Dynamic portfolio adjustment and capital controls: a Euler equation approach.

Jansen, W. Jos

1. Introduction

Empirical papers on (intertemporal) portfolio balance models fall into two categories. The first category assumes that asset holdings can be changed instantaneously and without cost. Asset demand is then determined by the expected returns and the covariance matrix of the returns and the attitude towards risk. Or, written in the form of an asset pricing relation, the expected returns depend on asset supplies, risk aversion, and the return covariance matrix. The empirical work, which often focuses on asset pricing relations, is geared toward testing the mean variance (MV) restrictions implied by the model. These papers typically estimate the structural parameters governing the portfolio problem, i.e., the risk aversion parameter and the conditional return covariances, under the assumption of rational expectations. Recent research has incorporated time-varying conditional covariances into the portfolio model, usually by specifying them as a member of the autoregressive conditional heteroskedasticity (ARCH) family.(1) The MV restrictions are virtually always strongly rejected.

The second body of literature abandons the idea of instantaneous portfolio adjustment and has established the lagged response of asset demand to permanent changes in expected returns as an empirical regularity, especially for less liquid financial assets. The dynamic specification is usually a variant of the multivariate stock adjustment model introduced by Brainard and Tobin (1968). According to that model, investors gradually adjust their asset positions to their desired levels implied by the static portfolio model. The papers in this vein all estimate reduced-form equations, usually do not assume rational expectations, and use interest rates as proxies for expected holding period yields. Moreover, they are only able to test some of the weaker implications of portfolio theory, like symmetry and positive definiteness of the matrix of return coefficients. Although several authors refer to quadratic adjustment costs to motivate their dynamic specification, they do not fully incorporate the theoretical restrictions in their empirical specification. Adjustment costs merely serve as an expedient to justify the appearance of lagged variables in the econometric specification.(2) From a choice-theoretic point of view, this is unsatisfactory because it remains unclear how the reduced form estimates should be interpreted in terms of structural parameters. The plausibility of the coefficients obtained is therefore hard to judge.

Zietz and Weichert (1988) demonstrate the importance of a correct dynamic specification of asset demand systems for testing hypotheses implied by portfolio theory. In the static version of their asset demand model, homogeneity and symmetry of the matrix of return coefficients were rejected, while in the dynamic version these hypotheses were accepted. This finding, in combination with abundant evidence that lagged asset holdings have statistically significant effects, strongly suggests that tests of MV restrictions based on structurally estimated models should also take dynamics into account if these tests are to be dependable. Unwarranted neglect of lagged portfolio adjustment may lie at the root of the rejection of MV efficiency because of misspecification bias in the parameter estimates. A similar argument applies with respect to capital controls, which were maintained in many OECD countries in the 1970s and part of the 1980s.

This paper aims to contribute to the two strands in the literature mentioned above. First, we examine the empirical validity of MV restrictions in an asset demand system in the presence of dynamic adjustment and capital controls. Second, because we estimate the structural parameters of the portfolio problem, we can judge the plausibility of the parameter estimates. In particular, we investigate whether adjustment costs, which are often thought to be rather low, can plausibly explain the observed lagged portfolio adjustment. Third, we explore the potential of existing capital controls and adjustment costs to explain the "home bias" observed in portfolios in industrialized economies, that is, the empirical observation that foreign assets are greatly underrepresented in portfolios as compared to an optimal portfolio selected on the basis of observed returns in a simple MV framework (see French and Poterba 1991).

Our multiasset dynamic portfolio model is explicitly derived from the optimization problem of a risk-averse consumer who maximizes an intertemporal utility function in consumption under uncertainty, capital controls, and quadratic adjustment costs. We derive the consumer's portfolio allocation rule as well as the consumption rule. We estimate the model's structural parameters, using quarterly observations on the portfolio of the German private sector in the period 1975.I-1990.II. We assess the effects of capital controls and adjustment costs, and also address the question of whether the empirical results are consistent with MV efficiency.

The remainder of the paper is organized as follows. In section 2 we give a short description of the relevant data. In section 3 we set out the model. Section 4 is devoted to empirical application issues, and section 5 presents the empirical results. The paper ends with a summary and some conclusions.

2. Data

We analyze the portfolio behavior of the German private sector in the period 1975.I-1990.I. Net wealth is allocated among three assets: assets from the U.S., the Rest of the World (RW), and Germany itself.(3) As Figure 1 shows, the German portfolio has become much more internationally diversified over time, especially since the early 1980s. The share of U.S. assets roughly tripled between 1975 and 1990, rising to approximately 7% in 1990, and the share of assets from the Rest of the World experienced an almost six-fold increase from 8 to 47%. The share of German assets steeply declined from 89 to 46%. However, the German portfolio still displays a considerable "home bias": its composition is a long way from the internationally completely diversified portfolio (world market portfolio) implied by simple theoretical portfolio models (Dumas 1994). Investors in other industrialized countries also exhibit a substantial home asset preference, as French and Poterba (1991) and Tesar and Werner (1992) show.

