European Economic Review 34 (1990) 1061-1078. North-Holland
MONOPOLISTIC
COMPETITION AND THE Q THEORY OF INVESTMENT F. SCHIANTARELLI*
Boston
L’nicersity
and IFS,
Boston,
MA
02215.
USA
D. GEORGOUTSOS Unicersity
of Essex, Colchester
CO4 3SQ, UK
Received January 1989, linal version received July 1989 In this paper we analyse the implications for Q models of investment of replacing the assumption of perfect competition in the output market with the assumption of monopolistic competition. The structural investment equation that can be derived in this case has a richer dynamic structure than the conventional one and it contains, in addition to present and future Q, output as an explanatory variable. In the applied section we discuss the extent to which monopolistic competition helps in providing a remedy for the empirical weaknesses of Q models. The estimates are obtained using aggregate data for U.K. industrial and commercial companies for the period 1951-79.
1. Introduction The existence of convex costs in adjusting the capital stock have provided a plausible rationale for the forward-looking nature of investment decisions. In this case investment can be shown to depend upon the relationship between the purchase price of investment goods and the shadow price of an additional unit of capital, i.e. the present value of the expected additional profits generated by a new machine. Although the shadow price is unobservable, it coincides with the average market value of capital under the assumption of perfect competition and linear homogeneity in the production and adjustment cost function [Hayashi (1982)-j. All this is very appealing because it rationalises the intuition by Keynes in the General theory (1936) and later by Tobin (1969) that the relationship between market valuation and replacement cost of the capital stock (defined as Q) is the crucial *This paper is part of a research project by the Institute of Fiscal Studies on company behaviour and has beneftted from discussions with R. Blundell, S. Bond. M. Devereux, F. Hayashi, R. Faini, M. Keen, G. Weber and J. Poterba who has also provided us with the data. We would also like to thank the participants of seminars at the University of Essex and Boston University for useful comments. 0014-2921/9O/S3.50 c
1990. Elsevier Science Publishers B.V. (North-Holland)
1062 F. Schiantarelli
and D. Georgoutsos,
Monopolistic
competition
and the Q theory
of investment
variable in determining firms’ investment decisions. In spite of their theoretical neatness and appealing features, the empirical performance of Q models has not been very satisfactory on their own terms and has not compared favourably with competing models. [See Clark (1979) for an early attempt at a systematic evaluation of different models.] Q variables, even when significant, do not usually have a high explanatory power. Accurate modelling of the tax system and of the relationship between investment and financing decisions [Summers (1981), Poterba and Summers (1983)], makes things better but does not alter the basic problems. They are summarised by the significance in the investment function of lagged investment for which there is not a satisfactory rationale and by autocorrelated residuals that suggest the presence of some form of misspecification. Finally, contrary to what the theory suggests, other variables that should not appear in the equation, like output, generally contribute significantly to the explanation of investment in addition to Q. Recent attempts to improve the empirical performance of Q models have analysed how the specification of the model changes if the existence of multiple capital inputs is allowed for [Chirinko (1984), Wildasin (1984), Hayashi and Inoue (1989)], debt policy is endogenised and the role of the capital market imperfection is examined [Hayashi (1985), Chirinko (1986), Fazzari et al. (1988)], marginal Q is allowed to differ from average Q [Abel and Blanchard (1986)] and delivery lags and non-separable adjustment costs are introduced [Dinenis (1985a, b)]. All these contributions are significant extensions to our understanding of the investment process but do not provide conclusive answers to the empirical weaknesses of Q models. In this paper we will explore the consequences for the specification of Q type of investment equation of removing the assumption that the product market is perfectly competitive. As it is well known [Hayashi (1982)-J, in this case marginal Q differs for average Q. In section 2 we will show how an estimable investment model can be derived under the assumption of monopolistic competition. The model has a more complex dynamic structure than the conventional ones and it contains actual and expected Q, expected investment one period ahead and output per unit of capital as explanatory variables. A monopolistically competitive market structure provides, therefore, a possible rationale as to why output has been found empirically to be a significant determinant of investment in Q type investment models. In section 3 the model is estimated on aggregate U.K. data for commercial and industrial companies for the period 1950-80. The results suggest that output is an important factor in explaining investment expenditure together with actual and expected future Q as it is implied by the assumption of monopolistic competition. The estimated equation has a high explanatory power and the direction of the effect of each explanatory variable is the one suggested by the theoretical model. This model also allows us to recover
f. Schianrarelli and D. Georgoutsos, Monopolistic competition and the Q theory oj investment 1063
estimates of the adjustment cost parameters and of the price elasticity of demand for the firm’s output. The estimates imply a fairly low demand elasticity and, like other studies, a high value for the adjustment cost parameters. In this section we also discuss which assumption concerning the marginal source of finance is more compatible with the data. The conclusion summarises the results and contains suggestions for further research.
