) and Otto (1992), suggest that the model is capable of explaining developments in the current accounts of the major countries. These empirical results suggest that even for large industrialized countries, general equilibrium effects, operating through changes in an endogenous world interest rate, are not large. The economy is assumed to be populated by a single, infinitely-lived, representative agent whose preferences are given by 5
1
t=O
(1 +r)~
EU(c,),
(1)
where U(.) is the instantaneous utility function, r is the world interest rate, and ct denotes consumption of the single good. With a view to empirical implementation, we assume
U(ct) = (1/ct)e -~c',
(2)
where e > 0 is the Arrow-Pratt measure of (absolute) risk-aversion. Although this utility function does not bound consumption away from zero, it is chosen because it yields a closed-form solution for the consumption function in the presence of time-varying uncertainty. It is simplest to work in terms of the social
5 The derivation here assumes that the subjective discount rate equals the world interest rate. When they differ, there will be a linear trend in the current account; we allow for such a trend in our empirical work below.
A.R. Ghosh, J.D. OstrylJournal o f Monetary Economics 40 (1997) 121-139
125
planner's problem, although the competitive equilibrium yields equivalent results. The planner maximizes (1) subject to the economy's dynamic budget constraint: bt=(1
(3)
+r)bt_l +qt-ct-it-gt,
where b is the net level o f foreign assets owned by the country, q is the level of output (GDP), i is the level o f investment, and 9 is the level o f government consumption. We assume that uncovered real interest rate parity holds at all times. Therefore, the assumption that the country is small in the world capital markets means that Fisherian separability will hold here. This implies that investment and output may be treated as given when choosing the optimal path for consumption. 6 Maximizing (1) subject to (3) yields the first-order condition:
(4)
e - ~ c, = E ( e - ~ c,+, [ (2t),
where f2t is the agent's information set at time t. At this point, it is easiest to postulate a process for consumption that satisfies the first-order condition (4) and use it to derive the consumption function. The appendix provides a full derivation. Under certainty equivalence, Hall (1978) shows that consumption follows a process such that its first difference equals the life-time innovation in income. 7 In the model developed here, however, the behavior of the change in consumption reflects a precautionary demand for external saving, which depends upon the variance o f shocks to life-time cash flow. One way to capture the effects o f uncertainty is to consider a comparative statics exercise in which the current account responds to exogenous changes in the variance of life-time cash flow. The problem with such an approach is that even though it tries to identify agents' systematic response to changes in uncertainty within the model, agents are assumed to have assigned a zero probability to such changes. Therefore, in this paper, we assume instead that agents make their consumption decisions taking explicit account o f the stochastic properties of the variance process. 8 Empirically, for our data sets, we find that the variance is either constant, or it follows a stochastic process with an AR(1 ) structure (and parameter p). Our guess for the consumption process is then ct - ct-1 = ~t + A t - 1
St
r+(1
-p)
(5)
6 Notice that the separability between the consumption and investment decisions allow us to write output as exogenous to the consumption decision, but not (necessarily) to the investment decision. 7 Hall (1978) showed that marginal utility follows a random walk; this translates into a random walk for consumption when, as is discussed below, innovations to national cash flow are normally distributed. 8 Caballero (1990) pioneers this approach in the context of a single household facing a labor income process with stochastic higher moments.
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A.I~ Ghosh, ,I.D. OstrylJournal of Monetary Economics 40 (1997) 121-139
where ~t is the life-time innovation in national cash flow, i.e., r oo 1 ~t -- 1 + r i_-~0(1 + r)J E(qt+j -- it+j - gt+j [ (2t) r
1 T- F
~ 1 j=~0(1 + r)J E(qt+j - it+j - Yt+j 1~2,_, ).
