Econometrics

conometrics can be defined as the application of mathematical statistics tools, and related techniques, to economic problems such as the analysis of economic data and the testing of economic theories and models. Although economists are not often able to collect primary experimental data, econometric tools are available that can readily be applied to secondary data, whether they be cross-sectional or time series in nature. In some ways, the analysis of this type of secondary data gives economists a better understanding of real world phenomena and processes than would more controlled -- but smaller in scope -- experimental studies that allow for the manipulation of variables. The combination of secondary data and econometric data allow economists to develop and test empirical models to better understand economies and make forecasts.

Economics is a social science focusing on the creation, allocation, and utilization of goods and services; the distribution of wealth; and the allocation of resources as well as the theory and management of economic systems. One of the primary goals of economics is to understand and explain how economies work and how economic decisions are made. To advance understanding in these areas, economics is concerned with the theories, principles, and models of economic systems. As a result, many economists are engaged in the development, testing, and application of economic theories with the ultimate goal of being better able to understand and predict real-world behavior. To help in such endeavors, economists apply the scientific method to better parse the large quantities of data available and understand the processes that underlie their action.

Testable Theories

To help them better understand the nature and actions of economies, economists are concerned with the development of testable theories and concomitant models that are based on empirical evidence. As shown in Figure 1, the theory building process begins with inductive reasoning in which inferences and general principles are drawn from specific observations or cases. This type of reasoning is a foundation of the scientific method and enables the development of testable hypotheses from particular facts and observations. For example, one might observe that employees with greater levels of training and education are more likely to have successful careers. However, unless one is able to operationally define these terms and articulate the exact theorized nature or the relationship between the variables of training/education and career success, this preliminary theory is nothing more than an opinion. Although it may be a considered opinion based on empirical evidence, un-testable theories are of little use to science on their own. The theory building process, therefore, goes on and builds on the work of the inductive reasoning process by applying deductive reasoning. This is a type of logical reasoning in which it is demonstrated that a conclusion must necessarily follow from a sequence of premises, the first of which is a self-evident truth or agreed-upon data point or condition. Deductive reasoning is the foundation upon which predictions are drawn from general laws or theories.

Inductive & Deductive Reasoning

As shown in Figure 1, both inductive and deductive reasoning are essential to the theory building process. Without careful observation of real-world phenomena and the development of these observations into testable theories and models, economics -- or any science -- cannot advance. Although one may be convinced, for example, that training and education are positively linked with eventual career success and salary, unless one can articulate a testable hypothesis and subject this preliminary theory to the rigors of the scientific method, this theory cannot be confirmed. For example, even in this simple example, there are many other variables that may influence career success such as job experience, intellectual capacity, native skills and abilities, and interest. Depending on their importance in determining career success, they, too, need to be included in the model.

Econometrics

To determine whether a model actually adequately and accurately reflects the phenomena and processes of the real world, it needs to be tested. Econometrics is a subfield of economics that is concerned with the application of quantitative tools to analyze economic data, validate theories, and test models of economic behavior. Econometrics is more than the mere measurement and capture of economic data as the word implies. Econometrics can be defined as the application of the tools of mathematical statistics and related techniques to economic problems, including the analysis of data and the testing of theories and models. Econometric tools are used to estimate economic relationships, test economic theories, evaluate economic policies, and forecast important macroeconomic variables (e.g., interest rates, inflation rates, gross domestic product). Econometric testing is an important component of economics because it helps economists to determine the adequacy and accuracy of their theories. Without econometrics and the objective checks that it provides for the reasonableness of models, it would be difficult (if not impossible) to test the validity of economic models and their strength in forecasting real-world situations. The application of econometrics to test economic theories and models is an important part of the theory building process for economics.

Secondary Analysis

In the physical sciences, one can often experimentally manipulate variables to establish the relationship between the independent variable and the dependent variable. For example, in metallurgy, one might be interested in the strength of a given metal after being subjected to various temperature ranges. In the social sciences -- including economics -- however, the direct manipulation of variables is often not possible not only for logistical reasons (e.g., difficulty collecting data, inability to manipulate variables), but for ethical ones as well. For example, not only would it be logistically impossible to deprive the people in a given country or economy from the education they need to succeed in a career, such an action would be considered morally and ethically reprehensible as well. Therefore, economists and other social scientists are often forced to rely on secondary analysis in order to collect data and test their theories. Secondary analysis is a further analysis of existing data that have typically been collected by a different researcher. The intent of secondary analysis is to use existing data in order to develop conclusions or knowledge in addition to or different from those resulting from the original analysis of the data. Secondary analysis may be qualitative or quantitative in nature and may be used by itself or combined with other research data to reach conclusions.