2. Q models and monopolistic competition The model underlying our empirical estimation retains most of the usual assumptions used in deriving a relationship between investment and the tax adjusted market value of capital. In particular it is assumed that there are internal convex costs in adjusting the capital stock. Adjustment costs are separable and the cost function, G(I, K), is linear homogeneous in investment, I and capital, K, while the gross production function, F(K,L), is linear homogeneous in capital and labour, L. Net output, F(K, f., I), equals therefore F-G. We will also maintain that debt policy as exogenous. The firm finances. part of its investment through debt, but this proportion (possibly variable) is not explained within the model.’ The major change is that now the firm is assumed to face a downward sloping demand function for its product. Output demanded is assumed to depend upon the price charged by the firm relative to the average price of competitors, PJP,, and upon a shift parameter, 6, that summarizes all the factors determining the position of the demand curve. The inverse of the demand function can, therefore, be written as cp(F,, a,) = PJP,. The average price level is taken as given by each individual firm. The setting up of the problem is standard. In equilibrium the following arbitrage condition must hold:
where K is the value of firm’s shares, pI is the (net of taxes) nominal discount rate for equity, m, the tax rate and gross dividends, D,, z, is the tax rate on capital gains, 0, is the dividend received by the shareholder when the firm distributes one pound of retained profits, and V: is the value of new shares issues. E, denotes expectations conditional on information available at time r. The firm’s objective is to maximise the wealth of existing shareholders. Solving (1) forward, one obtains: ‘The assumption of an exogenously given debt policy is also used in Summers (1981) and Poterba and Summers (1983). A fuller treatment of the choice of financial structure could be developed by introducing explicit agency costs for debt as in Chirinko (1986). King (1986) or by allowing for tax exhaustion [see DC Angelo and Masoulis (1980). Auerbach (1984) and Mayer (1986)], but this goes beyond the purpose of this paper.
1064 F. Schiantatelli and D. Georgoutsos.Monopoirstic compettfion and the Q rheory of inrestmenr
KzEI
2
(2)
BjCYr+jDt+j-K+jJ*
j=O
where y=(l -m)&‘(l -I) is the tax discrimination variable that determines the relative tax advantage of dividends versus retained earnings. flj is the discount rate defined as where Gross dividend can be substituted sources and uses of funds:
r, = p,/( 1 - 2,). out from (2) using the definition
of
where K,, L,, and I, denote capital, labour and investment, respectively. P: is the price of investment goods, q the nominal wage rate, T, the corporate tax rate, u, first year atlowances and A, the tax benefit due to writing down allowances as past investment, i, denotes the nominal rate of interest and 8, the end of period stock debt. As in Poterba and Summers (1983) the maximisation is subject to a nonnegativity constraint on dividends and on new share issues, the latter deriving from the 1948 Company Act. We also impose the constraint that dividend payments cannot exceed the excess of revenues over labour cost and interest rate payments:
Using (3), eq. (4a) can be rewritten as: B,-I?,_,+
v:+A,~(l-u,)P:f,,
which says that funds from external sources and from tax savings from past investment cannot exceed investment expenditure. Eqs. (4a) or (4b) are a very simplified version of the statutory provisions introduced in the 1981 Companies Act.’ However, the principle of maintenance of share capital was well established even before. Such a constraint is necessary to obtain a well defined maximisation problem since, after 1973 in the U.K., the tax parameters are such that there may be an incentive for investors to issue *In particular a term representing the excess of past retained earnings over dividend payments should be included on the right-hand side of (4a). See Edwards and Keen (1985a).
