Under adaptive learning, recursive algorithms are proposed to represent how agents update their beliefs over time. For applied purposes, these algorithms require initial estimates of agents perceived law of motion. Obtaining appropriate initial estimates can become prohibitive within the usual data availability restrictions of macroeconomics. To circumvent this issue, we propose a new smoothing-based initialization routine that optimizes the use of a training sample of data to obtain initials consistent with the statistical properties of the learning algorithm. Our method is generically formulated to cover different specifications of the learning mechanism, such as the least-squares and the stochastic gradient algorithms. Using simulations, we show that our method is able to speed up the convergence of initial estimates in exchange for a higher computational cost.

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

In this paper, we investigate real-time behavior of constant-gain stochastic gradient (SG) learning, using the Phelps model of monetary policy as a testing ground. We find that whereas the self-confirming equilibrium is stable under the mean dynamics in a very large region, real-time learning diverges for all but the very smallest gain values. We employ a stochastic Lyapunov function approach to demonstrate that the SG mean dynamics is easily destabilized by the noise associated with real-time learning, because its Jacobian contains stable but very small eigenvalues. We also express caution on usage of perpetual learning algorithms with such small eigenvalues, as the real-time dynamics might diverge from the equilibrium that is stable under the mean dynamics.

We explore real-time adaptive nonlinear learning dynamics in stochastic macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations. Further, we assume that these approximated expectations are updated in real time as new data become available. We argue that this method of real-time parameterized expectations learning provides a plausible alternative to real-time adaptive learning dynamics under linearized versions of the same nonlinear system, and we provide a comparison of the two approaches.

The credibility criterion commonly used in the strategic macroeconomic policy literature, subgame perfection or its variants, ignores a critical problem concerning intertemporal consistency of policy announcements. To capture this additional credibility constraint, this note applies two distinct notions of Renegotiation-Proof, originally proposed in the context of two-person repeated games. Macroeconomic policy games, where the benevolent government interacts with atomistic private agents, offers a new testing ground for these criteria to be evaluated. This note discusses the relative strengths and weaknesses of these criteria.

This paper investigates the quantitative importance of different savings motives on the distributions of wealth and consumption and aggregate capital accumulation by solving an overlapping generations model with intragenerational heterogeneity. Agents differ in age, ability, earnings shocks, and inherited bequests. In the baseline economy, there are uninsurable idiosyncratic risks associated with uncertain lifetime and earnings shocks. The model is calibrated to the U.S. economy and solved numerically. Then the allocations of the baseline economy are compared with those of an economy with complete annuity markets, one without earnings uncertainty, and one without altruism.

Over the past few decades, both the relative price of housing structures and housing services consumption relative to nondurables increased significantly in the United States. This paper explores demand-side factors such as an increase in idiosyncratic earnings risks and changes in housing institutions as potential explanations for the phenomenon. We build a general equilibrium incomplete markets model of housing and compare two steady states that correspond to the 1967 and 2000 U.S. economies. Our model can generate the simultaneous increase in the relative price of houses and housing services consumption relative to nondurables. We find that the increased earnings risks are crucial in replicating this pattern.

We derive a seminonparametric utility function containing the constant relative risk aversion (CRRA) function as a special case, and we estimate the associated Euler equations with U.S. consumption data. There is strong evidence that the CRRA function is misspecified. The correctly specified function includes lagged effects of durable goods and perhaps nondurable goods, is bounded as required by Arrow's Utility Boundedness Theorem, and has a positive rate of time preference. Constraining sample periods and separability structure to be consistent with the generalized axiom of revealed preference affects estimation results substantially. Using Divisia aggregates instead of the NIPA aggregates also affects results.

In a canonical monetary policy model in which the central bank learns about underlying fundamentals by estimating the parameters of a Phillips curve, we show that the bank’s loss function is asymmetric such that parameter overestimates may be more or less costly than underestimates, creating a precautionary motive in estimation. This motive suggests the use of a more efficient variance-adjusted least-squares estimator for learning about fundamentals. Informed by this “precautionary learning” the central bank sets low inflation targets, and the economy can settle near a Ramsey equilibrium.