(6)
At-1 is the stochastic slope of the consumption path between periods t - 1 and t, which depends on the variance ~t_l,denoted G~_1; and st is the innovation to At .9 Intuitively, under certainty equivalence, the first difference of consumption would just be equal to ~t. In our case, however, there are two additional terms, which reflect precautionary saving behavior. A high value of the variance last period raises At_l, which increases the growth rate of consumption (lowers ct-1), in line with the precautionary saving hypothesis. A positive innovation to the variance today - which implies a positive drawing for the shock st - lowers the growth rate of consumption (lowers ct). If p = 1, so that the innovation to today's variance is expected to be permanent, then agents revise their estimate of the future variance by the full amount of the shock and the effect on consumption growth is equal to the annuity value of the innovation stir. If p < 1, the shock gets reversed in the future, and the effect of the innovation is correspondingly smaller. Substituting (5) into (4) and evaluating the expectation in (4) under the assumption that the innovations are normally distributed yields an expression for At-1. Using this expression in (5) and the transversality condition that the present value of consumption must equal the present value of national cash flow, yields ct. Using the budget constraint (3) and the definition of the current account as the rate of accumulation of foreign assets, C A t = b t bt-l, yields (see Appendix) CAt=-~
j=l
1 (1 + r ) J { E A ( q t + j - i t + j - g t + J ) [ O t } +
c~pa~t 2(r + (1 p ) ) '
(7)
where A is the backward difference operator, A x t = x t - x t - 1 . Eq. (7) shows that the current account can be decomposed into a certainty equivalent term, equal to the expected present value of future declines in cash flow, and a precautionary term which depends on the degree of risk-aversion, ~, and the persistence, p, of the variance shocks. As noted above, the derivations ignore general equilibrium interest rate effects. To the extent that the changes in uncertainty are strongly correlated across countries (which does not appear to be the case empirically -
9 It is straightforward to verify that the innovation to the A process, st, is proportional to the innovation to the variance process; also, it is clear that if the variance process is an AR(1) with parameter, p, then the A process will also be an AR(1) with parameter, p. (See Appendix.)
A.R. Ghosh, ,I.D. O s t r y / J o u r n a l o f M o n e t a r y Economics 40 (1997) 121-139
127
see below), the incipient change in the current account would be absorbed by the world interest rate) ° Finally, if the variance process is constant a~ = 6¢2, then the optimal current account simplifies to ~c 1 0~ 2 CAt ----- ~--~ (1 + r)J { E A ( q t + j - it+j - gt+j) I f2t} + 2--rj=l
(8)
3. Empirical evidence
3.1. H o w i m p o r t a n t can p r e c a u t i o n a r y savin 9 be?
Before proceeding with the econometric analysis, it is worth pausing to ask how large precautionary saving effects could be, given plausible assumptions about the relevant parameters. Assume, for simplicity, that the variance of the innovation to national cash flow is constant, then the precautionary saving component of the current account is given by the second term of (8). Estimates of the degree of relative risk-aversion vary widely in the empirical literature; some of Hall's (1988) estimates would put this parameter well above 10, while estimates ranging between 2 and 5 are fairly common) 1 A reasonable range of values is therefore 1-10, with higher values possible, though less likely) 2 Now we need an estimate of the variance of the life-time innovation to national cash flow, (re2 . The simplest approach would be to estimate a univariate autoregression in national cash flow: A ( q t - it - y t ) = ~ l A ( q t - 1
- i t - l - g t - l ) + £t.
(9)
Then from (6) ~t - -
gt
1 - ~h/(1 + r ) '
(10)
so that an estimate of 5~ can be obtained from (10) directly. 13 The first two columns of Table l report the estimate of 5~ and the resulting precautionary
t0 The same logic applies to innovations to national cash flow in the context of the certaintyequivalent version of the model [see Ghosh (1995)]. ii Carroll (1992) notes that a consensus value of the coefficient of relative risk-aversion would be about 3; but he adds that empirical estimates frequently place its value well above 5. See also Mankiw and Zeldes (1990) for estimates from microeconomic data. On the interaction between risk-aversion and intertemporal substitution see Kimball and Weil (1992). t2 Note that the empirical literature typically identifies the coefficient of relative risk-aversion, ~ r while a is the degree of absolute risk-aversion. They are related by the formula a = cd/( where ~ is the mean level of consumption. 13 In all calculations below, 1/(1 + r ) - 0 . 9 5 .
