VARIATIONS ON THE THEME OF CONNINGa IN MATHEMATICAL ECONOMICS

Abstract The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples and one general discussion: dynamics, policy and rational expectations and learning are the examples; a game theory without ‘subjectivism’, based on the axiom of determinateness, is discussed in general terms. The focus is on the role and reliance of standard fixed‐point theorems in orthodox mathematical economics.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

General equilibrium in markets for lemons

This paper studies exchange economies in which agents have differential information about the goods that the other agents bring to the market. To study such a setting, it is useful to distinguish goods not only by their physical characteristics, but also by the agent that brings them to the market. Equilibrium is shown to exist, with agents receiving the cheapest bundle among those that they cannot distinguish from the truthful delivery. An example is presented as an illustration.     

Limited-dependent rational expectations models with future expectations

This paper examines limited-dependent rational expectations (LD-RE) models containing future expectations of the dependent variable. Limited dependence is of a two-limit tobit variety which may, for example, arise as a result of a policy of imposing limits on the movement of the dependent variable by means of marginal as well as intramarginal interventions. We show that when the forcing variables are serially independent the model has an analytical solution which can be computed by backward recursion. With serially correlated forcing variables, we discuss an approximate solution method, as well as a numerically exact method that, in principle, can be implemented by stochastic simulation, although in practice it is limited by available computational capacity. The paper discusses some properties of the approximate solutions and reports the results of a limited number of Monte Carlo experiments in order to illustrate the computational feasibility of using the exact solution when the fundamentals are serially independent and the approximate solution when they are serially correlated.     

House price dynamics: Fundamentals and expectations

We investigate whether expectations that are not fully rational have the potential to explain the evolution of house prices and the price-to-rent ratio in the United States. First, a stylized asset-pricing model solved under rational expectations is used to derive a fundamental value for house prices and the price–rent ratio. Although the model can explain the sample average of the price–rent ratio, it does not generate the large and persistent fluctuations observed in the data. Then, we consider a rational bubble solution, an extrapolative expectations solution and a near rational bubble solution. In this last solution agents extrapolate the future from the latest realizations and the degree of extrapolation is stronger in good times than in bad times, generating waves of over-optimism. We show that under this solution the model not only is able to match key moments of the data but can also replicate the run up in the U.S. house prices observed over the 2000–2006 period and the subsequent sharp downturn.     

Rational expectations equilibria and the ex-post core of an economy with asymmetric information

We study the relationship between the set of rational expectations equilibrium allocations and the ex-post core of exchange economies with asymmetric information.     

Risk premium or irrational expectations? An investigation into the causes of forward discount bias across 27 developed and developing economies forward rates

This study investigates the causes of forward discount bias in 27 forward rates for the period 2007–2016. First, it analyzes the forward discount bias across two horizons: 3-month and 12-month; across two sub-periods: financial crisis and non-crisis; and across two country groups: developed and developing. The regression results show that forward discount bias is present and significant, but has become smaller compared to many earlier studies. In general, 12-month forward discount is less biased compared to the 3-month. The study confirms that during the non-crisis period, developing country forward discount is less biased compared to the developed country across both the horizons. The crisis period has impacted the magnitude of the bias. For the developed country, the bias is higher during the crisis period compared to the non-crisis period at the 3-month horizon but lower at the 12-month horizon. Developing country forward discount is less biased during the crisis period compared to the non-crisis period at the 3-month horizon, but slightly more biased at the 12-month horizon. Second, the study decomposes the bias into two components: irrational expectations and risk premium. The results show that both irrationality and time varying risk premium are present in the bias. However, the irrationality component plays a minor role in the 3-month forward discount bias, but plays a major role in the 12-month forward discount bias. Irrationality is high during the crisis period for both the country groups. The risk premium component of the bias is highly significant across both the periods, country groups and horizons, and thus, plays a major role in the overall bias. Further, the non-parametric tests of comparison of statistical significance of the beta coefficient values between country groups, periods and horizons indicate that many differences are statistically significant supporting our conclusions.     