In Figure 2 we plot the time series of the (realized) total returns of the three assets, and in Table 1 we list some summary statistics.(4) The quarterly total return on the foreign assets displays far greater variability than the return on German assets, because these returns are dominated by exchange rate changes. For a German investor, holding a U.S. security is riskier than one from the Rest of the World because the latter is a composite asset, which is naturally more diversified. The American return does not seem to display the conventional risk-return trade-off: the average return is the lowest, while the variability is the largest. The return on RW assets follows a normal pattern: Investors have on average earned more on RW assets than on German assets as a compensation for greater exposure to risk.

Because there are no persistent trends in the three-return series, we need to introduce extra variables into the model to explain the observed international diversification. An obvious candidate is the worldwide liberalization of international capital movements that has taken place over the past two decades. Institutional barriers to cross-border capital flows were brought down on a massive scale, especially in the 1980s. The U.K. abolished all exchange controls at a stroke in 1979, and Japan liberalized from 1980 onward. The drive for greater European unity created a boost for the complete liberalization of intra-EC capital movements. OECD (1990, pp. 3234) gives a concise historical overview of the liberalization process. Because both the U.S. and Germany traditionally have had liberal regulatory regimes concerning international capital movements, the cause for the diversification must primarily lie with the liberalization in the Rest of the World.

Measuring the level or intensity of existing capital controls necessarily involves ad hoc methods. We base our capital control index on the extent countries comply with the OECD Code of Liberalization (OECD 1990, pp. 63-72). All OECD countries are signatories of this Code, which prohibits restrictions on cross-border financial flows. However, countries are allowed to lodge general derogations and full and limited reservations on individual items covered by the Code for both capital inflows and outflows. Our index is defined as the number of derogations and full reservations lodged by RW countries, expressed as a fraction of the total number of items under the Code.(5)

Table 1. Summary Statistics of Returns for German Investors

Mean Standard Deviation

Total Return U.S. 0.0143 0.0602
Total Return RW 0.0181 0.0293
Total Return Germany 0.0155 0.0064
Total Return Portfolio 0.0157 0.0112

[Delta] Exchange Rate U.S. -0.0060 0.0579
[Delta] Exchange Rate RW -0.0060 0.0282
Interest Rate U.S. 0.0203 0.0070
Interest Rate RW 0.0241 0.0047
Interest Rate Germany 0.0155 0.0064
Inflation Germany 0.0080 0.0062

Quarterly rates. Sample period: 1975.I-1990.I.

Figure 3 shows the development of our measure of capital inflow and outflow controls in the Rest of the World. Both indices gradually decrease until the mid-1980s, after which the decline accelerates. The majority of the remaining restrictions at the end of the sample period were in force in Greece, Ireland, Portugal, and Spain, which have a minor influence on international capital flows. Capital outflows (purchase of foreign securities by domestic agents) are more heavily regulated than capital inflows (sale of domestic securities to foreign agents). This reflects to a large extent prudential considerations on the part of the authorities, who want to protect ordinary domestic savers from dubious high-risk investments abroad (OECD 1990).

3. The Model

We assume that the representative investor/consumer allocates his wealth among n risky assets, [N.sub.1], . . ., [N.sub.n], with prices [p.sub.1], . . ., [p.sub.n] that follow an (n + 1)-dimensional stochastic process, jointly with the consumption price index [p.sub.0]

W(t) = [summation of] [p.sub.i][N.sub.i] [where] i = 1 to n (1)

dp(t) = diag(p)(t)){[Phi](t)dt + S(t)dz(t)} (2)

where W denotes nominal wealth, t denotes time, p = ([p.sub.0], . . ., [p.sub.n])[prime], S is an (n + 1) x (n + 1) matrix, [Phi] = ([Pi], [r.sub.1], . . ., [r.sub.n])[prime] = ([Pi], r[prime]) is the vector of instantaneous conditional expected growth rates of p (inflation rate and returns) and dz = ([d[z.sub.0], . . ., d[z.sub.n])' denotes a Brownian motion process. Partitioning S[prime] as (s, [S[prime].sub.n]), where [S.sub.n] is the n x (n + 1) submatrix of S consisting of the bottom n rows and s[prime] is the first row of S, we define

[Mathematical Expression Omitted]

where [Omega] denotes the conditional covariance matrix of the returns, [[Sigma].sub.r[Pi]] the vector of conditional covariances of returns and inflation, and [Mathematical Expression Omitted] the conditional variance of the inflation rate. The investor consumes out of his wealth at rate C(t). Merton (1971, p. 379) shows that, with free portfolio adjustment, this results in the following differential equation for nominal wealth (or budget equation):

dW(t) = [summaton of] [N.sub.i]d[p.sub.i] - C(t)dt [where] i = 1 to n. (3)

We extend the standard model with the assumption that changing the portfolio allocation is costly. The theoretical literature on adjustment costs in portfolio problems has focused on the case of linear adjustment costs; that is, the costs incurred are proportional to the value of the transaction. (See Constantinides [1986], Dumas and Luciano [1991] and Davis and Norman [1990], who analyze the problem in the context of two assets: one risky and one risk-free.) The optimal policy is to minimize transactions by keeping the portfolio share of the risky asset within a target zone. As long as this share is inside the interval there is no trade, and when it is outside the interval, the agent adjusts in one step to the nearest boundary. The higher the adjustment costs the wider the no-action band. Unfortunately, for more than one risky asset, the problem becomes virtually intractable (Davis and Norman 1990). Although linear (or even concave) transaction costs may be considered more realistic than quadratic adjustment costs on a priori grounds, we resort to the latter in order to be able to derive estimable equations.

