The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on the m-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean form

where X=(X1, X2, …, Xm) is some random vector, {Ej}j∈J is a finite family of finite sets.

The Hodrick–Prescott filter represents one of the most popular methods for trend–cycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick–Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal–noise matrix ratio to the parameters of the VARMA representation of the model. We then show that the parameters can be estimated using a recently introduced method, called “Moment Estimation Through Aggregation (META).” This method replaces traditional multivariate likelihood estimation with a procedure that requires estimating univariate processes only. This makes the estimation simpler, faster, and better behaved numerically. We prove that our estimation method is consistent and asymptotically normal distributed for the proposed framework. Finally, we present an empirical application focusing on the industrial production of several European countries.

The paper studies multivariate non linear economic dynamical systems with an expectations feedback subjected to exogenous perturbations. In these systems, agents form expectations on future variables based on subjective transition probabilities given by a Markov kernel. The notion of a perfect Markov kernel that generates rational expectations along all orbits of the system is proposed. Conditions are provided under which perfect Markov kernels exist. Applications are given to models of the Cobweb type, to multivariate affine-linear systems, and to the stochastic OLG model of economic growth. For the latter two models, it is shown when a globally attracting random fixed point with rational expectations exists.

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

This paper studies the transition dynamics predictions of an R&D-based growth model, and evaluates their performance in explaining income disparities across nations. We find that the fraction of the observed cross-country income variation explained by the transitional dynamics of the model is as large as the one accounted for by existing steady-state level regressions. Our results suggest that the traditional view of a world in which nations move along their distinct balanced-growth paths is as likely as the one in which countries move along adjustment paths toward a common (very long run) steady state.

This paper compares the conventional Calvo and Rotemberg price adjustments at the zero lower bound (ZLB) on nominal interest rates. Although the two pricing mechanisms are equivalent to a first-order approximation around the zero-inflation steady state, they produce very different results, based on a fully-nonlinear method. Specifically, the nominal interest rate hits the ZLB more frequently in the Calvo model than in the Rotemberg model. At the ZLB, deflation is larger and recessions are more severe in the Calvo model. The main reason for the difference in results is that price adjustment costs show up in the resource constraints in the Rotemberg. When they are rebated to the household, the two models behave similarly.

Unlike most existing studies on the endogenous institutions, literature on theoretical growth has traditionally considered institutions as exogenous. In this paper, a learn-by-doing-based growth model is adopted and integrated with endogenous institutions to study how economic agents’ incentives engage in institutional improvements or exploit institutional imperfections. From maximization of identical agent utility, the economic growth model includes capital, labor, technology, and institutions. The study is to analyze the effect of institutions on the stability of equilibrium, balanced economic growth path, and convergence rate in the process of economic growth. It is concluded that, firstly, improving institutions is a decisive factor for China’s high economic growth rate for the past years; secondly, improving institutions can increase the capital stock per unit of effective labor in steady state; thirdly, imperfect institutions can explain income difference among countries; and finally, technology plays a key role only under the conditions adapting to institutions.

The aggregation of sectoral or regional Phillips curves yields an inflation–unemployment trade-off that is not vertical in the long run if there are mismatches between supply and demand in the regional or sectoral labor markets. This remains true even when the individual Phillips curves are all vertical. This result stems from variations in the slope of the individual short-run Phillips curves, rather than from changes to the equilibrium level of unemployment. It implies a role for the management of the distribution of demand over different sectors or regions, in order to minimize the natural rate of unemployment.

Economic and social impacts of aging trends will be of the utmost importance in the near future. We embed a stylized pay-as-you-go (PAYG) pension system into a DSGE model with overlapping generations to assess the macroeconomic effects of aging in a small Euro Area economy. The simulations suggest large negative impacts on GDP and private consumption. In addition, external imbalances may widen significantly under the PAYG system. All results are conditional on the policy options addressing debt sustainability–the impacts tend to be very large if the government finances the aging with higher social security premia instead of lower replacement ratios. Sensitivity analysis reveals that GDP and private consumption impacts are less robust than those on external imbalances. Results also imply that supranational policy coordination may be crucial if the objective is to preserve economic and financial stability in the Euro Area.

Current data provide macroeconomic information for a large number of countries and for long periods of time (macropanels). In such panels, slope heterogeneity and cross-section dependence (CSD) are the rule rather than the exception, leading the fixed effects slope estimators to be biased and inconsistent. This paper analyzes gross capital flows to emerging economies employing the Augmented Mean Group (AMG) model to account for slope heterogeneity and CSD. The results suggest that the AMG performs better than the fixed effects model and that not only country heterogeneity is important to analyze capital inflows to emerging economies, but also are the differences among the types of capital inflows.

