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Effects of Macroeconomic Conditions and Firm-Level Productivity on Optimal Capital Structure: Theory and Evidence

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(1)2. Journal of Financial Studies Vol.l4 No.4 December 2006. ~1~*'#~~~iihfli~I*MI~~':~~~f.~~ Effects of Macroeconomic Conditions and Firm-Level Productivity on Optimal Capital Structure: Theory and Evidence*. I.. Introduction. Since the celebrated work of Modigliani and Miller (1958, 1963), the optimal capital structure has been becoming one of the most important fields in corporate finance. Many theoretical and empirical studies focus on the effects of finn-specific variables (e.g., size, profitability, tax shields ... etc.) on the finn's target leverage. However, little attention has been paid to the effects of macroeconomic conditions and finn-level productivity on the finn's optimal capital structure. This is rather surprising because the state of the economy in the business cycle and the finn-level productivity both have significant impacts on the finn's bankruptcy risk and the valuation of corporate debts, which in tum affect the optimal capital structure. The paper makes a contribution to fill this literature gap by providing a dynamic optimal capital structure model and empirically examining these effects. During the period of recession, the consumption demand is likely to be cut off, and hence the debtholders of the finn will suffer from an increase of default risk. For example, Duffie and Singleton (2003) report that macroeconomic conditions may affect the probability of default. They find that the correlation between. the. four-quarter. moving. averages. of default. rates. for. the. speculative-grade cotporate bonds and the GDP growth rates over the sample period 1983-1997 in U.S. is about -0.78, showing the significant negative relationship, especially in the recession period 1990-1991. Moreover, Korajczyk and Levy (2003) analyze the debt to asset ratios with the aggregate data of American non-financial finns and discover the systematic peaks appear during We are grateful to two anonymous reviewers for their valuable comments and suggestions. Any remaining errors are our responsibility.. 4.

(2) .. Journal of Financial Studies Vo1.l4 No .4 December 2006. ~-~ .........rnic. 3. downturns over the last fifty years. Such two observations suggest that. ~~",('l"\nnmir.. F,i nns. conditions indeed derive variations in finn's capital structure. undertaking. innovative. activities. typically. hold. specialized. equipment and a large share of immaterial assets, such as patents, research knowledge, and project-specific human capitaL Hence, more innovative (productive) finns tend to have a different capital structure from less innovative ones. For example, Nucci et al. (2004) show that finns with lower leverage (debt ratio) have a higher level of total factor productivity. The macroeconomic conditions and firm-level productivity factors have notable impacts not only on the default risk of the debt issuer, but also on the optimal capital structure of the finn . The finn detennines the optimal leverage with the tradeoff between tax benefits and bankruptcy costs, both of which should depend on macroeconomic condition shocks and finn-level productivity shocks. This is because the tax benefits and bankruptcy costs are associated with the cash flows of the finn, the level of which in tum depends on whether the economy (demand) is in an expansion or recession and whether the finn-level productivity (technology) is magnified or minified. The present paper constructs a partial equilibrium contingent claims model in which the cash flows incorporate. both. the. macroeconomic. condition. shocks. and. finn-level. productivity shocks. The model predicts that both of the shocks have negative effects on the finn's optimal debt ratio. In addition, the model implications are totally supported by the quarterly data of 311 Taiwanese manufacturing finns from 1994 to 2003. We further investigate the differences between high-tech electronics and other manufacturing finns. The effects of macroeconomic conditions on the debt ratio of high-tech finns are insignificant, while those of other manufacturing finns are very conspicuous. The finn-level productivity is significantly negatively correlated to both the high-tech electronics and other manufacturing firms. Therefore, our model definitely provides additional insights as well as complements to both of the earlier theoretical and empirical studies concerning the optimal capital structure of the finn .. .. The rest of this paper is organized as follows. Section II provides the.

(3) 4. Journal of Financial Studies Vol. 14 No.4 December 2006. theoretical model, and the implications are given in Section III. In Section IV, the theoretical implications are empirically examined, and the differences between the high-tech electronics and other manufacturing firms are further analyzed. Section V summarizes and makes concluding remarks.. II.. The Model. While most financial economists pay a great attention to qualitative analysis of the corporate capital structure, some recent papers attempt to provide quantitative guidance for the optimal capital structure. Pioneered by Merton (1974), Black and Cox (1976), and Brennan and Schwartz (1978), who employ / the option pricing technique to value corporate securities,] the literature on the quantitative analysis of the optimal capital structure has been substantially developed.. Quantitative capital structure models often take the total asset value. or un levered asset value as the underlying asset to price the firm's liability, and then derive the firm's optimal capital structure. For example, based on this setup, Leland (1994) and Leland and Toft (1996) both construct optimal capital structure models with consideration of the shareholder's endogenous bankruptcy decision. Goldstein et al. (2001) provide a pioneering view that the unlevered asset value results from the expected present value of the cumulative earnings before interest and taxes (EBIT). Nevertheless, the papers mentioned above do not explicitly demonstrate how the macroeconomic conditions and firm-level productivity could 'affect the firm's EBIT and unlevered asset value, while they are of importance to the firm's capital structure choices, especially for those of manufacturing firms . As far as we know, none of the existing theoretical literature takes the two factors into consideration. The present paper extends Goldstein et al. (2001) to construct a partial equilibrium model which. I. This approach is the so-called real options approach or contingent claims analysis. which is also used to price credit risk and known as the firm value model or structural model.. ...

(4) ~.. Journal of Financial Studies Vol.14 No.4 December 2006. incorporates. the. macroeconomic. condition. shocks. and. 5. the. firm-level. productivity shocks into a dynamic optimal capital structure model. In this paper we consider an industry consisting of a representative firm, and assume the information is perfect and complete. Furthennore, all agents are risk-neutral, and thus we could discount future cash flows at a constant risk-free rate r> O. This risk-neutrality assumption is innocuous. If the agents are not risk-neutral, the analysis may be conducted under the risk-neutral probability measure where the risk premium is incorporated. 2 Time domain is continuously varying over [0, <Xl), and uncertainty is represented by a naturally filtered probability space (W,F ,Q) over which all stochastic processes are defined with respect to their corresponding regular complete filtrations.. 1.. Macroeconomic Condition and Firm-Level Productivity Shocks The firm's demand, governed by the law of demand, is a decreasing. function of output price. The inverse demand function of the finn is:. pet) = h(t)yd-I/t:,. (1). where P is the output price, Yd is the demand of industry,. £. > 0 is the. elasticity of industry demand, and h represents the macroeconomic condition shocks, which reflects the state of the economy and is governed by a geometric Brownian motion as follows :. dh(t) h(t). - - = JLhdt + (ThdWh (t),. where. Jih. and. O'h. . h(O) == h > 0 given,. (2). are two positive constants denoting the drift and diffusion. terms of the macroeconomic condition shocks, and Wh is a Wiener process defined on (W,F ,Q). This setting implies that the industry demand is uncertain due to the macroeconomic condition shocks. For example, the level of the consumer confidence index or the total score of cJ:lrrent business monitoring indicators are two possible sources of macroeconomic condition shocks, which indeed have a random impact on the demand of industry (finn).. 2. See Harrison and Kreps (1979)..

