Hybrid Corn Revisited

Dixon, Robert

doi:10.2307/1912817

Cited by 150 publications

(64 citation statements)

References 7 publications

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“…To avoid the problems in the empirical analysis and to manipulate censoring independently from t,, we made the speed of diffusion low versus high by reducing the values of both p and 9 by 20 percent, leaving their ratio unchanged. Thus, our design has 160 cells: Signal (4) x Noise (5) 'Assuming that the true errors are proportional to the probability of adoption in period t (Debecker and Modis 1994, Dixon 1980, we created the perturbed adoptiondata x(t) using a multiplicative error speciiication: x ( f ) = yl(t)ctf), where yl(f) are the true adoption data series generated from the Bass model and dt) are random errors generated from a log-normal distribution with mean 1 and variance expia21 -1. We selected five levels of error variance: o equaling .06, .24, .42, .60, and .78.…”

Section: Simulation Analysismentioning

confidence: 99%

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

1997

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Studies estimating the Bass model and other macra-leveldiffusion models with an unknown ceiling feature three curious empirical regularities: (i) the estimated ceiling is often close to the cumulative number of adopters in the last observation period, (ii) the estimated coefficient of social contagion or imitation tends to decrease as one adds later observations to the data set, and (iii) the estimated coefficient of social contagion or imitation tends to decrease systematically as the estimated ceiling increases.We analyze these patterns in detail, focusing on the Bass model and the nonlinear least squares (NLS) estimation method. Using both empirical and simulated diffusion data, we show that NLS estimates of the Bass model coefficients are biased and that they change systematically as oneextends the number of observations used in the estimation. We also idenhfy the lack of richness in the data compared to thecomplexity of the model (known as ill-conditioning) as the cause of these estimation problems.In an empirical analysis of twelve innovations, we assess how the model parameter estimates change as one adds later observations to the data set. Our analysis shows that, on average, a 10% increase in the observed cumulative market penetration is associated with, roughly, a 5% increase in estimated market size m, a 10% decrease in the estimated coefficient of imitation q, and a 15% increase the estimated coefficient of innovation p.A simulation study shows that the NLS parameter estimates of the Bass model change systematically as one adds later observations to the data set, even in the absence of model misspecification. We find about the same effect sizes as in the empirical analysis. The simulation also shows that the estimates are biased and that the amount of bias is a function of (i) the amount of noise in the data, (ii) the number of data points, and (iii) the difference between the cumulative penetration in the last observation period and the true penetration ceiling (i.e., the extent of right censoring). All three conditions affect the level of ill-conditioning in the estimation, which, in turn, affects bias in NLS regression. In situations consistent with marketing applications, m can be underestimated by 20% p underestimated by the same amount, and q overestimated by 30%.The existence of a downward bias in the estimate of m and an upward bias in the estimate of q, and the fact that these biases become smaller as the number of data points increases and the censoring decreases, can explain why systematic changes in the parameter estimates are observed in many applications. A reduced bias, though, is not the only possible explanation for the systematic change in parameter estimates observed in empirical studies. Not accounting for the growth in the population, for the effect of economic and marketing variables, or for population heterogeneity is likely to result in increasing m and decreasing $ as well. In an analysis of six innovations, however, we find that attempts to address possible model mis...

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Section: Simulation Analysismentioning

confidence: 99%

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

1997

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“…The logistic function is often used to represent the S-shaped (sigmoid) diffusion process for agricultural innovations because of its relative simplicity (Griliches, 1957;Jarvis, 1981;Knudson, 1991;Karshenas and Stoneman, 1992). Other S-shaped functions used include the cumulative normal and the Gompertz model (Dixon, 1980). However, as Mahajan and Peterson (1985, p. 10) note, any unimodal distribution function will generate a (cumulative) S-shaped curve.…”

Section: Methodsologymentioning

confidence: 99%

Dynamic Diffusion with Disadoption: The Case of Crop Biotechnology in the USA

Fernandez‐Cornejo¹,

Alexander²,

Goodhue

2002

Agric. resour. econ. rev.

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Controversy over the use of genetically engineered (GE) crops may have induced some farmers to disadopt these seeds, making a traditional diffusion model inappropriate. In this study, we develop and estimate a dynamic diffusion model, examine the diffusion paths of GE corn, soybeans, and cotton, predict the adoption of those crops over the next two years, and explore the main determinants of the diffusion rate. Our estimates indicate that future growth of Bt crops will be slower or negative, depending mainly on the infestation levels of the target pests. Adoption of herbicide-tolerant soybeans and cotton will continue to increase, unless consumer sentiment in the United States changes radically.

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“…Hence these models are more difficult to use in the absence of diffusion time-series data (using the historical data on existing products, however, Easingwood (1989) has demonstrated how the NUl model can be used to develop analogical parameter estimates for a new product). agricultural innovations Dixon, 1980) 3. Mansfield (1961) qF ( 4.…”

Section: Flexible Diffusion Modelsmentioning

confidence: 99%

“…For applications of the Gompertz curve and its comparison with the Mansfield model, see Hendry (1972), Dixon (1980), andZiemer (1988). Several other growth models also have been proposed in the marketing, economics, and technological substitution literatures to depict the growth phenomenon (e.g., the Weibull distribution).…”

Section: Acknowledgmentsmentioning

confidence: 99%

Diffusion of Technologies and Social Behavior

1991

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Hybrid Corn Revisited

Cited by 150 publications

References 7 publications

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

Dynamic Diffusion with Disadoption: The Case of Crop Biotechnology in the USA

Diffusion of Technologies and Social Behavior

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