Never underestimate the importance of dumb luck. If Jimmy Carter wins this election, he may owe more to that than conscious political strategy. Since midsummer, the gods of the economy have played the numbers to his tune. Unemployment has declined, inflation has abated and consumer confidence has increased.

Chances are that the tune is false, that the outlook is worse than the numbers imply. But, meanwhile, the fleeting sense of improvement has rescued the Carter campaign from preordained defeat.

He trails badly, but at least he has a fighting chance. If people don't vote only their pocketbooks, economic conditions create a climate in which other issues are resolved. All the undecided voters -- an abnormally high number this year -- must come to terms with the prospect of change. Do they think things are so bad now that, almost at any risk, they will throw the current bum out? Or do they fear the next guy will prove a worse bum?

The economy's modest recovery is almost bound to make this delicate psychology work in Carter's favor. The decline in unemployment (from 7.8 percent in April to 7.5 percent in September) and the slowing of consumer price rises (from an annual rate of 18 percent in March to 7 percent in August) lend more credence to his implicit promise of slow, steady improvement.

Polls suggest that as people become more optimistic about their personal fortunes, they become less critical of the incumbent. And the consumer confidence index of the Conference Board, a research group, rose from 42 in May to 76 in September.

A cynic might conclude that Carter and his lieutenants somehow have manipulated the economy. That, however, credits them with excessive competence or power. The administration has erred consistently in its economic forecasts and blundered in its prescriptions. The current improvement is no exception; it was not foreseen.

But Carter is attempting to make the most of his good fortune. His recent outburst against the Federal Reserve Board was intended to erase the only splotch on the statistical canvas: rising interest rates. Even there, though, his luck holds. The current consumer price index reflects mortgage interest rate commitments made last spring. Rates were declining then, and those decreases help account for recent low rises in the index. Most of the effect of higher mortgage rates won't appear in the index until after the election.

Carter is no stranger to such flukes. Back in 1976, the situation was reversed -- also to his advantage. Just as the economy now has perked up, then it strangely stagnated. Unemployment, which had dropped from a peak of 9 percent in May 1975 to 7.3 percent in May 1976, rose in the months before the election. The last reported rate before the voting was 7.8 percent for September. The Conference Board consumer confidence index followed the same path. It slumped.

All this probably cost Gerald R. Ford the White House. The economy's sputtering performance confirmed the old party stereotype: The Republicans don't care about the unemployed. Postelection surveys indicated that party voting experienced a resurgence in 1976, but party voting meant that people reverted to the New Deal economic preconceptions. Remember, Ford lost by only 2 percent of the popular vote -- and less in some key states. Ironically, by January the unemployment rate had dropped to 7.3 percent.

The same thin arithmetic could reassert itself this year. Reagan's effort to demolish once and for all the Democratic claim to superiority on economic matters started with awesome advantages. The Democratic reputation rested on the party's commitment to low unemployment; but, as inflation has rivaled joblessness as a source of public anxiety, New Deal and New Frontier economics have lost their attractions.

Moreover, as the following table shows, it was Carter's bad luck that the 1979-80 recession concentrated unemployment in traditional Democratic strongholds of the industrial Midwest. The table gives regional unemployment rates for September 1979 and 1980 (in percentages with no seasonal adjustment). (TABLE) (COLUMN)Sept.(COLUMN)Sept. (COLUMN)1979(COLUMN)1980 Northeast(COLUMN)6.6(COLUMN)7.1 Midwest(COLUMN)5.2(COLUMN)8.3 South(COLUMN)5.2(COLUMN)6.4 West(COLUMN)5.7(COLUMN)6.9 National (unadjusted)(COLUMN)5.6(COLUMN)7.1 National (adjusted)(COLUMN)5.8(COLUMN)7.5(END TABLE)

Worse for Carter, joblessness in the Midwest lies largely in five states with 96 electoral votes: Illinois, Indiana, Michigan, Ohio and Wisconsin. The September rate for this area was 9.3 percent, up from 5.7 percent a year ago.

But now Carter has counterattacked with a program to aid the steel industry and calls for the Japanese to limit voluntarily auto exports to the United States. He is attempting to reassure the industrial heartland that its best hope lies with the Democrats. The economy's fortuitous improvement reinforces his general pitch that voters ought to play it safe with the incumbent. Reagan's unconvincing policy shifts -- on labor, for example -- could help Carter further.

What mars Carter's optimism is the rise in interest rates. It would be easy to conclude that a conservative Federal Reserve Board is trying to guarantee the president's defeat. In fact, the Fed simply is responding to the logic of a high underlying inflation -- 9 percent or 10 percent -- and the resurgent loan demand accompanying recovery. Both increase the public's desire for money. If the Fed accommodates this by increasing money supply growth, it only risks more inflation later.

Carter consistently cannot criticize Reagan for inflationary proposals and then suggest that the Fed relax its money supply targets. But, then again, Carter's greatest consistency is his inconsistency. He always makes sense so long as you never compare his statements.

Maybe the economy's modest recovery will put him back in the White House. But, just as the 1976 lull proved a mirage, so may this pre-election spurt. No matter who wins, the next president is likely to be stuck with stubborn inflation and slow growth.