Challenging the 'Law of diminishing returns'

[Abstract]: 'The Law of Diminishing Returns' (Spearman, 1927) states that the size of the average correlation between cognitive tasks tends to be relatively small in high ability groups and relatively high in low ability groups. Studies supporting this finding have tended to contrast very low ability subjects (IQ < 78) with subjects from higher ability ranges and to use tests that have poor discriminatory power among the higher ability levels. In the first study described in this paper, tasks that provide good discrimination among the higher ability levels were used. A sample of High ability (N = 25) and of Low ability (N = 20) 15-years old boys completed four single tests, two with low and two with high g saturations, and two competing tasks formed from these single tests. The results indicated that, contrary to the predictions of the Law of Diminishing Returns, the amount of common variance was greater in the High ability group. It is suggested that the Law of Diminishing Returns does not take into account the factor of task difficulty and that there are situations where the exact reverse of this law holds. A second study again compared correlations obtained with extreme groups (N=28 & N=29), this time on measures of Perceptual Speed, which are easy for all ability levels. Results indicated that correlations among the Perceptual Speed measures were the same for both groups. In neither of these studies was there any support for the Law, which seems to be dependent on the very high correlations obtained from samples at the extreme lower end of the ability continuum

Heterogeneous Response Functions in Advertising

De Fleur (1956) provides the earliest evidence of diminishing returns. He finds a common logarithmic pattern for leaflets dropped and message recalled in field experiment. Since then, many researchers have applied logarithmic or square root patterns to capture the effect of diminishing returns with their advertising response modeling across different media. But discussions with managers support the notion that the diminishing returns to incremental dollars spent on one medium (say, television) are not likely to be the same as those for equivalent dollars spent on other media (e.g., Print). But if diminishing returns indeed vary across media, how does that change the resulting allocation recommendation? To address this issue, we derive a dynamic model that captures the notion of differential diminishing returns and disentangles it from closely related notions of differential carryovers and differential ad effectiveness. Second, we develop a systematic method to estimate the model's parameters using market data and illustrate empirically that all three effects, diminishing returns, carryover and ad effectiveness vary across the four media employed. Finally, we investigate the normative implications for managerial decision-making. Here, we additionally account for varying media buying efficiencies across media. Taken together, the approach and its illustration should provide managers with a better toolkit to allocate their multimedia budgets. --

Are there Diminishing Returns to R&D?

Semi-endogenous models and, to some extent, also Schumpeterian models are based on the assumption of diminishing returns to R&D. This paper shows that the null hypothesis of constant returns to R&D cannot be rejected for the OECD countries.returns to R&D; endogenous growth theory

Big Neural Networks Waste Capacity

This article exposes the failure of some big neural networks to leverage added capacity to reduce underfitting. Past research suggest diminishing returns when increasing the size of neural networks. Our experiments on ImageNet LSVRC-2010 show that this may be due to the fact there are highly diminishing returns for capacity in terms of training error, leading to underfitting. This suggests that the optimization method - first order gradient descent - fails at this regime. Directly attacking this problem, either through the optimization method or the choices of parametrization, may allow to improve the generalization error on large datasets, for which a large capacity is required

Two More Classes of Games with the Fictitious Play Property

Fictitious play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for some important classes of games, including weighted potential games, supermodular games with diminishing returns, and 3x3 supermodular games. Extending these results, we establish convergence for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3xm and 4x4 quasi-supermodular games.Fictitious Play, Learning Process, Ordinal Potential Games, Quasi-Supermodular Games

Induced innovation and relavtive factor share

We build up an induced innovation model based on Popp's article in AER, 2002. His model measured the effect of energy prices on energy-efficient innovations. Using the relative factor shares of energy and labor instead of the energy prices per se, we are able to explain the patenting activity in a better way. Also, with the combination of theoretical and empirical research, we can prove that technological change of energy is related with prices and quantities of both energy factor and labor factor. Furthermore, we discuss on the possibility of the hypothesis of diminishing returns to knowledge, which reveals that diminishing returns are not necessary to exist in the induced innovation model. The result we got is not very strong but it shows more elasticity than Popp’s model

Accounting for Research and Productivity Growth Across Industries

What factors underlie industry differences in research intensity and productivity growth? We develop a multi-sector endogenous growth model allowing for industry specific parameters in the production functions for output and knowledge, and in consumer preferences. We find that industry differences in both productivity growth and R&D intensity mainly reflect differences in "technological opportunities", interpreted as parameters of knowledge production. These include the capital intensity of R&D, knowledge spillovers, and diminishing returns to R&D. Among these parameters, we find that the degree of diminishing returns to R&D is the dominant factor when the model is calibrated to account for crossindustry differences in the US.Multisector growth, total factor productivity, R&D intensity, technological opportunity