128
A.I~ Ghosh, ,I.D. Ostry/Journal of Monetary Economics 40 (1997) 121-139
saving component under alternative assumptions about the degree of relative riskaversion, expressed both as a percentage o f the mean current account and of the mean absolute current account. 14 Note that the first term o f (7) or (8) - the present value o f expected changes in NCF - can be either positive or negative while the second term, corresponding to precautionary motives, is necessarily non-negative. The fractions reported in Table 1 therefore indicate the extent to which precautionary motives might be an important factor in explaining observed external saving. Since this may be zero on average, we also report the ratio to the mean absolute value o f the current account as well. For a risk-aversion coefficient equal to 3, the fraction o f external saving which could be explained by precautionary motives is substantial, ranging around 6 - 4 5 % o f the (absolute value o f ) the current account. Such estimates suggest that, for reasonable values o f the behavioral parameters, uncertainty about national cash flow could indeed be a significant determinant o f the current account. One problem with this univariate approach, however, is that agents will typically have more information about the future evolution o f national cash flow than is contained in its own past values. This implies that the innovation to lifetime cash flow, ~t, calculated using expectations conditional on the econometrician's information set Ot will not, in general, equal the true innovation calculated using expectations conditional on agents' information set, ~2t; because Ot will be a subset o f f2t. Since the variance o f an expectation conditional on an information set is a non-decreasing function o f the size o f that information set, this means that the estimate of 6¢2 using (10) will generally be smaller than the true 6~2 (where the latter is the variance o f the innovation to lifetime cash flow using expectations conditional on agents' entire information set f2t). Under the null hypothesis that the model is true, however, it is possible to include all the relevant data in the econometrician's data set, 6)t. As argued by Campbell and Shiller (1988) in a somewhat different context, the current account itself should incorporate any additional information that agents may have: from (8) the certainty-equivalent portion o f the current account is equal to the expected present value o f changes in national cash flow where the expectation is conditional on agents' entire information set, f2t. Formally, if agents have substantially more information about the evolution o f national cash flow than is contained in its own past values, then the current account should Granger-cause changes in national cash flow. This suggests that a more appropriate way to calculate 6¢2 would be
14For the United States the units are billions of dollars (base 1985). For the remaining countries, national currencies were converted into dollars using the average exchange rate for the entire sample. Data are from the International Financial Statistics of the IMF. Private consumption, c; government consumption, 9; investment, i; GNP, y; GDP, q; c a - y - c - i - 9. All data are converted into real terms by dividing by the implicit GDP deflator. To construct the long time-series for the United States we use two sources. For the period 1919-1983 we use the historical national accounts put together in Gordon (1983), while for the subsequent period we use the IFS.
A.R. Ghosh, ,I.D. OstrylJournal of Monetary Economics 40 (1997) 121-139 Table 1 Potential magnitude of precautionary motive (univariate estimate of
Country United ~r ~r
_ _
=
a~
129
cry)
100 x - ~ / / C A
100
~2
__
States 1
215.5
18.2
3.3
3
215.5
54.7
9.9
215.5
182.3
32.9
c~r = 10 United States (1919-1990) c~r = 1
102.7
19.5
14.5
er = 3
102.7
58.4
43.6
~r = 10
102.7
194.8
145.4
Japan c~r = 1
27.7
8.0
6.4
c~r = 3
27.7
24.0
19.1
c~r = 10
27.7
80.2
63.8
Germany :~r = 1
9.6
2.1
2.1
c~r = 3
9.6
6.4
6.3
c~r - 10
9.6
21.3
21.1
~r = 1
23.6
30.9
7.1
cer -- 3
23.6
92.8
21.3
c~r = 10
23.6
309.3
71.0
United Kingdom
Canada cd = I
4.6
-5.3
c~r = 3
4.6
- 16.0
15.0
5.0
c~r = 10
4.6
-53.4
50.0
to first estimate the bivariate vector autoregression:
I
A(qt-it-gt) CAt
][ =
7[
~'11
~12
I//21
I//22 J
A(qt-l-it-l--g,-l) CAt-I
+
'st 2
,st
'
