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- Asymptotic theory (3)
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Articles 1 - 30 of 31
Full-Text Articles in Social and Behavioral Sciences
Default And Bankruptcy In A Multistage Exchange Economy, Martin Shubik
Default And Bankruptcy In A Multistage Exchange Economy, Martin Shubik
Cowles Foundation Discussion Papers
Either lending must be secured or otherwise some form of default or bankruptcy rules are required to provide a disincentive against strategic default. When many time periods are involved, the mere specification of a penalty which is sufficient for one period of trade, is not sufficient. The complete specification of even a two period game requires that both the treatment of creditors (including seniority conditions) and the nature of the rehabilitation of the debtor must be specified. This paper explores these problems.
A Strategic Market Game With A Mutual Bank With Fractional Reserves And Redemption In Gold (A Continuum Of Traders), Martin Shubik, Dimitrios P. Tsomocos
A Strategic Market Game With A Mutual Bank With Fractional Reserves And Redemption In Gold (A Continuum Of Traders), Martin Shubik, Dimitrios P. Tsomocos
Cowles Foundation Discussion Papers
We utilize the strategic market game approach to analyze the role and function of a mutual bank with variable fractional reserves, redemption in gold and endogenous interest rate formation. We specify the conditions of enough money and its distribution. Using the continuum of traders model, we show existence and optimality for the case of no bankruptcy as well as for the case in which there exists the potentiality of bankruptcy. Finally, we analyze the relationship of the gearing ratio and the bankruptcy penalty with respect to the resulting equilibrium allocations.
A Strategic Market Game Of A Finite Economy With A Mutual Bank, Martin Shubik, Jingang Zhao
A Strategic Market Game Of A Finite Economy With A Mutual Bank, Martin Shubik, Jingang Zhao
Cowles Foundation Discussion Papers
We introduce a strategic market game for an exchange economy not having enough commodity money. We show the existence of a non-cooperative equilibrium for any finite replication economy with a mutual bank, we then show that efficient trade can be achieved in the limiting economy by expanding the money supply through the use of fractional reserves, where the commodity money is demonetized and used for reserves. The means of exchange becomes bank credit backed in part, by “gold.” However, efficiency can not be achieved in general as a non-cooperative equilibrium of a finite player game or a finite exchange economy.
On The Convex Hull Of The Integer Points, Antal Balog, Imre Bárány
On The Convex Hull Of The Integer Points, Antal Balog, Imre Bárány
Cowles Foundation Discussion Papers
Let P r denote the convex hull of the integer points in the disc of radius r . We prove that the number of vertices of P r is essentially r 2 /3 as r approaches infinity.
Estimation Of Multinomial Models Using Weak Monotonicity Assumptions, Rosa L. Matzkin
Estimation Of Multinomial Models Using Weak Monotonicity Assumptions, Rosa L. Matzkin
Cowles Foundation Discussion Papers
This paper introduces a semiparametric method of estimating multinomial models that imposes extremely weak monotonicity assumptions about a function of observable characteristics. Previous methods have imposed stronger, typically parametric, conditions on this function. The only assumptions made in this paper about the function of characteristics are its monotonicity, upper-semicontinuity, and uniform boundedness. The method is applicable, among others, to polychotomous choice models. The estimation method is shown to be strongly consistent. A technique to calculate the estimator is provided.
Least Concavity And The Distribution-Free Estimation Of Non-Parametric Concave Functions, Rosa L. Matzkin
Least Concavity And The Distribution-Free Estimation Of Non-Parametric Concave Functions, Rosa L. Matzkin
Cowles Foundation Discussion Papers
This paper studies the estimation of fully nonparametric models in which we can not identify the values of a symmetric function that we seek to estimate. I develop a method of consistently estimating a representative of a concave and monotone nonparametric systematic function. This representative possesses the same isovalue sets as the systematic function. The method proceeds by characterizing each set of observationally equivalent concave functions by a unique “least concave” representative. The least concave representative of the equivalence class to which the systematic function belongs is estimated by maximizing a criterion function over a compact set of least concave …
The Price For The Widow's Cruse: Or The Value Of An Infinitely Productive Asset, Martin Shubik
The Price For The Widow's Cruse: Or The Value Of An Infinitely Productive Asset, Martin Shubik
Cowles Foundation Discussion Papers
This paper considers two basic problems: The first is the necessity for introducing government money (as contrasted with individual credit) and an infinitely lived government in an overlapping generations economy. The second concerns the evaluation of the price of an infinitely productive asset in an economy without a natural discount factor.
