Can publicly-traded corporations adjust earnings to meet analyst expectations?

Companies can manipulate earnings. There is illegal manipulation (i.e. fraud) and somewhat legal manipulation. Some of this somewhat legal manipulation is called "income smoothing" and "earnings management". Earnings management requires competent accountants.

You may be interested in reading The "Numbers Game", a 1998 speech by then SEC chairman Arthur Levitt, which also includes a brief overview of some earnings management methods:

• "big bath" restructuring charges - Report as much restructuring charges as you can. If you later "discover" that you have "overestimated" the restructuring charges, you can bleed back the restructuring charges in the future to make future earnings look higher.
• creative acquisition accounting
• "cookie jar reserves" - If current earnings are high, place the earnings in "cookie jar reserves". This will decrease the reported earnings today, but these reserves will be useful for inflating profits in future years. When there is low profit in future years, "earnings" can be taken out of the "cookie jar reserves" to report inflated profits.
• "immaterial" misapplications of accounting principles
• premature recognition of revenue - Shifts future earnings into current earnings.

The financial system we have relies on a system of checks and balances intended to prevent manipulation / fraud from occurring.

The primary way this is done, is through the requirement that public stock exchanges have, for companies to obtain a 3rd party audit of their financial results. If you open the financial report of any public company, at the front page there will be a statement from an accounting firm stating that to the best of their ability to audit, the numbers are not 'materially misrepresented'. This means that any error (intentional or not) should in theory be negligible to the overall results being reported.

However there are a few flaws with this system: audit firms intend to 'consider, but not detect' fraud. This means it is in the back of their mind, but primarily they are looking for accidental misstatement or non-hidden errors in accounting policy. The truth is that fraud through collusion is incredibly hard / expensive to detect. So a firm will observe whether internal controls are faulty enough to allow fraud to be directed by a single individual, but if multiple individuals collude, that is very hard to detect.

This means that sometimes fraud does occur in the reporting of financial results, leading to a significant misstatement of earnings. The most famous example these days would be Enron. To be simplistic, they were recording revenue to be earned from utility companies from infrastructure that had not been built yet, with the underlying 'justification' that their history of growth projected that the revenue would soon occur. The failure of the accounting firm, Arthur Andersen, was so great that it no longer exists.

For a company to not be fraudulent, it requires a competent auditor, but more than that it requires an internal culture of honesty and a strong presence of a board of directors with a willingness to listen to their internal audit committee (which is kind of like 'internal affairs' in that it works for the company but doesn't report to the CEO, it reports directly to the board). This is no guarantee that fraud doesn't occur, but it's the system we have in place currently.

Various other measures have existed from time to time to increase the ability to rely on financial results as reported, with varying successes. The risk of misstatement is always there.

To elaborate, imagine a hypothetical scenario in which they calculate the earnings for a certain quarter before a higher consensus earnings estimate comes out. Do they consider bumping up their earnings a little bit to match the consensus estimate, and then do the offsetting adjustment in one of the subsequent quarters hoping that it will be better? Or if the consensus earnings estimate is less than their independently calculated earnings, do they consider revising the earnings number downwards anticipating that they will need the extra earnings to top up possibly deficient earnings in later quarters?

this is just one example of a company (Fannie Mae) manipulating the numbers:

On December 18, 2006, U.S. regulators filed 101 civil charges against chief executive Franklin Raines; chief financial officer J. Timothy Howard; and the former controller Leanne G. Spencer. The three were accused of manipulating Fannie Mae earnings to maximize their bonuses. The lawsuit sought to recoup more than $115 million in bonus payments, collectively accrued by the trio from 1998 to 2004, and about $100 million in penalties for their involvement in the accounting scandal. After 8 years of litigation, in 2012, a summary judgment was issued clearing the trio, indicating the government had insufficient evidence that would enable any jury to find the defendants guilty.[76] Conflict of interest

Manipulating the numbers as you suggest is against the law. The bonus money was triggered by meeting certain numbers. They manipulated the performance of the company to make more money for themselves.

When companies do this they are defrauding investors. In many cases the auditing firm that doesn't catch it in the audit, or chooses to ignore the warning signs in the audit can also get in trouble.