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This paper investigates the stochastic properties of GDP series based on purchasing power comparisons for 125 countries from the Penn World Table (PWT) and a GDP series based on exchange rate conversions in 1987 constant dollars for 107 countries from the World Development Indicators (WDI) in the period 1965–90. Because many health and demographic variables are compiled at irregular intervals, models for economic growth are often estimated using data that are separated by 5-year intervals. Panel data on the GDP and growth rate series were analyzed using alternative econometric methodologies. First, the stochastic properties of the series were analyzed by applying classical tests for unit roots in a fixed effects framework. A new ratio was developed for the case where heterogeneous drift parameters are present under the null hypothesis. The 5% critical values of the most powerful invariant tests for unit roots are tabulated for different numbers of countries and time periods. Second, a dynamic random effects framework was used for testing the stochastic specification for the GDP and growth rate series. A sequence of Wald statistics was applied to test various structures for the variance covariance matrix of the GDP and growth rate series. Overall, the GDP series from PWT and WDI showed various forms of non-stationarity. Moreover, GDP growth rates at 5-year intervals possessed simple stochastic properties making them amenable to econometric modeling.

This chapter deals with seasonal time series in economics and it reviews models that can be used to forecast out-of-sample data. Some of the key properties of seasonal time series are reviewed, and various empirical examples are given for illustration. The potential limitations to seasonal adjustment are reviewed. The chapter further addresses a few basic models like the deterministic seasonality model and the airline model, and it shows what features of the data these models assume to have. Then, the chapter continues with more advanced models, like those concerning seasonal and periodic unit roots. Finally, there is a discussion of some recent advances, which mainly concern models which allow for links between seasonal variation and heteroskedasticity and non-linearity.

The effects of treatment and legal supervision on narcotics use and criminal activities were assessed by applying newly developed time-series methods that disentangle the long-term (permanent) and the short-term (temporary) effects of intervention. A multivariate systems approach was used to characterize the dynamic interplay of several related behaviors at a group level over a long period of time. Five variables — abstinence from narcotics use, daily narcotics use (or addiction), property crime, methadone maintenance treatment, and legal supervision — were derived by aggregating information from over 600 narcotic addiction histories averaging 12 years in length. Because of the long assessment period, age was also included as a control variable.

Overall, the system dynamics among the variables were characterized by long-term rather than short-term relationships. Neither methadone maintenance nor legal supervision had short-term effects on narcotics use or property crime. Methadone maintenance treatment demonstrated long-term benefits by reducing narcotics use and criminal activities. Legal supervision, on the other hand, did not reduce either narcotics use or property crime in the long run. Instead, there was a positive long-term relationship in which a higher level of legal supervision was related to higher levels of narcotics use and criminal activity. This latter finding is consistent with the observation that either narcotics use or criminal activity is likely to bring addicts to the attention of the legal system. However, these addicts, as a group, did not directly respond to legal supervision by changing their narcotics use or crime involvement except perhaps through coerced treatment. This chapter explores the policy implications of these findings.