An adaptive step-size algorithm [Kushner and Yin, Stochastic Approximation and Recursive Algorithms and Applications, 2nd ed., New York: Springer-Verlag (2003)] is used to model time-varying learning, and its performance is illustrated in the environment of Marcet and Nicolini [American Economic Review 93 (2003), 1476–1498]. The resulting model gives qualitatively similar results to those of Marcet and Nicolini, and performs quantitatively somewhat better, based on the criterion of mean squared error. The model generates increasing gain during hyperinflations and decreasing gain after hyperinflations end, which matches findings in the data. An agent using this model behaves cautiously when faced with sudden changes in policy, and is able to recognize a regime change after acquiring sufficient information.

This paper explores how retirement timing, together with life-cycle saving and human capital investment in children, responds to rising longevity in a recursive model with altruistic agents. We find that rising longevity raises the retirement age. If initial life expectancy is not too high, rising longevity also raises human capital investment in children and the saving rate. Through these channels, rising longevity can be conducive to long-run economic growth. A binding mandatory retirement age reduces human capital investment and the growth rate, raises the saving rate, and reduces welfare.

We consider a model-averaged forecast-based estimate of the output gap to measure economic slack in 10 industrialized economies. Our measure takes changes in the long-run growth rate into account and, by addressing model uncertainty using equal weights on different forecast-based estimates, is robust to different assumptions about the underlying structure of the economy. For all 10 countries in the sample, we find that the estimated output gap has much larger negative movements during recessions than positive movements in expansions, suggesting business cycle asymmetry is an intrinsic characteristic of industrialized economies. Furthermore, the estimated output gap is always strongly negatively correlated with future output growth and unemployment and positively correlated with capacity utilization. It also implies a convex Phillips Curve in many cases. The model-averaged output gap is reliable in real time in the sense of being subject to relatively small revisions.

In this paper, we consider the effects of population aging on a pay-as-you-go financed defined contributions pension scheme. We show that when retirement decisions are endogenous, aging increases the retirement age and the steady-state level of capital. The effect on pension payouts is in general ambiguous, except for the solution of full retirement, when this effect is unambiguously negative.

This paper proposes a multivariate unobserved-components model to simultaneously decompose the real GDP for each of the G-7 countries into its respective trend and cycle components. In contrast to previous literature, our model allows for explicit correlation between all the contemporaneous trend and cycle shocks. We find that all the G-7 countries have highly variable stochastic permanent components for output, even once we allow for structural breaks. We also find that common restrictions on the correlations between trend and cycle shocks are rejected by the data. In particular, we find that correlations across permanent and transitory shocks are important both within and across countries.

We consider a model that provides insight into the well-known Folk theorem in economics that when the discount factor β is sufficiently close to 1, expropriation will never occur. Although this Folk theorem is true in our model, our perspective is different. The discount factor β often is described as a “deep structural parameter” that is difficult to alter at a point in time. In contrast, we analyze the determinants of two thresholds β and β* that segment the unit interval on which β is defined into three subintervals. These subintervals correspond to the three possible equilibria for investment flows: autarky, underinvestment, and unconstrained optimal investment. These thresholds are of interest because they can be altered by specific policy interventions. As a consequence, even if β is small, some level of foreign investment can be supported. We construct measures of β for 40 countries, characterize β and β*, and discuss recent trends in investment flows.

A negative or nonsignificant empirical correlation between aggregate R&D intensity and the economic growth rate is a well-known fact in the empirical growth literature, but scarcely addressed in the theoretical growth literature. This paper develops an endogenous-growth~model that explores the interrelation~between horizontal and vertical R&D under a lab-equipment specification that is consistent with that stylized fact. A key feature is that the growth rate is fully endogenous both on the intensive and on the extensive margin. Strong composition effects between horizontal and vertical R&D, along both transition and the balanced-growth path, then emerge as the main mechanism producing those results. This setting also allows us to obtain a relationship between economic growth and firm dynamics that is consistent with the empirical facts.

