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Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

The purpose of the present study was to evaluate the role of context in the identification of learning disabilities (LD) within the responsiveness-to-intervention (RTI) model. In Study 1, using a sample of students with and without LD (N=167) and data from a reading assessment, we tested whether the decision making regarding literacy disabilities is significantly different if we take into account variability within the schools and school characteristics. Initially a logistic multilevel model was fit to the data to assess prevalence rates of LD identification. The validity of these estimates was substantiated by bootstrapping the sample's parameters using 1,000 replications and by evidencing negligible bias parameters. Subsequently, the relationship between reading ability and LD identification was established by means of a multilevel model including random effects. The significant slopes linking reading to LD identification (i.e., fluency and overall reading ability ratings by teachers) were predicted by cross-level interactions involving schools' location (rural, urban, and suburban). The results of Study 1 demonstrated the moderating role of school context, as the slopes linking fluency and reading achievement to LD placement were moderated by the area in which a school was located. Study 2 was designed to present a relative discrepancy identification model by taking into account information from the school (i.e., district). Using 29 students from one district, whose writing ability was evaluated three times within the semester, comparisons were made between a specific low-ability student and the rest of his/her class. Through fitting a multilevel model in which within-student and between-student variance was assessed, Study 2 demonstrated that the specific pattern of responsiveness of a target student can be tested against the norm of his/her school district in order to have a more sensitive relative criterion of what constitutes both responsiveness and the norm. Thus, by utilizing a multilevel framework that involves school characteristics into our assessment we demonstrated that decision making is much more informative and likely more “accurate” under the RTI model. Certainly more research is needed to verify the usefulness and applicability of the proposed “relative slope-difference discrepancy model.”

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

This chapter presents a structural model à la Leland (1994) that is, at the same time, novel, simple, and able to explain the quotes of credit default swaps (CDS), equity, and equity options. The model gives a closed-form formula for the term structure of default probabilities and can be calibrated to fit the CDS spreads. It also offers closed-form formulas for equity, equity volatility, and equity options. Differently from other structural models, debt has been modeled as a perpetual fixed-rate bond, instead of a zero-coupon bond with finite maturity. Therefore, default can happen at any time, and not only at the bond's maturity. The model (which belongs to the class of first-passage models) specifies default as the first time the firm's asset value hits a lower barrier. The barrier is endogenously determined as a solution of an optimal stopping problem (stockholders’ equity maximization). Equity is seen as a portfolio that contains a perpetual American option to default and can be valuated by using the results of Rubinstein-Reiner (1991) for barrier options. Equity options are valued by a closed-form formula that requires only an extra parameter (leverage) with respect to the standard input list of Black–Scholes–Merton equation. The formula is consistent with the volatility skew that is generally observed in the equity options markets and can be used to estimate the firms’ implied leverage, as it is perceived by traders. The chapter concludes with an application of the model to the case of Goldman Sachs.

It is generally believed that Middle Eastern countries are homogenous. Although this belief holds some truth, Middle Eastern countries have more differences than similarities. They differ in language, race, psychology, perception of threats, historical and colonial backgrounds, and political and economic developments. Realizing these differences, I expect that these countries have varying perceptions and interpretations of external threats and different methods of dealing with those threats. It is theoretically implausible to contemplate a general trend in defense spending across Middle Eastern countries; however, it is theoretically sound to view several broad trends within the region.

In this chapter, I explain the key trends in defense spending and arms procurement in the Middle East and test whether those trends were subject to Louis F. Richardson's action-reaction model. I assessed the “guns-versus-butter” trade-off and the future prospects for peace in the region in light of these trends. I explained the danger of transferring weapons knowledge and technology to non-state actors in the Middle East. I investigate the trend in defense spending based on Richardson's action-reaction model by considering rival pairs in each subregion: Algeria–Morocco in North Africa; Egypt–Israel, Jordan–Israel, and Syria–Israel in the frontline states; United Arab Emirates–Iran in the Arab–Persian Gulf; and Pakistan–India in the Indian subcontinent. I used ordinary least squares (OLS) method in testing those dyads. I used military expenditure data from the SIPRI Yearbook: World Armament and Disarmament published annually by the Stockholm International Peace Research Institute. I conclude the study with policy implications and recommendations for achieving permanent peace in the region.

The authors propose novel tests for the detection of Markov switching deviations from forecast rationality. Existing forecast rationality tests either focus on constant deviations from forecast rationality over the full sample or are constructed to detect smooth deviations based on non-parametric techniques. In contrast, the proposed tests are parametric and have an advantage in detecting abrupt departures from unbiasedness and efficiency, which the authors demonstrate with Monte Carlo simulations. Using the proposed tests, the authors investigate whether Blue Chip Financial Forecasts (BCFF) for the Federal Funds Rate (FFR) are unbiased. The tests find evidence of a state-dependent bias: forecasters tend to systematically overpredict interest rates during periods of monetary easing, while the forecasts are unbiased otherwise. The authors show that a similar state-dependent bias is also present in market-based forecasts of interest rates, but not in the forecasts of real GDP growth and GDP deflator-based inflation. The results emphasize the special role played by monetary policy in shaping interest rate expectations above and beyond macroeconomic fundamentals.