Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

The dog that did not bark: Insider trading and crashes

This paper documents that at the individual stock level insiders sales peak many months before a large drop in the stock price, while insiders purchases peak only the month before a large jump. We provide a theoretical explanation for this phenomenon based on trading constraints and asymmetric information. We test our hypothesis against competing stories such as patterns of insider trading driven by earnings announcement dates, or insiders timing their trades to evade prosecution. Finally we provide new evidence regarding crashes and the degree of information asymmetry.

Dynamic higher order expectations

In models where privately informed agents interact, agents may need to formhigher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectationsmodels in which privately informed agents form higher order expectations. The frameworkis used to demonstrate that the well-known problem of the infinite regress of expectationsidentified by Townsend (1983) can be approximated to an arbitrary accuracy with a finitedimensional representation under quite general conditions. The paper is constructive andpresents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricingmodel with disparately informed traders is used as a vehicle for the paper.

Inflationary expectations during Germany's great slump

Was the German slump inevitable? This paper argues that -despite thespeed and depth of Germany's deflation in the early 1930s - fear ofinflation is evident in the bond, foreign exchange, and commodity marketsat certain critical junctures of the Great Depression. Therefore, policyoptions were more limited than many subsequent critics of Brüning'spolicies have been prepared to admit. Using a rational expectationsframework, we find strong evidence from the bondmarket to suggest fearof inflation. Futures prices also reveal that market participants werebetting on price increases. These findings are discussed in the contextof reparations and related to the need for a regime shift to overcomethe crisis.

Do expectations matter? The Great Moderation revisited

We examine the role of expectations in the Great Moderation episode. We derive theoretical restrictions in a New-Keynesian model and test them using measures of expectations obtained from survey data, the Greenbook and bond markets. Expectations explain the dynamics of inflation and of interest rates but their importance is roughly unchanged over time. Systems with and without expectations display similar reduced form characteristics. Including or excluding expectations hardly changes the economic explanation of the Great Moderation. Results are robust to changes in the structure of the empirical model.

The economic effects of the Protestant Reformation: Testing the Weber hypothesis in the German Lands

Many theories, most famously Max Weber s essay on the Protestant ethic, have hypothesizedthat Protestantism should have favored economic development. With their considerablereligious heterogeneity and stability of denominational affiliations until the 19th century, theGerman Lands of the Holy Roman Empire present an ideal testing ground for this hypothesis.Using population figures in a dataset comprising 272 cities in the years 1300 1900, I find no effectsof Protestantism on economic growth. The finding is robust to the inclusion of a varietyof controls, and does not appear to depend on data selection or small sample size. In addition,Protestantism has no effect when interacted with other likely determinants of economic development.I also analyze the endogeneity of religious choice; instrumental variables estimates ofthe effects of Protestantism are similar to the OLS results.

Constraints and non-existence of rational expectations equilibria

In this article we show that in the presence of trading constraints, such as short sale constraints, the standard definition of a Rational Expectations Equilibrium allows for equilibrium prices that reveal information unknown to any active trader in the market. We propose a new definition of the Rational Expectations Equilibrium that incorporates a stronger measurability condition than measurability with respect to the join of the information sets of the agents and give an example of non-existence of equilibrium. The example is robust to perturbations on the data of the economy and the introduction of new assets.

Hypothesis on immigration and welfare

The number of hypothesis trying to explain which are the reasons behind the decision to migrate to work into a developed country are diverse and at the same time, difficult to test due to the multiplicity of factors which affect it. This papers attempts to move forward trying to disentangle which are the socio-economic factors that explain the differences in the figures of immigrants in the OECD countries. We show empirical evidence about the determinants of the migratory flows to 17 OECD countries from 65 countries in the 1980-2000 period. Our results reveal the importance to differentiate the inflows composition by at least income in the origin countries. Thus, regarding inflows from non-high-income countries, the results suggest that there is a pull effect from monetary and not real income, and then, the welfare magnets hypothesis should be rejected. This group reacts more to the migratory policy than the inflows coming from high-income countries, although those policies designed to slow down the inflows have not been able, in the aggregate, to reduce them.