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Appendix-I

Link to Appendix II

Appendix – I Timing Actual Investments in IT The statistical study of duration models, also called survival analysis, has become a methodology used by numerous researchers from different fields. These models are useful in situations where the timing of a certain event is important in the investigation. Although their initial applications were in the fields of medicine and engineering, more recently, they have also been used in economic research. Let T be the time of survival, measured as the period in years between the time when firm announces its intensions of substantial investment in IT, and the time when the actual investment take place. This survival time is considered to be a random variable where f (t) denotes the density function of T, and let the distribution function be

The probability that actual investment is not made in the interval (0, t), will be given by the survivor function

The hazard function h (t) is defined as

indicates the probability that the investments take place in (t, Dt). Therefore, h (t) denotes the instantaneous rate of investment at time t, given that the firm has not made previous investments.

Within survival analysis, proportional hazard models have the property that the individuals in the sample present hazard functions that are proportional. Therefore, the hazard function of T given x can be written as:

Since the ratio h (t / x1) / h (t / x2) of two individuals x1 and x2 will not depend on t. The introduction of regression models allows, when a heterogeneous population is considered, to include the relationship of the survival time with other factors. In these models, a dependent relationship with the covariates is explicitly admitted through a distribution function of the survival time that depends on them. Here we have used the Cox proportional hazard model. This approach has the advantage that does not make any assumption about the function h (t), with little cost in terms of efficiency (Lawless, 1982). Let be Xi = (x1, x2, ...., xi) a representative vector of the specific advantages of firm i. Under the proportional hazard assumptions, the hazard function of T, given x is of the form

where, b f?(b1 ,b2 , b3 , .. .. ,bn ) is a vector of unknown parameters. Under the Cox proportional hazard model, the hazard function of T is:

Let two firms are deciding to invest in major IT project. There is some benefit to having IT system installed; but the exact size of the benefit is uncertain. Sunk costs are incurred in setting up the system: skilled labor is required to specify, design, implement and train and similarly other expenditures are incurred. An increasingly important reason to pre-empt is the ability of first-movers to install system before anybody else. A first-mover advantage may also arise because the firm that acts first may face lower staff costs implementing staff being relatively abundant than later firms who have to hire when trained labor is scarcer. Finally, negative externalities arise through competition; positive externalities can also occur since a firm setting up IT system benefits from the efforts of other firms, both directly and indirectly.

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The models presented in appendix are adapted from other papers. These models indicate applicability of investment decision framework under uncertainty for the IT investments.   This framework in appendix-I is adapted from the paper ‘The timing of foreign direct investment under uncertainty: Evidence from the Spanish banking sector’ by Josep García Blandón. The framework in appendix-II is adapted from the paper ‘The Value Of Waiting In Lawmaking’ by Francesco Parisi and Nita Ghei, April 4, 2001, George Mason University.