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Inflation and Portfolio Choice

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1987
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THIS PAPER AIMS to examine the impact of inflation on portfolio decisions. To do this, a complete system of asset and liability demands is estimated for the U.K. nonbank private sector from 1976 through 1985. Such a system-wide approach has all the advantages emphasized by Brainard and Tobin in their classic (1968) paper. It also provides a fully comprehensive view of how investors seek to rearrange their portfolios when the level of inflation changes. Among the insights that emerge from the study are a rich and intuitively reasonable pattern of substitution among financial assets. Higher inflation induces investors to switch away from sight deposits, cash, and, to a lesser extent, government bonds into time deposits and national savings. Perhaps the most striking result relates to the broader allocation among financial assets, liabilities, and real capital. Increases in inflation lead to a marked expansion in overall balance sheets as investors take on more debt and spend the proceeds to acquire financial assets. Meanwhile, the demand for real capital appears unaffected.

Theoretical arguments suggest that inflation may influence portfolio decisions in several different ways. First, higher inflation may induce direct rate-of-return substitution from sight deposits and cash into bonds and real assets. Such effects may be demonstrated either in short-run business-cycle models (Mundell (1963)) or in long-run monetary growth models (Tobin (1965)). Second, inflation may systematically influence the risk characteristics of different assets and liabilities. Such effects could be attributed to changing probabilities of default by liquidity-constrained borrowers or to the absence of indexation in other parts of the economy (for example, nominal wage contracts).

Third, the presence of an imperfectly indexed tax system may have important implications for the interaction of inflation and portfolio demands. Feldstein (1980) attributed the poor performance of the United States stock market in the late 1970s to the fact that higher inflation raises the effective tax rate by reducing the real value of depreciation allowances. Finally, inflation illusion, if present, could cause significant portfolio shifts. Modigliani and Cohn (1979) have suggested that investors systematically undervalue equities in the presence of inflation because of a failure to take account of the depreciation in firms’ nominal liabilities.

The question of the importance of these various portfolio shifts is necessarily empirical. Previous studies have, by and large, limited themselves to examining the validity of reduced-form relations such as the so-called Fisher equation. Thus, nominal rates of return are regressed on measures of the real interest rate and of expected inflation to see if the latter has a unitary coefficient. Notable papers in this literature are Fama (1975) and Summers (1983). The intrinsic difficulty with this approach is that both right- and left-hand-side variables are clearly endogenous to a larger system. Finding suitable instruments to cope with this problem is virtually impossible. Thus Fama was obliged to make strong assumptions about constant real interest rates and to respecify the relation, whereas Summers resorted to elaborate band-spectral regression techniques to filter out short-term influences, his claim being that what remained was basically a steady-state relation. Neither solution seems entirely satisfactory; in any case, reduced-form approaches of this kind are incapable of yielding much economic insight.

The alternative approach taken in this study is to estimate directly a complete system of asset and liability demands. This procedure should permit differentiation of the several channels through which inflation affects portfolio decisions, thereby providing a much richer understanding of what actually occurs within asset markets when the level of inflation changes.

The recent literature on modeling asset demands suggests several possible starting points. Friedman and Roley (1979), Conrad (1980), Friedman (1985), Aivazian and others (1983), and Taylor and Clements (1983) have all presented portfolio models that involve explicit utility maximization. An important advantage of assuming such maximization is that it implies restrictions on the coefficients in the derived demand equations. The job of estimating asset demands, which typically have highly colinear explanatory variables, is much facilitated by such restrictions. The approach used in this paper comes closest to resembling that of Conrad, although the present model differs from his in some important respects.

Whereas Conrad (1980) derived his demand equations from an indirect utility function, this paper proceeds instead from an expenditure or cost-of-utility function. Using expenditure functions permits the employment of the so-called Almost Ideal Demand System (or AIDS), suggested by Deaton and Muellbauer (1980) in the context of consumer demand theory. This approach possesses highly desirable aggregation properties. Because restrictions based on utility maximization by individual investors will be applied to aggregate demand functions, it is important to be clear about the aggregation assumptions involved. Another major difference from Conrad’s paper is that the present study takes full account of expectations formation. Asset demands are functions of expected—not realized—rates of return. Because Conrad estimated his system with realized interest rates and yields, his parameter estimates were inconsistent.

