D.1. Limitations of Observational Studies for Derivation of Laws: Observational studies are insufficient for generating any Laws in Economics. (From 1.4.1).
E.1. The following are observations extracted from Robbins' An essay on the nature and significance of economic science, infused with some additional knowledge of social science research methods at disposal of author of summary.
I. A law must follow from the very definition of the subject of Economics in a logically valid manner such that it always follows definitely, no contradictory implications arise, and no implications are arbitrarily ignored. That is to say, a Law describes all implications and is complete, logically consistent and clear.
II. All laws inevitably follow from the fundamentals of a subject, in this case from the definition of economics. A proposition that does not follow inevitably is not a law, and, following 1.4.1, we know that observational studies only yield probabilistic statements i.e. "may or may not" statements which implies that what may follow, may also not follow i.e. it is evitable. And thus not a law.
III. If an experiment, or a regression etc, reports an observation, unless it can be explained using fundamentals of economics, it bears little value for Economic Analysis, and if it can be explained using fundamentals of economics which follow from its definition, it is no longer needed to appeal to an empirical regularity, or experimentation etc, for now it can be explained theoretically.
IV. The following are the reasons a law cannot be based on observational studies:
a. All real life data is generated by heterogenous, repeatedly changing, multiple, uncontrolled causal factors, most of which cannot be observed directly, several of which cannot be known with certainty.
b. The statistical techniques are insufficient to extract effects of one variable on another from data in presence of missing or insufficient data, let alone issues such as multicollinearity etc etc may render models useless. A host of identification problems exist.
c. All statistical techniques are subject to accuracies such as of data collection, of definition of variables, etc in addition to often inevitable problems of mathematical modelling, and statistical techniques themselves.
d. Any experimental or regression technique is subject to issues of joint hypothesis testing. Each hypothesis test in fact tests also that researcher took due care of all aforementioned accuracies, some of which are insoluble problems.
e. The data in an experimental study is not always sufficient to warrant even a generalization.
f. The experimental methods are subject to their own set of problems as is the data from a survey.
g. A self selection bias is always present in experiments or surveys i.e. those who chose to participate or answer may behave or report views differently from those who do not choose to be part of it.
h. Conclusion: For a host of reasons, it is extremely difficult, and in fact only impossible, to extract a law about human behaviour from a data generated by such uncontrolled, unknown, non-uniform circumstances, let alone that the data collection, data processing, etc are all methods subject to their own problems. A Law must follow clearly from fundamentals, and it is not possible that such roughness of inductive methods, and of data it uses, can help identify 'inevitable' Laws, let alone a law is only an implication i.e. something inductive reasoning cannot provide.
Any regularity, even if exists with 1.0 probability, must be explained using fundamentals of economics, and if not, there is a disconnect, a gap, between its self and our fundamental and in presence of this gap, it cannot be concluded that such a regularity is related to economics, let alone we are interested in Laws - the most definite of all conclusions.