Determinants of adoption timing

The arbitrage condition can be used to solve for ηi explicitly if we know the function

K(ηi). The functional form should be such that the cost of adoption falls over time.

An example is47

( ) t

K t k (4.26)

where k and λ are some positive constants. The parameter k indicates the magnitude of the adoption cost so that a higher value implies a higher adoption cost in all time periods. The parameter λ measures the rate at which adoption cost falls and the higher the value the faster the cost falls over time:

ln t dK k k dt      (4.27)

Substituting this and the profit differential (4.18) into the arbitrage condition (4.25) gives









1 1 0 0 1 1 1 2 2 ( ) ln ( 1) i N i j j i i j j i a a a N c a c c N c c k e e r k b N          _      _{ }   _  _       _{    } 





(4.28)

Taking logs and rearranging gives the optimal adoption date as a function





1 1 0 0 1 1 1 2 2 ( ) ln ( ln ) ln ( 1) ln i N i j j i i j j i a a a i N c a c c N c c e e r k b N k                                   





(4.29)

The optimal adoption date depends on i‟s unit costs; the extent of use elsewhere (the term Σc0+Σc1); the cost of adoption; demand parameters; the real interest rate; the

exchange rate; and the number of producers. The expression for ηi reveals the

following ceteris paribus effects of each of the determinants on adoption timing. 1. Greater usage discourages further use because adoption of the new technology by others reduces the (marginal) benefit of use. This stock effect is reflected in the negative relationship between other producers‟ unit costs and the adoption date.

2. A small and declining cost of adoption encourages further use. The lower is the price of furnaces the lower is the benefit of postponing adoption. A high value of λ means that the adoption cost is falling rapidly which is an incentive to postpone adoption. Because both k and λ enter the denominator of (4.29), their values also affect the magnitude of the effect that other determinants have on ηi.

3. Low unit costs and a big cost differential encourage early adoption. The optimal date is earlier the bigger is the cost advantage of basic oxygen, Δci. The level

of unit costs c0i+c1i has a negative effect on adoption so that a higher level delays

adoption.

4. A high real interest rate r delays adoption because it increases the opportunity cost of adoption.

5. A weak exchange rate (high e) delays adoption and an expected strengthening of the domestic currency speeds up diffusion.

6. A more inelastic demand delays adoption. A high value of b implies that demand is less responsive to changes in the price of steel. Both gross profit level and the profit differential are lower, ceteris paribus. Because the cost of postponing adoption is lower, the optimal adoption date is later.

7. An exogenous increase in the demand for steel encourages diffusion. The larger is the demand parameter a, the earlier is the optimal adoption date. (Although the profits of non-adopters also increase, the profits of adopters increase more so the profit differential increases.)

8. The effect of the number of producers in the market, N, on adoption timing is unclear. There is no entry or exit in our model, i.e. N is fixed, so ambiguity regarding the effect of N on adoption timing is not a central concern.

Most interesting for us is the stock effect which produces a negative relationship between current usage and future adoption. The reason for the stock effect is simply the microeconomic effect of the marginal adoption on the optimal adoption date of producers that have not yet adopted. Each additional adoption reduces the price of output and thereby the profit differential. For the producer who has not yet adopted the profit differential is the cost of postponing adoption and so a reduction in the profit differential is an incentive to postpone adoption.

On the country-level the stock effect means that diffusion elsewhere discourages further usage at home, in other words, international diffusion has a negative effect on intra-country diffusion. Note that in this model the distinction between domestic and foreign use is arbitrary from the point of view of the individual adopter. That is,

the stock effect concerns domestic and foreign use equally; the current extent of use, whether at home or abroad, has a negative effect on further adoptions. For the empirical researcher however the distinction is interesting because intra-country diffusion models in the literature so far have only considered domestic factors. Our model explicitly states that the extent of use elsewhere also matters for intra-country diffusion, if output is sold in a world market.

Note that the domestic stock effect only differs from the international stock effect if we compute the effect of exchange rates on the price of steel. Assuming that steel is traded in the world market not domestically, even in this case further diffusion at home affects the optimal adoption date through the world price of steel, and thus the sign of the stock effect is still negative. As explained above, comparative statics results regarding the effect of the domestic exchange rate in particular are inconclusive and for this reason we have only made explicit the effect of exchange rates on the domestic price of furnaces. This is essentially equivalent to assuming that the domestic exchange rate primarily affects the price of furnaces and that the effect of other countries‟ exchange rates on optimal output is negligible.

Other factors which affect the optimal adoption date of all producers equally are the world price of basic oxygen furnaces and the parameters N, a and b. While the stock effect holds back diffusion, the decline over time in the price of furnaces drives diffusion forward. The finding that λ (the speed with which furnace price falls) has a negative effect on ηi may seem surprising at first. Consider however the producer

who waits for adoption cost to fall to the level that satisfies the arbitrage condition. If price is not changing or is not expected to change i.e. K‟(ηi) is zero, then the

of adoption (the profitability criterion). The firm then acquires the new technology at the first date when the profit gain exceeds the opportunity cost of adoption.48

In the model we have assumed that demand for steel does not change in the sense that a and b are parameters rather than variables. However, if there is an unexpected change in the world demand for steel (higher a) this will increase the extent of use because the benefit of using the new technology increases. Indeed expressions derived earlier show that price, output, gross profits and the profit differential are all higher. A change in the price elasticity of demand also changes outputs and profits although not price. If a substitute for crude steel becomes available so that demand becomes more responsive to price (lower value of b) this increases output, gross profit and the profit differential, ceteris paribus. Postponing adoption is costlier and the extent of use increases. Note that under the assumption that the market for steel is global, a localized demand shock does not affect the local producers any differently than it affects producers elsewhere.49

The main factors which explain intra-country diffusion in this model are cost heterogeneity and the fall in adoption cost over time. In the firm-level diffusion literature a common approach has been to identify a source of heterogeneity in profitability, traditionally firm size, and use its distribution across firms to derive the aggregate diffusion curve. This is the so-called probit or rank approach. We have introduced firm-level rank effects into the Reinganum model through cost heterogeneity. Given the data we have at hand in the next chapter, we do not specify

48 _{The opportunity cost is}

a a a

r e k_{ }  e k_ . If the exchange rate is also not expected to change the opportunity cost is simply the first term.

49 _{With appropriate data we could test the world market hypothesis by examining whether the}

a distribution function for cost heterogeneity here. This implies that the order of adoption remains unspecified as in the original Reinganum model. However, clarity is not compromised because the implications of the model are easy to analyse. In particular it is clear how diffusion affects the optimal adoption date of the representative producer. The probit approach is helpful for explaining the identity of the adopter, however we are not particularly interested in this within a particular country and across countries we are most interested in the factors that are common to all producers within the country. The discussion in section 4.5.3 reflects a probit approach as much as our model allows.

A strength of our approach is that the model provides a framework within which the effect of institutional factors can be analysed. By this we mean variables that affect the adoption timing decision of all producers within a country. So far only two country-level factors have been specified: the real interest rate and the exchange rate. On a more structural level, the economic and political environment in which the firm operates is also expected to affect production and adoption costs and thus contribute towards explaining international diffusion. Relevant country factors also include common input costs such as the wage rate or the cost of electricity, or the cost of transport to the market. Such determinants are discussed in the context of the basic oxygen furnace in the next chapter.

In document International diffusion of new technology (Page 124-129)