Since the seminal work of Becker, the dynamics of endogenous fertility has been based on the trade-off faced by parents between the quantity and the quality of their children. However, in developing countries, where child labor is an indispensable source of household income, parents actually incur a negative cost by having an extra child, so that the trade-off disappears. The purpose of this paper is to restore the Beckerian quantity–quality trade-off when intergenerational transfers are upstream, in order to keep fertility endogenous. We do that by adding a negative “sibship size effect” on human capital formation to the standard Becker model. With a simple specification, we obtain multiplicity of steady states or, more fundamentally, the possibility of a jump from a state with high fertility and low income to a state with low fertility and high income, triggered by a continuous increase in the productivity of human capital formation.

This paper considers parental time investment in early childhood as an education input and investigates its relationships with other inputs in their contribution to human capital. I develop a 12-period overlapping generations model where human capital formation is a multistage process. The model is calibrated to the US economy so that the generated data matches patterns in parental education spending and child care time. The estimation results show that time input is complementary to education expenditure. I apply the model by implementing three early education policies. The first two involve more government spending and the third is paid parental leave. The policy experiments show that adopting paid parental leave is the most costly means of increasing human capital. An education subsidy is more effective than a direct increase in government spending at promoting human capital; however, its impact on earnings inequality and persistence is smaller.

Karl Shell is without a doubt one of the central players in the development of economic theory and macroeconomics in the latter part of the twentieth century. He has made important contributions on topics ranging from growth theory, to overlapping generations, to extrinsic uncertainty, to monetary economics, to market games, and to technological innovation. His collaborations with Dave Cass are legend, and include the seminal formulation of the concept of sunspot equilibria. His “Notes on the Economics of Infinity,” and his papers with Yves Balasko are overlapping-generations classics. Shell's many coauthors read like a Who's Who in economics, and include (in no particular order) Joe Stiglitz, Franklin Fisher, Miguel Sidrauski, Ned Phelps, Duncan Foley, Walt Heller, Albert Ando, Jim Peck, Rod Garratt, Aditya Goenka, Christian Ghiglino, and Todd Keister. This is also a club to which we are also proud to belong.

Shell's research is first rate and highly innovative, but his full contribution to economic theory must also be judged by his long service as the editor of one of the profession's premier journals, the Journal of Economic Theory. As the founding editor of JET, Shell took a small upstart journal, originally envisioned as a niche outlet for papers on mathematical economics, and turned it into one of the best in the profession. JET has published papers that have had major impacts on the development of economic theory in all its various flavors.

Because of Shell's long stewardship of JET, the story of his professional life—which we hope we have captured in this interview—is also a history of the evolution of economic theory over the past quarter century. We spoke with Karl in his office at Cornell University and over lunch at the faculty club in the Statler, and the interview tapes we made were very much a three-way conversation between Karl and the two of us. In editing the transcripts of these tapes for publication, we wished to keep the focus of the conversation on Shell, and have therefore adopted the same anonymous “MD” moniker we used in our interview of Dave Cass to mask the identity of the questioner. We hope you enjoy the conversation as much as we did.

This paper builds a stylized simple sticky-price New Keynesian model where agents' beliefs are not homogeneous. We assume that agents choose optimal plans while considering forecasts of macroeconomic conditions over an infinite horizon. A fraction of them (boundedly rational agents) use heuristics to forecast macroeconomic variables over an infinite horizon. In our framework, we study optimal policies consistent with a second-order approximation of the policy objective from the consumers' utility function, assuming that the steady state is not distorted.

We provide aggregate macroeconomic evidence on how, in the long run, a diverse degree of complexity in production may affect not only the rate of economic growth, but also the correlation between the latter, population growth and the monopolistic (intermediate) markups. For a sample of Organisation for Economic Co-operation and Development (OECD) countries, we find that the impact of population change on economic growth is slightly positive. According to our theoretical model, this implies that the losses due to more complexity in production are lower than the corresponding specialization gains. Using a finite mixture model, we also classify the countries in the sample and verify for each cluster the impact that the population growth rate and the intermediate sector’s markups exert on the 5-year average real gross domestic product (GDP) growth rate.

