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- Brownian motion (4)
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Articles 1 - 30 of 37
Full-Text Articles in Social and Behavioral Sciences
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F -tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple …
International Evidence On The Demand For Money, Ray C. Fair
International Evidence On The Demand For Money, Ray C. Fair
Cowles Foundation Discussion Papers
One of the current questions in the literature on the demand for money is whether the adjustment of actual to desired money holdings is in nominal or real terms. This paper describes a simple procedure that can be used to test the nominal against the real hypothesis. The test is carried out for 27 countries. The paper also tests the structural stability of the demand for money equations and the correctness of the dynamic specification.
A Strategic Market Game With Complete Markets, Rabah Amir, Siddhartha Sahi, Martin Shubik
A Strategic Market Game With Complete Markets, Rabah Amir, Siddhartha Sahi, Martin Shubik
Cowles Foundation Discussion Papers
Existence of equilibrium is proved for an exchange strategic market game with complete markets. An example of equilibrium with inconsistent prices is given.
Interest Rate And Exchange Rate Determination, Ray C. Fair
Interest Rate And Exchange Rate Determination, Ray C. Fair
Cowles Foundation Discussion Papers
It is well known that modeling exchange rates is difficult. Meese and Rogoff’s (1983) results show that a random walk model performs as well as or better than a variety of structural models, where the forecasts from the structural models are based on the actual values of the future explanatory variables. Because of these and other results, the view has become fairly widespread that structural models of exchange rates are not very good. There is, however, somewhat of a dichotomy in the literature between those who deal with small models, where the focus is almost exclusively on exchange rates, and …
The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors, John Y. Campbell, Robert J. Shiller
The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors, John Y. Campbell, Robert J. Shiller
Cowles Foundation Discussion Papers
A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for United States time series 1981-1986: versions using real interest rate data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.
Yale Political Monthly 1986 November, The Politic, Inc.
Yale Political Monthly 1986 November, The Politic, Inc.
The Politic
No abstract provided.
Knightian Decision Theory: Part 1, Truman F. Bewley
Knightian Decision Theory: Part 1, Truman F. Bewley
Cowles Foundation Discussion Papers
A theory of choice under uncertainty is proposed which removes the completeness assumption from the Anscombe-Aumann formulation of Savage’s theory and introduces an inertia assumption. The inertia assumption is that there is such a thing as the status quo and an alternative is accepted only if it is preferred to the status quo. This theory is one way of giving rigorous expression to Frank Knight’s distinction between risk and uncertainty.
Forecasting The Depression: Harvard Versus Yale, Ray C. Fair, Matthew D. Shapiro, Kathryn M. Dominguez
Forecasting The Depression: Harvard Versus Yale, Ray C. Fair, Matthew D. Shapiro, Kathryn M. Dominguez
Cowles Foundation Discussion Papers
Was the Depression forecastable? After the Crash, how long did it take contemporary economic forecasters to realize how severe the downturn was going to be? How long should it have taken them to come to this realization? These questions are addressed by studying the predictions of the Harvard Economic Service and Yale’s Irving Fisher during 1929 and the early 1930’s. The data assembled by the Harvard and Yale forecasters are subjected to modern statistical analysis to learn whether their verbal pronouncements were consistent with the data. We find that both the Harvard and Yale forecasters were systematically too optimistic, yet …
A Game Theoretic Approach To The Theory Of Money And Financial Institutions, Martin Shubik
A Game Theoretic Approach To The Theory Of Money And Financial Institutions, Martin Shubik
Cowles Foundation Discussion Papers
This is a sketch of a game theoretic and gaming approach to the development of an appropriate microeconomic theory of money and financial institutions. The phrase “money and financial institutions” is used to stress that a theory of money alone cannot be fruitfully constructed in an institutional vacuum. The monetary and financial system of an economy are part of the socio-politico-economic control mechanism used by every state to connect the economy with the polity and society. This neural network provides the administrative means to collect taxes, direct investment, provide public goods, trade. The money measures provide a crude but serviceable …
Enough Commodity Money And The Selection Of A Unique Competitive Equilibrium, Martin Shubik
Enough Commodity Money And The Selection Of A Unique Competitive Equilibrium, Martin Shubik
Cowles Foundation Discussion Papers
Suppose that we reformulate the exchange economy as a strategic market game. As all purchases are paid for in cash it is possible to attach precise meaning to what is meant by enough money. As the game is a single simultaneous bid and offered at m trading posts and m prices are all simultaneously determined, in essence the trading technology is completely specified.