We assume that adjustment costs do not fall on the increase in asset holdings due to the accumulation of wealth, but only on trading that relates to portfolio adjustment, that is on

[Mathematical Expression Omitted]

where [a.sub.i] = [p.sub.i][N.sub.i]/W (for a similar distinction between financial flows, see Friedman 1977). To maintain homogeneity in wealth we therefore specify the adjustment cost function as [Mathematical Expression Omitted], where a = ([a.sub.1], . . ., [a.sub.n])[prime] is the vector of asset shares, and C is an n x n symmetric positive definite matrix of adjustment cost parameters. The basic wealth accumulation equation changes from Equation 3 into

[Mathematical Expression Omitted], (4)

where [Gamma] is the rate of consumption out of wealth, [Gamma](t) = C(t)/W(t). To link wealth to the volume of consumption, we need the differential equation for real wealth. Applying Ito's lemma, we obtain

[Mathematical Expression Omitted]. (5)

Assuming that [Gamma](t) is integrable, the stochastic integral of Equation 5 is

[Mathematical Expression Omitted]. (6)

The investor maximizes the expected utility of his consumption stream given by

[Mathematical Expression Omitted] (7)

subject to the budget restriction, Equation 6,

[Iota]a = 1 (8)

Qa(t) [less than or equal to] q(t) (9)

where E is the expectation operator, I(0) denotes the information set available at time t = 0, [Rho] is the rate of time preference, 1 - [Beta] is the Arrow-Pratt coefficient of relative risk aversion, and [Iota] is an n-vector of ones. We assume [Beta] [less than] 1; that is, the investor is risk averse. [Beta] = 1 corresponds with risk neutrality, while [Beta] = 0 indicates logarithmic utility. The set of restrictions in Equation 9 reflects the r capital market restrictions, which are assumed to take the form of ceilings. Q is an a priori known r x n matrix and q is an r-vector of permitted maximum holdings. Mandatory minimum holdings can be fitted into this format by multiplying the restriction by - 1.

We show in the Technical Appendix that the open-loop policy for a and [Gamma] that maximizes Equation 7 conditionally on the information available at t = 0 satisfies the following differential equation:

[Mathematical Expression Omitted], (10)

where [Theta] is a Lagrange multiplier related to the capital market restrictions in Equation 9, and [Mu] is a shadow rate of return. The equilibrium equations are found to be

[Mathematical Expression Omitted], (11)

where [Mathematical Expression Omitted], and [Mathematical Expression Omitted]. This is the static portfolio model found in Parkin (1970), for example. In the Technical Appendix, we also show that the steady-state rate of consumption, [Mathematical Expression Omitted], satisfies

[Mathematical Expression Omitted]. (12)

The steady-state rate of consumption out of wealth depends positively on the rate of time preference r for a risk-averse investor ([Beta] [less than] 1). The sign of the effect of the portfolio yield and variance, however, depends on the sign of [Beta]. Investors with B [less than] 0 increase their consumption rate if the expected portfolio yield increases or the uncertainty around it decreases. This 'standard' outcome (see Sandmo 1970) is reversed for moderately risk-averse investors (0 [less than] [Beta] [less than] 1), however. This can be interpreted by noting that 1/(1 - [Beta]) serves as the intertemporal elasticity of substitution between consumption in different periods (Blanchard and Fischer 1989, p. 280). If this elasticity is high, higher expected returns will induce a substantial increase in savings. Also a higher variance of returns will make future consumption less certain and will lead to a substitution toward current consumption. When investors have logarithmic utility functions ([Beta] = 0) our model replicates Merton's (1971) result for the static model that the investment and consumption decisions are independent. In this case the consumption rate equals the rate of time preference [Rho].

