Parameters Of Production Function Research Articles

Estimating the Ideas' Production Function Using Macro‐Economic Persistence

AbstractIf productivity stems from the accumulation of ideas, then the ideas' production function can cause productivity and macro‐economic aggregates to be persistent. We use this insight to estimate the parameters of the ideas' production function in a general equilibrium model. We find that ideas become harder to produce as they accumulate. We quantitatively explore the propagation of different kinds of shocks through the ideas' production function, finding that nonpersistent shocks that affect R&D decisions may lead to persistent productivity changes as a result. The use of capital in R&D is important for propagation.

Optimal distribution of limited resource in a context of uncertainty

Object of research: methods of rational distribution of limited resource in a context of uncertainty. It is assumed that the system consists of a set of independently functioning elements, and effectiveness of these elements depends on the level of investment. The complexity of solving the problem using traditional methods depends on and is determined by the type of analytical description of production functions of the system elements. Significant difficulties arise if parameters of production functions are uncertain quantities, specified, for example, in terms of fuzzy mathematics. This circumstance emphasizes the relevance of studying approaches to solving the set problem of resource distribution for the case when its parameters are not clearly defined, and this circumstance also determines the goal of the work. Problems arising from the goal consist in developing mathematical models and methods for rational resource distribution for the main types of production functions with their parameters being fuzzy numbers of (L –R) type. To solve these problems, a method is proposed that transforms the original fuzzy problems into clear ones that can be solved using standard constrained optimization technologies. An important result of the research consists in the fact that the proposed method is universal, that is, it is applied in the same way to solve problems of resource distribution in systems wherein production functions of the elements can be of arbitrary nature. Refs.: 11 titles.

Comparative analysis of production function models of the machine building and metalworking industry in the Samara region

The published article is devoted to the development and identification of mathematical models of the functioning of the mechanical engineering and metalworking industry in the Samara region. The initial data of official statistics on the results of the functioning of the mechanical engineering and metalworking industry of the Samara region in the period from 1965 to 2021 have been collected and systematized. The parameters of Cobb-Douglas production functions have been identified at various study intervals in versions of the original and smoothed actual statistical data. Both the entire time period of the study and individual local intervals of stable and crisis functioning of the analyzed production system were considered as parameter identification intervals. The values of the parameters of production functions were calculated for different periods of the study and the qualitative characteristics of the obtained model solutions were calculated. A comparative analysis of the parameters and characteristics of the resulting models was carried out. Identification of unknown parameters considered in the work of production functions was carried out using the least squares method. The study used official statistical data from the Samara Regional Committee of State Statistics as empirical material.

Optimal Resilience in Multitier Supply Chains

Abstract Forward-looking investments determine the resilience of firms’ supply chains. Such investments confer externalities on other firms in the production network. We compare the equilibrium and optimal allocations in a general equilibrium model with an arbitrary number of vertical production tiers. Our model features endogenous investments in protective capabilities, endogenous formation of supply links, and sequential bargaining over quantities and payments between firms in successive tiers. We derive policies that implement the first-best allocation, allowing for subsidies to input purchases, network formation, and investments in protective capabilities. The first-best policies depend only on production function parameters of the pertinent tier. When subsidies to transactions are infeasible, the second-best subsidies for resilience depend on production function parameters throughout the network, and subsidies are larger upstream than downstream whenever the bargaining weights of buyers are nonincreasing along the chain.

Excess capacity and hysteresis in EU Countries. A structural approach

We develop a structural method to estimate the rate of capacity utilization in 12 EU countries that consists of identifying the structural parameters of a Leontief production function, using a parsimonious theoretical specification. Parameters are correctly identified, stable and robust to alternative specifications. Our results provide evidence of persistent excess capacity and hysteresis in the rate of capacity utilization in many EU countries, especially after the 2008′s global financial crisis, thereby supporting the claim that larger fiscal deficits would have contributed to absorb excess capacity without producing persistent inflationary pressures or debt unsustainability. Despite the simplicity of our model, the method allows more complex macroeconomic specifications for country-specific applications.