I. The Model

In deriving the model, it is supposed that there exists a utility function defined on the expected future values of current asset and liability stocks:

where

Here ria, rjk, and ril are, respectively, the expected real holding returns on the ith financial asset, j th form of real capital, and k th liability. As such, they include the expected appreciation in the value of the investment. Ait, Kjt, and Lkt represent the real stocks (deflated by the consumer price index) of the i th asset, i th real capital, and k th liability. By convention, liabilities are negative numbers.

The simplest way to justify such a utility function is to assume that investors care about expected future wealth and about the expected flows of services that they derive from their asset and liability holdings. If the service flows (housing and liquidity services, for example) are monotonically increasing functions of these holdings, then the utility function can be transformed into a function of expected future stocks. This approach follows Feige (1964). Since we are including expectations inside a utility function, we must assume that these expectations are held with subjective certainty.

In an earlier version of this paper (Perraudin (1987)), the author showed how the above utility function could be derived from a general, expected-utility, portfolio problem in which the covariance structure of returns remained fixed. That paper concluded that if investors cared about the second and higher moments of future wealth, then, although the model’s estimates would be consistent, Slutsky symmetry would break down in the estimated demand equations. This finding explains why, when the results are reported below, considerable stress is placed on the generally favorable results of the symmetry tests.

In the analysis below, it is assumed that the utility function is strictly quasi-concave, twice continuously differentiable, and strictly increasing in all its arguments. The investor’s problem is then

subject to

where W is the stock of real wealth, and time subscripts are omitted. Rewriting the budget constraint gives

Evidently the problem is identical to one of consumer demand in which the RAit, RKjjt, and RLkt, represent goods, and in which prices are of the form

Taking advantage of this isomorphism, one may define a cost or expenditure function as

subject to

where

Inflation appears in this cost function through rla, the real return on cash and sight deposits, which is, of course, the negative of the rate of inflation. It may also be included, however, together with a time trend, as a direct additional argument in the utility function. The idea here is that the flows of services derived from the asset and liability stocks might vary systematically with inflation or over time. It is also useful to include inflation terms as a gauge of possible misspecification. For example, this study uses pretax rates of return. If effective tax rates depend systematically on inflation, then one might expect this dependence to show up in nonzero coefficients on the direct inflation terms.

To keep the estimation problem tractable, the number of parameters is reduced by assuming quasi-separability of the cost function among financial assets, real capital, and liabilities.1 Although in practice one adopts such a separability assumption to simplify estimation, it may be rationalized as reflecting the presence of information costs that induce the investor to adopt a form of multistage budgeting. Thus, wealth is allocated first among broad groups of investments and then subsequently within those groups. The form of the cost function is then

where D is a vector containing a time trend and the expected rate of inflation.

One may note, in this context, the virtue of quasi-separability of the cost function compared with the more usual assumption of separability in the indirect utility function. The latter type of separability requires the additional assumption of homothetic subindirect utility functions in order to ensure multistage budgeting (see Geary and Morishima (1973)). In a sense, therefore, implicit separability is more general.

Separability of an indirect utility function or cost function involves a portioning of the price space in the consumer’s demand decision. This may seem unintuitive to those who are used to thinking in terms of traditional direct utility functions. Deaton (1979) demonstrates that quasi-separability implies a corresponding separability of the distance function (that is, the cost function’s dual) and, hence, a portioning in the space of goods. To ensure that separability in the indirect utility function implies separability in direct utility and therefore in goods space, however, requires the additional assumption of homothetic subutility functions (see Lau (1969)).

