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This chapter considers the turning of DSGE models into Bayesian versions by specifying a probability distribution for the innovations of the exogenous shock processes. There exists a wide variety of numerical techniques to solve DSGE models, but the chapter elaborates on a technique that involves the log-linearization of the equilibrium conditions and the solution of the resulting linear rational expectations difference equations. The approximate solution takes the form of a vector autoregressive process for the model variables, which is driven by the innovations to the exogenous shock processes, and is used as a set of state-transition equations in the state–space representation of the DSGE model. Under the assumption that these innovations are normally distributed, the log-linearized DSGE model takes the form of a linear Gaussian state–space model.

This chapter modifies the baseline DSGE model in three dimensions. First, it replaces the AR processes for technology growth and government spending by a VAR process, generalizing the law of motion of the exogenous shocks to make the DSGE model specification more flexible and improve its fit. Second, the chapter adds capital as a factor of production to the baseline New Keynesian DSGE model and includes nominal wage stickiness as well as other forms of rigidities. Finally, it considers a DSGE model that is designed to analyze fiscal as opposed to monetary policy. This model abstracts from nominal rigidities and instead focuses on fiscal policy rules that determine the level of government spending and taxation as a function of the state of the economy.

This chapter explains how the key difficulty that arises when the Bayesian estimation of DSGE models is extended from linear to nonlinear models is the evaluation of the likelihood function, and focuses on the use of particle filters to accomplish this task. The basic bootstrap particle filtering algorithm is remarkably straightforward, but may perform quite poorly in practice. Thus, much of the literature about particle filters focuses on refinements of the bootstrap filter that increases the efficiency of the algorithm. The accuracy of the particle filter can be improved by choosing other proposal distributions. While the tailoring (or adaption) of the proposal distributions tends to require additional computations, the number of particles can often be reduced drastically, which leads to an improvement in efficiency.

This chapter discusses how dynamic stochastic general equilibrium (DSGE) models are now widely used by academics to conduct empirical research macroeconomics, as well as by central banks to interpret the current state of the economy, to analyze the impact of changes in monetary or fiscal policy, and to generate predictions for key macroeconomic aggregates. With particular emphasis on the Bayesian estimation of DSGE models, the chapter shows how the DSGE model generates a likelihood function—a joint probability distribution for the endogenous model variables such as output, consumption, investment, and inflation that depends on the structural parameters of the model. These structural parameters characterize agents' preferences, production technologies, and the law of motion of the exogenous shocks.

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

This chapter presents computational techniques that can be used to estimate DSGE models that have been solved with nonlinear techniques, such as higher-order perturbation methods or projection methods. From the perspective of Bayesian estimation, the key difference between DSGE models that have been solved with a linearization technique and models that have been solved nonlinearly is that in the former case, the resulting state–space representation is linear, whereas in the latter case, it takes the general nonlinear form. The chapter also highlights some of the features that researchers have introduced into DSGE models to capture important nonlinearities in the data, wherein it uses the small-scale New Keynesian DSGE model as illustrative example.

This chapter analyzes Sequential Monte Carlo (SMC) algorithms and how they were initially developed to solve filtering problems that arise in nonlinear state–space models. The first paper that applied SMC techniques to posterior inference in DSGE models is Creal (2007). Herbst and Schorfheide (2014) developed the algorithm further, provided some convergence results for an adaptive version of the algorithm, and showed that a properly tailored SMC algorithm delivers more reliable posterior inference for largescale DSGE models with multimodal posteriors than the widely used RMWHV algorithm. An additional advantage of the SMC algorithms over MCMC algorithms, on the computational front, highlighted by Durham and Geweke (2014), is that SMC is much more amenable to parallelization.

Economic growth is significantly slower in fragile environments and twice as volatile as in other emerging economies. Backwardness also shows in exports, which have remained stagnant and non-diversified since the 1980s. We revisit the role of exchange regimes in fostering exports and economic growth and, thereby, in reducing political fragility. We use a DSGE model tailored to replicate key features of fragile economies: presence of frictions in market adjustment and learning, influence of external shocks, and the crucial role of governments in providing public investment and delivering social transfers to the population. Our DSGE model allows us to track the response of variables associated with fragility to shocks that are likely to be important in fragile economies. The simulations we perform below illustrate the types of general-equilibrium interactions that may complicate the analysis of the effects of shocks that typically affect fragile economies on endogenous variables that may influence fragility.

