Analytical Methods in Economics

In Analytical Methods in Economics Akira Takayama presents an exposition of the essential mathematical tools of economics and illustrates their applications to selected economic problems. Drawing on his own teaching experiences and research to provide concrete macro- and microeconomic illustrations of the concepts featured, Takayama clarifies the unifying analytical structure of economic theory and elucidates the mathematical tools that underlie it.

Following a thorough review of preliminary mathematical tools, Takayama discusses the nonlinear programming, uncertainty, differential equations, and optimal control theory. Emphasizing "why" rather than "how-to" questions, the author focuses on explanation, considerations of motivation, and economic application.

Analytical Methods is designed to enable economists, graduate students, and advanced undergraduates in economics to achieve a high level of comfort in the use of analytical techniques.

Methods of Economic Analysis

Methods of Economic Analysis

In economics, broadly we make use of two methods.

(i) Deductive method and

(ii) Inductive method

The deductive method is also known as abstract method or analytical method. This method is based on a priori reasoning and conclusions are drawn from certain fundamental assumptions. Deduction method was very popular among the Greeks. Here is an example :

All men are mortal Socrates is a man Socrates is mortal The deductive method moves from the general assumption to the specific application.

Ricardo, a classical economist, made use of the deductive method.

The inductive method moves from specific observations to generalization. It was Francis Bacon who advocated inductive method in scientific enquiry.

None of the above methods provides satisfactory system for solution of problems. So Darwin, who is famous for this theory of evolution, by introducing the concept of hypothesis, has combined deductive and inductive methods.

The important elements of Darwin's deductive-inductive method

are

1 Identification of a problem

2 formulation of hypothesis (a hypothesis is an assumption or an intelligent guess)

3 collection, organization and analysis of data

4 formulation of conclusions

verification, rejection or modification of the hypothesis after testing it.

In the past, there was a debate among economists about the question which is the best method ? inductive or deductive ? But the controversy is not there now. Today, economists feel that both induction and deduction are necessary for the science, just as the right and the left foot are needed for walking.

The Inductive Method-Methodology of Economics/ Microeconomics

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The inductive method refers to the process of reasoning from part to the whole, from specific to general, from narrow to wider, and from individual to the universe. Bacon described it as an ascending process in which facts are collected; arranged and then general conclusions are drawn.

It is also called the empirical, historical, and posterior method that derives economic generalizations based on experience and observations. In this method, detailed data are collected concerning a certain economic relationship, and efforts are made to arrive at a certain generalization that follows from the observations collected. It may require a large number of observations if it can yield a valid economic generalization.

The inductive method was strongly advocated by economists belonging to the German Historical School. It may be described as the technique of economic science. The idea here is to remove or reduce the gap between theory and practice. It holly depends on making or conducting research from historical information.

The historical or inductive method expects the economists to be primarily an economic historians who should first collect material, draw generalizations, and verify the conclusions by applying them to subsequent events. For this, it uses statistical methods. The chief architects of this method are Gustav von Schmoller, Wilhelm Georg Friedrich Roscher, and Hilde Brand.

Engel’s Law of Family Expenditure and the Malthusian Theory of Population have been derived from inductive reasoning. Engel propounded the law only after he had studied several family budgets in Austria. This law has significant applicability to date though it was formulated through the method of induction.

Steps used in the Inductive Method

The inductive method involves the following steps;

Identification of problem

To arrive at a generalization concerning an economic phenomenon, the problem should be properly selected and clearly stated.

Data Collection

In the next step, the collection, enumeration, classification, and analysis of data by using appropriate statistical tools and techniques existed. The collection of detailed data and the use of statistical methods to arrive at economic generalization describing the relationship between facts are being increasingly made. Some of the recent macroeconomic research like the nature of consumption function describing the relationship between income and consumption, the acceleration principle describing the factors which determine investment in the economy has been obtained through the use of induction or empirical method. However, it needs to be emphasized again that the use of induction or empirical method is not of much value if it is not supported by the economic theory or hypothesis established by the deductive method.

Observation

The collected data are used to observe particular facts concerning our problem. Economic relationships are of less uniform pattern in comparison with natural science. Furthermore, economists study the economic phenomenon in which pressure groups such as employer’s associations, trade unions, farming lobbies, and political parties with their different ideologies play a crucial part and their activities render it difficult to make controlled observations and experimentation on the economic world. Through observation, some of the theories of generalization are developed or refined with the help of statistical methods.

Hypothesis

Based on generalized theories or thoughts hypotheses are formulated for predicting the values of parameters considered in the problem. It helps to establish a general truth relating to a particular fact.

Verification and generalization

In the end, the hypothesis is to be verified and if it is verified against the real-world data then it will generate the generalization from a specific fact. It means if the prediction made by hypotheses is agreed with the fact then the generalized result is produced and established as law or theory.

For example, when a Scottish farmer found that in the cultivation of his field an increase in the units of labor and capital spent on it was bringing in less those proportionate returns year after year- Particular/specific/narrow.

An economist recognized such a problem and collected detailed data from the number of farmers. He observed the problem set the hypothesis and through testing and applying it against real-world data arrived at the generalization that is known as the law of diminishing returns.

Therefore, induction is the process of arriving at a generalization based on a particular observed fact. The inductive method can at best be used to empirically test the theory or hypothesis as to whether it is consistent with or refuted by fact.

Inductive Method-Process

Merits of Inductive Method

This method is realistic. It is based on facts and describes them as they truly are. Induction is actual and synthetic because it deals with the subject as a whole and does not divide it into parts artificially.

It helps in future inquiries. Once a generalization is established, it becomes the starting point of future inquiries.

Inductive methods require the use of statistical methods. This aids noteworthy improvements in the application of induction for analyzing economic problems of a wide range.

This method is dynamic. In this method changing economic phenomena can be analyzed based on experiences, conclusions can be drawn and appropriate remedial measures can be taken. Thus induction ensures from time to time new problems to pure theory for their solution.

A generalization drawn under the inductive method is often historic-relative in economics. Since it is drawn from a particular historical situation, it cannot be applied to all situations unless they are exactly similar. Thus induction method has the merit of applying generalizations only to related situations or phenomena.

Demerits of Inductive Method

Following are the major demerits of the inductive method;

Induction relies on statistical numbers for analysis that can be measured and misrepresented when the assumptions which are required for their use are forgotten.

The conclusion drawn from insufficient data may create greater risk.

Definitions, sources, and methods used in statistical analysis differ from investigator to investigator even for the same problem. Thus statistical techniques may lack correctness.

It is a time-consuming and costly method of generalization. It involves a detailed and painstaking process of collection, classification, analysis, and interpretation of data on the part of trained and expert investigators and analysts.

The use of statistics in induction cannot prove a hypothesis. It can only show that the hypothesis is not inconsistent with the known facts. In reality collection of data is not enlightening unless it is related to a hypothesis.

Conclusion

The induction method also known as the historical, empirical, and posterior method was advocated by economists related to German Historical School. It is the technique of a practical approach to the problem of economic science. In the induction method, statistical use is essential and it is required while generalizing the hypothesis of theory from particular to general structure. It means we proceed here from the particular to the general. The induction is experimental including clear and substantial advantages in economic investigations and research. This method is however a complicated, time-consuming, and expensive method of lawmaking.

References

Ahuja, H.L. (2017). Advanced Economic Theory. New Delhi: S Chand And Company Limited.

Jhingan, M.L (2012). Advanced Economic Theory. New Delhi: Vrinda Publications (P) LTD.