Validation of economic theories varies significantly depending on what is being validated.
For many microeconomic or behavioral economics theories, they are actually tested in controlled experiments. For example, they could select two test subjects, and play some sort of coordination game that pays money based on their choices.
Other theories, particularly in macroeconomics, are tested using statistical methods (usually called econometrics). At it’s core, econometrics tries to described the economy using linear equations often defined by regression analysis (ELI5, finding out which line has the best fit for the data set). For example, an equation could describe “for every X percentage point interest rates increase, unemployment will go up by Y percentage points”, etc.
It is extremely difficult to isolate variables in economic models. In the same way your weight is a function of many factors such as your age, how much you exercise, how many calories you eat, genetics, and stress unemployment is impacted by interest rates, commodity prices, government spending, education, and even the weather.
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