Aggregate Production Function Research Articles

What can we learn from industry-level (aggregate) production functions?

ABSTRACT Recent work has revived two intertwined challenges to aggregate production functions (the ‘identity’ and ‘aggregation’ problems). This paper examines both problems in the context of aggregate industry-by-country analysis, first demonstrating the relevance of the identity problem for industry-level analysis and tracing its origin in the System of National Accounts. Using a case study of materials quality in global forestry and logging, the paper then compares estimates from fully physical versus conventional (monetary) production functions to isolate the aggregation problem and show that credible inference depends on appropriately modelling heterogeneity in production processes. Materials quality is measured via finite mixture modelling applied to global satellite data. Attempting to estimate the parameters of a common production technology yields poor results, because of differences in production processes between countries. The paper offers a practical approach for dealing with heterogeneity via Data Envelopment Analysis and heterogeneous coefficient panel estimators, and concludes with guidance to help applied industry-level analysis recognize and avoid both the identity and aggregation problems.

The Aggregate Production Function and Solow’s 'Three Denials'

The Aggregate Production Function and Solow’s 'Three Denials'

Intelligent System of Estimation of Total Factor Productivity (TFP) and Investment Efficiency in the Economy with External Technology Gaps

This paper is the first to propose an aggregate S-trend factor production function to estimate total factor productivity (TFP) and investment efficiency in an economy. This function implements Charles R. Hulten's organizing principle: to what extent the growth of the economy is due to an increase in "productivity" (progress in technology and organization of production) and to what extent to "capital formation" (increased investment in human capital, knowledge and fixed capital). Estimation of future members of the series is usually done by a forecast model. It is a model that approximates a trend. The Verhulst's S-curve is used as the approximation function. Here A, B ,a are the parameters that change the shape of the S-curve, u, m are the parameters that change the position of the S-curve in the first quarter, t≥0. By aggregate S-trend production function we mean a two factor production function of the form z(t)= Here the function It represents the growth of the economy, which is by raw data and takes into account all influencing factors, and is certainly broader than the concept of " capital formation ", is a total factor productivity TFP. The error of approximation is quantitatively measured by the MAPE criterion.

Profitability and factors affecting production of pond fish culture under NATP project in Tangail district of Bangladesh

Profitability and input use efficiency of pond fish culture was studied at farming systems Research and Development (FSRD) site, Atia, Tangail from July 2019 to June 2020. The average pond fish production was recorded at 2808 kg/ha/year with the highest yield from the medium farms (2940 kg/ha/year) and lowest yield from marginal farms (2624 kg/ha/year). The highest gross return (Tk 352,800/ha) was found with medium farmers followed by small farmers (Tk 343,200/ha). The benefit cost ratio was also recorded higher (2.08) in marginal and small farms. Considering the aggregate production function for all groups of farmers, it was found that inorganic fertilizer, organic fertilizer, feed and human labour were statistically significant in explaining the variation in pond fish output but the results varied with different farm categories. Since there was positive correlation between input use and production of fish, it is probable that an increase in application of inputs could increase production further.
  

Optimal allocations in growth models with private information

AbstractThis paper considers a class of growth models with idiosyncratic human capital risk and private information about individual effort choices (moral hazard). Households are infinitely-lived and have preferences that allow for a time-additive expected utility representation with a one-period utility function that is additive over consumption and effort as well as logarithmic over consumption. Human capital investment is risky due to idiosyncratic shocks that follow a Markov process with transition probabilities that depend on effort choices. The production process is represented by an aggregate production function that uses physical capital and human capital as input factors. We show that constrained optimal allocations are simple in the sense that individual effort levels and individual consumption growth rates are history-independent. Further, constrained optimal allocations are the solutions to a recursive social planner problem that is simple in the sense that exogenous shocks are the only state variables. We also show that constrained optimal allocations can be decentralized as competitive equilibrium allocations of a market economy with a simple tax- and transfer scheme. Finally, it is always optimal to subsidize human capital investment in the market economy.