This paper reconsiders optimal inflation targeting in a model where persistence is generated by rational choices of the price makers because of a time-dependent pricing mechanism. In this framework, which generalizes the traditional Calvo model, inflation persistence is intrinsic, as it is micro-founded assuming that firms' pricing decisions depend on the time elapsed from the last price reset. We use a linear–quadratic approach to study the welfare effects and optimal policies. We disentangled two distortion sources showing how welfare falls in both the average of the probability of changing prices and its distribution among different firms. Described the underlying distortions of our setup, we analyze its normative implications for optimal inflation. The issues of uncertainty and robustness are also considered: By using robust control techniques, we, in fact, consider the consequences of implementing a “wrong” monetary rule due to a misinterpretation of sources of inflation inertia.

In models with a representative infinitely lived household, tax smoothing implies that the steady state of government debt should follow a random walk. This is unlikely to be the case in overlapping generations (OLG) economies, where the equilibrium interest rate may differ from the policy maker's rate of time preference. It may therefore be optimal to reduce debt today to reduce distortionary taxation in the future. In addition, the level of the capital stock in these economies is likely to be suboptimally low, and reducing government debt will crowd in additional capital. Using a version of the Blanchard-Yaari model of perpetual youth, with both public and private capital, we show that it is optimal in steady state for the government to hold assets. However, we also show how and why this level of government assets can fall short of both the level of debt that achieves the optimal capital stock and the level that eliminates income taxes. Finally, we compute the optimal adjustment path to this steady state.

Recently, Penn World Tables include new data that enable calculation of total factor productivity in addition to output for a large set of countries. We use these new data to examine convergence and divergence across countries by applying a new approach, which differentiates between the dynamics of output and of productivity. Our empirical results lead to two main new contributions to the literature. The first is on the interpretation of “β-convergence” in “growth regressions.” It means that output per worker in each country converges to productivity but does not imply convergence across countries, since productivity tends to diverge from the global frontier. The second contribution is to the literature, which finds that income gaps across countries are due mainly to differential technology adoption. This paper shows that the gaps in technology are not only large but keep growing over time.

Can monetary policy stimulate consumption through inflation expectations? We study how US consumers revise inflation expectations and readiness to spend in response to monetary policy shocks using a structural vector-autoregressive model, where we identify exogenous policy shocks with interest rate surprises around FOMC announcements. Based on survey data, we construct measures of changes in consumers’ readiness to spend conditional on how consumers update their inflation expectations. Expansionary policy shocks tend to increase readiness to spend conditional on higher expected inflation outside the zero lower bound (ZLB), but the effect is small. At the ZLB, consumers increasingly reduce their readiness to spend if they expect higher inflation. Overall, we find only limited evidence suggesting that policy-induced variations in inflation expectations are associated with adjustments that are in line with the predictions of standard macroeconomic models.

Occurrences of an old phenomenon, the expropriation of foreign-owned property, peaked in the 1970s when virtually every significant oil-producing developing country nationalized its oil. Nationalization was again on the rise in the 2000s. Using novel data, this paper quantitatively evaluates the effects of nationalization. First, the paper finds significant productivity losses associated with nationalization in a sample of oil-producing countries. Venezuela in particular experienced a striking decline in productivity. Second, the paper presents a new channel through which nationalization affects productivity: a long-term pre-announcement can shift the composition of the workforce with a huge decline in highly skilled foreign workers and result in higher extraction and lower exploration. Guided by a quantitative dynamic partial equilibrium framework disciplined by features of the Venezuelan data, this paper then evaluates the effects of nationalization. A comparison of the simulated and time series data shows that the model can explain about 80% of the productivity pattern over 1961–1980 in the Venezuelan oil industry. Counterfactual experiments suggest that the shift in the composition of the workforce is important in accounting for the productivity pattern. Furthermore, if nationalization had been sudden, long-run losses would have been lower.

