Reading through the Institutes of Christian Religion, I have come upon Calvin's interaction with the Ten Commandments. In discussing the second commandment's promises and curses, Calvin makes some tremendous statements about God's covenantal dealing with us and our children:

"There is a promise of mercy to thousands—a promise which is frequently mentioned in Scripture, and forms an article in the solemn covenant made with the Church—I will be “a God unto thee, and to thy seed after thee,” ( Gen. 17:7). With reference to this, Solomon says, “The just man walketh in his integrity: his children are blessed after him,” ( Prov. 20:7); not only in consequence of a religious education (though this certainly is by no means unimportant), but in consequence of the blessing promised in the covenant—viz. that the divine favour will dwell forever in the families of the righteous. Herein is excellent consolation to believers, and great ground of terror to the wicked; for if, after death, the mere remembrance of righteousness and iniquity have such an influence on the divine procedure, that his blessing rests on the posterity of the righteous, and his curse on the posterity of the wicked, much more must it rest on the heads of the individuals themselves." (Inst, 2.8.21) [Emphasis Added]

When witnessing engagement with proponents of infant baptism, one of the things I often hear from Reformed individuals is how blessed the children are in receiving a spiritual education. It is true that those who perceive their children to be members of the covenant often take catechesis more seriously than others. But one does not necessarily follow the other. Childhood education is still valued among credobaptists and it isn't suddenly "less spiritual" because a baptism has not been performed. No, a "religious education" is not the primary blessing of God's covenant dealings.

Further, this strange emphasis on knowledge and wisdom displays one of the problems that repeatedly plagues Protestants—infatuation with intellect. In his quote, Calvin affirms that a spiritual education is a blessing. But more specific is that "divine favour will dwell forever in the families of the righteous." Abstract knowledge of Divine properties is not enough. Protestants regularly run the risk of turning God into the Object of our religious-scientific research without allowing ourselves to be addressed by Him, the Subject of our covenantal relationship. Hence, Calvin in his Geneva Catechism said against the mere intellectual knowledge of God:

"12 M. What more is needful? 
C. That each one of us be fully convinced that God loves him, and that he is willing to be to him a Father and a Savior."

Our relationship to God—as He has sovereignly administered it—is the true blessing of God's covenantal dealings. This is true to such an extent that Calvin is not afraid to state that even after death God's workings and dealings are impacted by the righteousness (or lack thereof) of a generation. The reality for the covenantal believer is that in making Himself our God, God has made Himself the God of our offspring and extended promises to them. This is the fundamental basis of infant baptism, that God cares about our children before they care for Him.

Still, God has not tied Himself to this rule absolutely. And Calvin shortly after putting forth this covenantal dealing and promise from God, re-establishes God's ultimate freedom as Creator:

"Notwithstanding of this, however, the offspring of the wicked sometimes amends, while that of believers degenerates; because the Almighty has not here laid down an inflexible rule which might derogate from his free election. For the consolation of the righteous, and the dismay of the sinner, it is enough that the threatening itself is not vain or nugatory, although it does not always take effect. For, as the temporal punishments inflicted on a few of the wicked are proofs of the divine wrath against sin, and of the future judgment that will ultimately overtake all sinners, though many escape with impunity even to the end of their lives, so, when the Lord gives one example of blessing a son for his father’s sake, by visiting him in mercy and kindness, it is a proof of constant and unfailing favour to his worshipers. On the other hand, when, in any single instance, he visits the iniquity of the father on the son, he gives intimation of the judgment which awaits all the reprobate for their own iniquities. The certainty of this is the principal thing here taught. Moreover, the Lord, as it were by the way, commends the riches of his mercy by extending it to thousands, while he limits his vengeance to four generations." (Inst, 2.8.21)

The application for the Christian to the believer is simple. Live in light of God's cross-generational covenantal blessings and curses. But also, rest assured that the faithful freedom of God is not tied in any way to us.