## Research Methods in Economics & Business

With statistics, economists can study the intricacies of real world markets, forecast future business conditions and, most importantly of all, test the applicability of their models to the real world. Before statistics was introduced, economics was a strictly theoretical exercise. People accepted its principles because they made sense or "seemed" right. But the all important objective corroboration of theory with fact was missing. That bothered economists keen on making their discipline more scientific. They went on to found the field of econometrics that has since become a mainstay of economic analysis.

Keywords Analysis of Covariance; Analysis of Variance; Central Tendency; Cross-Sectional Analysis; Dependent Variable; Econometrics; Independent Variable; Null Hypothesis; Panel Analysis; Regression Analysis; Standard Deviation; Statistical Significance; Time-Series Analysis

### Economics: Research Methods in Economics

### Overview

As Adam Smith famously noted over two centuries ago, self-interest and competition collectively act like an "invisible hand" to shape the efficient allocation of resources in free and open markets. Ever since then, economists have sought to flesh out the way these forces are naturally harnessed and manifest themselves in mechanisms of exchange. Much of the work here has been, by necessity, descriptive. Observation in turn leads to the formation of intuitive models to explain otherwise random events. Scientists follow the exact same methodology. But economists cannot take the next all important step and experimentally validate their theories as scientists do. For no amount of ingenuity, alas, will successfully recreate real world economic activity in a laboratory.

A hypothesis cannot be proved or disproved unless it is tested in controlled conditions free from outside influences. Depending on the premises, what's more, the most patently absurd propositions can be successfully argued logically. No matter how brilliant the reasoning employed, then, a theory is treated as a fact only when it has been substantiated objectively. Barring that, it remains an assumption regardless of how elegant, insightful or useful it might be. As such, its applicability to real world phenomena is problematic, and any forecast based on it susceptible to unintentional error. Whereas businesses might lose money when predictions prove inaccurate, model-builders lose something much harder to recoup: credibility. In the absence of objective proof, the next best thing is a track-record of accurate predictions (Wallis, 1984).

What Adam Smith could not have foreseen was how intricate and complex these models could be when formulated as equations. Mathematics provides the means not only to build complex models of macroeconomic theory but also, crucially, to test their accuracy and statistical robustness. Econometrics in fact came about as a separate discipline when an enterprising economist in 1933 used the formulae describing harmonic oscillation to investigate and explain the business cycle (Bouhmans, 2001). Meanwhile, pure mathematics has proved a much suppler means of expressing economic concepts than words alone. So much so, in fact, that much of today's economic theory is elucidated using algebra, logarithms, calculus, group theory and symbolic logic, just as mathematical rules governing the manipulation of symbols and the advancement of formal proofs in general have given economists new ways to argue the legitimacy of their constructs ("Theoretical assumptions and nonobserved facts," 1985).

Moreover, Silvia Pala?c? writes, in the twenty-first century, one must pay attention to the use of software in economics, since software is built based on mathematical tools. The difference lies in the fact that the mathematics is hidden and is not directly accessible to the user, who often forgets the substrate of such software and makes use of it without fully understanding the results produced or ignoring the possible problems raised by the mathematical model behind the program (2013).

Only observable data can prove or disprove the veracity of their claims, and how can one ensure the accuracy and reliability of this data? What's to say the events in question are actually random in nature or an unrepresentative subset of the phenomenon under study? In other words, assuming your experimental design is sound, how do you know the data you've collected isn't just random? The short answer is statistics: the branch of mathematics specializing in the collection, assessment and analysis of large amounts of numerical data. And its roots interestingly lie in analytical geometry.

### Further Insights

Econometricians gather, collate and interpret real-world macroeconomic data (yearly figures on national output, employment, inflation, the money supply, etc.) going back over 60 years. Among all economists, then, they are perhaps the most outwardly-oriented and, due largely to statistics, the most "scientific." Their counterparts in the business world employ the very same statistical techniques to solve production problems, maximize customer service functions and plan and evaluate marketing campaigns. The tools of their trade are time-series data, cross-sectional data, panel data, and multidimensional panel data. In each case, a sample of the larger population is examined and the findings extrapolated. How this sample is collected is crucial: It must be selected indiscriminately from a large data set that encompasses the full range of possible outcomes. Time series data is measured periodically over an extended duration while cross-sectional data is measured all at once, much like a camera takes a photograph. Panel data combines both for purposes of analysis, and multi-dimensional panel examines the potential impact on the resulting findings that the introduction of another variable might have. The mathematics employed includes single- and multiple-equation modeling, hypothesis testing, statistical significance assessment, regression analysis, and analyses of variance and covariance.

### Modeling

To yield useful insights, models must take certain liberties with reality. For, a cause and effect relationship cannot be corroborated as long as any other possible influence might be in play. Economists would be particularly hard-pressed to provide any insight into the fundamental dynamics of the marketplace, in fact, if they could not avail themselves of the principle of *Ceteris paribus,* or "all other things being equal." It's a necessary presumption but one that nonetheless entails the deliberate oversimplification of complex processes. Model-builders are prepared to live with this trade-off because their primary concern is how faithfully they represent the phenomenon under study. Everything else is secondary. As such, bias-based error can and sometimes does creep unobserved into the model. Usually, however, it's tolerated because the risk and impact of any such error pales in comparison to the usefulness of the correlation demonstrated.

### Advantages of Mathematical Models

Mathematical models have certain built-in advantages. Data by its very nature is numerical. Equations or inequalities, moreover, can more precisely state the nature of the relationship between two or more types of events than words or diagrams. Using both, econometricians can build very sophisticated multi-variable models of macroeconomic activity. Now, the variables, or symbols, denote a range of possible values for the events being studied. They can be either a discrete set of numbers or a continuous function or equation stating the probable distribution of future values. When a cause and effect relationship is being modeled, any change in an independent variable triggers a change in its dependent variable. Critically, though, a change in the dependent variable does not cause a change in the independent variable. A model is said to be deterministic, moreover, only when prior values and its equations account for all the change. Eliminating randomness entirely, though, is very hard to do. So, the values of most econometric variables are expressed differently, as a continuous probability function that only gives the odds on a particular quantity occurring. A dynamic model, finally, factors in the passage time and thus frequently employs differential equations from calculus, a static model does not and generally employs linear equations from algebra.

### The Accuracy of Models

Curiously, though, testing the accuracy of any real world model is not a straight-forward affair, not at least when the burden of proof rests on statistics. For important reasons, in fact, the working hypothesis must first be turned into a negative statement called the null hypothesis. It asserts that there is no relationship even though the object is to show that...

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