Introduction For some macroeconomic applications it might be interesting to see whether a set of obserable variables depends on common drivers. The estimation of such common factors can be done using so-called factor analytical models, which have the form
\[x_t = \lambda f_t + u_t,\]
where \(x_t\) is an \(M\)-dimensional vector of observable variables, \(f_t\) is an \(N \times 1\) vector of unobserved factors, \(\lambda\) is an \(M \times N\) matrix of factor loadings and \(u_t\) is an error term.
During the past years I realised that econometric analyis can be understood as a craft. You learn your basics at school from more or less motivated/talented professors and then you are sent out into wild, where you are confronted with real life challenges that differ from the stylised exmples you have become used to during your studies. This comes with a bunch new insights that I want to document on this page.
Vector autoregressive (VAR) models constitute a rather general approach to modelling multivariate time series. A critical drawback of those models in their standard form is their missing ability to describe contemporaneous relationships between the analysed variables. This becomes a central issue in the impulse response analysis for such models, where it is important to know the contemporaneous effects of a shock to the economy. Usually, researchers address this by using orthogonal impulse responses, where the correlation between the errors is obtained from the (lower) Cholesky decomposition of the error covariance matrix.
Concepts Basically stationarity means that a time series has a constant mean and constant variance over time. Althouth not particularly imporant for the estimation of parameters of econometric models these features are essential for the calculation of reliable test statistics and, hence, can have a significant impact on model selection.
To illustrate this concept, let’s look at quarterly data on disposable income in billion DM from 1960 to 1982, which is data set E1 from Luetkepohl (2007).
Impulse response analysis is an important step in econometric analyes, which employ vector autoregressive models. Their main purpose is to describe the evolution of a model’s variables in reaction to a shock in one or more variables. This feature allows to trace the transmission of a single shock within an otherwise noisy system of equations and, thus, makes them very useful tools in the assessment of economic policies. This post provides an introduction to the concept and interpretation of impulse response functions as they are commonly used in the VAR literature and provides code for their calculation in R.
The cleaning and transformation of data belong to the most time consuming parts of any economic analysis. Many graphical or statistical functions in R require specifically formated data to work properly. Although the standard functions of R can be used to prepare your data for further analysis, some people find them a bit labourious for daily applications. Therefore, alternatives have been developed, which make data transformation in R easier and also faster.
One of the prerequisits for the estimation of a vector autoregressive (VAR) model is that the analysed time series are stationary. However, economic theory suggests that there exist equilibrium relations between economic variables in their levels, which can render these variables stationary without taking differences. This is called cointegration. Since knowing the size of such relationships can improve the results of an analysis, it would be desireable to have an econometric model, which is able to capture them.
Bayesian methods have significantly gained in popularity during the last decades as computers have become more powerful and new software has been developed. Their flexibility and other advantageous features have made these methods also more popular in econometrics. This post gives a brief introduction to Bayesian VAR (BVAR) models and provides the code to set up and estimate a basic model with the bvartools package.
Introduction This post provides the code to set up and estimate a basic Bayesian vector error correction (BVEC) model with the bvartools package. The presented Gibbs sampler is based on the approach of Koop et al. (2010), who propose a prior on the cointegration space.
Data To illustrate the estimation process, the dataset E6 from Lütkepohl (2007) is used, which contains data on German long-term interest rates and inflation from 1972Q2 to 1998Q4.
Introduction A general drawback of vector autoregressive (VAR) models is that the number of estimated coefficients increases disproportionately with the number of lags. Therefore, fewer information per parameter is available for the estimation as the number of lags increases. In the Bayesian VAR literature one approach to mitigate this so-called curse of dimensionality is stochastic search variable selection (SSVS) as proposed by George et al. (2008). The basic idea of SSVS is to assign commonly used prior variances to parameters, which should be included in a model, and prior variances close to zero to irrelevant parameters.
As international trade has become increasingly fragmented over the past decades the analysis of global value chains (GVC) has gained popularity in economic research. This post reproduces Timmer et al. (2015), who introduce the world input-output database (WIOD) and present basic concepts of GVC analysis.
Data Timmer et al. (2015) use the 2013 vintage of the world input-output database (WIOD). The following code downloads the data from the project’s website, unzips it and loads the resulting STATA file into R using the readstata13 package.
Word or tag clouds seem to be quite popular at the moment. Although their analytical power might be limited, they do serve an aesthetic purpose and, for example, could be put on the cover page of a thesis or a presentation using the content of your work or the literature you went through. This post uses text data from the Gutenberg project to give a step-by-step introduction on how to create a wordcould in R.
Since the seminal paper of Sims (1980) vector autoregressive models have become a key instrument in macroeconomic research. This post presents the basic concept of VAR analysis and guides through the estimation procedure of a simple model. When I started my undergraduate program in economics I occasionally encountered the abbreviation VAR in some macro papers. I was fascinated by those waves in the boxes titled impulse responses and wondered how difficult it would be to do such reseach on my own.
A major challenge in data analysis is to summarise and present data with informative graphs. The ggplot2 package was specifically designed to help with this task. Since it is a very powerful and well documented package1, this introduction will only focus on its basic syntax, so that the user gets a better understanding of how to read the supporting material on the internet.
ggplot graphs are built with some kind of blocks, which usually start with the function ggplot.