HOW TO MEASURE LABOUR MARKET EFFECTS OF IMMIGRATION: A REVIEW

Abstract.  This paper surveys available empirical evidence on labour market effects of immigration. Many different approaches have been used already to try to find out whether immigration hurts the labour market opportunities of natives. No doubt new approaches will follow in the future as globalization will keep the migration issue on the agenda. This literature review discusses the different approaches concentrating on both the methodology and the results. At the end, it tries to summarize available evidence.     

Social exclusion and labour market transitions: a multi-state multi-spell analysis using the BHPS

In this empirical paper, we assess how social exclusion arises in the context of labour market transition behaviour. We estimate a multi-state multi-spell competing risks model and identify five states: high skilled employment, intermediate skilled employment, low skilled employment, unemployment and out-of-the-labour market. Using data from the first seven waves of the British Household Panel Survey, we show that a substantial number of workers were trapped in a vicious circle of low-skilled employment, unemployment and inactivity in the 1990s. Workers who are part of the so-called flexible workforce are more likely to suffer social exclusion.     

Mitigation of the Lucas critique with stochastic control methods

Lucas (In: Brunner, K., Meltzer, A.H. (Eds.), The Phillips Curve and the Labor Markets, Supplementary Series to the Journal of Monetary Economics, 1976, pp. 19–46) pointed out, that when optimization is performed on a deterministic macro model, the resulting policy may not reflect the true optimal solution. Private agents may react to announced policies and consequently model parameters will start to drift. The aim of this paper is to develop a methodology for deriving an optimal policy in the presence of rational expectations and parameter drift. This drift is captured by a stochastic optimization framework with time-varying parameters. The resulting optimal policy is capable of tracking changes in the parameters due to policy changes. A numerical example illustrates how the methodology provides a way to mitigate the effects of the Lucas critique.     

Invertible and non-invertible information sets in linear rational expectations models

Rational expectations solutions are usually derived by assuming that all state variables relevant to forward-looking behaviour are directly observable, or that they are “…an invertible function of observables” (Mehra and Prescott, 1980). Using a framework that nests linearised DSGE models, we give a number of results useful for the analysis of linear rational expectations models with restricted information sets. We distinguish between instantaneous and asymptotic invertibility, and show that the latter may require significantly less information than the former. We also show that non-invertibility of the information set can have significant implications for the time series properties of economies.     

Immigration and occupational status: A study of Bangladeshi and Turkish fathers and sons in the London labour market

This paper examines the labour market experience of 300 fathers and 300 of their sons in the Bangladeshi and Turkish immigrant communities in various London boroughs in 1988. Probit estimates are made in relation to employment and unemployment, self-employment and employment, and upward mobility or lack of it. Human capital regressions are also run for each of the four groups and for the combined sample. The evidence is consistent with distinctive labour market experience among the various groups.     

On the impossibility of insider trade in rational expectations equilibria

Existing no trade results are based on the common prior assumption (CPA). This paper identifies a strictly weaker condition than the CPA under which speculative trade is impossible in a rational expectations equilibrium (REE). As our main finding, we demonstrate the impossibility of speculative asset trade in an REE whenever an insider is involved who knows the asset's true value. To model insider trade as an equilibrium phenomenon an alternative equilibrium concept than the REE is thus required.     

Learning in linear models with expectational leads

Models with expectational leads typically admit multiple rational expectations solutions. Based on the ordinary least-squares algorithm, this paper provides an adaptive learning scheme which allows a forecasting agent to select a particular solution on economic grounds. Conditions are given under which this scheme converges to rational expectations solutions globally for all initial conditions. We strengthen convergence results in relaxing standard assumptions and in providing conditions ensuring algorithm convergence which are easier to verify and to interpret than those previously known.