In this paper, we build on Ryan and Wales (1998) and Moschini (1999) and impose curvature conditions locally on the generalized Leontief model, introduced by Diewert (1974). In doing so, we exploit the Hessian matrix of second order derivatives of the reciprocal indirect utility function, unlike Ryan and Wales (1998) and Moschini (1999), who exploit the Slutsky matrix.

This paper quantifies the welfare gains from Social Security when individuals face uninsurable longevity risk. While past researchers have studied this basic question, we do so from a unique perspective. In contrast to traditional macroeconomic models that abstract from specific linkages between parents and children, in our model, children are born to specific parents whose longevity is uncertain. And because parental asset holdings evolve over the life of the parent, children face uninsurable bequest income risk in addition to their own longevity risk. We find that Social Security improves ex ante expected utility by 3.4% of lifetime consumption (for the second generation). Because our baseline analysis assumes full information and optimal hedging of longevity risk, we treat these welfare gains as a conservative estimate, and we show that the gains are significantly larger when individuals fail to hedge their longevity risk.

A recent finding of the SVAR literature is that the response of hours worked to a (positive) technology shock depends on the assumed order of integration of the hours. In this work we relax this assumption, allowing fractional integration in hours and productivity. We find that the sign and magnitude of the estimated responses depend crucially on the identification assumptions employed. Although the responses of hours recovered with short-run (SR) restrictions are positive in all data sets, long-run (LR) identification results in negative, although sometimes not significant responses. We check the validity of these assumptions with the Sims procedure, concluding that both LR and SR are appropriate to recover responses in a fractionally integrated VAR. However, the application of the LR scheme always results in an increase in sampling uncertainty. Results also show that even the negative responses found in the data could still be compatible with real business cycle models.

This paper examines the government spending multiplier when economic agents combine adaptive learning and knowledge about future fiscal policy to form their expectations. The analysis shows that the effects of a government spending shock substantially change when the rational expectations hypothesis is replaced by this learning mechanism. In contrast to the dynamics under rational expectations, a government spending shock in a small-scale new Keynesian DSGE model with learning crowds in private consumption and is associated with a positive comovement between real wages and hours worked. In the baseline calibration, the output multiplier under learning is above one and about twice as large as under rational expectations.

This paper studies a growth model with public and private education alternatives. The impact of education vouchers on economic growth and the evolution of income inequality are considered. Results indicate that introducing education vouchers can increase economic growth. Households switching from public to private education experience higher incomes. This raises the tax base, in turn raising public education expenditures and growth of the whole economy. Vouchers are found to generally increase income inequality. Welfare comparisons show that voucher schemes may in some cases gain majority support, depending on assumptions and parameters. The results add a new dimension on which vouchers can be evaluated in the continuing policy debate.

Using a panel of 54 countries between 1980 and 2013, we find empirical support for the view that changes in the fiscal policy stance (year-on-year change in the cyclically adjusted primary balance) have a significant positive correlation with inflation volatility. An increase in the volatility of discretionary fiscal policies by one standard deviation raises inflation volatility by about 6%. Moreover, results using alternative inflation volatility proxies confirm that an expansionary fiscal stance increases price volatility. Another relevant outcome is that in a context of economic expansions (recessions) the harmful impact of fiscal activism on price volatility is soft (heightened), while the negative impact of fiscal activism on price stability is higher when fiscal policy is expansionary. Finally, fiscal activism fuels inflation volatility much more pronouncedly in emerging market economies vis-à-vis advanced economies.

To what extent did deviations from the Taylor rule between 2002 and 2006 help to promote price stability and maximum sustainable employment? To address that question, I estimate a New Keynesian model with unemployment and perform a counterfactual experiment where monetary policy strictly follows a Taylor rule over the period 2002:Q1–2006:Q4. I find that such a policy would have generated a sizeable increase in unemployment and resulted in an undesirably low rate of inflation. Around mid-2004, when the counterfactual deviates the most from the actual series, the model indicates that the probability of an unemployment rate greater than 8% would have been as high as 80%, whereas the probability of an inflation rate above 1% would have been close to zero.