COST AND RETURN ANALYSIS OF IRRIGATED UPLAND TOMATO (Lycopersicon Esculentum) PRODUCTION IN GOMBE STATE, NIGERIA

The study examined the cost and return analysis of irrigated upland tomato (Lycopersicon Esculentum) production, in Gombe State, Nigeria. Multi-stage random sampling procedure was used to select 459 respondents. Data were collected using structured questionnaire and were analysed using descriptive and inferential statistics. The result revealed that Most of the types of farms implements use for dry season tomato production in the study areas were tractors (32.4%), hand tools (37.6%) and animal traction (30.0%). Capital for dry season tomato production, the respondents in Dukku, Nafada, funakaye and Yamaltu Deba LGA respondents had a mean capital of N212,747.36, N183,662.55, N261,540.30, and N204,785.956 respectively. The findings also revealed the result of maximum likelihood estimate of parameters of the stochastic frontier production function of dry season tomato farming in the study area reveal that farm size (P< 0.001), labour (P< 0.001), farming experience (P< 0.001), and capital (P< 0.001) were the major factors statistically affecting the respondents rice production at 1%. The analysis of dry season maximum likelihood estimate of the parameter of stochastic frontier cost of tomato production showed that ploughing (P< 0.001), transplanting (P< 0.001), harvesting (P< 0.001) and capital (P< 0.001) were the determinant of cost of output of the respondents. The result further reveals the costs and return of dry season tomato farming in the study area depicts that the total variable cost of production was ₦2,384,894 with a total cost of production which is the total variable plus the fixed cost of ₦3,266,031. The revenue realized was ₦4,070,558. The net farm income for the dry season tomato farmers for one hectare in the study area was ₦804,529.23. The profit index of the respondents was ₦1.7. The major constraints to the irrigated upland tomato production were inadequate water for irrigation (23.0%), lack of irrigation facilities (20.7%), heat stress and drought (27.2%) preventing maximum productions in the study area. In addition, constraints to irrigated upland tomato farming in the study area includes high cost of irrigation services (26.0%), high-cost fertilizer (19.3%), high cost of pesticide (20.9%) and high cost of insecticide (18.2%). It was concluded that the respondents are operating at a lost and again the labour cost looking at the high cost incurred from production which clearly shows that there was over utilization of resources especially in the area of labour cost. The study made the following recommendations; efforts should be made to improve access to adequate water for irrigation purposes, there is a need to provide modern irrigation facilities to farmers to improve water management and efficiency, there is a need to promote value addition in tomato farming through processing and packaging to increase the shelf life of tomatoes and reduce post-harvest losses and farmers should be encouraged to formed cooperatives to be united in one voice to have a bargaining power over labour cost and can also make request to government on their needs and access inputs and training from policy support programme to achieve optimal yield.

Algorithm for identifying parameters of production function models using a neural network

The purpose of the work is to ensure the monitoring and reliability of statistical data used for the analysis and forecasting of the production development on the basis of generalized indicators that take into account the volume of resources used and the ways of their use. An algorithm for parametric identification of production functions models from time series of statistical data using generalized regression, which provides the best estimation of the parametric optimization error by the method of least squares, is proposed. In contrast to existing assessment methods, neural networks are used to build models, which significantly expand the technical capabilities of modeling and contribute to improving the accuracy of calculations through the use of neural network technologies. It is shown that in order to solve the problems of this class, it is advisable to use generalized regression neural networks with simple training modes and high modeling accuracy. As a result, it is possible to propose an algorithm for quantitative assessment of the production functions parameters, which consists in the construction of a neural model with its subsequent use to fit the trajectory of the production model of a given structure to the obtained data by means of recurrent estimates of the vector of the desired coefficients at a given initial approximation. The proposed algorithm is demonstrated by estimating the parameters of the Cobb-Douglas production function and the discrete-dynamic model of the consumption function according to the corresponding statistical series. The calculations are performed using the functions of the Neural Networks package of the MATLAB software environment. The algorithm is applicable for quantitative estimation of the production models parameters with complex logical-probabilistic relationships, as well as for obtaining numerical values of target indicators and indicators for assessing the inland water transport development by statistical series and monitoring.

