ELSEVIER Journal of Monetary Economics 38 (1996) 303-330

JOURNALOF Monetary ECONOMICS

Taxation and inflation: A new explanation for capital flows

Tamim Bayoumi*'", Joseph Gagnon b aInternational Monetary Fund, Washington, DC 20431, USA

bBoard of Governors of the Federal Reserve System, Washington, DC 20551, USA

(Received October 1993; final version received May 1996)

Abstract

In a world of mobile capital, the current system of taxation implies that the after-tax cost of capital and return to saving in each country are negatively correlated with the rate of inflation. Thus a country's net foreign asset position ought to be negatively correlated with its long-run inflation rate. The magnitude of these effects is shown to be potentially large. For OECD countries, cross-section and time-series regressions confirm that inflation rates are good predictors of net foreign assets. The existing distr ibution of net foreign assets may therefore largely reflect tax distortions.

Key words: Cost of capital; Net foreign assets; Return to saving; Tax distortion

JEL classification: F21; F40; H20

*Corresponding author.

This research was performed in part while Bayoumi was at the Bank of England, and Gagnon was at the University of California at Berkeley and the OECD. We thank David Gruen for bringing this issue to our attention. We also thank Hali Edison, Jon Faust, Allen Frankel, Maxwell Fry, Edward Gardner, David Gordon, Dale Henderson, Lemma Senbet, Hans-Werner Sinn, James Wilcox, two anonymous referees, and seminar participants at the London Business School, the NYU Business School, Georgetown University, the Federal Reserve Bank of San Francisco, and the I M F for helpful comments, and Mark Unferth for able research assistance. This paper represents the views of the authors and should not be interpreted as reflecting the views of the International Monetary Fund, the Board of Governors of the Federal Reserve System, or other members of their staffs.

0304-3932/96/$15.00 1996 Elsevier Science B.V. All rights reserved PII S0304-3932(96)0 1 274-3

304 72 BayoumL J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

1. Introduction

What causes long-term movements of capital from one economy to another? Or, to rephrase the question in terms of the current account balance, what causes persistent current account surpluses or deficits between countries? To most macroeconomists in the 1960s this would have seemed a rather odd question; one of the objectives of economic policy was to ensure that current accounts were not allowed to deviate from their 'basic balance' (which, in practice, was usually zero) for any length of time. With the deregulation of international capital markets in the last two decades, however, persistent capital flows have become a feature of the international economic landscape, with countries like the United States, the United Kingdom, and Australia borrowing from the rest of the world, and Germany and Japan lending to it. This experience is similar to earlier periods with free capital markets. In particular, the period of the classical gold standard from 1880 to 1913 was characterized by large and persistent capital flows from rich and relatively developed countries, such as the United Kingdom and Germany, to nations on the periphery, such as Australia and Canada. 1

While the emergence of significant capital flows in the 1980s may come as little surprise, their incidence is less easy to explain. Unlike the situation during the gold standard, the main flows at present are not from the core developed industrial countries of Northern Europe and North America to the newly emerging periphery. Two of the main capital importers are the United States and the United Kingdom, both part of the industrial core, while one of the main exporters is Japan, the fastest growing country in the OECD. The lack of any unifying explanation is reflected in the discussion of international capital flows. Most explanations point to specific features of the country concerned: For example, the U.S. budget deficit, the high saving rate and demographic profile in Japan, and economic booms in the United Kingdom and Australia.

In this paper we suggest a single mechanism that explains a large part of the capital flows of the 1980s, namely the interaction between nominal interest payments and the tax system. The explanation has two crucial elements. First, since income taxation generally conforms to the residence principle, differences in inflation across countries are reflected one-for-one in before-tax interest rates. Second, because nominal interest receipts are taxable for consumers while payments are tax-deductible for corporations, real after-tax interest rates are low in high-inflation countries and high in low-inflation countries. As a result, capital flows from countries with a low rate of inflation to those with a high rate

1 These flows were considerable, with the average current account surplus of the United Kingdom over this period being 4.5 percent of GDP, while Australia ran an average deficit of 3.7 percent of GDP.

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of inflation. This mechanism can, we believe, explain a significant portion of the capital flows among nations in the 1980s.

The rest of this paper is organized as follows. The next section discusses the earlier literature looking at the relationship between inflation, taxation, and international capital flows. In Section 3, our model of the interaction between taxation and inflation is presented along with numerical simulation results. Section 4 reports empirical tests of the theory, while the final section contains conclusions.

2. Existing literature

The implications of taxing nominal interest income in a closed economy were originally explored by Darby (1975) and Feldstein (1976), who noted that inflation should increase nominal interest rates more than one-for-one in the presence of such taxes, with no effect on the stock of capital. Regressions of the nominal interest rate on measures of inflation expectations, however, have generally found a coefficient of one or less (e.g., Carlson, 1979; Tanzi, 1980). Other researchers noted that these results would be consistent with the Darby/Feldstein hypothesis if the real after-tax rate of interest were negatively correlated with the inflation rate for other reasons. 2

Theoretical research in the context of open economies provides what we believe to be an explanation for this negative correlation. Hartman (1979) showed that when taxation is based on the residence of the investor rather than the source of the income, international arbitrage enforces equality of real before-tax interest rates. A permanent increase in the rate of inflation raises the nominal interest rate by an equal amount, lowering the real after-tax return. Higher inflation increases a country's equilibrium capital stock and decreases its stock of net foreign assets.

Hartman's results were extended by other authors. Howard and Johnson (1982) showed that, while Hartman's result obtains in the long run, in the short run an increase in the inflation rate of a small open economy may lead to some combination of a lower real after-tax interest rate and an expectation of a depreciating real exchange rate. Schinasi (1986) showed how Hartman's finding is modified by the existence of different tax rates on exchange rate gains and interest income. Ben-Zion and Weinblatt (1984), Hansson and Stuart (1986), and McClure (1990) demonstrated that under some tax regimes it is not possible to eliminate all arbitrage opportunities when there are different tax rates and inflation rates across countries. Gruen (1991) appealed to nominal interest

2 In particular, Peek and Wilcox (1984) provided evidence that, despite the low response of nominal interest rates of inflation, agents do respond to taxes on interest income.

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taxation and imperfect goods markets to explain the high nominal interest rate and overvalued real exchange rate of Australia in the late 1980s.

The only empirical study of the international effects of nominal interest taxation, to our knowledge, is by Howard and Johnson (1983). They found evidence that countries with low inflation had appreciating real exchange rates in the mid-1970s, but that this correlation was reversed in the late 1970s. However, they did not provide any evidence on real interest rates or net foreign asset positions.

We believe that the interaction between international capital mobility and the residence principle of taxation can explain the empirical findings on the Darby/Feldstein hypothesis, by providing an explanation for why the real after- tax interest rate appears to be negatively correlated with expected inflation. These results imply that net asset positions ought to be negatively correlated with inflation rates across countries, forming the basis for our empirical analysis.

