[2]Specifically, the production function is assumed to be quasi-concave and monotonic (Varian 1992). Furthermore, specific functional forms, such as the Cobb-Douglas production function, emtail additional restrictions.

[3] It bears pointing out that *total* benefits of IT
spending can still be large even if *marginal* benefits are zero or
negative. In fact, a high marginal rate of return may be a sign of
underinvestment.

[4] When an industry is not perfectly competitive, the area under the derived demand curve will generally underestimate welfare.

[5] In particular, see Berndt (1991) for an excellent discussion of simultaneity in supply-demand systems and Gurbaxani and Mendelson (1990) on the role of technology diffusion.

[6]The pursuit of value need not be zero sum. Some types of competitive tactics, such as raising rivals' costs (Salop and Scheffman 1983), actually lead to a loss of total value, even though these behaviors may be privately beneficial.

[7]This sample size refers to a complete set of productivity variables. The sample size may increase or decrease for some analyses that use different subsets of the variables.

[8]The Cobb-Douglas form is by far the most commonly assumed type of production function. It has the virtues of simplicity and empirical validity, and can be considered a first-order approximation to any other type of production function.

[9] Since this data set is a panel of repeated observations on the same set of firms, it is likely that the error terms for a single firm will be correlated over time. One way to accommodate this feature is to employ ISUR to estimate separate equations for each year and allow the error terms for the same firm in different years to be correlated. Our use of ISUR is confirmed by the estimated correlation structure from the ISUR procedure: adjacent year correlations range from .46 to .76, suggesting a substantial amount of within-firm autocorrelation.

[10] For example, the instruments for the 1992 data points would be the 1991 values of IT Capital, Non-IT Capital and Labor Expenses, along with the sector and time dummy variables.

[11] The rate of return is equal to the elasticity divided by the percentage of IT in Value-Added which is .0355. Therefore, the gross marginal benefit is: .0307/.0355 = 86.5%.

[12] This estimate is derived from the Jorgensonian cost of capital (Christensen and Jorgenson 1969). The cost is a function of the risk free rate, a risk premium, depreciation charges, and capital gains or losses. Following Hall (1993b) we use 6% as the risk free rate and assign a risk premium of 3%. The Bureau of Economic Analysis (1993) assumes computers depreciate over a period of 7 years, or 14% per year. Finally, holders of computer capital face capital losses of approximately 19% per year because the quality-adjusted costs of new computers (and therefore the value of old computers), declines at this rate (Gordon 1987). Accounting for the above factors yields a total cost of capital of 42% per year. However, it should be noted that other factors, such as taxes, the benefits of learning, the options value of investments and unmeasured costs and benefits can also affect the true costs of capital, although they are difficult to quantify.

[13]Also, by including size, this specification can be compared to the IT investment ratio approach. If [[alpha]]1 = -[[alpha]]2, this formula is essentially a correlation between the logarithm of (IT investment/size) and performance.

[14] The above surplus calculation follows the convention of assuming that the net marginal benefit of the input (IT) is zero. However, if we use our production function estimate that IT created an excess return of 44.5% on each additional unit purchased, this amount has to be added in to get total consumer surplus. For 1990, this amounts to an additional $1.7 billion of consumer benefit, bringing the total surplus to $5.8 billion in 1990.

[15] In principle, the dummy variables we included for each industry in the basic performance regressions should have partially controlled for the effect of industry-wide IT spending on profits. However, in practice the effective competitors of the firms in our sample do not map perfectly on to the 2-digit SIC code definitions we used. Furthermore, IT spending changed over time in each industry, while the industry dummy was invariant over time. As a result, to the extent that a firm's IT budget is correlated with its competitors' spending, the coefficient on IT will in part reflect the indirect effects of higher overall industry spending on IT.

[16] Jensen (1993) makes a related argument about how technology-based productivity improvements in the tire industry created massive overcapacity, consolidation and exit from the industry for a number of firms.

[17] By contrast, an R^{2} of 95% or more has been
achieved for both production function analyses and consumer surplus analyses
(e.g. (Brynjolfsson 1993b; Brynjolfsson and Hitt 1993)).

[18] The hypothetical increase in firm return is based on the following rough calculation: increase in value added each year by IT as a fraction of total assets = {IT capital stock ($110 million) * net marginal benefit of IT (54%) }/ total capital ($8,420 million) = .7%. The standard error calculation is as follows: standard error on IT coefficient for model with both risk and market position controls (.00253)* log of average computer capital measured in millions of dollars (log(110) = 1.19%