Substitutability between older and younger workers and its implications for Japan

PurposeThis study investigates the impact of the increasing proportion of older workers in the workforce by establishing a theoretical framework and estimating the degree of substitutability between them and their younger counterparts.Design/methodology/approachThe first step is to establish a theoretical framework that combines older and younger workers with imperfect substitutability in the production of final goods within an aggregate production function. The author then derives an equation that relates the relative wage, relative supply and elasticity of substitution between the worker types, for use in estimation. Using data from Japan’s Basic Survey on Wage Structure and Population Census from 2010 to 2019 across 47 prefectures, the author estimates the elasticity of substitution between older and younger workers in Japan.FindingsThe author finds that workers aged 55 and over and their younger counterparts are gross substitutes, and the estimated elasticity of substitution is in the range of 2.33–2.86. This implies that a 10% increase in the relative number of workers aged 55 and older leads to a fall in their relative wage in the range of 3.5–4.3%. The study estimations suggest that since 2010, there has been a convergence in the relative wage of older workers across Japan’s prefectures.Originality/valueUnderstanding the degree of substitutability between older and younger workers is essential for quantitatively assessing the impact of workforce aging, technological advancements and labor policies on the wage distribution. This study estimates the elasticity of substitution between the two worker types based on a theoretical model, and utilizes recent datasets and methodology not adequately addressed in previous literature.

Automation and economic growth in a task‐based neoclassical growth model

AbstractThis paper incorporates a task‐based approach into the Solow growth model to analyze the effects of automation on economic growth. We find that if task producers smoothly adopt automation technology along the capital accumulation path, sustained growth is possible even without technological progress. This result is brought about by the fact that task automation makes the aggregate production function linear. In addition, we demonstrate that both the rental price of capital and the wage are constant on the growth path. In sum, while the interaction between task automation and capital accumulation can be a pathway for sustained growth in output, it leads to the cease of wage growth in the long run.

A Nexus Among Technology Input, Research Activity, Innovation, and Economic Growth: A vis-à-vis Analysis between Asia and Europe

This study attempts to analyze the influence of technological infrastructure development and the spill-over effect of dynamic growth of technological innovation on the Asian and European economies. Compared to European countries, the economic infrastructure of Asian countries has transformed significantly during the last three decades. Technological progress and higher growth of available engineers and researchers have become pivotal endogenous determinants in the aggregate production function and eventually became the key drivers of economic growth. Compared to European countries, rapid investment in technology import and a higher number of technologically competent available workforce galvanized uplifted and speedy productivity rates, causing positive economic growth in the Asian economy. The interrelation between technological progress and economic growth is summarized and analyzed by using quantitative methods. The paper stu­dies the nexus between technological progress, the availability of engineers and researchers, and economic growth by applying the dynamic Generalised Method of Moments (GMM) method to the available quantitative data (2013-2017) of chosen Asian and European countries. The econometric results show a significant effect of technological progress and innovation on economic growth. The empirical insight is of particular interest to policymakers as it helps to enhance internal and external technology and innovation development policies for sustainable economic growth in Asian and European countries.

Smallholders Are Not the Same: Under the Hood of Kosovo Agriculture

Economists and policy makers are interested in producers’ responses to policies in order to achieve some national or sectoral objectives, e.g., growth, employment, food security. The way producers respond to policy depends on their production function. If producers do not have homogenous production function, policy responses will be heterogeneous. We use the underlying functional relationship to derive homogenous groupings. The paper employs finite regression mixture models to specify and estimate farm groups with regard to pre-specified functional relationship. The proposed approach is illustrated with regard to the aggregate production function of Kosovo agriculture, characterised by high prevalence of small farmers. The results point out to two farm clusters. The first one extracts more output from labour and intermediate consumption. The second one makes a better use of land. Perhaps, surprisingly, both clusters appear quite similar in terms of their stock of production inputs. Cluster 1 however appears to be more specialised. We can conclude that in Kosovo agriculture appearances and size are not primary determinants of productivity.

ВЛИЯНИЕ ИНВЕСТИРОВАНИЯ В ОСНОВНОЙ КАПИТАЛ НА СОЦИАЛЬНОЭКОНОМИЧЕСКОЕ РАЗВИТИЕ РЕГИОНА

The article analyzes the problem of the development of regions as socio-economic systems under the influence of the factor of investment in fixed assets. Using the example of the Central Federal District regions, the differences between regions in the level of per capita GDP by region are investigated, depending on the per capita investment in fixed assets. The article concludes that there is a need for economic justification of regional and interregional investment programs based on the aggregated production function of the region, which allows a differentiated approach to each region depending on the current conditions of its development.

