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Inter-industry differences and the impact of operating and financial leverages on equity risk.

Several previous studies have analyzed the association between a firm's operating and financial leverages and its beta. Recently, Mandelker and Rhee (1984) examine, using a correlation-based analysis, the effect of a firm's degree of operating leverage (DOL) and degree of financial leverage (DFL) on its beta and conclude that the impacts of DOL and DFL on beta are positive and statistically significant. Their theoretical model and its empirical testing implicitly assume that DOL and DFL are independent of each other, and strictly multiplicative. Such traditional assumption of independence, however, has been questioned by Huffman (1983) and others who argues that a firm's capacity decision may lead to important interactions between its DOL and DFL.(1) Huffman further posits that such interactions and the resulting impacts on equity risk may vary across industries, depending on the growth potential facing the industry.

If Mandelker and Rhee's model specification is correct, no inter-industry differences should exist in the relationship between DOL and DFL, nor would it exist in the impact of these two variables on a firm's beta. If, on the other hand, Huffman's model does capture the true relationship among DOL, DFL and beta, then variations in the relationship should arise in inter-industry comparisons.

This article empirically examines which of the two models is correctly specified. In so doing, the article relies on a multivariate causality approach. It examines the reasons for employing the causality approach as opposed to the more traditional correlation-based analysis explained below. The article starts with a brief account of the issues involved, describes the data and methodology used, presents and analyzes the empirical results, and offers a summary and some concluding remarks.

The Issues

Table 1 provides an inexhaustive list of empirical studies pertinent to the relationships among the operating and financial leverages of a finn and the systematic risk of its common stock.(2) It is evident from the table that theses studies fall into two broad categories - one that chooses variables in a somewhat arbitrary fashion, and another that bases the variable selection on some theoretical grounds.

The studies Logue and Merville (1972), Breen and Lemer (1973), Melicher (1974), and Thompson (1976) fall in the first category.(3) In all of these studies, the operating leverage and/or financial leverage variables appear in a larger set of variables chosen arbitrarily without reference to theoretical priors. Some general observations regarding the findings of this first group are in order. First, the importance of the financial leverage variables as determinants of beta varies considerably across studies. Also, a few studies report that the effect of financial leverage is time-specific, being significant only over some periods but losing significance over other periods. Second, the sign of the financial leverage coefficient across studies is inconsistent across time. And, finally, the relationship between financial leverage and beta seems sensitive to a firm's industrial characteristics.

Studies by Hamada (1972), Rubenstein (1973), Lev (1974), and Mandelker and Rhee (1984) test the impact of operating and/or financial leverages on beta based on some theoretical priors. After decomposing the systematic risk into the firm's operating and financing risk, Hamada and Rubenstein compare the betas between levered and unlevered firms and report that financial leverage explains approximately 20 percent of the systematic risk. Lev first develops a theoretical model that establishes a positive association between a firm's operating leverage and its systematic risk (and total risk). He then empirically examines the relationship between these variables in three selected industries and finds that the observed relationships are as hypothesized, though with a weak explanatory power. While Hamada (1972) and Rubenstein (1973) decompose systematic risk into its operating and financial components, it is Mandelker and Rhee (thereafter MR) who are [TABULAR DATA FOR TABLE 1 OMITTED] credited for extending and testing the decomposition model by explicitly incorporating the DOL and DEL.(4)

Mandelker and Rhee express the need for a formula that would: (1) explicitly introduce the degrees of the two types of leverage; (2) avoid econometric problems stemming from a nonlinear multiplicative effect of the financial structure on operating risk; and (3) allow for risky debt. Consequently, MR transform the Hamaria-Rubenstein decomposition formula into a beta model that explicitly considers DOL and DFL. In MR's construct, a firm's DOL and DFL represent key determinants of the firm's systematic risk. Their sample consists of 255 firms distributed over ten difference industries under the 2-digit SIC Industry Code. They construct 51 portfolios (5 in each portfolio) based on the ascending order for each of the three variables employed in the study (DOL, DFL, and beta). On regressing average betas on the averages of DOLs and DFLs of these portfolios, MR found that the estimated coefficients of DOL and DFL are consistently positive, and that some trade-offs exist between DOL and DFL.(5)