In the Technical Appendix we also derive the asymptotic solution to the intertemporal portfolio problem, which can be written as

[Mathematical Expression Omitted]. (13)

Equation (13) describes the working of the dynamic portfolio model.(6) A rise in the expected return of an asset over a future time interval changes the desired static portfolio a over the same interval. The target portfolio [a.sup.d] changes immediately, however. Because the matrices [G.sub.1], [G.sub.2], and [[Theta].sub.2] are functions of the matrices B and C, the degree to which [a.sup.d] changes depends on the latter matrices as well. With low adjustment costs, [[Theta].sub.2] is high, and the investor discounts future returns at a high rate. In fact, when adjustment costs are zero, [[Theta].sub.2] is infinite, and the target portfolio is not affected until the expected change in returns is imminent. The rate of change in actual asset holdings depends on the adjustment speed matrix M, which also depends on C and B. M satisfies [Iota][prime]M = 0 (adding-up constraint) and is not in general symmetric. However, the matrix of impact (short-run) multipliers of the yields ([Mathematical Expression Omitted]) is symmetric asymptotically as well as positive semidefinite. This says that the impact effect of an expected permanent change in the return of asset i on the demand for asset j should be symmetric in i and j if the system is in equilibrium initially. We will use the estimates of M and [B.sub.i] to assess the significance and severity of adjustment frictions.

4. Empirical Specification Issues

We estimate the parameters of the model via the first-order conditions of the portfolio problem, as summarized in Equation 10 by the Generalized Method of Moments (GMM) described in Hansen (1982). Obtaining estimates in this way is easier and less computationally demanding than estimation of the stock adjustment model in Equation 13, which features the expected future path of the returns. The latter procedure requires estimation of an explicit model of expected returns simultaneously with the asset demand system. By projecting the observed returns on the information set available at the beginning of the period, GMM estimation of the Euler equation renders our estimates consistent with rational expectations. By contrast, papers on stock adjustment models of asset demand usually adopt static expectations or resort to an ad hoc formulation of expected yields (like interest rates or lagged yields). This approach violates rational expectations. Furthermore, by using an instrumental variables method, the estimation procedure corrects for the simultaneity that may exist between asset holdings and (expected) returns. This is particularly relevant in case the portfolio model is estimated as an asset demand system, since, as the supply of assets should be fairly inelastic in the short run, asset returns will be correlated with the disturbances in the asset demand relations.

The differential equation system in Equation 10 is linear, but with time-varying coefficients due to time-varying conditional second moments of returns and inflation. To make the model suitable for empirical testing, we use a steady-state approximation with constant coefficients(7) and convert the differential equations to their discrete time equivalents:

[Mathematical Expression Omitted] (14)

where [Epsilon] is a vector of disturbances. a(t) is known at the beginning of period t. When estimating Equation 14, we use the realized values of a(t + 1), a(t + 2), and [Mu](t) instead of planned or expected ones. We thus introduce measurement errors into Equation 14, which under rational expectations have mean zero and are uncorrelated with the information set in period t. However, the measurement errors cause e to be correlated with the explanatory variables in Equation 14. Our estimation problem can thus be seen as an errors-in-variables problem.

Because we want to employ as many theoretical restrictions as possible, we also estimate an equation for the consumption rate

[[Gamma].sup.*](t) - [Gamma](t) = [[Epsilon].sub.[Gamma]] (t) E[[[Epsilon].sub.[Gamma]] (t) [where] I(t)] = 0 (15)

where [Gamma] is the observed consumption rate and the expression for [[Gamma].sup.*] is taken from Equation 12. Because observations on the consumption rate are not readily available, we have constructed a series for this variable.(8) The sample mean of [Gamma] is 1.32% per quarter.

According to Equation 10, capital controls give rise to a subjective cost component in the shadow rate of return [[Mu].sub.i] of the directly affected asset. Since direct observations on restrictions or associated shadow prices are not available, we specify the CC premia as a function of our capital controls indices.(9) Capital import controls in the RW prevent German investors from buying as much of RW assets as they would like, because RW citizens are not allowed to sell. A negative premium ensues, making [[Mu].sub.2] [less than] [r.sub.2]. Similarly, capital export controls hinder RW investors from investing in German assets, depressing global demand for German assets. Consequently, German investors end up with more DM-assets in their possession than they want. This effect is captured by a positive premium, making [[Mu].sub.3] [greater than] [r.sub.3].(10) We parameterize the CC premia [[Theta].sub.i] as a nonlinear function of the appropriate capital control index,

[[Theta].sub.2](t) = -[{C[C.sub.I](t)}.sup.1/[Xi]I]. 0 [less than] [Xi]I [less than] 1,

[[Theta].sub.3](t) = [{C[C.sub.E](t)}.sup.1/[Xi]E], 0 [less than] [Xi]E [less than] 1, (16)

where C[C.sub.I] and C[C.sub.E] denote the index of capital import and export controls imposed by the Rest of the World. An increase in capital controls leads to a more than proportional increase in the CC premium because of the reduced scope for evasion through financial transactions that are still allowed (Mathieson and Rojas-Suarez 1993).(11) The powers in Equation 16 are 1/[[Xi].sub.i] rather than [Xi]i to facilitate the interpretation. Because [[Xi].sub.i] = 0 corresponds to a zero-capital control premium, the t-statistics provide a direct test for capital control effects. (Recall that C[C.sub.I] and C[C.sub.E] lie between zero and one by construction.)

