The International Monetary Fund’s $50 billion agreement with Argentina is failing. Earlier this month a scheduled $3 billion payment was postponed while the IMF and the country’s government continued to haggle in Buenos Aires. The peso extended its precipitous fall against the greenback.

The backdrop to this misery is President Mauricio Macri’s weak reform program combined with the IMF’s misdiagnosis of Argentina’s problems. Mr. Macri replaced the left-wing populist Cristina Fernández de Kirchner in December 2015. He inherited a rapidly growing public sector, huge fiscal deficits due to massive subsidies for key products, annual inflation of more than 30%, capital controls, and a dual exchange-rate system. With a slim majority in the National Congress, and facing midterm elections in October 2017, Mr. Macri adopted a gradualist approach to reform.

This strategy has yielded little. The purchasing power of the lower middle class—Mr. Macri’s main supporters—has deteriorated along with the economy. In a scramble to raise revenue, the government imposed a tax on nonresident holders of debt issued by Argentina’s central bank, effective April 25. This sparked capital flight and a cascade of events that have again put Argentina and the peso in the tank. By our measure, the annual inflation rate is now 123%.

In June Argentina did what it has repeatedly done—called in the IMF. The country has embarked on 20 such programs during the past 60 years. History doesn’t offer much reason for optimism about the current deal.

Consider the last program, which ended badly in 2001. Then-IMF Managing Director Horst Köhler delayed the disbursement of $1.3 billion scheduled for November 2001, even though Buenos Aires had complied with the IMF’s fiscal target for the third quarter. The IMF’s delay poured fuel on a raging fire. This ultimately resulted in the suspension of the IMF program, the collapse of the economy, and general political chaos. With its current postponement of payments, the IMF is again playing with fire.

The IMF traditionally obsesses over all things fiscal: the funding of debt rollovers and the trajectory of deficits. True to form, the IMF’s diagnosis has again focused mainly on Argentina’s fiscal shortfall. The organization has offered a standby loan agreement to underwrite a gradual closing of the deficit. While the loans are subject to conditionality, the IMF has overlooked the bulk of Argentina’s problems. Consequently, the country has signed up for a gradualist fiscal squeeze and a standard dose of IMF antigrowth medicine.

Yet what Argentina needs is sound money and pro-growth policies. For sound money we, like Nobelist Sir John Hicks, think there is nothing more important than a balance sheet. Consider the 2001 collapse of Argentina’s convertibility system. That system, unlike a true currency board, allowed the Central Bank of Argentina a great deal of discretion, which it used with reckless abandon. Its net domestic assets fluctuated wildly, which is incompatible with a truly fixed exchange rate. Inevitably, the balance sheet foretold the coming storm.

Delving into the central bank’s current balance sheet, we find three acute problems. The first is that its monetary liabilities—that is, the monetary base—have grown at excessive rates. From 2008 until Mr. Macri took the reins in 2015, base money grew at an average annual rate of 26%. With Mr. Macri’s arrival, that rate accelerated to 29%. These rates have made taming inflation to meet the central bank’s inflation targets a fantasy. It’s no wonder that Argentines have no confidence in their monetary system.

The second problem: The central bank engages in many activities that go well beyond the scope of its traditional monetary functions. The institution plays a large role in directly funding the government and acting as the government’s agent in the sourcing of foreign exchange to meet Argentina’s external obligations. This, in turn, has required the central bank to sterilize the creation of pesos resulting from those foreign-exchange operations. The largest single item on the liabilities side of the central bank’s balance sheet is the debt issued to absorb the excess pesos created in its role as the government’s agent in the foreign-exchange market.

The incestuous relationship between the federal government and the central bank shows up on the asset side of the balance sheet, too. The largest asset class is credit to the government—the result of the Kirchner government’s theft of the central bank’s foreign-exchange reserves for domestic spending and their replacement with peso-denominated government debt. More recently, it is the result of the Macri government’s quest to fund bloated government spending programs.

The third problem is simply the gigantic size of the balance sheet. Normally, central-bank balance sheets are only slightly larger than the monetary base and typically between 10% and 25% of broad money. In Argentina, the bank’s total liabilities are almost five times as large as the monetary base. And if that isn’t enough, the central bank’s balance sheet is larger than the broadest definition of money in Argentina.

The balance sheet has been abused for generations. Consider the horrendous results. Argentina’s average annual inflation rates in the 1950s, 1960s, 1970s, 1980s and 1990s were, respectively, 27.6%, 22.6%, 107.3%, 319.2% and 58.1%. Argentina experienced a bout of hyperinflation in 1989–90, when monthly inflation peaked at 197%. Multiple peso devaluations also accompanied that horrible inflation record.

It’s time to make official what Argentines embrace every time they sense a storm: dollarization. The central bank and the peso should be mothballed and moved into a museum.

Dollarization would guarantee a rapid return to growth in Argentina. At the same time, it also could solve Argentina’s debt overhang problem. To ensure success, the peso-dollar exchange rate employed in the dollarization process should be set at a level that undervalues the defunct peso. This pro-growth exchange-rate would make the economy highly competitive. Once assured of monetary stability in dollar terms, capital would flood in. Couple it with a 20-year debt pay-down schedule during which the government would be prohibited from borrowing at home or abroad, and Argentina would grow rapidly and could become debt-free.