Linear Regression

Linear regression belongs to the econometric methods of empirical research, which are applied in almost all sciences. Linear regression is a set of econometric methods of estimating statistical causality between two or more factors (variables of interest). A central assumption of linear regression is the ceteris paribus condition, which means nothing other than “if the conditions are the same” or “if other factors are kept constant“. The literature on linear regression can be found in almost every textbook on statistics, textbooks on econometrics, and research literature on methods of empirical economic research.

Simple Linear Model

In a simple linear model, it is assumed that only one variable $x_{1i}$ has significant impact on variable $y_i$ and all unexlained variance is explained by the error term $e_i$.

y_i=\beta_0 + \beta_1 \cdot x_{1i} + e_i \, \text{or} \, y_i=\beta_0+\sum_{j=1}^{k=1} \beta_i \cdot x_{ji} + e_i

Multi-Regression model

y_i=\beta_0 + \beta_1 \cdot x_{1i} + \beta_2 \cdot x_{2i} + ... + \beta_{k-1} \cdot x_{(k-1)i} + \beta_k \cdot x_{ki} + e_i
y_i=\beta_0+\sum_{j=1}^{k} \beta_i \cdot x_{ji} + e_i

Why is the linear regression method used in science?

Scientists use the regression method to explain the statistical causality between two or more factors so that they can identify the potential statistical correlations in their research question. However, a researcher also wants to test whether statistical estimates reflect reality, or at least whether the observation in the sample of his/her observations reflects reality in the population. Regression methods can be used to calculate or analyze relevant factors in a research question. While regression calculation aims to estimate the relevant coefficients (causality estimators), regression analysis aims to test relevant empirical hypotheses (inferential statistics).

Consider the following example. As an economics student, you are used to reading the following statements in almost all economics and business administration textbooks: “The law of demand says that when prices rise, the demand for a normal good falls”. Where does the statement of the law of demand come from? Can this assertion be proven empirically? When is a good a normal good? Although the answers to these questions can be found in any textbook, the background to their justifications and sometimes incomplete explanations are more likely to be found in empirical research using econometric methods.

Economists work with theoretical models that can be empirically tested to determine the extent to which they reflect your research question in reality. In the case of the law of demand, the Cobb-Douglas model can be applied, which assumes constant elasticity of demand. Here is where the first problem arises. This Cobb-Douglas theoretical model is not linear, as required by linear regression methods, but a non-linear (multiplicative) model. Utilizing the logarithm, however, the Cobb-Douglas model can be transformed into a (log-to-log) linear model (linear transformation). With a sufficient sample, a regression model can be estimated to statistically verify the claims. This example is one of many other applications of empirical analysis to test economic theories.

Simple and multi-regression analysis

In econometric regression analysis, a distinction is made between simple regression analysis and multi-regression analysis. In simple regression analysis, two factors are examined, e.g. a macroeconomic hypothesis could be that domestic consumption (C) has a positive influence on domestic income (Y). The propagated causality is that domestic income depends on domestic consumption – Y(C).

The aim of econometrics is to estimate empirical models that confirm or even refute the propagated causality between domestic consumption and domestic income of a country in the given population. The reverse causality, however, is also possible that domestic consumption tends to depend on domestic income – C(Y). Now, such an analysis, Y(C) and C(Y) takes place under the assumption of the ceteris paribus condition.

The simple regression is then extended by further variables – forming the multi-regression model.

Due to the ceteris paribus condition, the explanatory power of the simple model is limited to explaining the potential causality between domestic consumption and domestic income of a country, but without reference to other potential causalities between other (non-) observable factors, e.g. domestic and foreign investment, exports, imports, government expenditure, savings, taxes, etc. For this reason, the simple regression model is extended. If we now extend the propagated causality to other potential causalities, this results in the multi-regression model, e.g. domestic consumption (C) is influenced by disposable income (income (Y) minus taxes (T)) and other factors, the classical macroeconomic theory of consumption according to Keynes.

C(Y_V)=c_1Y_v+c_0
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The Economic Concept of Opportunity Costs

The economic concept of opportunity costs is the most fundamental issue of economics as a social science. It explains the decision-making and behavior of economic subjects. Economic subjects are private households, firms, and the government as a public household. While explaining the economic concept of opportunity costs, focus on the question: why do people choose to do, consume, or even spend time and resources on what they do? How do you make your choices and decisions?

