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The Study of Swiss Investment Expenditures using Tobin’s q Model 1948-1995 Lamia Ben Hamida ⊗ University of Fribourg Lamia.email@example.com Revised Version, November 2006 Abstract The purpose of this paper is to explain, using Tobin’s q i nvestment model, the Swiss investment movements from 1948 to 1995. This paper adds to previous work in two ways: firstly, it puts forward how to adjustthe model so as to take into account som e possible stock exchange disturbances, and secondly, it provides evidence that cash flow is a key determinant of the investment behavior. The results reveal that Tobin’s q m odel is relevant in explaining the Swiss investm ent movements only after controlling for the disturbances which begun in 1985. Keywords: Investment, Tobin's q model, Cash flow. 1. Introduction Investment is arguably the m ost im portant econom ic variable. Its wide fluctuations reinforce the business cycle. Al so, current capital expenditures condition the level and the composition of the future capital stock and therefore influence the potential growth of the economy. There exists a large the oretical and empirical literature on investm ent, trying to detect and model the factors that help explain and predict its movements, both in the short run and in the long run. This literature is m ainly dom inated by two theories of investment: the neoclassical theory originated by Jorgenson (1963) and later developed in his work (1972, 1996a, and 1996b) and the q th eory suggested by Tobin in 1969. The neoclassical theory sta rts f rom a firm ’s optimization behavior, wherein the present discounted of fir m’s net cash flow is m aximized subject to its production and capital stock functions. The flows of investm ent are function of adjustm ent costs in changing capital stock. W hile, the q theo ry suggests that th e rate of investm ent is function of marginal q, the ratio of the firm market value of new additional investment goods to their replacement cost. This theory draws inspiration from neoclassic fundaments, in that first, it is derived from the firm’s optimization and second, tadjustment costs reflected by the marginal Tobin’s q are i mportant in determining the flow of investmentThe marginal q includes all information needed for taking an investment decision, unfortunately, this is ⊗ This paper has been presented at the EcoMod International Conference on Policy Modeling, Hong Kong, June 28-30, 2006. I thank all the conference attendees and especially Prof. Salah El-Sheikh for his helpful comments and suggestions. All remaining errors are mine. 1 an unobservable variable. To solve this probl em, Tobin suggests an observable variable as a proxy for marginal q. This variable, called Tobin’s q or average q, can be defined as the ratio of the market value of the firm to the replacement cost of its capital stock. Among empirical applications of Tobin’s q m odel are Hayashi (1982) and Zarin- Nejadan (1989) who found evidence for Tobi n’s q in explaining respectively the US investment behavior from 1952 to 1978 and Sw iss investment behavior from 1948 to 1986. The aim of the present study is to analy ze the determ inants of investm ent in Switzerland. In particular, Iexamine the im portance of th e variable “m arginal q” in determining the flow of investment. In this paper, a theoretical model is developed along these lines. It is then tested empirically using Swiss data over the period 1948-1995. This paper is organized as follows. In the next section, I develop the basic theoretical fram ework of T obin's q m odel used in this study to explain the Swiss investment behavior. In section 3, I discuss the empirical implementation of the model. In section 4, I introduce and describe the data. In section 5, I p resent the empirical results. Finally, the main results are summarized in the conclusion. 