(5) 6. Journal of Financial Studies Vo1.l4 No.4 December 2006. The firm's production or output function Ys is assumed to be a standard Cobb-Douglas form, which is the mostly used type as given by. Ys(t) where. = A(t)L~ Krb,. (3). L is labor demand; K is capital demand; a, bE (0,1) respectively. show the output elasticities of labor and capital and their sum represents the returns to scale (taking a + b scale); A. =1. for example, it implies constant return to. is the firm-level productivity shocks governed by a geometric. Brownian motion as below. dA(/) A(/). - - = f.LAdl. + a ,dW. (I),. . A(O) == A> 0 gIven,. (4). 1 . .1. where f.LA and. O"A. are two positive constants denoting the drift and diffusion. terms, and WA is another Wiener process defined on (W,F ,Q). For example, the firm-level productivity shocks may be expressed by the firm's technological innovation in the production. In addition, the instantaneous correlation coefficient between the macroeconomic demand condition shocks and the microeconomic firm-level productivity shocks is denoted as PhAdt =EQ [dWhdWA ]. The positive correlation means that the firm-level productivity is pro-cyclical, while the negative one implies the counter-cyclical relationship. For instance, the productivity of the start-up industry is often pro-cyclical, and the productivity of the traditional industry might be counter-cyclical.. 2.. The Dynamics ofthe Firm's Un levered Asset Value Assume the input markets are competitive, and thus the firm takes the wage. of labor wand the cost of capital rk as given. The profit function of the firm is given by the value function of the following maximi::ation problem: max P(/)Ys(t) - wL, - rkK,. (5). L"K,. s.l.. P(/). = h(/)y. d. 1. /&;. Ys(/). = A(t)L;K,b.. After applying the following market-clearing condition Yd = ~ , at each point of time, we can set the profit function as a function of the levels of h and A. Solving this problem yields the profit function. 4.

(6) •. Journal of Financial Studies Vol. 14 No.4 December 2006. Y. H(h p A, ;a,b, w,rk ,&) = 17(h, (A,f , where Xl. '7= (I-w(l-b/a)x t )(xt t'(x,)h<. ,. e=(a+b)(&-I)/& ,. 7. (6). Xt. =a8/[w(a+b)]. ,. = (wb)/(rka) , y=l/(I-e), and ==8/[O-8)(a+b)]. The profit function can be. explained as the earnings before interest and taxes (EBIT) of the firm at each instant t, and the un levered asset value could be taken as the present value of all future EBIT. As a consequence, we define 8(t) = :r(h"A,;a,b, w,rk ,&) as the EBIT of the firm hereafter. Notice that the firm's EBIT here is affected by the macroeconomic condition shocks, the elasticity of industry demand, the return to scale, the prices of inputs, and the microeconomic firm-level productivity shocks. Applying the product rule of It6:S lemma with simplification, the dynamic process of the EBIT can be shown to be. (7). d5(t) = J.1i5 dt + (}i5 dWi5(t), 5(t) where J.15. = Y J.11r + ZJ.1 A + 0.5 y(y -1)(}~ + 0.5z(z - 1)(}~ + YZ(}h(} APIrA ' (}J. = ~(Y(}h)2 + 2YZ(}h(}APM + (Z(}A)2) , and. W" is another Wiener process also defined on (W,F ,Q). It is worth noting that the dynamics of the EBIT are derived from the macroeconomic and finn-level productivity conditions in comparison to Goldstein et al. (2001) who directly take the dynamics of the EBIT as exogenously given. As a result, our model has the merit to make a clear connection between the macroeconomic conditions and firm-level productivity and the EBIT of the firm. In view of Equation (7), both the expected rate of return and the return volatility of the EBIT depend on various parameters, including the elasticity of industry demand, the volatility of the macroeconomic condition shocks, the prices of inputs and the associated elasticities, and the volatility of the firm-level productivity shocks. Following Goldstein et al. (2001), the unlevered asset value of the firm V is the claim value on the entire EBIT, which can be defined as. v(t) = EQ. [r 5(S)e-. r. ( S-'). ds. IF,],. (8).

(7) 8. Journal of Financial Studies Vol. 14 No.4 December 2006. where. F, is the information set (sigma field) generated by. (Wh'W~) up to. time t. Equation (8) shows the un levered asset value is equal to the conditional expected present value of all future EBIT. According to Equation (7), the unlevered asset value at time t would turn into o(t)/ (r - fl.s ) ' where we assume r - fl.s > O. This implies both the EBIT and the un levered asset value share the same dynamics with the lognormal property. Accordingly, we can further show that. dV (t) + o(t)dt = rdt + a "dW.s (t). Vet). (9). Equation (9) demonstrates that the risk-neutral expected return on the un levered asset is the risk-free interest rate as necessary. The intuition behind this can be explained by the analogy between the unlevered asset value in our model and the stock price in the traditional option pricing framework as the EBIT behaves like the dividend payments of stocks.. 3.. The Firm's Optimal Capital Structure From the above analysis, we have endogenously derived the dynamics of. the firm's unlevered asset value with consideration of some macro and micro economic factors . In what follows , the firm's debt is regarded as a function of the un levered asset value. Because coupon payments of the debts are tax deductible, the firm has an incentive to issue debts . In our model debt contracts. P with continuous flows of. are assumed to be perpetual issued at par value. coupon payments C to the debtholders, while the remaining EBlT accrues to the shareholders. If the firm declares default on its debts, the debtholders immediately obtain the liquidation value (1- a)VB' and the shareholders get nothing,. a. where. E. (0,1). is. the. ratio. of. bankruptcy. costs,. and. VB « V == 0(0)/(r - fl.s)) is the bankruptcy trigger which is now an exogenous constant but will be endogenously determined later. By the risk-neutral pricing method, the value of the corporate debt is:. [r Ce- ds ] + EQ[(1- a)V8 e- J.. D(V;V8) = EQ. ". rs. rr. •. (10).