MR's model is based on the traditional assumption that the degree of total leverage (DTL) is simply the product of DOL and DFL. However, Huffman (1983) takes issue with this assumption. According to her, the traditional formula suffers from three inaccuracies. First, the DOL calculation(6) assumes that there is no upper bound on the firm's capacity production level, and consequently implies that DTL is "a simple timeless function of revenue and fixed costs." Huffman argues that this is simply not realistic. Second, the fixed production cost is considered exogenous in the traditional framework. However, Huffman points out that this cost is "endogenous to the decision environment of the rationally managed firm" and, therefore, would vary depending on the level of business risk.(7) Finally, following Myers (1977), Huffman argues that since an interaction should exist between the outstanding debt and subsequent investments, and since the fixed production costs should vary depending on the levels of outstanding debt, the impact of debt on the combined leverage is more complex than what is assumed in the traditional DTL formulation.

Employing Brennan's (1979) option pricing model, Huffman derives her own model for the degree of combined leverage (DCL). In Huffman's construct, DCL is not timeless but rather varies with the time-related arguments of the OPM probability density function. Huffman shows that DCL is an explicit function of the business risk of the firm as well as both explicit and implicit functions of outstanding debt. She discusses two properties of the capacity decision made by a levered firm. First, the increase in equity risk resulting from increased debt is partially offset by the firm's capacity decision. This offsetting ability, however, diminishes as the level of debt increases. Secondly, the capacity decision also partially offsets the impact of an increase in business risk. Again, this offsetting ability weakens if either revenue declines or debt level increases. Taken together, Huffman's model implies that the relationship among a firm's DOL, DFL, and equity risk should vary from industry to industry, based on the capacity decision flexibilities facing the industry.

If MR's proposition is correct, then changes in the DOL and DFL are expected to impact beta in the same direction, and DOL and DFL should exhibit a negative correlation for all firms irrespective of their industrial affiliations. However, if the alternative Huffman's construct is correct, we would observe such relationships to differ among industries. The basic purpose of this article is to empirically examine via a multivariate Granger-causality approach the validity of the two alternative propositions.

Data and Testing Methodology

Correlation-based Analysis Versus Causality Approach

To investigate whether or not the relationships among DOL, DFL and beta vary across industries, we employ a multivariate causality-approach. By doing so, we depart from the previous empirical studies in this area which have relied on correlation analyses whereby a measure of beta is regressed on contemporaneous values of some measures of the operating and financial leverages.

The implicit hypothesis in previous studies is that operating and financial leverages (or their proxies) cause beta. The presence of statistically significant coefficients on the right-hand-side variables in such a framework, however, does not necessarily imply that these variables have caused beta. For example, MR's finding of a significant coefficient on (the contemporaneous) value of DOL implies four alternative but equally plausible hypotheses.

H1: It is possible that changes in DOL "cause" changes in beta similar to the conventional view tested by MR.

H2: Given that changes in DOL are related to changes in beta, this may imply instead that beta "causes" DOL.

Clearly, a rising systematic risk could potentially induce the management to reduce the firm's operating risk (for example, by switching, if possible, from a capital intensive to a labor-intensive production mode). In the context of a CAPM model, a firm's cost of equity capital is determined by the beta of its common stock. Thus, the management may attempt to reduce systematic risk by lowering the firm's DOL.

H3: Beta and DOL are causally independent.

Granger (1980), for example, demonstrates that two variables may be highly correlated, yet not causally related at all. In this case, the apparent correlation between the two variables is simply the result of other variables causing them.

H4: DOL causes beta but with significant feedbacks (a combination of the first and second hypotheses).

In this case, causality between the two variables is bi-directional. Under this scenario, most previous studies that implicitly treat DOL as an exogenous variable would suffer from simultaneous-equation bias, rendering their results both biased and inconsistent. Similar remarks could also be made regarding the observed correlation between beta and DFL.

To summarize, a statistically significant coefficient on DOL (or DFL) in a beta equation is not a reliable evidence to support the underlying hypothesis that either variable has caused changes in beta. A more appropriate test to discriminate between the above four alternative hypotheses should focus not on the correlation between these accounting variables and beta, but rather on the direction of causality between them, a task that is performed in this paper using the concept of causality in the sense of Granger (1969).(8) Briefly, a covariance stationary time series {[y.sub.t]} is said to Granger-cause another stationary time series {[x.sub.t]}, if the prediction error of current x declines by using past values of y in addition to past values of x.