Because of the singular nature of the asset demand system, caused by [Iota][prime]a = 1, the system suffers from under-identification. We derive the necessary additional identifying restrictions in the Technical Appendix. They number 2n + 3 and are listed below.

(i) [Beta] = 1 - [Iota][prime] [[Omega].sup.-1][Iota] 1 restriction

(ii) C[Iota] = n[iota] n restrictions

(iii) [[Sigma].sub.r[Pi]] = 0 and [Mathematical Expression Omitted] n + 1 restrictions

(iv) [Rho] = 0.005 1 restriction.

We substitute 1 - [iota][prime][[Omega].sup.-1][iota] for [Beta] in the expressions for B and [[Gamma].sup.*]. Because [Mathematical Expression Omitted], each row of C is identified only up to an additive constant. Restriction (iii) reflects the assumption that inflation is nonstochastic. Without loss of generality, we may assume that S in Equation 2 is a lower triangular matrix. We estimate [Omega]'s Cholesky factor S rather than [Omega] itself to ensure that [Omega] is symmetric positive semidefinite. We estimate the off-diagonal elements of C; the diagonal elements are calculated via restriction (ii): [c.sub.ii] = n - [[Sigma].sub.i [not equal to] j] [c.sub.ij]. Structural estimation thus involves 11 parameters: six nonzero elements of the Cholesky factor S, three off-diagonal elements of C, and the capital control premium parameters [[Xi].sub.I] and [[Xi].sub.E].

As a consequence of the under-identification of C, the absolute magnitude of the elements of C bears no relation to the intensity of adjustment frictions, and the t-statistics of estimates of individual elements of C have no meaning. Of course, the relative sizes of the elements in each row of C do matter, and we follow several paths to assess the significance and severity of adjustment costs. First, we perform a joint test of significance of all parameters in C. Second, we calculate the estimated average adjustment costs per period [Mathematical Expression Omitted] and compare it to the average portfolio return. Third, we compare impact multipliers [B.sub.i] and long-run multipliers B. Fourth, to find out which asset demands are affected most by adjustment costs, we take a look at the response pattern of the asset demand system following a permanent shock.

5. Empirical Results

Table 2 presents the results of the estimation of Equations 14 and 15 by GMM. The sample period is 1975.I-1990.I (61 quarters).(12) Since we employ 37 moments to estimate 11 parameters, GMM-estimation involves 37 - 11 = 26 overidentifying restrictions. The model passes the test of overidentifying restrictions, which tests whether the instruments are indeed orthogonal to the disturbances. The [X.sup.2](26) statistic reaches only 19.84.

Return Coefficients

All but one element of the Cholesky factor S are significantly different from zero. The estimates point to an extremely large covariance matrix of the returns [Omega]. The order of magnitude is way off the (unconditional) return covariance matrix observed over the sample period, which is shown next to [Omega] in Table 2. For instance, the standard deviation of the U.S. return is estimated to be 2.775, while in the sample period it was only 0.060. Moreover, the correlation pattern implied by [Omega] differs from the sample correlation matrix. The latter features only positive correlations, the largest one between the U.S. and RW returns and the smallest one between the [TABULAR DATA FOR TABLE 2 OMITTED] RW and German returns. By contrast, 11 implies a zero correlation between the two foreign returns and a comparatively large correlation between the RW and German returns.(13)

The implied estimate of [Beta] is highly significant. The coefficient of relative risk aversion (1 - [Beta]) is about one, indicating moderate risk aversion. The intertemporal elasticity of substitution, 1/(1 - [Beta]), is also one. The utility function thus approaches the logarithmic function, which is often used in theoretical work. However, it should be noted that this outcome appears to be a direct consequence of the large estimate for [Omega]. [Beta] is determined by the consumption rate equation, which is dominated by the variance term 1/2[Beta]a[prime][Omega]a. In order to keep the contribution of this term at bay, [Beta] is forced toward zero.

The large [Omega] translates into a matrix of low return coefficients B, although all its elements save one are highly significantly different from zero. For instance, a permanent increase of one percentage point in the RW expected return (on an annual basis) only leads to an increase of 0.17 percentage point in the portfolio share of RW assets. The U.S. return coefficients are very small due to the high estimated variability of the U.S. return. The B-matrix does not show overall gross substitutability (Tobin 1982), which is commonly expected on a priori grounds in studies estimating reduced-form equations. Here we find that U.S. and RW assets are weak complements, as a result of their favorable risk characteristics (negatively correlated returns). Low estimates of return coefficients are regularly obtained in reduced form studies (see e.g., Davis [1986] and Van Erp et al. [1989]). Sometimes the insensitivity of asset demand is blamed on endogeneity of asset positions and returns or the use of interest rates rather than expected yields (bias due to errors in variables). Although neither argument applies in our case because the GMM estimator projects all yields and asset positions on predetermined variables, we still find low (but significant) return coefficients.

