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Full-Text Articles in Social and Behavioral Sciences

Spherical Matrix Distributions And Cauchy Quotients, Peter C.B. Phillips Feb 1987

Spherical Matrix Distributions And Cauchy Quotients, Peter C.B. Phillips

Cowles Foundation Discussion Papers

It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.


Are Cyclical Fluctuations In Productivity Due More To Supply Shocks Or Demand Shocks?, Matthew D. Shapiro Feb 1987

Are Cyclical Fluctuations In Productivity Due More To Supply Shocks Or Demand Shocks?, Matthew D. Shapiro

Cowles Foundation Discussion Papers

Measured productivity is strongly procyclical. Real business cycle theories suggest that actual fluctuations in productivity are the source of fluctuations in aggregate output. Keynesian theories maintain that fluctuations in aggregate output come from shocks to aggregate demand. Keynesian theories appeal to labor hoarding or off the production function behavior to explain the procyclicality of productivity. If observed productivity shocks are true productivity shocks, a function of factor prices should covary exactly with productivity. In annual data for United States industries, that function of factor prices and conventionally-measured productivity move together very closely. Moreover, their difference is uncorrelated with aggregate output.


The Future Of Social Security: One Economist's Assessment, James Tobin Feb 1987

The Future Of Social Security: One Economist's Assessment, James Tobin

Cowles Foundation Discussion Papers

Three interrelated issues must be faced in assessing the future of OASI. I shall discuss each in turn. Balancing Contributions and Benefits. The overriding long-run issue about OASI is the balance between the tax contributions of the young and the benefits of the old. The system is now geared to scale up benefits automatically so as to maintain the ratio of benefits to contemporaneous wages, the replacement ratio, at its historical level of roughly 40 percent. Payroll tax rates are the residual balancing item in the OASI financial equation. They have been raised steadily for years, and according to current …


Supply Shocks In Macroeconomics, Matthew D. Shapiro Feb 1987

Supply Shocks In Macroeconomics, Matthew D. Shapiro

Cowles Foundation Discussion Papers

Supply shocks played an important role in macroeconomic fluctuations during the 1970’s. Supply shocks are also increasingly important in Keynesian and neo-classical models of the business cycle. This paper is a short survey of these theoretical models. It also discusses the history of supply shocks in recent business cycles.


Optimal Choice Of Monetary Policy Instruments In A Macroeconometric Model, Ray C. Fair Jan 1987

Optimal Choice Of Monetary Policy Instruments In A Macroeconometric Model, Ray C. Fair

Cowles Foundation Discussion Papers

It has been nearly twenty years since Poole (1970) wrote his classic article on the optimal choice of monetary policy instruments in a stochastic IS-LM model. Poole assumed that the monetary authority (henceforth called the Fed) can control the interest rate or the money supply exactly. These are the two “instruments” of monetary policy. If the aim is to minimize the squared deviation of real output from its target value, Poole showed that the choice of the optimal instrument depends on the variance of the error term in the IS function, the variance of the error term in the LM …


Sources Of Output And Price Variability In A Macroeconometric Model, Ray C. Fair Jan 1987

Sources Of Output And Price Variability In A Macroeconometric Model, Ray C. Fair

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.


Ultimate Sources Of Aggregate Variability, Robert J. Shiller Jan 1987

Ultimate Sources Of Aggregate Variability, Robert J. Shiller

Cowles Foundation Discussion Papers

What, ultimately, is different from quarter to quarter or year to year that accounts for the fact that macroeconomic variables change over these intervals? That is, which are the biggest ultimate sources, in terms we may say of tastes, technology, endowments, government policy, industrial organization, labor-management relations, speculative behavior, or the like, that change to cause this variability? There are a bewildering variety of claims in the literature for such ultimate sources. Far fewer efforts have been made to give a breakdown of the variance of macroeconomic aggregates by Pigou (1929) and Fair (1987). The nature of the evidence for …


Financial Intermediaries, James Tobin Jan 1987

Financial Intermediaries, James Tobin

Cowles Foundation Discussion Papers

This is an essay on Financial Intermediaries written for the New Palgrave . It includes sections on national wealth, financial markets, assets, risk and regulation.


Conditional And Unconditional Statistical Independence, Peter C.B. Phillips Jan 1987

Conditional And Unconditional Statistical Independence, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Conditional independence almost everywhere in the space of the conditioning variates does not imply unconditional independence, although it may well imply unconditional independence of certain functions of the variables. An example that is important in linear regression theory is discussed in detail. This involves orthogonal projections on random linear manifolds, which are conditionally independent but not unconditionally independent under normality. Necessary and sufficient conditions are obtained under which conditional independence does imply unconditional independence.


Statistical Inference In Regressions With Integrated Processes: Part 2, Joon Y. Park, Peter C.B. Phillips Jan 1987

Statistical Inference In Regressions With Integrated Processes: Part 2, Joon Y. Park, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper continues the theoretical investigation of Park and Phillips [7]. We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of different orders, nonzero means, drifts, time trends and cointegrated regressors. The framework of analysis is general but has a common architecture that helps to simplify and codify what would otherwise be a myriad of isolated results. A good deal of earlier research by the authors and by others comes within the new framework. Special models of some importance are considered in detail, such as VAR systems with multiple lags and cointegrated variants.


Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips Dec 1986

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 …


Interest Rate And Exchange Rate Determination, Ray C. Fair Dec 1986

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 Dec 1986

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.


A Strategic Market Game With Complete Markets, Rabah Amir, Siddhartha Sahi, Martin Shubik Dec 1986

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.


International Evidence On The Demand For Money, Ray C. Fair Dec 1986

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 Game Theoretic Approach To The Theory Of Money And Financial Institutions, Martin Shubik Nov 1986

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 …


Knightian Decision Theory: Part 1, Truman F. Bewley Nov 1986

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 Nov 1986

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 …


The Unique Minimal Cash Flow Competitive Equilibrium, Martin Shubik Oct 1986

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 …


Enough Commodity Money And The Selection Of A Unique Competitive Equilibrium, Martin Shubik Oct 1986

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 Oct 1986

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.


Asymptotic Equivalence Of Ols And Gls In Regressions With Integrated Regressors, Peter C.B. Phillips, Joon Y. Park Sep 1986

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 …


On The Formulation Of Wald Tests Of Nonlinear Restrictions, Peter C.B. Phillips, Joon Y. Park Sep 1986

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.


Power In Econometric Applications, Donald W.K. Andrews Aug 1986

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.


Limiting Distributions Of The Number Of Pure Strategy Nash Equilibria In N-Person Games, Imelda Yeung Powers Aug 1986

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.


Temporal Dependence In Limited Dependent Variable Models: Theoretical And Monte-Carlo Results, Vassilis A. Hajivassiliou Aug 1986

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 …


Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips Jul 1986

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 …


Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron Jul 1986

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 Jul 1986

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 …


Survey Evidence On Diffusion Of Interest Among Institutional Investors, Robert J. Shiller, John Pound May 1986

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 …