Investment functions in Computable General Equilibrium models - Theory, Practice and Illustrations

Abstract

Already in the first versions of the general equilibrium models, both in terms of static and in terms of long-term equilibrium, arose the problem of the 'macroeconomic closure' and, in particular, the question of how to determine the investments.

In one of our earlier articles, published in Acta Oeconomica (Zalai-Revesz [2016]), we have reviewed various options to introduce investment functions into a CGE-model. However, the discussed CGE-models (one and five-sectors models, closed and open economy) were all ,,static", or better to say ,,timeless" (Cassel) in a sense that they described the main criteria of assumed long run equilibrium without specifying the industry-specific investment behaviour consistent with these criteria.

But in models of dynamic and incomplete equilibrium pathways the determination of investments by investing sectors presents almost insurmountable problems of theory, consistency and quantification, especially the difficulty of keeping the model's dynamic behaviour within acceptable limits.

Obviously, it is hard to construct a general investment function, since the circumstances and the investors' behaviour are rather different in the various branches of production and services. For example, investment into housing, agricultural, mining, health-care, defence sectors or in infrastructure or in environmental protection have characteristically different motives, legal constraints and technical circumstances, nothing to say about their different accounting methods in the national accounts or, in general, in the macrostatistics.

However, in CGE-models - which are not supposed to be highly detailed and accurate or capable to give perfect predictions - there are various mathematical methods, abstractions to group these circumstances and represent them by relatively simple formulas. By doing this they will provide insights into the underlying rationale of investment behaviour and may show the synergies of changes in the investment decision, which influence the factors and the characteristically different effects of different investment 'climates' and policies.

Accordingly, in section 2, we review the basic theoretical and modelling issues of investment behaviour, its various motives which could be found in the literature. In particular, I discuss the role of profit maximisation, profitability, demand, retained earning, interest rate, taxes and investment subsidies, which may be incorporated in a dynamic CGE-model, but to a minor extent, I consider the role of other factors too.

As the investment decision is a choice between alternatives with different expected returns (yields), I examine what indicator may represent these investment returns in an aggregate, synthetic way, and in which function this indicator can serve as an argument.

I devote especially much attention to the question of the possible use of the interest rate and profitability dependent investment behaviour. In particular, I try to find out, that from theoretical and practical point of view, what reference category can be the best to use in the investment behaviour function. I consider the most straightforward candidates, i.e. the average rate of return on capital, the benchmark profitability of the given branch and various definitions of the rental price/users cost of the capital.

A secondary issue related to this is the question whether one should compute ratios (so that the ratio of the profitability to this reference category is computed and used as an explanatory variable) or use a function in which the profitability and the reference category are separated. In the case of an isoelastic investment function, the problem boils down to determine the elasticity of each explanatory variable. The simulation results will of course depend to a large extent on the assumed value of the elasticities.

In section 3, I illustrate the sectorial investment functions developed so far in CGE models by presenting the investment function of the recursive dynamic GEM-E3 model. The GEM-E3 model has been developed by the National Technical University of Athens and is widely used by the European Commission to make climate policy simulations. This model is chosen because it uses the same type of investment function for each sectors but with different parameter values across sectors. After presenting and discussing the main features of this function, various recommendations are given about how to improve the GEM-E3 model's investment functions by modifying the present functional form and by introducing additional explanatory variables.

In the last section, I present the properties of the proposed and possible investment functions embedded in a multi-period CGE model calibrated for the Hungarian economy. This dynamic CGE-model was calibrated for 2010 and simulations were carried through up to 2020. I present the assumptions and results of simulations run with this dynamic CGE-model.

The simulation results confirmed that if we find a reasonable investment function, which reacts sufficiently (but does not overreact) to the capital price, the interest rate and the indebtedness, then we can be sure that the trajectory of the capital stock will move cyclically around gravitating to its equilibrium level.

The danger of overreacting to changes in the rate of return is especially pronounced when one assumes that capital is immobile across sectors, i.e. assumes branch specific capital stocks, which are inherited from the previous time periods. As a result, the rate of return on capital will, as a rule, fluctuate, especially wildly in the first periods. The model will therefore generate a time path of capital accumulation, which is difficult to justify.

However, -- as I demonstrated by simulations with my model -- by choosing a modest value for the rate of return elasticity and introducing flexible constraints like indebtedness effects into the investment function these too high fluctuations can be prevented and the trajectory of investment becomes plausible.

Finally I pointed out that government investment and government subsidy dependent investment including/and housing investment has to be formulated separately and that differentiating the parameters of the investment behaviour across sectors and countries may be essential (especially in a world model like the GEM-E3) if we wish to provide empirical relevance to our model and its simulation results.

In summary, the evaluation of the detailed results, while highlighting the positive effects of the developed investment functions in many sectors, also highlights the value of combining ("integrating") this method/specification with the various error correction and smoothing methods developed in the GEM-E3 model.