hamminga, B., (1991), "Comment on Hands: meaning and measurement of excess content", in: de Marchi, N.B. and Blaug, M., Appraising Economic Theories, Hants, Brookfield, Edward Elgar, pp. 76-84. (see II 1.5) Summary:
COMMENT TO WADE HANDS ON THE MEANING AND MEASUREMENT OF EXCESS CONTENT?
Wade Hands is discouraged in the hunt for novel facts in studying economic research programmes. By way of consolation, he argues that "novelty" is, after all, not so fundamental in the history of Popper-Lakatos methodology.
But when he comes to listing the useful part of the Lakatosian notions, he does not only omit "novel facts". He also omits "content", "excess content" and "corroborated excess content". So, Wade Hand's discouragement exceeds far the realm of "novelty".
I have no difficulty in understanding this. But the title of this session is "the meaning and measurement of excess content", and this suggests that the organisers like me to make some attempt to apply the "content" related Lakatosian concepts to economic research programmes. Let me try to do so in a more precize way than has, I suspect, hitherto been done.
1) The meaning of excess content?
Figure 1 shows what a theory does to events. Some events are forbidden. They are inside the circle. Some are allowed, they are outside the circle.
FIGUUR
Fig. 1: Theories and Events
The allowed events, if we are to believe Popper and Lakatos, are uninteresting, the forbidden events are the only ones that are interesting, because if a forbidden event occurs, your theory is falsified. The empirical content is associated with the set of forbidden events.
The path of degeneration is depicted by the path in the direction down left in fig. 2.
FIGUUR
Fig. 2: Progress and Degeneration
If, after observing a falsifying event of T you make a shift towards a T that simply narrows down content so as to allow for the event that falsifies the old theory T , your research programme will degenerate. This path yields ever smaller circles and ends with empty content, with not forbidding any event, with not saying anything.
Now, whatever T you choose to shift towards, some loss of content is unavoidable: the new T has to allow for the observed event that falsified T . But a problemshift to some T is "progressive" only if, by the same stroke, T forbids some events that were allowed by the old theory T . These events are called theTexcess content?of T over T (shaded in the box down right in fig. 2).
This excess content isTcorroborated?if, despite severe attempts, we fail to observe some of the events it contains (forbids). And "corroborated excess content" means the same as "a (discovered) novel fact".
According to Lakatos (please note!) the discovery of a novel fact is not, as in ordinary English, the novel observation of an event, but theTfailure, despite severe attempts, to observe a newly forbidden event.
These are the meanings of "content", "excess content" (or, what is the same: "predicted novel fact") and "corroborated excess content", (or, what is the same: "the discovery of a novel fact"). Let us turn to their measurement.
2) The measurement of excess content?
Let T be the theory that Samuelson presents as an "Illustrative tax problem" on p. 14,TFoundations of Economic Analysis?(Samuelson (1947)). T consists of (1) and (2):
(1) p := xp(x) - C(x) - tx
where p is profit, xp(x) is called "total revenue in function of output", C(x) is total production cost and t is a tax rate on output.
(2) = 0 , <0
Samuelson proves the following theorem:
(3) T 5 ( ) <0
Which events are forbidden by T , and which ones allowed? Before answering that question we have to determine the set of eventsTrelevant?to the theory. Profit is a function of x and tTonly?(prices and costs are functions of x), so we have only two variables t and x, which can go up (+), remain unchanged (0), and go down (-). The list of logically possible, relevant events evidently reads as in table 1.
TABEL
Table 1: T and "events"
The theory implies a downward effect of taxes on equilibrium output. Since there are no other variables, if taxes go up (events 1, 2, 3), equilibrium output should go down (event 3). Event 3 is allowed, events 1 and 2 are forbidden. They are in the "content" of T , Lakatos and Popper would say. Similarly 4 and 6 are in the content, because t is, according to T theTonly?variable affecting equilibrium output. If t remains unchanged, xU should remain unchanged (event 5 is allowed) and any change of xU in this case (events 4 and 6) is forbidden. Events 7, 8 and 9 now speak for themselves. The content of T , what is in the circle of figure 1, so to speak, is the set of events {1, 2, 4, 6, 8, 9}.
Kinship does exist between these Popper-Lakatos ideas and Samuelson's concept of an "operationally meaningful theorem". Samuelson calls theorems like the right hand side of (3) operationally meaningful because they "could conceivably be refuted, if only under ideal conditions" (Samuelson (1947), p. 4). That is what Popper and Lakatos mean by "having (nonempty) empirical content".