3. Theory

This section explores the relationship between nominal interest rates, tax- ation, the cost of capital, and real returns to saving for a small open economy. We start by discussing the relationship between nominal interest rates and inflation rates across countries under perfect capital mobility. We then consider the implications of inflation and taxation for the cost of capital, followed by an analysis of the implications for real returns to saving. Finally, we report the implications of these effects for capital stocks and net foreign assets using numerical simulations from a small theoretical model.

3.1. International capital mobility

Assume that corporations are able to borrow and lend freely across countries. Arbitrage ensures that the expected cost of borrowing in the domestic market is equal to the expected cost of borrowing in the foreign market. This relationship is shown by Eq. (1), where the domestic currency interest rate is i, the foreign currency interest rate is i*, the logarithm of the exchange rate is e, A is the difference operator, and % ri., and re are the tax rates on domestic interest income, foreign interest income, and exchange rate gains, respectively:

(1 -- ri)i = (i - zl.)i* + (1 -- ze)Ae. (1)

Assuming that taxation is based on the residency principle, tax rates are independent of the currency of the loan, and hence zi = z~, = re. 3 In long-run

Sin almost all OECD countries any gains or losses on foreign currency borrowing are treated as interest receipts or payments for corporate tax purposes (Alworth and Fritz, 1988; OECD, 1992).

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equilibrium the rate of change of the exchange rate must equal the difference between the domestic and foreign inflation rates, ~ and zt*, or else there would be ever increasing arbitrage opportunities across the domestic and foreign goods markets:

Ae = 7t - re*. (2)

Substituting Eq.(2) into Eq. (1) and simplifying terms yields the following expression for the domestic interest rate as a function of the foreign interest rate and the foreign and domestic inflation rates:

i = i* + 7r - 7z*. (3)

Finally, if we accept the foreign interest and inflation rates as exogenously determined, we can express the effect of a permanent change in the domestic inflation rate on the domestic interest rate in simple terms:

Ai = ATz. (4)

It is worth noting at this point that the open interest rate parity relation as defined by Eq.(1) (with equal tax rates) has been employed by almost all researchers who have explored the implications of tax structures and inflation in international finance. Two recent exceptions are Gordon (1986) and Sinn (1991), who look at interest rate arbitrage from the point of view of the individual saver rather than the corporate borrower or lender. By assuming that exchange rate gains or losses are taxed at a lower rate than interest income, these studies obtain a different interest rate parity relationship which implies that the domes- tic interest rate increases more than proportionally to any increase in the domestic inflation rate. There are several reasons for believing that the effective arbitrage relationship is best described by Eq. (1). First, corporate arbitrage with the rest of the world works identically through both borrowing and lending, whereas individual arbitrage works differently for borrowing and lending be- cause individuals cannot deduct interest payments from their income for tax purposes. Second, many OECD countries do not tax individual exchange rate gains at a lower rate than individual interest income. Third, while individuals in certain countries may see unexploited arbitrage opportunities, the inherent risk and expense of arbitrage at an individual level almost certainly places a compar- atively low ceiling on the total funds available for such arbitrage.

3.2. The cost o f capital 4

We now analyze the effect of domestic inflation on the cost of capital for a corporation in a small open economy. For simplicity we assume that physical

4For more detail on the methodology of this section, see Auerbach (1983).

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capital does not depreciate, and that all physical capital is owned by corpora- tions. 5 The results would be unaffected by a posit ive depreciat ion rate of capital if the tax al lowance for depreciat ion were indexed to the price level. In practice, firms can deduct only the historic depreciat ion cost of capital. The simulat ion results reported in Section 3.4 al low for a posit ive rate of depreciat ion and historical cost depreciat ion allowances. 6 For simplicity, we assume that each corporat ion employs capital and labor only in its home country - a l though it may engage in financial and real transact ions with residents of other countries. 7

The cost of f inancing physical capital by debt, CCd, is equal to the interest payment on debt minus the reduction in corporate taxes due to the deductibi l i ty of interest payments minus any increase in the value of physical capital caused by inflation. This relat ionship is expressed in Eq. (5), where z is the corporate tax rate, which is assumed to be equal for all types of income or loss:

CCd =- (1 -- z) i - - ~t. (5)

The cost of equity-f inanced capital is derived assuming that individual savers equate the real returns to holding debt and equity. The real return to holding debt, rrd, is

rrd = (1 -- Oi)i - - To, (6)

where 0i is the individual interest income tax rate. The real return to holding equity, rre, is the sum of after-tax dividends, d (taxed at rate 0d), and after-tax capital gains, c (taxed at rate 0c), minus inflation:

rr e = (1 - Od)d + (1 -- Oc)c - - ~z. (7)

Of course, the stream of dividend payments is determined endogenously by the firm in response to investment opportunit ies and tax considerations. However, to make the analysis tractable, we express the dividend payout ratio, p, from

5The obvious exception to this assumption is the stock of owner-occupied housing. The effects of inflation on the housing stock are likely to be similar to that on business capital as mortgage interest payments are tax detuctible in most OECD countries (OECD, 1994).

6De la Fuente and Gardner (1990) estimate the cost of capital under a wide range of assumptions. They show that under certain assumptions the inflation-induced tax losses associated with historic cost depreciation can outweigh the benefits from tax deductibility of interest payments. We believe that the assumptions required for this result are implausible: First, the agents arbitraging returns to debt and equity must not face taxes. Second, equity finance must be more important than debt finance at the margin. Third, the depreciation rate of capital must be higher than is typically estimated for total physical capital in OECD countries.

7 The tax treatment of foreign direct investment (FDI) in some OECD countries implies that the cost of capital may differ between domestically-owned and foreign-owned enterprises. Since FDI repre- sents only tiny fraction of the total capital stock in OECD counties, we focus on the cost of capital for domestically-owned finns.

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corporate net income, I, as a parameter. 8 In equilibrium, net earnings that are not paid as dividends must be translated one-for-one into capital gains since they represent an increase in the underlying asset value of the firm. Inflation also increases the nominal value of the firm. Thus, we have the formulae for dividends and capital gains:

d = pl, c = (1 - p)I + n. (8)

The cost of equity-financed capital, cc, can now be derived as the level of net income that is needed to equate individual real returns to debt and equity. This yields:

(1 - o i ) i - (1 - 0c )~ cc~ = I = (9)

(1 - Od)p + (1 - - Oc)(1 -- p)"

An extensive literature exists concerning the relationship between CCd and co,,. Some researchers have focused on specific aspects of the tax structure that might allow CCd and CCe to be equal for some combinations of the debt-equity ratio and the dividend payout ratio. Other researchers have considered omitted factors such as bankruptcy costs and imperfect information to explain the apparent inequality between CCd and cce for arbitrary values of the tax rates. In the interest of generality, we shall try to avoid making unnecessarily restrictive assumptions on the nature of CCd and cce.