(8) 11. Journal of Financial Studies Vol. 14 No.4 December 2006. 9. where r B = inf (t > 0; Vet) ~ VB) denotes the first passage time that the unlevered :v.. ;' ::'" . asset value goes down and touches the bankruptcy trigger VB' The first term of Equation (10) shows the expected present value of cumulative coupon payments which may be truncated by bankruptcy. The second term is the expected present value of the debt recovery value. It can be further shown that the debt value is equal to. .' . c[. "0·. I. (11 ). (v J-rJ +(I-a)VB (: VBvJ-r. D(V;VB)=-; 1- VB .. where r = (f.16 - O.5CJ~ + ~(f.1a - O.5CJ:. r. + 2m; ) /CJ; ,and. rr. (v IVB. can be explained. as the risk-neutral state price of bankruptcy, that is, the present value of one dollar upon future bankruptcy filing of the firm. The detailed derivation is provided in Appendix A. Following Leland (1994), the total firm value is equal to the unlevered asset value plus the tax benefits and minus the bankruptcy costs. Therefore, the value of the total finn value can be expressed as F(V;VB) = V + EO. [r ,Ce-rlds J- EO [aVBe-"· ]. (12). r] (V)-r . ,C [ (V =V + --;:1- ~). - aVB VB. G. !~ ~: ~. ~. .. i: . I~. itt· .j f' . .••.. where r. is the effective corporate tax rate. Similar to Equation (10), the second. term of Equation (12) expresses the expected present value of cumulative future tax benefits of coupon payments which may be truncated by bankruptcy, and the third term shows the expected present value of bankruptcy costs upon the firm's insolvency. The derivation is also in Appendix A. According to the accounting identity of balance sheet that the total firm value must equal the sum of equity and liability values, the equity value would therefore be:. i.. 'l . E(V ;Vs ) = F(VYB)- D(V;Vs) = V - (1-;)C. +(. (1-;)C. ~Vs )( ~. r. (13).

(9) 10. Journal of Financial Studies Vol. 14 No.4 December 2006. The intuition behind Equation (13) is as follows. If there is no uncertainty involved in the macroeconomic condition shocks and firm-level productivity shocks, the equity value will reduce to V -(\-r)C/r, which is exactly the same as the one derived from the traditional theory of capital budgeting without consideration of future randomness. Next, we are going to determine the endogenous optimal bankruptcy strategy. As far as the shareholders are concerned, the firm can decide when to declare bankruptcy by optimally selecting the default trigger in consideration of both the macroeconomic condition shocks and the firm-level productivity shocks. The solution of the following smooth-pasting condition shows that the firm optimally chooses the bankruptcy trigger to maximize the equity value: 3 _ 8E(V;VB)!V:V8 :v;. aE(V;VB)1. av. V=Ve:V;. -. aVB. =. o.. (14). Solving Equation (14) yields •. VB =. ---.r . r. (l-r)C r 1+. (15). Equation (15) shows that the optimal bankruptcy policy of the firm is associated with the effective tax rate, risk-free interest rate and coupon payments. Moreover, it also depends on the macroeconomic and firm-level productivity conditions, including the associated correlation coefficient, the input prices and associated output elasticities, and the elasticity of industry demand, all of which are involved through rand are rarely discussed in the previous literature. After substituting the optimal bankruptcy trigger back into Equations (11 )-( 13), we complete the derivation of the firm's optimal capital structure, and further define the optimal debt ratio as DR(V;V;) = D(V;V;)/F(V;V;). The next section will numerically investigate the impacts of the macroeconomic conditions and firm-level productivity on the finn's optimal debt ratio. J. See Leland (\994).. ~.

(10) Journal of Financial Studies Vol. 14 No.4 December 2006. 11. III. Theoretical Implications. This section attempts to analyze the effects of the mean growth rates of the macroeconomic conditions and the firm-level productivity on the firm's optimal debt ratio. To clearly identify the comparative static results, we first set some reasonable parameters. Let the coupon payments C = 800. ,4. the corporate. effective tax rate r = 0.35, and the proportional bankruptcy costs a = 0.5 . Here, the coupon payment is set to approximate the bond yields of 8% (i.e.,. P = 10,000 ), while the tax rate and proportional bankruptcy costs are set to be the same as those of Leland (1994). The risk-free interest rate as well as all the other parameters are adopted from the averages of the data over the sample. = 0.055, h = 478.8074, A = 44.7011 , Ph =0.0025, P A =0.0082, CYh =0.0204, CY A =0.2145, PhA = -0.0185, a = 0.5959, b = 0.2947, & = 1.3, rk = 0.068, w = 3.4. 5 In what follows,. period,. given as follows:. r. we will discuss the theoretical implications of the mean growth rates of the macroeconomic condition shocks Ph and firm-level productivity shocks PA.. 1.. Effect of Macroeconomic Conditions The effect of the mean growth rate of the macroeconomic conditions on the. optimal debt ratio is stated in the following Hypothesis 1.. Hypothesis 1. The optimal debt ratio DR' is negatively correlated to the mean growth rate ofthe macroeconomic condition shocks Ph. The optimal debt ratio is negatively correlated to the mean growth rate of macroeconomic conditions, namely, it is counter-cyclical. Hypothesis I is consistent with the pecking order theory and can be explained as follows . If the macroeconomic conditions improve, firms have to increase their investment, such as hiring more employees and purchasing more production equipment, and thus need more funds. According to the pecking order theory, external financing is more expensive for riskier securities, and thus firms would prefer to finance first with internal funds, then with debt, and lastly with equity. As a result, firms , All the dollar amounts in the paper are expressed in ten thousands of New Taiwan dollars.. l The description of our data is detailed in the next section..

