Central bank digital currency and the effectiveness of negative interest rate policy: A DSGE analysis

Implementing a negative interest rate policy (NIRP) in the traditional fiat system is less effective than desired because of the zero lower bound (ZLB) constraint on interest rates and the cash barrier. Would this problem be solved if a new form of currency was introduced, i.e., central bank digital currency (CBDC), in the economy? To answer this question, we construct a dynamic stochastic general equilibrium (DSGE) model to analyze the effectiveness of NIRP upon the introduction of CBDC. The results suggest that: (i) The CBDC can eliminate the ZLB constraint and stabilize the economic fluctuations caused by NIRP. (ii) The central bank can implement NIRP by directly adjusting the interest rate of digital currency to stimulate consumption, investment, and output and to accelerate macroeconomic recovery. (iii) Welfare analysis shows that the central bank can effectively choose different NIRP rules according to the economic objectives.     

Downward Nominal Wage Rigidity and Determinacy of Equilibrium

It is well known in the literature that there is a tension between the frequency and duration of the zero lower bound (ZLB) on the nominal interest rate and the determinacy of equilibrium. In this short paper, I show that the presence of downward nominal wage rigidity (DNWR) resolves the tension by preventing a vicious cycle of price declines and output contractions under the ZLB. Consequently, the model with DNWR can replicate the long-lived ZLB episodes observed in the data. It also implies a plausible size of output and inflation declines at the ZLB.     

COS method for option pricing under a regime-switching model with time-changed Lévy processes

We extend the regime-switching model to the rich class of time-changed Lévy processes and use the Fourier cosine expansion (COS) method to price several options under the resulting models. The extension of the COS method to price under the regime-switching model is not straightforward because it requires the evaluation of the characteristic function which is based on a matrix exponentiation which is not an easy task. For a two-state economy, we give an analytical expression for computing this matrix exponential, and for more than two states, we use the Carathéodory–Fejér approximation to find the option prices efficiently. In the new framework developed here, it is possible to allow switches not only in the model parameters as is commonly done in literature, but we can also completely switch among various popular financial models under different regimes without any additional computational cost. Calibration of the different regime-switching models with real market data shows that the best models are the regime-switching time-changed Lévy models. As expected by the error analysis, the COS method converges exponentially and thus outperforms all other numerical methods that have been proposed so far.     

Mortality Regimes and Pricing

Abstract

Mortality dynamics are characterized by changes in mortality regimes. This paper describes a Markov regime-switching model that incorporates mortality state switches into mortality dynamics. Using the 1901-2005 U.S. population mortality data, we illustrate that regime-switching models can perform better than well-known models in the literature. Furthermore, we extend the 1992 Lee-Carter model in such a way that the time-series common risk factor to all cohorts has distinct mortality regimes with different means and volatilities. Finally, we show how to price mortality securities with this model.     

Have We Underestimated the Likelihood and Severity of Zero Lower Bound Events?

Prior to the financial crisis, most economists probably did not view the zero lower bound (ZLB) as a major problem for central banks. Using a range of structural and statistical models, we find that previous research understated the ZLB threat by ignoring uncertainty about model parameters and latent variables, focusing too much on the Great Moderation experience, and relying on structural models whose dynamics cannot generate sustained ZLB episodes. Our analysis also suggests that the Federal Reserve's asset purchases, while materially improving macroeconomic conditions, did not prevent the ZLB constraint from having first‐order adverse effects on real activity and inflation.     

Multivariate Models of Equity Returns for Investment Guarantees Valuation

Abstract

In this paper we investigate the valuation of investment guarantees in a multivariate (discrete-time) framework. We present how to build multivariate models in general, and we survey the most important multivariate GARCH models. A direct multivariate application of regime-switching models is also discussed, as is the estimation of these models using maximum likelihood and their comparison in a multivariate setting. The computation of the CTE provision is further presented. We have estimated the models with a multivariate dataset (Canada, United States, United Kingdom, and Japan), and we compared the quality of their fit using multiple criteria and tests. We observe that multivariate GARCH models provide a better overall fit than regime-switching models. However, regime-switching models appropriately represent the fat tails of the returns distribution, which is where most GARCH models fail. This leads to significant differences in the value of the CTE provisions, and, in general, provisions computed with regime-switching models are higher. Thus, the results from this multivariate analysis are in line with what was obtained in the literature of univariate models.     