F. Schiantarelli
and D. Georgoutsos,
Monopolistic competition
and the Q theory
qi mcestmenr
1065
shares indefinitely in order to finance dividend payments. This is reflected in a weighted average of y that exceeds unity for full tax paying companies3 However if companies are tax exhausted, which was the case for a considerable number of them in the second half of the seventies. the specific features of the imputation system in use in the U.K. imply that it is not any longer profitable to issue shares in order to finance dividend payments up to the point where the constraint in (4) is binding. y can be thought of as being no greater than one in this case.4 Define with 2’. I”, AM, AK t h e (non-negative) multipliers associated respectively with the non-negativity constraints on dividends and on shares, with the maximum dividend payments constraint, and with the capital accumulation equation K, = (1 - 6)K, _ , + I,. Differentiating the objective function with respect to L, I, K and V” one obtains:
(5)
II
(6)
I
-0,
(7)
1 +,,‘+j-)‘,“+i} ~0.
(8)
=o,
x(l-nt+j)P:+j+~f+j
+C+j+ISj+1(1-6)
G{Y,+,+T+j-
E, represents here the elasticity of demand and in general is a function of P,/P, and CT,.n, denotes the present value per pound spent on new investment
of tax savings during the entire life of the machine. The first-order conditions ‘See Poterba and Summers (1983). Appendix, p. 165. The value of y presented there (and used in this study) is obtained by employing a weighted average of investors’ tax rates on dividends following the methodology in King (1977). For some investors with a high marginal tax rate, y remains smaller than one even after 1973. ?his is basically because the Advanced Corporation Tax (ACT) cannot be fully offset against the other components of corporate taxes. See King (1983) and Edwards and Keen (1985b) for details.
1066 F. Schianrarelli and D. Georgoursos, Monopolistic comp&tion and tk
Q tkory
of inresrmenr
include obviousIy the non-negativity conditions for D, and V:, the constraint on maximum dividend payments represented by (4), and the approp~ate complementary slackness conditions. Eq. (5) requires the marginal revenue product of labour to be equal to the wage. Eq. (6) is the first-order condition for investment and it implies (setting the non-negativity multipliers A* and AM equal to zero for simplicity) that the cost of a marginal unit of capital (including both its purchase and adjustment cost) must equal its shadow value 1.‘. Eq. (7) is the equation of motion for the marginal shadow value of capital, AK. Making use of (5), (6) and of the homogeneity assumption, it is easy to derive a simple relationship between the marginal and average value of capital.’ For instance, in the case of y< I:
jK_(~-AI+H,-C,)(l+r,f -8(l-6)&_,
’
where
IT
F
C= j=O Bj%+,Xl -7r+j)Pr+,Ifl. 4+j
(1W
a,+j equals one when the firm finances itself at the margin through new shares and equals yl+j when it uses retention.6 A, is the present value of the tax savings due to depreciation allowances on investment made before f. H, is the present value of all cash flows associated with debt, including interest rate payments and funds accrued to the firm because of the issue of new debt. C, is the most important term for our purposes and represents the present value of the reductions in revenues due to the fact that the firm, ceteris paribus, has to lower the price of additional output produced by a new machine in order to sell it. Whereas it is possible to think of reasonable “In order to derive eq. (9) consider the first-order conditions for j-0. Multiply (6) by f, and (7) by K, and add the two equations together. The tirst-order difference equation one obtains is then solved forward, making use of the first-order condition for labour and the homogeneity property of the gross production and adjustment cost functions. 6As Poterba and Summers (1983) have argued. firms will never issue new shares and simultaneously pay dividends when y < 1. Investment can be financed at the margin by new shares (J”=O) or by retained earnings (2 ‘==O). It is also clear that in this case the maximum constraint on dividends will be, in general, satisfied with strict inequality so that AMequals zero.
