Nonlinear DSGE Models Research Articles

The macroeconomic effect of COVID-induced economic policy uncertainty in Nigeria: a DSGE approach

PurposeThis study examined the macroeconomic effects of COVID-19-induced economic policy uncertainty (EPU) in Nigeria. The study considered the effects of three related shocks: EPU, COVID-19 and correlated economic policy uncertainty and COVID-19 shock.Design/methodology/approachFirst, the study presented VAR evidence that fiscal and monetary policy uncertainty depresses real output. Thereafter, a nonlinear DSGE model with second-moment fiscal and monetary policy shocks was solved using the third-order Taylor approximation method.FindingsThe authors found that EPU shock is negligible and expansionary. By contrast, COVID-19 shocks have strong contractionary effects on the economy. The combined shocks capturing the COVID-19-induced EPU shock were ultimately recessionary after an initial expansionary effect. The implication is that the COVID-19 pandemic-induced EPU adversely impacted macroeconomic outcomes in Nigeria in a non-trivial manner.Practical implicationsThe result shows the importance of policies to cushion the effect of uncertain fiscal and monetary policy path in the aftermath of COVID-19.Originality/valueThe originality of the paper lies in examining the impact of COVID-19 induced EPU in the context of a developing economy using the DSGE methodology.

Optimal policy design in nonlinear DSGE models: An n-order accurate approximation

We derive an n-order accurate approximation of optimal policy for a wide class of nonlinear DSGE models analytically. Using Taylor polynomials to approximate welfare and the equilibrium, the n,n+1 approximation relaxes symmetry in the objective and certainty equivalence in the solution, as implied by a Linear–Quadratic (LQ) approximation with n=1. When n>1, we illustrate how curvature in preferences and the constraints can affect optimal policy, deriving a solution that is n-order accurate as opposed to first-order accurate only. Comparing solutions when n=2 (a Quadratic–Cubic approximation) and n=1 (LQ), in a New Keynesian economy with nominal frictions, we find significant differences in the optimal response to shocks; the joint distributions of wage inflation, the output gap and nominal interest rates; welfare and accuracy.

Fiscal policy during a pandemic

I study the effects of the 2020 coronavirus outbreak in the United States and subsequent fiscal policy response in a nonlinear DSGE model. The pandemic is a shock to the utility of contact-intensive services that propagates to other sectors via general equilibrium, triggering a deep recession. I use a calibrated version of the model that matches the path of the US unemployment rate in 2020 to analyze different types of fiscal policies. I find that the pandemic shock changes the ranking of policy multipliers. Unemployment benefits are the most effective tool to stabilize income for borrowers, who are the hardest hit during a pandemic, while liquidity assistance programs are the most effective if the policy objective is to stabilize employment in the affected sector. I also study the effects of the $2.2 trillion CARES Act of 2020.

The Macroeconomic Effects of Commodity Price Uncertainty

This paper studies the macroeconomic effects of commodity price uncertainty (CPU) shocks. Using Australia as a case study, an econometric-based CPU index is proposed to reveal that Australia has experienced an unprecedented increase in uncertainty from the commodity market recently. Evidence from a VAR model shows that CPU shocks have a larger recessionary impact than other relevant uncertainty shocks such as financial, economic and trade policy uncertainty. The empirical results are then interpreted in a non-linear multisector DSGE model of the Australian economy by estimating key parameters in the DSGE model to match its responses to the VAR responses. CPU shocks in the DSGE model, via foreign commodity export demand with price rigidity, trigger a precautionary response and cause a decline in real economic activity.