As a final comment on this separability assumption, note (following Gorman (1976)) that, in practice, quasi-separability amounts to assuming a particular pattern of substitution within the Slutsky matrix. Thus, if i and j are members of groups A and K, respectively, then the Slutsky substitution term is of the form

Utility maximization and the various assumptions that have been made imply a cost function that, apart from quasi-separability and the usual properties of cost functions, is arbitrary and unknown. To approximate this, one may adopt one of the several flexible forms suggested in the consumer demand literature. These are almost all second-order approximations and, therefore, in principle possess the same degree of generality. The so-called PIGLOG (or Price-Independent, Generalized-Logarithmic) family of flexible forms has the advantage, however, of highly desirable aggregation properties (see Muellbauer (1975, 1976)). Because the aim is to impose the restrictions of individual utility maximization on aggregate demand, it is important to adopt reasonable aggregation assumptions. Within the PIGLOG class, the AIDS formulation proposed by Deaton and Muellbauer (1980) is chosen. This is used to represent both the upper and lower level cost functions.

The approximated upper- and lower-level cost functions may therefore be written as

Using Shephard’s lemma (see Diewert (1974) and Shephard (1953)), one may take the logarithmic derivative of the upper-level cost function, with respect to the composite price indices, to find Wj, the compensated desired portfolio shares for investment group j:

where

and where Xij is the consumer-price-deflated holding of asset or liability i within group j. To eliminate the unobservable variable U, one substitutes from the cost function itself to give

where

and C is total net wealth. Note that the subcost functions Ci that appear in this equation are unobservable, weighted indices of the rates of return within the group. The desired share of a particular asset or liability i within a group j may be found by taking the logarithmic derivative of the relevant subcost function or price index Cj. Thus,

for j = A, K, L, and where

Again, one may substitute for U to give

where

Although it is possible, in principle, to estimate the complete model described by equations (1) and (2) by using methods suggested by Pudney (1980), this procedure would involve a complicated sequence of iterations. Given the fairly large model and the fact that expected rather than realized returns are used, Pudney’s suggestion is impracticable. The problem really stems from the presence of Cjin both the upper and lower demand equations. Because the Cj are in themselves unobservable, they have to be substituted out before the system is estimated. One way to get around this problem is to assume that ξ10 = 0 for all i; in other words, that U does not enter into the lower cost functions. This amounts to assuming homothetic quasi-separability. The advantages of using quasi as opposed to direct separability might then seem to be reduced. Nevertheless, at least with quasi-separability it might be possible to test the exclusion of U from the subcost functions using limited information methods. In addition, the approach of using cost functions as the starting point has the important practical advantage of yielding linear estimating equations. These are both computationally easier to estimate and theoretically more satisfactory, since they allow a fairly general aggregation assumption.

Adopting the restriction, one ends up with the following demand system:

where

Following the suggestion of Deaton and Muellbauer (1980), the collinearity of the asset returns can be exploited by approximating P* with the expression

Absorbing the second term in the constant and taking account of the fact that a0 will not be separately identified from the equations’ constant terms allows one to write

and

As a last step in specifying the model, dynamics are introduced by a simple and classic stock-adjustment process. Actual demand is taken to equal lagged demand plus a fraction of the discrepancy between desired and lagged holdings. Thus,

where the asterisk denotes the desired share, t indicates time period, and j = A, K, L.

Clearly this is a strong assumption. It allows demand for a particular good to be affected only by the disequilibrium in that good. In other words, the adjustment matrix is diagonal. As Friedman (1977) points out, portfolio adding-up constraints imply (in the case of demand-share equations) that the columns of the adjustment matrix sum to a constant. If each column contains only a single nonzero element, then clearly these elements must be equal. The assumption of separability improves matters slightly, however, since the adding up requirements apply to shares within each of the three subgroups and to the shares explained by the upper-level equations. Thus, with three subgroups, there are effectively four adjustment parameters to be determined. Adding stochastic error terms to the equations completes the specification of the basic model.

In estimating the demand system, it is essential to take account of the fact that asset and liability demands respond to anticipated rather than realized returns. As is well known, using realized values to proxy the rational expectation of a variable leads in most cases to errors-invariables bias, since the realized variable effectively represents the rational expectation plus a random error. In the present case, the drawback in using realized values is even greater because rates of return are also endogenous. To illustrate, consider the effect of a random shock that increases the demand for an asset. With given supply, the own-return interest rate will tend to rise, pushing down the “price” and biasing the coefficient estimate upward. Although one cannot precisely predict the sign of the bias on individual coefficients, it seems likely that using realized data will yield higher estimates of own-return coefficients. This was indeed the finding when the model was estimated with realized rate-of-return series. For these reasons, Conrad’s (1980) reliance on realized return data is highly questionable.

