INTERNATIONAL KNOWLEDGE FLOWS: Econometric issues and interpretation

The first specification issue to consider is the difficulty of estimating effects associated with cited year, citing year and lag. This is analogous to estimating “vintage,” time, and age effects in a wage or a hedonic price model. If lag (our “age” effect) entered the model linearly, then it would be impossible to estimate all three effects. Given that lag enters our model non-linearly, all three effects are, in principle, identified. In practice, however, we found that we could not get the model to converge with the double-exponential lag function and separate a parameters for each cited year and each citing year. We were, however, able to estimate a model in which cited years are grouped into five-year periods, indexed by p. Hence we assume that a(t) is constant over t within these periods, but allow the periods to differ from each other.

The estimation is carried out including “base” values for p, and p2. Location, field, cited period and citing year effects are all estimated relative to a base value of unity. The various different effects are included by entering multiplicative parameters, so that the estimating equation looks as follows:

Thus we allow a to vary by cited period, cited field, citing year and all possible combinations of citing country and cited country. We allow P, to vary by cited field, and every possible combination of cited and citing countries. In this model, unlike the linear case, the null hypothesis of no effect corresponds to parameter values of unity rather than zero (except for y, and the “base” values of p, and P2). For each effect, one group is omitted from estimation, i.e., its multiplicative parameter is constrained to unity. Thus the parameter values are interpreted as relative to that base group.