The Vector Autoregressive Modeling Technique

This study uses the vector autoregressive (VAR) modeling technique (see Hsiao, 1981, 1982; Sims, 1982). Sims recommends the VAR procedure over the more general "structural modeling" framework on the grounds that VAR, in contrast to the structural approach, does not impose any prior restrictions on the dynamic interrelationships among the variables. Moreover, Webb (1984), and Lupoletti and Webb (1986) report empirical results showing the relative efficiency and usefulness of the VAR technique over other modeling techniques. Fisher (1981) further argues that the VAR approach is "a convenient way of summarizing empirical regularities and perhaps suggesting predominant channels through which relations work" (p. 402).

Of course, the VAR methodology is not without drawbacks. One drawback stems from the VAR approach being a reduced-form technique. As such, the VAR results may not be capable of discriminating among alternative structural hypotheses. Researchers like Cooley and LeRoy (1985) and Leamer (1985) also criticize some common uses of the VAR approach. Nevertheless, Cooley and LeRoy (1985) themselves, and also Eichenbaum (1985) point out that the VAR is still a valid procedure for many uses like forecasting, the description of the cyclical behavior of a system, the generation of stylized facts about the underlying behavior of the system for testing existing hypotheses or developing new ones, and for "determining the existence of Granger-causal orderings, even in the absence of any theoretical reason to expect them" (Cooley and LeRoy, 1985, p. 306). The VAR model may also be subject to the Lucas critique (Fackler, 1985). That is, there is the possibility that a change in the underlying structure would invalidate the model inferences. Needless to say, such concern is general and not unique with VAR models. Additionally, Sims (1982) argues that the VAR results would still be valid in the face of structural shifts provided that these shifts are not very frequent or very drastic.

The VAR procedure has become very popular in applied econometric literature, and thus elaborate details of the procedure are not produced here (for some details, see Darrat, 1988; Darrat and Barnhart 1989). Nonetheless, a few comments about the procedure as employed in this article are worth making. First, the Granger (one-sided) causality tests are selected from a number of other alternative procedures in light of the Monte Carlo evidence reported in Geweke, Meese and Dent (1983). These Granger tests require the data to be stationary. We induce stationarity for each variable (beta, DOL, and DFL) by purging significant trend components through the use of an appropriate degree of differencing.(9) Another requirement of the Granger tests is that the stationary series have zero mean. To achieve that, each stationary series are mean corrected either by subtracting the appropriate mean or, alternatively, by including a constant term in all regressions.

Secondly, rather than imposing arbitrarily a common lag length on all variables in the VAR model, we supplement the multivariate Granger-causality tests by Akaike's final prediction error (FPE) criterion and select the appropriate lag length for each variable. As noted by Ahking and Miller (1985), the assumption of equal lag lengths for all variable used, for example, by Lutkepohl (1982) and Plosser (1987) is too restrictive and could lead to biased results.

Thirdly, to, obtain consistent (and asymptotically efficient) estimates, we pool the four equations and estimate them by means of the Zellner seemingly unrelated regression (SUR) procedure. It should be emphasized that the SUR procedure incorporates the contemporaneous relationship among the variables which the OLS approach ignores due to the sole use of lagged values of the variables. As Hsiao (1981) and Sephton (1988) argue, these relationships can be reflected in the correlation of the contemporaneous error terms across equations. Finally, we subject the final model to diagnostic checking by under- and over-fitting the model, by testing for structural instability, and through testing for autocorrelation in the residuals.

The VAR/FPE procedure mentioned above may yield three alternative outcomes for each variable in the model - absence of Granger-causality, weak-form Granger-causality, and strong-form Granger-causality. When the procedure suggests exclusion of a variable from a given equation, the implication is that there is no Granger-causal ordering. On the other hand, when a variable satisfies the FPE criterion and thus appears in the model, Granger-causality exists either of the weak-form or the strong-form. We determine the type of causality by likelihood ratio tests on the joint significance of the parameters within the system estimations. If the parameters of the variable as a group fail to achieve statistical significance, the variable is said to Granger-cause the left-hand side variable only in the weak sense. If, however, the parameters prove jointly significant, the Granger-causal ordering is said to be of the strong-form.