We study how discount window policy affects the frequency of banking crises, the level of investment, and the scope for indeterminacy of equilibrium. Previous work has shown that providing costless liquidity through a discount window has mixed effects in terms of these criteria: It prevents episodes of high liquidity demand from causing crises but can lead to indeterminacy of stationary equilibrium and to inefficiently low levels of investment. We show how offering discount window loans at an above-market interest rate can be unambiguously beneficial. Such a policy generates a unique stationary equilibrium. Banking crises occur with positive probability in this equilibrium and the level of investment is suboptimal, but a proper combination of discount window and monetary policies can make the welfare effects of these inefficiencies arbitrarily small. The near-optimal policies can be viewed as approximately implementing the Friedman rule.

This paper proposes a method and a toolkit for solving optimal policy with imperfect commitment. As opposed to the existing literature, our method can be employed in the medium- and large-scale models typically used in monetary policy. We apply our method to the Smets and Wouters model [American Economic Review 97(3), 586–606 (2007)], for which we show that imperfect commitment has relevant implications for interest rate setting, the sources of business cycle fluctuations, and welfare.

Early research on the Taylor rule typically divided the data exogenously into pre-Volcker and Volcker–Greenspan subsamples. We contribute to the recent trend of endogenizing changes in monetary policy by estimating a real-time forward-looking Taylor rule with endogenous Markov switching coefficients and variance. The response of the interest rate to inflation is regime-dependent, with the pre- and post-Volcker samples containing monetary regimes where the Fed did and did not follow the Taylor principle. Although the Fed consistently adhered to the Taylor principle before 1973 and after 1984, it followed the Taylor principle from 1975 to 1979 and did not follow the Taylor principle from 1980 to 1984. We also find that the Fed only responded to real economic activity during the states in which the Taylor principle held. Our results are consistent with the idea that exogenously dividing postwar monetary policy into pre- and post-Volcker samples is misleading. The greatest qualitative difference between our results and recent research employing time-varying parameters is that we find that the Fed did not adhere to the Taylor principle during most of Paul Volcker's tenure, a finding that accords with the historical record of monetary policy.

Taken literally, the concept of “stabilization policy” implicitly assumes that the macroeconomy is unstable without imposition of a policy. Hence, selection of a “stabilization policy” can be viewed as selection of a policy to bifurcate the system from an unstable to a stable operating regime. The literature on dynamics of high-dimensional systems suggests that successful bifurcation selection is challenging. As an experiment to investigate this point of view, we use the continuous-time UK dynamic macroeconometric model. Under assumptions designed to be most favorable to stabilization policy, we find that policies that would produce successful bifurcation are very complicated. We also find that less complicated policies based upon reasonable economic intuition can be counterproductive, since such policies can contract the size of the stable subset of the parameter space. In fact, an economy that is dynamically stable without policy, but subject to stochastic shocks, could be bifurcated to instability with imposition of a poorly designed “stabilization” policy.

A time-varying-parameter VAR for real output growth and inflation is estimated with annual U.S. series dating back to 1870. Volatility for both variables rises quickly with World War I and its aftermath, stays high until the end of World War II, and drops rapidly until the 1960s. This Postwar Moderation yields the largest decline in volatilities, surpassing the Great Moderation. Conditional on temporary shocks, inflation and output growth are positively correlated. Our model implies that aggregate demand played a key role in inflation volatility fluctuations. Conversely, the two variables are negatively correlated conditional on permanent shocks. Our model suggests that aggregate supply played an important role in output volatility fluctuations. Most impulse responses support an aggregate supply interpretation for permanent shocks. However, before World War I, a permanent increase in output raised the price level at longer horizons, and these responses are frequently statistically significant. This evidence supports the hypothesis that aggregate demand had a long-run positive effect on output during the pre–World War I period.

Recent medical research shows that health is highly influential on learning and the ability to think laterally; however, past economic studies have failed to empirically examine the influence of health on learning, schooling, and ideas production, the main drivers of growth in endogenous growth models. This paper constructs a measure of health-adjusted educational attainment among the working age population based on their health status during the time they obtained their education. Using annual data for 21 OECD countries over the past two centuries, it is shown that health has been highly influential on the quantity and quality of schooling, innovation, and growth.

There is a family of models with physical and human capital and R&D for which convergence properties have been discussed [Lutz G. Arnold, European Economic Review 44, 1599–1605 (2000); Manuel Gómez, Studies in Nonlinear Dynamics and Econometrics 9(1), Article 5 (2005)]. However, spillovers in R&D have been ignored in this context. We introduce spillovers in this model and derive the steady-state and stability properties. This new feature implies that the model is characterized by a system of four differential equations. A unique balanced growth path, along with a two-dimensional stable manifold, is obtained under simple and reasonable conditions. Transition is oscillatory toward the steady state for plausible values of parameters. We discovered that these features are due to the presence of the R&D spillovers externality in the decentralized equilibrium.