(11) 12. Journal of Financial Studies Vo1.l4 No.4 December 2006. would like to use internally generated funds to finance the investment and hence usually have more internal funds during macroeconomic expansion. Therefore, the debt ratios would be lower.6 From the viewpoint of the model, when the macroeconomic conditions get better, other things being equal, the firm's revenues (EBIT) would increase, leading to the rising of the firm's unlevered asset value . Consequently, the possibility of the firm's bankruptcy filing would decrease, and the liability value would rise but is bounded above by the risk-less value. elr . This shows that. the liability value is increasing and concave to the macroeconomic conditions. Meanwhile, when the un levered asset value goes up, the total firm value would also increase without any upper bound, i.e., the total firm value is increasing and convex to the macroeconomic conditions. Accordingly, the increment of the total firm value will dominate that of the liability value, and therefore, the more the macroeconomic conditions improve, the lower the debt ratio would be.. 2.. Effect of Firm-Level Productivity The effect of the firm-level productivity on the optimal debt ratio is shown. in Hypothesis 2.. Hypothesis 2. The optimal debt ratio DR" is negatively correlated to the. mean growth rate ofthe firm-level productivity fL A . The intuition behind Hypothesis 2 is similar to Jensen and Meckling (1976) and can be explained as follows. If the firm has a larger share of tangible assets which could be more readily sold in the market, the bankruptcy loss of debtholders would be lower in case of default. More productive firms often own a larger share of intangible assets, such as patents, research knowledge and human capital, and therefore would have a smaller portion of tangible assets, which could result in higher risk premiums on the costs of their debt issuances. As a consequence, firms with higher productivity tend not to be reliant on debt financing, and thus their debt ratios are often lower.. 7. Based on the model, when the productivity of the firm is higher, other 6 7. See Korajczyk and Levy (2003).. See Nucci et al. (2004).. ~.

(12) ~. Journal of Financial Studies Vo1.l4 No.4 December 2006. 13. things being equal, the firm's EBlT and un levered asset value are expected to increase. By the same argument as in Hypothesis I, the higher the firm-level .. .•. productivity is, the lower the debt ratio would be . In the next section, we will further empirically examine Hypotheses 1 and 2 by the data of Taiwanese listed manufacturing firms.. IV. Empirical Evidence. This section first details the sample data, and then a pooled generalized least squares regression is used to empirically examine the theoretical implications. Next, the differences between the high-tech electronics firms and other Taiwanese manufacturing firms are also investigated. 1.. Data and Empirical Specification. The model is examined based on a quarterly data set which includes a sample of 311 manufacturing firms stratified from the Taiwan Stock Exchange (0.. C:. (TSE) over the period 1994 to 2003. All the data series are collected from Taiwan Economic Journal Data Bank (TEJ DB). The data are selected from the listed manufacturing firms whose TSE stock codes start with the first two digits of 12, 13, .", 24, Only the firms with records equal to or greater than five years. .~. are taken into consideration, since we are investigating the effects of. ~.. macroeconomic conditions. Our data are unbalanced due to the fact that the available data of some cross sections (firms) are less than 10 years, the whole sample period. Data sets are rarely complete, and therefore we are examining the panel data with some variables and/or some years missing for some firms,. ,. ,'.. ..;;,' t. :; ~. l. I. From our data of Taiwanese manufacturing firms, the negative relationship between debt ratios and macroeconomic conditions also prevails. Figure 1 shows the relationship between the macroeconomic condition (the total score of current.

(13) -------......... 14. Journal of Financial Studies Vol.l4 No.4 December 2006. business monitoring indicators) 8 and the average debt ratios of the 311 Taiwanese manufacturing firms over the sample period 1994-2003. In view of Figure 1, the average debt ratios are relatively low over the peak periods (such as 1994:Q3 and 1997:QI-1997:Q3), while the average debt ratios reveals comparatively high during the trough periods (such as 2001 :QI-2001 :Q3). In addition, the correlation coefficient behveen the average debt ratio of 311 manufacturing firms and the total score of current business monitoring indicators over the period 1994-2003 is approximately -0.48.. [Please insert Figure 1 about here] In light of the previous empirical studies, such as Hovakimian et al. (2001) and Fama and French (2002), the firm's size,9 long-term performance and growth opportunity, profitability, and tax shields are all substantial elements in determining the optimal capital structure. Consequently, the firm's market asset value, the market-to-book ratio, the ratio of the EBIT over the book asset value, and the ratio of the sum of tax and depreciation over the book asset value are respectively utilized as the proxies for those factors, which are included in the pooled regression model as the control variables. According to the previous literature, the debt ratio is expected to be negatively related to the firm's market-to-book ratio, the ratio of the EBIT over the book asset value, and the ratio of the sum of tax and depreciation over the book asset value, but it is anticipated to be positively related to the firm's market asset value. Due to the reason that debt ratio choices are varying over time and across firms, a pooled feasible generalized least squares (FGLS) estimation is employed to examine the model implications. Based on the previous literature, we first assume that the firms' debt ratios can be described by the following pooled linear equations, DR;" =c,DRi,,_, +c2 M4",_1 +c3MBi,H +c.RAi,H +csTAi,H +C6 J.iA,.H +C7 J.ih +CsJ.is,_, + ei,t'. S 9. H. (16). The score is monthly issued by Council for Economic Planning and Development, Executive Yuan, Taiwan. As noted by Chen and Jiang (2001), the finn size is often used as an inverse proxy for the probability of bankruptcy.. .1.

(14) l'. Journal of Financial Studies Vol. 14 No.4 December 2006. where i. =1,2, ... ,311. 15. and t = 1(1994: QI),2(1994: Q2, ...,40(2003: Q4), DR. is the firm-level debt ratio calculated by the debt book value over the total asset market value; MA is the natural logarithm of the total asset market value which is deflated by the wholesale price index; market-to-book ratio; value;. MB. is the firm's. RA is the ratio of the EBIT over the firm's book asset. TA is the sum of the firm's tax and depreciation, which is measured as a. fraction of book asset value; JiA is the mean growth rate of the firm-level productivity; Jih. is the mean growth rate of the manufacturing industry. demand shocks; Jis is the mean growth rate of the total score of current business monitoring indicators. As suggested by Korajczyk and Levy (2003), all the variables are lagged one quarter because of the delayed release dates. Due to significant autocorrelation, the one-period-Iagged value of the firm's debt ratio is also included as one of the independent variables. The descriptive statistics of the above variables are summarized in Table I.. [Please insert Table 1 about here] As for the calibration of the firm-level productivity, we use the firm's total factor productivity (TFP) to approximate it. Following the standard methodology, we first take natural logarithm of the Cobb-Douglas production function, and then run the following linear regression separately for each firm i:. In(Ys,) = Cj +aj In(Li ,t)+b j In(Kj)+ cj,t' where. Ys. is estimated from the firm-level net sales deflated by the wholesale. price index, 10 L is simply measured by the total number of employees (because there is no available information on the labor working hours of firms), II and K is the total fixed gross asset value deflated by the wholesale price index. 12 From this linear regression, we could obtain. £Ii and bi of each. finn i . By simply setting In(A;,,) = In(Ys) - 0; In(L;,,) -. b; In(K;,,),. 10 II. 12. we can. As mentioned by Levinsohn and Melitz (2003), output is typically me:fSured not in physical units but rather in terms of dollars, i.e., sales. See Wang and Tsai (2003). See Wang and Tsai (2003)..

