Zin Preferences Research Articles

Uncertainty shocks and monetary policy rules in a small open economy

Abstract Post the great financial crisis (GFC) of 2008–2009, there has been a surge in the macroeconomics literature on aggregate uncertainty. Although the recent literature has recognized the adverse real effects of global uncertainty shocks in emerging market economies (EMEs), the role of monetary policy in offsetting these adverse effects and their link with the exchange rates is not explored in the literature. We find that the currently followed interest rate rules (IRRs) under a flexible inflation-targeting regime are ineffective in stabilizing the domestic economy during periods of high global uncertainty in the EMEs. Using a small open economy new Keynesian DSGE model with Epstein–Zin preferences and second-moment demand shocks, we compare and propose alternate monetary policy rules that significantly reduce welfare losses. We find that the best monetary policy rule in terms of welfare depends on the nature of shock that is, first-moment or second-moment shock.

Discounting the Future: On Climate Change, Ambiguity Aversion and Epstein–Zin Preferences

We show that ambiguity aversion and deviations from standard expected time separable utility have a major impact on estimates of the willingness to pay to avoid future climate change risk. We propose a relatively standard integrated climate/economy model but add stochastic climate disasters. The model yields closed form solutions up to solving an integral, and therefore does not suffer from the curse of dimensionality of most numerical climate/economy models. We analyze the impact of substitution preferences, risk aversion (known probabilities), and ambiguity aversion (unknown probabilities) on the social cost of carbon. Introducing ambiguity aversion leads to two offsetting effects on the social cost of carbon: a positive direct effect and a negative effect through discounting. Our numerical results show that for reasonable calibrations, the direct effect dominates the discount rate impact, so ambiguity aversion gives substantially higher estimates of the social cost of carbon.

Dynamic spending and portfolio decisions with a soft social norm

We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to tolerate occasional dips below it. We do this by splicing two CRRA preference orderings, one with high curvature below the norm and the other with low curvature at or above it. We find this formulation appealing for many endowment funds and sovereign wealth funds, including the Norwegian Government Pension Fund Global, which inspired our research. We derive an analytical solution, which we use to describe key properties of the policy functions for consumption and portfolio allocation. We find that annual spending should not only be significantly lower than the expected financial return, but mostly also procyclical. In particular, financial losses should, as a rule, be followed by larger than proportional spending cuts, except when some smoothing is needed to keep spending from falling too far below the social norm. Yet, at very low wealth levels, spending should be kept particularly low in order to build sufficient wealth to raise consumption above the social norm. Financial risk taking should also be modest and procyclical, so that the investor sometimes may want to “buy at the top” and “sell at the bottom.” Many of these features are shared by habit-formation models and other models with some lower bound for consumption. However, our specification is more flexible and thus more easily adaptable to actual fund management. The nonlinearity of the policy functions may present challenges regarding delegation to professional managers. However, simpler rules of thumb with constant or slowly moving equity share and consumption-wealth ratio can reach almost the same expected discounted utility. Nevertheless, the constant levels will then look very different from the implications of expected CRRA utility or Epstein–Zin preferences in that consumption is much lower.

Credit risk pricing in a consumption‐based equilibrium framework with incomplete accounting information

AbstractWe present a consumption‐based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value. The imperfect information is generated by the underlying observed state variables and a noisy observation process of the firm value. In addition, the consumption, the volatility, and the firm value process are modeled to follow affine diffusion processes. Using the EZ equilibrium solution as the pricing kernel, we provide an equivalent pricing measure to compute the prices of financial derivatives as discounted values of the future payoffs given the incomplete information. The price of a zero‐coupon bond is represented in terms of the solutions of a stochastic partial differential equation (SPDE) and a deterministic PDE; the self‐contained proofs are provided for both this representation and the well‐posedness of the involved SPDE. Furthermore, this SPDE is numerically solved, which yields some insights into the relationship between the structure of the yield spreads and the model parameters.

Uncertainty Shocks, Innovation, and Productivity

Abstract In this paper, we argue that macroeconomic uncertainty shocks cause a persistent decline in economic activity, investment in R&D, and total factor productivity. After providing empirical evidence, we build a DSGE model with sticky prices and endogenous growth through investment in R&D. In this framework, uncertainty shocks lead to a short-term fall in demand because of precautionary savings and rising markups. The reduction in the utilised aggregate stock of R&D determines a fall in productivity, which causes a long-term reduction in the main macroeconomic aggregates. When households feature Epstein–Zin preferences, they become averse to these long-term risks affecting their consumption process (long-run risk channel), which severely exacerbates the precautionary savings motive and the overall adverse effects of uncertainty shocks.

Existence and uniqueness of recursive utilities without boundedness

This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of (stochastic) recursive utilities for several important classes of preferences. In order to accommodate models commonly used in practice, we allow both the state space and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single, primitive “thin tail” condition on the distribution of growth in per-period utilities. We present several applications to robust preferences, models of ambiguity aversion and learning about hidden states, and Epstein–Zin preferences.

