Analysis of time varying relationships in multi-country monetary time series.

The main goal of empirical macroeconomics is to understand the relationships between macroeconomic variables, such as the gross domestic product (GDP), inflation and interest rates. This allows for better macroeconomic predictions and helps macroeconomic policy makers to set a sound fiscal and monetary policy. For example, understanding the effect of the short term interest rate on inflation is essential for a central bank, which is responsible for price stability. Also, good GDP predictions allow governments to anticipate the future evolution of the economic activity by taking stabilizing actions in advance.

Empirical macroeconomic analysis usually starts from a time series dataset in which the variables of interest are observed for subsequent time periods, typically quarterly. Such datasets thus consist of historical data, where the observations are realizations of how the economy has behaved in the past, and which makes it difficult to derive causal relationships between the variables. In contrast, note that in experimental data, used in for instance pharmaceutical studies, cause and effect can be clearly distinguished by exogenously manipulating a variable, for example the intake of a certain drug, and then observing the consequences on another variable, for example the patient’s health. Still, also information on the linkages between macroeconomic variables can be obtained. First, instead of true causality, macroeconomists often study the incremental predictive power between variables instead, which is called ‘Granger causality’. A variable is said to Granger cause another variable if it improves the prediction of the other variable. Second, macroeconomists often make additional ‘identification assumptions’ on the causality between the variables, which allows them to extract exogenous shocks. One popular identification assumption is the ‘recursive ordering scheme’, in which the ordering of the variables determines how rapidly the different variables can react to exogenous shocks in the other variables. For example, it is typically assumed that inflation and GDP are relatively sluggish variables, such that they do not immediately react to an interest rate shock.

In order to extract patterns from the macroeconomic dataset, statistical models are used. In this thesis, we mainly use the Vector Autoregression (VAR) model, which is the workhorse in empirical macroeconomics to study linear relationships between multiple time series. Unlike more structural economic models, VAR models are fully data-driven and require no ex-ante expert knowledge on the dependencies between the variables. In the VAR model, each variable depends on both the past values of the variables in the model and a shock. The vector autoregression coefficients thus represent the effects of past values of the variables on the current value of each variable. While the standard VAR model assumes that these coefficients stay the same over time, this thesis focuses on modeling changing macroeconomic relationships. First, Time Varying Parameter Vector Autoregression (TVP VAR) models allow the vector autoregression coefficients to evolve smoothly over time. For example, the effect of an interest rate shock on inflation is found to be different in the 1970s compared to the period afterwards. Second, frequency domain techniques describe the time series as a weighted sum of sinusoidal components with different frequencies, for instance slowly fluctuating and quickly fluctuation. Interestingly, the relationships between the variables can differ across these different frequency components. Third, for a panel dataset in which the variables are observed both for subsequent time periods and different countries, also the cross-country variation in the coefficients can be analyzed.

This thesis contains essays on the empirical relationship between macroeconomic time series, often in a multi-country setting. While the standard VAR model is used in Chapter 2, the time variation in the coefficients is studied in Chapters 3 and 5, the frequency domain analysis is performed in Chapter 1 and the cross-country variation is analyzed in Chapter 4.

The first chapter studies the predictive power of domestic stock prices for the future domestic economic activity in the frequency domain. We develop a multi-country test for Granger causality for each of the frequency components. Using 1991Q1-2010Q2 quarterly data for the G-7 countries, we report that the slowly fluctuating components of stock prices have large incremental predictive power for the future GDP, while this is not the case for the quickly fluctuating components.

The second chapter analyzes impulse response functions of vector autoregression models for variables that are linearly transformed. The impulse response function of a vector autoregression model is an often used tool in empirical macroeconomics to analyze the response of the variables in the model to different types of shocks. For many empirical applications, it is of interest to know how the impulse response functions would change if one or more variables in the VAR model are replaced by a linear transformation of the original variables. One example of such a transformation is the replacement of a nominal growth rate variable in a VAR model that also includes inflation by its corresponding real growth rate variable, which is the difference between the nominal growth rate variable and inflation. We show that the new impulse response is equal to the linear transformation of the original impulse response if and only if the new shock is equal to the linear transformation of the original shock. Sufficient conditions for this relationship between impulse responses are derived for the setting where the same type of shock is studied in the linearly transformed and original model. In particular, we consider shocks in one error term only, orthogonalized shocks and generalized shocks.

The third chapter compares Bayesian estimators with different prior choices for the amount of time variation in the coefficients of time varying parameter vector autoregression models using Monte Carlo simulations. In Bayesian statistics, the posterior estimate of the parameters in the model is a combination of, on the one hand, the prior assumption on the distribution of these parameters and, on the other hand, the information contained in the data. When the sample size is very large, the prior specification is not that important as it is swamped by the large amount of information in the data. However, for typical macroeconomic time series, the prior is very important. Since the commonly used prior only allows for a tiny amount of time variation, less restrictive priors are proposed. Additional empirical evidence on the time varying response of inflation to an interest rate shock is then provided for USA: while a major and statistically significant ‘price puzzle’ is detected for the period 1972-1979, the estimated response of inflation to an interest rate shock is negative for most other time periods.

The fourth chapter investigates empirically how the impact of a residential house price shock on household credit and GDP is influenced by the degree of the mortgage market flexibility. Countries with a flexible mortgage market, such as United States and United Kingdom, are characterized by a high loan to value ratio, low transaction costs of mortgage refinancing and easy access to second mortgages and home equity loans. Countries with an inflexible mortgage market, such as France and Italy, are characterized by the opposite. We hypothesize a stronger effect of house price shocks for the former countries because the financial accelerator mechanism for existing home owners is expected to be stronger and because the effect of higher house prices on the required amount of savings of future first time house buyers is expected to be smaller. A panel vector autoregression model is estimated separately for a group of eight countries with a flexible mortgage market and for a group of eight countries with an inflexible mortgage market. While both household credit and GDP increase after a positive house price shock for both groups of countries, we do not find empirical evidence that these responses are stronger for countries with a flexible mortgage market.

The fifth chapter investigates the determinants of sovereign credit ratings, which are ordinal measures of the creditworthiness of a sovereign government assigned by a rating agency. We quantify for the three major credit rating agencies how the importance of the different sovereign credit rating determinants changed after the start of the European debt crisis in 2009. For this end, we estimate a multi-year ordered probit model, using a sample of 90 countries for the years 2002-2015. Our model allows for time variation in the importance of the different determinants and it takes into account the ordinal nature of the credit rating. We provide empirical evidence that the credit rating agencies changed their sovereign credit rating assessment after the start of the European debt crisis in 2009. The financial balance, the economic development and the external debt became substantially more important after 2009 and the effect of Eurozone membership switched from positive to negative. In addition, GDP growth gained a lot of importance for highly indebted sovereigns and government debt became much more important for countries with a low GDP growth rate.

In the epilogue chapter, I give my personal view on the way statistical inference should be used in business and economic applications. In particular, I call for more focus on the evaluation of ‘economic importance’, i.e. the estimated magnitude of an effect together with its estimation error, and for less focus on the often less relevant and frequently misunderstood concept of ‘statistical significance’, which only informs on the existence of the effect.