(11) and then use the relation
~,=[10][I-7t/(l+r)]-I
['S~] '$2
•
The first two columns of Table 2 report the variance of ff~ calculated using the VAR and the implied fraction of the current account surplus that could
130
A.1L Ghosh, J.D. O s t r y / J o u r n a l
of Monetary Economics 40 (1997) 121-139
Table 2 Potential magnitude of precautionary motive (VAR estimate of a ~ )
Country United States or = 1
8? -
100 X ~ 2t / - -
=r '/CA
100 X ~ 2t /
zr
--
/ICA[
I00× ~p~r~ / e ~ -
2<~+<,-v))/
100X~pa2t /
--
2 ,+ ,_L/IcAI
395.2
34,5
6.3
2.3
~r=3
395.2
103.5
18.7
6.9
0.4 1,0
~r = 10
395.2
345.0
62,5
19.0
3.4
(1919-1990) ~r = 1
104.9
26.9
19.7
1.5
1.1
c~r = 3 c~r = 10
104.9 104.9
80.7 270.0
59.2 197.4
4.6 15.3
3,4 11,4
~r = 1 0~r = 3
28.9 28.9
8.5 25.4
6.7 20.2
0.4 1.3
0,4 1.0
~r = 10
28.9
84.6
67.3
4.3
3.5
12.5 12.5 12.5
2.8 8.3 27,6
2.7 8.2 27.4
or = 1 ~r = 3
26.8 26.8
34.1 102.4
7.8 23.5
1.0 2.9
0.2 0.7
o r = 10
26.8
341.4
78.3
9.8
2.2
United States
Japan
Germany or = 1 c~r = 3 ~r = 10
United Kingdom
Canada c~r = 1 or = 3
5.1 5.1
--5.9 --17.6
5.4 16,4
c~r = 10
5.1
-58.6
54.3
be attributed to a precautionary motive; as expected, these are larger than the corresponding entries in Table 1 though the differences are modest. The major difference is for the two United States data sets; this is consistent with the results reported in Table 5 below where the evidence for Granger causality is strongest for the United States. The estimates reported in the second and third columns o f Table 2 are derived under the assumption that the variance of it is constant and, as such, represent the maximum precautionary saving effect. 15 When the variance is not constant, the precautionary saving effect is given by the second term in (7), where p is the persistence of the variance process. To obtain an estimate of p we estimate an
15 Notice from (7) that the precautionary saving term is at a maximum when p = 1.
A.R. Ghosh, J.D. Ostry/Journal o[ Monetary Economics 40 (1997) 121 139
131
Table 3 ARCH Estimates of p Country United States United States (1919 Japan Germany United Kingdom Canada
1990)
p
SE
0.57 0.39 0.50 0.39 0.39 0.04
0.22** 0.08** 0.18"* 0.26 0.18"* 0.31
Note: ** indicates significance at the 5% level.
ARCH model for the process A ( q t - i t - gt). 16 We find strong evidence in favor of such a time-varying variance of the error term in four of the six data sets (both US data sets, the UK and Japan) though not for Canada and Germany. 17 Table 3 reports maximum likelihood estimates of the ARCH coefficient, p, together with its standard error. Allowing for time-varying variances lowers the estimate of the maximum precautionary saving motive considerably but it can still account for an appreciable portion of observed current account surpluses (see the fourth and fifth column of Table 2).
3.2. Direct evidence The results reported above indicate that precautionary saving could be important for the behavior of the current account, but do not, of course, provide any direct evidence that such effects have been present. To test for such effects, we use Eq. (7). Since we identify the effects of precautionary saving behavior by changes in uncertainty about the macroeconomic environment, our test cannot be applied to countries in which there is no time-varying component of azt (Canada and Germany). This does not imply that precautionary saving motives are unimportant for explaining the behavior of the current account of these countries but simply that our methodology cannot identify such effects. (In essence, the precautionary saving effect would be captured entirely by the constant term of the regression and therefore would not be easily distinguishable from any other effects that may be present.) We thus proceed for the remaining data sets in which national cash flow follows an ARCH process. As a preliminary step, Table 4 reports augmented Dickey-Fuller statistics for the current account (with deterministic trend removed) and the level of national cash flow for the four data
16Eq. (11) can be estimated by a multivariate ARCH model [see Kraft and Engle (1983), Bollerslev et al. (1988)] but in practice we find little evidence of a time-varying error variance in the current account process. We also experimented with more general processes for a~2t, but found the ARCH(I ) process to be adequate. 17 See note to Table 3.