Testing For Cointegration Using Principal Component Methods, Peter C.B. Phillips, Sam Ouliaris
Testing For Cointegration Using Principal Component Methods, Peter C.B. Phillips, Sam Ouliaris
Cowles Foundation Discussion Papers
This paper studies cointegrated systems of multiple time series which are individually well described as integrated processes (with or without a drift). Necessary and sufficient conditions for cointegration are given. These conditions form the basis for a new class of statistical procedures designed to test for cointegration. The new procedures rely on principal components methods. They are simple to employ and they involve only the standard normal distribution. Monte Carlo simulations reported in the paper indicate that the new procedures provide simple and apparently rather powerful diagnostics for the detection of cointegration. Some empirical applications to macroeconomic data are conducted.
The Unique Minimal Cash Flow Competitive Equilibrium, Martin Shubik
The Unique Minimal Cash Flow Competitive Equilibrium, Martin Shubik
Cowles Foundation Discussion Papers
The exchange economy E can be reformulated as a strategic market game. In particular the point of concern here involves the introduction of a specified amount of credit or fiat money to monetize exchange. Dubey and Shubik (1979) and Shubik and Wilson (1977) have studied the possibility of introducing a fixed amount M of money to finance trade. When one formulates exchange as a game of strategy using any form of credit or fiat money where there is any possibility whatsoever that an individual will be unable to pay back that which he has borrowed, the rules of the game …
On The Formulation Of Wald Tests Of Nonlinear Restrictions, Peter C.B. Phillips, Joon Y. Park
On The Formulation Of Wald Tests Of Nonlinear Restrictions, Peter C.B. Phillips, Joon Y. Park
Cowles Foundation Discussion Papers
This paper utilizes asymptotic expansions to investigate alternative forms of the Ward set of nonlinear restrictions. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case. When specialized to the simple cases that have been studied recently in the literature, these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors. It is further shown how the correction delivered by the Edgeworth expansion may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution.
Asymptotic Equivalence Of Ols And Gls In Regressions With Integrated Regressors, Peter C.B. Phillips, Joon Y. Park
Asymptotic Equivalence Of Ols And Gls In Regressions With Integrated Regressors, Peter C.B. Phillips, Joon Y. Park
Cowles Foundation Discussion Papers
In the multiple regression model y t = x’ t β + u t where { u t } is stationary and x t is an integrated m -vector process it is shown that the asymptotic distributions of the ordinary least squares (OLS) and generalized least squares (GLS) estimators of β are identical. This generalizes a recent result obtained by Kramer (1986) for simple two variate regression. Our approach makes use of a multivariate invariance principle and yields explicit representations of the asymptotic distributions in terms of fuctionals of vector Brownian motion. Some useful assumption results for hypothesis tests in …
Limiting Distributions Of The Number Of Pure Strategy Nash Equilibria In N-Person Games, Imelda Yeung Powers
Limiting Distributions Of The Number Of Pure Strategy Nash Equilibria In N-Person Games, Imelda Yeung Powers
Cowles Foundation Discussion Papers
In this paper, we study the number of pure strategy Nash equilibria in a “random” n -person non-cooperative game in which all players have a countable number of strategies. We provide explicit expressions for the expected number of pure strategy Nash Equilibria, and show that the distribution of the number of pure strategy Nash Equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to infinity.
Power In Econometric Applications, Donald W.K. Andrews
Power In Econometric Applications, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper is concerned with the use of power properties of tests in econometric applications. Power radius and inverse power functions are defined. These functions are designed to yield summary measures of power that facilitate the interpretation of test results in practice. Simple approximations are introduced for the power radius and inverse power functions of Wald, likelihood ration, Lagrange multiplier, and Hausman tests. These approximations readily convey the general qualitative features of the power of a test. Examples are provided to illustrate their usefulness in interpreting test results.
