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.

This paper examines an infinite-horizon model of nonlinear income taxation in which the probability that the government can commit is high, but not certain. In this “loose commitment” environment, we find that even a little uncertainty over whether the government can commit yields substantial effects on the optimal dynamic nonlinear income tax system. This result holds even though separating taxation remains optimal, as in the case of full commitment. Under an empirically plausible parameterization, our numerical simulations show that high-skilled individuals must be subsidized in the short run, despite the government's redistributive objective, unless the probability of commitment is higher than 98%. Loose commitment also reverses the short-run welfare effects of changes in most of the model's parameters, and yields some counterintuitive outcomes. For example, all individuals are worse off, rather than better off, in the short run when the proportion of high-skilled individuals in the economy increases.

This paper studies the effects of monetary policy in an inventory-theoretic model of money demand. In this model, agents keep inventories of money, despite the fact that money is dominated in rate of return by interest-bearing assets, because they must pay a fixed cost to transfer funds between the asset market and the goods market. In contrast to exogenous segmentation models in the literature, the timing of money transfers is endogenous. As a result, the model endogenizes the degree of market segmentation as well as the magnitudes of liquidity effects, price sluggishness, and the variability of velocity. I first show that the endogenous segmentation model can generate the positive long-run relationship between money growth and velocity observed in the data, which the exogenous segmentation model fails to capture. I also show that the short-run effects of money shocks on prices, inflation, and nominal interest rates are not robust.

We study the microeconomic and macroeconomic effects of longevity insurance. Using a tractable discrete-time overlapping-generations model of a closed economy we first study different types of government redistribution of accidental bequests in general equilibrium. Individuals face longevity risk, as there is a positive probability of passing away before the retirement period. We find nonpathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal, it is not socially beneficial, because of adverse general equilibrium repercussions.

This note demonstrates analytically that a persistent catastrophic shock on endowment growth, even if moderate, yields negative equity premiums when a representative agent is relatively prudent. In particular, it derives the minimum persistence necessary to have zero equity premiums.

This paper estimates Taylor rules featuring instabilities in policy parameters and switches in policy shocks’ volatility for the post-World War II (WWII) U.S. economy. We contrast a rule embedding a fixed-inflation target with another featuring trend inflation, i.e., a time-varying inflation target. The rule embedding trend inflation turns out to be (a) empirically superior according to a marginal likelihood-based comparison and (b) more able to pin down some relevant episodes of the post-WWII U.S. monetary policy history. Estimates conducted with Greenbook data confirm the empirical superiority of the rule featuring a time-varying inflation target. A comparison with recently published estimates of trend inflation is also conducted.

This paper tests for output convergence across n = 51 economies, employing the definition of Pesaran [Journal of Econometrics 138, 312–355 (2007)]. The definition requires output gaps to be stationary around a constant mean. But when all n(n − 1)/2 pairs of log per capita output gaps are considered, this results in more than 1,000 unit root tests to be conducted. Hence, because of the ensuing multiplicity of the testing problem, a nontrivial number of output gaps will be falsely declared to be stationary when each of the n(n − 1)/2 hypotheses is tested at some conventional level like 5%. To solve the problem, we employ recent multiple testing techniques that allow us to bound the expected fraction of false rejections at a desired level. Monte Carlo results illustrate the usefulness of the techniques. The empirical results show that the data do not support the notion of output convergence after controlling for multiplicity.

Long-run income convergence is investigated in the U.S. context. We employ a novel pairwise econometric procedure based on a probabilistic definition of convergence. The time-series properties of all the possible regional income pairs are examined by means of unit root and non-cointegration tests, where inference is based on the fraction of rejections. We distinguish between the cases of strong convergence, where the implied cointegrating vector is [1, −1], and weak convergence, where long-run homogeneity is relaxed. To address cross-sectional dependence, we employ a bootstrap methodology to derive the empirical distribution of the fraction of rejections. We find supporting evidence of U.S. states sharing a common stochastic trend consistent with a definition of convergence based on long-run forecasts of state incomes being proportional rather than equal. We find that the strength of convergence between states decreases with distance and initial income disparity. Using Metropolitan Statistical Area data, evidence for convergence is stronger.

