# A Quick Overview of the “q Theory” of Investment

Tobin’s q is defined as the ratio of market value to replacement value for a firm’s capital.

The market value in the numerator reflects the profitability to the firm of one additional unit of capital.  The replacement cost in the denominator can be thought of either as the cost of acquiring new capital or the price earned by selling existing capital.

If q>1, then the additional profit a firm could expect from one more unit of capital (equipment, buildings, etc) is greater than its replacement/acquisition cost.  The firm should increase its capital stock.

If q<1, then the additional profit would be less than the acquisition cost.  We assume diminishing marginal productivity of capital, so this also means that the last unit of capital the firm acquired is producing less for the firm than its market value.  The firm should reduce its capital stock (sell equipment, etc).

In both cases, diminishing marginal utility means q should tend toward 1.  If q>1 and a firm acquires more capital, average productivity will decrease until the market value of the next machine will equal the acquisition costs.  Firms are indifferent to paying \$1 for \$1 worth of equipment.  If q<1 and the firm sells capital, average productivity will rise until the market value of the remaining capital equals the replacement/sales price.  Firms are also indifferent to selling \$1 worth of equipment for \$1.

In q theory, a firm acts to maximize the present value of its after-tax net receipts.  A firm’s investment level is a function of its marginal q.  For the specifics of the theoretical model, and for the explicit relationship between marginal q and average q, see “Tobin’s Marginal q and Average q:  A Neoclassical Interpretation,” (Hayashi 1982).

Marginal q refers to the market-value-to-replacement-cost ratio of the next unit acquired.  This cannot actually be observed.  What can be observed is the firm’s average q, or the ratio of market value to acquisition cost for the firm’s entire existing capital stock.

# Enjoying the Quiet Life? –commentary

This paper uses a clever check for reverse causality.  The authors find that for firms whose incorporating state adopts anti-takeover laws in the preceding twelve months, wages rise and productivity falls.  The reverse causality story is that rising wages (perhaps due to union pressure) and falling productivity threaten firms in a certain state, and therefore make that state more likely to enact anti-takeover laws.  The authors’ story depends on causality in the right direction.

The paper’s main tests use a binary variable BC to indicate whether a firm’s incorporating state enacted anti-takeover laws in the prior 12 months.  The coefficients on BC in the several regressions are the paper’s main findings.

In the reverse-causality check, the authors replace BC with four dummy variables:

• Before-1 for firms incorporated in states that had not yet passed legislation but would do so in the next 12 months
• Before0 for firms incorporated in states that had passed legislation in the prior 12 months
• After 1 for firms incorporated in states that had passed legislation between 12 and 24 months prior
• After2+ for firms incorporated in states that had passed legislation two or more years previously

Significant coefficients on Before-1 would have suggested that legislation was passed in response to an already-changing business environment.

Before0 was the variable of primary interest.

Small and Insignificant coefficients on After 1 and After2+ would have suggested that the effects of legislation were short-lived and therefore economically much less interesting.

In this case, the coefficients on Before-1 were small and statistically insignificant, ruling out the reverse causality.  The coefficients on After 1 and After2+ were significant and even larger than the coefficients on Before0, strengthening support for the authors’ story since their reported effects of anti-takeover laws continued to grow in the longer term.