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The two sector endogenous growth model: an atlas
In this paper we investigate the underlying structure of the Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today
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The impact of immigrant dynasties on wage inequality
I construct a set of dynamic macroeconomic models to analyze the effect of unskilled immigration on wage inequality. The immigrants or their descendants do not remain unskilled–over time they may approach or exceed the general level of educational attainment. In the baseline model, the economy’s capital supply is determined endogenously by the savings behavior of infinite-lived dynasties, and I also consider models in which the supply of capital is perfectly elastic, or exogenously determined. I derive a simple formula that determines the time discounted value of the skill premium enjoyed by college-educated workers following a change in the rate of immigration for unskilled workers, or a change in the degree or rate at which unskilled immigrants become skilled. I compare the calculations of the skill premiums to data from the U.S. Current Population Survey to determine the long-run effect of different immigrant groups
on wage inequality in the United States
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
A Comment on Budach's Mouse-in-an-Octant Problem
Budach's Mouse-in-an-Octant Problem (attributed to Lothar Budach in a 1980
article by van Emde Boas and Karpinski) concerns the behaviour of a very simple
finite-state machine ("the mouse") moving on the integer two-dimensional grid.
Its decidability is apparently still open. This note sketches a proof that an
extended version of the problem (a super-mouse) is undecidable.Comment: 3 pages, 2 bibliographic reference
On Decidable Growth-Rate Properties of Imperative Programs
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple "core"
programming language - an imperative language with bounded loops, and
arithmetics limited to addition and multiplication - it was possible to decide
precisely whether a program had certain growth-rate properties, namely
polynomial (or linear) bounds on computed values, or on the running time.
This work emphasized the role of the core language in mitigating the
notorious undecidability of program properties, so that one deals with
decidable problems.
A natural and intriguing problem was whether more elements can be added to
the core language, improving its utility, while keeping the growth-rate
properties decidable. In particular, the method presented could not handle a
command that resets a variable to zero. This paper shows how to handle resets.
The analysis is given in a logical style (proof rules), and its complexity is
shown to be PSPACE-complete (in contrast, without resets, the problem was
PTIME). The analysis algorithm evolved from the previous solution in an
interesting way: focus was shifted from proving a bound to disproving it, and
the algorithm works top-down rather than bottom-up
Drones and Dirty Hands
The period known as the “War on Terror” has prompted a revival of interest in the idea of moral dilemmas and the problem of “dirty hands” in public life. Some contend that a policy of targeted killing of terrorist actors is (under specified but not uncommon circumstances) an instance of a dirty-handed moral dilemma – morally required yet morally forbidden, the least evil choice available in the circumstances, but one that nevertheless leaves an indelible moral stain on the character of the person who makes the choice. In this chapter we argue that, while dirty hands situations do exist as a persistent problem of political life, it is generally a mistake to classify policies of target killing (such as the current US policy) as examples of dirty hands. Instead, we maintain, such policies, if justified at all, must ordinarily be justified under the more exacting standards of just war theory and its provisions for justified killing – in particular the requirement that (with limited and defined exceptions) non-combatants be immune from intentional violence. Understanding this distinction both clarifies the significance of dirty hands as a moral phenomenon and also forestalls a set of predictable and all-too-easy appropriations of the concept to domains it was never intended to address
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