2. Development of Theoretical Framework of Tobin's q model This section aims at developing the investment model suggested by Jam es Tobin in 1969 and formalized by Hayashi (1982). Based on such a model, investments is shown to be a function of m arginal q. Tobin’s q m odel is the result of the m aximization of the firm’s present value under the capital accumulation constraint. The firm’s present value is given by ∞ ⎡ t ⎤ ω = ∫ R t exp⎢− ∫r s ds dt 0 ⎣ 0 ⎦ (2. 1) where r is the discount rate andR is the firm’s profit less its investment expenditures. I assume that cash flow is the only source wh ich firms use to finance their investm ent projects and for the sake of sim plicity I don’t take into acc ount taxation. ThR t) is given by R t =π t − p t Ι t (2. 2) where p is the price of output as well as investment goods, Ι is the gross investm ent, and π is the profit, given by π t = p t F Κ t ,Ν t −φ Ι t ,Κ t] −γ t Ν t) (2. 3) where Κ is the stock of capital, Ν is the labor force,γ is the wage rate, and F is the production function. In addition, equatio1 ( 2. 3) integrates the adjustment costsich are an increasing and convex function of Ι . Υ is the real output, related to capital and labor as follows 1Further explanations are given in Ben Hamida, L. (2002). 2 Υ t =F Κ t ,Ν t ] (2. 4) Hence, the problem of maximization can be written as follows ∞ ⎡ t ⎤ Max ω = ∫ [π(t − p t Ι t exp ⎢− ∫ s ds ⎥t 0 ⎣ 0 ⎦ (2. 5) under theconstraint : Κ t = Ι t −dΚ t) where d is the depreciation rate of capital. The first condition equations are the following FΝ = γ p (2. 6a) p 1+φ Iλ (2. 6b) λ= r+d λ− p F −φ ) Κ Κ (2. 6c) where λ is the shadow price related to the capital accum ulation constraint and the do t over indicates its time derivative. Equation (2.6a) describes the neoclassical marginal condition. Equation (2.6c) interprets the shadow price λ as th e present value of the f uture extra profits resulting from the installation of one further unit ofinvest ment. And equation (2.6b) shows that the marginal revenue of the installation of an a dditional unit of investment goods is equal to its cost. By resolving the first order condition equations, under the assum ption thats homogeneous of degree 1 in Ι and Κ , I derive the investment function which relates the capital accumulation ratio to the marginal q variable Ι λ = β q m with β > 0, andqm = (2. 7) Κ p Ι where Κ is the capital accumulation rate anm q is the marginal q. Therefore, according to this m odel, the marginal q var iable represents the m ain determinant of investment. This variable is defined as the ratio of the increase of firm’s value resulting from the installation of one further unit of i nvestment to the cost of this unit. 3. Empirical Implementation of Tobin’s q model In this section, I discuss the em pirical app lication of the Tobin’s q m odel developed in section 2. As previously noted the marginal q variable is unobservable and can be substituted by the Tobin’s q variable or the average q. This variable can be defined 3 as the ratio of the market value of the firm to the replacement cost of its capital stock. If this ratio is less than or equal to unity, then there is no incentives for the firm to invest in plant and equipm ent. In this case, the firm ’s shareholders could earn a higher return elsewhere. If the value of Tobi n’s q is grater than unity, th en the firm should invest in capital goods in order to maximize the return to its shareholders. From a macroeconomic point of view, Tobin’s q is presented as the ratio of the firms’ stock market capitalization to the replacement cost of their physical capital q = V (2. 8) pΚ where V is the stock market capitalization of private firms and pΚ is the replacement cost of their physical capital. Hence, Tobin’s q investment model becomes ⎛ Ι⎞ ⎛ Ι⎞ ⎜Κ ⎟ = α + β1qt+ β 2⎜Κ ⎟ +ξ t (2. 