Introduction to Identification and Causal inferences

It is natural for human beings to draw conclusions and link them to something else. And in economics, both consumers and manufacturers are seen as decision-makers who rely on certain conditions to take specific directions. It is always assumed that one thing leads to the liking or disliking of the other.

Identification and causal inferences are two of the most critical aspects of modern microeconomics. Whether it is for individual or firm decisions or academic studies, these two aspects have always been used to ascertain microeconomic models. We have seen the importance of economic models, and it continues to be a hotly discussed subject. In this article, we shall be introducing you to identification and causal inferences as part of microeconomic model studies.

Causal inference

Causal inference can be described as the process of drawing conclusions about a causal relationship based on the evidence in the circumstances surrounding the incident. As stated above, we all draw a conclusion and made decisions based on the best outcome. Causal means something that stirs the happening of another. For instance, consumers make decisions based on the most beneficial outcome. A family may have been saving for a vacation, but they may be faced with another challenge of buying a new car when the time comes. And since scarcity is something that affects all human beings, they will make the decision based on what makes them more satisfied.

Causal inferences help people make conclusions, sometimes on assumptions, about the connecting causal effect on a specified condition. Sometimes people confuse causal inference and inference of association to mean more or less the same. However, they are mainly differentiated by the fact that the former critically looks at the effect variable's response when the cause is altered. Also, causal inference is a good example of causal reasoning.

Economics is seen as a scientific study of economic behavior. It takes into consideration how consumers and producers react to different conditions that affect economic growth and development. In other words, we can say that economics studies human psychology by analyzing consumer and producer behaviors. We can always conclude that people must interact under different circumstances to make the world a better place. There would be no moving forward if these links were not there. A single consumer may not make such a big difference in an economy, but collectively they will create a huge effect.

Subjects such as health, social sciences, and behavioral sciences are motivated by causal and not associational. For instance, a medical team could be seeking to establish how efficient a certain drum may be to a population. They will mostly consider the reactions from users, and how they have been benefiting from it. In this case, the drug will be seen as efficient if it leads to the desired results. Hence, there is a causal reason to pursue a specified line of action. Also, a question such as whether data carries enough evidence to implicate an employer for hiring discrimination or not? If there is enough data, it brings out the desired evidence that a specific line of action leads to a specific reaction. Or, what are the chances that bringing a new product to the market will be received passively?

All these are causal questions. They demand some form of data-generating process. However, data alone, or distributions that govern the data is not enough to create a computational situation for the right answers. Causal questions seek to dig the underlying truth the links one thing to another. Surprisingly, much of the conceptual framework and algorithm tools necessary for solving such issues are now well established. However, they are not very much known to researchers who could apply them in real-life situations. The main reason is their educational nature. To systematically solve causal problems, one is expected to have a certain extension in mathematical language and statistics. This means studying causal inference is not a general subject that anyone can take on and succeed. It calls for someone with dipper understanding of mathematics and statistics. This not only goes for the researcher but also for the person trying to interpret the data. If you are not well equipped with mathematical knowledge, understanding come aspects causal inferences will not be possible. Besides, mainstream literature and education do not emphasize these extensions, which makes it even harder to study them. This is large sections of statistical research in communities that do not easily appreciate and benefit from causal analysis results. Over the past two decades, there have been various researches of these nature, which do not seem to matter to many, even though they are very crucial for different aspects so human existence. The causal analysis makes economists and other people understand the reasons behind certain decisions and make more informed plans for their futures.

Testing for statistics and economics

Statistics and economic are two subjects that work with closest ties. When a government wants to make a new fiscal or monetary policy, they look at data and effects of previous decisions. If, for instance, there is a major recession within an economy, it becomes vital for policymakers to know where to begin in their search for a solution.

In this case, causality is mostly tested through regression analysis. There are many methods that can be applied in identifying the actual casualty from spurious correlations. Economic analysts must establish the best method to determine the most appropriate path to follow. Economist construction regression modes must first distinguish the causal relation direction by looking at a specified economic theory. Note that causality studies are theory-driven economics. The importance of models in establishing and proving theories can never be overemphasized.

For instance, it is determined that the amount of rainfall with a specified period led to increased sales. This could be something the consumers need a lot during the rainy season, like umbrellas. This will then mean the manufacturer should adjust its production level to ensure there is enough supply on the market. Also, theory (broadly construed) shows that rainfall can affect pricing. If demand is high, there are higher chances of suppressing supply, which leads to an increase in prices. These are normal occurrences with economies, and they are the wheels that drive economic growth and development.