We are now able to look at the effect of inflation on the cost of capital. Increasing the rate of inflation unambiguously lowers the cost of debt-financed capital, and it lowers the cost of equity-financed capital for plausible values of the relevant tax rates. To see this, we rewrite Eqs. (5) and (9) in first-difference form using Eq. (4) assuming that tax rates and the dividend payout ratio are fixed: 9

ACCd = -- rAft, (10)

(0~ - Oi)An Acc,, = (11)

(1 - Oa)p + (1 - 0c ) (1 - p ) "

8The following analysis assumes that the dividend payout ratio is invariant to the inflation rate. Whle it is possible to reverse the results of this section if the dividend payout ratio is positively related to the inflation rate, it can be shown that the required sensitivity of the dividend payout ratio of inflation would be implausibly high. In fact, evidence for the Unted States suggests that inflation is negatively correlated with the dividend payout ratio. See Auerbach (1982).

"These equations assume purchasing power parity (PPP) and are therefore betst considered as long-run relationships. I fPPP does not hold in the short run, then a change in the inflation rate may have no effect on the cost of capital initially. However, if agents are rational, then the real exchange rate must have appreciated immediately upon the expectation of higher inflation so that it could begin a gradual real depreciation during the transition to long-run equilibrium. During the transition, the real exchange rate would be overvalued, and therefore would tend to cause a capital inflow. This argument is developed further in Howard and Johnson (1982) and Gruen (1991l.

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Inflation unambiguously lowers the cost of debt-financed capital and it also lowers the cost of equity finance as long as the effective tax rate on individual capital gains is lower than the tax rate on individual interest income.

These inflation effects are large for reasonable values of the various tax rates. In the case of debt finance with a 35 percent corporate tax rate, each additional percentage point of inflation lowers the cost of capital by 35 basis points. For low values of the capital gains tax rate, similar results are obtained for the effect of inflation on the cost of equity capital. By way of contrast, changes in tax rates generally have small and ambiguous effects on the overall cost of capital. For example, increasing the dividend or capital gains tax rate raises the cost of equity capital but has no effect on the cost of debt capital, while increasing the tax rate on interest income lowers the cost of equity finance with no effect on the cost of debt finance. Finally, increasing the corporate profit tax rate lowers the cost of debt capital, but it has no effect on the cost of equity capital. Perhaps more significantly, a percentage point increase in the tax rate has a much smaller effect on the cost of capital than a percentage point increase in the inflation rate in all cases. Assuming a 10 percent interest rate, the effect on the cost of capital of a 1 percentage point change in any tax rate is approximately 10 basis points at most.

3.3. The return to sav ing

The previous section demonstrated that changes in the domestic inflation rate have a large effect on the cost of domestic capital and, by implication, on the desired capital stock. This section considers the effect of inflation on the return to saving and desired national asset holdings. By substitution of Eq. (4) into Eq. (6) we see that an increase in the inflation rate will lower the real return to debt. Because we assumed that individual behavior equates the returns to debt and equity, it follows that inflation reduces the real return to equity by an equal amount:

Arre = Arra = -- OiAIr. (12)

If we allow individuals to hold foreign equity, we must consider the implica- tions of arbitrage on equity returns across countries. 1 Since the domestic country is small, the nominal return to foreign equity in the foreign currency is unaffected by an increase in domestic inflation. A rise in inflation is offset by an expected appreciation of the foreign currency, leaving the real before-tax return in domestic currency unaffected. However, this higher nominal return on foreign

10Consideratio n of corporate arbitrage of equity returns is complicated by tax rates that depend on the fraction of outstanding shares held in the foreign firm. In any event, it seems more reasonable to assume that individuals are the marginal investors in equity.

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holdings is taxed, hence the real after-tax return declines. The same analysis applies to the return on foreign debt. These relat ionships lead to Eq. (13), where foreign asset returns, rr f, depend negatively on the domestic inflation rate:

Arrfe = Art f = - 0eArc. (13)

If the tax rate on exchange rate gains, 0e, is the same as the tax rate on interest income, the real return to domestic individuals declines equally for all assets. 11 These results imply a large effect of inflation on the real return to saving. In the case of a 30 percent tax rate on interest income, each percentage point of addit ional inflation reduces the real return on domestic debt by 30 basis points.

3.4. Numerical analysis

The previous two sections indicate that, ceteris paribus, a higher domest ic inflation rate will reduce both the cost of capital and the return to saving in a small open economy. These effects encourage more domestic investment and less domestic saving, thereby inducing a decline in the current account balance and a lower net foreign asset posit ion. There is a large academic l i terature that discusses the impact of real interest rates on saving and investment. By and large, the macroeconomic l i terature has not found large real interest effects on either variable, which would imply little feedback from the real interest rate to capital flows. However, more recent studies using panel data sets have found significant real interest rate effects (see Attanasio and Weber, 1989, on saving; Auerbach and Hassett, 1991, on investment), suggesting that the earlier time- series results may have been influenced by problems with aggregation and simultaneity. 12 These newer results imply a significant feedback from the real interest rate to capital flows.

To gauge the potential magnitude of the effects of long-term inflation rate differentials on net foreign assets, we conducted numerical s imulations of a model of a small open economy. The model has a Cobb-Doug las product ion function, an interest-elastic money demand, a positive depreciat ion rate of capital, historical cost deduct ion of depreciat ion expense, a positive populat ion growth rate, and an interest-elastic saving rate. Further details are given in the

' ~ If the tax rate on exchange rate gains for individuals is lower than the tax on interest income, the real return on foreign assets does not decline as much as the real return on doemestic assets when domestic inflation increases. In this case, it is impossible for both corporations and individuals to fully arbitrage domestic and foreign returns. In such circumstances, we assume that corporate arbitrage dominates. ~ZBy using the current account - the difference between saving and investment our time-series analysis may have more power to identify a real interest rate effect than by looking at the two series individually.

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Table 1 Effects of changes in inflation and taxation on the capital stock and real net foreign asset holdings (percent of initial output after 5 years)

Simulation Capital stock Real net foreign assets

Inflation + 1% 17 -22 Corporate tax + 1% 4 - 4 Individual interest tax + 1% 0 - 3

appendix. Table 1 displays the effects on the capital stock and real net foreign assets of permanent changes in the inflation rate, the corporate tax rate, and the tax rate on individual interest income. As shown in the first row of the table, a 1 percentage point increase in underlying inflation raises the steady-state capital stock by 6 percent, or 17 percent of initial output. The capital stock reaches its long-run equilibrium in approximately 5 years. Real net foreign assets fall by even more than the increase in the capital stock (22 percent of initial output) due to reduced savings caused by the lower rate of return associated with higher inflation.

The second and third rows of Table 1 show the impact of permanent changes in the tax rates on corporate profit and individual interest income. A 1 percent- age point increase in the corporate tax rate raises the stock of physical capital by 4 percent of output and lowers the stock of net foreign assets by the same amount. This effect is only i of that due to a 1 percentage point rise in inflation. Changes in the tax rate on individual interest income have no effect on the capital stock and a small effect on real net foreign assets.

These results - that capital and net foreign assets are more sensitive to long-term changes in inflation and less sensitive to long-term changes in tax rates are robust to reasonable changes in the values of all of the model parameters. The magnitude of the predicted effect of domestic inflation on net foreign assets is sufficiently large that one would expect to be able to find evidence for it in the data, despite the existence of imperfections in international capital markets.

