This chapter deals with features of data that suggest a certain model or method, but where this suggestion is erroneous. We highlight a few cases in which an econometrician could be directed in the wrong direction, and at the same time we show how this can be prevented from happening. These situations happen in cases where there is no strong prior information on how the model should be specified. The data are then used to guide model construction. This guidance can be in an inappropriate direction. We review a few empirical cases where some data features obscure a potentially proper view of the data and may suggest inappropriate models. We discuss spurious cycles and the impact of additive outliers on detecting ARCH and nonlinearity. We also focus on a time series that may exhibit recessions and expansions, allowing you to (wrongly) interpret the recession observations as outliers. Finally, we deal with structural breaks and trends and unit roots, and see how data with these features can look alike.

This last chapter summarizes most of the material in this book in a range of concluding statements. It provides a summary of the lessons learned. These lessons can be viewed as guidelines for research practice.

We first discuss a phenomenon called data mining. This can involve multiple tests on which variables or correlations are relevant. If used improperly, data mining may associate with scientific misconduct. Next, we discuss one way to arrive at a single final model, involving stepwise methods. We see that various stepwise methods lead to different final models. Next, we see that various configurations in test situations, here illustrated for testing for cointegration, lead to different outcomes. It may be possible to see which configurations make most sense and can be used for empirical analysis. However, we suggest that it is better to keep various models and somehow combine inferences. This is illustrated by an analysis of the losses in airline revenues in the United States owing to 9/11. We see that out of four different models, three estimate a similar loss, while the fourth model suggests only 10 percent of that figure. We argue that it is better to maintain various models, that is, models that stand various diagnostic tests, for inference and for forecasting, and to combine what can be learned from them.

In practice it may happen that a first-try econometric model is not appropriate because it violates one or more of the key assumptions that are needed to obtain valid results. In case there is something wrong with the variables, such as measurement error or strong collinearity, we may better modify the estimation method or change the model. In the present chapter we deal with endogeneity, which can, for example, be caused by measurement error, and which implies that one or more regressors are correlated with the unknown error term. This is of course not immediately visible because the errors are not known beforehand and are estimated jointly with the unknown parameters. Endogeneity can thus happen when a regressor is measured with error, and, as we see, when the data are aggregated at too low a frequency. Another issue is called multicollinearity, in which it is difficult to disentangle (the statistical significance of) the separate effects. This certainly holds for levels and squares of the same variable. Finally, we deal with the interpretation of model outcomes.

This chapter opens with some quotes and insights on megaprojects. We turn to the construction and the use of prediction intervals in a time series context. We see that depending on the choice of the number of unit roots (stochastic trends) or the sample size (when does the sample start?), we can compute a wide range of prediction intervals. Next, we see that those trends, and breaks in levels and breaks in trend, can yield a wide variety of forecasts. Again, we reiterate that maintaining a variety of models and outcomes is useful, and that an equal-weighted combination of results can be most appropriate. Indeed, any specific choice leads to a different outcome. Finally, we discuss for a simple first-order autoregression how you can see what the limits to predictability are. We see that these limits are closer than we may think at the onset.

This chapter uses a range of quotes and findings from the internet and the literature. The key premises of this chapter, which is illustrated with examples, are as follows. First, Big Data requires the use of algorithms. Second, algorithms can create misleading information. Third, algorithms can lead to destructive outcomes. But we should not forget that humans program algorithms. With Big Data come algorithms to run many and involved computations. We cannot oversee all these data ourselves, so we need the help of algorithms to make computations for us. We might label these algorithms as Artificial Intelligence, but this might suggest that they can do things on their own. They can run massive computations, but they need to be fed with data. And this feeding is usually done by us, by humans, and we also choose the algorithms to be used.

In practice we do not always have clear guidance from economic theory about specifying an econometric model. At one extreme, it may be said that we should “let the data speak.” It is good to know that when they “speak” that what they say makes sense. We must be aware of a particularly important phenomenon in empirical econometrics: the spurious relationship. If you encounter a spurious relationship but do not recognize it as such, you may inadequately consider such a relationship for hypothesis testing or for the creation of forecasts. A spurious relationship appears when the model is not well specified. In this chapter, we see from a case study that people can draw strong but inappropriate conclusions if the econometric model is not well specified. We see that if you a priori hypothesize a structural break at a particular moment in time, and based on that very assumption analyze the data, then it is easy to draw inaccurate conclusions. As with influential observations, the lesson here is that one should first create an econometric model, and, given that model, investigate whether there could have been a structural break.

This chapter deals with missing data and a few approaches to managing such. There are several reasons why data can be missing. For example, people can throw away older data, which can sometimes be sensible. It may also be the case that you want to analyze a phenomenon that occurs at an hourly level but only have data at the daily level; thus, the hourly data are missing. It may also be that a survey is simply too long, so people get tired and do not answer all questions. In this chapter we review various situations where data are missing and how we can recognize them. Sometimes we know how to manage the situation of missing data. Often there is no need to panic and modifications of models and/or estimation methods can be used. We encounter a case in which data can be made missing on purpose, by selective sampling, to subsequently facilitate empirical analysis. Such analysis explicitly takes account of the missingness, and the impact of missing data can become minor.

Currently we may have access to large databases, sometimes coined as Big Data, and for those large datasets simple econometric models will not do. When you have a million people in your database, such as insurance firms or telephone providers or charities, and you have collected information on these individuals for many years, you simply cannot summarize these data using a small-sized econometric model with just a few regressors. In this chapter we address diverse options for how to handle Big Data. We kick off with a discussion about what Big Data is and why it is special. Next, we discuss a few options such as selective sampling, aggregation, nonlinear models, and variable reduction. Methods such as ridge regression, lasso, elastic net, and artificial neural networks are also addressed; these latter concepts are nowadays described as so-called machine learning methods. We see that with these methods the number of choices rapidly increases, and that reproducibility can reduce. The analysis of Big Data therefore comes at a cost of more analysis and of more choices to make and to report.