To resolve these problems, the process of expectations formation is modeled directly, with the demand system expanded to include equations that explain rates of return as optimal distributed lags on past returns and other lagged variables. Substituting these equations wherever rates of return appear in the demand equations, one may achieve efficient and consistent estimates by imposing cross-equation restrictions between the demand and the rate-of-return equations. This substitution amounts to assuming a form of backward-looking rational expectations that is close to the original Muthian sense of the term (Muth (1961)). Individuals use information optimally, but the only information they have consists of lagged rates of return and a selection of other variables. A representative example of such methods used in another context can be found in Mishkin (1982).

II. The Data

U.K. data were used in this study. This choice seemed appropriate, first, because U.K. inflation has varied quite considerably since the mid-1970s. Compounded quarterly inflation rates have ranged from 3 percent to 45 percent in the past ten years. Second, U.K. data are unusually complete. The Central Statistical Office has recently begun to publish full, quarterly balance sheets for the main sectors of the U.K. economy. The series have been extended back to the first quarter of 1975. For this study, a data set of 39 observations, from the second quarter of 1976 through the last quarter of 1985, was used. The aggregate examined is the nonbank private sector, whose balance sheets include information on 15 financial assets and 12 liabilities, all calculated at market value.

When several of these aggregates were combined, six financial assets and two liabilities were found. Broadly speaking, these asset categories were (1) sight deposits and cash; (2) time deposits; (3) national savings (nonmarketable government savings bonds and deposits); (4) short-term assets, including treasury bills and trade credit; (5) government bonds; and (6) net foreign assets. Liabilities were divided into sterling bank lending and non-sterling bank lending (by U.K. banks).

It seemed important as well to include some form of real capital in the study, especially since the ultimate objective was to trace the impact of inflation on real interest rates. The substitutability of real and financial assets therefore had to be considered. The two real capital series included were the capital stock of industrial and commercial companies (including the North Sea sector) and dwellings owned by the personal sector. These aggregates should provide close proxies for the housing and productive capital stocks of the nonbank private sector. Consumer durables and land were omitted from the study because of the lack of comparable data.

In constructing the rate-of-return series for marketable instruments, an attempt was made to calculate the full return including appreciation. Thus, percentage changes in either investment price indices or representative asset prices were added to coupon and dividend-based rates of return. The list of asset returns included (1) the negative of the percentage change in the retail price index, (2) the seven-day Clearing Bank deposit rate, (3) an index of National Savings Bank and certificate interest rates, (4) the three-month treasury bill rate, (5) an index of government bond interest rates, and (6) an index of Bank of England rates of return for foreign assets and liabilities.

The government bond index was constructed by weighting the coupon and price appreciation for three categories of 5-year, 10-year, and 15-year “gilt-edged” securities. The weights chosen reflected the non-bank private sector’s holdings of 0-to-5-, 5-to-15-, and over-15-year gilts as reported by the Bank of England. Unfortunately, the figures on holdings referred to nominal rather than market holdings, but these were the best available. The index for net foreign assets was constructed by weighting rates of return for foreign assets and liabilities, using Bank of England estimates of the United Kingdom’s external balance sheet. Because the figures were annual, they were interpolated to obtain quarterly series.

For the two liabilities, indices were again constructed. The return on non-sterling bank lending was approximated by using an SDR interest rate (constructed, in turn, as a basket of national money market rates) plus the appreciation in the SDR against sterling. This was taken to be a reasonable proxy for the true return, since the primary components in the SDR basket are the major European Monetary System (EMS) currencies and the dollar. The sterling bank lending category includes a number of disparate assets and liabilities—for example, bank shares held by the nonbank private sector. As far as possible, the rate-of-return index takes account of these various components, many of which were, in any case, quite small.