A Quantitative Analysis of the Countercyclical Capital Buffer

What are the quantitative macroeconomic effects of the countercyclical capital buffer (CCyB)? I study this question in a nonlinear DSGE model with occasional financial crises, which is calibrated and combined with US data to estimate sequences of structural shocks. Raising capital buffers during leverage expansions can reduce the frequency of crises by more than half. A quantitative application to the 2007-08 financial crisis shows that the CCyB in the 2:5% range (as in the Federal Reserve's current framework) could have greatly mitigated the financial panic of 2008, for a cumulative gain of 29% in aggregate consumption. The threat of raising capital requirements is effective even if this tool is not used in equilibrium. JEL Classification: E4, E6, G2

Data Science in Stata 16: Frames, Lasso, and Python Integration

Stata is one of the most widely used software for data analysis, statistics, and model fitting by economists, public policy researchers, epidemiologists, among others. Stata's recent release of version 16 in June 2019 includes an up-to-date methodological library and a user-friendly version of various cutting edge techniques. In the newest release, Stata has implemented several changes and additions that include:<br />• Lasso<br />• Multiple data sets in memory<br />• Meta-analysis<br />• Choice models<br />• Python integration<br />• Bayes-multiple chains<br />• Panel-data ERMs<br />• Sample-size analysis for CIs<br />• Panel-data mixed logit<br />• Nonlinear DSGE models<br />• Numerical integration <br />This review covers the most salient innovations in Stata 16. It is the first release that brings along an implementation of machine-learning tools. The three innovations we considered are: (1) Multiple data sets in Memory, (2) Lasso for causal inference, and (3) Python integration.

Missing wage inflation? Estimating the natural rate of unemployment in a nonlinear DSGE model

During the recovery from the global financial crisis, most advanced economies have experienced a surprisingly weak response of wage inflation to the decline in unemployment. In this study, we investigate whether downward wage rigidity (DWR) is the source of the flattening wage Phillips curve and the lack of wage inflation in the four advanced economies: Japan, the euro area, the UK and the US. We estimate a nonlinear New Keynesian model with asymmetric wage adjustment costs and the natural rate of unemployment. Wage adjustment costs are found to be highly asymmetric in Japan, the euro area and the UK, but not in the US. The L-shaped wage Phillips curves between wage inflation and the unemployment gap clearly emerge in these three economies. Our policy simulations present a possibility that the missing wage inflation is not a permanent phenomenon and wage inflation is likely to reappear with further improvement in the labor market. Our analysis shows the usefulness of incorporating DWR into models for understanding the background of missing wage inflation and obtaining monetary policy implications.

Financial Frictions and the Wealth Distribution

We postulate a nonlinear DSGE model with a financial sector and heterogeneous households. In our model, the interaction between the supply of bonds by the financial sector and the precautionary demand for bonds by households produces significant endogenous aggregate risk. This risk induces an endogenous regime-switching process for output, the risk-free rate, excess returns, debt, and leverage. The regime-switching generates i) multimodal distributions of the variables above; ii) time-varying levels of volatility and skewness for the same variables; and iii) supercycles of borrowing and deleveraging. All of these are important properties of the data. In comparison, the representative household version of the model cannot generate any of these features. Methodologically, we discuss how nonlinear DSGE models with heterogeneous agents can be efficiently computed using machine learning and how they can be estimated with a likelihood function, using inference with diffusions.

Posterior Inference on Parameters in a Nonlinear DSGE Model via Gaussian-Based Filters

This paper studies Gaussian-based filters within the pseudo-marginal Metropolis Hastings (PM-MH) algorithm for posterior inference on parameters in nonlinear DSGE models. We implement two Gaussian-based filters to evaluate the likelihood of a DSGE model solved to second and third order and embed them into the PM-MH: Central Difference Kalman filter (CDKF) and Gaussian mixture filter (GMF). The GMF is adaptively refined by splitting a mixture component into new mixture components based on Binomial Gaussian mixture. The overall results indicate that the estimation accuracy of the CDKF and the GMF is comparable to that of the particle filter (PF), except that the CDKF generates biased estimates in the extremely nonlinear case. The proposed GMF generates the most accurate estimates among them. We argue that the GMF with PM-MH can converge to the true and invariant distribution when the likelihood constructed by infinite Gaussian mixtures weakly converges to the true likelihood. In addition, we show that the Gaussian-based filters are more efficient than the PF in terms of effective computing time. Finally, we apply the method to real data.