Monetary Policy Expectations at the Zero Lower Bound

We show that conventional dynamic term structure models (DTSMs) estimated on recent U.S. data severely violate the zero lower bound (ZLB) on nominal interest rates and deliver poor forecasts of future short rates. In contrast, shadow‐rate DTSMs account for the ZLB by construction, capture the resulting distributional asymmetry of future short rates, and achieve good forecast performance. These models provide more accurate estimates of the most likely path for future monetary policy—including the timing of policy liftoff from the ZLB and the pace of subsequent policy tightening. We also demonstrate the benefits of including macroeconomic factors in a shadow‐rate DTSM when yields are constrained near the ZLB.     

Dealing with financial instability under a DSGE modeling approach with banking intermediation: A predictability analysis versus TVP-VARs

In the dynamic stochastic general equilibrium (DSGE) literature there has been an increasing awareness on the role that the banking sector can play in macroeconomic activity. We present a DSGE model with financial intermediation as in Gertler and Karadi (2011). The estimation of shocks and of the structural parameters shows that time-variation should be crucial in any attempted empirical analysis. Since DSGE modelling usually fails to take into account inherent nonlinearities of the economy, we propose a novel time-varying parameter (TVP) state-space estimation method for VAR processes both for homoskedastic and heteroskedastic error structures. We conduct an exhaustive empirical exercise to compare the out-of-sample predictive performance of the estimated DSGE model with that of standard ARs, VARs, Bayesian VARs and TVP-VARs. We find that the TVP-VAR provides the best forecasting performance for the series of GDP and net worth of financial intermediaries for all steps-ahead, while the DSGE model outperforms the other specifications in forecasting inflation and the federal funds rate at shorter horizons.     

Analytic value function for optimal regime-switching pairs trading rules

We introduce a regime-switching Ornstein–Uhlenbeck (O–U) model to address an optimal investment problem. Our study gives a closed-form expression for a regime-switching pairs trading value function consisting of probability and expectation of the double boundary stopping time of the Markov-modulated O–U process. We derive analytic solutions for the homogenous and non-homogenous ODE systems with initial value conditions for probability and expectation of the double boundary stopping time, and translate the solutions with boundary value conditions into solutions with initial value conditions. Based on the smoothness and continuity of the value function, we can obtain the optimum of the value function with thresholds and guarantee the existence of optimal thresholds in a finite closed interval. Our numerical analysis illustrates the rationality of theoretical model and the shape of transition probability and expected stopping time, as well as discusses sensitivity analysis in both one-state and two-state regime-switching models. We find that the optimal expected return per unit time in the two-state regime-switching model is higher than that of one-state regime-switching model. Likewise, the regime-switching model’s optimal thresholds are closer and more symmetric to the long-term mean.     

How Sticky Is Sticky Enough? A Distributional and Impulse Response Analysis of New Keynesian DSGE Models

In this paper, we add to the literature on the assessment of how well data simulated from new-Keynesian dynamic stochastic general equilibrium (DSGE) models reproduce the dynamic features of historical data. In particular, we evaluate sticky price, sticky price with dynamic indexation, and sticky information models using impulse response and correlation measures and via implementation of a distribution based approach for comparing (possibly) misspecified DSGE models using simulated and historical inflation and output gap data. One of our main findings is that for a standard level of stickiness (i.e., annual price or information adjustment), the sticky price model with indexation dominates other models. We also find that when a lower level of information and price stickiness is used (i.e., bi-annual adjustment), there is much less to choose between the models (see Bils and Klenow 2004 , for evidence in favor of lower levels of stickiness). This finding is due to the fact that simulated and historical densities are "much" closer under bi-annual adjustment.     

我国DSGE模型的开发及在货币政策分析中的应用

DSGE模型是近年来宏观经济及货币政策分析方面关注的一个重要研究方向,也是中央银行在经济建模方面的一个新视角,该模型的显性建模框架、理论一致性、微观和宏观分析的完美结合、长短期分析的有机整合等独特性日益受到中央银行的青睐。本文结合我国的实际情况,建立了一个带有金融加速器的开放经济DSGE模型,基于我国的数据,采用Bayes技术估计了我国的DSGE模型,并利用该模型进行了政策分析。     

A Regime-Switching Model of Long-Term Stock Returns

Abstract

In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model.     

What Drives the Owner‐Occupied and Rental Housing Markets? Evidence from an Estimated DSGE Model

Most dynamic stochastic general equilibrium (DSGE) models with a housing market do not explicitly include a rental market and assume a tight mapping between house prices and rents over the business cycle. However, rents are much smoother than house prices in the data. We match this feature of the data by adding both an owner‐occupied housing market and a rental market in a standard DSGE model. The intertemporal preference shock accounts for more than half of the variation in house prices and contributes to residential investment fluctuations through the liquidity constraint, and nominal rigidity in rental contracts captures the variation in the price‐rent ratio.     

