D.1. Role of Empirical Methods: Empirical Studies can assist in either defining, measuring, refining, or extending the theory within bounds of 1.1.1, and 1.2.1.
E.1. There are at least four ways in which empirical work can, in fact, be of great benefit to the theory. However, beyond these four ways, mentioned below, there is no reason that a science whose method is deductive and is decided by its definition (See 1.4.1), such a subject engages in inductive reasoning to generate its laws, refine itself, extend it or somehow mostly depend on inductive logic, or empirical observations.
1. To Operationalize: The operational definitions of abstract ideas are of key importance, if theory is to be applied for good use. For instance, theory uses the term "money" but in practice there is a whole lot of many things that can be treated as money. Which is treated as money, and which is not, is the task an empirical study may very well perform. This is called operational definition in research methods. An error in operationalization can render the application of theory fruitless despite the theory being perfectly valid. The task of operational definition is subject to revision as time and technology changes.
2. To Measure: Two measures are needed:
First, the theory may postulate something, for instance about elasticity of demand under certain conditions, and remains only abstract. The actual measure, for any time or market, is a useful information which can be obtained by collecting data after operationalization. This too requires revision because of fundamental asymmetry of time series relations.
Second, while economic analysis takes the means and ends as given, their distribution across the cross section or dynamics over the time are of interest because these variations are the key input to Economic Analysis. Thus, the empirical study may as well study distribution of means and ends. For instance, information about fertile lands, numbers of hospitals and schools needed, dynamics of income distribution, also general findings of other sciences such as available techniques of production, their costs, their productivity, or the most frequently pursued ends, or fashions or trends or etc etc.
3. To Identify Logical Gaps:While the theory may make assumptions about affairs of world, the real world changes fast, and can produce conditions which are alien to the theory. Pointing out those gaps in such a way that later on research can be carried out for explaining these gaps using the fundamentals of economics (1.1.1, also 1.2.1) is another key role in empirical work. Such a work refines the theory. Such a work may often require regression analysis etc. For instance, while exchange rates between countries are generated by highly predictable human economic activities, they remain unpredictable in practice. It is impossible to predict them, and the theory has yet to provide sufficient reasons. This has been called Exchange Rate Puzzle, a phenomenon long awaiting its logical treatment in theory of Economics.
4. To Identify Logical Contradictions: If an observation, say an experimental setting, controls all possible intervening variables, sets conditions closest to ceteris paribus, and then identifies a phenomenon which contradicts the one predicted by theory, this too can help refine the theory by motivating research how can fundamentals explain the observed. For instance, it has been observed that when information is complex, or large, agents tend to make decisions which look as if they are irrational ones. Now what awaits is its explanation using fundamentals of economics. One such attempt was to explain this by means of costlier information processing. Information processing incurs costs, and under conditions of scarcity, it is logical to rationaly ignore some alternatives whose evaluation can exhaust already scarce resources which can be used elsewhere. This is called Rational Inattention as introduced by Professor Dr. Sims.
E.1. In preceding two cases, of gaps and contradictions, it is quite possible that additional concepts are introduced in theory but what is not possible is that such observations alone begin to define Laws of Economics.
Reference: Chapter 04 of Robbins, L. (2007). An essay on the nature and significance of economic science.