(15) 16. Journal of Financial Studies Vo1.14 No.4 December 2006. obtain J.l A /, ( = In(A I, () - In(A; , (_I) . In Equation (16), there are two variables utilized as the proxies of macroeconomic conditions. The mean growth rate of the total score of current business monitoring indicators can be easily calculated from the available data. On the other hand, the mean growth rate of industry demands could be measured by the similar method used for calibrating the firm-level productivity. We again take natural logarithm of the industry demand function, and then run the following linear regression:. In(p,) = a + ,8ln(Yd, ) + £(' where P is the wholesale price index of manufacturing industry, and Yd is measured as the total sales of manufacturing industry, which is deflated by the wholesale price index.13 The estimated. i = 1.3. Hence we have. produce. jJ. approximates. -lj £. ,. and this will. J.1h, == In(hJ -In(h{_I)' where In(h{) == In(E;) +. (1/ i) In(Y. d, ) '. It is also worth exploring the effects of the macroeconomic conditions and firm-level productivity on the optimal debit ratios between the high-tech electronics firms and other manufacturing firms . To examine the differences in a more systematic way, we split the sample into two groups,. 14. high-tech. electronics firms (lIS firms) whose TSE stock codes start with the first two digits of 23 and 24, and other manufacturing firms (196 firms). Table 2 presents the descriptive statistics of the firm-level variables for the high-tech electronics and other manufacturing firms.. [Please insert Table 2 about here) 2.. Estimation Results Estimation of Equation (16) with cross-section time-series data are. achieved by the pooled feasible generalized least squares.)5 Table 3 shows the. Il. I' I'. See the footnote 10. It is suggested by Wang and Tsai (2003). More details on how we treat the unbalanced panel data in pooled FGLS estimation are provided in Appendix B.. 4.

(16) •. r". Journal ofFinancial Studies Vo1.l4 No.4 December 2006. 17. pooled FGLS estimation results of the pooled cross-section time-series regressions, accounting for cross-equation heteroskedasticity by minimizing the w'eighted sum of squared residuals. The weights are the inverses of the estimated equation variances, and are derived from the unweighted estimation of the parameters of the system. The pooled cross-section time-series regressions allow firm-level debt ratios to vary over time and across companies, and generate more efficient parameter estimates due to the greater variation of the data. Overall, the adjusted R-squared of the regression is 0.9260, with F-statistic of 17196.55 and Durbin-Watson statistic of 2. 100. The estimation results totally support the model implications in the last section, i.e., the macroeconomic condition, manufacturing industry demand, and firm-level productivity all have significant negative impacts on the optimal debt ratio. As for the control variables, most of the estimation results are also significant and consistent with the predicted signs except for the insignificance of the tax shield variable.. [Please insert Table 3 about here] We further explore the effects of the macroeconomic conditions and firm-level productivity on the optimal debt ratios between the high-tech electronics firms and other manufacturing firms. Therefore, we rerun the regression model, Equation (16), separately for these two groups. Table 4 reports the estimation results, most of which are consistent with the model predictions. In particular, there are two important differences between the high-tech electronics and other manufacturing firms. First, the optimal debt ratio of the high-tech electronics sector does not have significant connections with both the industry demand shocks and the total score of current business monitoring indicators (i.e., the macroeconomic conditions), whereas the results of other manufacturing firms agree well with the model predictions. The rationale is that most of the high-tech electronics firms in Taiwan are export-oriented, while other traditional manufacturing firms are mainly import-oriented . Therefore, the debt ratios of the high-tech electronics firms are not tied up with Taiwanese macroeconomic conditions, but may still have a connection with international high-tech electronics industry conditions. Next, the market-to-book asset ratio of. •. high-tech electronics firms is significantly negatively correlated to the debt ratio,.

(17) 18. lournal of Financial Studies Vo1.14 No.4 December 2006. whereas that of other manufacturing finns is significantly positively correlated to the debt ratio. This could be explained as follows. In view of Table 2, the mean debt ratio of high-tech electronics finns is lower than that of other finns, while the mean market-to-book ratio of high-tech electronics finns is higher than that of other finns . Since the market-to-book ratio represents the finn's growth opportunity, high-tech electronics finns on average have more growth opportunities and tend to use equity financing in capital market. On the other hand, other manufacturing firms on average with lower market-to-book ratios are likely to use debt financing. In addition, many high-tech electronics finns are newly established with only a few years of credit records, and thus it is somewhat harder for them to obtain cheaper funds from debt markets. Therefore, the high-tech electronics firms would rather choose equity financing, which would reduce their debt ratios. [Please insert Table 4 about here). v.. Summary and Concluding Remarks. This paper develops and examines a partial equilibrium contingent claims model to explore the effects of the macroeconomic conditions and finn-level productivity on the finn's optimal debt ratio. The model extends Leland (1994) and Goldstein et al. (2001) to not only consider the macroeconomic condition shocks and finn-level productivity shocks, but also take account of the elasticity of industry demand, mean industry wage, cost of capital, and output elasticities of production inputs. The model predicts that the macroeconomic conditions and the firm-level productivity impose significant negative effects on the optimal debt ratio. The theoretical predictions are also totally supported by the pooled feasible generalized least squares estimation results with the quarterly data of 311 Taiwanese manufacturing finns over the sample period 1994 to 2003. The. ".