F. Schiantarelli
and D. Georgoutsos,
Monopolistic
comperition
and the Q
theory o/
incestment
1067
assumptions that allow one to derive adequate proxies for A, and H,,the presence of the C, term says that one has to forecast the entire future path of output in order to find an observable counterpart for 2,“. This makes Q-based theories of investment less appealing in their static formulation because now there is an additional wedge, difficult to quantify. between the shadow value of capital and its market value. However, it can be shown that through an appropriate transformation, it is possible to derive an easily estimable investment equation without having to specify an arbitrary time series model for output in order to obtain a proxy for C,. Finally, it should be noted that when y is greater than one and there is an incentive to issue new shares in order to allow the distribution of all retentions as dividends, the expression for 1: is very similar to the one under retention financing. The only difference is in the definition of the terms containing debt, where interest payments, but not the change in debt, are multiplied by y,+,.’ In order to derive the equation to be estimated, assume that adjustment costs are quadratic and equal to 4/2(I/K-C)‘K, consider now the first-order condition for investment, (a), expected to hold at time t + 1, multiply it by K,IK, - I and subtract the resulting equation from the one holding for time t.* Make use- of eqs. (9) and (10) and assume, in order to obtain a manageable specification, that the elasticity of demand is constant through time. For y< 1, in the case of new shares issues, the investment rate at time t can be written as:
1 FUGA 1,) +& xt-~(~-l)(l-~)K~_~
where
1)
(I--r,+#‘,+~
K,
(11) (124
“=(l-r,+J(l-r,)J’,K,_,’ ‘More precisely in this case both J.p- rl”=O, (4a) is binding and H, now equals H.=,fOPJy,+,i,+j(l
_
-G+,)B,+,-i
-(4+,-4+,-111.
‘Abel (1980) also uses a similar transformation in order to obtain his investment equation under adjustment costs. In his case the firm treats output prices as parametric (or output as given) and the marginal value of capital is derived by specifying the functional form of the production function.
1068 F. Schtanzurelii and D. Georgoursos,
(V;-4)(l+r,) Q:= Pj(l-6)K,_,
Monopolists
comperlraon and the Q theory of inuestnenr
PI ’1P,(l -t*)’
_l+n
and
xl=i,(~-~,)gl-l-(B,-B,-,f (1 -r,)P,(l-&K,_,
(W
’
In the case of financing through retentions, and Jlf which are defined by:
QP-
G=
(K--+4)fl +rr) _ Yz:Pf(1 -m,
-1
1
+n
’
1e
Qy and Jiy are replaced by Qp
P,( 1 - r,)’
Yr*1(1-%+1Pt+1 K,
[ Y,(f.-“&+A(1 +w,K,-
(12b)
1
*
where
(134
Wb)
So the two cases differ basically because the variable y that contains the personal tax parameters appears in the equation, whereas it is absent in the case of financing through new shares. When y> 1 the Q variable is identical to the one that holds under retention financing. In the term containing the cash flow related to debt, X,, however, the change in debt is divided by 3. The investment equation in (11) is quite appealing. Current investment depends upon expected future investment, actual and expected Q, current cash flows related to debt, X,, relative to the capital stock and upon output per unit of capital. One could omit the X variable from the equations and include the present value of changes in debt, net of interest payments, H, in the definition of Q. If we then approximate H by B we obtain the usuai specification of the Q variable containing at the numerator the total value of the firm (shares plus debt), adjusted for the value of depreciation allowances on past investment. The two main characteristics of (11) are its rich dynamic structure and the presence of an additional output term that would not appear as a regressor under the assumption of perfect competition. The case of a perfectly competitive firm in fact can be seen as a special case of (11) when the elasticity of demand, E, tends to infinity. The introduction of monopolistic competition has, therefore, the potential to rationalize why output variables are frequently significant in Q-type of investment equations and also why they display autocorrelated residuals or a signi~cant role far the fagged dependent variable and lagged Q. Note that when (I/K), is used as the left-hand side variable, the output variable FJK,._, enters with a negative sign. If eq. (11) is solved for (l/K),+ 1, then the latter is positively correlated with FJK,_,. Indeed the positive correlation between investment and lagged output is what is often observed empirically. The problems of the stochastic
F. Schlantarelli
specification section.
