Evaluating parameters of econometric models with linear limitations and a rank deficient observation matrix

Production function is the econometric model used to study the business relationship between input and output. In this paper, it uses Cobb-Douglas (C-D) production function as based model, and it uses regression analysis and Solow residual as the theoretical support. It simulates the production function model of railway transportation. Through the empirical study and quantify the railway transport enterprise production function analysis, the authors reveal factors affecting investment in the railway transport enterprise output volume. This research is helpful for future.

Based on the analysis of the quantitative assessment of the influence of the factors of innovative activity on the dynamics of economic development and the endogenous determination of its contribution to the economic growth of the country, it is revealed that in foreign researches it is identified with the concept of the influence of scientific and technological progress. However, the impact of innovative factors on economic growth is not considered separately. Attempts of such a definition in Ukrainian researches are limited to well-known approaches: methods of integral assessment, methods of expert assessments, the method of multipliers, econometric models. Most of the approaches considered are focused on defining the innovative impact on economic development, rather than on economic growth. The main tool for assessing the role and innovative contribution to economic growth is the aggregate supply function model, usually based on the Cobb-Douglas production function. The analysis of the approaches used revealed a number of comments on econometric approaches. In contrast to this, an approach is proposed based on the neoclassical production function of Cobb-Douglas with a constant return to scale in the form of J. Tinbergen, with technical progress neutral according to J. Hicks, decreasing marginal productivity of macrofactors with limited interchangeability, which provides a causal functional (and not a statistical) relationship between input and output variables; does not require long time series. It is characterized by dynamic coefficients of elasticity, capital utilization rate and taking into account the innovation factor in each separate period. The innovation factor includes: the gross domestic expenditures on research and development, the expenditures on innovation, general expenditures on education. To define the contribution of formal innovation factor in economic growth applied "method of Solow residual", which by taking the logarithm and obtaining logarithmic derivatives in the production function, provides a formalized information about the contribution of each factor to economic growth and allows to develop the necessary regulatory measures. The method has been tested at the level of the country and old industrial regions of Ukraine: Dnepropetrovsk, Zaporozhye and Kirovograd regions of the Dnieper economic region of Ukraine. The role, importance and influence of the main factors of economic growth along with innovative ones on the part of the aggregate supply are considered and the cost-effectiveness of innovative factors is estimated.

The article considers a comprehensive approach to predicting the security index of local computer networks of organizations using modern econometric tools. The main attention is paid to the adaptation of classical production functions, in particular the Cobb–Douglas model, to the sphere of information security. The application of two modifications of the Cobb–Douglas production function — linear and nonlinear forms — is proposed to model the impact of key factors on the level of security of information infrastructure. The econometric models presented in the study take into account the impact of investments in cybersecurity, human capital, as well as technical and software protection tools used within organizational information systems. In particular, the following independent variables are included in the model: the amount of investment in security hardware (for example, firewalls, firewalls, routers with security functions), the cost of security software (intrusion detection and prevention systems, antivirus, SIEM), as well as parameters characterizing the human factor, in particular the number of information security specialists involved in the enterprise. The article provides a theoretical justification for the choice of the model, identifies the main endogenous and exogenous variables, analyzes their impact on the resulting variable, and also considers approaches to collecting, validating, and pre-processing empirical data. An econometric model was built based on real data collected from a number of organizations of various profiles, which made it possible to test the model in real conditions. The estimation of model parameters was carried out using multiple regression methods using the Statistica econometric analysis software. The modeling results confirmed the feasibility of using Cobb–Douglas functions in the field of cybersecurity and made it possible to combine the volumes of input data to model the future situation and determine the overall level of security of organizational networks. The conclusions obtained can be useful for forming an effective information security management policy, optimizing costs for cyber protection, as well as for strategic planning of investments in the development of information infrastructure. The proposed approach is flexible and scalable, which allows it to be adapted to the specifics of individual industries or organizations.

Utilizing the urban water demand function and the Cobb-Douglas (C-D) production function, an economic control model for the multi-input-multi-output (MIMO) nonlinear system was designed and implemented to describe urban comprehensive water consumption, where the urban water demand function was expressed as the product of the number of water users and per capita comprehensive water consumption, and the urban water supply function was expressed as a C-D production function. The control variables included capital investment and labor input for the urban water supply. In contrast to the Solow model, Shell model and aggregate model with renewable labor resources, the proposed model eliminated value constraints on investment and labor input in the state equations and hence avoided the difficulty in applying these models to urban water supply institutions. Furthermore, the feedback linearization control design (FLCD) method was employed to accomplish stability of the system. In contrast to the optimal control method, the FLCD method possesses an explicit solution of the control law and does not require the solution of a two-point boundary value problem of an ordinary differential equation, making the method more convenient for application. Moreover, two different scenarios of urban water consumption, one for the growth period and the other for the decline period, were simulated to demonstrate the effectiveness of the proposed control scheme.

