The present disclosure is directed to methods of catalytically reducing carbon dioxide, each method comprising: contacting a composition comprising a spinel-type transition iron oxide with an alkali metal carbonate, bicarbonate, or mixture thereof at a first temperature to form CO, and an alkali metal ion-transition metal oxide; hydrolytically extracting at least a portion of alkali metal ions from the alkali metal ion-transition metal oxide by the reaction with CO2 and liquid H2O at a second temperature; and thermochemically reducing the transition metal composition of the second step at a third temperature, with the associated formation of O2.