Stock Prices And Bond Yields: Can Their Co-Movements Be Explained In Terms Of Present Value Models?, Robert J. Shiller, Andrea E. Beltratti
Stock Prices And Bond Yields: Can Their Co-Movements Be Explained In Terms Of Present Value Models?, Robert J. Shiller, Andrea E. Beltratti
Cowles Foundation Discussion Papers
Real stock prices seem to overreact to changes in long-term interest rates. That is, real stock prices drop when long-term interest rates rise (and rise when they fall) more than would be implied by a rational expectations present value model where expectations are based on a vector autoregression. This overreaction is not associated with any overreaction to changes in the short-run inflation rate. Over the last century real stock prices have shown little reaction to changes in inflation rates, and according to the model they should show little reaction. These conclusions were reached from an analysis of annual data in …
The Hybrid Solutions Of An N-Person Game, Jingang Zhao
The Hybrid Solutions Of An N-Person Game, Jingang Zhao
Cowles Foundation Discussion Papers
We introduce a solution concept intermediate between the cooperative and noncooperative solutions of an n -person game in normal form. Consider a partition p of the players, with each s in p a coalition. A joint strategy x = { x s | s in p } is a hybrid solution for the partition p if, for each s in p , x s is a core solution of the corresponding parametric subgame, where this game isplayed by the players in s and is parameterized by x -s , the strategies played by all outside players. This assumes that players …
Smooth Unbiased Multivariate Probability Simulators For Maximum Likelihood Estimation Of Limited Dependent Variable Models, Vassilis A. Hajivassiliou, Axel Borsch-Supan
Smooth Unbiased Multivariate Probability Simulators For Maximum Likelihood Estimation Of Limited Dependent Variable Models, Vassilis A. Hajivassiliou, Axel Borsch-Supan
Cowles Foundation Discussion Papers
We apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models. The simulation method has four key features: the simulated choice probabilities are unbiased; they are a continuous and differentiable function of the parameters of the model; they are bounded between 0 and 1; and their computation takes an effort that is nearly linear in the dimension of the probability integral, independent of the magnitudes of the true probabilities. We also show that the new simulation method produces probability estimates with substantially smaller variance …
Inefficiency Of Strategy-Proof Allocation Mechanisms In Pure Exchange Economies, Lin Zhou
Inefficiency Of Strategy-Proof Allocation Mechanisms In Pure Exchange Economies, Lin Zhou
Cowles Foundation Discussion Papers
In this paper I prove that in the standard model of 2 times n ( n > 2) pure exchange economies there is no allocation mechanism that is efficient, non-inversely-dictatorial, and strategy-proof. This strengthens two previous results on this subject by Hurwicz and by Dasgupta, Hammond, and Maskin.
Popular Attitudes Towards Free Markets: The Soviet Union And The United States Compared, Robert J. Shiller, Maxim Boycko, Vladimir Korobov
Popular Attitudes Towards Free Markets: The Soviet Union And The United States Compared, Robert J. Shiller, Maxim Boycko, Vladimir Korobov
Cowles Foundation Discussion Papers
Random samples of the Moscow and New York populations were compared in their attitudes towards free markets by administering identical telephone interviews in the two countries in May, 1990. Although the Soviet respondents were somewhat less likely to accept exchange of money as a solution to personal problems, and their attitudes towards business were less warm, we found that the Soviet and American respondents were basically similar in most dimensions. Soviets showed no difference from Americans in their feelings that price increases may be unfair. There appears to be little difference between the Soviets and Americans in their concern with …
A Functional Central Limit Theorem For Strong Mixing Stochastic Processes, Donald W.K. Andrews, David Pollard
A Functional Central Limit Theorem For Strong Mixing Stochastic Processes, Donald W.K. Andrews, David Pollard
Cowles Foundation Discussion Papers
This paper shows how the modern machinery for generating abstract empirical central limit theorems can be applied to arrays of dependent variables. It develops a bracketing approximation based on a moment inequality for sums of strong mixing arrays, in an effort to illustrate the sorts of difficulty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development are offered. The paper is largely self-contained.