In Italy, there is a large gap between the water supplied to the distribution networks and the water delivered to users. Reducing the dispersion along the aqueduct network has several advantages for water service operators, such as reducing the production and distribution costs of the resource, limiting the volumes of water purchased wholesale, and improving the users’ perception of the service. The aim of the paper is to define an econometric model that allows water utilities to determine the optimal budget to be used to finance the maintenance work required to reduce water losses. The model, which uses a Cobb-Douglas production function with increasing returns to scale, identifies the maximum level of profit that the manager can obtain by investing the optimal amount. The higher profits obtained can be used to self-finance new maintenance. A key parameter is the coefficient of return-on-investment α, which is a measure of the degree of user satisfaction with the service offered. The water tariff is dependent on financial (capital and operating), environmental and resource costs. The model is applied to a water utility in the Campania region (Italy).

This small note with a swollen Appendix illustrates how foreign ownership data and aggregate production function assumptions can be used to deduce what Canadian domestic output and national income might be if there were less foreign capital. The appendix spells out the calculation procedure, which depends heavily on the assumed ease with which labour can be substituted for capital in the production process. Consider first two extreme possibilities. On the one extreme, if there were no substitution possible between capital and labour, then any reduction in the stock of capital would lead to proportionate drops in output and employment. In this sort of world, anything that jeopardizes the inflow of capital required to finance the technically-necessary capital-labour ratio has high costs in terms of unemployment and foregone income. At the other extreme, if there is perfect substitution between capital and labour, and if foreign capital is paid the value of its marginal product, then changing the amount of foreign capital would have no effect on national income. Domestic output would drop if the foreign capital were not present, but the amount of the drop would be just equal to the amount of output formerly used to pay the return on the foreign capital. Somewhere between these two extremes lies the constant-returns CobbDouglas production function assumed in the present calculations. Under these assumptions, we need both capital and labour to get any output, but any combination of capital and labour can be usefully employed in cooperation. However, as labour is substituted for capital, the amount of extra labour required to replace one unit of capital increases as the amount of capital decreases. Under these conditions, therefore, it comes 1 The idea of using a Cobb-Douglas production function to estimate the consequences of less foreign investment is based on earlier work by Phil Neher. 2 The foreign ownership data and the assumed production function for business output have been developed as parts of the aggregate quarterly model RDX2. The theory, equations, and variables of the model are described in J. F. Helliwell, H. T. Shapiro, G. R. Sparks, I. A. Stewart, F. W. Gorbet, and D. R. Stephenson: The Structure of RDX2. Ottawa, Bank of Canada, 1971. (Bank of Canada Staff Research Studies, No. 7.)

The output elasticities of inputs seem all about what an applied researcher is concerned with. The Cobb-Douglas production functions formulae possess the convenient property that the exponents of inputs readily represent the output elasticities of inputs such that the sum of these exponents reveal whether there are increasing, constant or decreasing returns to scale. However, there are also some inconveniencies with this type of production functions. In this paper we will investigate three of them. First of all, the short run marginal cost functions obtained from the Cobb-Douglas type of production functions can be both convex and concave depending on the magnitude of the technical coefficient of labor input. Unfortunately, this awkward behavior cannot be explained with the economic theory. Secondly, when the variable input labor with a given level of Technical productivity is complemented with a once-and-for-all increase in the amount of physical capital input, the labor becomes more and more productive as the usage of labor increases. This clearly stands in contrast with the Law of Diminishing Marginal Returns. Finally, we find ever-increasing returns to ‘Technical productivity of labor’, keeping the amounts of labor and physical capital constant, which is again surprising. Key words : paradox; convex and concave marginal costs; Cobb-Douglas production function; increasing rate of return to Technical productivity of labor. JEL classification : D2, D3, D4. DOI : 10.7176/EJBM/11-1-12

The objective of the present study is to determine the status of technical efficiency for a sample of beekeepers in Malaysia. This is because determining the efficiency status of farmers are very important for policy purposes. Efficiency also is a very important factor of productivity growth. In an economy where resources are scarce and opportunities for new technologies are lacking, inefficiency studies will be able to show that it is possible to raise productivity by improving efficiency without the resource base or developing new technology. Estimates on the extent of inefficiency can help decide whether to improve efficiency or to develop new technologies to raise agricultural productivity. In this study, a Cobb-Douglas production function was employed to beekeeping data. Using the method of Maximum Likelihood Estimation (MLE) procedure, we derived the stochastic frontier production function. The technical efficiency index computed shows a mean efficiency ratio of 0.625 implying that substantial inefficiency exists among the Malaysian beekeepers in the sample under study. Our results indicate that there are great potentials for the beekeepers to further increase output using the available inputs and technology.