(18) ,. Journal of Financial Studies Vol.l4 No.4 December 2006. 19. estimation results are consistent with Korajczyk and Levy (2003) and Nucci et al. (2004). We further investigate the differences between the high-tech electronics and other manufacturing firms. The debt ratios of high-tech electronics firms are not tied up with macroeconomic conditions whereas those of other firms are. Moreover, the market-to-book ratio (the growth opportunity) has a significant negative impact on the debt ratios of high-tech electronics firms, but imposes a significant positive effect on those of other firms. The findings provide us a better understanding of how both the macroeconomic conditions and firm-level productivity affect the determination of the firm's optimal capital structure. In addition, the results are important to investors, financial managers of firms and officials of the relevant supervisory authorities. For future research, it might be an interesting and important extension to examine the model with the data of other manufacturing firms in different markets.. Debt. Total. O~~O 0.4 30. 20 10 0. 0.2. o ~. \0 0"1. 00 0"1. o o. 0l. 0"1. ~. ~. ~. ~. ~. ....ro I. ....ro I. ....ro I. ~. oI. ....ro. Debt Ratio -.- Macroeconomic condition Figure 1 The Relationship between Macroeconomic Condition and Debt to Asset Ratio. The macroeconomic condition is measured by the total score of current business monitoring indicators monthly reported by Council for Economic Planning and Development, Execlttive Yuan, Taiwan. The dcbt ratio is defined as the avcrage debt ratio of the 311 manufacturing finns, where each finn 's debt ratio is calculated by the debt book value over the total asset market value. The finn data is collected from Taiwan Economic Journal Data Bank..

(19) 20. Journal of Financial Studies Vol. 14 No.4 December 2006. Table I Variable. Descriptive Statistics of Variables for Manufacturing Firms. Mean. Median. Max.. Min.. Std. dev.. Observations. AR(I)". DR. 0.3261. 0.2806. 1.0000. 0.0054. 0.2070. 10282. 0.9264. MA MB. 11.4471. 11.3132. 16.7287. 7.5663. 1.2390. 10282. 0.9716. 1.6961. 1.3483. 29.3663. 0.1365. 1.4577. 10282. 0.9022. R4. 0.0191. 0.0180. 0.2144. -0.4416. 0.0273. 10877. 0.5736. TA. 00096. 0.0081. 0.2735. -0.0754. 0.0091. 10936. 0.6607. Ii... 0.0082. 0.0101. 0.9707. -0.9966. 0.2145. 10571. -0.2707. Ph. 0.0025. 0.0045. 0.0603. -00466. 0.0204. 12129. 0.02970. lis. 0.0079. 00000. 0.5108. -0 .5596. 0.2495. 12129. 0.3255. • The total number of observations without missing values is equal to 12,440, but for the gro ....1h rates, the total number of the observations is 12,129 due to the calculation. Because we utilize the data with all the firms whose records are equal to or greater than five years, the number of the unavailable observations of some specific firm-level variables may seem a bit larger. It is worth noting that the number of the observations which really result from missing accounting records is rather small . •• AR( I) is the one-period autocorrelation of the variables.. Noles: The variables are defined as follows . DR is the firm-level debt ratio which is calculated by the debt book value divided by the total asset market value ; MA is the namral logarithm of the market value of the firm 's total asset which is deflated by the wholesale price index; MB is the firm's market-to-book ratio; RA is the ratio of the EBIT over the firm's book asset value; TA is the sum of the firm's tax and depreciation, which is measured as a fraction of the book asset value; fJ . is the mean gromh rate of the firm-level productivity; JJ, is the mean gromh rate of industry demand shocks; JJs is the mean gromh rate of the total score of current business monitoring indicators.. Table 2. Descriptive Statistics of Firm-Level Variables for High-Tech Electronics and Other Manufacturing Firms DR. Variable Firm Type. Hi-Tech. MA Hi-Tech. Others. Hi-Tech. TA. RA. MB. Others. JJ.<. Others. Hi-Tech Others Hi-Tech Others Hi-Tech Others. Mean. 0.2593. 0.3588. 1\.8942. 11.2286. 2.3528. 1.3752. 0.0258 0.0157 0.0096 0.0095 0.0105 0.0070. Median. 0.2099. 0.3232. 1\.6599. 11.1 469. 1.1355. 1.2121. 0.0250 0.0153 0.0068 0.0087 0.0159 0.0081. Max.. 0.9723. \.0000. 16.7287. 15.3351. 29.3663. 8.4270. 0.2144 0.2018 0.2735 0.1020 0.9702 0.9707. Min.. 0.0054. 0.0190. 8.4081. 7.5663. 0. 13 65. 0.2043. -0.4416 -0.4212 -00702 -0.0754 -0.9966 -0.9945. Std dey.. 0.1944. 0.2052. 1.3306. 1.1 292. 2.2073. 0.6850. 0.0322 0.0237 0.0124 0.0068 0.2385 0.20 11. Observations. 3376. 6907. 3375. 6907. 3375. 6907. 3694. 7183. 3727. 7209. 3589. 6982. NOles : The variables are defined as follows. DR is the firm-level debt ratio which is calculated by the debt book value divided by the total asset market value; MA is the natural logarithm of the market value of the firm's total asset which is deflated by the wholesale price index; MB is the ftrm's market-to-book ratio; RA is the ratio of the EBIT over the firm's book asset value; TA is the sum of the fIrm's tax and depreciation, which is measured as a fraction of the book asset value; Ii A is the mean gromh rate of the firm-level productivity; JJ, is the mean gromh rate of industry demand shocks; lis is the mean gromh rate of the total score of current business monitoring indicators. The number of high-tech electronics firms is I 15, and that of other manufacturing firms is 196 .. ...