III. Estimation

For purposes of estimation, 4 of the total of 12 demand equations were dropped. This was necessary because both the upper-level demand equations and the three sets of lower-level demand equations explain desired shares summing to unity; hence, the error terms are dependent and lead to a singular covariance matrix. In principle, with full information maximum likelihood, it should not matter which equations are dropped. The categories chosen for omission were national savings, housing, and non-sterling bank lending (at the lower level), and liabilities (at the upper level).

These categories were also selected as the numeraire variables for the purpose of imposing homogeneity. Symmetry of the underlying substitution parameters was expected to hold, given the fairly reasonable aggregation assumptions. The use of pretax rates of return, however, and the potential importance of the variance and higher moments of future wealth implied that the price coefficients in the estimated demand equations might not be symmetric. Hence, although homogeneity was imposed from the outset and not subsequently examined, symmetry was left as a restriction to be tested.

In the notation used earlier, symmetry and homogeneity imply, respectively, that at the lower level

for all i, k members of j and for all j, and

for all i, j; and that at the upper level

for all i, j, and

for all i, j. Because equations had been dropped, the adding-up restrictions were not imposed but were used instead to identify parameters in the omitted equations. In this notation, the adding-up constraints were

Estimation was carried out using nonlinear minimum distance (MINDIS) techniques based on methods suggested by Amemiya (1974) and developed by Berndt and others (1974). The resultant estimator is essentially nonlinear three-stage least-squares, reducing (in the case of the model) to nonlinear SURE (Seemingly Unrelated Regression Estimation). Asymptotically, SURE has all the desirable properties of maximum likelihood.

Because of the size of the model, it was not possible to start with the most general specification and work down. The approach taken was, therefore, to begin by estimating the expectations-formation equations and to eliminate variables progressively. Each rate of return was regressed on itself (lagged from one to four quarters), on inflation (lagged one and two quarters), on a constant, and on a measure of the gap between actual and trend gross national product. It also was necessary to insert a dummy variable for the changes in the value-added tax in 1979. The expectations equations initially contained 90 parameters, reduced to 27 at the end. The likelihood-ratio statistic for the 53 excluded parameters was 110, which satisfied the 5 percent χ3 value for rejection of the null hypothesis given small-sample adjustment.

The next step would normally have been to run the reparameterized rate-of-return equations jointly with the full demand system. Computational limits prevented this manipulation, however, so that a compromise was struck by running expectations and subdemand equations together. With the fitted rates of return used as independent variables, the upper-and lower-level demand equations were estimated as a complete system. The procedures used imply that, although the cross-equation restrictions between upper and lower demand systems and between rate-of-return and lower demand systems were correctly imposed, the restrictions between the two upper demand equations and the rate-of-return forecasting equations were neglected. This method made no difference in the consistency of the estimates, but some small degree of efficiency was sacrificed.

After estimating the full demand system in the manner outlined above, the analysis proceeded by testing for symmetry. The likelihood-ratio statistic for symmetry at the lower level proved to be 10, well below the relevant 5 percent χ2 value of 18.3, When the further restriction of symmetry in the upper-level demand equations was imposed, however, the likelihood ratio rose sharply to 22.0. This occurred despite the fact that only a single additional parameter was being constrained. Although one can still show that this much higher likelihood ratio falls short of a strict 5 percent rejection level when full allowance is made for small-sample bias (see Meisner (1979)), the data nevertheless appear to show that upper-level symmetry does not hold.

With lower-level but not upper-level symmetry imposed, the next step was to set equal to zero those parameters with /-ratios less than unity. Some own-price coefficients were kept despite their low significance. The likelihood-ratio test for the joint removal of the omitted parameters was 8.0, well inside the 5 percent significance level of 15.5. As a final check, the residuals were examined for autocorrelation. In plotted form, the residuals showed a reasonable pattern, and the equation-by-equation Durbin H statistics registered acceptable values.

IV. Empirical Results

In general, the other empirical results from the model were very pleasing. The symmetry test reported in the preceding section lends one reasonable confidence in the basic specification of the model. Furthermore, all the own-price elasticities were of the right sign, a considerable achievement in itself. Twenty-one of the 41 unconstrained parameters in the final demand system had t-ratios greater than 2.0, and all but 3 had t-ratios greater than unity.