ВИКОРИСТАННЯ ФУНКЦІЇ КОББА-ДУГЛАСА ДЛЯ АНАЛІЗУ ЕКОНОМІЧНОЇ ДИНАМІКИ

The purpose of the study is to enhance the capabilities of analyzing the dynamics and efficiency of the national economy, as well as forecasting its development, based on the use of the Cobb-Douglas production function apparatus. To this end, the article demonstrates that production functions, including the Cobb-Douglas function, are powerful tool for analyzing economic dynamics. The advantages of the Cobb-Douglas function and its application peculiarities are analyzed. Production functions enable the evaluation of production efficiency and the productivity of factors such as labor, capital, etc. They can be used to forecast trends in the national economy's development. However, using the Cobb-Douglas production function can cause some problems and limitations. The article presents four calculation options based on actual statistical data of the Ukrainian economy. The analysis of the calculations revealed that it is advisable to use the following indicators to obtain accurate results. The dependent output variable is gross domestic product at actual prices. The independent variables are the cost of capital investment at actual prices and the effective volume of labor. Based on the calculations, the parameters of the Cobb-Douglas production function for the Ukrainian economy were found. The adequacy of the constructed econometric model and the feasibility of its application for analyzing the dynamics of the national economy of Ukraine have been demonstrated. 93.6% of the variation in the gross domestic product depends on the variation in the effective volume of labor and the variation in capital investment. The economic interpretation of the parameters of the constructed Cobb-Douglas production function is provided. It was concluded that labor-intensive economic growth is occurring in the economy of Ukraine, along with a certain tendency towards intensive economic growth. The constructed Cobb-Douglas model was applied to find a point forecast of the gross domestic product. The values of capital return and labor productivity for the economy of Ukraine were determined. The results of the work can be used to analyze the economic dynamics of indicators of the national economy.

Marital sorting, family output, and wealth inequality

Abstract In this article, we analytically model marital sorting, intergenerational transfers, and inequality in a household optimization model with uncertainty. We modify and apply a ‘sorting, reverse sorting’ numerical approach by Demirtas in the context of marriage market mating, illustrating the robustness of our analytical results. We show that the parameters of the family production function play an important role in driving the path of an economy’s inequality. One finding is that, under assortative mating, factor shares in the family production function positively affect inequality, while under disassortative mating, the relationship between the factor shares and inequality is U-shaped. This and other results that we obtain can stimulate further empirical research, holding potentially important policy implications.

Forever young: where older workers keep on working

AbstractThis paper examines inter-industry patterns of the employment of older workers over the last 20 years to understand where employment opportunities have grown the most. The underlying premise is that firms strategically align their age mix depending on production function and labor cost parameters. The industries that had the largest increases in the percentage of older workers were those that had the broadest pension coverage and those that made the greatest use of high-tech capital. There also is evidence in 2001–07 that the percentage of older workers increased more in the industries most exposed to increased Chinese imports.

Evaluation of technical, allocative and economic Efficiencies of rubber-cassava based farming system In edo state, nigeria

This paper evaluated the technical, allocative and economic efficiency of rubber- cassava intercrop system among smallholder rubber farmers in Edo Sate Nigeria through a survey of 160 rubber farmers in a multi stage purposive and simple random sampling techniques. Data collected were analyzed using budgetary techniques and stochastic frontier production function analysis. Budgetary analysis reveals an average total cos/ha of 93350. S583.44) with N169,560 (S1,059.75) accrues to the farmer as revenue and N76210(S476.31) as gross margin with a net farm income of N70,710(S441.94). The rate of return and return per capital invested were N1.82 and N0.82 showing both viability and profitability of rubber- cassava farming. The Maximum Likelihood Estimate (MLE) of the parameters of the stochastic frontier production function of the sampled farmers revealed that planting materials, agrochemicals, labour and farm size were significantly related with cassava output. The mean technical efficiency (TE) of respondents' was 0.82 with the scope of improving their efficiency by 18%. Education and extension contact were the significant factors that increase the technical efficiency of farmers. The estimates of the parameters of stochastic cost frontier also showed that the cost of planting materials, agrochemicals, depreciation, cost of labour and output were significantly related with cost of production with mean allocative efficiency (AE) of 0.67. Age, education, farming experience and extension contact enhance the allocative efficiency of rubber farmers. The economic efficiency index ranged from 0.18 to 0.85 with the mean of 0.55 indicating wide differentials between the least and efficient farmer with the scope of improving economic efficiency among rubber farmers by 45% in the short-run. Recommendations to improve efficient allocation of resources in a rubber cassava based farming system have been made in the study in the study.