International Diversification Of Social And Private Risk: The Us And Japan, Stephen S. Golub
International Diversification Of Social And Private Risk: The Us And Japan, Stephen S. Golub
Cowles Foundation Discussion Papers
This paper concerns the gains from international trade in risky assets, with an application to the United States and Japan. I examine the role of international financial markets in diversifying the risks associated with the aggregate consumption opportunities of a nation (social risk) and the risks related to individual agents’ consumption opportunities (private risk). The main empirical result is that international portfolio diversification between the United States and Japan leads to small reductions in social risk but large reductions in some private risks, especially for corporate profits.
A Shortcut To Lad Estimator Asymptotics, Peter C.B. Phillips
A Shortcut To Lad Estimator Asymptotics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator and the results of some earlier simulation …
Testing Covariance Stationarity Under Moment Condition Failure With An Application To Common Stock Returns, Peter C.B. Phillips, Mico Loretan
Testing Covariance Stationarity Under Moment Condition Failure With An Application To Common Stock Returns, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
This paper studies tests for covariance stationarity under conditions which permit failure in the existence of fourth order moments. The problem is important because many econometric diagnostics such as tests for parameter constancy, constant variance and ARCH and GARCH effects routinely rely on fourth moment conditions. Moreover, such tests have recently been extensively employed with financial and commodity market data, where fourth moment conditions may well be quite tenuous and are usually untested. This paper considers several tests for covariance stationarity including sample split prediction tests, cusum of squares tests and modified scaled range tests. When fourth moment conditions fail …
To Criticize The Critics: An Objective Bayesian Analysis Of Stochastic Trends, Peter C.B. Phillips
To Criticize The Critics: An Objective Bayesian Analysis Of Stochastic Trends, Peter C.B. Phillips
Cowles Foundation Discussion Papers
In two recent articles, Sims (1988) and Sims and Uhlig (1988) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as “sterile ideas,” the application of nonstationary limit theory as “wrongheaded and unenlightening” and the use of classical methods of inference as “unreasonable” and “logically unsound.” They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to reevaluate the …
Operational Algebra And Regression T-Tests, Peter C.B. Phillips
Operational Algebra And Regression T-Tests, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Data reduction involves a physical transition from sample data to econometric estimator and test statistic. This transition induces a mapping on the probability law of the sample, whose image is the distribution of the statistic of interest. At a general level, the mapping can often be captured by means of an operational algebra. Some methods than employ nonlinear functions of differential operators are suggested which can perform this task. The methods are related to pseudodifferential operator techniques that are used in abstract mathematics to solve systems of partial differential equations. They also generalize the fractional calculus methods developed by the …
The Frobenius Problem And Maximal Lattice Free Bodies, Herbert E. Scarf, David F. Shallcross
The Frobenius Problem And Maximal Lattice Free Bodies, Herbert E. Scarf, David F. Shallcross
Cowles Foundation Discussion Papers
Let p = ( p 1 ,…, p n ) be a vector of positive integers whose greatest common divisor is unity. The Frobenius problem is to find the largest integer f * which cannot be written as a non-negative integral combination of the p i . In this note we relate the Frobenius problem to the topic of maximal lattice free bodies and describe an algorithm for n = 3.
The Generalized Basis Reduction Algorithm, Herbert E. Scarf, László Lovász
The Generalized Basis Reduction Algorithm, Herbert E. Scarf, László Lovász
Cowles Foundation Discussion Papers
Let F ( x ) be a convex function defined in R n , which is symmetric about the origin and homogeneous of degree 1, and let L be the lattice of integers Z n . A definition of a reduced basis, b 1 , …, b n , of the lattice with respect to the distance function F is presented, and we describe an algorithm which yields a reduced basis in polynomial time, for fixed n. In the special case in which the bodies { x : F ( x ) < t } are ellipsoids, the definition of a reduced basis is identical with that given by Lenstra, Lenstra and Lovasz (1982) and the algorithm is the well known basis reduction algorithm. We show that the basis vector b 1 , in a reduced basis, is an approximation to a shortest non-zero lattice point with respect to F and relate the basis vectors b i to Minkowski’s successive minima. The results lead to an algorithm for integer programming which executes in polynomial time for fixed n, but which avoids the ellipsoidal approximation required by Lenstra’s algorithm. We also discuss the properties of a Korkine-Zolotarev basis for the lattice.