Adjustment Costs

The hypothesis C = 0 is strongly rejected on the basis of a Gallant-Jorgenson (1979) test (see also Godfrey 1988, pp. 167-173). The estimated adjustment costs matrix is positive-definite (the smallest eigenvalue is 0.94). On average, actual adjustment costs were only 0.023% of financial wealth per quarter. By comparison, the difference between the (ex-post) return on the instantaneously optimal portfolio and that on the actually observed portfolio was 0.122% per quarter on average. Hence, adjustment costs appear to be low, which is in accordance with a priori beliefs. Comparing the matrix of short-run multipliers [B.sub.i] with the matrix of long-run multipliers B, we observe that the elements of [B.sub.i] are in general significantly smaller in absolute value than the corresponding elements of B, indicating that adjustment is not completed within one quarter.

In order to find out which asset demand is most hindered by adjustment costs, we present in Table 3 the demand system's response after permanent one percentage point increases (on an annual basis) in various expected returns starting from the steady state. The calculations are based on the asymptotic solution in Equation 13. Table 3 also reports the matrix of adjustment speeds M. The dynamic response pattern points to a pretty quick pace of adjustment. After one quarter, approximately 50% of the total desired adjustment is realized. After two quarters the [TABULAR DATA FOR TABLE 3 OMITTED] figure is about 75%.(14) The median lag - the number of periods it takes to accomplish half of the required change is about one quarter.(15) The demand for U.S. assets reacts fastest to an increase in its own expected return, about two times as fast as the other assets' demand. This is not a completely plausible pattern. Since RW assets are a composite of assets from a lot of countries, portfolio investment in RW securities involves much higher costs of information, analysis, and transactions than portfolio investment in U.S. or German securities. One would therefore expect the demand for RW assets to display a slower speed of adjustment than the demand for U.S. assets, while the adjustment speed of German asset demand is expected to be highest.

Effects of Capital Controls and the Home Bias

The capital import premium parameter is very large but insignificant, while the capital export control premium parameter is significant. Can the two types of frictions studied in this paper - capital controls and adjustment costs - account for the observed home bias of the German portfolio? Our estimates imply an (unrealistically) large CC premium of -0.0923 in the RW return and one of 0.0223 in the German return at the end of 1990. Abolishment of all remaining capital controls is thus equivalent to a permanent change in r of (0.0000, 0.0923, -0.0223)[prime]. This will lead to the following changes in the portfolio: The share of U.S. and RW assets will increase by 0.61 and 8.06 percentage points, respectively, while the share of German assets will go down by 8.67 percentage points. This demonstrates that the share of German assets will remain hovering around 40% of the portfolio, indicating a substantial bias. Because adjustment costs only give rise to an adjustment lag of less than one year, they cannot explain the domestic bias phenomenon either.

Because unconstrained estimation leads to implausibly large capital control premia, which may unduly affect the outcomes, we also report estimates for the case in which we use prior information on the order of magnitude of these premia. In this way, we can assess the robustness of the results. Starting from simple portfolio theory, French and Poterba (1991) provide some rough calculations on the (subjective) expected return differentials that may rationalize the observed home bias in equity portfolios under full capital mobility. Investors have optimistic views on domestic returns and pessimistic views on foreign returns. For example, U.K. investors are found to expect that U.K. stock yields are about five percentage points higher than U.S. (or German) stock yields. For Japanese investors, the figure is 3.5 percentage points. Similarly, U.S. investors have more pessimistic expectations on U.K. returns than U.K. investors (about five percentage points).

French and Poterba's results imply that a reasonable order of magnitude of subjective expected return differentials is 1% on a quarterly basis. We therefore assume that remaining capital controls in the Rest of the World caused a comparable CC premium at the end of the sample period. More specifically, we require the sum of the CC premia to be in the neighborhood of 0.01 in the last three years of our sample (1987.I-1990.I)

[Mathematical Expression Omitted]. (17)

We impose the restriction in 1987-1990 only, because French and Poterba's calculations refer to the situation at the end of 1989, after major liberalizations had taken place. The variance of [[Epsilon].sub.p](t) is held fixed at an a priori value. Due to this (stochastic) parameter restriction we compute one moment extra, and the criterion function contains an extra term which amounts to a quadratic penalty for deviations of [[Theta].sub.3] - [[Theta].sub.2] from .01.

The estimation results are shown in Table 4. As expected, we get lower estimates of the parameters associated with the capital control premia which imply a gap equal to 0.75% between the expected return on RW assets and that on German assets in 1990. Although asset demand has become more sensitive to variations in expected returns - the elements of B have roughly tripled - the return coefficients are still small. Both capital control premium parameters are now significant. In other respects, the picture of Table 2 is not much changed. Adjustment costs are low but highly significant, and the estimated covariance matrix of the returns [Omega] is implausibly large. Foreign assets and German assets are gross substitutes, but the two foreign assets are complements. We conclude that capital controls cannot explain the home bias that is still present.