Sample

Application of the above FPE/VAR procedure could prove very costly in large samples. Consequently, we restrict our sample size to 48 firms selected from eight 4-digit (six 2-digit) SICs. We conduct the selection in the following manner.

First, we select eight 4-digit SIC manufacturing firms - 1311, 2834, 2911, 3312, 3711, 3714, 4911, and 4931.(10) Then, for the sake of convenience and also to avoid the seasonality effect, we establish a list of 206 firms whose fiscal year ends at the same time (December 31). The next step is to ascertain the data availability on these firms. Since we prefer a maximum often in each of the eight SIC codes, we randomly selected ten firms from those industries where a complete data set was available for more than ten firms (2911, 3711 + 3714, and 4911 + 4931). For three industries (1311, 2834, and 3312), the required data set was available for less than ten firms. Our final sample consists of the following:

[TABULAR DATA OMITTED]

Computation of the Variables

In order to ensure at least thirty time-series observations on each variable for each firm in the sample, we employ quarterly data from COMPUSTAT tapes over the period spanning from the fourth quarter of 1975 (1975:4) through the fourth quarter of 1987 (1987:4).

We use the well-known market model to estimate the beta ([[Beta].sub.j]) of each common stock for each of the thirty quarters for the period 1980:3-1987:4. Thus:

[Mathematical Expression Omitted], t = -19 to 0, (1)

where: [Mathematical Expression Omitted] = return of the stock j at quarter t

[Mathematical Expression Omitted] = returns on S&P 500

[Mathematical Expression Omitted] = the disturbance term.

The estimation period consists of twenty quarters ending in the quarter for which the beta is being estimated. For example, the beta for the third quarter of 1980 is computed by employing stock returns and S&P 500 returns for twenty quarters from 1975:4 to 1980:3. Similarly, for the 1987 fourth quarter beta, we use stock returns and S&P returns data for twenty quarterly periods ending in 1987:4.

DOL and DFL for each of the thirty quarters (1980:3-1987:4) are computed by using the following time-series regressions:

[Mathematical Expression Omitted], t = -19 to 0, (2)

and,

[Mathematical Expression Omitted], t = -19 to 0, (3)

where: [Mathematical Expression Omitted] = the earnings before interest and taxes for firm j at quarter t

[Mathematical Expression Omitted] = the sales for firm j at quarter t

[Mathematical Expression Omitted] = the after-tax earnings for firm j at quarter t

[Mathematical Expression Omitted] and [Mathematical Expression Omitted] = disturbance terms;

[c.sub.j] and [d.sub.j] = DOL and DFL respectively.

As before, the estimation period for computing DOL or DFL of a given quarter consists of twenty quarterly periods ending in the quarter in question.

Equations 2 and 3 follow the elasticity definition of DOL and DFL(11) employed by MR with one minor difference being that we have used first-differences of [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted] instead of their levels to avoid the spurious correlation phenomenon discussed by Granger and Newbold (1974).

Empirical Results

To investigate whether industry-specific relationships exist, we apply the VAR/FPE approach to each of the six industries in the sample - Crude Petroleum (SIC 1311), Pharmaceutical (SIC 2834), Petroleum Refining (SIC 2911), Blast Furnaces (SIC 3312), Motor Vehicles (SIC 3711 and 3714), and Utilities (SIC 4911 and 4931). A particular variable for a given industry is derived by taking the mean value of this variable for all firms in the industry. Details of the individual coefficients on each industry are not provided here to conserve space, but are available upon request. We report the summary findings in Table 2.

As to the relationship between DOL and beta, Table 2 results generally support the standard assumption. Specifically, in four out of the six industries, casuality in the strong form flows from DOL to beta (at the 5 percent significance level) without significant feedbacks. Of the remaining two industries, Blast Furnaces exhibits causality from beta to DOL, while Crude Petroleum shows causal independency between DOL and beta.

As regards the relationship between DFL and beta, only one industry (Crude Petroleum) shows evidence of a positive bi-directional causality between the two variables. For the remaining five industries, causality between DFL and beta is either [TABULAR DATA FOR TABLE 2 OMITTED] [TABULAR DATA FOR TABLE 3 OMITTED] nonexistent (Petroleum Refining, Blast Furnaces and Motor Vehicles) or weak causality exists flowing from beta to DFL (Pharmaceutical and Utilities).

