## Gray: Innovation in the states

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Gray. 1973. Innovation in the states: A diffusion study. APSR 67:1174-1185.

## Contents |

## Three Research Questions

1.How do ideas diffuse across states? (There's a bandwagon effect)

2.What explains why some states adopt new ideas earlier than other states? (Wealth and competitiveness)

3.Is innovativeness a trait, or not? (No, it isn't)

## 1. A Model of Diffusion

The rate of diffusion is a function of (1) how many states have already adopted a policy, (2) how many states might potentially adopt it, and (3) how strongly adopters influence potential adopters (an interaction). Thus A(t) = A(t-1) + b*A(t-1)*(L � A(t-1)), which rearranged is A(t) = (1 + b*L)*A(t-1) � b*A(t-1)^2 + c + e where

- A(t) is the proportion of states that will adopt the policy in year t;
- A(t-1) is the (cumulative) proportion of states that had adopted the policy as of t-1;
- b is "the probability that when 'leaders' from two states meet, their interaction results in another adoption" (p 1178);
- L is the maximum number of potential adopters (might be lower than 50; for example, cultural or constitutional obstacles may prevent any possibility of adoption);
- c is the intercept and e is the error term.

As shown in Fig 1 (p 1177), the model predicts adoption over time well. Table 2 shows that this model predicts adoption in each of 12 issue areas with an R2 over 0.9. More central to Gray's point, the interactive term is statistically significant in half of the 12 regressions (see Table 3), suggesting that states do, in fact, influence on another: As more states adopt a policy, more states become willing to adopt a policy ("everybody's doing it").

Several variables can influence these diffusion patterns. Most notably, federal intervention can lead to dramatic shifts (compare Fig 8, which has federal intervention, to Figs 4-7, which don't).

## 2. Analysis of First Adopters

As Walker (1969) showed, state wealth and partisan competitiveness make states more likely to be early adopters.

## 3. Patterns of Innovation

By aggregating across issue areas, Walker (1969) assumed that "innovativeness" exists as a trait among states. By disaggregating issue areas, however, Gray finds that states vary widely in their innovativeness in different policy areas (Table 5). Moreover, innovativeness doesn't appear to correlate strongly across her 12 policies (though you might disagree if you look at Table 6).

## Concerns

The R2 values in Table 2 aren't what they seem; wouldn't you always expect really high values in an autoregressive equation like this?

Table 3 doesn't persuade me that the quadratic model is really better. Sure, there is strong statistical significance in a few cases, but substantive significance appears low. For example, do I really care about a difference of 0.0009 in two R2 values, even if the F test does give a significant value?

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