and D. Georgoutsos, Monopolistic
competition and the Q theory of mrestment
of (11) and of its estimation
1069
will be dealt with in the next
3. Econometric specification and results In replacing the expected values of future variables by their realisations a measurement error is introduced. If expectations are rational, the method of instrumental variables can be used in estimation [see McCallum (1976) and Wickens (1982)]. Under the rational expectations assumption, any subset of the information available to the agents when expectations are formed is a legitimate instrument set in the sense of being uncorrelated with the white noise forecast error 0,+ 1. If this is the only component of the error term and there are no delivery lags, variables dated t can be used as instruments. We could include an additive stochastic term o, in the adjustment cost function that now becomes $/2[(Z/K),- C-o,]‘&. If we assume o, to be serially uncorrelated, the composite error term in the investment equation o,+u,+ 1 will be moving average of order one [MA(l)]. This is because o, and v, will, in general, be correlated since o, represents new information that will affect the error made in forecasting variables dated t, i.e. u,.’ How serious this problem is dipends upon the strength of the correlation between o, and u,. When the error term has an MA( 1) structure, then only variables dated r - 1 or earlier should be used as instruments. The model has been estimated for the period 1951-1979 on the aggregate data for U.K. industrial and commercial companies used in Poterba and Summers (1983).” Under the assumption that firms are identical this will allow us to recover estimates of the structural parameters. The assumption of a constant elasticity of demand across industries is rather strong and it would be very useful in future work to re-estimate the model on industry or individual firms data allowing for inter-industry differences in elasticity. In table 1 we summarize the estimates of eq. (11) under alternative assumptions about investment financing, obtained by using only lagged variables as instruments. After 1973 we follow Poterba and Summers (1983) in assuming that the firm treats 7 as being one. We have also estimated the model under the assumption that ;‘> 1 for the post-1973 period so that firms issue new shares until they reach the permissible ceiling set by (4). The results are very similar to the ones presented in table 1 and therefore we do qWe could also have MA( 1) errors if it is assumed that for investment there is a one period delivery lag between order and expenditure. In this case investment expenditure at time t will depend upon information formed at t - 1. This means that in eq. (11) E,( ) should be replaced by E,_ ,( ) and it is easy to show that in this case the forecast error will be MA( 1). loIn deriving proxies for A and n we assume static expectations about the discount factor and all tax parameters. There is a slight contradiction between the assumptions of static expectations and the specification of eq. (11) in which no such assumption is made. If static expectations about tax parameters are used all the way through, the empirical results are very similar and are not reported here.
1070 F. Schiantarefii and D. Georgouuos.
Monopolistic competition and the Q theory I$ mcestmznt
3
n
-.. o(
4F
c91
c91
1.21
Cl1 4.70
I21 3.63
Cl1
1.54
c11
PI
4.51
3.08
PI
GJ13
GJ23
1.89
0.0052
WI
10.8
0.57
1.77
&
0.72
Constant,
0
i
,_,, $j..s, K,_,. iE,,Q:-,,
X,_,.
(F,_,/(I-@K,_,),
(‘-78-1)Pf-1 (,+r,_,)(l_7,_2)p,_2.
7,-b
ml-,.
7,-l.
4-t.
klv
kl.
Ica) i= V or R; r statistics in round brackets; SE: standard error regression; BG: Breusch-Godfrey test for MA(l) and AR(I) errors, distributed as a standardised normal. DW: Durbin-Watson; ST: Sargan misspecification test distributed as x’(m) where m is the number of instruments minus the number of regressors, GJ: Gallant-Jorgenson test on restrictions, distributed as 1: where p is the number of restrictions. Numbers in square brackets denote degrees of freedom for x2 tests. A small sample adjustment is used. (b) Cut-OB points for x2 test at 5 percent critical level: xi =3.84. xi = 5.99. xi= 16.9, x:e= 18.3, ,r:, = 19.7. (c) List of instruments:
SE in general model with (f/K,) as dependent variable
GJ12
0.0048
10
12.98 WI
12.32
ST
1.88 0.69
1.67 0.35
1.79 0.092
1.73 0.19
BG
DW
1072 F. Schiunfarelli and D. Georgoutsos, Monopolisrlc comperlrlon and the Q rheory of rnresrment
not discuss them here but they are available upon request. The modeliing strategy is to start an unrestricted version of eq. (1 I) and successively impose the restrictions implied by the theory. The restriction that the coefficient of I(lf(UK),+ I is unity is never rejected, where i= V, R. Therefore we present the results with (I/K),- $:(1/K),+ , as a dependent variable. The explanatory power of all the equations is very good. For instance for both models (1) and (2) the ratio of the explained to the total variance of the dependent variable is 0.96. This is a more than satisfactory fit, given that our dependent variable is in (quasi) differenced form. The coefficients in all the specifications have the sign suggested by the theory. Both Q variables are always highly significant. Also the output per unit of capital term plays an important role. In the equation under the assumption of new share issues it is always significant at the 5 percent level in a one-tail test. In the case of financing through