On the Interplay Between Speculative Bubbles and Productive Investment

In recent years there has been renewed interest in studying the link between productive and purely speculative investments. Questions that naturally emerge are whether speculative investments are good or bad for capital accumulation and production, whether bubbles are compatible with dynamic efficiency, and what role speculative assets actually play. To address these issues, most of the literature assumes that people can invest either in productive capital or in an asset without fundamental value, which is a pure bubble when its price is positive. These two assets provide returns in the same period and are traded in each period, i.e. both assets have the same liquidity.

The purpose of this paper is to examine whether bubbles still exist, and how they affect production, when a differential is introduced into the liquidity of assets. We introduce a speculative asset giving returns in the short run and that can be traded in each period and a productive asset providing returns in the longer run. This distinction implies that the speculative asset is more liquid than the productive one. A clear example of investment with returns in the long term is investment in human capital through education. This investment takes place during youth, implies lifelong returns, and depreciates with death.
The model we examine is an overlapping generations model with three-period lived households. When young, households can borrow through debt and invest in two assets: human capital used in production and providing returns in middle and old age, and an asset without fundamental value, also traded in middle age. This asset is a bubble when it is positively valued. The amount invested is limited by a credit constraint using human capital as collateral. In middle age, agents finance credit and can invest only in the bubble to transfer purchasing power to old age.
In accordance with empirical evidence that bubbles occur in periods of high GDP, we show that bubbles may be productive because they are able to increase production through larger investments in human capital. Considering that the credit constraint is binding at the bubbleless steady state (i.e. without bubbles) and that this steady state is dynamically efficient, we show that the bubbly steady state (i.e. with bubbles) fosters production. This is because the bubble is used to finance productive investment and relax the binding credit constraint. Therefore, our model is also with empirical evidence that credit is higher in periods of expansion and of bubbles.
The mechanism behind all this is based on the interaction between two effects, a crowding-in effect through credit and a crowding-out effect through saving. The first effect is caused by young agents selling the speculative asset short to finance investment in productive human capital. In other words, the agent is selling an asset acquired by borrowing that will be repaid next period. This leads to greater human capital and production than in the credit- constrained bubbleless economy. Selling the speculative asset short can lead to an equilibrium, because middle-aged agents repay the loan and also buy the speculative asset to transfer purchasing power to old age. This is the crowding-out effect, which allows the golden rule to be respected and gives the bubble a positive value. 
Since long-term investment in human capital is a key element of our story, we show that a biased technological shock implying a larger return in the longer term may reduce capital. This happens because the bubble may disappear and, hence, can no longer be used to finance productive investment. Contrastingly, if the technological shock is biased toward short-term returns on capital, or increases both short- and long-term returns on capital in like manner, we observe an increase in capital, production and bubble size. These shocks are typically the result of innovations. Our results thus explain why episodes of bubbles are associated with innovations, as documented in several contributions. 
We further apply our framework to the debate on the design of fiscal policy aimed at promoting long-term investment. This reveals that the most effective fiscal policy crucially depends on the existence and the nature of bubbles.

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