For the relationship between DOL and DFL, two industries (Motor Vehicles and Pharmaceuticals) reveal no evidence of causality. Two other industries (Blast Furnaces and Utilities) show significant unidirectional causality from DOL to DFL. Interestingly, for Petroleum Refining, the results indicate the presence of significant and negative bi-directional causality between DOL and DFL. Thus, only this latter industry supports MR's trade-off hypothesis between DOL and DFL.

These empirical results suggest that a study of the relationships among operating and financial risks and beta may be better approached by considering a firm's industrial characteristics, and therefore, its growth potential (or the flexibility that the firm has in terms of its capacity decisions). Thus, the evidence so far seems to favor the Huffman proposition. A further support of Huff man's proposition is found in Table 3 in which we display the results of the Granger-causality tests on the aggregate sample.

Basic variables for the causality analysis in Table 3 were derived by taking the mean value of all 48 firms. The aggregate results in Table 3 suggest the presence of significant causal effects of beta on DOL, and that the general cumulative effect is negative. This finding is of course contrary to the general inference from Table 2 that DOL causes significant positive changes in beta in line with the conventional view. Regarding the aggregate relationship between DFL and beta, Table 3 suggests that causality is unidirectional from DFL to beta (positive, though insignificant). However, industry-specific information rejects this implication of the aggregate data as none of the industries shows unidirectional causality from DFL to beta. Instead, causality in Table 2 is found to vary from bidirectional, to unidirectional from beta to DFL, and then even to absence of any causal linkage between the two variables.

One conclusion that stands out when comparing the results in Table 2 and Table 3 is that the aggregate data seem to obscure important industry-specific information, possibly yielding misleading interpretations of the actual linkages among the variables. An example of flagrant misinterpretation would be to conclude that causality from beta to DOL is significantly negative (Table 3). However, in four of the six industries considered, such causality is significantly positive and in the opposite direction.

Besides supporting the Huffman position, the above results also make a strong case for using a causality-based analysis for this type of research. For example, in Crude Petroleum industry, beta and DFL are mutually causal. Therefore, standard beta equations for this industry in which DFL is implicitly assumed exogenous would suffer from serious simultaneous-equation bias. Hence, a simultaneous-equation model for beta in this industry provides a more fruitful inquiry into the determination of beta. On the other hand, a beta equation for the Pharmaceutical and Utility industries may be spurious since the direction of the effect (if it exists) is primarily from beta to DFL, opposite to the implicit assumption of the correlation-based analysis. For the remaining three industries, beta and DFL appear to be causally independent.

It is interesting to finally note that the predictive power of the estimated VAR models for each of the four variables for 1988:1 was on average much higher for the segregated sample than for the aggregative data. This result (not reported here but available from the authors) also suggests that the relationship among the model variables are sensitive to a firm's industrial characteristics.

Summary and Concluding Remarks

Based on Hamada-Rubenstein's beta decomposition model, Mandelker and Rhee demonstrate theoretically that interactions among a firm's DOL, DFL, and the intrinsic business risk determine the firm's level of systematic risk. Using correlation-based regression analysis, they conclude that DOL and DFL exert positive impacts on a firm's beta, and that a trade-off exists between DOL and DFL. Huffman casts serious doubts on the traditional assumption that the degree of total leverage is simply the multiplication of a firm's DOL and DFL. Using the argument of endogenous capacity decision, Huffman posits that an interaction exists between a firm's DOL and DFL, and that the impact of the two variables on a firm's equity risk may vary across industries. The main purpose of this paper is to examine if inter-industry differences do exist in the relationships among DOL, DFL and beta. Our article examines the causal linkages among the three variables by means of the VAR/FPE modeling technique. Our quarterly sample consists of 48 firms, divided into six different industries (2-digit SIC codes).

Using industry-specific data, we find that in four of the six industries examined, DOL causes significant unidirectional positive changes in beta. In one of the two remaining industries, DOL and beta are causally independent, while in the other industry causality flows from beta to DOL. As to DFL and beta, only one industry displays a bidirectional causality between DFL and beta and in two other industries causality flows from DFL to beta. In the three remaining industries, DFL and beta are found causally independent. For the relationship between DOL and DFL, causality linkages range from significantly bidirectional, significantly unidirectional (from DOL to DFL), to causal independency. This finding also provides an indirect support of Dammon and Senbet's (1988) proposition that "firms with higher investment-related tax shields . . . need not have lower debt-related shields . . . if firms utilize different technologies . . ." (p. 309). This variety of industry-specific relationships is obscured when causality tests are performed on the aggregate sample. In particular, the aggregate results generally suggest that causality is rather from beta to DOL without feedbacks.