retentions it is somewhat less significant in models (1) and (3) but highly significant in model (2). The general conclusion is that output, as implied by the assumption of monopolistic competition, should be included in Q-type of investment function.” If the investment equation had been estimated in its static form including only Q,, its coefficient would have been smaller and less precisely determined. This is what one would expect if firms are monopolistic competitors and the wedge between marginal and average Q, represented by C, and containing the output terms [see eqs. (9) and (IOc)], is incorrectly omitted from the model. The test for MA( 1) and AR(I) errors [see Breush and Godfrey (1981)] suggests that the residuals are not serially correlated. In this case it would be legitimate to use contemporaneous variables as instruments. The results obtained in this case do not differ from the ones presented in table 1 and therefore are not reported here. The Sargan (1964) test of over-identifying restrictions, ST, tests if the instruments are correlated with the disturbances in the equation. The values it takes imply that there are no obvious forms of misspecification in the estimated equations. The x2 test of restrictions [see Gallant and Jorgenson (1979)] indicates that the restriction that the Q terms should enter in quasi differenced form (Qy - $,Qr+ r) is easily accepted (see GJ12). The restriction that the debt term X, has the same coefficient as this quasi difference of Q cannot be rejected either when tested against model (1) (GJ13) or against model (2) (GJ23). However, in this case we are much closer to the rejection values of the statistics at conventional levels. This suggests that the debt term may play a wider role than the one envisaged by standard Q theory. “Dinenis (1985b) reaches the conclusion that output is not a significant determinant of investment, using U.K. aggregate data for the manufacturing and non-manufacturing sectors. Notice however that, even in his case, output lagged once is an important determinant of investment (with a r-statistic of 1.85) in the equation for manufacturing.
f. Schiantareiii
and D. Georgoutsos.
Monopolisric
competition
and the Q theory
of investment
1073
The significance both of Q variables and output is quite strongly supported by the data and this is comforting. The qualitative results obtained here do not change if we approximate H by the market value of debt at the beginning of period t, include this proxy for H in the definition of Q and omit the separate debt term X,. They are not sensitive either to the choice of the discount rate or to the inclusion of a fixed risk premium.i2 They are also robust to a different selection of the instruments. For instance, if we augment the instrument set with lagged values of real government expenditure, of the real money supply and of an index of world trade, the qualitative conclusions reached so far do not change. In a more general specification than the one adopted here, the elasticity of demand may depend upon these variables that capture the position of the demand function. The Sargan test of overidentifying restrictions provides, in this case also, a check on the adequacy of the assumption of constant elasticity. Again there is no evidence of serious misspecification. For instance ST for Model (1) in the case of new equity issues in table 1 equals 14.81 (with 12 degrees of freedom). Moreover if the three demand variables are added as regressors to the equation, the GallantJorgenson test has a value of 3.48 and does not reject the hypothesis that their coetlicients are jointly zero. An identical result is also obtained when one lag of Q and f/K are used as additional regressors. This confirms that the equations possess an adequate dynamic structure. Note that this structure is consistent with the theory and it is simpler than the rather ad hoc one found in Poterba and Summers (1983). Their equation contains contemporaneous and lagged values of Q and a second-order autoregressive error term. One drawback of our estimates is that the restriction that the coefficient of the constant and I# should be equal in absolute value is clearly rejected by the data. It is possible however to recover an estimate for the structural parameters E and 4. For instance, (I 1) implies that the value of the elasticity of demand, e, can be obtained by taking the ratio between the absolute value of the coefficient of (Q,- $fQ,+ 1+X,) and F/( 1 -6)K,_ , in the most restricted model presented in colume 3 of table 1. Two observations are necessary at this stage. First, because of data availability, the variable used here as a proxy for output is value added for industrial and commercial companies. Second, the model we have used so far for illustrative purposes should be enriched by the introduction of raw materials in the production function. If we assume that the gross production function is linear homogeneous in capital, labour and materials, all the derivations still go through, but it is now clear that output (net of adjustment costs), not value added is the relevant variable that appears in (11) and that should therefore be used “The results presented in table 1 are obtained when r,=(l -m,)if/( I-z,) where 1: is the interest rate of debentures. Similar results hold if r, is set equal to ip. In this case the model for 7~ I and new equity financing is indistinguishable from a model in which personal taxation is completely ignored.