(20) ,. r. Journal of Financial Studies Vol.l4 No.4 December 2006. Table 3. 21. Pooled Feasible Generalized Least Squares Estimation Results t. Van able. Predided sign. CodTicicm est.. DR(-I). + +. 0_963292'" 0_001837'". MA(-I). -0000447'" ·0.227423'··. MB(-l) RA(-I). T..t( - I) .11.(-1). 00000 00000. -9.148401. 0.0000 0.2460. -1.160233 -2.803447. -0.083245"" -0.020496'". -3 .689831. .11,(-1)_. -v3.l~. 316.5083 15 .15905 -3.070349. -0.052210 -0.006671'". .11,(-1). p. -.sulistic. 0.0021. 0.0051 0.0002 0.0000. -IOJl65]0. Noles : The dependent variable is the finn-level debt ratio DR which is calculated by the debt book value divided by the total asset market value, and the independent variables are: the one-period lagged debt ratio DR(-I) ; the natural logarithm of the one-period lagged market value of the finn's total asset W(-I) which is deflated by the wholesale price index; the one-period lagged firm's market-to-book ratio MB(-t); the ratio of the one-period lagged EBIT over the firm's book asset value RA(-I); the one-period lagged sum of firm's tax and depreciation TA(-I), which is measured as a fraction of the book asset value; the mean growth rate of the one-period lagged firm-level productivity PA(-I); the mean growth rate of one-period lagged industry demand shocks p,( - I); the mean growth rate of the one-period lagged total score of current business monitoring indicators p,(- I). The F-statistic, 17196.55, is considerably high, and the adjusted R-squared of the regression is 0.925972, with the Durbin-Watson statistic of 2.100448_ The coefficients that are statistically significant different from zero at the 10%,5%,1% confidence levels are marked with " •• and "', respectively.. Table 4 Pooled Feasible Generalized Least Squares Regression Results between High-Tech Electronics and Other Manufacturing Firms Industry Variable DR(-I) MA(-I). MB(-I). RA(-I). rA(-I). High-tech electronics t -statistic Coefficient 0.9096'·' 101.2944 0.0021'" 9.891308 -0 .0006'·' -3_545768 -0.2198'·' -6.461076 -0.0900'· -2.007970. ,Li, (-I). -0.0063'. ,Li, (-I). 0.0122. ,Lis (-I). 0.0019. -1.896338 0.330425 0.635287. F-stat. 1213.213'··. Adjusted R-squared Durbin-Watson stat.. 0.731351 2.034075. Others. t -statistic. Coefficient 0.9695"· 0.0015'" 0.002s'· -0.2589·'·. 243.6026 6.476978 2.455697 -6.250253. -0.0130 -0.0068'· -0.1369'" -0_0333"'·. -0.124564 -2.116994 ·5 .022300 -12.92655 13188.44"· 0.934171 2.106133. Noles : The dependent variable is the finn-level debt ratio DR which is calculated by the debt book. value divided by the total asset market value, and the independent variables are: the one-period lagged debt ratio DR(-I); the natural logarithm of the one-period lagged market value of the finn's total asset MA(-I) which is deflated by the wholesale price index; the one-period lagged firm's market-to-book ratio MB(-I); the ratio of the one-period lagged EBIT over the firm's book asset value RA(-I) ; the one-period lagged sum of the firm's tax and depreciation TA(-I) , which is measured as a fraction of the book asset value; the mean gro"1h rate of the one-period lagged firm-level productivity ,11.(-1) ; the mean growth rate of one-period lagged industry demand shocks ,11, (-I); the mean growth rate of the one-period lagged total score of current business monitoring indicators .u.. (-IL The coefficients that are statistically significant different from zero at the 10%, 5%, I % confidence levels are marked with " •• and "., respectively..

(21) 22. Journal of Financial Studies Vol.I4 No.4 December 2006. Appendix A To derive Equations (11) and (12), we need the distribution of r 8 ==. ~. inf (t > 0 : V (I) VB)' which is well known and can be easily derived by the reflection principle and Girsanov 's Theorem (see, for example, Harrison (1985» . The distribution is given as follows:. 8 !(t;V,v8) dPr(T dt :5t). I In Y/Y, )+,l ,. In'bra; (v/Vt8 )e- 2[ "" 3. ' J ,where,i=(,u,, -O.Sai).. (A. I). Because Equation (10) can be expressed as. [fa" Ce-"cts] + EO[(I-a)V8e-rr. J =7(I- EO[r e-rr.cts])+(I-a)V8EO[r e-rr,cts]. D(V;V8) = EQ. (A. 2). "~(I-(;' J} (I-a)V.(;' J, all what we need to do is to prove. EQ[f e-""' dr]=(Vl v8f '. with the technique of. completing squares and changing variables as follows.. EQ[ fe-n'ds] =f e- / (/;V,v8)ds= f ert. o. rt. '("'(1';1', )•.u)'dr JrlftJe"2--;;r,2JCai /J. " (";1" )"" )' V -[;'-: ", ') In VI V8 "2'['~ ( ) • = II8 ds, where 2JCai/ J e. r};;d. (.!:'.-)f;nr. =. ~. °. 2. -~[~ ' ~~'~·). ·')' dr(bY d(-In (VIV. AOI e. J2JC~/J. ~ =J~ + 2ra; 8) -. ~~. (by completing squares). AOI) = (In(VIV8)- AOI )dl]. "r:.trJr:'J~' (bYd(- m(~y+AOI) "r:. t n"rd" "'1'1r--(;;-0---'5,,1)'­""1 r:. r. J2JC~tJ. (In (VIV8)+ AOI )dl]. <. By the same way, Equation (12) can therefore be derived.. 4. J2JCaj/ J.

(22) •. Journal of Financial Studies Vo1.l4 No.4 December 2006. 23. Appendix B The panel structure of our data requires an econometric method that accounts for both cross-section and time-series data. As suggested by Beck and Katz (1996), we first attempt to reduce serial autocorrelation by means of a one-period lagged dependent variable. Since the pooled OLS in presence of pure heteroskedasticity is sill not efficient, we then utilize the pooled GLS to correct standard errors of parameters. Finally, the White's robust covariance is employed to parameter testing. To be more precise, we provide the detailed procedure of the estimation and testing in the following. First of all, we transform the unbalanced data to a balanced one by adding "na" for those data that are not available. Therefore, the econometric program we utilized, EViews, could deal with the unbalanced data as those are balanced. Next, denote our pooled linear regression model in stacked form as. j. [. YI [XI ~l = ? ;". 0 ... Xl.. 0 :. j[flj~ [el~l j. ~...~. ,~" ~. +. 0 Y. =. X. fl + e ,. ~" "~I "~k ~I. (B.l). "T-I. where Yi is T vector, Xi is a T x k matrix, and f3 is a k vector of coefficients. 16 The errors are assumed to be heteroskedastic across the n cross sections and contemporaneously uncorrelated, i.e.,. E (cc ') 0 V = diag( U 1 , ui,... ,un ® I r · 2. (B.2). Then the feasible GLS estimator is given by:. R - (X'V-1X)-1 X'V- 1y,. (B.3). !JGLS -. where V=diag(slps22' ... ,s"J®Ir is a consistent estimator of V,and sij is the residual variance estimator as below. 16. For our data,. n. = 311,. T. = 40. and. k. =8 ..