The economic implications of the parameter values were also quite interesting. Looking at the parameter estimates for the financial asset demand system (Table 1), one is immediately struck by the insignificance of the direct inflation terms. (The only exception appears in the net foreign assets equation, suggesting that a rise in inflation induces some transfer of funds abroad.) This finding may be regarded both as evidence that services from assets do not vary systematically with inflation and as an indication that the use of pretax rates of return (that is, ignoring the possible inflation dependence of effective tax rates) was not too egregious an error.

Table 1.Lower-Level Demand Equations: Financial Assets
Price Coefficients
AssetConstantCash andsight depositsTime depositsNational savingsShort-term marketablesecuritiesGovernment bondsNet foreign assetsTimeInflation
Cash and sight deposits0.066–0.550.7910.0919–0.226–0.0364–0.0705
(11.67)(–2.41)(3.73)(–3.12)(–1.42)(–1.28)
Time deposits0.02750.791–0.890–0.4770.622–0.04600.00034
(2.86)(3.73)(–2.59)(2.45)(–1.15)(1.99)
National savings0.8730.0919–0.4770.08080.00160.09090.2118aa
Short-term marketable securities0.622–0.0016–0.306–0.0331–0.0585
(–3.12)(2.45)(–1.22)(–1.60)(–1.20)
Government bonds0.0997–0.0364–0.04600.0909–0.03310.0246
(22.0)(–1.42)(–1.15)(–1.60)(0.559)
Net foreign assets–0.0661–0.07050.2118–0.0585–0.08280.002690.282
(–3.42)(–1.28)(–1.20)(–0.742)(7.0)(1.63)
Note: Dashes indicate coefficients set to zero; where appropriate, t-ratios are given in parentheses.
Table 2.Lower-Level Demand Equations: Real Capital
Dependent variable (desired shares in total real capital)ConstantHousingProductive CapitalTimeInflation
Housing0,557–0.4220.4220.00332
Productive capital0.4430.422–0.422–0.00332
(17.6)(2.44)(–5.71)
Note: Dashes indicate coefficients set to zero; where appropriate, t-ratios are given in parentheses for unconstrained parameters.

Although it does not directly influence the allocation of financial assets, inflation does lead to sizable substitution effects through the price terms of sight deposits and cash. This substitution consists mainly of a switch from sight deposits and cash into savings deposits, although higher inflation also discourages the demand for marketable government bonds while increasing the desired share of national savings. The one nonintuitive result is the marked shift away from short-term securities. Interpreting the demand for these short-term instruments, however, is fraught with difficulty because the Bank of England was intervening on a massive scale in this market during much of the sample period.

Tables 2 and 3 present the results for the real capital and liability demand systems. These parameter estimates require rather less comment than the financial asset equations. Once again, inflation has no direct impact. Time trends, however, are very important. Price sensitivity appears surprisingly high, although this is in part because the dependent variables are larger, owing to the high degree of aggregation within these categories.

Some of the most interesting results are found in the upper-level demand equations reported in Table 4. These show the allocation of total net worth between financial assets, liabilities, and real capital. In contrast to the lower-level equations, inflation has a highly significant direct influence. In particular, a rise in inflation causes investors to increase their holdings of both financial assets and liabilities, leaving their stock of real capital unchanged.

Table 3.Lower-Level Demand Equations: Real Capital
Dependent variable (desired share in total liabilities)ConstantSterling Bank LendingNon-Sterling Bank LendingTimeInflation
Sterling bank lending–0.024–0.1530.153–0.00203
(–1.456)(–1.49)(–5.67)
Non-sterling bank lending1.0240.153–0.1530.00203
Note: As mentioned at the outset, liabilities are treated as negative assets. Hence, arise in a liability’s yield produces a fall in notional price 1/(1 + ril) and, thus, an increase in compensated demand. Because liabilities are negative numbers, an increase in demand represents a decline in the absolute value of the desired liability. Hence, own-pnce elasticities should be negative (or small and positive) just as for financial assets and real capital. Dashes indicate coefficients set to zero; where appropriate, t-ratios are given in parentheses.
Table 4.Upper-Level Demand Equations
Dependent variabls (desired share in total net worth)Price Coefficients
ConstantAssetsCapitalLiabilitiesTimeInflationReal Wealth
Financial assets0.9740.1380.137–0.2750.003490.3270.067
(1.23)(1.01)(–1.05)(4.15)(2.36)(–1.02)
Capital–0.160–0.157–0.1740.331–0.001950.331
(–0.240)(–1.33)(–1.66)(–2.67)(1.49)
Liabilities0.1860.0190.037–0.056–0.00154–0.327–0.016
Note: Dashes indicate coefficients set to zero; f-ratios are given in parentheses for unconstrained parameters.

