ABSORPTIVE CAPACITY IN HIGH-TECHNOLOGY MARKETS: THE COMPETITIVE ADVANTAGE OF THE HAVES TECHNICAL APPENDIX. Controlling for Truncation Bias in the Prior Stock of Innovation (INNOVSTOCK): As discussed in the paper, we measure the innovation stock of a firm using cation-weighted patent counts. Formally, k t INNVSTOCK k δ t-k TECH_INNV k. Since our data only goes up to 998, patents issued in or near that year would not have all their cations captured, causing a truncation bias. We now discuss how we explicly control for such potential biases while calculating TECH_INNV. We considered all patents issued in 985, and looked at the pattern of their cations through 994. We make the assumption that all the cations a patent is likely to get fall whin 0 years of the issue date. To put this in perspective, past lerature suggests that a five year period is likely to capture all possible cations, especially for new technologies in this industry (Dutta and Weiss, 997). Our sample of 0 years is thus extremely conservative. By looking at the pattern, we know, for example, what percentage of the total cations to a patent would occur whin three years of issue. Suppose this number is 40% (i.e., 0.4). We use the inverse of this number as the appropriate weight. To make this clear, consider a patent issued in 996. Our sample captures cations for this patent for a period of three years (996-98). Hence, we weight the number of cations this patent has received by.5 (/0.4). This gives us the number of cations this patent could be expected to receive, if we had data for 0 years. We construct similar weights for each of the years, and weight every patent accordingly.. Estimating R&D and Marketing Capabilies We estimate both R&D and marketing capabilies using a technique identical to that for estimating AC, i.e., the Stochastic Frontier Estimation. In what follows, we fill in some details on the estimation, and then discuss the specifics of the variables used for marketing and R&D. Some of the exposion here overlaps that in the text, and is provided for completeness.. Details of Stochastic Frontier Estimation Consider the frontier transformation function (, α) (, α) Y f Y ε η f Y e, (TA.)
where Y denotes the appropriate function of the output for the h sample firm, i,,, N, in the tth time period, t,,, T; X is the vector of appropriate functions of inputs/resources associated wh the h sample firm in the tth time period; and α is the vector of the coefficients for the associated independent variables in the transformation function impacting innovative output. Thus, f ( Y,α) represents the deterministic component of the efficient frontier and represents the maximum expected output given that firm i employs X level of resources efficiently. Let ε represent the purely stochastic error component (random shocks) impacting output, assumed to be independent and identically distributed as N ( 0, ε ). Further, let η represent the inefficiency error component in the transformation process adversely affecting the output, assumed to be an independent and identically distributed non-negative random variable, defined by the truncation (at zero) of the N ( μ, η ) distribution wh mode μ > 0. We further assume that the random shock, ε, and the inefficiency error, η, are independent, i.e., E[ ε η ] 0, and that these error components are independently distributed of the independent variables in the model, i.e., E ' [ X ε ] E[ X ] and ' η 0. Given the above assumptions, the distributions of ε and η are as follows: ( ) ε ( η ) ε exp π ε ε [ Φ( μ )], for ε [ ] η μ exp π η η η 0 else where Φ (.) is the standard normal distribution function. for η [ ], (TA.) 0, (TA.3) The distribution of the compose error term, e ε η, therefore is given by (Stevenson, 980) ( ) g e e η ε Φ η ε ε η ε η η ε μ where (). denotes the standard normal densy function. e μ μ Φ, (TA.4) η ε ε Given a sample of N firms wh T observations for each firm, the sample likelihood function the Stochastic Frontier formulation corresponding to the maximization problem (equation TA.) is given by