4. Empirical results

The theoretical model implies that, if taxation is based on the residence principle and purchasing power parity is expected to hold, long-term inflation differentials should have no effect on the real before-tax interest rate and a negative effect on the real after-tax interest rate. This in turn implies that the net foreign asset position of a country should be directly related to long-term differences between its rates of inflation and taxation and those of the rest of the

T. Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330 313

world, with the major effect coming through differences in inflation rates. This section investigates the empirical validity of these propositions.

4.1. Interest rates and inflation rates'

For there to be a stable relationship between net foreign assets and inflation, inflation rate differentials must be persistent. To test this proposition, average inflation rates across 22 OECD countries were calculated over 1973-76, 1977 80, 1981 84, and 1985 88. We carried out two tests of the links between inflation differentials over time: first, we calculated cross-country correlation coefficients for inflation over these different periods; next, we ran regressions of inflation across countries in one period on inflation in the previous period. All of the correlation coefficients - including that between inflation in 1973-76 and 1985-88 - were over 0.8, indicating that inflation differentials were highly correlated over time. The regressions yielded coefficients on lagged inflation of 1.3, 1.2, and 0.5 for 1977-80, 1981-84, and 1985-88, respectively. All the coefficients were highly significant, with standard errors of 0.1 or lower, again illustrating the important role of past inflation differentials in predicting future inflation behavior over the period.

One of the crucial assumptions made in the theoretical model is that purchas- ing power parity (PPP) is expected to hold, and hence that future movements in the exchange rate are related to inflation differentials. Empirically, PPP is not a good model of short-term movements in exchange rates, however it does appear to be useful in explaining long-term exchange rate changes (Abuaf and Jorion, 1990; MacDonald and Taylor, 1992).

Our empirical analysis starts with an investigation of the relationship between interest rates and inflation rates across countries. Earlier studies on this topic have focused on the time-series relationship in individual countries. 13 In this section, we test the cross-sectional relationship between inflation and interest rates. 14 Annual data on short- and long-term interest rates were collected over the 1980 89 period from International Financial Statistics for 17 industrial countries.iS The short rates generally represent interbank rates, and the long rates represent government bond rates. Inflation rates, measured using the implicit consumption deflator from OECD Annual National Accounts, were collected for all 17 countries from 1980 to 1990.

~3 MacDonald and Taylor (1990) has a survey on the literature relating interest rates to exchange rates and inflation rates. Other references are given below.

14For a panel-data study of real interest rates in OECD countries, see Gagnon and Unferth (19951.

L SCanada, the United States, Japan, Australia, Austria, Belgium, Denmark, France, Germany, Ireland, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland, and the United Kingdom.

314 T. BayoumL J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

We next proceed to test whether inflation expectations are reflected one-for- one in long-term interest rates. If we assume rational expectations in the bond markets, then the actual inflation over the lifetime of the bond will represent an unbiased estimate of the expected inflation rate over the future. Hence, the coefficient fl in the equation

ii(t, t + k) = at + fl~zj(t, t + k) (14)

will represent the relationship between inflation and the nominal interest rate, where ij(t, t + k) is the interest rate in country j over period t to t + k and rtj(t, t + k) is the actual inflation over the same period. The intercept term is allowed to vary over time to control for movements in the real rate of interest, however, the estimate of fl is not sensitive to constraints on the intercept.

The long-term interest rates generally represent a composite of bonds of different maturities. 16 In the estimation, we used inflation over the subsequent four years as our measure of future inflation. For the last three years, this measure was truncated due to the lack of the full future data set. To increase the power of the test all of the time periods were pooled, producing a data set of 170 observations, iv This regression produced the following results:

ij, t ---- at + 1.037Zj, t+k, (o.o9)

Adj. R 2 = 0.55, No. of obs. = 170,

where the number in parentheses represents the standard error. The estimate of fl is not significantly different from unity. The estimate is, however, significantly smaller than the tax-adjusted coefficient 1/(1 - z) for corporate tax rates above 16 percent, implying that real after-tax interest rates are significantly negatively correlated with inflation rates across countries.18

When short-term rates were used, the estimated coefficient on inflation over the next year was 1.01, with a standard error of 0.07, again implying that the coefficient on inflation is insignificantly different from unity. These results are striking, since earlier time-series work (Cumby and Obstfeld, 1984; Mishkin, 1984) indicated that short-term interest rates do not fully reflect inflation differentials. One feature of our estimates which may help to explain the

16It would be preferable to use a more consistent data set, however, as long as this diversity is unrelated to inflation performance the coefficient estimates reported below are unbiased. 17An F-test indicated that the hypothesis that the fl coefficient was equal across all time periods could not be rejected at conventional significance levels. lSThis conclusion assumes the same tax rate across all countries. If tax rates were negatively relatived to inflation rates, then real after-tax interest rates might not be negatively correlated with inflation. However, there is remarkably little variation in corporate tax rates across OECD countries (OECD, 1992).

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difference in results is that, by exploiting the panel data set, we are better able to control for movements in the real rate of interest over time. 19 Another is the lack of country-specific intercepts, as we are interested in behavior of interest rates across countries in response to inflation differentials.

4.2. Net Jbreign assets and inflation

Having established that our assumption that inflation enters into nominal interest rates on a one-for-one basis is reasonable, this section looks at the relationship between net foreign assets across countries and long-term differ- ences in inflation. The theoretical model implies that the net asset position of a country should be directly related to its rates of inflation and taxation. Furthermore, of these two factors, the major effect comes through differences in inflation rates.

This section tests the validity of the theory by estimating cross-section regressions looking at the relationship between inflation and net foreign assets across OECD countries. Data on corporate tax rates in 1988 were also collected and used in some regressions, where they generally had the correct sign but were insignificantly different from zero. The fact that the coefficients were insignifi- cant may well reflect the smaller role of tax rates in the determination of net asset positions as well as the complexity of most corporate tax systems, which makes it difficult to relate published corporate tax rates to actual tax incidence. This is one reason why we did not attempt to calculate real after-tax interest rates directly from our data.

The basic estimating equation involves regressing the net foreign asset posi- tion across different countries on a measure of the inflation rate of those countries over the recent past. Inflation was measured by taking the average of the actual inflation rate for the previous four years. The data were averaged over several years in order to get rid of short-term cyclical influences, and hence to get a more accurate estimate of long-term levels of inflation. The choice of a four- year average was somewhat arbitrary, however, tests with other inflation measures (longer lags, future inflation, etc.) gave similar results, indicating that our results are robust to alternative definitions of the inflation rate.

Of course, inflation may not be the only influence on net foreign assets. Of the other factors that might have an influence, two are particularly important. The first is government borrowing, since it is often argued that current account imbalances reflect fiscal imbalances. 2 The second is the demographic structure

~We also restrict our sample to the 1980s, a period in which interest rates may have been tess subject to government regulations and capital markets were more open.

2See Bernheim (1988) for an examination of the role of fiscal policy in determining the current account balance.

