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New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near-unit-root and weak-unit-root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

This paper proposes a new approach to testing in the generalized method of moments (GMM) framework. The new tests are constructed using heteroskedasticity autocorrelation (HAC) robust standard errors computed using nonparametric spectral density estimators without truncation. While such standard errors are not consistent, a new asymptotic theory shows that they lead to valid tests nonetheless. In an over-identified linear instrumental variables model, simulations suggest that the new tests and the associated limiting distribution theory provide a more accurate first order asymptotic null approximation than both standard nonparametric HAC robust tests and VAR based parametric HAC robust tests. Finite sample power of the new tests is shown to be comparable to standard tests.

The author develops and extends the asymptotic F- and t-test theory in linear regression models where the regressors could be deterministic trends, unit-root processes, near-unit-root processes, among others. The author considers both the exogenous case where the regressors and the regression error are independent and the endogenous case where they are correlated. In the former case, the author designs a new set of basis functions that are invariant to the parameter estimation uncertainty and uses them to construct a new series long-run variance estimator. The author shows that the F-test version of the Wald statistic and the t-statistic are asymptotically F and t distributed, respectively. In the latter case, the author shows that the asymptotic F and t theory is still possible, but one has to develop it in a pseudo-frequency domain. The F and t approximations are more accurate than the more commonly used chi-squared and normal approximations. The resulting F and t tests are also easy to implement – they can be implemented in exactly the same way as the F and t tests in a classical normal linear regression.

We analyze Lagrange Multiplier (LM) tests for a shift in trend of a univariate time series at an unknown date. We focus on the class of LM statistics based on nonparametric kernel estimates of the long run variance. Extending earlier work for models with nontrending data, we develop a fixed-b asymptotic theory for the statistics. The fixed-b theory suggests that, for a given statistic, kernel, and significance level, there usually exists a bandwidth such that the fixed-b asymptotic critical value is the same for both I(0) and I(1) errors. These “robust” bandwidths are calculated using simulation methods for a selection of well-known kernels. We find when the robust bandwidth is used, the supremum statistic configured with either the Bartlett or Daniell kernel gives LM tests with good power. When testing for a slope change, we obtain the surprising finding that less trimming of potential shift dates leads to higher power, which contrasts the usual relationship between trimming and power. Finite sample simulations indicate that the robust LM statistics have stable size with good power.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.

The phenomenon of positive autocorrelation in daily stock index returns is often viewed as a consequence of stable behavioural patterns of certain investor groups (see, e.g., Sentana & Wadhwani, 1992; Koutmos, 1997). However, such patterns may change due to extreme events, that is, financial crises, and thus affect the autocorrelation in returns. Emerging markets and especially BRIC countries have experienced severe crises in the last 20 years and are therefore a suitable object for studying this effect.

The focus of this chapter is on identifying substantial changes in the autocorrelation of BRIC markets' index returns after experiencing upheavals of the financial system. For this purpose, we look for structural breaks in the parameters of an ARMA–GARCH model with the standard endogenous search procedure.

Our approach yields no statistically significant evidence of the autocorrelation changes due to the crises. Only in India the decline in autocorrelation in 1998 seems to be economically relevant, but is not significant statistically. Significant shifts that we could identify were rather related to microstructural changes, such as abolishment of price change limits by China and the removal of a leading player in India's market in 1992. All in all our results suggest that even though extreme negative events on financial markets may induce changes in feedback trading strategies, their influence on autocorrelation is not pronounced enough. The impact of other factors, in the first place of regulatory changes, seems to be of larger relevance.

Structural models' inflation forecasts are often inferior to those of naïve devices. This chapter theoretically and empirically assesses this for UK annual and quarterly inflation, using the theoretical framework in Clements and Hendry (1998, 1999). Forecasts from equilibrium-correction mechanisms, built by automatic model selection, are compared to various robust devices. Forecast-error taxonomies for aggregated and time-disaggregated information reveal that the impacts of structural breaks are identical between these, helping to interpret the empirical findings. Forecast failures in structural models are driven by their deterministic terms, confirming location shifts as a pernicious cause thereof, and explaining the success of robust devices.

Using intraday prices for the S&P 500 and Nikkei Stock Average stock indexes and aggregate trading volume for the New York and Tokyo Stock Exchanges, we show how short-run comovements between national stock market returns vary over time in a way related to the trading volume and liquidity in those markets. We frame our analysis in the context of the heterogeneous-agent models of trading developed by Campbell, Grossman and Wang (1993) and Blume, Easley and O’Hara (1994) and Wang (1994) which predict that trading volume acts as a signal of the information content of a given price move. While we find that there exists significant short-run dependence in returns and volatility between Japan and the U.S., we offer new evidence that these return “spillovers” are sensitive to interactions with trading volume in those markets. The cross-market effects with volume are revealed in both close-to-open and open-to-close returns and often exhibit non-linear patterns that are not predicted by theory.