9) ⎝ ⎠t ⎝ ⎠t−1 where Ι is the rate of capital accu mulation, ⎛ Ι ⎞ is the lagge d rate of c apital Κ ⎝Κ ⎠ t−1 accumulation and refers to the investm ent process lag s, qtis Tobin’s q, and α is an intercept . The res idual ξ is in itially assum ed to be id entically and independen tly distributed. A further variab le th at can play an im portant role in explaining investm ent behavior is the cash flow. This variable , first suggested by Meyer and Kuh (1957), represents the firm’s self-financing capacity and is supposed to facilitate investment by procuring low-cost and less co nstrained financing. I propose to include in the equation (2.9) the cash flow variable (af ) as follows ⎛ Ι ⎞ ⎛ Ι ⎞ ⎛ caf ⎞ ⎜ ⎟ = α + β 1 t+ β2⎜ ⎟ + β3⎜ ⎟ +ξ t (2.10) ⎝Κ ⎠t ⎝ Κ ⎠t−1 ⎝ Κ ⎠t I note that the Tobin’s q can also be (arithm etically) defined as a ratio of the expected rate of return on capital ( Ra ) to the exp ected cost of capital (Ca ) (Zarin- Nejadan, 1989). The expected ra te of return o n capital is defined as the ratio o f the expected profits (πa) to the nominal value of the capital stock. While, the expected cost of capital is defined as the ratio of the expect ed profits to the stock m arket value of the firm. Tobin’s q variable can then be rewritten in the following way π a q = V = pΚ = Ra (2.11) t p Κ π Ca a V 4 Since expected profits ( π ) are unobservable, they can be replaced by the ex post a realized profits. In order to com pare the separate im pacts of these variab les ( Ra and Ca ) with that of Tobin’s q presented in model (2.9), I can rewrite this equation differently ⎛ Ι ⎞ ⎛ Ι ⎞ ⎛ caf ⎞ ⎜ ⎟ = α + β 2⎜ ⎟ + β 3 ⎟ + β4Ra t β C5 +ξt t (2.12 ) ⎝ Κ ⎠t ⎝Κ ⎠t−1 ⎝ Κ ⎠t I use the ordinary least squares method to estimate the models (2.9), (2.10) and (2.12). 4. Description and interpretation of the data In the present study I am interested in flows of fixed capital formation by Swiss private firms. These flows are defined as the sum of private expe nditures in equipment and nonresidential structures. I applied these data to explain the behavior of Swiss private investment from 1948 to 1995 . Figure 1 shows the profiles of Swiss Tobin’s q for structures, equipment, and both (respectively qs, q e and q). These profiles have the sam e trend and present overestimated values of Tobin’s q from 1987 to 1995. This overestim ation can be attributed to the widening gap between the real investment decisions of the firms and the financial market fluctuations since mid-1980s. In fact, this separation is explained by the strong growth of stock market capitalization since 1985 3. This growth might be the result of speculative movements. Furthermore, figures 3, 4 and 5 depict the profiles of Tobin’s q and the capital accumulation rate respectively for q, q , and q . In th ese three figures, the trends of e s Tobin’s q and the capital accu mulation rate have a quas i-perfect match, with a certain time lag, from 1948 to 1985 but they diverge since 1986. This divergence could be the consequence of the financial m arket boom that started in m id-1980s. To solve this problem and yet to bring out the relevance of Tobin's q variable in explaining Swiss investment move ments from 1948 to 1995, I propose to integrate in the m odel an additional explanatory variable that includes information about this boom. In addition, Tobin’s q can be written as the ratio of the expected rate of return on capital (Ra ) to the expected cost of capital ( Ca ). Figure 6 shows the profile of the expected rate of return on capital from 1948 to 1995. It has an increasing trend from 1948 to 1972 and then decreases from 1973 to 1995. Th is trend is similar to the profile of the 4 share of profits in gross domestic product (GDP) . Thus, I can assert thatRa 's behavior is the result of the trend of profit share in GDP. Figure 8 presents the profile of the expected cost of capital from 1948 to 1995. It has an increasing trend from 1963 to 1982 and decreases from 1982 to 1995. The Ca 's trend is negatively correlated to the evolution of capital acc umulation rate from 1948 to 2The data definitions and sources are given in appendix. 3Figure 2 depicts the evolution of Swiss stock market capitalization. 4Figure 7 shows the profile of profit share in GDP. 5 5 1995 . The investm ent rate has a decreasing trend from 1963 to 1984 and then an increasing trend for the remaining period. 