NEW YORK — The deal announced Thursday to end the fighting in Ukraine will face the same obstacle the previous such agreement has faced — how to ensure that Russia will abide by it. Frustrated by Russia’s continued support for Ukrainian separatists, Western statesmen have begun discussing military assistance for the Ukrainian government. But in trying to determine what would actually deter Moscow, it might be worth listening to what seems to scare Russians themselves — and it’s not military aid to Kiev.

When asked recently about the possibility of “SWIFT” sanctions, which would bar Russia from participating in the international payments system centered on the U.S. dollar, Prime Minister Dmitry Medvedev warned that Moscow’s response would be “without limits.” Andrei Kostin, the head of Russia’s second largest bank, explained at the World Economic Forum in January that such a move would instantly lead to the expulsion of the American ambassador from Moscow and the recall of Russia’s ambassador to Washington. It would mean “the countries are on the verge of war, or they are definitely in a cold war,” Kostin added. By contrast, Russia seems to be relishing its contra war in Eastern Ukraine, which at very low cost can keep Ukraine unstable and on the defensive almost indefinitely.

It’s understandable why Putin’s closest associates are so rattled by the prospect of additional economic sanctions. The Russian economy is in free fall. In a report released this week, the International Energy Agency said that Russia is “facing a perfect storm of collapsing prices, international sanctions and currency depreciation.” As former U.S. Deputy Treasury Secretary Roger Altman has said, “In this age, if the currency of a major nation collapses or its access to borrowing ends, it just can’t function.”

The IMF projects Russia’s economy will contract by 3 percent in 2015. And Putin needs strong oil revenues to maintain his power in the country. From 2008 to 2009, when oil revenues collapsed during the global financial crisis, the Russian government increased its spending by a staggering 40 percent to preserve social stability, according to The Economist. In recent years, defense spending has risen by 30 percent and food and housing subsidies have also grown. These props cannot be held up indefinitely. Over time, the money will run out.

On the other hand, Russia could easily handle continuing its military skirmishes in Eastern Ukraine. While its economic cards are weak, its military ones remain strong, especially compared with those of Ukraine. Moscow’s defense budget in 2014 was roughly 20 times Kiev’s, according to figures published this week by The International Institute for Strategic Studies. Russia has 771,000 active duty forces and 2 million soldiers in reserve, plus 8,000 nuclear weapons, of course. Adding to that, Ukraine is next door and its eastern regions are dominated by ethnic Russians, providing Moscow with manpower and a rationale for its mischief.

The argument against sanctions is that, while they might raise the costs for Russia, Putin has shown that he does not respond to higher costs in a rational, calculating manner. But if that’s the case, then military aid for Ukraine wouldn’t work either. No one believes that Kiev can prevail in a military contest with Moscow. A recent think tank report by former government officials urging military aid itself acknowledges that the package would merely raise the costs for the Kremlin in order to force it to negotiate. In other words, the consensus among experts is that the only possible strategy is to raise the costs for Russia. The disagreement is really about what kinds of costs Putin finds more onerous.

Military aid to Ukraine would stoke the fires of Russian nationalism, let Putin wrap himself in military colors and defend his “fellow Russians” in an arena in which he will be able to ensure that Moscow prevails. For a regime that waged two bitter and costly wars in Chechnya, a region far less central to the Russian imagination than Ukraine, the loss of some men and money in a military operation is not likely to be much of a deterrent.

Why would the West want to move from its area of strength — economic pressure — to an area where it will be outgunned in every sense? If Russia breaks this fragile peace deal, then more sanctions should be considered.

Sen. Lindsey Graham, R-S.C., recently offered the most honest reason why some in Washington are advocating military assistance. Even though it doesn’t seem likely to work, it’s a way of doing something in the face of Russian aggression. “I don’t know how this ends if you give [Ukraine] defensive capability,” Graham said at the recent Munich Security Conference, “but I know this: I will feel better because when my nation was needed to stand up to the garbage and stand by freedom I stood by freedom.”

But the purpose of American foreign policy is not to make Lindsey Graham feel better. It is to actually achieve objectives on the ground. That means picking your battles and weapons carefully.

Fareed Zakaria is a syndicated columnist. His email address is: comments@fareedzakaria.com.