استفاده از شبکه های عصبی در اقتصاد خرد : نقشه برداری ورودی و خروجی در یک سکتور فرعی تولید برق از صنعت برق ایالات متحده

The use of the artificial neural networks in economics and business goes back to 1950s, while the major bulk of the applications have been developed in more recent years. Reviewing this literature indicates that the field of business benefits from the neural networks in a wide spectrum from prediction to classification, as most of the applications in economics primarily focus on the predictive power of the neural networks. Time series analysis and forecasting, econometrics, macroeconomics constitute the main areas of economics, where there is an increasing interest in application of neural networks. Although their promising contributions to the area of microeconomics, the applications of neural networks in this area are limited in number. This study provides a microeconomic application of an artificial neural network by input–output mapping for 82 US major investor-owned electric utilities using fossil-fuel fired steam electric power generation for the year 1996. We construct a multilayer feed-forward neural network (MFNN) with back-propagation to represent the relationship between a set of inputs and an electricity production as an output. The network is trained and tested by using approximately 80 percent and 20 percent of the data, respectively. The network is trained with 97% accuracy and performance of the network in testing is 96%. Therefore, this network can be used in calculating electricity output for the given inputs in this subsector of the US electricity market, and these estimations can be employed in policy design and planning.

The applications of neural networks in business and economics have been increasing for the last decades. Within this literature, the studies are mostly concentrating on business-related problems. Wong, Bodnovich, and Selvi (1997) reviewed 213 journal articles in business from 1988 to 1995 and classified them into the following fields: accounting/auditing, finance, human resources, information systems, marketing/distribution, production/operations, and others. Among the reviewed articles, production/operations and finance were the top two fields in which the neural networks are used as application tools, with the shares of 25.4% and 53.5%, respectively. Neural networks were compared with the traditional methods in related fields in 38.5% of the 213 studies. Similar to Wong et al. (1997), a more updated rather concentrated literature review was provided by Vellido, Lisboa, and Vaughan (1999) on the applications of neural networks in business between 1992 and 1998. The study reviewed research related to management, marketing and decision making finding a particular interest in financial forecasting and planning since the early 1990s and the application of neural networks in these fields were relatively large in number. Consequently, surveys find strong evidence that there has been a significant effort to use neural networks in mathematical forecasting and time-series prediction. While the applications in various fields entail the use of prediction, estimation and classification power of the neural networks, most of the applications in economics focus on prediction power. Time series modeling and forecasting, non-parametric estimation, learning by economic agents, finance, macroeconomics and econometrics are some of the areas in economics studying the possible uses and associated benefits of neural networks. Noting considerable interest in application of neural networks in economics particularly in financial statistics and exchange rates, Kuan and Liu (1995) used feed-forward and recurrent neural networks to investigate nonlinear patterns in exchange rates and test the performance of the selected networks in forecasting. In another area addressing economic prediction, Tkacz (2001) employed neural networks to determine more accurate leading indicator models of Canadian output growth by analyzing the forecast performance of multivariate neural networks and finding that there are gains in the short-run forecast accuracy of the neural networks in comparison to the best linear model due to the neural networks’ ability to capture non-linear relationships in the data. Heravi, Osborn, and Birchenhall (2004) used neural networks and linear models to forecast seasonally unadjusted monthly real industrial production data of important sectors of German, French and UK economies. They compared the forecast performance of the neural networks with linear models and found that while linear models outperform the neural networks up to a year forecasts, the neural networks perform better than the linear models in predicting the direction of change. Nakamura (2005) assessed the usefulness of neural networks in inflation forecasting and found that the neural networks outperform univariate autoregressive models in predicting short-horizon of one and two quarters inflation rates. In the light of the literature review of the recent publications, there are a relatively small number of applications of neural networks in economics (relative to business), mostly in macroeconomic forecasting, econometrics and time series analyses, and there is still a lack of both theoretical and empirical studies in microeconomic applications. There are few applications of neural networks in microeconomics. Hippert, Bunn, and Souza (2005) used neural networks in forecasting electricity load profile. In comparison to conventional regression-based models, the authors find that the large neural networks perform well. Another interesting application of neural networks is in forecasting of employment at regional level (Longhi, Nijkamp, Reggianni, & Maierhoffer, 2005). Longhi et al. compared neural networks with commonly used methods in panel data analysis. Santin, Delgado, and Valino (2004) reviewed the application of the neural networks in measuring the technical efficiency and compare traditional approaches, econometric models and non-parametric methods with neural networks. Upon comparing traditional methods in efficiency analysis, parametric and non-parametric techniques, with neural networks, they found that the neural networks are possible alternatives to the existing tools in measuring technical efficiency. Similarly, Delgado (2005) employed the neural networks for efficiency analysis in public sector, refuse collection services, and found that it was useful to employ the neural networks as complementary tools in efficiency analysis. In addition to the aforementioned studies, the neural networks are employed in few other areas such as productivity analysis (Boussabaine & Duff, 1996), identifying market structures (Gruca & Klemz, 1998), and estimating marketing margins (Mainland, 1998). As these studies indicate, the neural networks can be useful tools in mapping and estimation problems in microeconomics. 