5. Estimation Results and Analysis The estimation results of the Tobin’s q investm ent model (2.9) for the period 1948-1986 confirms those reali zed by Zarin-Nejadan (1989) for the sam e period. In addition, these results remain valid even w hen investment is com posed into equipm ent and nonresidential structures. The coefficients take their theoretically expected signs and are significant. The Chow tests of t he inter-temporal stability of investm ent equations corroborate the model for all three investm ent specifications (structures, equipm ent and aggregate). Therefore, variab les q s q end q can b e considered as relevan t leading indicators of Swiss private investments from 1948 to 1986. Nonetheless, model (2.9) performs less well when I extend the period of observation to 1995. The coe fficients of variables q , q and q take their theoretically 6 s e expected signs but are n ot significant . Thus, these variables seem not to be appropriate leading indicators of Swiss pr ivate investment for the en tire period from 1948 to 1995. 2 Still, I obtain a good fit ( ) in equations (1), (9) and (14). Therefore, I can assume that q , q and q explain a fair am ount of variance of the capital accumulation rate during s e the extended period, despite their weak significance. To solve the problem of variables insignificance, I propose to add a dummy variable noted k in equations (1), (9) and (14). k is a binary variable (1 or 0) defined in accordance with the presence or not of the presumed speculative movements on the stock market. Indeed, I have assumed that the stock market “bubble”, which dates back to mid- 1980s, is the main source of insignificance of the variables q , q and q in explaining s e the Swiss investm ent behavi or. The dum my variab le is def ined as f ollows: in th e equations (2) and (15), it takes the value 0 from 1948 to 1990 and the value 1 from 1991 to 1995; in equation (10), it takes the valu e 0 from 1948 to 1989 and the value 1 from 1990 to 1995. My choice is based on two statistical criteria: R and the standard error of regression. I vary the period in which k takes the value 1 and then choose the equation that has the maximum R and the m inimum standard error of regression. The dummy variable k takes the theoretically expected sign and is significant . Finally, the equations (1), (9) and (14) are re-specified as follows: • for the private equipment: ⎛ Ιe ⎞ ⎛ Ιe ⎞ ⎛ caf ⎞ ⎜ ⎟ = α + β 1 et−1+ β 2⎜ ⎟ + β 3⎜ ⎟ + β 4 tξ t (3. 1) ⎝Κ e⎠t ⎝Κ e⎠t−1 ⎝ Κ ⎠t • for the private nonresidential structures : 5Figure 3 analyzes the profile of the capital accumulation rate. 6Eq. 1, 9, and 14. 7Eq. 2, 10, and 15. 6 ⎛ Ιs ⎞ ⎛ Ιs ⎞ ⎜caf ⎟ ⎜ Κ ⎟ = α + β1qs,t+ β 2⎜Κ ⎟ + β 3⎜Κ ⎟ + β 4 t +ξ t (3. 2) ⎝ s ⎠t ⎝ s⎠t−1 ⎝ ⎠t • for private aggregate investment : ⎛ Ι ⎞ ⎛ Ι ⎞ ⎜ caf ⎟ ⎜ ⎟ = α + β1qt + β2 ⎜ ⎟ + β 3⎜ ⎟ + β 4 t + ξ t (3. 3) ⎝Κ ⎠t ⎝Κ ⎠t1 ⎝ Κ ⎠t Using these new versions of the models, al l coefficients take their theoretically expected signs and are significant 8. R remains relevant in equations (2), (10) and (15) . Therefore, I can conclude that qs, qeand q have significant im pacts on Swiss investments. Furtherm ore, the Chow tests of inter-tem poral stability of investm ent functions confirm the robustness of the result s for the three investm ent specifications (structures, equipment and aggregate) 9. As shown above, Tobin’s q can be written as the ra tio of the expec ted rate of return on capital ( Ra ) to the expected cost of capital ( Ca ). This modelisation shows as good a fit as the model (2.9). Although the coefficient of Ra is significant, that ofCa is not, these two variables takes th eir theoretically expected signs 1. In addition, the F statistic rejects the hypothesis of equality between the coefficients of variables Ra and Ca 11. Therefore, the expected cost of capital is dominated by the expected rate of return on capital because ( Ra ) is significant while (Ca ) is not. Hence, Ra reflects by itself the whole information embodied by Tobin’s q. Finally, the coefficient of the cash flow variable takes its theoretically expected 12 sign and is significant . Therefore, I con clude that fi nancial liquidity has a positive impact on Swiss investment movements. 