Types of Data

To develop and test practical models to be used in forecasting, most economists rely on two types of data: cross-sectional and time series. Cross-sectional data are quantifiable observations or measurements on a wide variety of variables during one time period rather than across time periods. For example, one might be interested in the training and education level of individuals from a representative cross-section of the general population in order to determine the relationship of training and education to career success. Therefore, one would look not only at assembly line workers in the garment industry, for example, but across industries and along all career levels as well. Otherwise, the theory -- even if validated -- would only be applicable to assembly line workers in the garment industry. The second type of data commonly used by economists is time series data. These are data gathered on one or more specific characteristics of interest over a period of time at intervals of regular length. These data series are used in business forecasting to examine patterns, trends, and cycles from the past in order to predict patterns, trends, and cycles in the future. Time series analysis typically involves observing and analyzing the patterns in historical data. These patterns are then extrapolated to forecast future behavior.

Random Sampling

Whether the economist uses cross-sectional or time series data, it is important that the data be randomly sampled. Rather than collecting data from a group from which it is easy to collect data but that has a low likelihood of representing the population that one wishes to test, one instead should take a sample of individuals from the larger group that reflects the characteristics of the larger population. A random sample is a sample that is chosen at random from the larger population with the assumption that such samples tend to reflect the characteristics of the larger population. The sample that is selected in this way can then be used in econometric analysis to represent a cross-section of the population as a whole. It is very important that sample selection allows one to draw a sample that is representative of the population and the characteristics in which one is interested. Otherwise, the sample may be biased and the results of model will not represent the results that would have been obtained from the population in general.

Applications

Data Patterns

One of the major uses of econometric methods is in the development and testing of models that can be used to forecast how behavior patterns will continue into the future. In this meaning of the term, models are a concise mathematical description of past events. To develop such models, time series are analyzed through several techniques including naïve methods, averaging, smoothing, regression analysis, and decomposition. These econometric techniques assume that the sequence of observations is a set of jointly distributed random variables. Through the analysis of time series data, one can study the structure of the correlation (i.e., the degree to which two events or variables are consistently related) over time to determine the appropriateness and usefulness of the model in predicting future behavior.

Stationarity, Trends & Business Cycles

Time series data can take several distinctive forms. As shown in Figure 2a, sometimes data remain fairly constant over time and are said to be constant about the mean (an arithmetically derived measure of central tendency in which the sum of the values of all the data points is divided by the number of data points). This characteristic of the data is referred to as stationarity. If a process is assumed to be stationary, the probability of a given fluctuation in the process is assumed to be the same at any given point in time. If time series data do not demonstrate stationarity (see Figure 2b), however, in some cases they may be transformed to approximate stationarity so that they can be econometrically analyzed. Such approximations allow the development of models to help the economist better understand the underlying mechanisms in the data series. Time series data can also be influenced by variables for which there are specific causes or determiners (see Figure 2c). These deterministic variables include trends, business cycles, and seasonal fluctuations. Trends are persistent, underlying directions in which a factor or characteristic is moving in either the short, intermediate, or long term. Business cycles are continually recurring variations in total economic activity. Business cycles tend to occur across most sectors of the economy at the same time. Seasonal fluctuations are changes in activity that occur in a fairly regular annual pattern and which are related to the seasons of the year, the calendar, or holidays.

Modeling

Econometrics offers several approaches to modeling time series data. One of the primary tools for analyzing time series data and developing a mathematical model of real-world situations is regression analysis. This is a family of statistical techniques that allows the economist to develop a mathematical model for use in predicting one variable from the knowledge of another variable. Modeling of time series data can also be done through autoregression, a multiple regression technique in which future dependent variable values are estimated based on previous values of the variable. Autoregression takes advantage of the relationship of values to the values of previous time periods. Another family of techniques used in building models from time series data is smoothing techniques. One approach to smoothing time series data is the use of naïve forecasting models that assume that future outcomes are best predicted by the more recent data in the time series. Smoothing of time series data can also be done using averaging models. These techniques take into account data from several time periods, thereby neutralizing the problem of naïve models in which the forecast is overly sensitive to irregular fluctuations.