316 7". Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

of the economy. An economy that has a part icular ly high ratio of dependents to workers might be expected to run down its net foreign assets in order to provide for these economical ly unproduct ive members of society (Masson and Tryon, 1990). To the extent that demographic trends are anticipated, we might expect an economy to bui ld up its net foreign assets in advance of an increase in the dependency ratio. Hence, the age structure of the populat ion should be related to both the level of net foreign assets and to the flow of these assets.

Accordingly, two extra variables, general government net debt (measured as a rat io to GDP) and age dependency (defined as the percentage of the popula- tion below 15 or above 60) were included in some of the regressions. The basic est imating equations were:

(NFA/Y) j = ~ + fl~j, (15)

(NFA/Y) j = ~ + flzri + 7(DEBT/Y) j + OAGEj, (16)

where NFA is the net foreign asset posit ion, Y represents GDP, ~ is the rate of inflation, DEBT is the level of general government net debt, and AGE is the demographic variable described above. The coefficients on inflation and govern- ment debt are expected to be negative. The coefficient on age dependency is expected to be posit ive if past savings ant ic ipated demographic developments correctly.21

Data on foreign assets and liabilities were collected for 18 OECD countries for the per iod 1981-89. 22 The data come from External Assets and Liabilities of Industrial Countries (The Institute of Internat ional Finance, Washington, Feb- ruary 1991) and are, to our knowledge, the most complete data avai lable on a comparab le basis over a number of years. Net foreign assets were calculated by taking the difference between total assets and total liabilities, normal ized as a percentage of GDP. 23 Inf lation was measured as the average increase in the

21 When we extended the regression to include variables such as the unemployment rate and the rate of growth of output over the preceding four years, the results were very similar to the results in Table 2.

22The countries were Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, the United Kingdom, and the United States.

23The data represent national estimates of the stock of net assets. Unfortunately, valuation principles used by different countries vary widely. One source of possible bias in our estimates is that direct investment is generally recorded at original book value in local currency, which will tend to underrepresent net asset positions of low inflation countries and overrepresent those of high- inflation countries. This bias acts against our prediction of a negative correlation between inflation and net foreign assets. A spurious negative correlation could be created between net assets and inflation if the net assets were not updated for current changes in exchange rates. However, it appears that in most cases (and certainly in the United States and United Kingdom, where we studied the valuation principle in more detail) the data are adjusted for exchange rate fluctuations. Also, see IMF (1992).

T. Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330 317

consumption deflator over the previous four years. 24 Both the consumption deflator and nominal GDP were collected from OECD Annual National Ac- counts. The data on general government net debt were collected from Blanchard et al. (1991). Finally, age dependency ratios for 1981, 1985, and 1988 were collected from United Nations Statistics in Brief and World Bank Social and Economic Statistics.

Government debt was not available for New Zealand or Switzerland. The data on Belgium were excluded because Belgium is in an economic union with Luxembourg, for which net foreign asset data are not available. Hence the final data set comprised 15 countries. 2s Given this relatively small sample, it is useful to use an estimation technique that is robust to the impact of outlying observa- tions. Accordingly, we used the jackknife technique (Efron, 1982) to generate our results. In this procedure, the equation is reestimated sequentially, eliminating each data point in turn, and the empirical distribution used to calculate the coefficient values and standard errors. This technique is particularly robust in the face of problems associated with small numbers of outlying observations; in the event, the jackknife results proved to be quite similar to those from ordinary least squares.

Table 2 shows the results from estimating Eqs. (15) and (16). The left side of the table shows the results for regressions on inflation alone; the right side shows the results when government debt and age dependency ratios are included in the regressions. The top half of the table shows the results using the full data sample and net foreign asset data for three different years, 1981, 1985, and 1989. Since much of the deregulation of international financial markets has occurred over the course of the 1980s, the effect of inflation might be expected to be becoming more important over time. This does indeed appear to be the case. In the regressions with inflation as the sole explanatory variable, the coefficient on inflation has the expected sign in all three regressions, however, its value and statistical significance increase steadily over time, from -0.38 in 1981 (and insignificantly different from zero) to -6.18 in 1989, when it is highly signifi- cant, with a t-statistic of over 10. This implies that by 1989 a 1 percentage point rise in underlying inflation was associated a 6 percentage point reduction in net foreign assets to GDP, a relatively powerful effect. The adjusted R 2 statistics indicate that inflation, which has very little explanatory power in 1981, explains 40 percent of the variance in net foreign asset positions by 1989. Fig. 1 presents a scatter plot of the 1989 data, with net foreign assets on the vertical axis and

24Similar results were obtained using the GDP deflator. 25We were able to estimate the simple regression of net foreign assets on inflation for the full sample of 18 countries and we obtained even larger estimates of the effect of inflation on net foreign assets than those presented in Table 2.

318 T. BayoumL ,1. Gagnon /Journal of Monetary Economics 38 (1996) 303-330

Table 2 Cross-sectional net foreign asset regressions

Simple regression Extended regression

Year Inflation Adj. R 2 Inflation Govt debt Age Adj. R 2 No. obs.

Full sample

1981 -0.38 -0.07 -0.90* 0.50** 0.66 0.01 15 (0.24) (0.38) (0.08) (0.92)

1985 -3.42** 0.28 -4.31"* 0.13 2.50* 0.19 15 (0.24) (0.53) (0.07) (1.02)

1989 -6.18"* 0.37 -6.92** 0.20** 2.69 0.32 15 (0.36) (0.68) (0.05) (1.39)

Smaller sample

1981 - 7.35** 0.46 -7.27 0.46 2.56 0.25 7 (1.79) (4.49) (1.03) (6.43)

1985 -7.54** 0.42 -9.65** -0.08 5.17 0.28 9 (1.02) (1.93) (0.54) (3.89)

1989 -7.93** 0.36 -10.73"* 0.02 5.98 0.18 9 (0.84) (3.37) (0.20) (5.60)

The full sample comprises Australia, Austria, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, the United Kingdom, and the United States. The smaller sample excludes Austria, France, Italy, Norway, Spain, and Sweden due to significant capital controls. The United Kinmgdom and Japan were also excluded from the 1981 regressions since they had extensive capital control until 1979 and 1980, respectively. Single and double asterisks indicate that the coefficient is significant at the 5% and 1% level, respectively. The constant terms are not reported.

inflation over the previous four years on the horizontal axis. This plot clearly illustrates the strong negative correlation found in our regressions.

A similar pattern emerges when the other explanatory variables are included. The coefficients on inflation in these regressions are very similar to those in the simpler regressions discussed earlier, moving from -0 .90 in 1981 to -6 .92 by 1989. The other two explanatory variables, government debt and age depen- dency, do not appear to be important factors in determining net foreign asset holdings across countries. The coefficient on age dependency is correctly signed, but it is significant in only the 1985 regression. 26 The coefficient on government

Z6One explanation for this result is that changes in the share of dependents in the population have been shown to affect both the rate of saving and investment, with little net effect on the current account. See the survey in Bosworth (1993).

T. Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330 319

1 20 o ao o - l o

u_ -20

-30

-40

GE

j~IE

I I o I

UK

FR

AT IT

US

FI SO SP

CA NO AU

DE I I I I I 1 1 2 3 4 5 6 7 8 1985-88 Average In f la t ion Rate

Fig. 1. Inflation and net foreign assets.

debt is incorrectly signed in all three regressions and is significantly different from zero in two of the three. One explanation of this latter result is that countries with large public debt use capital controls relatively extensively to avoid external borrowing.

To investigate the issue of capital controls further, we reestimated Eqs. (15) and (16) after eliminating those countries that maintained significant capital controls over the sample, namely: Austria, France, Italy, Spain, Sweden, and Norway. 27 Since this new sample represents those countries with relatively free capital markets, we would expect the significance of the coefficient on core inflation to increase and to become more stable over time.

The bottom half of Table 2, where the results from this smaller sample are reported, confirms this intuition. In the regressions with inflation as the sole right-hand-side variable, the coefficient on inflation is larger in this subsample than it is for the full sample in all three regressions. The effect of inflation is substantial, highly statistically significant, and increases slightly over time

27 The information on capital controls comes from Liberalization of Capital Movements and Finan- cial Services in the OECD Area, OECD, Paris 1990. Japan and the United Kingdom were also excluded from the 1981 regression becuse they had significant capital controls until 1980 and 1979, respectively.

320 7". Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

from -7.35 in 1981 to -7.93 by 1989. (This small rise presumably reflects the steady liberalization of capital flows over time in the rest of the world.) The adjusted R 2 statistics indicate that inflation alone explains between one third and one half of the underlying variance in net asset positions in the 1980s. These patterns are repeated in the regressions using the other explanatory variables, where the coefficient on inflation is both larger than in the full sample and getting larger over time. By contrast, the coefficients on the other explanatory variables, government debt and age dependency, are insignificant in all of the regressions, and reduce the adjusted R 2 statistic in all three cases.

As a check on the robustness of the results, several alternative specifications were also estimated: To check for simultaneity bias, the equation using only inflation as an explanatory variable was reestimated using two-stage least squares, the instruments being a constant and inflation over the four year period prior to the data being used in the regression; to see if the results reflected the choice of a four-year time horizon, the regressions were reestimated using averages of data over the previous eight years (regressions were also run using inflation over the subsequent four years where available); to see if the results were sensitive to cyclical factors, the regressions were reestimated with various measures of the cyclical position of each country instead of the demographic variable; 28 to see if the results were an artifact of the particular data set being used, IMF data for year-end 1988 net foreign assets were substituted in the 1989 regressions; 29 finally, the countries that were members of the European ex- change rate mechanism (ERM) were excluded to see if the results reflected competitiveness effects caused by inflation differentials in the face of fixed exchange rates. The pattern of behavior in these regressions (not reported for the sake of brevity) was similar to those reported in Table 2; in particular, the coefficient on inflation always had the proper sign, which became larger and more significant over time, with the subsample results outperforming the full data set.

To summarize the results, inflation appears to have a significant effect on the net foreign asset position across countries with open capital markets, and its importance appears to be rising over time. This result is true both when inflation alone is included in the regression and when measures of government borrowing and demographic structure are added. The coefficient of - 7.88 that is estimated for 1989 is somewhat smaller than the value of -22 calculated in our numerical simulations. However, given the simplicity of the theoretical model and the

2SThe cyclical indicators included the OECD standardized unemployment rate and the growth rate of real GDP, both averaged over the previous four years. Regressions were also estimated using each country's unemployment rate divided by its average unemployment rate over the 1970s and 1980s and each country's growth rate divided by its average growth rate over the 1970s and 1980s.

29These data were obtained from IMF (1992).

T. Bayoumi, J. Gagnon/Journal of Monetary Economics 38 (1996) 303 330 321

imperfections of actual markets, this estimate does not appear unreasonable. We now extend the analysis to look at the adjustment of net foreign asset positions over time.

4.3. Time-series evidence

The previous section reported cross-sectional results on the relationship between net international asset positions and long-term differences in inflation. This section extends this work by reporting the results for similar time-series equations. Annual data on the ratio of the current account to GDP, the rate of inflation of the consumption deflator, the growth of real GDP, and the ratio of general government net lending to GDP were collected from the OECD Annual National Accounts for the 1960-88 period. The current account and general government net lending were used in place of the data on net international assets and government debt in the cross-sectional analysis since we were unable to extend the stock data back before 1981. Flow data may, in any case, be more natural in a time-series context.

Our hypothesis links movements in expectations of future inflation to move- ments in the desired stock of net assets. This affects the current account since (abstracting from the effect of exchange rate revaluations) the current account measures the change in international net assets for a country. 3 Accordingly, our empirical specification relates expected future changes in inflation to movements in the current account. The relationship between general government net lend- ing and government debt is very similar to that between the current account and the net international asset position, in that it measures the change in the underlying stock of debt. Hence, general government net lending is the obvious fiscal variable to use in conjunction with the current account. No data were collected on the age distribution of the population, the other explanatory variable used in the cross-section regressions, because it was felt to be unlikely that variations in the age structure would have an important influence at an annual frequency.

Including a lagged dependent variable to measure the speed of the dynamic response to the independent variables, and the growth in GDP as a cyclical variable, the following set of time-series equations were estimated:

(CA/Y) i , , - -o~i + fli~i,t+l + ItiAyi. t + Ti(NL/Y)i . t + Oi(CA/Y)i,t I. (17)

The current account for country i is related to future inflation, the growth of output, general government net lending, and lagged values of the current

3Since it includes factor payments to owners of capital, the equilibrium current account will move in the same direction as the underlying net foreign asset position of a country in a steady-state growth equilibrium.

322 T. Bayoumi, J. Gagnon /Journal of Monetary Economics 38 (1996) 303-330

account. Since the theory implies that it is behavior relative to other countries that is important, all of the variables were adjusted by subtracting a GDP- weighted average of the variable across all countries for which the full data set existed. 31 Adjusting for leads and lags, the estimation period was 1963-87.

The theory implies that the inflation effect will only operate in those countries which have maintained relatively open international capital markets. Accord- ingly, we limited our estimation to the seven countries identified earlier as having had open markets throughout the late 1970s and early 1980s, namely Australia, Canada, Denmark, Finland, West Germany, the Netherlands, and the United States. Unfortunately, the data on general government net lending for Denmark only started in the 1970s, so it was dropped from the estimation. The six equations were estimated as a system using three-stage least squares, with instrumental variable techniques being used in order to adjust for the inclusion of future inflation in the specification: the instruments were a constant, a time trend, output growth for each of the six countries, and the lagged current account, also for each of the countries. 32 Instrumental variables were used since we wish to test the impact of expected changes in future inflation. This technique ensures that the coefficients are based on the predictable part of future inflation.

The results from the estimation are shown in Table 3. Expected future inflation has the anticipated negative sign in four of the six countries, and is significant (at the 10 percent level) in three cases: Canada, Germany, and the United States. The coefficients on output growth also have the anticipated negative sign in four of the six cases, indicating that faster growth leads to a deterioration in the current account, and are significant in all these cases. Those on government net lending indicate a difference in behavior between large and small economies. Both the United States and Germany have the expected positive coefficients, which are significant. By contrast, the coefficients for the other four countries are either insignificant or (in the case of Canada) significant but incorrectly signed. From this extremely limited sample it would appear that fiscal policy has an impact on the current account of large economies, but not in smaller ones. This may explain our failure to find fiscal effects in the cross- sectional analysis.