Temporal Dependence In Limited Dependent Variable Models: Theoretical And Monte-Carlo Results, Vassilis A. Hajivassiliou
Temporal Dependence In Limited Dependent Variable Models: Theoretical And Monte-Carlo Results, Vassilis A. Hajivassiliou
Cowles Foundation Discussion Papers
This paper analyzes the consistency properties of classical estimators for limited dependent variables models, under conditions of serial correlation in the unobservables. A unified method of proof is used to show that for certain cases (e.g., Probit, Tobit and Normal Switching Regimes models, which are normality-based) estimators that neglect particular types of serial dependence (specifically, corresponding to the class of “mixing” processes) are still consistent. The same line of proof fails for the analogues to the above models that impose logistic distributional assumptions, thus indicating that normality plays a special role in these problems. Sets of Monte-Carlo experiments are then …
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Cowles Foundation Discussion Papers
This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory …
Quasirents, Influence And Organization Form, Paul R. Milgrom
Quasirents, Influence And Organization Form, Paul R. Milgrom
Cowles Foundation Discussion Papers
When changing jobs is costly, efficient employment arrangements are characterized by complex contracts, rather than simply wages. Under these contracts, workers are not generally fully compensated for the effects of post-employment events or decisions. As a consequence, if there is a central office executive with discretionary authority to make decisions, employees will be led to waste valuable time in attempts to influence his decisions. Efficient organization design balances these “influence costs” against the benefits of improved appraisal, coordination, and planning that such an executive can provide. Identifying influence costs requires first identifying the kinds of decisions about which employees will …
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫ 0 1 WdW , where W ( r ) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form ∫ 0 1 BdB ’, where B ( r ) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 BdB ’ under quite general conditions. The theory is …
Resources, Technology, And Development: Will The Table Be Bare When Poor Countries Get There?, William D. Nordhaus
Resources, Technology, And Development: Will The Table Be Bare When Poor Countries Get There?, William D. Nordhaus
Cowles Foundation Discussion Papers
This paper discusses the net effect of these two economic forces on developing countries: Is the drag to economic advance from dwindling resources outweighed by the accompanying technological advances? Or will the potential scarcity of resources during the next century on balance weigh down the pace of economic progress?
Survey Evidence On Diffusion Of Interest Among Institutional Investors, Robert J. Shiller, John Pound
Survey Evidence On Diffusion Of Interest Among Institutional Investors, Robert J. Shiller, John Pound
Cowles Foundation Discussion Papers
Contagion or epidemic models of financial markets are proposed in which interest in or attention to individual stocks is spread by word of mouth. The models give alternative interpretations of the random walk character of stock prices. A questionnaire survey of institutional investors was undertaken to ascertain the relevance of such models. Questions elicited what fraction of these investors were unsystematic and allowed themselves to be influenced by word-of-mouth communications or other salient stimuli. Rough indications of the infection rate and removal rate were produced. Investors in stocks whose price had recently increased dramatically to a high P/E ratio were …
Issues Arising In Management And Control Of Naval Forces, Paul Bracken, Martin Shubik
Issues Arising In Management And Control Of Naval Forces, Paul Bracken, Martin Shubik
Cowles Foundation Discussion Papers
This paper takes the context of political and military command as given and considers the fundamental question of how a modern navy fits in with the usual conception of nuclear deterrence between the United States and the Soviet Union. We here summarize the major issues, questions, and conclusions from this research as they serve to provide the context for our observations on the relevance of and potential for operations research and decision sciences contributions to providing understanding and analysis for these critical and highly qualitative problems.
Defense Economics And Economic Warfare Revisited, J. Hoult Verkerke, Martin Shubik
Defense Economics And Economic Warfare Revisited, J. Hoult Verkerke, Martin Shubik
Cowles Foundation Discussion Papers
In this paper we paint with a broad brush. Our purpose is to present an overview, a status report, and by implication, an indication of what needs to be done at this time. We first provide a survey of topics in the economics of defense and in economic warfare, then we comment on some naval aspects of these topics.