Now let us study, by way of exercize, a hypothetical falsification and subsequent shift to a new theory T . Suppose we observe event 4 (this is symbolized by the mark of exclamation). Now, T is falsified. Any new T that does nothing but omit event 4 from the content would lead us into degeneration. T should at least "newly" forbid some event allowed by the old T ! So, a theory T say, giving in by allowing event 4 and in the same stroke forbidding, say, event 3, that was allowed by T , would mean "progress", Popper and Lakatos would say. But there is another way that is more typical and illustrative; and that is to introduce a theory T that contains an additional variable that is used toTexplain?why we have observed this falsifying event.
Let us consider a shift towards some theory T that stops treating price as a function p(x) of output, and turns p into an exogenously given variable. The additional variable p can of course go up, down and remain unchanged, and this triples our list of relevant events. (table 2).
To event 1 of table 1 (t and x both rising) there correspond events 1, 2 and 3 of table 2 (p going up, remaining unchanged, or going down), etc. We now have tripled the size of the boxes of figures 1 and 2, so to speak. This does not affect the content of T , of course. To every one forbidden row in table 1, there now correspond three forbidden rows in table 2. But where do we place our mark of exclamation, symbolizing the falsifying event? Our old falsifying event 4 in table 1, corresponds to events 10, 11 and 12 in table 2. Now we have to go back to our falsifying event to see what happened to prices! Suppose it is observed that they went up. So our mark of exclamation should be on row 10. T may still forbid events 11 and 12, they were not yet observed. But it should allow for event 10.
Now suppose we have a theory T maximizing p(x, t, p) and suppose two "operationally meaningful" theorems can be derived
T 5 ( ) <0tand?( )> 0
That is, taxes keep having a downward effect on equilibrium output, and prices now have an upward effect. Event 1 of table 2 is allowed by T , because tax and price changes work in opposite directions and T does not say which effect will dominate. But events 2 and 3 of table 2 are forbidden by T as they were by T . Likewise, we loose content by newly allowing event 4, 10, 18, 24 and 27. But we gain content too! Events 13, 14 and 15, all allowed by T because they correspond to event 5 of table 1, are notTall?allowed by T . With price + and tax change 0, equilibrium output should go up (event 10), and therefore event 13 is forbidden by T . Similarly, event 15 is forbidden by T . These two events 13 and 15, form theTexcess content of T over T , symbolized by the shaded area in the box down right in fig. 2.
Given a falsification of T by an event of type 4, from the perspective of table 1, that turned out to be event 10 from the new perspective of table 2, T does all that Lakatos requires of a theoretically progressive problemshift: it removes event 10 from the content, at the same stroke adding events 13 and 15.
The problemshift is, above this, also empirically progressive if this excess content is also "corroborated"; that is, if, despite severe attempts, we fail to observe the events 13 and 15. "Severe attempts" means here: collecting observational reports on events with rising prices and no tax change (events 10, 13, 16), andTnever?finding an event 13 (always finding 10, since 16 is also forbidden).TCorroboration of the excess content of T over T means failure to observe event 13. And, similarly, failure to observe event 15.
3) Conclusion?
These exercizes in economic Lakatosianism should suffice to make clear what blueprint of economics it implies.Does?economics conform the blue- print?Should?it do so?
I do not know whether itTshould, so I am happy with not being in power. But, contrary to Wade Hands, these purely empirical questions seem interesting to me and not useless all:Tdo successive comparative static theories in economic research programmes have "excess content", in the specific logical meaning given to this notion by Popper and Lakatos? Is some of this excess content "corroborated"##
Note thatTany two?comparative static theories can be compared in the aboveshown way,Tno matter the variables they contain!?Simply lump all variables together to construct your table of relevant events.
Note that this procedure obeyes nice mathematical laws, from the realm of combinatoric theory.
My present bet for the answer is that each shift (say in the history of demand theory or in the history of the theory of international trade, job search theory etc.) involves heavy losses in "content", very small gains, some falsification, and no "corroboration". This does of course not mean raising your eyebrows about economics. But any outcome whatever would mean some growth of knowledge about it. And it would throw some novel light upon Lakatos. Why not do some calculation!
PHiLES 0.1: Top of Page Menu