Belief-driven growth slowdowns and zero-bounded risk-free rate

The literature presents mounting evidence that global long-run growth has been declining since the recession of 2008. Thus, to explore possible reasons for the growth slowdown and its risk-free rate and risk premium implications, this study constructs an endogenous growth model to examine the US economy before the 2008 recession and during the subsequent recovery period. The model features technological externalities that imply multiple perfect foresight balanced growth paths. In this setup, a change in agents’ beliefs may trigger persistent slumps, low interest rates, and elevated risk premium, consistent with the recent US experience. Numerically, using the Epstein and Zin preferences, the model calibration suggests that the historical data moments can be accommodated by persistent regimes and high intertemporal elasticity of substitution. Notably, the study’s simple-structured model with multiplicity and a regime-switching structure is a preliminary contribution to the field of economics, paving the way for future empirical studies.

Growth risks, asset prices, and welfare

I connect interest rates, risk premia and welfare costs of long-run consumption uncertainty in a setting with Epstein and Zin (1989) preferences. I find that long-run uncertainty can create significant welfare costs even when risk aversion is moderate and the short-run consumption volatility low. I document that the risk-free rate puzzle is a key determinant of the welfare costs.

NOTE: An Equilibrium Asset Pricing Model for Stocks and Bonds under Growth and Inflation Risks

This technical note details an equilibrium asset pricing model for stocks and bonds under economic growth and inflation uncertainties using the Epstein and Zin preferences. Specifically, the results show that both equity and bond risk premiums are priced by growth and inflation uncertainties. This note provides a theoretical justification on the common industry choice of considering growth and inflation as the underlying drivers for assets' returns.

Optimal Fiscal Policy with Epstein–Zin Preferences and Utility-Enhancing Government Services: Lessons from Bulgaria (1999–2016)

ABSTRACT This article compares and contrasts exogenous (observed) and optimal fiscal policy in an economy with Epstein–Zin (1989, 1991) preferences, with consumption tax, and with a common income tax, using a dynamic general-equilibrium model, calibrated for Bulgarian data (1999–2016). The focus is on the relative importance of consumption versus income taxation, as well as on the provision of utility-enhancing public services. The main findings are: (i) The optimal steady-state income tax rate is zero. (ii) The benevolent Ramsey planner sets optimally the utility-enhancing public services, which are now 25% higher. (iii) The optimal steady-state consumption tax is approximately 50% higher.

Stochastic volatility implies fourth-degree risk dominance: Applications to asset pricing

What is the contribution of stochastic volatility to the resolution of asset pricing puzzles? I demonstrate that increasing the risk surrounding the variance of future consumption does not change its unconditional variance, but it generates a fourth-degree risk deterioration in future consumption, yielding in particular an increase in its excess kurtosis. If shocks to the volatility of consumption growth are persistent, the term structure of annualized excess kurtosis is increasing. In a Lucas economy with a EU representative agent, this increases the aggregate risk premium if and only if the fourth derivative of the utility function u is negative, and it makes its term structure increasing. Persistent stochastic volatility also reduces the interest rate if and only if the fifth derivative of u is positive, and it makes its term structure decreasing. These conditions are satisfied under constant relative risk aversion, and these results are robust to Epstein–Zin preferences. We show that persistent stochastic volatility is supported by the evidence that the excess kurtosis of consumption growth is positive and has an increasing term structure, using quarterly growth data in the U.S. between 1947 and 2016.

The term premium in a small open economy: A micro-founded approach

We study the term premium on government bonds in a small open economy within a micro-founded DSGE model with Epstein–Zin preferences. A model with technological spillovers from the global economy to the small open economy succeeds in replicating the main macroeconomic and bond-pricing moments as well as international co-movement in accordance with the data. We identify two opposing effects of the openness of the economy on the nominal term premium, which in our model roughly offset each other, so that the term premia in the open and closed economies are similar, provided that both enjoy technological spillovers from abroad.

Uncertainty Shocks in a Model of Effective Demand: Comment

Basu and Bundick (2017) show a second moment intertemporal preference shock creates meaningful declines in output in a sticky price model with Epstein and Zin (1991) preferences. The result, however, rests on the way they model the shock. If a preference shock is included in Epstein-Zin preferences, the distributional weights on current and future utility must sum to 1, otherwise it creates an asymptote in the response to the shock with unit intertemporal elasticity of substitution. When we change the preferences so the weights sum to 1, the asymptote disappears as well as their main results—uncertainty shocks generate small increases in output and comovement with consumption and investment that is at odds with the data. We examine three changes to the model—recalibration, a risk-premium shock, and a disaster risk-type shock—to try and restore their results, but in all three cases the model is unable to match VAR evidence.

