## Quantitative Economics Analysis

Economists are interested in interpreting data in order to better understand and predict the behavior of economies and economic variables. To do this, they need to be able to quantitatively analyze data in order to determine the effect of changes on variables of interest, or to weigh the relative merits of econometric models. Quantitative analysis techniques used in economics include many of the tools of inferential statistics as well as various tools for building empirical, testable models. Through the use of quantitative analysis, economists can test and validate their theories and revise them so that they better reflect the realities of real world economies.

Economists can be found working in a wide spectrum of situations: From academicians who work in universities and develop and test theoretical models of various aspects of economies; to economists working in government and industry who apply those models to the real world in an attempt to forecast future trends based on past and current data. The application of economic theory is the stuff of headlines. In the government, economists may analyze the pros and cons of various alternative economic policies under consideration based on various facts and figures. Economists working in banks may evaluate whether or not interest rates should be change. In the private sector, economists may be called upon to forecast the change in various economic variables such as exchange rate movements and their effect on the exports of their organization. In all these situations, it is important that the economist is able to quantitatively analyze data in order to determine the effect of changes on variables of interest or to weigh the relative merits of econometric models. Having a theory based on one's observations of historical trends or current conditions is a good start in understanding the realities of an economy. However, such observations on their own are insufficient for reliably forecasting the future. Economists must be able to quantify the facts known about various economic conditions and analyze these in order to test the validity of an economic model and forecast trends (Koop, 2009).

### Applications

### Mathematical Statistics

### Descriptive Statistics

Mathematical statistics give economists a number of quantitative tools that enable them to develop and test theories which help them better understand and predict economic behavior. These tools range from ways to organize and summarize data so that they are more easily understandable, to methods for predicting future trends using data and models. At the simpler end of this continuum, descriptive statistics help economists to clearly describe large amounts of data using pie charts, histograms, and frequency. Other methods of descriptive statistics include measures of central tendency (i.e., mean, median, and mode) that give the "average" for a particular variable of interest as well as measures of variability (i.e., range and standard deviation) that help one understand how widely dispersed the values of the variable are.

### Inferential Statistics

In addition to such descriptive tools, mathematical statistics also offer economists tools which allow them to make inferences about data. These techniques, called inferential statistics, allow one to draw conclusions about a population from a sample and test hypotheses to determine if the results of a study occur at a rate that is unlikely to be due to chance (i.e., have statistical significance). For purposes of hypothesis testing, the hypothesis is stated in two ways. A null hypothesis (H0) is the statement that there is no statistical difference between the status quo and the experimental condition. In other words, the treatment being studied made no difference on the end result. The alternative hypothesis (H1) states that there is a relationship between the two variables and that the intervening variable did make a difference in the outcome. In order to determine whether one should accept or reject the null hypothesis, one must first determine how the data are to be statistically analyzed. This decision is made during the design of the experiment so that the appropriate statistical tool can be chosen and the necessary data collected. One frequently used class of statistical tests used in hypothesis testing is the family of tools known as t-tests. These tests are used to analyze the mean of a population or compare the means of two different populations. (In other situations where one wishes to compare the means of two populations, a z statistic may be used.)

### Correlation Techniques

Correlation techniques are another classification of techniques that can be used by economists. These techniques help economists better understand the degree to which two variables are consistently related. For example, correlation can help one understand the relationship between various economic indicators and purchasing behavior. Correlation coefficients show the degree of relationship between the two variables, and vary between 0.0 and 1.0. A correlation of 1.0 shows that the variables are completely related: a change in the value of one variable will signify a corresponding change in the other variable. A correlation of 0.0, on the other hand, shows that there is no relationship between the two variables: knowing the value of one variable tells nothing about the value of the other variable. A correlation coefficient also signifies how the two variables are related. If the correlation coefficient is positive, then as the value of one variable increases so does the value of the other variable. A negative correlation, on the other hand, means that as the value of one variable increases the value of the other variable decreases.

### Analysis of Variance

Another family of inferential techniques that is used for analyzing data in applied settings is analysis of variance (ANOVA). This family of techniques is used to analyze the joint and separate effects of multiple independent variables on a single dependent variable and to determine the statistical significance of the effect. Multivariate analysis of variance (MANOVA) is an extension of this set of techniques that allows economists to test hypotheses on more complex problems involving the simultaneous effects of multiple independent variables on multiple dependent variables. The work of Kureshi, Sood, and Koshy (2009) offers an example of how analysis of variance can be...

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