The coefficients on the lagged dependent variables are positive and generally significant, as might be expected. The average lag (the period over which half of the long-term impact of the independent variables occurs) varies from just over

31 Australia, Canada, Finland, West Germany, Japan, the Netherlands, the United Kingdom, and the United States.

32 We could not incorporate additional instruments, such as the lagged rate of inflation or current net lending, since in three-stage least squares all instuments are included in all equations, which used most of the degrees of freedom. Single-equation results, using a wider array of instruments for each individual country, produced similar results.

7". Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

Table 3 Time-series regressions

323

Expected Lagged future Output Government dependent Q(4)

Country inflation growth net lending variable R 2 {Z2(3)1

Australia 0.08 0.31 0.53 0.57** 0.10 2.0 (0.17) (0.27) (0.53) (0.19)

Canada - 0.21 * 0.04 - 0.40"* 0.13 0.34 3.7 (0.12) (0.18) (0.15) (0.19)

Finland -0.07 -0.48** -0.01 0.82** 0.54 1.5 (0.13) (0.13) (0.28) (0.26)

Germany -0.37* -0.41"* 0.54** 0.80** 0.75 4.4 (0.13) (0.14) (0.19) (0.12)

Netherlands 0.19 -0.48* 0.45 0.88** 0.54 5.4 (0.16) (0.22) (0.29) (0.13)

USA -0.29** -0.32** 0.48** 0.59** 0.90 2.5 (0.08) (0.06) (0.06) (0.06)

All -0.13"* -0.36** 0.17"* 0.71"* 0.21-0.87 1.5 11.7 {0.05) (0.06) (0.06) (0.06)

Standard errors are reported in parentheses. Single and double asterisks indicate that the coefficient is significant at the 10% and 1% level, respectively. The models were estimated using three-stage least squares, with the instruments being a constant term, a time trend, output growth for each country, and the lagged value of the current account for each country.

a year in the case of Finland to over eight years for the Dutch results. The descriptive statistics for the models are satisfactory. The equations explain between 10 and 90 percent of the original variance in the current account, while the adjusted Box Pierce statistics indicate no serial correlation over the first four lags of the residuals.

The bottom row of Table 3 reports the results from estimating the model under the constraint that the coefficients on the independent variables (except the constant terms) were equal across countries. These restrictions are rejected by a Wald test, so the results should be regarded as indicative of overall properties of the equations, rather than being statistically well determined. At -0.13, the coefficient on future inflation is correctly signed and highly signifi-

cant. Output growth also has a significant negative impact, while the budget surplus has a significant positive effect. The coefficient on the lagged dependent variable implies an average lag of over three years, and the long-run effect of a one percentage point rise in the rate of inflation is a 0.45 percent of GDP decline in the current account balance. Assuming a real rate of return of 7 percent on foreign assets, this implies a long-run deterioration in the ratio of

324 11 Bayoumi, J. Gagnon/Journal of Monetary Economics 38 (1996) 303-330

net international assets to GDP of 6.5 percentage points for every percentage point change in relative inflation.

5. Conclusions

One of the most striking economic developments of the 1980s has been the emergence of large capital flows between industrialized nations. This paper shows that nominal tax distortions may provide an important explanation for the pattern of capital flows over this period. With the liberalization of inter- national markets for capital, the tax treatment of interest income may have powerful effects on desired national net asset positions, and thus on capital flows. Under the existing system of nominal income taxation, differences in inflation rates across countries are not neutral with respect to real variables, even when tax rates are the same across countries. In particular, we show that countries with higher inflation rates must have lower real after-tax interest rates, at least in the long run. A movement to a higher long-run inflation rate therefore increases the desired capital stock and may decrease the saving rate. This implies a lower desired net foreign asset position, and hence a capital inflow. Experi- ments using a small numerical model indicate that this effect of inflation is likely to be large.

We estimate this effect empirically using cross-section and time-series tech- niques. With open international capital markets a 1 percentage point increase in inflation is estimated to reduce the stock of net foreign assets by between 6 and 9 percent of GDP over the long run. An implication of these results is that recent international capital flows (current accounts) among industrial countries may largely reflect tax distortions caused by differences in inflation rates, rather than an optimal allocation of world savings. In other words, international saving and investment decisions do not reflect the true economic returns to society. This inefficiency will remain as long as governments tax nominal instead of real interest income.

Another implication of our theoretical model is that monetary policy can have a powerful effect on aggregate demand even when it is perfectly anticipated. Indeed, it is precisely the expectation of future inflation that provides the mechanism for money to affect the economy through the effect of lower real after-tax interest rates on consumption and investment. A topic for future research is to examine the intermediate mechanisms through which inflation affects aggregate demand and net foreign assets.

Appendix

This appendix describes numerical simulations of the effect of inflation and taxation on the capital stock and net foreign assets using a theoretical model of

T. Bayoumi, J. Gagnon /Journal of Monetary Economics 38 (1996) 303-330 325

a small open economy. The model has a Cobb-Douglas production function, an interest-elastic money demand, a positive depreciation rate of capital, historical cost deduction of depreciation expense, a positive population growth rate, and an interest-elastic saving rate. In order to keep the analysis tractable, we assume that marginal investment projects are always financed by debt, that corporate arbitrage equates the cost of borrowing in domestic and foreign currency, and that individuals have limited opportunities to hold assets denominated in foreign currency so that their saving decision is determined by the real return on domestic currency debt. Our basic findings are that the effect of the inflation rate on net assets and the current account balance is large, and that it is robust to alternative assumptions.

The numerical model is defined by Eqs. (A.1) to (A.1 1). Because we allow for population growth, all real and nominal quantities are expressed in per capita terms. Eq. (A.1) gives output as a Cobb Douglas function of capital and labor, with per capita labor normalized at unity; Q denotes the level of technology of the production function, which is assumed to be constant. Disposable income is defined in Eq. (A.2) as output less depreciation of the capital stock plus monetary injections and real returns on net foreign assets and the money stock. For simplicity, we assume that all tax revenues are rebated to individuals in the form of lump-sum transfer payments so that tax rates do not appear in Eq. (A.2). Consumption is a simple function of disposable income that may depend on the real return to saving. The total money stock grows at the exogenous rate,/~, but per capita money balances increase at a slower rate when population growth is positive. Real money demand is proportional to real income, but it reacts negatively to increases in the after-tax nominal interest rate. Eq. (A.6) defines the inflation rate. Eq. (A.7) is the open interest rate parity condition combined with the purchasing power parity condition. The reel return to saving is defined in Eq. (A.8), and the cost of capital is defined in Eq. (A.91. Eq. (A.9) allows for nominal cost depreciation of capital at an accelerated rate, where ,5 is the real rate of depreciation and 7 is the rate allowed for tax purposes. 33 Eq. (A.10) determines the capital stock by setting the (after-tax) cost of capital equal to the after-tax marginal product of capital. Finally, per capita net foreign assets are given by the budget constraint and population growth. Because of the open interest parity condition, we are free to model net foreign assets in either domestic or foreign currency, and we choose domestic currency for simplicity.