These findings provide some empirical support for Huffman's theoretical proposition that the combined leverage is more than the mere product of operating and financial leverages and, consequently, its impact on equity risk may differ across industries. Another implication of this study is also worth emphasizing. Our results provide some support for the use of the causality approach in studying the relationship among the variables in the MR model. The presence of significant lag adjustments (for example, in causality form DOL to beta) imply that a correlation-based procedure in which only contemporaneous values are considered may fall short of adequately explaining this relationship. Also, the existence of bidirectional causality between DFL and beta in the Crude Petroleum industry, and between DOL and DFL in the Petroleum Refining Industry, further suggest that an analysis of the relationships among these variables for these two industries should be better examined in the context of a simultaneous-equation framework.

Acknowledgments: We would like to thank the Editor of this Review and two anonymous referees for many helpful comments and suggestions. The late Terry Wilford, the former Editor of this Review also provided valuable suggestions and encouragement. The usual caveat applies.

Notes

1. For example, theoretical work of Greenberg, Marshall and Yawitz (1978), and Shrieves (1981) suggests that operating leverage and business risk are simultaneously determined. Dammon and Senbet (1988) argue that the relationship between investment and financing decisions should vary across firms depending on the production technologies facing these forms.

2. Since Huffman's study did not empirically test the proposed theoretical model, her study is not reported in Table 1.

3. The model developed by Thompson (1976) is "based on a widely used stock evaluation technique" (p. 187). It is a behavioral model that eschews the theoretical framework expounder by Modigliani and Miller (1958, 1963). Thompson added additional variables based on "prior research into corporate behavior and characteristics" (p. 187) resulting in a total of 43 variables. Because of these reasons, this study should be more appropriately classified in the first category.

4. Although Gahlon and Gentry (1982) relate DOL and DFL to the beta decomposition model, "it is difficult," as pointed out by Mandelker and Rhee (1984), "to investigate the impact of two types of leverage on operating and financial risk in the framework of Gahlon and Gentry" (p. 46). Besides, Gahlon and Gentry do not. empirically test their model.

5. S. Huffman (1989), not to be confused with L. Huffman (1983) in the text, tests the relationship among DOL, DFL, and beta using a methodology and proxies for DOL and DFL similar to those used by MR. Inconsistent with MR, however, he finds a negative relationship between DOL and beta and finds no consistent trade-off relationship between DFL and DOL. Although Li and Henderson (1991), do not find a statistically significant negative coefficient on DOL and DFL, they do find significant positive coefficients on both DOL and DFL in the beta regression. It appears that the MR model produces conflicting results.

6. Note that DOL = [x(p - v)]/[x(p - [Nu]) - F], where x is the number of units produced, p is the selling price per unit, [Nu] is the unit variable cost, and F is the fixed production cost.

7. Of course, wheat DOL is endogenous or exogenous remains a hypothesis subject to empirical verification.

8. The standard caveats involved in employing and conducting Granger-causality tests apply. See, for example, Jacobs, Leamer and Ward (1979) and Zellner (1979). At the outset, we should note that the Granger-causality concept as employed here deals only with the predictive content of information without necessarily involving the more controversial aspect of "causality."

9. We also use the Dickey-Fuller (1979) test to examine the presence of unit roots (nonstationarity) in the series, and none is found. Further, Engle and Granger (1987) argue that co-integration among the variables included in a VAR model would likely bias its results if the co-integrating relationships are ignored. Thus, we employ the Engle and Yoo (1987) procedure to test for co-integration and the results do not reveal strong evidence of co-integration in the estimated VAR system. Details of the test results are available upon request.

10. Hamada (1972), Lev (1974), and Mandelker and Rhee (1984), among others, have also limited their analysis to manufacturing firms.

11. As Dugan and Shriver (1989) observe, this elasticity approach is conceptually the most appropriate.

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Author:Darrat, Ali F.; Mukherjee, Tarun K.
Publication:Review of Financial Economics
Date:Mar 22, 1995
Words:5896
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