/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

Convex Analysis: (pms-28)

All Matlab and C++ programs necessary to produce the results of the article. There is also a Excel spreadsheet with Mexican data.

Code and data files for "Fiscal Policy and Default Risk in Emerging Markets"

Probability and measure, by Patrick Billingsley. Pp 515. £15·20. 1979. SBN 0 471 03173 9 (Wiley)

We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromowitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.

A Nonsmooth Approach to Envelope Theorems

Emerging market economy business cycles are typically characterized by high consumption and output volatility, strongly counter-cyclical current accounts, and counter-cyclical real interest rates. Evidence from the wider EME and less developed economy business cycle experience suggests however that real interest rates can also be pro-cyclical. We reconcile the pro-cyclicality of real interest rates with the above facts by embedding fiscal policy into a standard emerging market business cycle model. We show that fiscal policy makes real interest rates a-cyclical or pro-cyclical. We use the model to replicate some of the key features of the Indian business cycle.

https://www.isid.ac.in/~epu/wp-content/uploads/2014/12/dp14-11.pdf

Fiscal policy in an emerging market business cycle model

A nonsmooth approach to envelope theorems

Nonconvex optimization is becoming the fashion to solve constrained optimization problems in economics. Classical Lagrangian does not necessarily represent a nonconvex optimization problem. In this paper, we give conditions under which the Classical Lagrangian serves as an exact penalization of a nonconvex programming. This has a simple interpretation and is easy to solve. We use this Classical Lagrangian to provide su¢ cient conditions under which value function is Clarke dif"

Optimization in economies with nonconvexities

We build a small open economy RBC model with financial frictions to analyze expansionary fiscal consolidations in emerging market economies (EMEs). We calibrate the model to India, which we view as a proto-typical EME. When factor income tax rates are low, a contractionary fiscal shock has an expansionary effect on output. The economy's debt/GDP ratio falls, and tax revenues rise. When factor income tax rates are high, a contractionary fiscal shock has an expansionary effect on output if government spending is valued sufficiently highly relative to private consumption by households in utility. We identify the mechanisms behind these results, and their implications for actual economies undertaking fiscal reforms.

/pdf/fiscal-austerity-in-emerging-market-economies-2nrc1yohtn.pdf

Suchismita Tarafdar

Papers

A Nonsmooth Approach to Envelope Theorems

Fiscal policy in an emerging market business cycle model

A nonsmooth approach to envelope theorems

Optimization in economies with nonconvexities

Fiscal Austerity in Emerging Market Economies