6. Conclusion Tobin’s q investm ent model turns out to be a powerful tool for explaining the Swiss investment behavior from 1948 to 1986. It can be applied either to equipment or to nonresidential structures or to aggregate investment. However, the model becomes less irrelevant when the period of observations is extended to 1995. This decrease in the performance of the m odel can a priori be explained by the stock market disturbances, which intensified since m id-1980s. To solv e this problem and check the “bubble” hypothesis, I have introduced a dumm y vari able which takes the value 1 for the occurrence of the speculative movements on the stock m arket and 0 otherwise. In the presence of this variable, all regression coefficients take their theoretically expected signs and become significant. Theref ore Tobin’s q rem ains a rele vant leading indicator of Swiss private investment even during the extended period, when the “bubble” 8Eq. 2, 10 and 15. 9Eq. 6, 7, 11, 12, 16 and 17. 10 11Eq. 3 12Eq. 4 and 5. Eq. 8, 13 and 18. 7 phenomenon is taken into account. Financial liquidity also plays a significant role in explaining the investment flows. Future studies should f ocus on includi ng other variables such as taxes 13and technological changes, which may determine the behavior of investment. Bibliography • Ben Hamida, L. (2002) : “L’étude des m ouvements de l’investissem ent par le modèle de q de Tobin : Le cas de la Suisse 1950-1995” Mémoire du postgrade en statistique, Université de Neuchâtel. • Hall, Robert E. and Jorgenson, Dale W. (1967): “Tax Policy and Investm ent Behaviour”, American Economic Review, vol. 57, pp. 391- 414. • Hayashi, Fumio (1982): “Tobi n’s Marginal q and Aver age q: A Neo-classical Interpretation”, Econometrica, vol. 50, pp 213-238. • Jorgenson, D. W. (1996a): Investment, Capital Theory and Investment Behavior, Cambridge, MIT Press. • Jorgenson, D. W. (1996b ): Inves tment, Tax Policy an d C ost of C apital, Cambridge, MIT Press. • Jorgenson, D. W. (1972): “Investment Behavior a nd the Production Function”, Bell Journal of Economics, Cambridge, MIT Press. • Jorgenson, Dale W . (1963): “Capital Theory and Investm ent Behaviour”, American Economic Review, vol. 3, No 2, pp. 220 -251. • Meyer, J. R. and Kuh, E. E. (1957): The investment Decision: An E mpirical Study, Cambridge, Mass, Harvard University Press. • Poterba, Jam es M. and Lawrence, H. Summ ers (1982): “Dividend Taxes, Corporate Investm ent, and Q”, Journal of P ublic E conomics, vol. 22, pp. 135-167. • Tobin, James (1969): “ A General Equilib rium Approach to Monetary Theory”, Journal of Money: Credit and Banking, vol. 1, pp. 15-29. • Zarin-Nejadan, Milad (1989) : “L ’évaluation financière et l’investissem ent physique privé en Suisse 1949-1986” Revue Suisse d’Economie Politique et de Statistique, No 4, pp. 557-581. 13 In this respect, one could see Jorgenson (1996), Hall and Jorgenson (1967), and Poterba et al. (1982) for further discussions. 8 Figures: 7 6 5 qe 4 qs 3 q 2 1 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 1 q, qe, qs 700000 600000 500000 400000 S. M. Capi 300000 200000 100000 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 2 The Swiss stock market capitalization (CHF m) 2.5 2 1.5 q 1 I/K(*10) 0.5 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 3 q, I/K(*10) 9 7 6 5 4 qe 3 Ie/Ke(*10) 2 1 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 4 qe, Ie/Ke (*10) 3.5 3 2.5 2 qs 1.5 Is/Ks(*10) 1 0.5 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 5 qs, Is/Ks (*10) 0.5 0.45 0.4 0.35 0.3 0.25 Ra 0.2 0.15 0.1 0.05 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 6 The expected rate of return on capital (%) 10 0.3 0.25 0.2 0.15 profit share of GDP 0.1 0.05 0 1940 1960 1980 2000 YEARS Figure 7 The profit share of GDP (%) 0.45 0.4 0.35 0.3 0.25 Ca 0.2 0.15 0.1 0.05 0 1940 1950 1960 1970 1980 1990 2000 YEARS Figure 8 The expected cost of capital (%) 11 Tables: Table 1: Estimation results of the function of capital accumulation rate from 1948 to 1995 ⎛Ι ⎞ Dependent variable : ⎜ ⎟ ⎝Κ ⎠t Expla. Eq. 1 Eq. 2 Eq. 3 Eq. 4 Eq. 5 Eq. 6 Eq. 7 Eq. 8 Var. Const. 