Monetary Policy Uncertainty, Credit Risk and China's Macroeconomic Fluctuations

This paper examines the effects of monetary policy uncertainty (MPU) on China's banks' credit risks and China's macroeconomic fluctuations. By incorporating the stochastic volatility into the quantity-based monetary policy rule, we provide a specific measure for China's MPU through Bayesian MCMC method. The bank-level evidences show that an increase of China's MPU could bring about the rise of non-performing loan ratio and thus exacerbate banks' credit risks. The historical decompositions from the Bayesian SVAR model reveal that the dramatic increase of China's MPU after 2008 financial crisis brought about -0.75% output growth rate loss in 2009 Q1. And our nonlinear VAR model shows that the negative impacts of MPU on economic activities are much stronger and more persistent when the economy enters the high credit risk regime.Simulations from the nonlinear DSGE model featuring credit risk and uncertainty shock confirm that banks' credit risks might be potential transmission channel through which China's monetary policy uncertainty shock affect its real economy.

A Framework for Solving Non-Linear DSGE Models

We propose a framework to solve non-linear DSGE models combining approximation and estimation techniques. Instead of relying on a fixed grid, we use Monte Carlo methods to draw samples from the state space, which are used to estimate an approximation for the value or policy functions of interest. By using estimators from high-dimensional statistics we can attenuate the curse of dimensionality while maintaining flexibility, theoretical guarantees for convergence and upper bound for the errors. In particular, we propose two different methods: a regularized projection and a support vector machine algorithm. To illustrate these solution procedures, we apply the first algorithm to solve a standard growth model, which has a known linear solution, and show that it achieves good accuracy, correctly shrinking the coefficients of a polynomial basis. Moreover, we use the support vector machine algorithm to solve a New Keynesian model with a Zero Lower Bound (ZLB) and compare our results with the ones from the Smolyak Method, which is widely used in the literature. We show that the latter overestimate the impact of the ZLB in the economy, achieving a lower accuracy than the one from our solution.

Keynesian Models, Detrending, and the Method of Moments

One important question in the DSGE literature is whether we should detrend data when estimating the parameters of a DSGE model using the moment method. It has been common in the literature to detrend data in the same way the model is detrended. Doing so works relatively well with linear models, in part because in such cases the information that disappears from the data is usually related to the parameters that also disappear from the detrended model. Unfortunately, in heavy non-linear DSGE models, parameters rarely disappear from detrended models, but information does disappear from the detrended data. Using a simple real business cycle model, we show that both the moment method estimators of parameters and the estimated responses of endogenous variables to a technological shock can be seriously inaccurate when detrended data are used in the estimation process. Using a dynamic stochastic general equilibrium model and U.S. data, we show that detrending the data before estimating the parameters may result in a seriously misleading response of endogenous variables to monetary shocks. We suggest building the moment conditions using raw data, irrespective of the trend observed in the data.

Tractable likelihood-based estimation of non-linear DSGE models

This paper presents a simple and fast maximum likelihood estimation method for non-linear DSGE models that are solved using a second- (or higher-) order accurate approximation. The method requires that the number of observables equals the number of exogenous shocks. Exogenous innovations are extracted recursively by inverting the observation equation, which allows easy computation of the likelihood function.

Tractable Likelihood-Based Estimation of Non-Linear DSGE Models

This paper presents a simple and fast maximum likelihood estimation method for non-linear DSGE models that are solved using a second- (or higher-) order accurate approximation. The method requires that the number of observables equals the number of exogenous shocks. Exogenous innovations are extracted recursively by inverting the observation equation, which allows easy computation of the likelihood function.

The Empirical Implications of the Interest-Rate Lower Bound

Using Bayesian methods, we estimate a nonlinear DSGE model in which the interest-rate lower bound is occasionally binding. We quantify the size and nature of disturbances that pushed the US economy to the lower bound in late 2008 as well as the contribution of the lower bound constraint to the resulting economic slump. We find that the interest-rate lower bound was a significant constraint on monetary policy that exacerbated the recession and inhibited the recovery, as our mean estimates imply that the zero lower bound (ZLB) accounted for about 30 percent of the sharp contraction in US GDP that occurred in 2009 and an even larger fraction of the slow recovery that followed. (JEL C11, C32, E12, E23, E32, E43, E52, G01)