1.1. Estimating relationships in economics In the theory and practice of econometrics, the model, the method and the data are interdependent associations in both information recovery and inference. How to develop “reasonable” quantification of economic relationships is the challenge facing the applied business and economic analysts. Oftentimes, the economic analysts are dealing with a non-experimental data generation process and the models that are used involve forces that are unobserved and even not capable of direct observation.2 Classical econometric approaches pose a parametric form, y = Xβ, where the covariates X determine the level of y which is measured noisily, with β being the unknown weights to be determined. To account for the indirect measurements and forces that are not measured, a noise component, ε, is appended linearly. The probabilistic structure of ε is a critical focal point in econometric specification and estimation (Greene, 2007). This classical approach to generalizing estimates of the unknown parameters β focus on the statistical inference of the estimated parameters. When there is not enough information contained in the covariates, X, and the noisy data y to permit recovery of estimates of β by classical regression techniques, the model is said to be ill-posed and maximum entropy methods emerge as an alternative. Ill-posed problems may arise when the number of unknown parameters exceeds the number of data points. In this case, traditional estimation methods cannot be used unless restrictions on a sufficient number of parameters are imposed so that the remaining ones can be estimated (Golan, Judge, & Miller, 1996). However, these restrictions may lead to erroneous interpretations and conclusions. The maximum entropy (ME) formalism reveals a powerful tool that provides the “best” conclusions possible based on the data at hand (Golan et al., 1996). When one knows little about the functional form of the relationship being estimated and the number of covariates is small, nonparametric regression methods can have much to offer (Li & Racine, 2007). In the end, this is a search for a specification that can legitimately be used to bring to the surface the flashes of value that may be buried in the data, Leamer (1978) embarked on the classification and characterization of specification searches and a meta-statistical perspective, where the analysts opinion, motives and even biases, influence the choice of model and data. The neural network approach to econometric modelling emerges as a natural progression in the development of a modelling framework to describe economic relationships with a view toward prediction and description of economic decision making structures. Kuan and White (1992) provide a detail discussion on the use of neural networks in econometrics. When building microeconomic models, the use of functional forms to represent the relationship among the variables is important, e.g. estimation of elasticities, neural networks can be used to guide the modeling process. If the use of functional forms is not the primary concern for the analyses, the neural networks themselves can be used as models or model builders. Neural networks can provide assistance in constructing more realistic models by helping characterizing and formulating nonlinearities among the model variables and can strengthen the model specifications. This complementary use of neural networks benefits the field of econometrics (Lee et al., 1993 and Kuan and White, 1992). The importance of this benefit is more pronounced as the number of inputs and outputs increase (Santin et al., 2004). As the integration of markets has increased and economic activities have become more sophisticated, the volume and the complexity of data have also increased. The ability of neural networks working with large number of data in existence of nonlinearities certainly provides advantages to microeconomic modelers. Moreover, there is no doubt that the applications of neural networks in forecasting or predicting economic variables are very important, but equally important is the use of neural networks in estimation of economic variables. Microeconomic agents, institutions as well as individuals, face economic decisions which are multi-dimensional and complex. Furthermore, these decisions do not only have implications for the society as a whole, but also have implications on the distribution of welfare. For example, a regulatory decision may alter societal overall welfare and its allocation through reduced output and pollution. Various microeconomic decision units employ a variety of quantitative techniques in modeling real life scenarios and rely on these techniques to develop their strategies. Given the multifaceted effects of microeconomic decisions on the society, the decision-making processes of economic agents require precision and accuracy in estimations of microeconomic variables and simplicity in handling of nonlinearities. In order to fulfill these needs in decision processes, economists have started to develop and used more advance statistical and mathematical techniques to process and analyze data. Among the techniques, the neural networks stand as a promising tool. As Hill, Marquez, O’Connor, and Remus (1994) states neural networks can be valuable tools if there are nonlinear elements in the decision problem or when some of the other advantages of neural networks are important in a given application. A disadvantage of the neural networks is the selection of the architecture, where these selections have implications on empirical results. Trial and error process in determining the structure of the neural networks and algorithm convergence are the drawbacks (Santin et al., 2004). In addition, when the data is not large enough, the neural networks can learn the noise and overfit the data. Moreover, may be the most important drawback for microeconomic modeling, is the lack of structures where economic interpretations can be attached to. This also holds for forecasting, i.e. the neural network models are harder to interpret than many forecasting models (Hill et al., 1994). The primary advantage of the neural networks for