Case Study: Analysis of Oil Supply

An example of the analysis of time series data is given in a study of the seasonality of non-OPEC oil supply by Jazayeri and Yahyai (2004). The cost of oil has far-reaching effects not only on the individual's pocketbook but also on the ability of businesses to support the travel of personnel and the transportation of goods. For this reason, it is vital to be able to accurately predict oil supply trends and changes. Although decisions about supply are coordinated between the member countries of OPEC (which supplies approximately two-thirds of the world's oil supply), this is not true for non-OPEC countries. Therefore, analysis of this industry segment is particularly important for forecasting the supply of oil.

Time series data of oil supply in non-OPEC countries show the effects of seasonality, an important factor in understanding and predicting the availability of oil from these countries as well as for planning within these countries. Some of the factors affecting the seasonality include demand for oil, price of oil, stock levels, annual maintenance schedule at production facilities, the psychology and manipulation of the market, timely completion of development projects, as well as irregular and random factors including severe weather, floods, earthquakes, and strikes. Seasonal weather fluctuations and the concomitant changes in demands for heating oil, cooling systems, and vacation travel also affect the demand for oil.

Jazayeri and Yahyai performed an analysis of seasonality of non-OPEC supply in order to help improve the accuracy of short-term supply forecasts. In their analysis, the authors assumed that observed seasonality cycles are independent of other factors and that they will continue into the future. The authors then decomposed the data into the four components of trends, business cycles, seasonal fluctuations, and irregular or random variables in order to better understand the phenomena related to oil demand. Using the decomposition technique of Fourier spectral analysis, they found that non-OPEC supply follows a seasonal pattern that repeats annually irrespective of other trends. These results can be very useful for analysts forecasting oil supply across the various seasons of the year.

Conclusion

Econometrics is the application of the tools of mathematical statistics and related techniques to economic problems, including the analysis of data and the testing of theories and models. The use of such quantitative methods allows economics to be a science in which theories are empirically tested rather than an armchair philosophy whose theories cannot be empirically tested. Although it is rare that an economist can manipulate variables and collect primary data as is possible in many of the physical sciences, econometric tools are available that can readily be applied to secondary data whether they be cross-sectional or time series in nature. In some ways, the analysis of this type of secondary data gives economists a better understanding of real-world phenomena and processes than would more controlled -- but smaller in scope -- primary studies that allow for the manipulation of variables. The combination of secondary data and econometric data allow economists to develop and test empirical models to better understand economies and make forecasts.

Terms & Concepts

Cross-Sectional Data: Quantifiable observations or measurements on a wide variety of variables during one time period rather than across time periods. (Cf. time series data)

Deductive Reasoning: A type of logical reasoning in which it is demonstrated that a conclusion must necessarily follow from a sequence of premises, the first of which is a self-evident truth or agreed-upon data point or condition. Deductive reasoning is the foundation upon which predictions are drawn from general laws or theories.

Econometrics: The application of mathematical statistics and related techniques to economic problems, including the analysis of data and the testing of theories and models.

Economics: A social science focusing on the creation, allocation, and utilization of goods and services; the distribution of wealth; and the allocation of resources as well as the theory and management of economic systems. Economics is concerned with the theories, principles, and models of economic systems.

Empirical: Theories or evidence that are derived from or based on observation or experiment.

Forecasting: In business, forecasting is the science of estimating or predicting future trends. Forecasts are used to support managers in making decisions about many aspects of the business including buying, selling, production, and hiring.

Hypothesis: An empirically-testable declaration that certain variables and their corresponding measures are related in a specific way proposed by a theory.

Inductive Reasoning: A type of logical reasoning in which inferences and general principles are drawn from specific observations or cases. Inductive reasoning is a foundation of the scientific method and enables the development of testable hypotheses from particular facts and observations.

Mathematical Statistics: An offshoot of mathematics concerned with the analysis and interpretation of data. Mathematical statistics provides the theoretical underpinnings for various applied statistical disciplines, including business statistics, in which data are analyzed to find answers to quantifiable questions.

Model: A representation of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. Mathematical or computer models are mathematical representations of the system or situation being studied.

Regression Analysis: A family of statistical techniques used to develop a mathematical model for use in predicting one variable from the knowledge of another variable.

