Hall 1999 (The stock market and capital accumulation.)
In this paper Hall seeks to quantify the price and stock of capital in the economy from 1960 to 2000 using data from the stock market.
To do this he proposes the following simple model.
- Discrete time, infinite horizon
- Constant returns to scale production
- All produciton inputs except capital adjust frictionlessly
- Adjustment to capital stock can be fully adjusted in the long run (no long run rents)
- Factor markets are competitive
In this setting firm profits is equal to capital times the product of capital, where the product of capital depends on non-capital production inputs.
Each period the firm pays out profits, less capital investment and adjustment costs to shareholders as dividends.
The value of the firm is the present discounted value of all dividend payments
Capital stock depreciates at a constant rate each period.
A firm’s problem is to choose a sequence of investment levels to maximize the present discounted value of all shareholder payouts, subject to capital stock depreciation and quadratic adjustment costs. The Lagrange multiplier on the time t capital accumulation equation is the shadow price of capital.
Under the assumptions in the model, the following is true:
Security (stock) price of firm = value of firm = PDV of future dividends = shadow value (price) of firm’s capital times stock of capital
The last part of that equivalence chain is the most surprising, but most useful in this context.
Hall uses this condition as well as the first order condition for firm investment as two equations in terms of time t-1 capital stock and time t security price in order to solve for the two unknowns: time t capital stock and time t shadow price. Thus, if Hall makes an assumption about the initial level of the capital stock and data on stock prices, he can use his mini-theory to trace out time series of capital stock and price.
Using the Flow of Funds Accounts data set from the Fed Board, he follows exactly this procedure. The data contain balance sheet information for all non-farm and non-financial US corporations.
His main findings
- Application of a simple empirical test that the security price of a firm represents the present value of future payouts to shareholders seems to hold across his dataset. He summarizes his findings by saying “I see nothing in the data that demonstrates a systematic failure of the standard valuation principle – that the value of the stock market is the present value of future cash payouts to shareholders”
- Results for the quantity and price of capital were dependent on the quadratic adjustment cost parameter. He took a lower and upper bound of values for this parameter from the related literature.
- For low adjustment costs, prices remained fairly constant over the whole sample, but the quantity rose steadily – especially after 1980.
- For high Over the time horizon, the quantity increased smoothly across the whole sample and most of the variation in the value of the capital stock came from movements in the shadow price.
- The stock of capital implied by the low and high adjustment cost parameterizations forms a fairly uniform band around the value of capital inferred from data on capital investment.
- Tobin’s q (ratio of value of a firm to the reproduction cost of its plant and equipment rose sharply from 1980 to 2000 (From 0.5 to approximately 3.5). Under the hypothesis that the securities markets reveal the value of the firm, this could happen if there were large persistent movements of the price of installed capital, or if the firm accumulated significant quantities of intangible capital.
- Earlier evidence refutes the idea that there were large movements in the price of capital, making the story of firms accumulating intangible capital more likely.
Hall’s main takeaway is that under the expectations of rational securities markets, the evidence he uncovered on prices and stocks of physical capital point to a large increase of intangible capital that added value to firms.