1074 F.
Schiantarelli
ond D. Georgoursos,
Monopolistic
competition
nnd
the
Q theory
of inuesrmenr
as a regressor. From the input-output tables it is possible to obtain an estimate of the ratio between value added and output that has remained fairly close to 40 percent for manufacturing.” Using this figure, the estimated coefficient in the most restricted model under new equity financing yields an estimate for the elasticity of demand of 1.58 with a standard error of 1.03. This estimate is consistent with the theory, although it implies a quite inelastic demand function. i4 There is another possible, although not very convincing, explanation for the low estimate of the elasticity of demand. If returns to scale are not constant, so that the net production function is homogeneous of degree 1 +K, then it is easy to show that the coefficient in front of F/5/(l-6)&_ I in eq. (15) becomes l/&s- 1) -K/& If returns to scale are decreasing then, by assuming constant returns, one underestimates the elasticity of demand. However, the converse is true if returns to scale are increasing. It is important also to discuss the implications of our estimates for the size of the adjustment costs. The derived value of 4 is approximately 216 and the constant, C, 0.11. Since the sample average for the rate of investment, Z/K, is 7.5 percent, the estimate for C implies negative marginal adjustment costs. The explanation is probably that the estimated value of the constant term, subsumes also the approximation errors made in deriving eq. (11). One reason for the large estimate of 4 (and the low one for E) may also be that the stock market value is not a good proxy for market fundamentals because of the presence of fads or bubbles. What conclusions can be derived from our results concerning the way in which investment is financed? When the models are estimated in their most unrestricted form the equations under new equity financing have a greater explanatory power. Using the assumption y= 1 after 1973, the standard error of the regression is approximately 9 percent lower for new equity as opposed to retention financing. The results are basically identical if y is allowed to be greater than one after 1973.” To calculate y we have used here the weighted 13For instance, the input-output tables yield a tigure of 41 percent in 1954 and 38 percent in 1973. “The estimate of the mark-up by Hall (1986a. b) for the manufacturing sector in the United States suggests an average elasticity of demand of 6-7 when an adjustment is made for materials, and 3 where no adjustment is used. 15The results also do not change when we try to take into account the fact that from the midseventies onward a large fraction of U.K. companies have been tax exhausted and therefore have been unable to enjoy all the tax beneftts associated with initial allowance, depreciation allowances and the like. As an ad hoc way to capture for the decreased value of tax incentives we have multiplied the corporate tax rate T (and therefore A and n) by the percentage of tirms that were not fully tax exhausted. To take into account the eflect of tax-exhaustion on y and therefore on the choice of Anancial policy, for the period after 1973 we have taken a weighted average of the value of Q, JI and X for fully tax paying companies (for which y> 1) and for tax exhausted companies. The estimated equations have the same qualitative characteristics as the ones obtained for full tax paying companies but their explanatory power is slightly reduced. The conclusion concerning alternative sources of tinance remains also unchanged.