Solution methods for models with rare disasters

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with rare disasters along the lines of those proposed by Rietz (1988), Barro (2006), Gabaix (2012), and Gourio (2012). DSGE models with rare disasters require solution methods that can handle the large nonlinearities triggered by low‐probability, high‐impact events with accuracy and speed. We solve a standard New Keynesian model with Epstein–Zin preferences and time‐varying disaster risk with perturbation, Taylor projection, and Smolyak collocation. Our main finding is that Taylor projection delivers the best accuracy/speed tradeoff among the tested solutions. We also document that even third‐order perturbations may generate solutions that suffer from accuracy problems and that Smolyak collocation can be costly in terms of run time and memory requirements. Rare disasters DSGE models solution methods Taylor projection perturbation Smolyak C63 C68 E32 E37 E44 G12

Uncertainty-induced dynamic inefficiency and the optimal inflation rate

I construct an overlapping-generations model of money with Epstein and Zin (1989) preferences and study how aggregate output uncertainty affects the optimal rate of inflation for aggregate consumption. When money only serves as savings instruments, I find that the optimality of Friedman rule breaks up only if agents prefer late resolution of uncertainty. However, if an additional role of money as a medium of exchange is introduced, then the Friedman rule achieves generally suboptimal level of aggregate consumption regardless of agents’ preferences for the timing of uncertainty resolution. The aggregate output uncertainty, nevertheless, crucially determines the level of optimal inflation rate in this case. Lastly, the optimal degree of aggregate output uncertainty given a positive inflation rate turns out to be generally non-zero regardless of the role of money.

Uncertainty Shocks in a Model of Effective Demand: Comment

Basu and Bundick (2017) show a second moment intertemporal preference shock creates meaningful declines in output in a sticky price model with Epstein and Zin (1991) preferences. The result, however, rests on the way they model the shock. If a preference shock is included in Epstein-Zin preferences, the distributional weights on current and future utility must sum to 1, otherwise it creates an asymptote in the response to the shock with unit intertemporal elasticity of substitution. When we change the preferences so the weights sum to 1, the asymptote disappears as well as their main results—uncertainty shocks generate small increases in output and comovement with consumption and investment that is at odds with the data. We examine three changes to the model—recalibration, a risk-premium shock, and a disaster risk-type shock—to try and restore their results, but in all three cases the model is unable to match VAR evidence.

The price of variance risk

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.

Asset Pricing in Production Economies When Capital Inputs are Heterogeneous

This paper studies asset pricing implications of heterogeneity across capital inputs. We build a general equilibrium model including two types of capital. The agents in our economy have Epstein and Zin (1989) preferences and technology is exposed to long-run risks in productivity growth. Following the literature, production inputs differ with respect to rates of depreciation and adjustment cost. We explain both, differences in returns and investment behaviour for two types of capital. Model implied asset pricing and relevant macroeconomic moments are in line with empirical data. To fully capture the effect of small but persistent shocks to the expected growth rate of productivity in a DSGE framework, the model is solved with a global non-linear solution algorithm. It is shown, when including long-run risks in productivity growth in conjunction with capital heterogeneity, using local Taylor-expansion based methods will not suffice, to obtain a satisfactory accuracy of approximation.

Asset Prices, Local Prospects and the Geography of Housing Dynamics

I uncover a novel link between economic fundamentals and real estate returns. First, using a measure of (i.e. MSA) growth prospects from both industry level employment and financial data, I am able to explain a substantial portion of variability in excess real estate returns and price-to-rent ratios. A one standard deviation decline in local growth prospects is associated with a 120bp drop in the housing risk premia and a 500bp increase in the price to rent ratio. Second, I establish the underlying dynamics of relative, housing versus non-housing, consumption in the MSA-level cross section of economic agents. I document that a one standard deviation decline in local growth prospects is associated with a 1000bp rise in level and 700bp decrease in variance of relative consumption. In contrast, a one standard deviation increase in local growth prospects is also associated with a rise in relative consumption. This suggests that housing acts as a hedge against long-run economic growth. I then investigate these empirical facts through the lens of a consumption based, asset pricing model. I combine a persistent component in consumption, Epstein and Zin (1989) preferences, and nonseparable consumption of non-housing goods and housing services. Consumption of housing services provides a hedge to long-run growth prospects. The model is able to replicate the excess returns and price to rent ratio regression results from the data.

Monetary policy uncertainty and investor expectations

How does monetary policy uncertainty affect the behavior of market participants? In a New-Keynesian DSGE model with Epstein–Zin preferences, an increase in interest rate uncertainty is found to increase precautionary savings for households, and depress output, inflation and the short- and long-term asset yields. These effects are similar to a negative demand shock. The monetary policy uncertainty shock is calibrated using ex-ante uncertainty of investors about the future changes in Treasury yields, extracted from Options and Futures data. Incorporating the monetary policy uncertainty shock is also found to lower the term premium generated by the model, relative to the case without stochastic volatility in the interest rate rule.