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We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

This chapter presents several approaches for identifying and dating the speculative bubble on real estate market. Using the real estate price index (IPAI), statistical and structural approaches were combined in order to detect the existence of a bubble on the Moroccan real estate market. The results obtained affirm that the Moroccan real estate market experienced a speculative bubble during the period 2006–2008 explained mainly by the boom of credit during the same period. The use of the Markov switching model affirmed that the speculative bubble on Morocco is cyclic and consequently corroborates the critic formulated by Evans (1991) concerning the traditional approaches for the detection of financial bubbles. Thus, the analysis of the series of the bubble, extracted using the Kalman filter, affirms the existence of two regimes, namely an explosive regime and a normal regime. The first regime describes the periods of explosion of the bubble and lasts for about 9 quarters, while the second, lasting for 14 quarters, describes the periods of return to the average cycle.

This paper surveys the treatment of expectations in estimated Dynamic Stochastic General Equilibrium (DSGE) macroeconomic models.

A recent notable development in the empirical macroeconomics literature has been the rapid growth of papers that build structural models, which include a number of frictions and shocks, and which are confronted with the data using sophisticated full-information econometric approaches, often using Bayesian methods.

A widespread assumption in these estimated models, as in most of the macroeconomic literature in general, is that economic agents' expectations are formed according to the Rational Expectations Hypothesis (REH). Various alternative ways to model the formation of expectations have, however, emerged: some are simple refinements that maintain the REH, but change the information structure along different dimensions, while others imply more significant departures from rational expectations.

I review here the modeling of the expectation formation process and discuss related econometric issues in current structural macroeconomic models. The discussion includes benchmark models assuming rational expectations, extensions based on allowing for sunspots, news, sticky information, as well as models that abandon the REH to use learning, heuristics, or subjective expectations.

The chapter considers parameter identification, estimation, and model diagnostics in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2012). The analysis uses Smets and Wouters (2007) as an illustrative example, motivated by the fact that it has become a workhorse model in the DSGE literature. For identification, in addition to checking parameter identifiability, we derive the non-identification curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be fixed to achieve local identification. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find notably different parameter values and impulse response functions. A further comparison between the nonparametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. Overall, the results suggest that the frequency domain based approach, in part due to its ability to handle subsets of frequencies, constitutes a flexible framework for studying medium scale DSGE models.