Alternative specifications of human capital in production functions

In this paper we argue that some empirical specifications may not be appropriate to estimate accurately the returns to human capital. In particular, we show that the inclusion in aggregate production functions of the ratio of skilled labor force over total labor force as a proxy for human capital may not be a good way to control for the heterogeneity of labor.

Construction of an aggregated production function with implementation based on the example of the regions of the Central Federal District of the Russian Federation

A three-dimensional case is considered on the basis of a method developed for estimating the parameters of the aggregated production function used to calculate dynamic standards and build integral indicators of the performances of the functioning of socio-economic systems. The aggregated production function is determined by the quadratic convolution of the production functions of the results of the functioning of the elements of the subsystem and their correlation matrix. The parameters of the aggregated production function are determined from solving the problem of maximizing the likelihood function of a random variable – the residuals of production functions aggregated according to a similar rule. On the example of a project subsystem within the framework of the Kleiner’s spatial-temporal classification of socio-economic systems we obtained adjusted values of the parameters of a function that includes power-law multiplicative models of the relationship between the volume of gross domestic product by region for sections F (construction), G (wholesale and retail trade), K (financial activity) according to NACE 2 and the cost of fixed assets (total for section K, for sections F and G), the average annual number of employees (for sections F and G) and the average annual population (for section K), based on data for 2015–2020 (sections G, K) and 2018–2020 (section F) for the regions of the Central Federal District. The EFRA software package and Python’s project were used as tools. The results obtained can be used by regional authorities in assessing the functioning of the regions and the formation of appropriate standards in the short term.

Combining aggregate production function and technical efficiency: Indonesian case study

Besides frontiers and Data Enveloped Analysis approaches, a combination between the aggregate production function and technical efficiency can be performed using the Corrected Ordinary Least Square approach. Unfortunately, there are no studies in Indonesia that use this approach. This paper mainly studies how the Corrected Ordinary Least Square approach combines aggregate production function and technical efficiency. The methods are aggregate production function modeling, aggregate production function correcting, and technical efficiency measuring. The data are Gross Regional Domestic Product at a constant price, the number of workers, investment expenditure, education, and health data of Indonesian provinces from 2015 to 2020. There are three results. First, the Indonesian fixed effect panel data aggregate production function is the best model. In this model, Gross Regional Domestic Product at a constant price is influenced by the number of workers, investment expenditure, and human capital. Human capital consists of education and health level. Second, the deterministic frontier aggregate production function shifts the best-fixed effect model so that the constant becomes –15.36. Third, the Indonesian technical efficiency when no factors influence inefficiency is on average 0.9936. All the results indicate that human capital, aggregate production and technical efficiency combination, and the Corrected Ordinary Least Square approach are practical values.

An Evolutionary Game to Model Offshoring and Reshoring of Production Between Developed and Developing Countries

A dynamic model is proposed to describe the time evolution of production location choices of a multinational enterprise that can decide between two possible manufacturing locations: a stylized developed economy and a developing economy. The model is based on an evolutionary approach according to a replicator dynamics driven by expected profits. The production in each country is determined by the availability of labor inputs and their relative productivity, on wages of skilled and unskilled workers, as well as on cost externalities due to knowledge spillovers and public goods availability. The model includes the effects of relative demand and supply on earnings distribution with two different types of workers (high and low skilled) and the substitution between the two categories is captured by a CES aggregate production function. Behavioral parameters are also considered, such as the cognitive bias that overestimates the convenience of offshoring in term of labor cost and the “made in” effect that brings consumers to pay higher prices for products manufactured in a developed country.

Using the aggregate production function to determine the sources of economic convergence of voivodships in Poland

The article deals with economic convergence, which has long been one of the most important issues in the field of economics. The aim of the study is to identify the factors which determine the economic convergence of voivodships, i.e. provinces (and more specifically, factors responsible for the regional differentiation of GDP per working person) and to assess the strength of their impact. The study was conducted for the years 2014–2019 on the basis of data provided by the Local Data Bank of Statistics Poland. The aggregate production function of the Cobb-Douglas type was used. It allows the influence of the accumulation of production factors to be separated from the influence of the changes occurring in the applied technology on economic growth in voivodships and, consequently, on the process of economic convergence. The achievement of the aim of the research necessitated the decomposition of the aggregated production function. The results of the study did not confirm the occurrence of economic convergence in voivodships. A tendency was observed for the regional differentiation of the GDP per working person to deepen during the examined period, which resulted from the differences in the spatial accumulation of physical capital and technological progress.

