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:

or

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 σ_st is the covariance between S* and I*, σ²_l is the variance of I*, and σ_ZI is the covariance between Z* and I*. After a little manipulation. (2) can be rewritten as follows:

or

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 σ²_s<σ²_l. Thus, θ will be zero only if β = 1 and σ²_l=σ²_s. It follows, therefore, that Feldstein and Horioka’s finding that $\hat{\beta }$ is not significantly different from unity is consistent with $\hat{\theta }$ being negative and statistically significant, as in Sachs’s papers. Indeed, this is what Penati and Dooley (1984, Table 1, rows 9–12, p. 4) obtained when they used the same data set to run the Feldstein-Horioka and Sachs regressions. Penati and Dooley invoke the accounting identity (1) to require θ to be zero if β is unity; but it is precisely that identity that will not permit this except in the special case where β is unity and the variances of I* and S* are equal.³

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 $\hat{\theta }$ is, by and large, insignificant. It may well be, as Penati and Dooley argue, that the Feldstein-Horioka regression represents the structural model, and that the Sachs results are unreliable and influenced by outliers. But this is different from arguing that Sachs’s results are inconsistent with those of Feldstein and Horioka. In fact, Sachs’s original results are no more in conflict with Feldstein and Horioka’s than are Penati and Dooley’s results from the Sachs equations in which $\hat{\theta }$ is not statistically significant.

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).