Scientific Method: A cornerstone of the social sciences in which a systematic approach is used to understand some aspect of individual or group behavior. The scientific method is based on controlled and systematic data collection, interpretation, and verification in a search for reproducible results. In organizational behavior theory, the goal is to be able to apply these results to real-world applications.

Time Series Data: Quantifiable observations or measurements gathered on a specific characteristic over a period of time. Time series data are used in business forecasting. To be useful, time series data must be collected at intervals of regular length. (Cf. cross-sectional data)

Validity: The degree to which a survey or other data collection instrument measures what it purports to measure. A data collection instrument cannot be valid unless it is reliable. Content validity is a measure of how well assessment instrument items reflect the concepts that the instrument developer is trying to assess. Content validation is often performed by experts. Construct validity is a measure of how well an assessment instrument measures what it is intended to measure as defined by another assessment instrument. Face validity is merely the concept that an assessment instrument appears to measure what it is trying to measure. Cross validity is the validation of an assessment instrument with a new sample to determine if the instrument is valid across situations. Predictive validity refers to how well an assessment instrument predicts future events.

Variable: An object in a research study that can have more than one value. Independent variables are stimuli that are manipulated in order to determine their effect on the dependent variables (response). Extraneous variables are variables that affect the response but that are not related to the question under investigation in the study.

Bibliography

Bendic, V. (2013). Econometric model of multiple equation of different shape. Internal Auditing & Risk Management, 8 (2), 211-218. Retrieved November 26, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=90542677&site=ehost-live

Black, K. (2006). Business statistics for contemporary decision making (4th ed.). New York: John Wiley and Sons.

Coleman, R. D. (2006). What is econometrics? Retrieved March 2, 2009, from http://www.numeraire.com/download/WhatIsEconometrics.pdf

Dosescu, T., & Raischi, C. (2011). Another category of the stochastic dependence for econometric modeling of time series data. Economic Computation & Economic Cybernetics Studies & Research, 45 (4), 1-15. Retrieved November 26, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=70704747&site=ehost-live

Jazayeri, S. M. T. & Yahyai, A. (2004). An analysis of seasonality of non-OPEC supply. Maritime Policy & Management, 30(3), 213-224. Retrieved March 19, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=14352172&site=ehost-live

Koop, G. (2009). Analysis of economic data (2nd ed.). New York: John Wiley and Sons.

Mastrangelo, C. M., Simpson, J. R., & Montgomery, D. C. (2001). Time series analysis. In Saul I. Gass, S. I. & Harris, C. M. (eds.), Encyclopedia of operations research and management science (pp. 828-833). New York: Wiley. Retrieved September 11, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=21891965&site=ehost-live

McMillen, D. P. (2012). Perspectives on spatial econometrics: Linear smoothing with structured models. Journal of Regional Science, 52 (2), 192-209. Retrieved November 26, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=74437728&site=ehost-live

Pindyck, R. S. & Rubinfeld, D. L. (1998). Econometric models and economic forecasts. Boston: Irwin/McGraw-Hill.

Nazem, S. M. (1988). Applied time series analysis for business and economic forecasting. New York: Marcel Dekker.

Wooldridge, J. (2008). Introductory econometrics: A modern approach. Florence, KY: South-Western College Publishing.

Suggested Reading

Barelli, P. & De Abreu Pessôa, S. (2009). On the general equilibrium costs of perfectly anticipated inflation. Annals of Finance, 5(2), 243-262. Retrieved March 19, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=36177072&site=ehost-live

Foroni, C., & Marcellino, M. (2013). A survey of econometric methods for mixedfrequency data. Norges Bank: Working Papers, (6), 1-42. Retrieved November 26, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=88480177&site=ehost-live

James, R. N. III. (2009). An econometric analysis of household political giving in the USA. Applied Economics Letters, 16(5), 539-543. Retrieved March 19, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=366 49277&site=ehost-live

Partridge, M. D., Boarnet, M., Brakman, S., & Ottaviano, G. (2012). Introduction: Whither spatial econometrics?. Journal of Regional Science, 52 (2), 167-171. Retrieved November 26, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=74437724&site=ehost-live

Tabak, B. M. & Lima, E. J. A. (2009). Market efficiency of Brazilian exchange rate: Evidence from variance ratio statistics and technical trading rules. European Journal of Operational Research, 194(3), 814-820. Retrieved March 19, 2009, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=35072128&site=ehost-live