33See King and Fullerton (1984, p. 20). Strictly speaking, this formula applies only to the steady- state cost of capital. The exact dynamic formula contains the expected path of the interest rate over the infinite future. We experimented with expectations of i set five and ten years ahead, and we found no significant change in our numerical results.

326 T. BayoumL J. Gagnon /Journal of Monetary Economics 38 (1996) 303-330

Yt = QK~_ 1, (A.1)

YDt = Y, -- JKt_ 1 + ( i t -1 - - 7~t)(At-1/Pt) + (~t - rct)(M,_ 1/Pt), (A .2)

C, = (1 - So - &r r , )YDt , (A.3)

M, = ((1 + #t)/(1 + n) )Mt -1 , (A.4)

Mt/Pt = mYt/(1 + (1 - E,0t+l)it) ~', (A.5)

7it = (Pt - Pt - 1 ) /Pt - 1, (A.6)

i t = i* + Etrc,+l - - Et~t*+ 1, (A.7)

rrt = (1 - EtOt+l ) i t - Etrct+l, (A.8)

cct = [1 - E/rt+ ~7/((1 - Et'rt+ ~)it + y)]

x [(1 - Etzt+l)it - Et=t+l + 6], (A.9)

cct = (1 - "r)o~QK~-1, (A.10)

At = ((1 + i,- 1)/(1 + n) )A , - i + (YtPt - CtPt)/(1 + n)

+ (1 - - 6)Kt - lP t / (1 + n) -- K tP t . (A .11)

Table A.1 presents the parameter and variable values for the initial steady state of the model; they were chosen to mimic the typical developed country with output normal ized at unity. The initial set of s imulations ignores the effect of interest rates on saving. We then extend the model to include this effect. The real

Table A. 1 Initial steady state

Parameters Variables

Q 0.711 ct 0.30 6 0.30

0.10 s o 0.095 s I 0.0 n 0.02 m 1.253 2 3.0

Y 1.0 K 3.112 A 0.0 Y D 0.864 C 0.782 M/P 1.0 i 0.12 i* 0.12 it 0.05 7t* 0.05 ,u 0.071 r 0.35 0 0.35 rr 0.028 cc 0.096

T. BayoumL J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330 327

Table A.2 Effects of changes in inflation and taxation on the capital stock and real net foreign asset holdings (percent of initial output after 5 years)

Simulation Capital stock Real net foreign assets

Inflation + 1% 17 - 16 Corporate tax + 1% 4 -4 Individual interest tax + 1% 0 -0

s~ = 5, so - - 0.04, and

Inflation + 1% 17 -22 Corporate tax + 1% 4 -4 Individual interest tax + 1% 0 -3

;, = 0.05, so = 0.09, Q = 0.73, and

Inflation +1% 16 -16 Corporate tax + 1% 2 - 3 Indiviual interest tax + 1% 0 0

depreciation rate is 5 percent, but firms can deduct historical depreciation costs at the faster rate of 10 percent. The interest semi-elasticity of money demand is 3. Both tax rates are 35 percent, and the population growth rate is 2 percent. The inflation rate is 5 percent at home and abroad. Capital's share of output is 30 percent, and the capital-output ratio is approximately 3. Households save almost 10 percent of their disposable income.

Table A.2 displays the effects of changes in the exogenous variables on the capital stock and real net foreign assets. 34 As shown in the first row of the table, a 1 percentage point increase in the inflation rate raises the steady-state capital stock by 6 percent, or 17 percent of initial output. The capital stock reaches its long-run equilibrium in approximately 5 years. This increased capital stock is financed almost completely by foreign borrowing, as shown by the change in real net foreign assets after 5 years. The dynamics in the model arise from the interaction between the money demand function, inflation, and the cost of capital. The price level, and hence inflation and the cost of capital, are deter- mined through the money demand equation. Money demand depends on real output, which is in turn a function of the lagged value of the capital stock. This dependence of the price level on initial conditions prevents the cost of capital,

34The model was solved using the Fair Taylor algorithm in TROLL. This procedure for solving rational expectations models generates both the transition dynamics and the long-run steady state under the assumption of perfect foresight.

328 T. Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330

and hence the capital stock, from jumping immediately to their new long-run steady states.

The effect of increasing the inflation rate on the current account balance is given by the change in nominal net foreign assets period by period. Under the initial parametrization of the model, a 1 percentage point increase in the inflation rate leads to current account deficits of 8 percent of output in the first year, 5 percent in the second year, and 3 percent in third year. The current account deficit stabilizes at 1 percent of nominal output after the fourth year. The current account deficit persists indefinitely in order to maintain the level of real per capita net foreign assets in the face of inflation and population growth.

In addition to the impact of the inflation rate, the second and third rows of Table A.2 show the impact of changes in the tax rates on corporate profit and individual interest income. A 1 percentage point increase in the corporate tax rate raises the stock of physical capital by 4 percent of output and lowers the stock of net foreign assets by the same amount. This effect is only one-fourth of that due to a 1 percentage point rise in inflation. Changes in the tax rate on individual interest income have no effect on the capital stock and net foreign assets.

Next, we report simulations that assume a positive interest elasticity of saving. This is the set of simulations that is reported in Table I of the text. The parameter sl is the slope of the saving rate as a function of the real return to saving. We chose a value of sl that would overstate the elasticity of saving with respect to the real return. With sl = 5, a 1 percentage point increase in the real return induces a 50 percent increase in the saving rate, from 10 percent of disposable income to 15 percent. The parameter So, the intercept, was changed to keep the overall saving rate at its initial level. The results indicate that the capital stock is invariant to saving behavior. Real net foreign assets are only slightly lower than under the assumption of insensitive saving after the first 5 years. Over a longer horizon, however, the lower real after-tax return to saving leads to further declines in net foreign asset holdings.

To check on the sensitivity of these results to our assumption that firms can write off depreciation expense at an accelerated rate, we conducted the same experiments under the assumption that firms can deduct historical depreciation costs only at the rate of economic depreciation. Setting the rate of depreciation for tax purposes (7) equal to the rate of economic depreciation (6 = 0.05) increases the cost of capital from 0.096 to 0.104 and decreases the steady-state capital stock from 3.11 to 2.90. We made corresponding changes in the saving rate and technology factor to keep output normalized at 1. We then examined the effects of changes in the inflation rate and tax rates relative to the new initial capital stock of 2.90. The effect of inflation on the capital stock and net foreign assets is nearly identical to the situation in which firms can take accelerated depreciation deductions. The effect of increasing the corporate tax rate is somewhat lower when firms cannot take accelerated depreciation deductions.

T. Bayoumi, J. Gagnon / Journal of Monetary Economics 38 (1996) 303-330 329

There is still no effect on the capital stock and net foreign assets of increasing the interest income tax rate.

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