[ Y f ( X,α)] N T L η ε μ Φ i t η ε ε η ε η η ε ( ) Y f X,α μ μ Φ. (TA.5) η ε ε The parameters of interest can be estimated by maximizing this sample likelihood function. Let α denote the consistent estimate of the model parameters, α, obtained by maximizing the sample likelihood function, equation (TA.5). Then, the realized value of the compose error term, e Y Y i.e., the difference between the observed output,, for firm i in period t is given by Y, and the predicted output, Y f ( X, ) α. Given the predicted value of the compose error term, e, the econometric task is to obtain a consistent estimate of the realized value of the inefficiency term, η. Battese and Coelli (988) show that the condional distribution of η, given e e, is defined by the truncation (at zero) of the normal distribution wh mean μ [ μ ε ηe ][ η ε] and variance [ ] η ε η ε A consistent estimate of the inefficiency for firm i in period t is given by. where μ η E[ η e e ] μ Φ, (TA.6) μ ˆ μ i ε ˆ i e ε μ η i η T i Ti and, η ε ε T i η Wh the above in hand, the estimate of capabily would be given as: Capabily. ( η ) (TA.7) We now turn to the specific details of the estimation of marketing and R&D capabilies. In each case we specify the inputs used and the estimation equation, skipping estimation details which have been covered above.. Note that while the random shock, ε, can take any posive or negative value, the inefficiency error component, η, can only take posive values. It is this difference in their supports of distribution which allows for identification. 3
.. Estimating Marketing Capabily We suggest that the objective of marketing activies is to efficiently deploy the resources available to, to maximize sales. We use two resources in our estimation of marketing capabily, namely, Sales, General and Administrative (SGA) expenses, and Receivables. Following past lerature (Dutta et. al., 999), we suggest that SGA is a proxy for the amount the firm spends on s market research, sales effort, trade expenses, and other related activies. Similarly, receivables is a proxy for the firm s resources devoted to building customer relationships, and is defined as claims against others collectible in cash. Formally, using a Cobb-Douglas production formulation, the sales frontier (i.e., the transformation function from marketing resources to output can be specified as: ( ) ( ) ln( SALES ) β0 β ln SGA β ln RECEIVABLES ε η (TA. 8).3 Estimating R&D Capabily We suggest that the objective of R&D activies is to maximize the production of innovative technologies (Dutta et al.999). The major resources that the firm has at s disposal to fulfill this objective include s R&D expendure, and the technological knowledge base of the firm. Formally, using a Cobb-Douglas production formulation, the R&D frontier can be specified as: ( ) ( ) ln( TECH _ INNV ) α0 α ln RDEXP α ln TECH _ INNV ε η (TA. 9) Where TECH_INNV represents the cation-weighted output for firm i in year t RDEXP represents the R&D expendure of firm i in year t-, and TECH_INNV -, is year t- s cation-weighted output for firm i. 3. Estimating Operations Capabily The key goal of operations in high-technology markets is to produce at the lowest possible cost whout compromising on product qualy (Hayes, Wheelwright, and Clark, 988). Thus, we adopt cost minimization as the objective for operations activies. The formulation for the minimization problem is slightly different from that for the maximization problem, that was used for estimating R&D and marketing capabilies. We wre the frontier cost function as: (, α) (, α) Y f Y ε η f Y e, (TA.0) where we make the same set of assumptions on the error terms as in Section.. 4
Derivation of the Likelihood Function: Following similar steps to those given in Section., can be shown that given a sample of N firms wh T observations for each firm, the sample likelihood function the SF formulation corresponding to the minimization problem (equation TA.0) is given by L [ Y f ( X,α)] μ ( ) Y f X,α μ μ Φ. (TA.) η ε ε N T ε η Φ i t η ε η η ε ε η ε 3. Specification of Operations Capabily As suggested above, we adopt cost minimization as the goal of operations activies. Consistent wh economic theory (Silberberg, 990), the exogenous variables in the cost function are output volume and factor prices, i.e., cost of capal and un labor cost. ( ) ( ) ( ) ( ) ln COST α α ln OUTPUT α ln LABCOST α ln CAPCOST η ε 0 3 (TA. ) where: COST is defined as all costs directly allocated by the company to production, such as material and overhead, and is a proxy for the average cost of production, for firm i in year t OUTPUT is the dollar amount of production for firm i in year t LABCOST is defined as the cost of employees wages and benefs allocated to continuing operations, divided by the total number of employees, for firm i in year t CAPCOST is the long-term cost of capal, and represents the average interest rate for long-term borrowings for for firm i in year t. 5