Based on a multisector general equilibrium framework, we show that the sectoral elasticity of substitution plays the key role in the evolution of asymmetric tails of macroeconomic fluctuations and the establishment of robustness against productivity shocks. A non-unitary elasticity of substitution renders a nonlinear Domar aggregation, where normal sectoral productivity shocks translate into non-normal aggregated shocks with variable expected output growth. We empirically estimate 100 sectoral elasticities of substitution, using the time-series linked input-output tables for Japan and find that the production economy is elastic overall, relative to a Cobb-Douglas economy with unitary elasticity. In addition to the previous assessment of an inelastic production economy for the USA, the contrasting tail asymmetry of the distribution of aggregated shocks between the USA and Japan is explained. Moreover, the robustness of an economy is assessed by expected output growth, the level of which is led by the sectoral elasticities of substitution under zero-mean productivity shocks.

This paper provides conditions under which an algorithm for the computation and simulation of Bewley–Huggett–Aiyagari models, based on state-space discretization, will converge to all true solutions. These conditions are shown to be satisfied in two standard examples: the Aiyagari model and its extension to endogenous labor. Bewley–Huggett– Aiyagari models are general equilibrium models with incomplete markets and idiosyncratic, but no aggregate, shocks. The algorithm itself is based on discretization, while the theory importantly allows for making simulations using the approximate computational solution of the value function problem rather than the true model solution. The numerical results of applying the algorithm to both models are provided and investigated in terms of replication, revealing that the Aiyagari model overestimates the degree of precautionary savings in the high-risk-and-high-risk-aversion case. The results also show that both models almost certainly have a unique general equilibrium. Theoretically, the existence of equilibria was known, but uniqueness remained an open question.

This paper analyzes exchange-rate dynamics following a money-based disinflation under different degrees of exchange-rate pass-through. Using a microfounded dynamic general equilibrium model with imperfect competition and nominal rigidities, it is shown that a monetary slowdown causes an appreciation of the exchange rate and a short-run fall in employment. Varying the degree of pass-through, however, significantly alters the magnitudes of these effects. As the degree of pass-through is reduced, the extent of the short-run appreciation of the exchange rate increases and the short-run impact of the disinflation on employment falls.

Benhabib and Farmer show that in a laissez-faire one-sector real business cycle model under aggregate increasing returns, under sufficiently high degrees of productive externality, the demand-side effect in the labor market triggered by agents' expectations about the economy's future outweighs the supply-side effect, making agents' expectations become self-fulfilling. This paper analytically demonstrates that the conduct of monetary policy under nominal gross domestic product (GDP) targeting reinforces the supply-side effect in the labor market, thereby making belief-driven aggregate fluctuations more difficult to occur. This reinforcement effect on labor supply is absent under nominal consumption targeting and inflation targeting. Hence, under these two monetary regimes, the necessary and sufficient conditions for the economy to display equilibrium indeterminacy and sunspot fluctuations are identical to those in Benhabib and Farmer's laissez-faire economy. The results are robust to an endogenous growth extension of the model, implying that targeting the nominal GDP growth rate is more desirable than targeting the nominal consumption growth rate or the inflation rate in terms of macroeconomic stability.

Introducing susceptible-infected-recovered epidemiology dynamics with vaccines into an endogenous growth model, we investigate the impact of government infectious disease policy on macroeconomic performance. We find that any expenditure that improves health, whether to reduce the contact rate or increase the recovery rate or the vaccination rate, and regardless of whether it comes directly from the households or the government, has a positive impact on economic growth, but does not necessarily improve the welfare. The reason people’s health has improved but their welfare has fallen is because government expenditures must be covered by taxes, which will reduce their disposable income and consumption.

Costas Azariadis was born in Athens, Greece, in 1943. He attended the National Technical University in Athens and received a degree in chemical engineering in 1969. He then attended Carnegie Mellon University, receiving an MBA in 1971 and his Ph.D. in 1975. His doctoral dissertation was advised by Edward Prescott and Robert Lucas. Azariadis's first academic appointment was as an assistant professor at Brown University between 1973 and 1977, after which he moved to the University of Pennsylvania. In 1992, he moved to UCLA. In addition, Azariadis spent two semesters at Hebrew University and Princeton and has held briefer visiting positions all over the world.