Has EMU had any Impact on the Degree of Wage Restraint?

We find in cross-sectional investigations that wage restraint is either unchanged or increased following EMU in the vast majority of countries. This contradicts the predictions of a widely-cited family of models of labor market bargaining. In those, Germany would have been expected to display the greatest decline in wage restraint post-EMU, and we find no indication of such a decline. The time-series evidence on Italy shows a significant increase in wage restraint after eurozone entry. This pattern is consistent with the models that emphasise the gains from monetary credibility. The eurozone increase in wage restraint is matched by the increase seen in the UK and Sweden after adopting inflation targeting, another means to credibility.EMU, wage bargaining, monetary credibility, productivity

A second derivative SQP method: theoretical issues

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second-derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which “guides” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established

A second derivative SQP method: local convergence

In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact ℓ1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were intended to improve the efficiency of the algorithm. \ud \ud Although we established global convergence of the algorithm, we did not discuss certain aspects that are critical when developing software capable of solving general optimization problems. In particular, we must have strategies for updating the penalty parameter and better techniques for defining the positive-definite matrix Bk used in computing the predictor step. In this paper we address both of these issues. We consider two techniques for defining the positive-definite matrix Bk—a simple diagonal approximation and a more sophisticated limited-memory BFGS update. We also analyze a strategy for updating the penalty paramter based on approximately minimizing the ℓ1-penalty function over a sequence of increasing values of the penalty parameter.\ud \ud Algorithms based on exact penalty functions have certain desirable properties. To be practical, however, these algorithms must be guaranteed to avoid the so-called Maratos effect. We show that a nonmonotone varient of our algorithm avoids this phenomenon and, therefore, results in asymptotically superlinear local convergence; this is verified by preliminary numerical results on the Hock and Shittkowski test set

A second-derivative trust-region SQP method with a "trust-region-free" predictor step

In (NAR 08/18 and 08/21, Oxford University Computing Laboratory, 2008) we introduced a second-derivative SQP method (S2QP) for solving nonlinear nonconvex optimization problems. We proved that the method is globally convergent and locally superlinearly convergent under standard assumptions. A critical component of the algorithm is the so-called predictor step, which is computed from a strictly convex quadratic program with a trust-region constraint. This step is essential for proving global convergence, but its propensity to identify the optimal active set is Paramount for recovering fast local convergence. Thus the global and local efficiency of the method is intimately coupled with the quality of the predictor step.\ud \ud In this paper we study the effects of removing the trust-region constraint from the computation of the predictor step; this is reasonable since the resulting problem is still strictly convex and thus well-defined. Although this is an interesting theoretical question, our motivation is based on practicality. Our preliminary numerical experience with S2QP indicates that the trust-region constraint occasionally degrades the quality of the predictor step and diminishes its ability to correctly identify the optimal active set. Moreover, removal of the trust-region constraint allows for re-use of the predictor step over a sequence of failed iterations thus reducing computation. We show that the modified algorithm remains globally convergent and preserves local superlinear convergence provided a nonmonotone strategy is incorporated

Has EMU Had Any Impact on the Degree of Wage Restraint?

This working paper investigates the European Monetary Unification’s (EMU) effect on wage restraint—the degree to which wage increases do or do not exceed productivity growth. We find in cross-sectional investigations that wage restraint either is unchanged or has increased following EMU in the vast majority of countries. This finding contradicts the predictions of a widely cited family of models of coordination of labor market bargaining. In particular, one would have expected Germany to display the greatest decline in wage restraint post-EMU under these models, but in our time-series analysis we find no indication of such a decline. The overall shift toward greater wage restraint is consistent with the models that emphasize the gains from monetary credibility. The time-series evidence on Italy, which shows a significant increase in wage restraint after eurozone entry, also supports this view. That said, the increase in wage restraint in the eurozone is matched by that associated with the increase in credibility seen in the United Kingdom and Sweden after their adoption of inflation targeting post-1992.EMU, wage bargaining, monetary credibility, productivity

Gothic Representations: History, Literature, and Film

Gothic storytelling has come a long way since the publication of Horace Walpole\u27s The Castle of Otranto in 1764. This short novel created the standard motifs and tropes that will forever be associated with the genre-the destitute castle, the foreboding atmosphere, supernatural or inexplicable events, omens, prophecies, heroes, villains, and of course, a deteriorating world facilitated by the unconscious evils within hwnanity causing the complete destabilization of society. This paper will examine the evolution of Gothic fiction and how it has been represented from its romantic heritage and Victorian upbringing to the American Gothic traditions of the nineteenth century and the contemporary Gothic scene. It will concentrate focus on the classic, most widely recognized Gothic icons, Dracula and Frankenstein, comparing and contrasting the inherent Gothic elements within each work to Walpole\u27s The Castle of Otranto, and examining how certain criteria were transformed to fit the singularity of each novel. It will also study the development of Gothic literature in the United States by analyzing the most prolific early American author, Edgar Allan Poe, and how his works morphed European Gothic into a new literary tradition inspired by the unique landscapes and conditions of the United States of America. It will investigate the contemporary Gothic scene with special focus on the works of Stephen King, and explore how Gothic fiction underwent severe and radical changes over a short period of time from the end of World War II through the turn of the twenty-first century, stressing the timeless Gothic features, but also 2 divulging new Gothic elements that are completely original to the time period, or an adapted component from the Romantic and Victorian eras. Finally, it will analyze American Gothic film by selecting four individual works singular to their generations, The Wolfman, Psycho, Jaws, and The Sixth Sense, highlighting the Gothic elements within the films that are impervious to temporal changes in culture and society, but also revealing how each film is unique to the time period in which it was produced

On solving trust-region and other regularised subproblems in optimization

The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, Mor´e and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both globally and asymptotically at least superlinearly convergent in all cases, including in the notorious hard case. Numerical experiments validate the effectiveness of our approach. The resulting software is available as packages TRS and RQS as part of the GALAHAD optimization library, and is especially designed for large-scale problems

Friends of the Rhode Island Meeting, Daniel Gould, Matthew Gould and John Easton, Phineas Pemberton, August 3, 1700

Letter dated August 3, 1700 (July 23, 1700 Old Style) from Friends of the Rhode Island Meeting to Phineas Pemberton