Alternative assumptions

In this section we look in some detail at how alternative assumptions change the results of the model in particular how the model may be modified to accommodate an endogenous adoption cost.

The main advantage of the exogenous adoption cost assumption is that it simplifies the model greatly. As the price of furnaces does not depend on the demand for furnaces we only need to model one market, the market for output. That is, we do not engage with the supply-side diffusion literature (see Stoneman 2002 and Stoneman and Battisti 2010, forthcoming). The price of furnaces can be endogenous to the diffusion process for example because of learning-by-doing, economies of scale, or strategic behaviour. The first two reduce the cost of adoption and thereby create a type of feedback loop with a positive effect on further adoption. If there are scale economies in the production of furnaces, the unit cost decreases as quantity increases. This is a very realistic scenario especially when a technology is new; the first unit is the most expensive to build. Because firms behave strategically in the output market in our model, there is no particular reason to expect that they do not do so in the furnace market as well. The result is a complicated model that is possibly a closer representation of reality but at the cost of analytical clarity.

Two types of learning can lead to a feedback loop. First, learning can occur on the buyers‟ side if learning from other adopters takes place. Here the argument is that late adopters have low adoption costs because they can obtain valuable information from more experienced users of the new technology. For example, Teece (1977) argues that adoption of a technology requires the transfer of unembodied technological knowledge such as engineering drawings, and as the technology

diffuses this information becomes more generally available. The learning-by-doing argument and the epidemic literature have a common element in the emphasis on information. Endogenising the adoption cost therefore provides a possible way to incorporate epidemic effects into a decision-theoretic model of diffusion.

Second, learning-by-doing can take place on the supply-side. Learning spillovers mean that the cost of producing the technology (furnaces) falls with cumulative output as in David and Olsen (1986). This argument provides an interesting opportunity to endogenise the supply side of the diffusion process and thereby establish an alternative hypothesis about the mechanism by which international and domestic diffusion are linked. That is, we can argue that the direction of causality is not simply from a falling price of technology to further diffusion but that the extent of use also affects the price of technology. However, this is a step too far for the present study. Our objective here is to establish a theoretical connection between domestic and international diffusion and we propose the stock effect as this connection. Endogenising the price of technology is an alternative, and it can be also considered an extension which is an interesting direction to be pursued in the future. Furthermore, the data available to us for the empirical study would not permit to test hypotheses arising from such a model. Therefore, the endogenous adoption cost alternative is not explored further here.

Relaxing the assumptions of perfect foresight and full information is another avenue along which the model can be developed. In the first instance, uncertainty introduces the option value of waiting into the arbitrage condition (Stoneman and Toivanen 2006; also Dixit and Pindyck 1994). We have assumed that the representative producer knows exactly how its gross profits and the cost of adoption

change over time. The adoption decision then involves comparing the costs and benefits of postponing adoption. A first step would be to allow the cost of adoption and its time path to be uncertain. Then the assumption that other producers‟ adoption dates are known in advance could be relaxed in which case decisions are based on expectations about future diffusion. As the true extent of use becomes known, beliefs about future diffusion are updated.

We consider the assumptions we have made to be justified given our twin objectives in this chapter, namely to give micro-economic foundations to the hypothesis that the extent of use elsewhere matters for domestic diffusion, and also to give a theoretical framework for the empirical analysis of a number of empirical determinants of intra-country diffusion in the next chapter. Note that we argued already in the introduction (section 4.1) that the negative stock effect does not depend on the assumption of Cournot competition. We have explained in detail the difficulties that arise from allowing heterogeneity in both production and adoption costs. Even a general model with certainty and exogenous adoption cost is difficult to solve. We recognise the value of generality but also that the more general the model, the more difficult it is to analyse. We use a specific model with an imposed structure which does not aspire to generality but allows detailed predictions about the determinants of diffusion that provide a basis for empirically testable relationships.

4.7 Conclusion

The analysis in this chapter is based on the individual producer‟s adoption timing decision and is an extension of the work by Reinganum (1981b). Each firm has two decisions to make over its lifetime: the amount of output it produces in each period,

and the date at which it switches from the old production technology to the new one. The adoption decision is not strategic but output decisions are. Competition in the output market is of the Cournot type: optimal output depends on the output levels of all other producers, and the equilibrium is such that each producer‟s output is the optimal response to other firms‟ output levels. The price of new technology is taken as given, i.e. it is exogenous to diffusion. Price falls over time which drives diffusion forward. Strategic adoption decisions are the subject of the pre-emption literature or order models (Fudenberg and Tirole 1985) and we do not consider that here.

