In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper I will review methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and minimax estimation. On the other hand there exists a large variety of Bayesian methods using Monte Carlo integration or Markov Chain Monte Carlo (MCMC) methods. The different methods are discussed and some of them are compared by means of a simulation study.
The possibility of a Pareto-improving transition from a pay-as-you-go to a fully funded pension system is discussed intensively in the literature. In this paper, the problem is analyzed within a model where the lump-sum contributions to the pension system follow a stochastic process. Applying the criterion of conditional Pareto-efficiency we derive a sufficient condition for the fully funded system to be preferred by all future generations and show that, in contrast to deterministic models with lump-sum contributions, a Pareto-improving abolition of the pay-as-you-go system is possible with probability one.
This paper analyzes the existence, stability and uniqueness of steady states in overlapping generations models with social security. For a fully funded system it is shown that such a steady state exists under plausible sufficient conditions, no matter how contributions are levied. For a pay-as-you-go system, similar conditions can only be derived if contributions are proportional to income. With lump-sum contributions, severe problems with respect to the existence of steady states and even short-run equilibria arise. In both cases, a pay-as-you-go system can lead to non-existence of steady states even though there is one in a fully funded system.
This paper analyzes the existence, stability, and uniqueness of stationary equilibria in a stochastic overlapping generations model with social security, and the impact of pension systems on the stochastic process for the capital stock. It is shown that the probability distribution of the capital stock in a fully funded system equals the corresponding distribution in absence of social security and dominates the one in a pay-as-you-go system in the sense of stochastic dominance. Furthermore, the study shows that the sufficient conditions for the existence and uniqueness of stationary equilibria in a pay-as-you-go system are more restrictive than without social security.
This paper analyzes the efficiency of pay-as-you-go pension systems in a small open economy with stochastic wages and interest rates. Applying the criterion of conditional Pareto-optimality it is shown that the introduction as well as the extension of an existing pay-as-you-go system can be Pareto-improving even though its expected rate of return is below the expected interest rate. This result is only based on efficiency grounds and not due to any intergenerational risk sharing. It follows from the fact that a pay-as-you-go system acts as a means of diversification by reducing the overall risk of individual saving portfolios.
In linear regression biased estimators like ridge estimators, Kuks-Olman estimators, Bayes and minimax estimators are mainly used in order to circumvent difficulties caused by multicollinearity. Up to now, the application of the minimax principle to the weighted scalar mean squared error yields explicit solutions solely in specific cases, where e.g. ridge estimators or Kuks-Olman estimators are obtained. In this paper we introduce a new objective function in such a way that we always get an explicit minimax solution which, in an important special case, can be interpreted as a Kuks-Olman estimator. Our functional may be viewed as a measure of relative rather than absolute squared error.
Missing values in time series are a common experience. This paper addresses the nonparametric estimation of values that are missing at random. Four methods are investigated, least squares estimation, substituting the missings by the mean, linear and spline interpolation of the gaps. The comparison is done by means of a simulation study. It comes out that the least squares estimation performs best. The last two methods yield acceptable results only in special cases which can be classified. In most cases they are worse than using the mean to substitute the missings.
In linear regression models, predictors based on least squares or on generalized least squares estimators are usually applied which, however, fail in case of multicollinearity. As an alternative biased estimators like ridge estimators, Kuks-Olman estimators, Bayes or minimax estimators are sometimes suggested. In our analysis the relative instead of the generally used absolute squared error enters the objective function. An explicit minimax solution is derived which, in an important special case, can be viewed as a predictor based on a Kuks-Olman estimator.
In this article we present a new Bayesian estimate in the linear model with inequality constrained parameters that incorporates positive probabilities for binding constraints. By estimating these quantities from the data using the classical inequality constrained least squares (ICLS) method we obtain a procedure which is a combination of Bayesian and frequentist methods. This estimator is shown to dominate the ICLS in a simulation study thereby avoiding some shortcomings of the conventional Bayes estimator.
In order to determine estimators and predictors in a generalized linear regression model we apply a suitably defined relative squared error instead of the most frequently used absolute squared error. Our approach includes generalized least squares estimators as well as Kuks-Olman and ridge estimators which play a prominent role when multicollinearity is prevailing. In an important special case a general relation between estimators and predictors is derived.
Der vorliegende Beitrag geht an Hand verschiedener Indikatoren der Frage nach, ob sich von der finanziellen Seite her die wirtschaftlichen Risiken bei westdeutschen Unternehmen vergrößert haben. Die Untersuchung stützt sich auf eine Sonderauswertung der Bilanzstatistik der Deutschen Bundesbank für Unternehmen verschiedener Größenklassen. Die Auswertung legt den Schlußnahe, daß sich im Zeitraum 1987-1996 insbesondere bei kleineren und mittleren Unternehmen in Westdeutschland die finanzwirtschaftlichen Risiken spürbar erhöht haben. Hinweise dafür sind der trendmäßige Anstieg des erschuldungsgrades und der Zinsdeckungsquote, sowie eine nachlassende Fähigkeit, aus dem Cash Flow Verbindlichkeiten zu tilgen bzw. Eigenkapital zu bilden. Zusätzliche Tests zeigen überdies, daß sich bei kleineren und mittleren Unternehmen veränderte Risiken auch im Investitionsverhalten niederschlagen. Angesichts der großen Bedeutung solcher Unternehmen ergeben sich aus alledem gesamtwirtschaftlich beträchtliche Risiken für Wachstum und Beschäftigung. Zudem wird die Wirksamkeit geldpolitischer Impulse beeinträchtigt und der Handlungsspielraum der Geldpolitik eingeschränkt.