A.R. Ghosh, J.D. Ostry/Journal of Monetary Economics 40 (1997) 121-139
132
Table 4 t-statistics for ADF tests on CA and NCF Country
CA
(q - i - g)
United States United States (1919-1990) Japan United Kingdom
-3.90 -4.25 -3.67 -3.11
1.90 3.52 2.32 1.59
sets. For the relevant infinite sums to converge we require that the variables in the VAR estimated below be stationary, which they will be as long as (qt- it- 9t) is I ( 1 ) and CAt is I(0); as indicated in Table 4 these conditions are satisfied in each case. Since we use a maximum likelihood technique for estimating the ARCH models, we obtain the time-series for a~t directly. The coefficient on a~t is then a function of the coefficient of absolute risk-aversion, the interest rate, and the persistence of the variance process, as summarized by the second term of (7). To obtain the first term we follow Ghosh (1995) Sheffrin and Woo (1990) and Otto (1992) and project the vector autoregression (11) forwards:
Et [A(qt+k--it+k--gt+k)]
= [1~21 ~t22~q2]k[A(qt--it--Yt) CAt
so that 1
PDV
=- - ~
j=l - tl
(I + r)J {EA((qt+J - it+j - 9t+j))If2t}
0]~P/(1 + r ) [ I
(12)
- W/(1 q-r)] -1 [ A(qt - i t - 9 t ) ]
1
CAt
J
(13)
which is just a linear combination of the change in national cash flow and the current account; where the VAR parameters W are reported in Table 5. Substituting for the present discounted value of expected changes in national cash flow, PDV, from (13) into (7) then yields our regression test:
CAt = flo + flla~t + fl2PDVt + v,. We use lagged values of the current account and the change in national cash flow to instrument for PDV. In addition, as stressed by Pagan (1984), the standard error on the precautionary saving term will be incorrect unless it is estimated by an instrumental variable since our proxy of macroeconomic uncertainty, a~t, constitutes a 'constructed' regressor; we use lagged values of a~t as instruments. Table 6 reports the coefficients from this regression together with their heteroscedastic-consistent standard errors. For each of the four data sets we find
A . R . Ghosh, .LD. O s t r y / J o u r n a l
133
o f M o n e t a r y E c o n o m i c s 40 ( 1 9 9 7 ) 121 139
Table 5 VAR parameters (row variables regressed on column variables) Country
A ( q t - 1 -- it-1 -- Or-1 )
SE
CAt_l
SE
--0.009 -0.194
0.083** 0.068**
--0.135 0.860
0.039** 0.036**
0.172 -0.019
0.059** 0.032
--0.097 0.931
0.040** 0.021"*
--0.003 -0.045
0.080 0.748
--0.03 0.903
0.048 0.051"*
--0.408 --0.088
0.083** 0.074
--0.051 0.874
0.055 0.005**
United States A ( q t -- il -- gt) CAt
United States (1919-1990) A ( q t -- it -- .qt) CAt
Japan A ( q t -- it -- Or) CAt
United Kingdom A ( q t -- it -- 9t) CAt
Note: ** indicates significance at the 5% level.
Table 6 Effect of precautionary saving on CA Country
~l
Se(~l )
~2
Se(~2 )
United States United States (1919-1990) Japan United Kingdom
0.004 0.019 0.001 0.180
0.002** 0.009** 0.0006"* 0.112"
1.12 0.93 3.23 2.97
0.006** 0.010"* 0.007"* 0.035**
Note: • and ** indicates significance levels at the 10% and 5% levels, respectively. evidence in favor o f a precautionary saving effect on the current account with the coefficient o n trot b e i n g positive and statistically significant as predicted by the t h e o r y ) 8 The results are particularly e n c o u r a g i n g for both U S data sets and for Japan, where the precautionary saving term is significant at the 5% level or better. U s i n g the point estimates o f p obtained above, moreover, the regression coefficients i m p l y degrees o f relative risk-aversion r a n g i n g from s o m e w h a t over unity for Japan to about 10 for the U n i t e d States. In turn, these imply that precautionary motives can account for about 1% o f the observed current account surplus o f Japan and about 5 - 1 9 % o f the US surplus (Table 7). For the U K , the results are more mixed. The statistical significance is lower and the implied degree o f relative risk-aversion seems i m p l a u s i b l y high
18If macroeconomic uncertainty moves together in different countries, the increase in uncertainty would be reflected in the interest rate rather than the current account. Empirically, however, the cross-country correlation of a~2tare extremely small, ranging between -0.02 and 0.13.
