Knowledge that Transforms

This paper develops Instrumental Variables statistics for testing non-nested hypotheses when the hypotheses considered are single equations from a system of linear dynamic simultaneous equations. Asymptotic distributions of those statistics and of comparable Maximum Likelihood statistics are derived under the null hypothesis, a local non-nested alternative hypothesis, and a local “comprehensive” alternative hypothesis. The asymptotic powers of the non-nested hypothesis tests are compared with those of tests of nested hypotheses, and a numerical application is given.

We study a rational expectations partial equilibrium model of a market for a single storable commodity whose output each period is a function of previous period effort on production and a realization of a shock that affects equally all producers. The final demand is non-random and depends only on each period's price. Risk-neutral producers make production and storage decisions based on forecasts of future price distributions. Existence of equilibrium is proved, and for the case of i.i.d. shocks several comparative statics results are established as well as the existence and stability of a unique stationary distribution.

Majority rule voting with smooth preferences on a smooth policy space W is examined. It is shown that there is an integer w(n), which is 2 when the size of the society n is odd and 3 when n is even such that (i) when the dimension of W is at least win) then, for almost preference profiles on W, the core of the voting game is empty (ii) when the dimension of W exceeds win I then for almost all preference profiles on W, there exist dense preference cycles in W. Moreover in dimension w(n) + I the policy space can be partitioned into a finite number of path connected components, such that any two points in one of the components can be connected by a majority voting trajectory. In dimension greater than w (n) + 1 there exists only one such component. 1.

We describe aggregate inflation as a stochastic process in which the rate of change of the price level can be positive or zero, where the times spent in each state are of random duration. This class of processes includes Two-State Markov Chains and Renewal Processes as special cases. It is shown that the optimal pricing policy of a monopolistic firm with non-convex costs of price adjustment is (S, s) in its real-price, i.e. its nominal price relative to the price level. A basic certainty-equivalence result is proved: i.e. the firm behaves as if it faces a certain and fixed rate of inflation, higher than the actual expected rate, the difference between the two rates being a risk premium which depends on the real interest rate and the parameters of the stochastic process. One can thus apply previous results from the case of certainty (Sheshinski and Weiss, The Review of Economic Studies, 1977) to obtain comparative static results. In particular, one finds that an increase in the variance of expected inflation leads firms to choose a pricing policy with larger amplitude in real price. The paper also addresses the question of consistency in firms' expectations when the price level is determined by the firms' actions.

The paper proposes a multi-period model of hedging which allows for a futures position to be revised within the cash market holding period. Within this framework, we assess the robustness of the two-period theory of hedging when generalized to many periods. We characterize the normal time path of a hedge and the way it is affected by the requirement that futures accounts “mark to market” daily. Finally we show how the resolution of production uncertainty over time affects hedging behavior and determines the volatility of futures prices.

Traditionally, restrictions on systems of demand equations have been tested using static models, whilst being estimated with time series data. This paper develops a vector time series model of expenditure shares in the context of a singular dynamic demand system. The model allows for non-symmetric and non-homogeneous short run behaviour. The homogeneity and symmetry restrictions are only examined in the long run structure. Results based on Canadian time series data are presented and reject the current practise of static modelling while restrictions suggested by economic theory are not rejected when imposed on the long run structure.

A model of borrowing for production is presented where default leads to exclusion from the capital market. This means contracts are enforceable, provided the current payment is less than or equal to the value of future access to the capital market. The main result of the paper is to show that if this constraint binds then credit is rationed.

Non-manipulable direct revelation social choice functions are characterized for societies where the space of alternatives is a euclidean space and all voters have separable star-shaped preferences with a global optimum. If a non-manipulable choice function satisfies a weak unanmity-respecting condition (which is equivalent to having an unrestricted range) then it will depend only on voters' ideal points. Further, such a choice function will decompose into a product of one-dimensional mechanisms in the sense that each coordinate of the chosen point depends only on the respective coordinate of the voters' ideal points. Each coordinate function will also be non-manipulable and respect unanimity. Such one-dimensional mechanisms are uncompromising in the sense that voters cannot take an extreme position to influence the choice to their advantage. Two characterizations of uncompromising choice functions are presented. One is in terms of a continuity condition, the other in terms of “phantom voters” i.e. those points which are chosen which are not any voter's ideal point. There are many such mechanisms which are not dictatorial. However, if differentiability is required of the choice function, this forces it to be either constant or dictatorial. In the multidimensional case, non-separability of preferences leads to dictatorship, even if preferences are restricted to be quadratic.

The Review of Economic Studies has instituted a new series of lectures to be given annually by a "younger" British economist at the Association of University Teachers of Economics Meetings. The choice of lecturer is determined by a panel whose members are currently Professors Hahn, Mirrlees and Nobay. This paper is a revised version of the first lecture in the series. It was presented at the AUTE Meeting held at the University of Surrey in April 1982, and was refereed in the usual way.—MAK.

The paper considers the problem of statistical inference with estimated Lorenz curves and income shares. The full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates is derived and shown to depend only on conditional first and second moments that can be estimated consistently without prior specification of the population density underlying the sample data. Lorenz curves and income shares can thus be used as tools for statistical inference instead of simply as descriptive statistics.