Research Discussion Paper – RDP 32 A Theoretical Intertemporal Choice Model of the Firm


The aim of this paper is to develop a model to explain the time path of labour demand, physical investment, financial investment and borrowing of a competitive firm. The model emphasises the simultaneity and interrelatedness of all the economic decisions of the firm and is essentially dynamic in that it focuses on the intertemporal aspects of these choices.

The model's ancestry lies in the one hand on the work of Jorgenson [4] on corporate investment in physical capital, and on the other on the empirical work on interrelated factor demands such as that of Nadiri and Rosen [8].

Jorgenson's analysis is, however, essentially static in that no attempt is made to derive an optimal path of accumulation of capital over time. Nor is it acknowledged that alternative accumulation paths may affect the long-run optimal stock itself. Rather, partial capital stock adjustment is simply appended to the theory, and is rationalised on the basis of continuously occurring, but nevertheless unforeseen, delivery lags.

This ad-hoc explanation of the adjustment path has been widely criticised. To overcome this objection, Eisner and Strotz [2] presented a theoretical derivation of the optimal path of capital accumulation by specifying that factors which prevent immediate adjustment to the long-run optimum should be taken into account by the firm at the time it is making its investment decisions. These costs of adjustment are specified to be a function of the degree of adjustment (and might also be a function of time).

The Eisner-Strotz model is an optimal-adjustment model in that the constrained path of capital accumulation is determined under optimising conditions. This can be contrasted with the Jorgenson model which is a non-optimal model (in the short run) because it suggests only partial adjustment towards the theoretically derived optimal point. The Eisner-Strotz model demands full adjustment each period to the optimal path.

Although Eisner and Strotz assume that the optimal path approaches a long-run stationary point, Lucas [6], in an extension of their model, shows that this result is derivable from the theory and need not be asserted a priori, as is necessary in the Jorgenson model. Lucas' model, though particular in its assumptions, is powerful in its conclusions. Treadway [17] has presented a more general form of the model with consequently weakened, but interesting, conclusions. Both the Lucas and Treadway models deal with the multivariate input case, and this extension offers strong theoretical underpinning to the empirical work on interrelated factor demands.

The Lucas-Treadway type of model stresses the simultaneity involved in decision making. It may be objected that it is not necessary to use the Lucas-Treadway analysis to model interrelated asset and factor decisions. The Jorgenson model could still be used to derive long-run equilibrium stocks (and flows) and a second stage cost minimisation process could be used to derive the optimum path.

For a number of reasons, the Lucas-Treadway simultaneous decision model seems superior. First, it is possible to specify the economic simultaneities and feedbacks at an earlier stage, and in greater generality. Second, it is intuitively appealing that the model derives the stability of the long-run levels of inputs rather than asserts it a-priori. Third, the precise formulation of the properties of the price and interest rate response matrices, and the determination of the conditions under which various properties hold, is dependent upon adjustment costs being introduced at the earliest decision stage.

The dynamic intertemporal choice models discussed so far all employ the assumption of static price expectations. In the present paper, after deriving the basic model in this tradition, the model is extended to allow for variable prices. This extension is closely based on Tinsley's work [12, 13, 14].

In the basic model all variables are measured net of tax. The assumption is that of Jorgenson that the tax incidence is measured by tax accruals. In a further extension to the model, timing considerations of tax payments are dealt with explicitly.

In analysing both the basic model and these extended versions, the emphasis is on the derivation of econometrically implementable estimating equations.

Section II sets out the basic model. Section III treats the extensions. The Conclusion outlines areas requiring future research.