By Arnold Zellner
This can be a classical reprint version of the unique 1971 variation of An creation to Bayesian Inference in Economics. This ancient quantity is an early creation to Bayesian inference and method which nonetheless has lasting worth for state-of-the-art statistician and pupil. The assurance levels from the basic suggestions and operations of Bayesian inference to research of purposes in particular econometric difficulties and the trying out of hypotheses and types.
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Additional info for An introduction to Bayesian inference in econometrics
Xn) ERn: plxl + PzXz + ... 11) B is convex. Let x, y E B then plxl + ... pnXn ~ m } (0 < f.. )m -. -. 12) (2 13) . 15) and B is convex. Exercise Consider a firm producing output y using inputs Xu ... , xn. Let Y be set of points (y, xl> ... , xn) which the firm can produce; its production set. Show that convexity of Y corresponds to diminishing (or constant) returns to scale. It is now possible to define a concave function. Such a function is simply one which bounds a convex set. In Fig. 12 are depicted two functions, f and g mapping a convex set S to the real line.
If a constraint holds with equality: g;(x) = 0, it is said to be binding, if it holds with strict inequality: g;(x) > 0, it is said to be slack. 1) gives rise to binding or slack constraints. :; 0 be real variables. Denote (A. 11 A.. ;'s are called multipliers or shadow prices. The reason for these mathematical entities to have such an economic sounding name will be discussed later in the chapter. ) with respect to each X; (i = 1, ... 1 (j = 1, ... ). ) We now turn to the central theorems of this chapter.
Baumol calls this satisficing behaviour. 3 provides a means of modelling this type of firm. 1). 3 are satisfied, and suppose that Q, A > 0, for otherwise the firm's behaviour would be uninteresting. 7) Then: A = R"/(1 - R") (from (3. 3, the corresponding constraint must bind. e. the firm's marginal revenue is strictly positive. For an unconstrained revenue maximiser we would have RQ = 0. How does the firm compare with a straightforward profitmaximiser? 9) since A > 0, CQ > 0) A pure profit-maximiser would have nQ = 0 Exercise Show that, with 'normal' marginal revenue and cost curves, the satisficer's output is greater than the profit-maximiser's but less than the unconstrained revenue maximiser's.
An introduction to Bayesian inference in econometrics by Arnold Zellner