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We give a short international history of econometric software development, with an emphasis on the origin of the main existing econometric packages. We provide a Dutch perspective on this development. We identify the characteristics of econometric software in comparison with mathematical and statistical software. Finally, a number of recent developments connected with the reuse of code across econometric softwares are discussed.

The notion of cointegration has led to a renewed interest in the identification and estimation of structural relations among economic time series. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over‐identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so‐called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.

To reconcile forecast failure with building congruent empirical models, we analyze the sources of mis‐prediction. This reveals that ex ante forecast failure is purely a function of forecast‐period events, not determinable from in‐sample information. The primary causes are unmodelled shifts in deterministic factors, rather than model mis‐specification, collinearity, or a lack of parsimony. We examine the effects of deterministic breaks on equilibrium‐correction mechanisms, and consider the role of causal variables. Throughout, Monte Carlo simulation and empirical models illustrate the analysis, and support a progressive research strategy based on learning from past failures.

AbstractUK top income shares have varied hugely over the past two centuries, ranging from more than 30% to less than 7% of pre‐tax national income allocated to the top 1 percentile. We build a congruent dynamic linear regression model of the top 1% income share allowing for economic, political and social factors. Saturation estimation is used to model outliers and trend breaks, proxying underlying structural changes driving income inequality in the UK. We use the model to forecast the top 1% income share over the last 15 years, and compare to a range of forecast devices. Despite a well‐specified constant parameter model conditioning on significant explanatory variables, the best performing forecasts are obtained from a random walk and a smoothed random walk. These results are explained by the presence of shifts in the income share over the forecast period, resulting in forecasts from equilibrium correction models converging to the wrong equilibrium. Our best prediction for 2026 based on the most recent data from 2021 (a 5‐year ahead projection) is that the pre‐tax top 1% income share will remain at the most recent realized value of 12.7%, but there is a large degree of uncertainty, with a 95% confidence band ranging from 10% to 15.7%.

AbstractObjectiveWe analyze the number of recorded cases and deaths of COVID‐19 in many parts of the world, with the aim to understand the complexities of the data, and produce regular forecasts.MethodsThe SARS‐CoV‐2 virus that causes COVID‐19 has affected societies in all corners of the globe but with vastly differing experiences across countries. Health‐care and economic systems vary significantly across countries, as do policy responses, including testing, intermittent lockdowns, quarantine, contact tracing, mask wearing, and social distancing. Despite these challenges, the reported data can be used in many ways to help inform policy. We describe how to decompose the reported time series of confirmed cases and deaths into a trend, seasonal, and irregular component using machine learning methods.ResultsThis decomposition enables statistical computation of measures of the mortality ratio and reproduction number for any country, and we conduct a counterfactual exercise assuming that the United States had a summer outcome in 2020 similar to that of the European Union. The decomposition is also used to produce forecasts of cases and deaths, and we undertake a forecast comparison which highlights the importance of seasonality in the data and the difficulties of forecasting too far into the future.ConclusionOur adaptive data‐based methods and purely statistical forecasts provide a useful complement to the output from epidemiological models.