134
A.R. Ghosh, J.D. Ostry/Journal of Monetary Economics 40 (1997) 121-139
Table 7 Average contributionof uncertaintyto current account (absolute values) Country
~¢2t
United States United States (1919-1990) Japan United Kingdom
420 98 30 23
100 × fl%~
ICAI
5 19 1 45
(around 100). It should be emphasized, however, that these implied risk-aversion coefficients are only approximate, being predicated on (and rather sensitive to), inter alia, the estimated degree of persistence, p. Another way to understand these results is to undertake the same exercise reported in Zeldes (1989). Suppose that a¢2., were one (of its own) standard deviations higher; what would be the effect on the (absolute value) of the current account? Using these estimates, we find that the (absolute value) of the US current account would have been 2.7% higher (and 13.4% higher for the long sample); the Japanese current account would have been 0.5% higher; and the UK current account some 35% higher. 19 Turning to the P D V term, it is positive and highly significant, suggesting that the intertemporal model performs reasonably in its other implications as well. Consistent with the findings of Ghosh (1995) (who examines the US, Japan, Germany, the UK, and Canada) and Otto (1992) (who examines the US and Canada), this coefficient is greater than unity for countries other than the United States. It bears emphasis that this effect is quite independent of any precautionary saving motives of external saving; Ghosh (1995) discusses this finding in terms of excess volatility of the current account in response to speculative capital flows. The P D V term captures much of the high-frequency movement of the current account. If precautionary saving is to explain the remainder, then (CA - P D V ) should be positive. Fig. 1 provides a graphical presentation of the regression results, with the solid line representing our measure of uncertainty, and the dashed line the current account controlling for its certainty-equivalent component. As required by the model, the residual of (CA - P D V ) is generally positive and, particularly for the United States, well correlated with uncertainty. The oil shocks (1974 and 1979) appear to be the only periods in which the uncertainty measure is correlated across our three countries. Both the United States and Japan responded by sharp increases in their current accounts (controlling for the P D V term); in the United Kingdom an increase in the current account is only seen one year later. During the second oil shock, the United States and the United Kingdom show improvements in the current account, but not Japan (again, controlling for the 19The effect on the average current account (as opposed to the average of the absolute value of the current account) is of course larger.
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z~.
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~.~! ~.m~.
~
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~.~ o0~ zz~
z.~. tm~.
.~..~6~.
~.t-
t
i!
" '
~
,~
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"i
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-
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g~-[
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096T
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136
A.K Ghosh, J.D. OstrylJournal of Monetary Economics 40 (1997) 121-139
P D V term). Finally, for the United States, there are various spikes of heightened uncertainty during the 1980s, generally matched by increases in external savings.
4. Conclusions This paper develops a simple optimizing model of an open economy in order to examine the role of macroeconomic uncertainty in determining the current account. The current account may be decomposed into two additive terms: (i) a component which is equal to the present value of expected declines in national cash flow; and (ii) a component which depends upon the degree of macroeconomic uncertainty. The second component, corresponding to the individual's precautionary saving motive, depends upon the degree of risk-aversion, the variance of the life-time innovations to national cash flow, and the degree of persistence of such innovations. The variance of the life-time innovation to national cash flow, in turn, is increasing in the degree of persistence of the underlying stochastic process for national cash flow. Under plausible assumptions about preferences, and the degree of risk aversion, precautionary motives can account for quantitatively important fractions of observed external saving in each of the six data sets considered here. Our results suggest that, at times of heightened macroeconomic uncertainty, agents will seek to increase their external saving and this should be reflected in current account surpluses. To the extent that all of the major industrialized countries attempt to increase their surpluses, of course, the net effect would be a change in world interest rates. Typically, however, our measure of uncertainty is not highly correlated across countries, presumably because even common shocks (such as oil price changes) affect the major industrialized countries differently. Thus, macroeconomic uncertainty may indeed be an important determinant of current account dynamics.
Appendix In this appendix we derive the expression for the current account, given in Eq. (7) of the text. We proceed in three steps. First we show that our guess for the consumption process satisfies the Euler equation (5). Substituting (6) into (5) yields: e-~C, = Ete-~[c,+~,+~-s,+d(r+O-p))+Ad.
