290 F
. Verschueren Economics Letters 69 2000 289 –297
exercise between investment, output, Tobin’s q and debt using United Kingdom data. An argument for this lack of interest is that theory of optimal stock of capital gathers variables with flow and with
stock profiles. Recognizing that investment has a rather volatile profile with respect to smoother economic variables, the search for balanced specifications in a time-series point of view is hence
made more difficult. The direction proposed in the paper is based on co-integration inference in a present value model linking the value and the profit of the firm when these two variables are
integrated of order 1, or I1. The main result is that acceptance of stable long-run residuals
i.e. co-integration hypothesis
in our specifications, which are constructed from a neoclassical model with convex adjustment costs
, implies that the factors are chosen optimally with respect to the economic model. The paper is organised as follows. Section 2 gives details on the economic model. The general
framework involving the co-integration hypothesis, and from which are deduced long run relations and investment specifications, is set up in Section 3. Empirical results with OECD data are presented
in Section 4 and Section 5 summarizes the paper.
2. The economic model
In a neoclassical behaviour with adjustment costs, the value of the firm is defined as the maximum of the discounted sum of current and expected future flows of profits
` i
V 5max
O
b E P 1
f g
t t
t 1i I,L,K i50
21
with V the value, P the profit and b the discount factor, b 5 1 1 r , r the interest rate assumed to
t t
be constant, and E . the expectation of . based on information available at time t.
f g f g
t
The profit variable has the usual definition P 5 p Y 2 w L 2 I 2 G
2
t t
t t
t t
t
Y is the output from the production function FK , L ; K is the end-period capital stock and L the
t t 21
t t
t
labour force; I is the amount of investment; p and w are the price of output and the wage cost
t t
t I
respectively, both expressed in terms of p the price of investment; GK , I is the adjustment
t t 21
t
function reflecting the costs of installing new capital goods. The installation technology is a convex function in I the more is invested, the more the associated costs and is inversely related to current
t
capital stock scale effects. Both production and adjustment technologies are assumed to be homogeneous of degree 1 in respective arguments. The dynamic constraint on K is
t
K 2 K 5 I 2
dK 3
t t 21
t t 21
To solve the optimization problem 1 with 2 and 3, the current-value Hamiltonian is constructed as H[
l ] 5 p Y 2 w L 2 I 2 G 1 l I 2 dK so that the necessary first-order conditions for a
h j
t t
t t
t t
t t
t t 21
maximum are given by ≠G
t
]] H 5 2
2 1 1 l 5 0
4
I t
≠I
t
F . Verschueren Economics Letters 69 2000 289 –297
291
≠Y
t
] H 5 p
2 w 5 0 5
L t
t
≠L
t
≠Y
t
]] l 2 l
5 r l
2 p 2
dl 6
H J
t t 21
t 21 t
t
≠K
t 21
with the transversality condition
i
lim b l K 5 0
7
t t
t →
`
3. The empirical specifications