Voting By Committees, Salvador Barberà, Hugo Sonnenschein, Lin Zhou
Voting By Committees, Salvador Barberà, Hugo Sonnenschein, Lin Zhou
Cowles Foundation Discussion Papers
Problems of social choice frequently take the following form. There are n voters and a set K = (1,2,…, k ) of objects. The voters must choose a subset of K . We define a class of voting schemes called voting by committees. The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and non-manipulability on the domain of separable preferences. This result is analogous to the literature on the Groves and Clarke scheme in that it characterizes all of the non-manipulable voting schemes on …
Further Evidence On The Great Crash, The Oil Price Shock, And The Unit Root Hypothesis, Eric Zivot, Donald W.K. Andrews
Further Evidence On The Great Crash, The Oil Price Shock, And The Unit Root Hypothesis, Eric Zivot, Donald W.K. Andrews
Cowles Foundation Discussion Papers
Recently Perron (1989) has carried out tests of the unit root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil price shock. His analysis covers the Nelson-Plosser macroeconomic data series as well as a post-war quarter real GNP series. His tests reject the unit root null hypothesis for most of the series. This paper takes issue with the assumption used by Perron that the Great Crash and the oil price shock can be treated as exogenous events. A variation of Perron’s test is …
Tests For Parameter Instability And Structural Change With Unknown Change Point, Donald W.K. Andrews
Tests For Parameter Instability And Structural Change With Unknown Change Point, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers tests of parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models including models that satisfy maximum likelihood type regularity conditions and models that are suitable for estimation by generalized method of moments procedures. The paper considers likelihood ratio and likelihood ratio like tests, as well as asymptotically equivalent Wald and Lagrange multiplier tests. Each test implicitly uses an estimate of change point. Tests of both “pure” and “partial” structural change are discussed.
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
Cowles Foundation Discussion Papers
This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vetor autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t -statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is …
Financial Integration, Liquidity And Exchange Rates, Vittorio Grilli, Nouriel Roubini
Financial Integration, Liquidity And Exchange Rates, Vittorio Grilli, Nouriel Roubini
Cowles Foundation Discussion Papers
We present a two-country extension of Lucas’ (1988) work on how cash-in-advance constraints in asset markets affect the pricing of financial assets. In the model, there is some degree of separation between the goods markets and the assets markets, and money is used for transactions in both markets. The main results of the paper are the following. First, the equilibrium level of the exchange rate depends on the share of money used for asset transactions; a greater share corresponds to a more appreciated currency. Second, under uncertainty the liquidity effects deriving from stochastic shocks to bond creation lead to an …
Generic Uniform Convergence, Donald W.K. Andrews
Generic Uniform Convergence, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics. The results given here have the following attributes, (1) they extend results of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law …
Aggregation And Imperfect Competition: On The Existence Of Equilibrium, Andrew S. Caplin, Barry Nalebuff
Aggregation And Imperfect Competition: On The Existence Of Equilibrium, Andrew S. Caplin, Barry Nalebuff
Cowles Foundation Discussion Papers
We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces …
A Colored Version Of Tverberg's Theorem, Imre Bárány, D. G. Larman
A Colored Version Of Tverberg's Theorem, Imre Bárány, D. G. Larman
Cowles Foundation Discussion Papers
The main result of this paper is that given n red, n white, and n green points in the plane, it is possible to form n vertex-disjoint triangles Δ 1 ,…,Δ n in such a way that the Δ i has one one red, one white, and one green vertex for every i = 1,…, n and the intersection of these triangles is nonempty.
Aggregation And Social Choice: A Mean Voter Theorem, Andrew S. Caplin, Barry Nalebuff
Aggregation And Social Choice: A Mean Voter Theorem, Andrew S. Caplin, Barry Nalebuff
Cowles Foundation Discussion Papers
A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voter’s most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates differ in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voter’s most preferred outcome is unbeatable according to a 64%-majority rule. The weaker conditions supporting this result represent a significant generalization of Caplin and Nalebuff (1988). The proof of our mean voter result …
Growth And Distribution: A Neoclassical Kaldor-Robinson Exercise, James Tobin
Growth And Distribution: A Neoclassical Kaldor-Robinson Exercise, James Tobin
Cowles Foundation Discussion Papers
Kaldor’s capital/labor income distribution theory relied on differential saving propensities from profits and wages. Robinson’s growth models typically specified constant-coefficient technologies in which marginal productivities cannot determine distribution. Here these two insights are combined in a two-sector (capital goods, consumption goods) economy. Two technologies are available, but only as either-or alternatives. The choice of technology and the income distribution depend on the saving propensities. Steady-state consumption need not be greater when the economy is more capitalized and profit rates are lower.