(A. 1)
Since ct and At are in the information set at time t, we can solve for the slope of the consumption process, At
1
¢rrt+ I
At = - [ l n E t e - ~ ¢ ' + ' + l n E t e ~ ] . O~
(A.2)
A.R. Ghosh, ,I.D. OstrylJournal o f Monetary Economics 40 (1997) 121-139
137
Under the assumption that ~t+l is normally distributed with mean zero and variance ~r~t+l, the expectation in (A.2) can be evaluated to yield: At=
(A.3)
2Etff~t+l + const.
If ¢r~ follows an AR(1) process with parameter p, then the expression for At simplifies to: 2° ~P 2 At = --f tr~t+ const.
(A.4)
Clearly, with At so defined, our guess for the consumption process satisfies the Euler equation. Second, we show that the consumption function is ct = yP
At r+(1 -p)
(A.5)
where yP, 'permanent cash-flow', is given by ytp = rbt + ~
OO
Y~j=0 (7@+~)JE,(qt+j
-- it+j -- gt+j).
To verify the consumption function, we need to show that (A.5) satisfies (6), which, as shown above, satisfies the Euler equation with At given by (A.4). Substituting (A.5) into the consumption process, (6) gives Ct - - C t - - I
A t -- A t - I
r + ( 1 - p)'
=YP - Y : - I
but from the budget constraint, YP -- Y Pt--I = ~t +
rAt-1
21
r+(1 -p)"
2o Notice At will also follow an AR(I ) with parameter p since: ~P
2
Et nat = ~Et-lcr~t = ~ p a ~ t _ t = p A t - l .
y: - yL~ = y f - (l + r ) y L , +ryf_, -- 1 + r
~
~
Et(qt+j - it+j -- Ot+j) --Et-l(qt+j -- it+j -- Yt+j)
j=0 (1 + r ) ( q t - I -- it-I -- Yt-1) / + r[bt -- (1 +r)bt_l + YP-I]" Using (3) and (A.5): bt--(1 + r ) b t - l - - ( q t - l - - i t - i --gt 1)=c~-t, Ct-l = Y t Q I - - A t _ l / [ r + ( 1 --p)]. Therefore, yf - ytP_l = ~t + (rAt_l/r + (1 - p)).
138
A.R Ghosh,J.D. OstrylJournalof Monetary Economics40 (1997) 121-139
Therefore, ct - c t - 1 = it + A t - 1 - ( st/r q- ( 1 - p ) ) since A t = p A t - 1 -'If-St. Thus the consumption function (A.5) satisfies the Euler equation. Finally, substituting (A.5) into (3): cat=bt-bt-l=(qt+rbt-it-gt)-
=qt--it--gt r
--
yP
r+(1---p)
r ~ ( 1 )j A, l~r.j~_o ~ Et(qt+j-it+j-gt+J)+r+(l_p )
° ° ( 1 )
j
l~_r.j~=l ~
which, upon substitution of At,
At EtA(qt+j-it+J--gt+J)+r+(1-p) is
Eq. (7) of the text.
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Miller, B., 1976. The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case. Journal of Economic Theory 13, 154 167. Otto, G., 1992. Testing a present value model of the current account: Evidence from US and Canadian time-series. Journal of International Money and Finance 11, 414-430. Pagan, A., 1984. Econometric issues in the analysis of regressions with generated regressors. International Economic Review 25, 221-247. Pratt, J., 1964. Risk aversion in the small and in the large. Econometrica 32, 122 136. Sachs, J., 1982. The current account and the macroeconomic adjustment process. Scandinavian Journal of Economics 84, 147 159. Sandmo, A., 1970. The effect of uncertainty on savings decisions. Review of Economic Studies 37, 353 -360. Sheffrin, S., Woo, W.T., 1990. Present value tests of an intertemporal model of the current account. Journal of International Economics 29, 237-253. Skinner, J., 1988. Risky income, life-cycle consumption, and precautionary savings. Journal of Monetary Economics 22, 237-255. Zeldes, S., 1989. Optimal consumption with stochastic income: Deviations from certainty equivalence. Quarterly Journal of Economics 104, 275-298.