Consistency In Nonlinear Econometric Models: A Generic Uniform Law Of Large Numbers, Donald W.K. Andrews
Consistency In Nonlinear Econometric Models: A Generic Uniform Law Of Large Numbers, Donald W.K. Andrews
Cowles Foundation Discussion Papers
A basic tool of modern econometrics is a uniform law of large numbers (LLN). It is a primary ingredient used in proving consistency and asymptotic normality of parametric and nonparametric estimators in nonlinear econometric models. Thus, in a well-known review article, Burguete, Gallant, and Sousa [8, p. 162] introduce a uniform LLN with the statement: “The following theorem is the result upon which the asymptotic theory of nonlinear econometrics rests.” So pervasive is the use of uniform LLNs, that numerous authors appeal to an unspecified generic uniform LLN. Others appeal to some specific result. The purpose of this paper is …
Two Misspecification Tests For The Simple Switching Regressions Disequilibrium Model, Vassilis A. Hajivassiliou
Two Misspecification Tests For The Simple Switching Regressions Disequilibrium Model, Vassilis A. Hajivassiliou
Cowles Foundation Discussion Papers
Two specification tests for switching regimes disequilibrium models are developed. The first is an asymptotically locally optimal Lagrange multiplier test of endogeneity of a set of regressors, which takes the convenient form of a LM significance-test of certain regression residuals. The second is a Hausman specification test of the accuracy of regime classification information.
Trends Versus Random Walks In Time Series Analysis, Steven N. Durlauf, Peter C.B. Phillips
Trends Versus Random Walks In Time Series Analysis, Steven N. Durlauf, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the effects of spurious detrending in regression. The asymptotic behavior of traditional least squares estimators and tests are examined in the context of models where the generating mechanism is systematically misspecified by the presence of deterministic time trends. Most previous work on the subject has relied upon Monte Carlo studies to understand the issues involved in detrending data that is generated by integrated processes and our analytical results help to shed light on many of the simulation findings. Standard F tests and Hausman tests are shown to inadequately discriminate between the competing hypotheses. Durbin-Watson statistics, on the …
Toward A Theory Of Discounted Repeated Games With Imperfect Monitoring, Dilip Abreu, David G. Pearce, Ennio Stacchetti
Toward A Theory Of Discounted Repeated Games With Imperfect Monitoring, Dilip Abreu, David G. Pearce, Ennio Stacchetti
Cowles Foundation Discussion Papers
This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in external equilibria. We characterize these equilibria, and provide computational and comparative statics results. The “self-generation” and “bang-bang” propositions which were at the core of our analysis of optimal cartel equilibria [2], are generalized to asymmetric games and infinite action spaces. New results on optimal implicit reward functions include the necessity (as opposed to sufficiency) of bang-bang functions, and the nature of optimal punishment regions.
Cointegration And Tests Of Present Value Models, John Y. Campbell, Robert J. Shiller
Cointegration And Tests Of Present Value Models, John Y. Campbell, Robert J. Shiller
Cowles Foundation Discussion Papers
In a model where a variable Y is proportional to the present value, with constant discount rate, of expected future values of a variable y , the “spread” S – Y – qy will be stationary for some q whether or not y must be differenced to induce stationarity. Thus, Y and y are cointegrated. The model implies that S is proportional to the optimal forecast of S *, the present value of future changes in y. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y is the long-term interest rate and …
Edgeworth Equilibria In Production Economies, Charalambos D. Aliprantis, Donald J. Brown, Owen Burkinshaw
Edgeworth Equilibria In Production Economies, Charalambos D. Aliprantis, Donald J. Brown, Owen Burkinshaw
Cowles Foundation Discussion Papers
An Edgeworth equilibrium is an allocation that belongs to the core of every n -fold replica of the economy. In [2] we studied in the setting of Riesz spaces the properties of Edgeworth equilibria for pure exchange economies with infinite dimensional commodity spaces. In this work, we study the same problem for economies with production. Under some relatively mild conditions we establish (among other things) that: 1. Edgeworth equilibria exist; 2. Every Edgeworth equilibrium is a quasiequilibrium; and 3. An allocation is an Edgeworth equilibrium if and only if it can be “decentralized” by a price system.