In what cases is best to use "to" or "for" after the words "stimulus" and "impetus"?

Question

In what cases is best to use "to" or "for" after the words "stimulus" and "impetus"?

Is there any difference in the use of the prepositions with each of the last two words?

I exclude from the question the cases in which "to" is followed by an infinitive.

I have collected examples from English dictionaries to make it easier to test candidate usage rules.

Examples using "stimulus":

▪ The book will provide a stimulus to research in this important area.

▪ Foreign investment has been a stimulus to the industry.

▪ The surge in new housing construction should provide a stimulus to the economy.

▪ Tax cuts are the classic stimulus for a sluggish economy.

▪ The pay raise was a stimulus for production.

▪ This knowledge may have served as an additional stimulus for his interest in the field.

Examples using "impetus":

▪ Often the impetus for change in education has had to come from outside the school establishment.

▪ The exceptional quality of the festival is an indicator of the impetus for this celebration.

▪ The report may provide further impetus for reform.

▪ The constructivist turn in the study of world politics provides new impetus to studies of the political deliberations of human agents.

▪ He gave a tremendous impetus to dynamic economics.

▪ The discovery gave fresh impetus to the research.

▪ The Surgeon General’s speech will give new impetus to the anti-smoking campaign.

▪ The recent publicity surrounding homelessness has given a fresh impetus to the cause.

Answer 1

An answer for "stimulus" only

Here is the SOED's definition of "stimulus"; it shows that "to" is the usual preposition used with this word. (SOED: Shorter Oxford English Dictionary)

stimulus 1 A thing that provokes, increases, or quickens bodily activity; esp. (Biol.) a material agency that evokes a specific reaction in an organ or tissue. L17. b gen. An agency or influence that rouses or spurs something or someone to action or quickens an activity or process; a spur, an incentive. (Foll. by to an action etc.) L18 c Psychol. Any change or event which excites a nerve impulse and gives rise to a response or reaction. L19.

(L< number >: since the late < number >th century; late: last 30 years in the century)

As pertains to the general definition of the word (see "b gen."), "to" is the unique preposition that can be used.

The preposition "for" can be justified when the object of the preposition is not what is being stimulated but instead is something to which the stimulus is simply associated. We find below a telling example from the medical field.

International Handbook of Cognitive and Behavioural ... - V.E. Caballo · 1998 Failure to recall the location of objects is a frequent problem of dementia patients. For example, individuals might forget or become confused about where they have placed specific articles of clothing. Stimulus control can be enhanced in the case of clothing loss by simply insuring constancy of the stimulus that is associated with the clothing. Storage of the clothing in the same location at all times can increase the likelihood that the clothing is found. Individuals may also forget or become confused about the location of their own room in an institution or at home. The stimulus for the bathroom can be made more distinct and apparent by color coding the door (Harris, 1980), hanging a flag from the wall with "restroom" written on it […].

Here is another telling example in the same vein.

President Clinton's Proposals for Public Investment and ... United States. Congress. House. Committee on Ways and Means · 1993 Deficit reduction will make an ipmortant contribution to our long-term economic health. But we also need to take immediate action to create jobs and to stimulate investment spending. Thus, we are proposing a modest stimulus for the immediate problems facing us, […]

Another type of context obtains when the stimulus operates on someone or something in the way of causing an event or action to take place through the agency of that person or thing, and then the noun of that event or action is introduced by "for". The object of the preposition does not name what is being directly stimulated but instead something to which the stimulus is simply associated as an indirect effect.

Surgery for Snoring and Obstructive Sleep Apnea Syndrome: ... Mario Fabiani · 2003 GH is necessary for normal growth. Its lack causes deficient growth, its excess giantism; GH does not seem to act directly on growth, rather it indirectly stimulates the formation of other hormones. These factors are known as stomatomedin or insular-similar factors (IGF-I), they are dependent on GH, and seem to be accountable for the stimulus for growth.

Active Assessment for Science: Thinking, Learning and ... Stuart Naylor, ‎Brenda Keogh, ‎Anne Goldsworthy · 2013 The most important aspect of writing a letter is that it offers a motivating stimulus for writing.

The Rest Principle: A Neurophysiological Theory of Behavior - J. D. Sinclair, ‎John David Sinclair · 2014 The "S_h" part is clear—it is simply input from hunger—but the "nonfood stimuli" part implies activation by the absence of stimuli related to food rather than by the presence of particular nonfood stimuli. In this way the S_{h+nonfood stimuli} neurons, or S_{h +no food} for short, ate similar to the "off" neurons in the visual system activated by the absence of light stimulation. Nevertheless, this must be the stimulus for searching for food rather than merely S_h, otherwise the animal would continue searching for food-related stimuli after they already have been located and other responses such as approaching the food and eating it are needed.

It will be found that a certain number of the cases found in the Google research "stimulus for" are of the two types just referred to.

The OP's sentences in which "for" is used

▪ Tax cuts are the classic stimulus for a sluggish economy.

▪ The pay raise was a stimulus for production.

▪ This knowledge may have served as an additional stimulus for his interest in the field.

In all of these examples it seems fairly clear that what or who is being stimulated directly is not the entity named by the noun introduced by "for"; not the economy but those that participate in it, not the production but those that are responsible for it, not the interest but those possessed of that interest, are subjected to the stimulus, and so all cases fall outside of the definition in the SOED.