(23) 24. Journal of Financial Studies Vol. 14 No.4 December 2006. A. A. s . = CYi - Xj30LS )'Cy, - X /POLS ) 'J. (B.4). maxu;,T). where the inner product is taken over the non-missing common elements of and j . The max function in Equation (B.4) is designed to handle the case of unbalanced data by down-weighting the covariance tenns.17 For testing the significance of the parameters fl ' we use White 's OLS robust coefficient asymptotic covariance matrix as follows: A. (. n. .~' k' )(i)X,,.) '(X,..»)" (2:: £;:,(X,.,)'(X,.,»)(2:: (X,,.) '(X,;»)" 'I. 1,1. (B .S). ' .1. where the leading tenn is a degrees of freedom adjustment depending on the total number of observations in the staked data, n", and the total number of estimated parameters, k" .. 17. For more details, see EViews 5 User's Guide, Quantitative Micro Software, LLC.. -. _~•• "~~ .~ . ~ '" . ___. 1111_]1.. ".

(24) ,. Journal of Financial Studies Vol.l4 No.4 December 2006. 25. References 1. . Athanassakos, G. and P. Carayannopoulos, 2001, "An Empirical Analysis of the Relationship of Bond Yield Spreads and Macroeconomic Factors,". Applied Financial Economics 11, 197-207. 2. . Basu, S. and J.G. Fernald, 1997, "Returns to Scale in U.S. Production: Estimates and Implications," Journal ofPolitical Economy 105,249-283 .. 3. . Beck, N. and J.N. Katz, 1996, "Nuisance V.S. Substance: Specifying and Estimating Time-Series-Cross-Section Models," Political Analysis 6, 1-36.. 4. . Black, F. and J. Cox, 1976, "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal ofFinance 31, 351-367.. 5. . Brennan, M. and E. Schwartz, 1978, "Corporate Income Tax, Valuation, and the Problem of Optimal Capital Structure," Journal of Business 51, 103-114.. 6. . Brennan, M. and E. Schwartz, 1984, "Optimal Financial Policy and Firm Valuation," Journal ofFinance 39,593-607.. 7. . Brennan, M., 1995, "Corporate Finance Over the Past 25 Years," Financial. Management 24, 9-22. 8. . Chen, L.H. and GJ. Jiang, 2001, "The Determinants of Dutch Capital Structure Choice," Working Paper, Finance Department, Eller College of Business & Public Administration, University of Arizona.. 9. . Duffie, D. and K. Singleton, 2003, Credit Risk: Pricing, Measurement and Management (Princeton University Press, Princeton, N.J .) .. 10. Fama, E.F. and K.R. French, 2002, "Testing Tradeoff and Pecking Order Predictions about Dividends and Debt," Reviews of Financial Studies 15, 1-33 .. 11. Goldstein, R., N. Ju, and H. Leland, 2001, "An EBIT-Based Model of Dynamic Capital Structure," Journal ofBusiness 74, 483-512. 12. Hackbarth, D., J. Miao, and E. Morellec, 2004,· "Capital Structure, Credit.

(25) 26. Journal of Financial Studies Vo1.l4 No.4 December 2006. Risk, and Macroeconomic Conditions," Working paper, Department of Economics, Boston Universiy. 13. Harrison, J. and D. Kreps, 1979, "Martingales and Arbitrage in Multiperiod Securities Markets," Journal ofEconomic Theory 20, 381-408. 14. Harrison, J., 1985, Brownian motion and stochastic flow systems (Wiley, New York). 15. Hovakimian, A., T. Opler, and S. Titman, 2001, "The Debt Equity Choice,". Journal ofFinancial Quantitative Analysis 36, 1-24. 16. Jensen, M.e. and W.H. Meckling, 1976, "Theory of the Finn: Managerial Behavior, Agency Costs, and Capital Structure," Journal of Financial. Economics 3, 305-329. 17. Korajczyk,. R.. and. A.. Levy,. 2003,. "Capital. Structure. Choice:. Macroeconomic Conditions and Financial Constrains," Journal of. Financial Economics 68, 75-109. 18. Leland, H., 1994, "Corporate Debt Value, Bond Covenants, and Optional Capital Structure," Journal ofFinance 49,1213-1252. 19. Leland, H. and K. Toft, 1996, "Optimal Capital Structure, Endogenous Bankruptcy, and the Tenn Structure of Credit Spreads," Journal of Finance 51,987-1019. 20. Levinsohn, J. and MJ. MeIitz, 2003, "Productivity in a Differentiated Products Market Equilibrium," Working paper, Department of Economics, Harvard University. 21. Marchetti, D. and F. Nucci, 2004, "Price Stickiness and the Contractionary Effect of Technology Shocks," European Economic Reviews, forthcoming. 22. Melitz, MJ., 2001, "Estimating Finn-Level Productivity in Differentiated Product Industries," Working paper, Department of Economics, Harvard University. 23. Merton, R., 1974, "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal ofFinance 29, 449-470 .. •.

(26) .. Journal of Financial Studies Vo1.l4 No.4 December 2006. 27. 24. Miao, J., 2004, "Optimal Capital Structure and Industry Dynamics,". Journal ofFinance, forthcoming. 25. Modigliani, F. and M. Miller, 1958, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review 48, 267-297. 26. Modigliani, F. and M. Miller, 1963, "Corporate Incomes Taxes and the Cost of Capital: A Correction," American Economic Review 53, 433-443. 27. Nucci, F., A.F. Pozzolo, and F. Schivaridi, 2004, "Is Firm's Productivity Related to Its Financial Structure? Evidence from Microeconomic Data,". Working Paper, University of Roma "La Sapienza", DCNAPS. 28. Tang, D.Y. and H. Yang, 2004, "Macroeconomic Conditions and Credit Spread Dynamics: A Theoretical Exploration," Working paper, Department of Finance, McCombs School of Business, University of Texas at Austin. 29. Wang, J.e. and K.H. Tsai, 2003, "Productivity Growth and R&D Expenditure in Taiwan's Manufacturing Firms," NBER Working Paper, No. 9724..

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