EVALUATION OF THE LATVIAN LABOUR MARKET USING THE COBB-DOUGLAS PRODUCTION FUNCTION AND THE BEVERIDGE CURVE MODEL

INTRODUCTION
 One of the biggest problems in the Latvian labour market is related to insufficient work productivity, but this is an important aspect of sustainable economic growth, and special attention needs to be paid to it from a macroeconomic point of view. Productivity is measured as gross domestic product per hour worked. One of the most important macroeconomic questions is the one that tries to understand how the gross domestic product depends on capital and labour. Cobb-Douglas production function is related to both – gross domestic product and labour market – and, despite being developed more than 90 years ago, it is still an object of interest. There are unresolved issues related to the function, one of which is whether parameters α and β are equal to 1 or not. Considering the long GDP, labour, and capital time series for one country, it has been recognised that the sum does not have to be equal to 1. The aim of this research is to find what parameters of Cobb-Douglas function for Latvia are equal to and evaluate the Latvian labour market using the Cobb-Douglas production function and the Beveridge curve model.
 METHODS
 When evaluating the Latvian labour market using the Cobb-Douglas production function, the statistical data of Latvian gross domestic product, labour market and capital were taken, and multilinear logarithmic regression was performed to evaluate parameters α and β of the Cobb-Douglas production function. When evaluating the Latvian labour market using the Beveridge curve, the statistical data of the unemployment rate and the vacancy rate in Latvia were chosen.
 RESULTS
 When evaluating the Latvian labour market using the Cobb-Douglas production function, the regression analysis gave α + β > 1 (α = 0.74 and β = 1.55). Here, a certain contradiction with the standard scaling condition α + β = 1 arises.
 When evaluating the Latvia labour market using the Beveridge curve model, the analysis showed that the ratio between the unemployment rate and vacancy rate grows during the economic decline periods and drops during the economic growth periods.
 DISCUSSION
 The condition α + β = 1 has been discussed in the literature since the original Cobb and Douglas paper, and the main problem of the discussion is that the clear scaling reasons based on a theoretical explanation of this condition does not meet the experimental data. There is a condition called the scaling condition. If we merge two identical countries in one country that is two times larger, then GDP, capital and labour will be doubled. Cobb-Douglas function can be tested to see how it works in one country. However, when tested empirically on the data taken from one country, the requirement about the sum of parameters being equal to 1 is not met.
 The interest in the values of the parameters of the Cobb-Douglas production function is based on the fact that they affect the labour market equilibrium. Parameter β of the Cobb-Douglas production function is used in the utility function of firms, and the condition of utility function maximisation determines the average wage in the country.

Improvement of Crop Production Planning in Ukraine Using the Cobb-Douglas Production Function

The relevance of the study is conditioned by the need to improve the process of planning the crop production by agricultural enterprises of Ukraine through the construction of a functional relationship between the results of production activities of enterprises and the factors that determine these results. The purpose of the study is to improve the process of planning crop production by agricultural enterprises of Ukraine through the development of an econometric model in the form of a Cobb-Douglas production function. To model the processes of crop production, it is proposed to use the Cobb-Douglas production function, which describes the dependence of the crop production index on the indices of agricultural land acreage and labour productivity. Based on statistical information for 1996-2020, unknown parameters of the Cobb-Douglas production function were found by regression analysis. The high quality of the constructed model is substantiated. High predictive properties of the model are proved. To analyse the efficiency of resource use in crop production by agricultural enterprises, the coefficients of average, marginal products of labour and capital are calculated. The sensitivity of crop production to changes in crop areas and labour productivity is investigated. It is determined that if the index of agricultural areas is increased by 1%, the index of crop production will increase by 0.77%; and if the index of labour productivity is increased by 1%, the index of crop production will increase by 0.81%. An increasing return on the scale of resources spent is revealed, which indicates an increase in production volumes with an increase in the volume of resources in the crop production industry.

Convex non-parametric least squares, causal structures and productivity

In this paper we consider Convex Nonparametric Least Squares (CNLS) when productivity is introduced. In modern treatments of production function estimation, the issue has gained great importance as when productivity shocks are known to the producers, input choices are endogenous and estimators of production function parameters become inconsistent. As CNLS has excellent properties in terms of approximating arbitrary monotone concave functions, we use it, along with flexible formulations of productivity, to estimate inefficiency and productivity growth in Chilean manufacturing plants. Inefficiency and productivity dynamics are explored in some detail along with marginal effects of contextual variables on productivity growth, inputs, and output. Additionally, we examine the causal structure between inefficiency and productivity as well as model validity based on a causal deconfounding approach. Unlike the Cobb-Douglas and translog production functions, the CNLS system is found to admit a causal interpretation.

