In a set of papers, Feldstein and Horioka (1980) and Feldstein (1983) examined data for industrial countries and concluded that there was little capital mobility between them. However, results from a set of studies by Sachs (1981, 1983) are viewed by Penati and Dooley (1984, pp. 5–6), and Dooley, Frankel, and Mathieson (1987, p. 512), as being in conflict with the Feldstein-Horioka findings. The Penati-Dooley study attempts to resolve this conflict (see Section III of their paper) by reexamining the evidence. They conclude that the Feldstein-Horioka findings are robust, and the conflicting results obtained by Sachs are largely a result of statistical problems.
The purpose of this comment is not to question the robustness of the Feldstein-Horioka findings or, for that matter, the substantive issues dealt with in the studies by Penati and Dooley and Dooley, Frankel, and Mathieson.1 Rather, we argue that there is no conflict between the Sachs and Feldstein-Horioka findings, and that the analysis conducted by Penati and Dooley to resolve that “conflict” suffers from some problems of its own.
In order to develop our argument, we start with the basic identity that underlies each of the aforementioned studies:
where S denotes saving, I denotes investment, Z denotes current account balance, and S*, I*, and Z* are these variables deflated by gross national product/gross domestic product (GNP/GDP). Feldstein and Horioka ran regressions of I* on S* for a sample of industrial countries and found that the slope coefficient in those regressions was consistently not statistically different from unity and hence indicated low capital mobility between those countries. Sachs, however, regressed Z* on I* and found a statistically significant negative slope coefficient.2 These findings are viewed as being in conflict by Penati and Dooley and by Dooley, Frankel, and Mathieson; they contend that if, as the Feldstein-Horioka findings imply, an increase in saving translates into an almost equivalent increase in investment, then one could expect that, given the underlying identity (1), Z* should be independent of I*. But although this argument is perfectly logical, it need not be implied in the aforementioned regressions. This can be seen as follows.
Using (1), it can be shown that the covariance between I* and S* is
where σst is the covariance between S* and I*, σ2l is the variance of I*, and σZI is the covariance between Z* and I*. After a little manipulation. (2) can be rewritten as follows:
where β is the slope coefficient in a regression of I* on S*, and θ is the slope coefficient of a regression of Z* on I*. It follows immediately that even if β= 1, θ can be negative, provided that σ2s<σ2l. Thus, θ will be zero only if β = 1 and σ2l=σ2s. It follows, therefore, that Feldstein and Horioka’s finding that
In light of the above, it is not clear what Penati and Dooley achieve when they re-estimate the Feldstein-Horioka and Sachs equations over various sample periods and find that the Feldstein-Horioka results are robust, but
In this context, it may be noted that Penati and Dooley estimate the Sachs and Feldstein-Horioka equations jointly under the restriction β + θ = 1. As we have argued, this restriction is not permitted by equation (3), and is hence incorrect. Joint estimation under this restriction, not surprisingly, biases the results. This can be seen as follows. The two regressions in question are
It can be shown that estimating equations (4) and (5) jointly under the aforementioned restriction is equivalent to regressing S* on I* under the restriction that the slope coefficient is unity. We can thus write
where δ0 = (α + γ)/(1–β), δ1 =–θ/(β–1), and η = w/(1 - β). Clearly, if the restriction θ + β = 1 is imposed, δ1 = 1. But given (2), this forces θ to zero and β to unity. Thus, the joint estimation of (4) and (5) under the aforementioned restriction is a priori biased against the Sachs finding (and in favor of the Feldstein-Horioka finding). In actual estimation, the estimates of β and θ may differ from unity and zero, respectively. But this would be so only because of rounding errors, or if I*, S*, and Z* were measured such that the identity (1) is not exactly satisfied. The latter appears to be the case in the Penati and Dooley study (see Table 6 and the discussion on p. 17), since they do not include inventory investment in their measure of I.
Finally, it may be noted that when Penati and Dooley estimate Sachs’s equation (5) using instrumental variables, the estimate of θ is found to be insignificant. Although we agree that an instrumental variables approach to estimation is correct under the circumstances, Penati and Dooley’s choice of the instrument is open to question. They use the fitted values of I* obtained from an ordinary-least-squares regression of Feldstein and Horioka’s equation (4), ordinarily a good choice for an instrument, since it is likely to be highly correlated with I*. However, in the current context, there are weighty arguments against this choice. The need for the instrumental variables method is no less applicable in the Feldstein-Horioka regressions than it is in the Sachs equation, a point recognized by Feldstein and Horioka themselves and by others as well, in view of the likely existence of shocks common to I*, S*, and Z* .4 This implies that S* would be correlated with the disturbance term in the Feldstein-Horioka regression, and I* would be correlated with the disturbance term in the Sachs equation, thereby necessitating the instrumental variables approach in both equations. However, Penati and Dooley’s choice of instrument for the Sachs equation is questionable, because their method is equivalent to regressing Z* on a linear transformation of S*. This defeats the very rationale for the instrumental variables approach, since the chosen instrument is correlated with the disturbance term. Consequently, it is not clear why Penati and Dooley’s instrumental variables regressions “are sufficient to cast doubt on the specification of the Sachs equation” (p. 16).
DooleyMichaelJeffreyFrankel and Donald J.Mathieson“International Capital Mobility: What Do Saving-Investment Correlations Tell Us?”Staff PapersInternational Monetary Fund,Vol. 34 (September1987) pp. 503–30.
FeldsteinMartin“Domestic Saving and International Capital Movements in the Long Run and the Short Run,”European Economic ReviewVol. 21 (March/April1983) pp. 129–51.
FeldsteinMartin and C.Horioka“Domestic Savings and International Capital Flows,”Economic JournalVol. 90 (June1980) pp. 314–29.
MurphyR.“Capital Mobility and the Relationship between Saving and Investment Rates in OECD Countries,”Journal of International Money and FinanceVol. 3(1984) pp. 327–42.
PenatiAlessandro and MichaelDooley“Current Account Imbalances and Capital Formation in Industrial Countries, 1949–81,”Staff Papers International Monetary Fund Vol. 31 (March1984) pp. 1–24.
SachsJeffrey D.“The Current Account and Macroeconomic Adjustment in the 1970s,”Brookings Papers on Economic Activity: 1 (Washington: The Brookings Institution,1981) pp. 201–68.
SachsJeffrey D.“Aspects of the Current Account Behavior of OECD Economies,”in Recent Issues in the Theory of Exchange Ratesed. by E.Claassenand P.Salin (Amsterdam and New York: North-Hoiland1983).
Atul A. Dar is Associate Professor at Saint Mary’s University in Halifax, Nova Scotia.
Saleh Amirkhalkhali is also Associate Professor at St. Mary’s University.
Indeed, the robustness of the Feldstein-Horioka findings appears to be borne out by the study by Dooley, Frankel, and Mathieson (1987), who conduct an exhaustive empirical examination of Feldstein and Horioka’s findings.
In the Feldstein and Horioka and Sachs studies the dependent and independent variables are measured as averages over specific time intervals, as well as changes in the averages between two subintervals. Although the argument in the text is not cast in terms of changes, it applies equally in those terms too.
Note that a test for the significance of θ is the joint test that σ2s= σ21and β = 1. This is equivalent to testing for the significance of the variance of Z*.