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A General and Intuitive Envelope Theorem
Get PDFWe present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis
Rebellion against Reason? A Study of Expressive Choice and Strikes
Get PDFIn this paper we challenge the conventional view that strikes are caused by asymmetric
information regarding firm protability such that union members are uninformed. Instead,
we build an expressive model of strikes where the perception of unfairness provides the
expressive benefit of voting for a strike. The model predicts that larger union size increases both wage offers and the incidence of strikes. Furthermore, while asymmetric information is still important in causing strikes, we find that it is the employer who is not fully informed about the level of emotionality within the union, thereby contributing to strike incidence. An empirical test using UK data provides support for the predictions. In particular, union
size has a positive effect on the incidence of strikes and other industrial actions even when asymmetric information regarding protability is controlled for
Partial Equal Treatment in Wage Offers
Get PDFWe analyse a labour matching model with wage posting, where- refl ecting
institutional constraints-fi rms cannot dfferentiate their wage offers within certain subsets of workers. Inter alia, we find that the presence of impersonal wage offers leads to wage compression, which propagates to the wages for high productivity workers who receive personalised offers
Still More On Why We Should Bury The Marginal Productivity Theory Of The Price Of Capital: A Supplementary Note
Get PDFThe purpose of this note is to supplement the author’s earlier remarks on the unsatisfactory nature of the neoclassical account of how the return on capital is determined. (See Strathclyde Discussion Paper 12-03: “The Marginal Productivity Theory of the Price of Capital: An Historical Perspective on the Origins of the Codswallop”). The point is made via a simple illustration that certain matters which are problematical in neoclassical terms are perfectly straightforward when viewed from a classical perspective. Basically, the marginalist model of the nature of an economic system is not fit for purpose in that it fails to comprehend the essential features of a surplus-producing economic system as distinct from one merely of exchange
Expert Information and Majority Decisions
Get PDFThis paper studies dichotomous majority voting in common interest committees where each member receives not only a private signal but also a public signal observed by all
of them. The public signal represents, e.g. expert information presented to an entire
committee and its quality is higher than that of each individual private signal. We identify
two informative symmetric strategy equilibria, namely i) the mixed strategy equilibrium
where each member randomizes between following the private and public signals should
they disagree; and ii) the pure strategy equilibrium where they follow the public signal for
certain. The former outperforms the latter. The presence of the public signal precludes
the equilibrium where every member follows their own signal, which is an equilibrium in
the absence of the public signal. The mixed strategy equilibrium in the presence of the
public signal outperforms the sincere voting equilibrium without the public signal, but
the latter may be more efficient than the pure strategy equilibrium in the presence of the
public signal. We suggest that whether expert information improves committee decision
making depends on equilibrium selection
Rational Expectations Dynamics: A Methodological Critique
Get PDFThis paper analyses RE macromodels from the methodological perspective. It proposes a particular property, robustness, which should be considered a necessary feature of scienti cally valid models in economics, but which is absent from many RE macromodels. To restore this property many macroeconomists resort to detailed and implausible assumptions, which take their models a long way from simple Rational Expectations. The paper draws attention to the problems inherent in the technique of local linearisation and concludes by proposing the use of nonlinear models, analysed globally
Anticipation, Learning and Welfare: the Case of Distortionary Taxation
Get PDFWe study the impact of anticipated fiscal policy changes in a Ramsey economy where agents form long-horizon expectations using adaptive learning. We extend the existing framework by introducing distortionary taxes as well as elastic labour supply, which makes agents. decisions non-predetermined but more realistic. We detect that the dynamic responses to anticipated tax changes under learning have oscillatory behaviour that can be interpreted as self-fulfilling waves of optimism and pessimism emerging from systematic forecast errors. Moreover, we demonstrate that these waves can have important implications for the welfare consequences of .scal reforms. (JEL: E32, E62, D84
On Cobb-Douglas Preferences in Bilateral Oligopoly
Get PDFBilateral oligopoly is a simple model of exchange in which a finite set of sellers
seek to exchange the goods they are endowed with for money with a finite
set of buyers, and no price-taking assumptions are imposed. If trade takes place
via a strategic market game bilateral oligopoly can be thought of as two linked
proportional-sharing contests: in one the sellers share the aggregate bid from the
buyers in proportion to their supply and in the other the buyers share the aggregate
supply in proportion to their bids. The analysis can be separated into two
‘partial games’. First, fix the aggregate bid at B; in the first partial game the sellers
contest this fixed prize in proportion to their supply and the aggregate supply
in the equilibrium of this game is X˜ (B). Next, fix the aggregate supply at X; in
the second partial game the buyers contest this fixed prize in proportion to their
bids and the aggregate bid in the equilibrium of this game is ˜B (X). The analysis of
these two partial games takes into account competition within each side of the market.
Equilibrium in bilateral oligopoly must take into account competition between
sellers and buyers and requires, for example, ˜B (X˜ (B)) = B. When all traders
have Cobb-Douglas preferences ˜ X(B) does not depend on B and ˜B (X) does not
depend on X: whilst there is competition within each side of the market there is
no strategic interdependence between the sides of the market. The Cobb-Douglas
assumption provides a tractable framework in which to explore the features of
fully strategic trade but it misses perhaps the most interesting feature of bilateral
oligopoly, the implications of which are investigated
Unemployment Risk and Wage Differentials
Get PDFWorkers in less secure jobs are often paid less than identical-looking workers in more secure jobs. We show that this lack of compensating differentials for unemployment risk can arise in equilibrium when all workers are identical and firms differ only in job security (i.e. the probability that the worker is not sent into unemployment). In a setting where workers search for new positions both on and off the job, the worker's marginal willingness to pay for job security is endogenous: it depends on the behavior of all firms in the labor market and increases with the rent the employing firm leaves to the worker. We solve for the labor market equilibrium, finding that wages increase with job security for at least all firms in the risky tail of the distribution of firm-level unemployment risk. Meanwhile, unemployment becomes persistent for low-wage and unemployed workers, a seeming pattern of 'unemployment scarring' created entirely by firm heterogeneity. Higher in the wage distribution, workers can take wage cuts to move to more stable employment
Tractable Consumer Choice
Get PDFWe derive a rational model of separable consumer choice which can also serve as a
behavioral model. The central construct is [lambda] , the marginal utility of money, derived
from the consumer's rest-of-life problem. We present a robust approximation of [lambda],
and show how to incorporate liquidity constraints, indivisibilities and adaptation to
a changing environment. We fi nd connections with numerous historical and recent
constructs, both behavioral and neoclassical, and draw contrasts with standard partial
equilibrium analysis. The result is a better grounded, more
flexible and more intuitive description of consumer choice