Mean-Variance Efficiency

The extremely large estimate of the return covariance matrix constitutes bad news for the empirical validity of the portfolio model, the static variant of which is close to the familiar mean-variance model. The reduced-form coefficients cannot be interpreted as being generated by the structural parameters. This can also be seen by starting from the other end: What would the matrix B look like if we combined a reasonable value for the risk aversion parameter and [TABULAR DATA FOR TABLE 4 OMITTED] the sample (unconditional) covariance matrix of the returns, which is at least of the right order? Taking [Beta] = -1, we get

[Mathematical Expression Omitted].

These return effects are too large to be plausible. A similar point has been made by Engel and Rodrigues (1993). Consequently, the perceptions of economists regarding the actual degree of return uncertainty and a reasonable degree of risk aversion appear to be fundamentally irreconcilable within the framework of mean-variance optimization. Reckoning with lags of adjustment and capital controls does not alter this conclusion.

The strong rejection of mean-variance efficiency may be attributed to several causes. An important candidate is violation of the rational expectations hypothesis that underlies our estimation method. Frankel and Froot (1987), Ito (1990), and Cavaglia, Verschoor, and Wolff (1993) analyze survey data and reject rational expectations in the foreign exchange market. An alternative possibility is the presence of a "peso problem," in which case observed returns are poor measures of otherwise rational expectations due to their high volatility. This is essentially a problem of insufficient observations. Table 1 shows that, measured over the sample period, U.S. assets earned on average less than German and RW assets, but that their return was much more uncertain. In consequence, U.S. assets are mean-variance dominated by the other two assets if covariances are neglected, implying zero demand for U.S. assets. Since German investors did hold U.S. assets it is likely that the true (average) expected U.S. return is greater than the historically recorded average return. Lewis (1991) presents evidence that peso problems played a role in U.S. financial markets during the 1979-1982 period.

Rejection may also be the result of our specification of the utility function, which features only one parameter [Beta] to describe two types of preferences: the degree of relative risk aversion (1 - [Beta]) and the degree of intertemporal substitutability of consumption across periods (1/(1 - [Beta])). These preferences are captured by separate parameters in a nonexpected utility framework. The portfolio rule depends on the degree of risk aversion, while the consumption rule depends on both the degree of risk aversion and the intertemporal elasticity of substitution (Svensson 1989). Our finding of low risk aversion and high volatility may be due to the fact that the equation for the consumption rate confuses effects of risk aversion and intertemporal substitution.

6. Summary and Conclusions

This paper presents an empirical dynamic portfolio balance model describing the portfolio behavior of the German private sector in the period 1975.I-1990.I. Net wealth is invested in assets from the U.S., the Rest of the World, and Germany. We solve the optimization problem of the representative German investor who maximizes the expected value of an intertemporal, time-separable, constant relative risk aversion (CRRA) utility function in consumption under uncertainty. The optimization problem is complicated by two factors: Investors incur costs when they change the portfolio composition, and they may be constrained in their behavior due to capital market regulations. Our empirical analysis contrasts with other work on dynamic asset demand models in that it relies on structural estimation (as opposed to reduced-form estimation). Assuming rational expectations, we estimate the model's structural parameters by applying the Generalized Method of Moments (GMM) estimation technique to the transformed Euler equations of the portfolio shares and the rate of consumption. We then make use of the full solution to the portfolio problem to compute short-run and long-run return effects and adjustment speeds of asset demand.

Estimation of a dynamic portfolio model by way of its structural parameters enables us to address several issues. First, we can examine whether the reduced-form coefficients are consistent with sensible values of the structural parameters. For example, we can find out whether low adjustment costs in financial markets are able to generate the empirically observed phenomenon of lagged portfolio adjustment. This is a contribution to the literature on empirical dynamic portfolio models. Second, we can investigate whether the rejection of mean-variance efficiency, consistently obtained in another body of literature, can be ascribed to the improper neglect of adjustment lags and capital controls in these studies. This is a contribution to the literature testing mean-variance restrictions under rational expectations. Third, we can examine whether existing capital controls and adjustment costs can explain the home bias in the portfolio.

We find that the structural parameters are significantly different from zero. Adjustment costs indeed are low, but nevertheless highly significant. The asset demand system displays very moderate adjustment lags. The median lag is about one quarter. The parameter of relative risk aversion is slightly less than one, implying a near-logarithmic utility function. Capital controls can explain part of the international diversification of the German portfolio, but cannot account for the domestic bias still present in the portfolio. Asset demand is rather insensitive to changes in expected returns, both in the long run and the short run. However, the return coefficients are significantly different from zero. The estimated structural parameters imply an estimate of the covariance matrix of the returns which is several orders of magnitude too large to be plausible. The finding that extremely high variances govern portfolio selection provides strong evidence against the portfolio model. Consequently, incorporating adjustment costs and capital controls into the portfolio model does not suffice to reverse the negative judgment on the validity of mean-variance restrictions generally found in the literature.

We thank Laura van Geest and two referees for helpful comments on earlier drafts. Accompanying the paper is a Technical Appendix, which contains details on the solution of the model various econometric issues, and the sources and construction of the data. It is available upon request from D.P.B.