Definition of Opportunity Costs

Opportunity costs are defined as costs incurred by a forgone alternative (opportunity). A foregone opportunity can either be the opportunity to incur costs, the opportunity to gain revenues, earn profits or cause losses. Economic subjects constantly get involved in decision-making processes, where choices have to be made. Take the following examples:

• Example 1: non-monetary opportunity costs – the reason why a student would attend high school (an institution of education) is determined by the opportunity cost incurred if the student would not attend the school e.g. the impression of the parents about their daughter or son. Such opportunity cost are not measurable in monetary units.
• Examples 2: mental accounting – whenever you act or choose not to act in certain manner, you are weighing alternative options and therefore intrinsically accounting for cost that would be incurred by alternative mode of behavior.
• Example 3: relative costs – a job-seeker may prefer a job that pays less, but offers a better work-life balance, at the cost of a better paying job under worse work-life balance.
• Example 4: Specialization and relative cost/benefit advantage – the opportunity cost of Germany producing autos are the cost incurred for not producing other goods that Germany prefers to import from other countries, e.g. Coffee from Kenya.

Literature

The following Literature will help you to expand the spectrum of knowledge in this Field:

• Varian, H. R. (2020). Intermediate Microeconomics: A modern approach ; media update (Ninth Edition, International Student Edition). New York, London: WW Norton et Co.

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What is Economics?

What is Economics, and how can students define economics as a science? Therefore, our motivation in this article is to find a general definition of economics. In much of economic literature, there is also consensus and conflict on some description of economics as a science. So how do we start? To neatly define economics in lectures, we need a broad view of the term economics.

Consequently, Economics can be defined as an interdisciplinarysocial, and behavioral science. Therefore, economic research focuses on explaining the behavior of decision-makers. Economics also explains the implications of the behavior of the decision-makers that affect society at the microeconomicmacroeconomic, and political levels. Such an analysis of different decision-makers consequently needs an interdisciplinary approach. Decision-makers in economics are in particular private households, firms, and governments.

Microeconomic level

At the microeconomic level, economics explains the human nature of making both individual rational and irrational decisions, social interactions, and behavior under risk. Individuals, organizations, and governments make allocation and distribution decisions daily, which economic subjects would like to evaluate. Economics derives the rules of determining; how efficient or optimal the decisions of economic subjects are. It, therefore, determines the necessary rules and coordination mechanisms usable in decision-making processes. Some of the coordination mechanisms include market, government, private, entrepreneurial coordination in an economy. An economy is the environmental unit of economic analysis.

Macroeconomic level

Economics is also an environmental dimension of macro-environment analysis in the PESTEL-Framework in strategy management. Other PESTEL dimensions include the political, social, ecological, technological, and legal environment. At the macroeconomic level, economics discusses the aggregated effect at the level of the whole economy using the six macroeconomic objectives (magic hexagon).

Policy Level

At the political level, economics deals with the implication of economic decisions of different interest groups in an economy and derives policy recommendations to help maximize social welfare. Consumers, entrepreneurial, government interests are not always similar. Employees’ and employers’ political interests also differ. Therefore, economic policies are essential and help in balancing the different interests as well as maximizing the welfare of society.

Economics deals with Rational and Irrational Behavior

Evident in all economic literature is the issue of rational and irrational behavior as the central point of discussion. In economic theory, the economist tries to explain how people should make decisions depending on their goals and restrictions they face. Rational decisions are those decisions that respect the restrictions and goals of an individual, while irrational behavior could e.g. incur either a higher cost (not respecting restrictions) or lower utility (not respecting the goals) as compared to the rational decision. Rational decision is influence by the cost of opportunities.

Economics is about the Maximum and the Minimum Principle

Economists derive two principles of decision-making that drive the process of making decisions within economic subjects. The maximum principle and the minimum principle.

The Maximum Principle

The maximum principle suggests the following: Attain the maximum output with a predefined amount of inputs.

The Minimum Principle

The minimum principle suggests the following: Utilize the minimum input to attain a predefined amount of output.

Find a detailed definition of Economics in the International Encyclopedia of the Social & Behavioral Science (2001, Pages 4158-4159) via Science Direct.

Understanding the definition of Economics

In order to understand Economics, it is essential to differentiate between decision-making from three different perspectives: private consumption and income decisions, public consumption and revenue generation, entrepreneurial production and supply of goods and services in an economy. As discussed above, economics is the science of rational decision-making. Firstly, economists try to explain how economic subjects make rational decisions, the limitations of rational decision-making, human interactions and their outcomes. Secondly, economists try to capture the limits of rational behavior and explain how decision-making takes place under imperfect environment conditions; e. g. information asymmetries, uncertainty, imbalance in power between decision-makers … etc.

Economic subjects

The concept of economic subjects is the notion of viewing people in an economy as (1) private households, (2) as firms (or organizations) and as (3) the government (also a form of organization). In general, this means that there are three economic subjects;

• Private Households
• Firms (private and public organizations)
• Government (Public household and organization)

What is an Economy?

An economy is the analytical unit of interest for all economic analysis and includes the people, biosphere and all resources available e.g. a political unit (e.g. Germany, China, France, Ghana) or a unit specified by certain characteristics such as a continent, a supranational unit, an international coalition of nations, etc.

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