This chapter combines the SMC algorithm with the particle filter approximation of the likelihood function to develop an SMC2 algorithm. As with the PFMH algorithm, the goal is to obtain a posterior sampler for the DSGE model parameters for settings in which the likelihood function of the DSGE model cannot be evaluated with the Kalman filter. The starting point is the SMC Algorithm 8. The chapter adds data sequentially to the likelihood function rather than tempering the entire likelihood function. Moreover, the evaluation of the incremental and the full likelihood function in the correction and mutation steps of Algorithm 8 are replaced by the evaluation of the respective particle filter approximations.

The final Part IV attends Schumpeter’s legacy. To begin with, this chapter examines how his monetary ideas got left behind during his lifetime and the subsequent decades. First, it addresses the success of Keynes. While his Treatise on Money had pre-empted the field by advocating some very similar ideas, the General Theory was even more detrimental to Schumpeter, precisely because Keynes had abandoned many of the very elements they had previously held in common. Next the chapter turns to the Neo-Keynesian synthesis, which attracted many of Schumpeter’s disciples at Harvard such as Paul Samuelson or James Tobin. After a brief discussion of monetarism, the attention finally turns to the evolution of modern general equilibrium models, beginning with its origin in the Real Business Cycle analysis and moving on to the New Keynesian DSGE models.

Turkey is an interesting case study because it was one of the hardest hit countries by the crisis, with a year-over-year contraction of 15 percent during the first quarter of 2009. At the same time, anticipating this fallout from the crisis, the Central Bank of the Republic of Turkey (CBRT) cut policy rates by an astounding 1025 basis points over November 2008–November 2009. In this context, this chapter addresses the following question: If an inflation targeting framework underpinned by a flexible exchange rate regime was not adopted, how much deeper would the recession have been? Counterfactual experiments based on an estimated structural model provide quantitative evidence which suggests that the recession would have been substantially more severe. In other words, the combination of exchange rate flexibility and the interest rate cuts implemented by the CBRT substantially helped soften the impact of the crisis.

The author analyses inflation in the Central African Economic and Monetary Community. First, a semi-structural VAR is used to identify the sources of inflation empirically; the chapter finds that fiscal shocks and the commodity price shocks that generally drive them have been important sources of inflation volatility, with monetary policy passively accommodating. A DSGE model is then developed and calibrated to replicate the empirical findings and to study the implications of a more active monetary policy. This active policy would involve greater (sterilized) reserve accumulation, which under the plausible assumption of limited capital mobility can help contain equilibrium appreciation pressures and therefore inflation, but at the cost of crowding out the private sector. Attempting to use monetary policy to contain inflation under a fixed exchange rate has important drawbacks, which highlights the need to rely on fiscal policy for macro and price stability in these countries.

The authors develop a dynamic stochastic general equilibrium (DSGE) model with a banking sector to analyse the impact of the financial crisis in developing countries and the role of the monetary policy response, with an application to Zambia. The crisis is interpreted as a combination of three related shocks: a worsening in the terms of the trade, an increase in the country’s risk premium, and a decrease in the risk appetite of local banks. Model simulations broadly match the path of the economy during this period. The model-based analysis reveals that the initial policy response contributed to the domestic impact of the crisis by further tightening financial conditions. The authors derive policy implications for central banks, and for dynamic stochastic general equilibrium modelling of monetary policy, in low-income countries.

Part III of the book presents various applications of quantitative dynamic stochastic general equilibrium models to SSA countries. Unlike the previous chapters, which provided broad guidance, the emphasis here is on specific policy questions faced by the country under study and on quantitative guidance for central banks. Each chapter mixes theory and data, along with close attention to the broader economic context. In addition to summarizing the results in the rest of Part III, this overview chapter describes the collaboration between IMF staff and staff in central banks in the region that resulted in the material in Part III. It also explains the eclectic approach used in building and using these models, as well as the relationship between these models and those of Part II.

Part II of the book reflects on the authors’ efforts to use simple dynamic general equilibrium models to analyse monetary policy issues facing countries in sub-Saharan Africa. This overview explains the genesis of this research agenda, both in terms of the approach and the choice of topics. Experience in the operational aspects of the IMF’s work suggested that better policy analysis—including with respect to the response to supply shocks, exchange rate management, and the modernization of policy regimes—would benefit from greater use of these models, suitably adjusted to incorporate structural features of low-income countries. Compared to Part III, the analysis in Part II is on qualitative insights from more structural micro-founded models, which are meant to provide general guidance and ultimately undergird the more country-specific and operational applications.