0.03 0.02 -0.06 -0.69 -0.069 0.017 0.019 -0.09* (0.08) (0.02) (0.03) (2.33) (0.33) (0.009) (0.03) (0.02) q 0.013 0.02* 0.04 0.07* 0.026* t (0.014) (0.01) (0.11) (0.01) (0.011) qt−2 0.03* (0.01) k -0.028* -0.029* (0.011) (0.011) 0.57* 1.31 Ra t (0.10) (0.24) Ca t -0.08 -0.129 (0.05) (0.09) ⎛caf ⎞ 0.74* ⎜ ⎟ (0.11) ⎝ Κ ⎠t ⎛ Ι ⎞ 0.70 0.72 0.37* 0.61 0.27 0.72* 0.68* 0.35* ⎜ ⎟ ⎝Κ ⎠t−1 (0.55) (0.14) (0.11) (1.35) (0.11) (0.05) (0.18) (0.09) ρ 0.315 0.215 0.265 0.375 0.245 0.205 0.155 0.075 R 2 0.926 0.928 0.948 0.937 0.955 0.968 0.817 0.959 S. E 0.012 0.011 0.009 0.08 0.067 0.01 0.01 0.008 F F(1,41) = 18.2 F(4,37 = 1.79 No. Obs. 45 45 45 45 45 22 23 45 The estimated standard errors in brackets. 2 R : The corrected coefficient of multiple determination. S. E: The estimated standard errors of regression. F (m,n) : Fisher’s statistic : F (1,41) = 4.08 and F (4,37) = 2.619 at the 95% confidence level. ρˆ: First-order autocorrelation coefficient. All equations have been corrected for first-order autocorrelation. * Denotes significance at the 5% level. 12 Table 2: Estimation results of the function of capital accumulation rate of private equipment from 1948 to 1995 ⎜Ιe⎟ Dependent Variable : ⎝Κe⎠ t Expla. Eq. 9 Eq. 10 Eq. 11 Eq. 12 Eq. 13 Var. Const. 0.058 0.043 -0.007 0.036 0.11* (0.099) (0.042) (0.011) (0.04) (0.05) q 0.009 0.047* e,t (0.008) (0.009) q e,t−1 0.018* 0.02* (0.007) (0.007) q 0.018* e,t−2 (0.007) k -0.038* -0.04* (0.018) (0.01) ⎛ ⎞ 0.99* ⎜caf ⎟ ⎜ Κ ⎟ (0.22) ⎝ ⎠t ⎛ Ι ⎞ 0.67 0.66* 0.62* 0.62* 0.32* ⎜ e ⎟ (0.41) (0.16) (0.069) (0.18) (0.13) ⎝ Κ e⎠t−1 ˆ 0.19 0.175 0.135 0.13 0.2 ρ R 2 0.927 0.932 0.974 0.76 0.948 S.E. 0.02 0.019 0.016 0.02 0.015 F F(4,37) =1.55 No. Obs. 45 45 22 23 45 The estimated standard errors in brackets. R : The corrected coefficient of multiple determination. S. E: The estimated standard errors of regression. F (m,n) : Fisher’s statistic: F (4,37) = 2.619 at the 95% confidence level. ρˆ: First-order autocorrelation coefficient 13 Table 3: Estimation results of the function of capital accumulation rate of private nonresidential structures from 1948 to 1995 Dependent Variable :⎜ Ιs⎟ ⎝Κ s⎠t Expla.Var. Eq. 14 Eq. 15 Eq. 16 Eq. 17 Eq. 18 Const. 0.020 0.008 -0.016 0.005 -0.08* (0.05) (0.018) (0.009) (0.024) (0.024) q s,t 0.005 0.012* 0.011* (0.007) (0.005) (0.005) q s,t−2 0.03* 0.012* (0.008) (0.005) k -0.026* -0.023* (0.008) (0.007) ⎛caf ⎞ 0.55* ⎜ ⎟ (0.09) ⎝ Κ ⎠t ⎛ Ι ⎞ 0.703 0.74* 0.71* 0.72* 0.4* ⎜ s ⎟ (0.63) (0.136) (0.082) (0.19) (0.10) ⎝ Κ s ⎠t−1 2 0.885 0.901 0.922 0.86 0.93 R ρ 0.33 0.225 0.295 0.385 -0.06 S. E. 0.009 0.009 0.009 0.007 0.007 F F(4,37) = 1.01 No. Obs. 45 45 22 23 45 Th2 estimated standard errors in brackets. R : The corrected coefficient of multiple determination. S. E: The estimated standard errors of regression. F (m,n) : Fisher’s statistic: F (4,37) = 2.619 at the 95% confidence level. ρˆ: First-order autocorrelation coefficient All equations have been corrected for first-order autocorrelation. * Denotes significance at the 5% level. 14 Appendix: Variable definitions and data sources Ιs: the private nonresidential structures. Ι : the private equipment. e Κ : the capital stock. I calculate a v alue of this variable by applying the m ethod of permanent inventory. The value of the capital stock from 1948 to 1986 is given by Zarin- Nejadan (1989). d : the rate of depreciation. It is fixed at 4% for structures and 20% for equipment. V : Stock market capitalization. The data for 1948 to 1986 are given by Zarin-Nejadan (1989). Those of the rest of the period are obtained by using the statistics of Zurich stock exchange. Π :aexpected profits. These profits are calculated in the following way, in which data are provided by the Federal Bureau of Statistics Π = surplusnet of exploitation +savingof privatefirms a + paymentof interest +depreciation of fixedcapital+direct taxes 15
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