the microeconomists is that the use of neural networks in input-output mapping does not require functional form specification for characterization of the relationship. Their flexible forms do not require to imposition of functional forms on the data. The neural networks can estimate, predict, or forecast economic variables with less number of assumptions about the relationship among the variables and the data. Therefore, the neural networks are important tools when these relationships are unknown (non-parametric method) and non-linear (non-linear method) (Santin et al., 2004). The neural networks are usually applied in economics when the theory does not provide any information in regard to the functional forms used in modeling the data. If the primary objective is to forecast values of variables rather than the estimation of the functional forms, the neural networks are the preferable tools (Papadas & Hutchison, 2002). Some disadvantages become the advantages depending on the nature of the problem under study (Santin et al., 2004). In this study, we map the sets of inputs to an output set in a subsector of US electricity industry, and estimate the production levels to be used possibly in microeconomic analysis, such as policy making or supply planning in deregulating and regulating the electricity market. Neural networks are intensively used in short-term electricity load forecasting during the past few years and in over 30 US electric utilities, and the artificial neural network-based load forecasting is a regular practice. Furthermore, opening the electricity market to competition induces an increase in value of accurate load forecast due to profit dynamics (Hippert et al., 2005). Similarly, it also increases the value of high performance in estimating production levels or capacities of the utilities. Regulators in planning and managing electricity supply and demand in deregulated markets need these accurate estimates for their scenario analyses. To illustrate the possible use of the neural networks in microeconomic analysis, we construct an input–output mapping for the investor-owned fossil fuel-fired steam electric power generation by using MFNN with backpropagation. Production data consists of three inputs, namely fuel, labor and maintenance, and capital, and an output, electricity production, for 82 utilities. The MFNN is designed and then trained with approximately 80% of the observations from the data set. Then, we used the network to estimate the electricity production of 14 utilities which are introduced to the network for the first time. The performance of the network is then tested by using regression analyses. We found that the neural network explain the relationship between the inputs and the output, and estimate the production levels of the utilities with a high level of accuracy. The structure of this paper is as follows. Section 2 gives a brief description of the data, while Section 3 reports the method in use. The results for input-output mapping and estimation analysis are presented in Section 4. Some conclusions are drawn in Section 5.

The neural networks are available tools for economists to estimate, predict and forecast economic variables. If modeling economic data does not require any specification of certain functional forms or exact form of functions are not know, the neural networks are good alternatives to the existing tools. Within the field of economics, econometrics, times series analysis and forecasting, finance and macroeconomics are the areas increasingly benefiting the neural networks in social sciences. Despite the growing interest for the neural networks in these fields in economics, there is relatively small number of applications in the field of microeconomics. In microeconomic analyses where the accuracy of estimations of variables is one of the most important criteria in determining the success of decision making, such as welfare analysis, regulatory design, the neural networks can be very beneficial tools. In this paper, we performed an application of neural networks in microeconomics. Our first objective was to specify a neural network structure to do input–output mapping for the investor-owned utilities using fossil fuel-fired steam electric power generation in US electric industry. After defining the appropriate neural network structure, our second objective was to accurately estimate the electricity production for a set of utilities. We used a MFNN with backpropagation algorithm. The network we designed has three input neurons, linked to a hidden layer with nine neurons through connections, and an output neuron. We estimated the electricity production of 14 utilities in the subsector of US electricity industry. In order to measure the performance of the network, we post-processed the data and conducted the regression analyses. In other words, we run linear regressions between the network outputs and the actual outputs for training, validation and test data. The correlation coefficients between the actual outputs and their corresponding neural network estimates are 0.97, 0.99 and 0.96 for training, validation and testing. Given the regression results and the correlation coefficients, we can conclude that our MFNN estimates the production relations between inputs and outputs accurately and it has a high performance in out of sample estimation. We believe that application of this sort can enhance microeconomic analyses and modeling, especially in policy making arena. Furthermore, for relatively more theoretical applications where the specification of function forms has particular importance, the neural networks can be useful in guiding the model building and functional form specification processes. In addition to the value-added they provide through accurate estimation of the economics variables, neural networks can be excellent complementary tools for traditional analyses in microeconomics that focus on identifying the structure of economic decision making by addressing cost function estimations, frontier analyses, and efficiency decomposition and analyses. So far the progress in the literature is slow. A useful future investigation is the possibility to use neural networks in estimation of production and cost functions together with parametric and nonparametric methods used in microeconomics. This line of work could provide information on the structure of the production decision making, such as returns-to-scale, homotheticity, and technical change, as well as the performance of these traditional techniques.