This paper tests the ability of New Keynesian models to match the data regarding a key channel for monetary transmission: the dynamic interactions between macroeconomic variables and their corresponding expectations. We exploit survey expectations data and adopt a dynamic stochastic general equilibrium (DSGE)-VAR approach to assess the extent and sources of model misspecification. The results point to serious misspecification in the expectations-formation side of the DSGE model. The rational expectations hypothesis is primarily responsible for the model's failure to capture the co-movements between observed macroeconomic expectations and realizations. Alternative models of expectations formation help partially reconcile the New Keynesian model with the data.

This paper studies the evolution of European fiscal policies in three periods: the pre-Maastricht phase (to 1991); the runup to monetary union (1992–1997), and the stability pact phase (1998 onward). Using three separate indicators, we search for structural breaks that could signify a change in the average level of discipline in these periods. We find increased fiscal discipline only up to 1997. We conclude the new fiscal discipline was a temporary phenomenon, a product of the sanction of being denied entry to the Euro. After EMU, fiscal policy gradually loosened. A single structural break test will miss these dynamic effects, and could easily generate the false conclusion that fiscal discipline had tightened since the start of phase two of EMU.

We construct an endogenous growth model that includes productive public capital and government debt. We assume that the government debt-to-GDP ratio is gradually adjusted to a target level, reflecting the permanent commitment rules in the Stability and Growth Pact or the Maastricht Treaty in the European Union (i.e., the well-known 60% rule). These rules affect government borrowing and public investment. Here, we examine the welfare implications of the permanent commitment rules. We find that fiscal consolidation based on the rules improves social welfare. Moreover, the improvement in welfare accelerates as fiscal consolidation progresses more rapidly. Last, we also discuss and derive the optimal long-run debt-to-GDP ratio.

This paper develops a monetary endogenous growth model with capital and skill heterogeneity to analyze the relationship among inflation, growth, and income inequality. In the model inflation, growth, and inequality are jointly determined. We show that an increase in the long-run money growth rate raises inflation and reduces growth, but its effect on income inequality depends on the relative importance of the two types of heterogeneity. Inequality shrinks with the rise of inflation when capital heterogeneity dominates and enlarges when skill heterogeneity dominates. Therefore, our model supports a negative (positive) inflation–inequality relationship and a positive (negative) growth–inequality relationship when capital (skill) heterogeneity dominates. In any event, inflation and growth are negatively related.

We consider an agent-based model of financial markets with asynchronous order arrival in continuous time. Buying and selling orders arrive in accordance with a Poisson dynamics where the order rates depend both on past prices and on the mood of the market. The agents form their demand for an asset on the basis of their forecasts of future prices and their forecasting rules may change over time as a result of the influence of other traders. Among the possible rules are “chartist” or extrapolatory rules. We prove that when chartists are in the market, and with choice of scaling, the dynamics of asset prices can be approximated by an ordinary delay differential equation. The fluctuations around the first-order approximation follow an Ornstein–Uhlenbeck dynamics with delay in a random environment of investor sentiment.

In this paper, we develop a small open economy New Keynesian dynamic stochastic general equilibrium (DSGE) model to understand the relative importance of two key technology shocks, Hicks neutral total factor productivity (TFP) shock and investment specific technology (IST) shock for an emerging market economy like India. In addition to these two shocks, our model includes three demand side shocks such as fiscal spending, home interest rate, and foreign interest rate. Using a Bayesian approach, we estimate our DSGE model with Indian annual data for key macroeconomic variables over the period of 1971–2010, and for subsamples of pre-liberalization (1971–1990) and post-liberalization (1991–2010) periods. Our study reveals three main results. First, output correlates positively with TFP, but negatively with IST. Second, TFP and IST shocks are the first and the second most important contributors to aggregate fluctuations in India. In contrast, the demand side disturbances play a limited role. Third, although TFP plays a major role in determining aggregate fluctuations, its importance vis-à-vis IST has declined during the post liberalization era. We find that structural shifts of nominal friction and relative home bias for consumption to investment in the post-liberalization period can account for the rising importance of the IST shocks in India.