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

PROFITABILITY OF RED SWEET PEPPER (CAPSICUM ANNUUM L.) PRODUCTION IN FIELD CULTIVATION

The aim of the study was to assess the profitability of red sweet pepper (Capsicum annuum L.) production in relation to incurred labor and capital inputs in selected horticultural farms. The analyzed group consisted of farms producing sweet pepper in traditional cultivation in the districts of Przysucha and Radom. To determine the correlation between income in the analyzed farms and expenditure, in this study, the multiple Cobb-Douglas production function was applied. Data were generated by implementing the cost accounting method for estimating the feasibility of production and it was analyzed by using project evaluation methods, like the Pay Back Period (PBP), Benefit Cost Ratio (BCR), Net Present Value (NPV) and Internal Rate of Return (IRR). The results of the estimation of Cobb-Douglas production function parameters show that the dominant positive impact on the gross return value was the cost of seedlings, irrigation costs and overhead costs. The conducted analyzes showed that the NPV for the investment is PLN 240,148, with a B/C ratio of 1.78. On the other hand, the PBP, in this case, amounts to 1.45 crop season and the IRR reached a level of 22% annually.The sensitivity analysis carried out showed that the most important factors affecting the profitability of pepper production in field cultivation are product prices, seed costs, fertilizer costs and human labor costs.

ANALYSIS OF EFFICIENCY OF TECHNICAL AND FACTORS AFFECTING IN AROMATIC RICE FARMING IN THE SELUMA REGENCY

The research objective is to determine the level of technical efficiency and the factors that influence the level of technical inefficiency, to analyze the relationship between input and output in the production process of aromatic rice farming in Seluma regency.Total number of respondents were 73 farmers who planted Aromatic rice. The Cobb Douglass of Frontier Stochastic approach was used, whereas for the factors that influence the inefficiency function as the initial answer of the above analysis results of the production function parameter were obtained through the Maximum Likelihood Estimation (MLE), with an LR value of 14.3620 which was higher than t table 99% (2.39). It had a significant effect on the 99% confidence level. It was seem that, there was no meaning that all aromatic rice farmers in the regency were 100% efficient. It could be seen that the MLE log-likelihood value of 29.9157 was higher than the OLS log-likelihood value of 22.7347. The lowest technical efficiency value was achieved by the farmers by 0.55 and the highest by 0.97. In the research area, the majority of the use of production factors was efficient, from 73.34% already in the value of efficiency between 0.90-1.00, meaning that 73.34% had approached the maximum efficiency. The result of the disseminated coefficient (R2) of 0.277 could mean a significant effect of 27.7 percent on the inefficiency variable while the remaining 72.3 percent is influenced by other factors not included in this research variable.

Consumption in Polish households - production function parameters and monetary value of non-market goods

Consumption in Polish households - production function parameters and monetary value of non-market goods

Assessment of CES Function Parameters in Oil-Rich CIS Countries

The article analyses balance between the capital and labor market in the CIS countries rich in hydrocarbon resources – Azerbaijan, Kazakhstan and Russia. For this purpose, the impact of capital (fixed assets) and labor (employed population) on the production volume (on GDP) was estimated based on the relevant statistical data from these countries using production function analysis. The parameters of CES production function were determined in the Mathcad system by the nonlinear least-squares method. The subject of the research has enhanced relevance due to the lack of extensive research of the problem posed in the oil and gas-rich countries of the CIS, and the research evaluates the balance between capital and labor markets for the first time in resource-abundant countries. From the results, it can be seen that for each of these three countries the distribution coefficient for capital is significantly higher than that for the labor factor. This means that there is an excess of capital that cannot be started. This is typical for the countries rich in natural resources. The main reason for this process is the complex structure of increasing capital with oil revenues and low level of specialization of the existing labor force to launch this capital. Moreover, according to the results obtained from the CES production function, the substitute elasticity coefficient in oil-rich countries of the CIS is less than one. The study summarizes the current problem as an imbalance between the capital (fixed assets created using modern technology) and the labor market (labor to leverage key assets using potential opportunities). Based on the analysis, the results obtained from modeling is formulated and scientifically grounded recommendations have been provided for the improvement of education and its quality in these three countries, especially in Russia and Azerbaijan.

Identification of generalized Cobb-Douglass production functions with multiplicative errors in variables

The article discusses the identification of a class of generalized Cobb-Douglas production functions with multiplicative errors in all variables. The article proposes a generalization of Cobb-Douglas production functions in the presence of memory for input and output variables. Parametrization of noise in the form of multiplicative noise in all observable variables is proposed. The logarithmic transformation of such production functions leads to the need to solve the problem of estimating the parameters of a linear difference equation in the presence of additive errors in all variables. To identify the parameters of production functions, a modification of the method of total least squares was used. Computational experiments have shown high accuracy of parameter estimation based on the proposed algorithm.