[I]t must not be imagined that authority knows no bounds. Since its starting point is the permission to govern in accordance with right reason, there is no escaping the conclusion that it derives its binding force from the moral order, which in turn has God as its origin and end. ...The authority of governments is limited, and not just by the constitutions by which they are structured (whether they abide by those constitutions or not is a separate question). They are bound by the restraints of right reason and natural law, which are from God. Hence they are not free to do whatever they wish. They don't get to decide what's right and wrong in a vacuum; they don't get to make wars on their own terms; they don't get to make laws that ignore moral order.
Hence, a regime which governs solely or mainly by means of threats and intimidation or promises of reward, provides men with no effective incentive to work for the common good. And even if it did, it would certainly be offensive to the dignity of free and rational human beings. Authority is before all else a moral force. For this reason the appeal of rulers should be to the individual conscience, to the duty which every man has of voluntarily contributing to the common good. But since all men are equal in natural dignity, no man has the capacity to force internal compliance on another. Only God can do that, for He alone scrutinizes and judges the secret counsels of the heart. [§§47, 48]
Obviously there are many directions we might go in considering the implications here, but the thing that interests me for the purposes of this post is that PT rejects the use of coercion or bribery as the primary or exclusive means by which governments ought to promote the common good, favoring instead moral persuasion. What are the implications of that? One that pops into my mind is that all sorts of social engineering laws, by which governments intend to manipulate citizens to do their will, are illegitimate. These might take the form of punitive taxes on goods intended to discourage their consumption, or maybe even tax credits or deductions for other goods and activities. It doesn't matter, on this account of things, whether such laws "work." To approve of them on that score is to take a utilitarian view. The point, according to the Holy Father, is that such things are offensive to human dignity, which includes free will and the use of reason.
It seems to me also that this principle undergirds the Church's rejection of the welfare state (see, for example, Compendium of the Social Doctrine of the Church §351). Our contributions for the sake of the poor should not be coerced from us, as they most certainly are when we are taxed for them. In the same way we should not be bribed by the promise of "free" (or nearly so) health care into supporting a nationalized or socialist model of medical care (and we shouldn't be coerced into providing it for others, either, for that matter).
The Pope doesn't rule out literally any sort of coercion or reward when it comes to advancing the common good, but it seems to me that instances of it are supposed to be limited to certain aspects of the common good (for example, deterrents to violations of the moral law) or else limited in significant ways. It might make sense, for example, to particularly encourage charity by way of tax deductions for contributions to disaster relief.