The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications

This paper studies the pruned state-space system for higher-order approximations to the solutions of DSGE models. For second- and third-order approximations, we derive the statistical properties of this system and provide closed-form expressions for first and second unconditional moments and impulse response functions. Thus, our analysis introduces GMM estimation for DSGE models approximated up to third-order and provides the foundation for indirect inference and SMM when simulation is required. We illustrate the usefulness of our approach by estimating a New Keynesian model with habits and Epstein-Zin preferences by GMM when using first and second unconditional moments of macroeconomic and financial data and by SMM when using additional third and fourth unconditional moments and non-Gaussian innovations.

The Natural Rate of Interest in a Nonlinear DSGE Model

This paper investigates how and to what extent nonlinearity, including the zero lower bound on the nominal interest rate, affects the estimates of the natural rate of interest in a dynamic stochastic general equilibrium model with sticky prices and wages. We find that the estimated natural rate of interest in a nonlinear model is substantially different from that in its linear counterpart because of a contractionary effect of the zero lower bound, and that other nonlinearities such as price and wage dispersion, from which a linear model abstracts, play a minor role in identifying the natural rate.

South Africa’s economic response to monetary policy uncertainty

PurposeThe purpose of this paper is to study the evolution of monetary policy uncertainty and its impact on the South African economy.Design/methodology/approachThe authors use a sign restricted SVAR with an endogenous feedback of stochastic volatility to evaluate the sign and size of uncertainty shocks. The authors use a nonlinear DSGE model to gain deeper insights about the transmission mechanism of monetary policy uncertainty.FindingsThe authors show that monetary policy volatility is high and constant. Both inflation and interest rates decline in response to uncertainty. Output rebounds quickly after a contemporaneous decrease. The DSGE model shows that the size of the uncertainty shock matters – high uncertainty can lead to a severe contraction in output, inflation and interest rates.Research limitations/implicationsThe authors model only a few variables in the SVAR – thus missing perhaps other possible channels of shock transmission.Practical implicationsThere is a lesson for monetary policy: monetary policy uncertainty, in isolation from general macroeconomic uncertainty, often creates unintended adverse consequences and can perpetuate a weak economic environment. The tasks of central bankers are incredibly difficult. Their models project output and inflation with relatively large uncertainty based on many shocks emanating from various sources. It matters how central bankers react to these expectations and how they communicate the underlying risks associated with setting interest rates.Originality/valueThis is the first study that looks into monetary policy uncertainty into South Africa using a stochastic volatility model and a nonlinear DSGE model. The results should be very useful for the Central Bank as it highlights how uncertainty, that they create, can have adverse economic consequences.

Asymmetric Macro-Financial Spillovers

The 2008 financial crisis has shown that financial busts can influence the real economy. However, there is less evidence to suggest that the same holds for financial booms. Using a Markov-Switching vector autoregressive model and euro area data, I show that financial booms tend to be less procyclical than financial busts. To identify the sources of asymmetry, I estimate a non-linear DSGE model with a heterogeneous banking sector and an occasionally binding borrowing constraint. The model matches the key features of the data and shows that the borrowers’ balance sheet channel accounts for the asymmetry in the macro-financial linkages. The muted macro-financial transmission during financial booms can be exploited for macroprudential policies. By comparing capital buffer rules with monetary policy ‘leaningagainst- the-wind’ rules, I find that countercyclical capital buffers improve welfare.

Interest-Rate Pegs, Central Bank Asset Purchases and the Reversal Puzzle

We analyze the macroeconomic implications of a transient interest-rate peg in combination with a QE program in a non-linear medium-scale DSGE model. In this context, we re-examine what has become known as the reversal puzzle (Carlstrom, Fuerst and Paustian, 2015) and provide an analytical explanation for its appearance. We show that the puzzle is intimately related with agents' expectations. If, for instance, agents do not anticipate the peg, the reversal does not appear. The same is true if agents' inflation expectations are influenced by a monetary authority which follows a price-level-targeting rule instead of a standard Taylor rule. In this case, sign reversals do not occur even for very long durations of pegged nominal interest rates.