It may well be that this result reflects the influence of inflation-dependent effective tax rates. An alternative explanation might be that risk is an important consideration in the broad allocation among these upper-level categories of financial assets, liabilities, and real capital. Either taxes or risk could also explain the apparent failure of the symmetry test for the upper-level demand system, and either explanation of the results can be made reasonably convincing.

As regards effective tax rates, Feldstein (1980) showed for the United States that plausible parameter values imply that inflation markedly reduces the after-tax return on capital. Yet the chance to offset nominal interest payments against tax might encourage investors to increase their indebtedness and to acquire more financial assets and real capital. The net impact of these two effects could well be that the demand for real capital stays unchanged while liability and real asset demands rise.

As regards the importance of risk, it is possible that inflation could alter both the absolute and relative riskiness of real capital, financial assets, and liabilities. Greater overall risk might encourage a general diversification of portfolios, whereas an increase in the relative riskiness of real capital might mean that its desired share remained unchanged. Why might the relative riskiness of real capital rise? A possible answer, at least for productive capital, is that nominal wage contracts in the presence of high and variable inflation might make returns to capital quite unpredictable, especially because of the high gearing that such returns are likely to have with respect to variations in the real wage rate.

The last results to report concern the speed at which desired shares adjust (Table 5). As may be seen from the table, the estimated values are quite reasonable for quarterly data, suggesting that the bulk of adjustment occurs within two years of a shock to the system. These figures for speed agree fairly well with those reported in the literature on money demand (see Judd and Scadding (1982)).

Table 5.Speed of Stock Adjustment
StockRate of Adjustment

(In percent per quarter)
Upper level desired shares16.1
Financial asset shares16.4
Liability shares13.2
Real capital shares11.7

V. Conclusions

The general message of this study has been that inflation is highly significant to portfolio choice and affects both the broad allocation between liabilities, real capital, and financial assets and the more detailed allocation within those categories. Substitution effects between financial assets produce a major rearrangement of portfolios in the face of inflation. Many of the substitution terms estimated in the study were pleasingly in accord with theory and intuition (negative own-price elasticities and a major switch from cash and sight deposits into time deposits when inflation rises, for example). Other effects, like the reduced demand for government bonds (as a share of financial assets) in the presence of higher inflation, are interesting and somewhat less obvious. Perhaps the most striking result occurs in the upper-level demand equations, where increased inflation appears to induce a major expansion in liabilities that is offset by acquisition of financial assets. Unfortunately, an unambiguous interpretation of this phenomenon could not be given because the competing explanations—inflation-dependent tax rates and risk effects—can both be argued with reasonable conviction.

Of course, these conclusions are subject to caveats. One issue dealt with cursorily in the paper is the initial decision to look at the balance sheet of the nonbank private sector. It is quite possible that banks’ portfolio behavior partially offsets changes in the asset demands of the nonbank private sector. Thus, for example, a switch by nonbank agents from deposits to government bonds might be offset, with very little pressure on interest rates, by a fall in the banks’ holdings of government bonds. The possibility of such offsetting effects suggests that a further step in this research might be to examine banks’ portfolio behavior.

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Mr. Perraudin is currently doing research in economics at Harvard University; he holds degrees from Oxford University and the London School of Economics and Political Science. This paper is a shortened version of one prepared while the author was a summer intern in the Fiscal Affairs Department of the Fund (Perraudin (1987)). The author thanks Nicola Rossi for numerous helpful discussions, and Benjamin Friedman, Dale Jorgenson, and Fund staff economists for comments on earlier drafts.

The notion of quasi-separability was introduced by Gorman (1976).

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