What Backus, Kehoe and Kydland found in their article from 1992 was the opposite, namely that consumption is much less correlated across countries than output.
[1][2] Backus, Kehoe, and Kydland (1992) calculate the correlation of HP-filtered consumption and output for 11 advanced countries relative to the US.
[5] Stockman and Tesar (1995)[6] suggests two means of breaking the link between prices and quantities and making it hard for households to smooth consumption by trade.
If there is a positive technology shock raising their supply, they can’t smooth their consumption of these goods by exporting them abroad.
The second is "taste shocks": If consumption rises in one country without any change in the economic environment, it will borrow abroad, driving up the interest rate and inducing the foreign country to cut back on its consumption.