In this note, we study the basic Ramsey models with labor–leisure choice. We first study the deterministic model and find that a closed-form solution exists and is represented by the Gauss hypergeometric functions. We next incorporate stochastic productivity shocks into the model. We prove that the analytical solution path still exists if the coefficient of relative risk aversion is equal to the capital share.

This paper analyzes the process of decision-making on consumption in a two-period consumption setting, assuming the return on savings is uncertain in the sense of Knight [Risk, Uncertainty, and Profit. Boston: Houghton Mifflin (1921)]. The results imply that a naïve strategy to save zero is optimal for a continuum of income values. Under the Permanent Income Hypothesis, consumption equals current income only when current income is equal to permanent income. Indeed Campbell and Mankiw [in Olivier Blanchard and Stanley Fischer (eds.), NBER Macroeconomics Annual, pp. 185–214. Cambridge, MA: MIT Press (1989)] assumed that consumers who spend their total income are only following a simple rule of thumb. However, the naïve strategy obtained casts doubt on their interpretation.

Prior to the financial crisis, mainstream monetary policy practice had become disconnected from money. We outline the basic rationale for this development using a simple model of money and credit in which we explore the conditions under which money matters directly for the conduct of policy. Then, using a DSGE model, we examine the circumstances under which money becomes more closely linked to inflation. We find that money matters when the variance of the supply of lending dominates productivity and the velocity of money demand. This is because amplifying the role of loans supply leads to an expansion in aggregate demand, via a compression of the external finance premium, which is inflationary. We consider a number of alternative monetary policy rules, and find that a rule which exploits the joint information from money and the external finance premium performs best.

Trade in intermediate goods is an important feature of trade in developed small open economies. We show that a model that assumes trade in intermediate goods brings the dynamics of an otherwise standard small open economy closer to what is observed in the data. With trade in intermediate goods, movements of international relative prices affect the economy through an additional channel, denoted the “cost channel.” A model embedding this channel comes closer to business cycle data in several dimensions compared to models with trade in final goods only. It increases the share of output variance explained by foreign shocks, lowers the exchange rate pass-through, and delivers a positive international correlation of outputs. In addition, the matching of other business cycle moments is at least as good as in a model with trade in final goods only.

We offer an explanation for why perks are overprovided to high-profile CEOs. Hidden saving by an agent makes it difficult for a principal to control the agent's moral hazard problem. However, an agent typically cannot save perks; for example, a CEO who owns the right to use a private jet for personal use cannot bank the unused airplane hours. Thus, the principal may oversupply the agent perks to avoid the hidden saving problem. When the agent can both exert lower effort and save wage income, i.e., in the presence of the double deviation problem, we show that the principal supplies more perks than the agent would have purchased on his own (i.e., excessive perks).

This paper surveys the contributions of David Cass, Tjalling Koopmans, and Edmond Malinvaud over the decades during which modern optimal growth theory was developed. By utilizing material ranging from dissertations, drafts, and working papers through conference presentations, discussions, and published papers, we show that both Malinvaud and Cass had significant impacts on the evolution of Koopman's thought, and the development of his part of what is known as “the Cass–Koopmans model.” Based on our findings, we conclude that the modern optimal growth model should include the contributions of Malinvaud, and be retitled “the Cass–Malinvaud–Koopmans” model accordingly.

Using international data, this paper explores whether the efficient market hypothesis for real stock prices is supported for different panels. The stationarity of a real stock price has important implications for modeling and forecasting financial activities. On a global scale, we implement the recently developed nonlinear heterogeneous panel unit root test, which allows us to account for possible nonlinearity and cross-section dependence and to identify how many and which countries of the panel contain a unit root. The primary conclusion is that the stationarity of real stock prices varies between regions and levels of economic development. Overall, our empirical results illustrate that real stock prices in these countries are a mixture of stationary (integrated of order zero) and nonstationary (integrated of order one) processes.