The implications of embodiment and Putty-Clay to economic development

In this paper we construct and analyze a growth model with the following three ingredients. (i) Technological progress is embodied. (ii) The production function of a firm is such that the firm makes both technology upgrade as well as capital and labor decisions. (iii) The firm’s production technology is putty-clay. We assume that there are disincentives to the accumulation of capital, resulting in a divergence between the social and the private cost of investment. We solve a single firm’s problem in this environment. Then we determine general equilibrium prices of capital goods of different vintages. Using these prices we aggregate firms’ decisions and construct the theoretical analogues of National Income statistics. This generates a relationship between disincentives and per capita incomes. We analyze this relationship and show the quantitative and qualitative roles of embodiment and putty-clay. We also show how the model is taken to data, quantified and used to determine to what extent income gaps across countries can be attributed to disincentives.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.