 After establishing the causal direction, the economist may use the instrument variables (IV) method to eliminate any effects of reverse causation. They do this by introducing the role of the other variables (instruments) that are automatically affected by the dependent variable. This means they have to consider that something else could be the reason why the results don't come out as expected. Then comes the final step of the regression analysis in which economists look at the time precedence when choosing the right model specification. Time is a critical factor, considering that economic development goes through different cycles. The right way to get desired results, therefore, involves setting the analysis on a specific time frame. It becomes crucial to observe everything based on the real results of what happened within the given time and then compare to what might happen.

Causality can be considered based on its probabilistic view as well. In this case, economic analysts used the assumption that causes must come earlier in time than their effects. There will be no effect if the cause has been established earlier in time. It is crucial to set the right timing because then, it will lead to the right decisions. As stated in economics and statistics require some math knowledge when describing and using causal inferences. Time is one factor used in the development of numerical evidence. As such, analysts may use variables that represent phenomena happening in a former time as the independent variable, as well as developing econometric tests for causality – like the Granger-causality tests- as applied in a time-series study.

Another very important step the analyst must take is the inclusion of other regressors. These come in to make sure that the confounding variables are not the cause for the causing regressor's appearance spuriously. However, when considering the areas suffering from multicollinearity issues, like in macroeconomics, it is principally impossible to add all confounding factors. This is the main reason why econometric models are susceptible to common-cause fallacy. In recent times, movement-oriented econometrics has made the use of natural experiments and quasi-experimental research designs quite popular in addressing the issue of spurious correlation.

Economic identification

Economic identification is just meaning features or model components being determined in unique ways from an observable population, which creates data. There are many variations of the term identification now appearing in the modern economical literature. However, they all come down to the idea of building something noticeable and processes that become apparent in the study of econometric models. Such terms include Bayesian identification, causal identification, essential identification, local identification, point identification, set identification, and many others.

To understand what identification truly means, it is vital to consider some historical aspects of the same. We can go ahead and isolate, hence identifying the impact of one variable to another, but it is critical to understand the thought of 'ceteris paribus,' which means holding other things equal. This concept was formally applied to an economic analysis by Alfred Marshall (1890). Or rather, he may have been the first person to use the term. But Perky (1990) states that the use of ceteris paribus as a term in economics dates way back to William Petty (1662).

Phillip Wright (1915), shares that what seemed to be an upward sloping demand curve for pig iron was the rail supply curve that originated from the demand curve, hence, presenting the first textbook example of identification issues in economics. While many who looked at the curve believed it was for the consumers seeking the commodity, Wright identified as suppliers delivering the good. Letter Sewall, Philips' came up with the idea of using causal path diagrams in statistics. Hence Sewall Wright (1925) used his own discovering in the construction of instrumental variables estimator. However, it was easy to already to use ordinary least squares in identifying exogenous regressors.

Apart from the two Wrights, Holbrook (1927) and Elmer J. Working (1927) published their early papers in relation to this subject. They both mentioned the issues of statistical demand curves. It was Holbrook, whom the Working-Leser Engel curve was named after. Other analysts followed the same idea, including Jan Tinbergen (1930), who proposed the indirect least squares estimation, though his work does not appear very useful in solving identification issues. Trygve Haavelmo (1943), and Franklin Fisher (1966) are among the most recent analysts in this area. Their work most dwelt on the exclusion restrictions for resolving identification in a simultaneous system. Nevertheless, identification could also emerge from restrictions on the covariance matrix or error. Sometimes it could also come from the combination of the two.

The general definition of Identification in econometrics

Take that P stands the real distribution of observed data X. which is shown as P= {Pθ: θ ∈ Θ}, as a model for the distribution of this observed data. It can be assumed that P ∈ P = {Pθ: θ ∈ Θ}. Its simple terms, we are assuming that there is a correct specification of the model so that we can notice some θ ∈ Θ, in which Pθ = P. Our interest is majorly on θ or another function f of θ.

If we already know that the distribution of observed data P ∈P. And because this model is correctly specified by assumption, we know priori, that the existence of θ ∈ Θ such that Pθ = P is eminent. It is hard however to differentiate all θ ∈ Θ linked to all θ∗ ∈ Θ such that Pθ∗ = θ ∈ Θ such that Pθ = P. We already know P alone, hence we can conclude that θ ∈Θ0(P).

In this case, model P comes identified as a 'structural' model for the supply of observed data. A structural model is used because all the statistics describe the data, but they don't assist in understanding the mechanism. Identification, just like causal inference, is majorly identified through Linear regression.

Author: James Hamilton