When should I use "to do" and "to doing"

Last year, two of her ministers suggested that convicted tycoons be pardoned if they could contribute to boosting economic growth.

"Boosting economic growth" is a noun phrase that is an indirect object of "contribute to".

He also argued that the heavy-handed approach taken by the government to promoting innovation is in fact retarding it.

"Promoting innovation" is a noun phrase that is an indirect object of "taken to".

Both examples may look confusing because the "to" next to the verb makes it look like an infinitive, but that is pure coincidence. In both cases "to" is a preposition.

In your sample sentences, boosting and promoting are gerunds - words that end "ing" and act like nouns. I like swimming and Swimming is fun are interchangeable with "I like cheese" and "Cheese is delicious", for example.

So the minister could suggest that tycoons contribute to a fund, or contribute to a repository - those are both nouns. And they can contribute to boosting economic growth, in much the same way. And the government might have an approach to poverty, or an approach to corruption, or an approach to promoting innovation. These gerund phrases work just like nouns, and can be the subject or object of sentences, for example.

1. Last year, two of her ministers suggested that convicted tycoons be pardoned if they could contribute to boosting economic growth.

2. He also argued that the heavy-handed approach taken by the government to promoting innovation is in fact retarding it.

Sentence (1)

In the first sentence the verb CONTRIBUTE takes a prepositional phrase as a complement. Specifically this verb takes phrases with the preposition TO. We can use this verb plus preposition combination with nouns:

• He contributed to our fund.

Here the preposition to is taking a noun phrase as a complement. In the original example it takes a clause. Now, the preposition to does not takes finite clauses. We cannot use a clause with a tensed verb after to. If we want to use a clause after to, we need a clause with an -ing form of the verb. In this case that clause is:

• boosting economic growth.

Alternative sentence (1)

Now, we could make a sentence that looks very similar, but which would in fact have a different structure and different meaning. The verb CONTRIBUTE can be used without a complement:

• We want you to contribute.

So we could make a sentence where the tycoons will be pardoned if they contribute, but we don't say what they are contributing to. We could also add on an adjunct (sometimes called an "adverbial phrase") which explains why they will contribute. We can use an infinitive of purpose to show this. Infinitives of purpose are used to explain why an action is done:

• I came to London to learn English
• Tycoons should be pardoned if they contribute to boost economic growth

In the first sentence the purpose of coming to London was: to learn English. In the second the purpose of making a contribution was: to boost economic growth. So we could have another sentence that looks like sentence (1) but means something slightly different:

3. Last year, two of her ministers suggested that convicted tycoons be pardoned if they could contribute to boost economic growth.

This is the alternative sentence that the OP is asking about. It looks similar to (1) but means something very slightly different.

Sentence (2)

Sentence (2) has some interesting grammar. It includes an example of heavy element shift. This sounds complicated, but it isn't. Sometimes when the complement of a verb or noun is very long, we like to shift it from it's normal position so that it occurs towards the end of the phrase. So for example in:

• She made the man very happy

... the phrase the man is the complement of the verb make, more specifically the direct object. There's another phrase there very happy which is a predicative complement comes after the object. Notice that if we change the order of the phrases the result is not good:

• She made very happy the man.

However, if the direct object is long, heavy, we can move it to the end of the verb phrase:

• She made very happy the man whom she had spent so many years chastising.

This is what has happened in sentence two. If we put the parts of the noun phrase in their normal order it's easier to see what's happening:

• He also argued that [the heavy-handed approach to promoting innovation [taken by the government]] is in fact retarding it.

Here it is easier to see that the noun approach takes a complement headed by the preposition to. We normally say the "approach to something". As with sentence (1) the preposition in this sentence cannot take a finite clause it takes a clause headed by an -ing form of the verb:

• promoting innovation

In the original sentence the preposition phrase has been moved over the rest of the noun phrase (taken by the government) and put at the end.

Alternative sentence (2)

Now the original sentence (2) could have a very different structure if it contained the plain form of the verb, promote. This is the Original Poster's alternative to sentence (2):

4. He also argued that the heavy-handed approach taken by the government to promote innovation is in fact retarding it.

In this sentence the noun approach does not have a complement. The noun phrase is being modified by this clause:

• taken by the government to promote innovation

In this version of the sentence the phrase to promote innovation is an infinitive of purpose. It explains why the government took this approach. They did it in order to promote innovation. The to here is not a preposition. It is part of the infinitival construction. Again the meaning of this sentence is subtly different from the original sentence, number (2).

Conclusion

The word to in the original sentences is a preposition which only takes -ing clauses, not finite ones. For this reason it has -ing forms of the verbs boost and promote. In the Original Poster's examples, the word to is part of an infinitival construction. It introduces infinitives of purpose. Although the alternative sentences look very similar and the meanings are comparable, the underlying structure and the more subtle shades of meaning are actually different.

In short, if you can replace the verb with a noun, the verb is a gerund:

I look forward to seeing this film / I look forward to it.

It contributed to killing her / It contributed to her death.

If you can't, it's an infinitive. I want to do it = > You can't say "*I want to it"

I came to see you => I came [in order] to see you.