F. Schianrarelli and D. Georgoutsos, Monopolistic
competition and the Q theory of incestmenl 1075
averages for the marginal personal tax rate, m, and the estimates of the effective rate of capital taxation, I, provided in Poterba and Summers (1983). It has been argued, King (1986), that if the debt choice is endogenized and if the personal tax parameters are allowed to vary across investors, in the regime where retentions are used, (1 -m)/( l-z) must equal 1 -r (Miller equilibrium). If (1 -m)/( 1 - z) is replaced by 1 -T the estimated equation still has a lower explanatory power than the one for new share financing. The standard error of the equation under new equity financing is 17 percent lower compared to this version of the model based on retention financing. As a way to assess more formally the adequacy of the different assumptions about the sources of finance, we have performed a set of non-nested tests using the equations with I/K as a dependent variable, using the encompassing methodology suggested in Godfrey (1983) and Mizon and Richard (1986). The results suggest that the data are not informative enough about firms’ financial policies. Neither new equity nor retention financing can be rejected when each one of them is, in turn, used as the maintained hypothesis. For instance, setting y= 1 after 1973, when new equity financing is used as the null, the x2 test with four degrees of freedom on the joint significance of the variables that would appear under retention financing is 7.13. When the null and the alternative are interchanged the test statistic has value of 6.43. Both of them are below the critical level at the 5 percent significance level. When the equality between (1 -m)/(l -2) and 1 -r that holds in the Miller equilibrium is taken into account, again neither the model under equity financing (x:=6.4) nor the one under retention financing (1: = 5.52) can be rejected. This conclusion differs from the one reached by Poterba and Summers (1983) who cannot reject new equity financing in favour of the alternative. Retention financing can instead be rejected when the null and alternative hypothesis are interchanged. Dinenis (1985a) has reached the same conclusion as Poterba and Summers for the manufacturing sector but cannot discriminate between new share issues and retentions for the nonmanufacturing sector. One should treat all these results obtained from aggregate data, including ours, with caution since different firms may be on different financial margins. In this case the investment equation would be a weighted average of the specification for new equity and retention financing, with weights that are likely to change over time. 4. Conclusions In this paper we have discussed the implications for Q models of investment derived from the assumption of monopolistic competition in the product market. We have argued that the structural investment equation that can be derived in this case has a richer dynamic structure and provides a sound justification for the inclusion of output as an explanatory variable.
1076
F.
Schianrarelli
and D. Georgoutsos,
Monopolistic
competition
and rhe Q theory
of
inrestmenr
The empirical results are quite encouraging and lend some support to the investment model based on monopolistic competition developed in this paper. The equation has a rich dynamic structure and output variable is significant as the theory suggests. The equations have a high explanatory power and the diagnostic tests suggest that there are no obvious forms of miss~ci~cation. All the relevant variables have the sign suggested by the theory and most, but not all, of the restrictions implied by the theoretical model are not rejected. The estimated value of the demand elasticity is rather low and there are problems concerning the adjustment cost parameters. However fruitful, the introduction of imperfect competition in Q models of investment leaves still problems open and it is certainly not the only way to improve their empirical performance. Two interesting directions of research that can be pursued in this respect include the derivation of Q type investment models when labour is also a fixed factor, and a more satisfactory treatment of ~nan~ng decisions especialiy when there are im~~ections in the capital markets. The integration of these extensions with the assumption of monopolistic competition will be the subject of future research. Data appendix ratio of gross investment to the net capital stock. Source: Poterba and Summers (1983) (PS). marginal personal tax rate. Source: PS. elective amount of dividends received bv shareholders when the firm distributes one pound. Source: PS. effective tax rate on capital gains. Source: PS. present value of depreciation allowances on new investment. Source: PS. corporate tax rate. Source: up to 1975. King (1977); from 1976, Inland Revenue Statistics. present value of depreciation allowance on past investment. Source: P.S. book value of stocks and work in progress. Sourre: PS.
U/W,: m,: 0,: 2,:
n,: T,:
A,: INK:
K-A,
P:(l-b)K,_,+INV,_,:valuation Pi: P*: 3,: I<,:
Tw,,I..,,I,):
if:
ratio. Source: PS. gross Rxed investment price index. Source: Economic Trends (ET). gross domestic product price index. Source: ET. market value of debt = market value of debentures plus loan stock plus stock of bank advances. Unpublish~ Series. the net value of the capital stock at replacement cost. Source: PS. value added output for industrial and commercial companies. This series is taken for the period 1969-1980 from the Blue Book (BB). For the period 1950-1968 we have used a backward extrapolation based on the value added figure for industrial. commercial and financial companies (BB). interest rate on debentures. Source: Annual Abstract of Statistics.
References Abel, A., 1980. Empirical investment equations: An integrative framework, in: K. Brunner and A.
F. Schiantarelli and D. Georgoursos, Monopolistic comperition and the Q theory o/inrestment
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aA
the Q theory of investment
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