In aggregation theory, the admissibility condition for clustering components to be aggregated is blockwise weak separability, which also is the condition needed to separate out sectors of the economy. Although weak separability is thereby of central importance in aggregation and index number theory and in econometrics, prior attempts to produce statistical tests of weak separability have performed poorly in Monte Carlo studies. This paper introduces a new class of weak separability tests, which is seminonparametric. Such tests are both based on a necessary and sufficient condition and are fully stochastic, allowing to take into account measurement error. Simulations show that the tests perform well, even for large measurement errors.

This paper analyzes the aggregate growth and distributional effects of tax policy using an endogenous growth model with heterogeneous agents having “catching up with the Joneses” (CUJ) types of preferences. We characterize the aggregate equilibrium of this economy, as well as its distributional properties, and show that the consumption externality present with CUJ preferences produces greater income inequality than is obtained with conventional time-separable preferences. The consumption externality substantially alters the effects of tax policy, mostly quantitatively, but in some cases qualitatively as well. Extensive numerical simulations are conducted and used to compare the consequences of different modes of taxation, highlighting the tradeoffs involved.

We examine the welfare implications of two types of central-bank transparency: the publication of the information underlying the central bank's decision (decision transparency) and the release of the information that the central bank observes afterwards (postdecision transparency). Decision transparency does not make the public better informed in equilibrium. Even so, it may be socially desirable because it eliminates harmful equilibria. Postdecision transparency has ambiguous effects. It reduces output variance and the distortions stemming from heterogeneous information. In this sense, it can be used as a substitute for monetary policy. However, postdecision transparency generally raises the variance of inflation. We argue that a conflict of interests may arise between society and the central bank with regard to transparency.

This paper characterizes the saving rate in the Ramsey–Cass–Koopmans model analytically with a general production function when there exist both exogenous and endogenous growth. It points out conditions involving the share of capital and the elasticities of factor and intertemporal substitution under which the saving rate path to its steady-state value exhibits overshooting or undershooting or is monotonic. Simulations illustrate these interesting dynamics. The paper also identifies the general class of production functions that render the saving rate constant along the entire transition path and hence make the Ramsey–Cass–Koopmans model isomorphic to that of Solow and Swan.

We study a generic optimal control problem with a stock that accumulates with constant delay. We show that the optimal system dynamics reduces to a system of ordinary differential equations, implying monotonic optimal paths, if the objective function is additively separable in the stock and the control. This is, however, not true for general objective functions, which may exhibit nonmonotonic and oscillatory optimal paths. The reason is that the impact of the stock on the objective depends on the current level of the control, whereas the control influences the dynamics of the stock with a delay.

This paper analyzes optimal paths in a one-sector growth model when the technology is not convex. In such a case, we prove that optimal paths converge to the upper steady state iff the initial wealth is above a critical level. Then, we first show that, thanks to debt and/or R&D, the poverty trap may be avoided. Second, we introduce a distortion: corruption that mostly has dramatic consequences on growth, but may have a beneficial effect if it is not high and if it improves productivity (incentive effect).

This paper investigates the effects of R&D subsidies on aggregate product variety and endogenous productivity growth without scale effects. In a two-country model with imperfect knowledge diffusion, the larger country has a greater share of firms with higher productivity levels. The concentration of relatively productive firms increases knowledge flows between firms, causing an increase in firm-level employment in innovation. Accordingly, the aggregate growth rate is higher when counties are asymmetric than when they are similar in size. The larger scale of firm-level innovation activity reduces market entry, however, and aggregate product variety falls. In this framework, national R&D subsidies have positive effects on the industry share, relative productivity, and wage rate of the implementing country. If the smaller country introduces an R&D subsidy, aggregate product variety rises and productivity growth falls. If the larger country introduces an R&D subsidy, productivity growth rises, but aggregate product variety may rise or fall.

This paper studies the nature of long-run behavior in a two-sector model of optimal growth. Under some restrictions on the parameters of the model, we provide an explicit solution of the optimal policy function generated by the optimal growth model. Fixing the discount factor, we indicate how long-run optimal dynamics changes as a key technological parameter (labor output ratio) changes. For a particular configuration of parameter values, we also provide an explicit solution of the unique absolutely continuous invariant ergodic distribution generated by the optimal policy function.

Discrete-time and continuous-time models with time to build do not possess the same dimension. In this paper we address the dimensionality issue by revising the way time to build is traditionally measured when transforming the economic dynamics from discrete to continuous time. We propose our new procedure as an alternative approach which allows for a unifying theory of the two classes of economic growth models. Interestingly enough, discrete-time models admit a change in stability for a value of the time-to-build parameter where their continuous counterpart admits an Hopf bifurcation.

This paper builds a macroeconomic model of equilibrium unemployment in which firms persistently face difficulties in selling their production, and this affects their decisions to create jobs. We show that the competitive search equilibrium is not efficient and that inflation is detrimental to unemployment.