Conclusion

The objective of this chapter was twofold: first, to make a theoretical case for the international effect in an epidemic model of diffusion and second, to test the resulting hypothesis using data on steam- and motor ship diffusion. Our theoretical argument is that the extent of use abroad is a source of information about the technology, its characteristics and profitability. The greater the use of new

technology elsewhere, the more information about the technology is available to potential domestic users and therefore the lesser the degree of uncertainty about the benefits of adoption. The hypothesis is therefore that international diffusion has a positive effect on the domestic extent of use.

We introduced international diffusion to the Bass (1969) and Mansfield (1961) models as an additive effect similar to the γ parameter of the Bass model. World diffusion is measured as the simple average of steam- and motor ship diffusion in 13 countries, from which each country‟s own contribution is subtracted so that the explanatory variable is the extent of use elsewhere. Using non-linear least squares on country time-series for two periods of different length, we found some evidence that a world effect exists. The sign of the effect is not robust: there is an equal number of positive, negative and insignificant estimates. The time-series properties of the model may explain this to some degree. However, it is clear that the negative coefficient estimates are inconsistent with the theoretical argument that international diffusion matters because use abroad is a source of information.

We need to examine then whether a theoretical explanation can be made for a negative international effect. It seems to us that this is difficult given the focus on information-spreading unless we relax the assumption that all information has the same value. The history of shipping reveals that technological progress and market segmentation interacted. By this we mean that sailing ships were first replaced by steamships on shorter routes and the transport of passengers and valuable cargo but as steam technology (in particular fuel efficiency) improved, steamships were adopted on ever longer routes. This suggests a hypothesis which is consistent with the lack of robustness in our results, namely that ship owners are primarily

interested in information which comes from others operating in the same market. If so, then information from the early steamships which are not yet competitive on all routes is of low value to those sailing ship owners who operate exclusively in the long-haul market. In this case, the lack of international diffusion acts as a negative signal which may be stronger than the positive sign given by the adoption of steam- and motor ships in markets that are not relevant. If we put together all diffusion into one international measure estimation results will be muddled because all information is given the same weight.

The challenges posed by this argument are considerable. The study should begin with a definition of markets, say according to length of journey and the nature of the cargo. This argument leads towards a desire for micro-level data i.e. information on the level of the ship owner. Since we have only country-level data, we could instead attempt to define for each country the proportion of their fleet that operates in each market. The international diffusion measure would then reflect the degree to which diffusion elsewhere is based in the markets in which the domestic fleet operates. Models developed in the spatial econometrics literature may be of use here. There is a way forward then even with country-level data, however in our view the approach just outlined would require such detail that the challenge is not proportional to the objective which is to provide a first attempt to extend a closed-economy epidemic model to include a link with the extent of diffusion elsewhere. We have not intended to build a model particularly of steam- and motor ship diffusion but rather to use this as an example or context in which the international diffusion hypothesis can be tested.

The lack of robustness in our results has two implications in terms of the estimation method. First, panel data methods may provide more robust results than individual time series because in a panel, information about cross-country variation in diffusion can be used in addition to the time-series information which we have relied on here. On the other hand, a drawback of standard panel methods is that parameters are assumed to common, that is, it is assumed that the true values of α, β and γ are the same for all countries. If this assumption is false and parameters are in fact country-specific – for example, the international effect is only positive for a subset of countries – then panel estimates will be inconsistent. Second, the lack of robustness may also be due to nonstationarity. We tested the time series properties of variables, allowing for structural breaks in the time series, and found that nonstationarity cannot be rejected in the variables of the classic epidemic models. This means that it is possible that the results are due to spurious correlation. The question is then how to develop an epidemic diffusion model which does not have this problem. We experimented with a logistic transformation of the diffusion measure and found that nonstationarity can be rejected in most of the transformed series. However, the results were not robust enough to be satisfactory. It seems to us that another important direction in which the study here could be extended is to take the time-series properties of the model as the main objective. This would potentially make a considerable contribution to the epidemic literature.

We conclude our discussion of epidemic models here. In the next two chapters we investigate the relationship between international and domestic diffusion in an alternative theoretical framework, so-called decision-theoretic models. The international effect is given a wholly different role in the diffusion process as information-spreading is not the driving force of diffusion in these models. The

result is a hypothesis that the international effect is negative. We begin by developing a detailed model of how in a world of Cournot competition adoption of the new technology by foreign competitors changes the benefit of adoption. In Chapter 5 the hypothesis is tested using panel data on the diffusion of the basic oxygen furnace, also a process technology.