Asset pricing and the role of macroeconomic volatility

Standard Real Business Cycle (RBC) models are well known to generate counter-factual asset pricing implications. This study provides a simple extension to the prior literature by studying an economy that follows a regime-switching process in conjunction with Epstein–Zin preferences for consumers. We provide a detailed theoretical and numerical analysis of the model’s predictions. We also show that a reasonable parameterization of our model conveys financial figures in line with US postwar data. Furthermore, we provide evidence in support of modeling a regime-dependent macroeconomic risk.     

Fiscal Policy in a Currency Union at the Zero Lower Bound

This paper constructs a two‐country core–periphery New Keynesian model of a currency union to address the interaction between the objectives of regionally directed fiscal policy constrained by a single currency and the aggregate use of fiscal policy in face of the zero lower bound (ZLB) on policy interest rates. We identify an optimal path of aggregate and relative fiscal policy responses to a negative region‐specific demand shock. Our results show that (i) in a monetary union, the optimal policy response to an asymmetric reduction in demand concentrated in the periphery always entails a relative shift of fiscal expenditure toward the worse‐affected regions, (ii) though no aggregate fiscal response is required outside the ZLB, and (iii) optimal union‐wide fiscal policy is expansionary at the ZLB. Therefore, optimal policy always entails an expansion in the periphery at the ZLB, but the optimal fiscal response in the core regions can be either expansionary or contractionary depending on the parameters of the model. However, (iv) fiscal expansion in the core is warranted if the periphery cannot implement an expansion due to constraints on public spending.     

The Effect of Uncertainty on Optimal Control Models in the Neighbourhood of a Steady State

For both discrete and continuous time this paper derives the Taylor approximation to the effect of uncertainty (in the simple sense of risk, not Knightian uncertainty) on expected utility and optimal behaviour in stochastic control models when the uncertainty is small enough that one can focus on only the first term that involves uncertainty. There is a close and illuminating relationship between the discrete-time and continuous-time results. The analysis makes it possible to spell out a tight connection between the behaviour of a dynamic stochastic general equilibrium model and the corresponding perfect foresight model. However, the quantitative analytics of the stochastic model local to a certainty model calls for a more thorough investigation of the nearby certainty model than is typically undertaken.     

Equity market and the transmission channels of monetary policy: Before and after the zero lower bound

We examine the effectiveness of the interest rate channel and the credit channel of monetary policy before and after the zero lower bound (ZLB), using intraday stock returns. We construct a number of industry-specific and firm-specific indicators to capture the sensitivity of firms' demand to interest rates (interest rate channel) and firms' financial constraints (credit channel). We find that the transmission of monetary policy has shifted across both periods. Conventional monetary policy works through both the neoclassical interest rate channel and the credit channel, while unconventional policy is propagated primarily via the credit channel which became even more effective at the ZLB. Before the ZLB the transmission channels operate primarily through target rate shocks rather than forward guidance announcements, whereas both forward guidance and large scale asset purchases were equally important for the credit channel at the ZLB. We also find strong evidence that transmission channels are asymmetric depending on the state of the stock market (bull/bear, tighter/easier credit conditions, high/low volatility), and the type of policy surprises (positive/negative). Our findings are robust with respect to a number of model extensions and alternative specifications.     

REGIME-SWITCHING IN AUSTRALIAN SHORT-TERM INTEREST RATES

This paper applies a generalized regime-switching (GRS) model of the short-term interest rate to Australian data. The model allows the short rate to exhibit both mean reversion and conditional heteroscedasticity and nests the popular generalized autoregressive conditional heteroscedasticity (GARCH) and regime-switching specifications. It is shown that empirical estimates of many popular interest rate models provide curious results which imply that innovations to the short rate process are extremely persistent, and that the short rate is potentially non-stationary. The source of these curious results, which are also present in US and European interest rates, is identified in the context of the GRS model, which is shown, via specification and forecasting tests, to capture the features of Australian short-term interest rate data better than existing models. The stochastic process of short-term interest rates in Australia is compared with evidence from the US and Europe, highlighting a number of important differences.     

House Prices and Government Spending Shocks

We show that dynamic stochastic general equilibrium (DSGE) models with housing and collateralized borrowing predict a fall in house prices following positive government spending shocks. By contrast, we show that house prices in the United States rise persistently after identified positive government spending shocks. We clarify that the incorrect house price response is due to a general property of DSGE models—approximately constant shadow value of housing—and that modifying preferences and production structure cannot help in obtaining the correct house price response. Properly accounting for the empirical evidence on government spending shocks and house prices using a DSGE model therefore remains a significant challenge.