It seems difficult to say anything insightful about The Chase after reading Robin Wood's essay, but I'll try. I want to focus my discussion of The Chase on its invocation of and the family melodrama and the Western genres, using Wood's schemata as a guideline. As Wood notes, The Chase works effectively in conveying meaning through its use and inversion of genre conventions. I want to try to identify some of those conventions, compare/contrast what Penn does with them, and suggest how they either fit into Wood's schemata or have some other implied meaning.
The melodrama I am most reminded of is Sirk's Written on the Wind, especially in the oil tycoon as father figure. Jasper Hadley and Val Rogers are both rich men with one son to whom they wish to pass down their fortune. Like Jasper, Val Rogers is disappointed in his son, seeing more strength of character in someone else. For Jasper, it is Mitch Wayne; for Val, it is Calder. However, unlike Jasper, it becomes apparent that Val actually did love his son as he cries out for him as he lay dying. Calder, unlike Mitch, also does not return affection for Rogers, to whom he makes a final break from when he refuses to allow him into the jail cell. The result of this, as Wood notes, is a "collapse of confidence in patriarchal authority," and marks the complete isolation and destruction of Rogers and his empire - any potential candidates have walked away (Calder, Anna) or died (Jake). In Written on the Wind however, Marylee is left to inherit the family business which is her great tragedy. In this case, the patriarch figure, though dead, continues to hold a grip on his family, which Sirk makes clear through Jasper's portrait holding the same oil rig statuette that Marylee cries on. Thus, I would suggest that the view of the patriarch of Sirk's '50s film is much bleaker than Penn's. Wood notes this slight hopefulness at the end of this essay by noting how Anna is able to walk away as a representative of a new generation unrestrained by the father figure (Anna also disowns her father-in-law early in the film when we first see her). I would say that Anna is able to do what Marylee is not.
An idea that I see run through The Chase and some Westerns is that of the Western hero being ushered out by capitalism; the days of the gun come to a close and the cowboy becomes irrelevent. We saw this idea with The Professionals through the juxtaposition of the old-fashioned Western heroes and J.W. Grant, the capitalist businessman. The Professionals made those heroes relevant by reinforcing their ideals of justice and goodness through their saving of Raza and Maria and their rejection of Grant's money. There is a certain nostalgia for those heroes and those values and even though their future is probably limited as cowboys by the film's end, Brooks reasserts their value by showing how they can survive against people like Grant and the age of capitalism. In The Chase, however, the spirit of the Western hero, as conveyed through Calder, is absolutely defeated. Calder is the connection to the past, signified by his hat and old-fashioned holster and he is not respected nor is able to protect anybody - Bubber is shot, Lester is beaten, Jake dies, and he himself is beaten to a pulp - and eventually has to leave with his head down. Unlike the professionals of Brooks' film, Calder's old-fashioned values and heroics cannot keep up with the time he is in. A poignant moment comes when he laments with "I should have called for backup," when he realizes that he can not do it on his own as the old-fashioned Western hero. I believe Penn's film is the most pessimistic in its view of the Western hero being killed out. In a film like The Man Who Shot Liberty Valance, the Western hero, Tom, at least makes the choice to hand over the West to Rans after doing his last noble act; though he does not go publicly recognized, he still has some dignity left recognized by Rans. In The Professionals they have one last grand adventure. In Penn's film Calder is simply defeated on all fronts. It is particularly interesting to compare The Professionals with The Chase because they were made in the same year, meaning that they are reflecting the same time historical period in America, only with incredibly different views.