In this paper we study a stochastic growth model with lags in the operation of new technologies. Technological innovations arrive exogenously to the economy and impact stocks through their option values. These innovations, however, cannot be readily implemented and undergo a process of adoption that involves the production of new varieties of intermediate goods. Our model is a simplified variant of those in Romer (1990) and Comin and Gertler (2006), but our objectives are quite different. Romer (1990) is concerned with innovations and economic growth and Comin and Gertler (2006) with a quantitative analysis of eco-nomic fluctuations. Our main goal is to build a quantitative framework in order to explore the possible channels of influence that technological innovations have on stock prices. As is commonly realized, financial markets can respond to various types of shocks and new information. Besides the high-frequency volatility that is deeply rooted in stock prices, the US stock market displays protracted episodes of high growth intertwined with shorter spells of price decreases and much lower returns. Jovanovic and Rousseau (2001) associate these long fluctuations in the stock market with three technological revolutions: Electricity, World War II, and IT. These authors document long lags in the operation and diffusion of new technologies. There are, however, plenty of other explanations for the long swings in stock values. Geanakoplos, Magill and Quinzii (2004) contend that these changes are driven by demographic trends, whilst Lustig and Nieuwerburgh (2006) cite credit access from home equity collateral. Our model is also intended to explain the overall evolution of the US stock market.
In contrast, several recent works have focused on the collapse of stocks in the 70s and subsequent periods of recovery. A large body of research [Greenwood and Jovanovic (2001), Hobijn and Jovanovic (2001), Laitner and Stolyarov (2003) and Peralta–Alva (2006)] elaborates on the effects of IT on the values of old and new companies. Mcgrattan and Prescott (2005) attribute fluctuations in stock values to changes in the tax system, whilst Hall (2001) attributes them to intangible investments. We will delve into this literature in Section 2 after discussing some empirical evidence. Of course, it will be instructive to check how these explanations for the behavior of stocks in the 70s may fare in some other time periods. An important consideration in our model is that asset prices incorporate the option value of technological innovations that have yet to be implemented. Hence, the value of a firm may differ from the book value of its durable factors of production.
This disconnection of the stock price from the replacement cost of capital is attained in our model without resorting to commonly used frictions such as borrowing constraints, irreversibility of investment, and adjustment costs. The arrival of new technologies creates new possibilities for existing and potential firms –even though these technologies cannot yet be used. Then, there is a process of wealth creation in which local adopters produce extra varieties of intermediate goods embodying the new technologies. Hence, in our model a long swing in the stock market occurs after a lasting process of technology adoption. This propagation mechanism is likewise present in the partial equilibrium setting of Abel and Eberly (2005), and in the tree economy of Panageas and Yu (2006). None of these papers incorporates explicitly an aggregate production sector.
At a later stage we report some quantitative exercises. The model is solved numerically by a high-order approximation method that picks non-linearities in the evolution of stock values. We assign parameter values which allow the model to fit some basic facts in economic growth and business fluctuations. Most of the discussion will center on those parameters defining the processes of arrival and adoption of new technologies. These parameters are calibrated to replicate the volatility of trademarks registered. Then we perform several numerical exercises to see how technological innovations may affect the dynamics of stock prices and other aggregate variables. The model can account for long-term fluctuations in stock prices although it does not display the short-run volatility firmly established in the data. Hence, technological innovations seem a plausible explanation for long moves in stocks, but other types of factors (i.e., monetary and fiscal policies, international trade, etc.) seem necessary to generate their observed short-term volatility.
The paper will proceed as follows. In Section 2 we gather some facts on the stock market and related macro aggregates. This evidence is the starting point of our analysis, and it becomes handy for a a brief discussion of related contributions. In Section 3 we lay out our model of technology adoption and derive some qualitative properties of the solution with emphasis on a fundamental asset pricing equation that considers the change in the stock price brought about by a technological innovation. Section 4 is devoted to the computation and calibration of the model, and Section 5 reports various numerical experiments. We conclude in Section 6 with a further evaluation of our results.