In this paper the Hurwicz decision rule is applied to an adjustment problem concerning the decision whether a given action should be improved in the light of some knowledge on the states of nature or on other actors' behaviour. In comparison with the minimax and the minimin adjustment principles the general Hurwicz rule reduces to these specific classes whenever the underlying loss function is quadratic and knowledge is given by an ellipsoidal set. In the framework of the adjustment model discussed in this paper Hurwicz's optimism index can be interpreted as a mobility index representing the actor's attitude towards new external information. Examples are given that serve to illustrate the theoretical findings.
We consider a two-period life-cycle model where uncertainty about future labour income is modelled by a fuzzy set. Applying a defuzzification strategy that explicitly takes the individual's behaviour towards risk into account, we show that pessimistic individuals engage in precautionary savings even if marginal utility is not convex, e.g. in case of a quadratic utility function.
In hedonic pricing models there is prior knowledge available which has the form of interval constraints on the coefficients. These are stemming from the considerations of submarkets for the characteristics involved. In this article we briefly discuss some well known estimators that allow for incorporation of this knowledge. Additionally we introduce two new approaches for the same purpose. We present the results of a Monte Carlo experiment in which these estimators are compared. It is illustrated that estimates and confidence intervals for the unknown coefficients can be improved substantially by applying some of these methods.
We consider a model of an economy consisting of heterogenous firms that are faced with uncertainty in future prices when deciding upon production and financing. It is shown that the aggregate supply curve depends on this price uncertainty as well as on the current real cash flow and the current price level if at least some firms choosing loan financing take the bankruptcy risk resulting from the uncertain prices into account. In particular, the aggregate supply curve is increasing in the price-quantity-graph even in the long-run.
In the present paper a general solution to a matrix problem is derived which occurs when determining a relative squared error estimator or predictor in linear regression analysis. This general solution is discussed and applied to important special cases, where, e.g., a generalized least squares estimator, a general ridge or Kuks-Olman estimator, and predictors based on these estimators are obtained.
This essay examines Keynes‘s views on central banking and the structure of monetary policy. The analysis starts with an early Keynes plan for the establishment of a central bank in India of 1913, and ends with the nationalisation of the Bank of England in 1946, when Keynes was a director at the Bank. Particular attention is paid to a Keynes proposal for a sound structure of monetary policy in the UK of 1932, which delineates a particular form and degree of independence which he believed would be conducive to efficiency in the conduct of monetary policy. We argue that this proposal should be seen as an original contribution to the issue of central bank independence that is relevant to modern discussions of this topical issue.
In many applications of the linear regression model there is prior knowledge available which has the form of inequality constraints on the unknown parameters. Classical procedures for incorporation of this type of information are based on least squares, maximum likelihood, Bayesian or minimax approach. From a practical point of view prior knowledge is often vague, i.e. the user is not completely sure about the exact formulation of the constraints. Modelling this feature by using fuzzy sets Arnold and Stahlecker (1997) introduced a generalized minimax estimation principle. In this paper we adopt their approach for modelling fuzzy inequality constraints. It will be shown that this offers an interesting and manageable way for incorporation of this type of prior information.
We consider a profit maximizing monopolistic firm that sets prices in the presence of improper information about the demand for its products. This information deficiency is viewed as being vagueness rather than stochastic uncertainty and modelled by a family of fuzzy sets. Applying a defuzzification strategy that explicitly takes the firm's attitude towards the possibility of deviations of actual demand from its most possible values ("behaviour towards risk'' or its degree of pessimism) into account, we derive explicit solutions to the maximization problem of a single-product and a general multi-product firm. Furthermore, some comparative static results are established.
We consider a model where the individuals have to decide simultaneously on their optimal investment in risky assets, riskless time deposits and their holdings of cash money in view of uncertain payments during the planning period. It is shown that the resulting demand functions for narrow and broad money depend rather differently on income, wealth and interest rates, and that there is some potential for unstable money demand functions. The latter result follows from the existence of different "regimes'' being separated by specific parameter constellations. Changes in those parameters may thus lead to "regime switching'' which implies substantially changing properties of the money demand functions.
We consider a model of an oligopolistic market with heterogenous firms and
products where neither the cost technologies nor the demand functions are
common knowledge. Instead, each firm only has some vague ideas about the
quantity strategies adopted by its competitors which is modelled by a fuzzy
set. Following the notion of an "equilibrium of actions and beliefs'' we
define a generalized "fuzzy'' Nash-equilibrium and show the existence and
uniqueness of such an equilibrium in the model framework considered.
Furthermore, the impact of the fuzzy information on the equilibrium outcome
is analyzed within a comparative static analysis.
This paper analyses the impact of input and output spillovers on the expected effective cost reductions in a two-stage model
of R&D where all R&D projects are risky. It is shown that output spillovers tend to reduce expected cost reductions whereas
input spillovers tend to increase investment in R&D and hence expected cost reductions. In particular, the relations between
cost reductions in the presence of input and output spillovers known from deterministic models may be reversed under certain parameter constellations.
