Endogenous savings rate with forward-looking households in a recursive dynamic CGE model: application to South Africa

In the vast majority of recursive dynamic CGE models, the savings rate is constant and exogenous. Intertemporal CGE models, by contrast, are solved simultaneously for all periods, and agents optimize intertemporally. But the theoretical consistency of intertemporal optimization is achieved only at the cost of more aggregated, less detailed models, due to computational limitations. In some applications, therefore, recursive dynamics should be preferred to intertemporal dynamics for practical reasons of computability. This paper presents a recursive dynamic CGE model in which households determine their savings rate from intertemporal optimization, by solving a simplified form of their intertemporal problem. This approach we call « truncated rational expectations » (TRE). In the TRE framework, households have rational expectations for the current period and the following one. Accordingly, the model is solved simultaneously for two periods at a time, the current period τ and the following one. Household (rational) expectations for period τ +1 are given by the model solution. For subsequent periods, household expectations are formed by extrapolating from τ and τ +1 solution values, assuming a constant rate of change. The TRE framework is implemented in a modified version of the Decaluwé et al. (2013) PEP-1-t model, and applied to South Africa, using a 2005 SAM by Davies and Thurlow (2011). Several simulations are run, with two variants of the 2005 SAM, the original one and a modified one with a high initial household savings rate. The results are compared with those of a static expectations model with intertemporal optimization, and of a fixed-savings rate model. The main difference is that in the first two models, the household savings rate is not constant, even in the BAU scenario. It is also responsive to changes in the rate of return on assets. On the other hand, an exogenous reduction in household wealth has very little effect.
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