1 Recent works includes Frankel (1985), Giovannini and Jorion (1989), Attanasio (1991), Engel and Rodrigues (1989, 1993), Thomas and Wickens (1993), and Jansen (1995). See Bollerslev, Chou, and Kroner (1992) for a comprehensive survey of ARCH applications in portfolio models and asset pricing relations.

2 Van Erp et al. (1989), Pain (1993), and Bettendorf and Van de Gaer (1991) derive asset demand relations under adjustment costs to show that the shape of their (general) dynamic system is consistent with optimal demand relations. Conrad (1980), Davis (1986), Perraudin (1987), and Bikker and van Els (1993) introduce dynamics without much discussion. Dinenis and Scott (1993) estimate a flexible-form asset demand system, extended with quadratic adjustment costs. This paper does not fit in the MV framework, however, because it is not based on the maximization of total wealth or consumption, but on a general utility function in asset returns and wealth. Pain (1993) and Dinenis and Scott (1993) apply instrumental variables estimation.

3 The limitation to three asset categories is imposed by the requirements of the estimation procedure (see section 5). The Technical Appendix contains details on the sources and construction of the data.

4 The total return (or holding period yield) on the assets is measured as the local three-month interest rate plus capital gains in the form of exchange rate changes. We follow the literature on the MV testing in measuring returns in local currency as the local short-term interest rate. The return on RW assets is a weighted average of the returns on assets from eight OECD countries. See the Technical Appendix for more details.

5 We do not count limited reservations, because they are often hardly restrictive and mainly reflect prudential considerations (Poret 1992).

6 Note that Equation 13 is the portfolio solution for an individual investor (or a group of identical investors). It is not a general equilibrium solution. In the empirical analysis we only focus on the German contribution to the global demand for all types of assets. Holdings of U.S. and RW assets by Germans represent only a small part of the global supply of those assets.

7 We assume that covariances are time independent. Jansen (1995) finds that rejection of mean-variance restrictions is unlikely to be caused by time variation of second moments of the returns or variations in risk aversion. Moreover, a test on ARCH effects in the returns yielded insignificant statistics. Consequently, the assumption of a time-independent [Omega] seems reasonable.

8 Because the only source of income in our model is investment income, it is not immediately obvious what the empirical counterpart to [Gamma] should be. Standard intertemporal models imply that aggregate consumption is proportional to aggregate total wealth, independent of the composition between financial and human wealth (see Blanchard and Fischer 1989, p. 119; Merton 1971). This suggests that we may measure [Gamma] by aggregate consumption as a fraction of total private wealth, defined as financial wealth plus discounted labor income. See the Technical Appendix for details on the calculations.

9 See Dooley and Isard (1980) and Spiegel (1990) for a similar approach to modeling capital control effects.

10 This restriction pertains to the liability side of the balance sheet, which in our portfolio is consolidated with the asset side. The portfolio model describes net positions of assets, hence asset trade occurs in one direction. In reality, cross-border financial flows move in opposite directions simultaneously, as residents of different countries swap claims on each other. Capital outflow restrictions in the RW frustrate this two-way exchange of financial assets and thus affect the portfolio composition.

11 We also tried linear and quadratic specifications for [[Theta].sub.i] (t), but these produced less satisfactory results.

12 For the asset demand equations we use as instruments: one- and two-period lagged values of actual total returns on foreign assets, the current German short-term rate and its one-period lagged value, the current value and two lags of the portfolio shares of foreign assets, the current value of the RW capital control indices, and a constant (15 instruments). For the consumption rate equation we take: the one- and two-period lagged total returns on foreign assets, the current and one-period lagged short-term German interest rate, and a constant (seven instruments). The need for adequate instrumentation puts an upper limit on the number of asset demand equations that can be successfully estimated. With four assets, a similar selection of lagged returns and asset holdings as instruments would lead to a total of 69 moments, which is clearly unfeasible with 61 observations. Reducing the number of instruments is no viable option here, because it leads to a lack of correlation between instruments and regressors and inferior estimator properties (on the optimal choice of instruments; see e.g., Bowden and Turkington 1984).

13 This pattern can be explained with the help of Table 1. Because U.S. assets are mean-variance dominated (ignoring covariances) by the other two assets. holding them can only be for risk diversification considerations (i.e., low correlations). For this reason, the correlation between the U.S. and RW returns is estimated to be zero, while the correlation between the RW and German returns is estimated to be rather high.

14 The exception is the response of U.S. assets to a change in the RW expected return, which in the long run is a tiny increase. However, there is undershooting in the short run, because the short-run and long-run coefficients have opposite signs. This peculiar adjustment pattern holds little economic significance because both coefficients are insignificantly different from zero. It is probably more realistic to put the desired change at zero.

15 Our results are more plausible in this respect than those of Dinenis and Scott (1993), who found that adjustment is spread over a large number of periods. implying large adjustment costs.

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