From reswitching to zero substitution: A surprising turn in the debate on capital theory

Abstract The focus of debate on capital theory still is on the macroeconomic aggregate production function, almost seventy years after Joan Robinson attacked this concept. It has turned out that reswitching is rare in large systems. Reswitching and reverse capital deepening once were the most effective arguments against the production function. Later it was shown that an approximate surrogate production function could be constructed, using the approach of random matrices. This seemed to weaken the critique, but a new one has emerged, which shows that the number of effective techniques on the wage curve is small and that the possibilities of substitution between capital and labour are quite restricted in the relevant range or profit. This paper reconstructs the path by which the new results were arrived at and presents a new variant of the proof of zero substitution.

The Impact of Renewable Energy Supply on Economic Growth and Productivity

The threat of the negative consequences of global warming makes the discussion about the relationship between economic growth, productivity, and increasing renewable energy involvement an important topic. Hence, the aim of this study is to analyze the impact of renewable energy and energy supply on economic growth and productivity at the national level using stochastic frontier analysis and the aggregate production function framework. In doing so, we analyzed a panel of annual data from 133 countries from 2008 to 2014. We apply a generalized stochastic frontier model, which allows us to differentiate between persistent and transient inefficiency, as well as individual effects. Our results indicate a threshold level in terms of a country’s development that needs to be obtained to benefit from increasing renewable energy involvement over time. However, if this threshold level is obtained, productivity gains are evident. We also found that the role of the energy supply in aggregate production is nontrivial. That is, its inclusion changes the relationship between key input factors (capital and labor) by decreasing their overall elasticities and increasing the observed economies of scale.

After the Cambridge Controversies: Reflections Old and New

Abstract Perfect foresight is a consequence of applying the Pontryagin Maximum Principle to the analysis of an intertemporal general equilibrium. For this reason, the capital theory controversy ended in an intellectual impasse. The critique of mainstream theory largely ignored the perfect foresight entailments of intertemporal equilibrium analysis, while its defenders, with notable exceptions, too often failed to acknowledge this implication of the technique of dynamic programming. From this standpoint, the long debate over the existence or non-existence of an aggregate production function is secondary. This leaves open the theoretical question of how to proceed with an analysis of the actual dynamics of capitalist development. The critique of mainstream capital theory remains a ‘prelude’, caught up in an ever deeper analysis of the implications of alternative representations of the technique of production. The first part of this paper deals with the question of how perfect foresight came to infect mainstream theory; the second part turns to a consideration of a weakness in the dual representation of the technique of production in the simplest Sraffian framework. Neither part addresses the bigger questions of how to analyze the process of uneven development under the capitalist rules of the game.

What Remains of the Cambridge Critique? A New Proposal

Abstract The debate on capital theory is no more about the historical formation of neoclassical ideas in their original, most abstract form, but about the tools—certainly influenced by those ideas—which are used in teaching applied economics. One focus still is on the economy’s aggregate production function, almost 70 years after Joan Robinson attacked this concept. It has turned out that reswitching—once the most effective argument against the production function—is rare, and that an approximate surrogate production function can be constructed, using random matrices. This seems to weaken the critique, but a new one has emerged, which shows that the number of effective techniques on the wage curve is small and that the possibilities of substitution between capital and labour are quite restricted in the relevant range.

Should the government subsidize innovation or automation?

AbstractThis study introduces automation into a Schumpeterian growth model to explore the effects of R&D and automation subsidies. R&D subsidy increases innovation and growth but decreases the share of automated industries and the degree of capital intensity in the aggregate production function. Automation subsidy has the opposite effects on these macroeconomic variables. Calibrating the model to US data, we find that raising R&D subsidy increases the welfare of high-skill workers but decreases the welfare of low-skill workers and capital owners, whereas increasing automation subsidy increases the welfare of high-skill workers and capital owners but decreases the welfare of low-skill workers. Therefore, whether the government should subsidize innovation or automation depends on how it evaluates the welfare gains and losses of different agents in the economy.