This week Prime Minister Mariano Rajoy announced new tax hikes and spending cuts to reduce Spain’s monstrous budget deficit, prompting demonstrators to join striking coal miners to protest the austerity measures on the streets of Madrid. But for all the talk of tough cuts, Spain’s default risks have not nearly been eliminated. The Spanish state still spends at a level far surpassing the economy’s capacity to yield revenues to support it.

Among this week’s measures—which Spain’s cabinet will officially approve today—is a hike in the rate of VAT to 21% from 18%. Civil servants’ wages are being slashed by 7%, unemployment benefits beyond the sixth month will be reduced by 15%, and some bureaucratic expenditures and subsidies will be cut by a third. The planned increase in the retirement age to 67 from 65 will be sped up, and the pension amount for new entrants will be lowered.

Until now, the Rajoy government had tried to maintain the oversized public sector by raising taxes on families and enterprises. As one of his first actions after entering office, Mr. Rajoy raised marginal income-tax rates, placing them at some of the highest levels in Europe. In March, his government closed corporate tax loopholes but didn’t lower the headline rate, thereby imposing, in effect, a tax hike on many businesses. Like many of his fellow European heads of government, Mr. Rajoy has preferred to impose austerity on the private sector rather than on the state.

This week’s spending cuts are a step in the right direction, but Madrid is still far from a sustainable fiscal position. It’s not even certain whether the new measures will allow the Spanish government to meet its EU-mandated target of a 6.3% deficit for 2012 given that only five months of the year remain.

The sad part of this story is that the bloat in the Spanish public sector is actually quite recent. Government spending swelled thanks to the extraordinary revenue growth provided by the housing bubble. Between 2001 and 2007, total revenues grew by 67% while expenditures increased by 57%. Spain ran modest budget surpluses for a few of those years, but those vanished as bubble revenues ran out while spending continued to grow. A 1.9% surplus in 2007 turned into an 11.2% deficit in just two years.

By the end of 2011, public expenditures were 75% higher (33% higher after adjusting for inflation) than a decade before.

In fact, Spain would have a balanced budget today if Madrid had frozen its spending per capita during the bubble years of 2001 and 2007, as Germany did. If the Spanish government wants to balance its books, it only needs to burst the public-sector bubble that was born out of the financial and housing bubbles.

Public spending would shrink by €21 billion, for instance, if the real income and number of civil servants per citizen were reduced to 2001 levels. If pensions were cut (in real terms) to 2001 levels, that would reduce expenditures by some €20 billion. Another €15-20 billion would be saved if unemployment benefits were consolidated. Eliminating subsidies to nonproductive industries, associations, trade unions and politicians would save more than €20 billion.

In other words, rationalizing some of the most patently inflated portions of Spain’s public sector would provide around €80 billion in savings. That would reduce our 2011 deficit by 90%—without any tax hikes.

The good news is that Prime Minister Rajoy has finally admitted that all budget items must be considered for cuts, even those which up to now were said to be untouchable. But for Spain’s economy to grow and not simply to stabilize, we need both additional spending cuts and tax cuts—precisely what the People’s Party had promised to do before last year’s elections. It is time for Mr. Rajoy to deliver on that pledge.

Far from calming the markets, Spain’s request for a €100 billion loan to bail out its banks has sent Spanish interest rates soaring and led to multiple downgrades from the credit-rating agencies this week.

There’s no question that the Spanish banking sector faces huge problems, thanks to its high exposure to a housing and real-estate market that continues to decline after a massive boom. But the Spanish state, with its own deficits and official unemployment of 25%, cannot afford to save the banks, even with the help of a soft loan from Brussels. This is the clear message from the markets at least.

Fortunately, there is a better solution for Spain’s banks: Instead of a bailout, the Spanish state should force a “bail-in,” in which all of the banks’ subordinated debt and some of its senior unsecured debt is converted to equity. This would reduce the banks leverage and increase the capital available to absorb the coming losses.

First of all, consider the grim fact that even €100 billion may not be enough to put Spain’s banks back on their feet, as they could easily face losses of perhaps three times that amount: Real-estate loans amount to €298 billion, construction credits to €98 billion, mortgages to €656 billion and other loans for families and firms to €683 billion. Assuming a 50% loss in real-estate and construction loans, a 5% loss in mortgages and a 10% loss in other credits to the national private sector, brings us quickly to the worrying figure of €300 billion in losses. And don’t forget the banks’ additional exposure of €78 billion to Portugal and €10 billion to Greece and Ireland, which could add losses of between €40 billion or more to our calculation.

Spanish banks currently report total equity of €377 billion, so losses on this scale would leave them with just €50 billion to €70 billion in remaining equity. To bring them back to reasonable levels of capital would then require €150 billion to €170 billion—well above the €100 billion line of credit that the EU plans to offer. Thus, even if the Spanish government chose to borrow the full amount on offer, national banks would still be undercapitalized by an amount equivalent to two or three years of their pre-provision operating profits.

However, the bigger reason for being skeptical about the success of the EU bailout is not the insufficiency of the loan, but its disproportionate size for an economy, such as the Spanish one, that has already reached its debt saturation point. The fact that our government would have been unable to raise those €100 billion directly from the market shows that at the moment, no private investors believe our solvency. Adding some €100 billion in extra liabilities to an economy whose ability to pay its debts is already in doubt just pushes that economy even closer to default.

Neither the government nor taxpayers can afford even more debt. Spanish economic agents, both public and private, must deleverage themselves by increasing their saving rates and paying down their disproportionately large financial obligations. This is why real public austerity (based on spending cuts, not tax increases) is so important.

Fortunately, Spain’s inability to bail out its banks does not mean that our country must go through a disorderly and devastating national bankruptcy. Which brings us back to the healthier and much cheaper alternative, as the Spanish free market think-tank Instituto Juan de Mariana has recently shown: a forced debt-for-equity swap for the subordinated and senior unsecured liabilities of the Spanish banking system.

Converting into equity 100% of the €88 billion of subordinated liabilities, and 40% of the €160 billion of senior unsecured debt, would generate more than €150 billion of loss-absorbing equity for the Spanish banking system. Together with the estimated €25 billion in expected operating profits for 2012, before loss provisions, that would yield about €175 billion in new bank equity, without increasing the debt burden of the Spanish taxpayer or requiring a loan from Brussels.

In other words, there is a solution to the problems facing the Spanish banking system: not a bail-out, but a bail-in, whereby investors bear the vast majority of the cost of their own mistakes, without liquidating the banks and without pushing the Spanish economy into bankruptcy.

Certainly, a compulsory bail-in may initially cause some turmoil in interbank lending markets. But since the beginning of 2012, Spanish bank financing has already relied heavily on liquidity provided by the European Central Bank. After some time, short-term credit would flow again inside a country with much more robust and solvent financial institutions.