Accusations of politicians excessively favouring short term spending over investment are frequent. Unfortunately, this is a near-inevitable feature of any system of government with regular elections, as politicians will optimise for probability of re-election rather than long-run incomes. However, the extent to which this is an issue likely depends on the time horizons of the politicians themselves, as this issue would be severe under 1-day terms and irrelevant under 1000 year terms - but how important is it under the range of term lengths democracies currently use? This blog post aims to answer that question.
In 1956 Robert Solow and Trevor Swan independently developed a simple model of economic growth that takes into account the level of capital, labour and technology in an economy. Using a production function with constant returns to scale (doubling every input would double total output), diminishing marginal returns (positive first derivative but negative second derivative for all positive values of inputs) and capital depreciation, they showed that the optimal savings rate in an economy is the capital elasticity of output.
This blog post assumes that politicians are aiming to maximise income at the time of the subsequent election. This assumption could be reasonable if the public was unaware of the general level of investment spending and merely knew, and voted according to, the state of their own finances: given that public knowledge of the distribution of government spending is sufficiently dire that median estimates for some areas are wrong by over an order of magnitude , this appears robust empirically. This model does require voter irrationality in the economic sense to reconcile with the numbers of voters observed, but is consistent with a model where voters feel a limited sense of civic duty to vote but not one large enough to spend the necessary time parsing the national accounts. Politicians have control over more than just the proportion of government spending invested in achieving the end of maximising post-election income however, as they can uses taxes or subsidies to set economy-wide saving at any level that they wish.
The Solow Model has two key parameters for our purposes here, as population and technological growth will be assumed to be independent of population for the purposes of this model. These are the capital elasticity of output alpha and the capital depreciation rate delta: the higher both are the higher the optimal rate of investment according to politician time horizons, as a higher alpha raises the theoretically optimal investment rate and a higher delta means that the costs of underinvesting will manifest sooner. Alpha is equal to the capital share of income, so is roughly 0.4, while delta has been around 4.6% historically.
As can be seen above, the differences in income from moving between different term regimes appear substantial, with the the no investment that occurs under terms less than about 2 years causing incomes to fall below 5% of their potential level in one hundred years time. The more relevant result for most democracies is that moving from the 5 year terms common today to the 7 year terms more common historically would boost real incomes by 19.4%, going from 61.2% of potential to 73.1% of potential, over a timeframe of 100 years, implying that over long timescales the costs may be very substantial of using shorter term lengths.
There may however be reasons to be cautious of declaring results as large as the above estimates. Politicians may not be free to set investment rates under some circumstances due to the risk of being ousted midway through their terms. Additionally, politicians may already set investment rates higher than the above figures in some elections if they see themselves as potentially in power to fight the subsequent election as well, an effect which will be larger under shorter than longer term lengths. Finally, the idea of optimizing investment rates as such assumes politicians are rational agents setting the capital levels as social planners in a planned economy, but politicians in modern democracies may have neither the political capital nor the knowledge of economic theory to vary investment rates as would benefit them most.
Additionally, as one of the principal reasons for democracy is to allow the bloodless ejection of poorly performing leaders, increasing term lengths would come at a cost in accountability for leaders who are substantially worse in government than predicted, resulting in low-ability leaders remaining in post for longer. The size of this cost is essential for determining optimal term lengths, and will be explored in a future post.