Starting in the 50s with films like Mario Monicelli's Big Deal on Madonna Street (1958), comedies in the Commedia all'Italiana vein satirized the human condition with reams of black humor. Though The Overcoat was co-adapted by Cesare Zavattini, a leading member of the Neo-realist movement, from Russian author Nikolai Gogol's most famous work, it has much more in common with Monicelli's film, which follows a bumbling group of unemployed schnooks who turn to crime when jobs become too scarce and too laborious for their liking.
The Overcoat similarly parodies Carmine De Carmine (comedian Renato Rascel in an inspired, elastic performance), a menial bureaucrat who grows more attached to his new fur-lined coat than his impoverished neighbors, who beg him to petition his pompous superiors with their grievances. Carmine instead leaves them in the lurch and goes all out for his handsome-looking new garment: he takes photos of himself in it, he proposes toasts to it and even winds up haunting the streets after he's dead looking to get it back. His story can only be qualified as a slice of life if we can call Jerry Lewis films somber tributes to the common man.
Which isn't to say that The Overcoat isn't a wonderful counterpoint to, say, Vittorio De Sica's Umberto D. (1952), a canonical masterpiece some historians would argue is too much like a fairy tale to be technically a Neo-realist film. The titular protagonist in De Sica's film is similarly left destitute with nowhere and nobody to turn to, but as in a traditional Commedia all'Italiana, Carmine's vanity, as innocent as it may seem, is ultimately the cause of his demise.
The Overcoat wouldn't be as effective in its moralizing it is if its tragicomic hero wasn't as pathetic as he is (a highlight of the film comes when Carmine embarrasses himself and his superiors by reading back only the most scatterbrained and unflattering snippets of their official conversations). It also wouldn't be a good Commedia all'Italiana without a believable patsy.