The Great Moderation is characterized as a period of stable macroeconomic conditions, especially with regard to inflation. Under the sticky information theory, this environment may provide a few incentives for agents to update information on inflation, thus, producing a new slope of the sticky information Phillips curve. We estimate the degree of information rigidity implied by the sticky information Phillips curve. Using threshold models, we identify two regimes of high and low inflation, finding that each identified regime is associated with a specific degree of information stickiness. This evidence is consistent with agents that update information faster when inflation is higher.

We analyze the channels through which institutional quality can impact the corruption–growth nexus. To do this, we develop an endogenous growth model and test its implications empirically, through panel data models using GMM and PSTR settings. Our sample consists of 136 developed and developing countries analyzed over the period 1984–2015. We show, both theoretically and empirically, that (i) the corruption–growth relation can be subject to nonlinearities highly influenced by countries’ institutional development; and (ii) private investment and public spending are two main channels through which institutional quality affects, positively or negatively, the relation between corruption and economic growth.

Gold is a globally traded asset and held in large quantities by investors and central banks. Since there is no established model to assess whether the price of gold is overvalued or undervalued, we propose a relative valuation framework based on gold price ratios. This idea is not confined to gold but offers the foundation for relative valuation of a broad range of different assets or asset classes. We analyze gold prices relative to commodity prices, consumer prices, stock prices, dividend, and bond yields and find that the relative value of gold varies significantly over time. An analysis of the factors which drive these variations demonstrates that inflation expectations and uncertainty have a strong influence on gold ratios while macroeconomic fundamentals are less important. More specifically, a boost in confidence decreases the relative price of gold while heightened uncertainty increases the relative price of gold, which confirms the role of gold as a safe haven.

This paper investigates conditions under which a long-run recursive model can be used to identify a structure. Economists frequently employ this type of empirical model. I define the class of long-run partially recursive structures. If an economic system is a member of this class, then certain long-run recursive empirical models will obtain some of the structural impulse response functions. This sufficient condition for a structure is first shown in a vector autoregression. A well-known example from the literature is used to illustrate this particular class of structures and to present some useful applications of the result. Then the result is shown in models of cointegrated time series. Necessary conditions for a long-run recursive model to identify structure are addressed in the conclusion.

A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.

By considering a simple endogenous growth model, we propose a new theoretical channel through which the presence of asset bubbles can promote economic growth. In the model economy, long-lived value-maximizing firms continuously improve the quality of their specific products through in-house research and development (R&D), while simultaneously new firms enter into the market. The key feature is endogenous market structure: The number of firms is endogenously determined, which leads to variation in firm size measured in terms of the scale of production at the level of an individual firm. The presence of asset bubbles unambiguously gives rise to larger firms. This allows in-house R&D expenditure to be spread over the greater numbers of goods that the firms produce, which can increase incentives to undertake in-house R&D.

This paper explores the consequences of tax enforcement policies for monetary policy. Agents may evade taxes by working in the informal sector, but they are detected with positive probability. Workers are rewarded with government benefits that are proportional to formal (taxed) work. When enforcement is imperfect and collecting taxes is costly, the optimal inflation rate is positive and inflation becomes a second-best tax. Deviations from the Friedman rule are optimal and depend on the tax enforcement policies. Using U.S. data, we compute the quantitative effect of different tax structures on inflation and interest rate. We show that different tax enforcement and government spending (benefits) policies induce different optimal outcomes for inflation and interest rates.

This paper introduces structural VAR analysis as a tool for investigating the anchoring of inflation expectations. We show that US consumers' inflation expectations are anchored in the long run because macro-news shocks are long-run neutral for long-term inflation expectations. The identification of structural shocks helps to explain why inflation expectations deviate from the central bank's target. Our results indicate that the recent decline in long-term inflation expectations does not result from deanchoring macro-news but can be attributed to downward adjustments in consumers' expectations about the central bank's inflation target.