This week Richard Vedder, an Ohio State economist who runs the Center for College Affordability and Productivity, and his student, Christopher Denhart, ran a provocative piece in the Wall Street Journal on “How the College Bubble Will Pop.” They argued “the benefits of a degree are declining while costs rise.”

Looking at earning potential, Professor Vedder and Mr. Denhart suggest that a “key measure of the benefits of a degree is the college graduate’s earning potential and . . . their advantage over high-school graduates is deteriorating.” As a direct result of this perceived loss of value, total college enrollment has fallen by 1.5% since 2012. The result? The college bubble will pop.

Reaction was swift. Jordan Weissmann countered in The Atlantic. In his response, Mr. Weissmann looked at the same data from the National Student Clearinghouse and determined that enrollment actually grew at traditional 4-year colleges. By examining the data by category of institution, Mr. Vedder found that students are not giving up on traditional colleges but on “for-profit schools, whose business models and horrible loan records make them patently untraditional.”

The argument is an important one principally because it signifies a more important debate about the value of a college degree. In truth, to borrow from the commercial jingle made famous when Rice Krispies were poured into a bowl filled with milk, it may be more important first to listen for the snap and crackle before identifying the pop.

In the statistics battle, Mr. Weissmann is right. Declines are skewed to for-profit providers and 4-year non-profits have maintained a kind of steady state. We will need more analysis to determine the impact of 2-year transfer and foreign students to American higher education.

Deeper analysis will determine whether these institutions have added them into the enrollment mix, balanced by tuition discounting and better efforts to address demographic shifts in applicant pools, to explain the modest increases.

Further, the value the data overwhelmingly support the argument that a college degree provides substantially higher lifetime earning power. The gap discussed by Mr. Vedder may be caused as much by recessionary wage depression, declining median family income, and higher unemployment that places new graduates in a buyer’s market.

The statistics battle this week is less important for the hypothesis offered than for the deeper sense that fundamental changes must occur soon in American higher education. Those listening for the “snap” will suggest that how colleges finance education no longer works. Discount rates at four-year private approach 50 percent and a surprising number of colleges failed to meet their first-year enrollment targets this year.

Additionally, Moody’s issued a sector-wide downgrade in bond ratings. Further, the loss of traditional undergraduate 4-year markets to for-profits and community colleges indicates that something is broken that must be fixed.

And then there is the “crackle” that may be the most dominant sound in the milk-filled cereal bowl. American higher education is losing the perception battle in the media and with consumers. There’s a lot of background noise and little of it supports American higher education. Blaming social media may be accurate but it doesn’t matter in the end. Perception takes on a life of its own. You can win the intellectual battle within academia and lose the war with American families.

Training broadly educated citizens is a noble undertaking but an insufficient recessionary argument. College and universities must adapt what they teach to how students have learned as they enter the classroom, blend technology with traditional pedagogy, and differentiate their programs, teaching methods, and clinical experiences to survive in a highly competitive market.

Even more basic, however, colleges and universities must pay attention to outputs. Higher education has always been reasonably good at measuring inputs and developing process but it has almost uniformly ignored outputs. Students are broadly educated because professors teach them how to read insightfully, write, communicate, use technology, apply quantitative methods, and work in collaborative settings. These traits define a liberal arts education. They also meet workforce needs.

In making the case, American higher education must look at outputs as the first, best line of defense. Colleges and universities must develop stronger career centers, alumni linkages, and practical career pathways linked to internships and externships, whatever the major. They must set into place a social contact with students who become graduates by providing a lifelong “cradle through career” network.

In the end, the best higher education policy is seldom set by snap shot anecdotal evidence. What does matter is what’s behind the “pop.” If the enrollment bubble pops, it won’t be because Americans no longer perceive the value of a college degree. It may be because higher education refused to imagine a new future in a post-industrial economy, failing to innovate, create and imagine fast enough.

Higher education leadership — including trustees, administrators and faculty — must not risk continue to live in a world that they wish existed. The end of the recession cannot signal a return to older ways of financing, educating, and assessing how we educate globally. In the brave new world ahead, what matters most is value not measured by sticker price but by outputs that support the enterprise.