We extend the Reinganum model by introducing heterogeneity in production costs and by interpreting the model in an international context. We are not particularly interested in the order in which firms adopt within each country, but heterogeneity provides a way to analyse differences across countries in the diffusion process. By assuming linear demand and a particular form for adoption costs we derive the arbitrage condition and solve for the optimal adoption date. The arguments of the arbitrage condition are divided into market variables common to all producers namely the price of new technology, demand for output and the extent to which the new technology is used by producers; country-level determinants of the costs and benefits of adoption of which we have discussed the exchange rate and the interest rate; and producer heterogeneity. Analysing the determinants of intra-country diffusion on the basis of the arbitrage condition gives microeconomic foundations to the hypotheses about the determinants of international diffusion.

We propose that a link between international and domestic diffusion is established through the price of output in a so-called stock effect. The extent to which the technology is used is positively related to total output and negatively related to the

price of output. The gross profit from production falls with diffusion as does the benefit of using the new technology, the profit differential. The stock effect means that adoption of the new technology by others makes adoption less attractive to those who have not yet adopted.

An important feature of our model is that the stock effect is domestic as well as international. By this we mean that further use at home has the same negative effect on the profit differential as further use abroad. As we have presented it, the model states that the size of the stock effect depends primarily on the cost differential of the marginal adopter so that the bigger is the cost reduction enjoyed by the marginal adopter, the bigger is the fall in the profit differential for all who have not yet adopted. In other words for an individual producer an adoption by a domestic competitor is as „bad‟ as an adoption by a foreign competitor; both reduce gross profits from production in each period and the profit gain that the producer obtains when it adopts.

More insight to the country determinants of diffusion can be gained if we impose some structure on cost heterogeneity. A particularly useful assumption is that a proportion of the cost differential is common to all producers within a country. Reasons may be the costs of inputs such as the wage rate or cost of electricity, or the effects of institutions or policies that affect the firm‟s ability to reduce costs through adoption. We analysed a two-country model in which heterogeneity is restricted to cross-country differences only (section 4.5.3) and found that in this extreme case a likely outcome is that countries adopt one after the other: inter-country diffusion increases only once intra-country diffusion in one country has been completed. Combined with a degree of cost heterogeneity within a country, we have a model in

which intra-country diffusion takes places simultaneously across countries and country-level heterogeneity contributes to cross-country differences.

Because of the interdependence of producers in Cournot competition, the arbitrage condition determines not only a particular producer‟s adoption timing but it also affects all other producers‟ optimal decisions. The interesting implication is that the country-specific cost factors not only affect diffusion within that country but through the stock effect they also affect international diffusion. This difficulty was discussed here in relation to exchange rates. Because the domestic exchange rate determines the price producers actually receive for their output, it affects both production and adoption decisions. There is then a second-order effect due to the assumptions of Cournot competition and perfect information, namely that all countries‟ exchange rates affect all producers‟ decisions because producers are interdependent through the market for output. The same first- and second-order effects are present when an element of the benefit of adoption is country- not just producer-specific. To illustrate, this would mean that a policy which changes the benefit of adoption in one country has a first-order effect on domestic diffusion but also a second-order effect on international diffusion as producers elsewhere react to the change in diffusion in one country.

We also discussed the other determinants of the optimal adoption date. A high interest rate and a low or inelastic demand delay adoption. A faster falling adoption cost and an expected strengthening of the domestic exchange rate also encourage producers to postpone adoption. Low unit costs of production, a high cost differential, and small adoption costs encourage adoption. Therefore diffusion is likely to occur faster in countries where the cost of adoption is small, the cost

advantage of the new technology is large, costs of production are low, the real interest rate is low and the exchange rate is strong.

The stock of potential adopters is one of the two main determinants of diffusion in the epidemic framework and our results support the importance of this factor. The absolute number of producers is a parameter in the arbitrage condition and as such simply a constant term. We examined where the next adoption is likely to take place in a two-country model and found that the distribution of producers across countries matters as a mediator of the „advantage‟ of a large cost differential. Generally, the marginal adopter is more likely to be found in the country where the cost advantage of oxygen is high; however, this result may be reversed if the stock of producers is considerably higher in the other country. The number of producers does not have a central role as in epidemic models or in pre-emption models in which it is the adoption timing decision which is strategic. Our finding regarding the distribution of producers does not have an obvious theoretical reason other than it is an outcome of the assumption that there is strategic interaction of the Cournot type in the output market.

The depth of the analysis which we have engaged in using a rather simple model of diffusion illustrates the power of the decision-theoretic approach more generally. Aggregate diffusion patterns can be analysed as the outcome of each producer‟s decisions on optimal output and adoption timing. We have chosen not to specify the distribution of heterogeneity within countries as would be done in the so-called probit approach (Davies 1979). The reason is essentially that we apply the model to a particular empirical setting in the next chapter and only country-level data is available to us for estimation. However we have demonstrated how the arguments of

the arbitrage condition can be used to derive hypotheses about the country-level determinants of diffusion.

5 Empirical analysis of the diffusion of the basic oxygen