This research presents a comprehensive analysis of sustainable port operations in two countries, utilizing econometric models, including the stochastic frontier and Cobb–Douglas models, to examine critical elements such as the number of empty containers and vessel traffic. These factors, driven by globalization, significantly impact the environmental and social dynamics within port operations. By integrating these models, this study assesses efficiency and sustainability, addressing methodological gaps in existing research, particularly in the quantification and generalization of CO2 emissions. Findings indicate that, despite differences in port management and operations, CO2 levels can be estimated using operational variables without the need for complete CO2 traceability throughout the logistics chain. This study concludes by emphasizing the importance of incorporating international environmental standards into port operations and recommends the use of econometric models as tools for assessing and managing port sustainability effectively.

The development of non-linear mixed pharmacokinetic/pharmacodynamic models for continuous variables is usually guided by graphical assessment of goodness of fit and statistical significance criteria. The latter is usually the likelihood ratio test (LR). When the variable to be modeled is categorical, on the other hand, the available graphical methods are less informative and/or more complicated to use and the modeler needs to rely more heavily on statistical significance assessment in the model development. The aim of this study was to evaluate the type I error rates, obtained from using the LR test, for inclusion of a false parameter in a non-linear mixed effects model for ordered categorical data when modeling with NONMEM. Data with four ordinal categories were simulated from a logistic model. Two nested multinomial models were fitted to the data, the model used for simulation and a model containing one additional parameter. The difference in fit (objective function value) between models was calculated. Three types of models were explored; (i) a model without interindividual variability (IIV) where the addition of a parameter describing IIV was assessed, (ii) a model with IIV where the addition of a drug effect parameter (either categorical or continuous drug exposure measure) was evaluated, and (iii) a model including IIV and drug effect where the inclusion of a random effects parameter on the drug effect was assessed. Alterations were made to the simulation conditions, for example, varying the number of individuals and the size and distribution of the IIV, to explore potential influences on the type I error rate. The estimated type I error rate for inclusion of a false random effect parameter in model (i) and (iii) were, as expected, lower than the nominal. When the additional parameter was a fixed effects parameter describing drug effect (model(II)) the estimated type I error rates were in agreement with the nominal. None of the different simulation conditions tried changed this pattern. Thus, the LR test seems appropriate for judging the statistical significance of fixed effects parameters when modeling categorical data with NONMEM.

We directly observed a Cobb–Douglas symmetric plane using the index of surface openness, which is used in geography, and successfully identified it. Based on this observation, we measured the capital shares (capital elasticity) and labor shares (labor elasticity) and compared them with the results of multiple regression analysis used in economics. We confirmed consistent agreement in seven countries: Japan, Germany, France, Spain, Italy, the United Kingdom, and the Netherlands. Thus, we show that the Cobb–Douglas production function can be clearly captured in empirical data as a geometric entity with a quasi-inverse symmetry of variables. Based on the above discussion, we theoretically clarified why the Cobb–Douglas production function is better fit to empirical data in economics, because it uniquely derives the fact that their variables follow a power-law distribution.

The neoclassical Solow-Swan economic growth theory of 1956, also known as the exogenous growth model, advocates for the accumulation of physical capital as an important driver of economic growth in the short run, while technological advancement is the key determinant of economic growth in the long run (Chirwa & Odhiambo, 2016). The main aim of this study is to measure the impact of some key macroeconomic factors, which influence the economic growth of a developing country, in our case, the Republic of Kosovo. This study uses secondary data from The World Bank Indicators for the time period 2010–2020. In this study, the ordinary least squares (OLS) econometric model is employed, the dependent variable used is the gross domestic product (GDP) growth, and the independent variables used are private consumption, remittances, export, and employment. Growth in an economy is measured by a change in the volume of its output or the real expenditure or income of its residents (The World Bank, n.d.-d). The study comes to the conclusion that the OLS model is important under the study circumstances thus the independent variables such as consumption, employment, exports, and remittances have a positive impact on Kosovo’s economic growth measured by GDP. The study comes with further recommendations such as increasing employment, using more effectively the remittances received from the diaspora, and increasing the exports for Kosovo to gain economic growth and sustainability.

In this work we deal with the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss' Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

In the past, growth models have been constructed and analyzed with the help of a production function subject to certain restrictive features. For quite some time, the Cobb-Douglas production function (CD) with its input exponents adding upto unity and a unitary elasticity of substitution were mostly used by the economists for analysis. In recent times, the constant elasticity of substitution production function (CES) which includes CD, as well as Leontif production function as its special case has been widely used in various studies. One major limitation of this production function is that the elasticity of substitution parameter is not variable along an isoquant, though it can take different values for different values for different industries. We have made an attempt to test whether the estimated values of elasticity of substitution between labour and capital for a sector tend to change from one year to another and also whether it is CD or CES production function that characterizes a particular sector.

This paper estimates a series of production functions that explain the number of points a National Football League team will score during a season based on six measures of its offensive performance. The models that are estimated are linear and Cobb-Douglas production functions, using data for each team for each season from 2000 to 2018. Additionally, separate production functions are estimated for two sub-periods to determine whether the production functions vary over time and an accuracy check is performed at the end of the paper, where each team’s actual points are compared to its predicted points for the 2018 season.