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Stochastic models are seldom used when we analyze the stability and the efficiency of enterprise cost systems. Despite of numerous restrictions, along with the complexity of mathematic formalization, this approach would encourage more rational use of resources under conditions of extreme change in external and internal business environments. Different methods of Maximum Likelihood Estimations (MLE) have been introduced to weaken these parametric drawbacks.

However, the high computational complexity makes its use difficult. This work prevailingly demonstrates the use of coenosis theory to design and analyze cost systems of industrial enterprises, including the use of numerically reliable statistical computations.

This approach can also be observed as a delicate parametric adjustment of economic coenosis structures ensuring stability and sustainability. The chapter provides the example of the mentioned methodology within the frame of an ordinary industrial enterprise.

Rainfall–runoff relationship is one of the most complex hydrological phenomena. A conventional neural network (NN) with backpropagation algorithm has successfully modelled various non-linear hydrological processes in recent years. However, the convergence rate of the backpropagation NN is relatively slow, and solutions may trap at local minima. Therefore, a new metaheuristic algorithm named as cuckoo search optimisation was proposed to combine with the NN to model the daily rainfall–runoff relationship at Sungai Bedup Basin, Sarawak, Malaysia. Two-year rainfall–runoff data from 1997 to 1998 had been used for model training, while one-year data in 1999 was used for model validation. Input data used are current rainfall, antecedent rainfall and antecedent runoff, while the targeted output is current runoff. This novel NN model is evaluated with the coefficient of correlation (R) and the Nash–Sutcliffe coefficient (E²). Results show that cuckoo search optimisation neural network (CSONN) is able to yield R and E² to 0.99 and 0.94, respectively, for model validation with the optimal configuration of number of nests (n) = 20, initial discovery rate of alien eggs (painitial) = 0.6, hidden neuron (HN) = 100, iteration number (IN) = 1,000 and learning rate (LR) = 1 for CSONND4 model. The results revealed that the newly developed CSONN is able to simulate runoff accurately using only precipitation and runoff data.

In this chapter, we consider the possibility that a firm may use costly resources to improve its technical efficiency. Results from static analyses imply that technical efficiency is determined by the configuration of factor prices. A dynamic model of the firm is developed under the assumption that managerial skill contributes to technical efficiency. Dynamic analysis shows that the firm can never be technically efficient if it maximizes profits, the steady state is always inefficient, and it is locally stable. In terms of empirical analysis, we show how likelihood-based methods can be used to uncover, in a semi-non-parametric manner, important features of the inefficiency-management relationship using a flexible functional form accounting for the endogeneity of inputs in a production function. Managerial compensation can also be identified and estimated using the new techniques. The new empirical methodology is applied in a data set previously analyzed by Bloom and van Reenen (2007) on managerial practices of manufacturing firms in the UK, US, France and Germany.

Time-varying proportions arise frequently in economics. Market shares show the relative importance of firms in a market. Labor economists divide populations into different labor market segments. Expenditure shares describe how consumers and firms allocate total expenditure to various categories. We introduce a state space model where unobserved states are Gaussian and observations are conditionally Dirichlet. Markov chain Monte Carlo techniques allow inference for unknown parameters and states. We draw states as a block using a multivariate Gaussian proposal distribution based on a quadratic approximation of the log conditional density of states given parameters and data. Repeated draws from the proposal distribution are particularly efficient. We illustrate using automobile production data.

We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.