Aggregate level examination

There are several methodological approaches that have been used in the literature for examining the international transmission and spillover effects of various shocks on output, prices, and other variables at the aggregate level of total economies. Multi-equation or system models are often a more intuitive framework for analyzing issues related to the topic and have gained popularity in recent years, but for several questions single-equation models also have their advantages.

In the essays included in this work, we utilize both types of models as discussed in this section. We have opted for a more data-oriented approach at the cost of structural considerations, and, thus, dynamic stochastic general equilibrium (DSGE) models are not used in this work. Although they have plenty of advantages, the downside is that DSGE models also require posing several ex ante restrictions, which are not always in line with the statistical properties of the data. Canova and Ciccarelli (2013) even argue that, due to the restrictions, much of the responses produced by these models are often largely determined by the assumptions of the model. Multi-country DSGE models are also quite tedious to build and calibrate, which is beyond the scope of the current essays. Such models have been developed, for example, by the IMF, and also used in the analysis of international shock transmission (Freedman et al. 2010).

A key challenge related to this type of analysis (as in many macroeconometric applications) is the curse of dimensionality. Here, the curse of dimensionality refers to the common feature in most macroeconomic panels in that the number of cross-sectional units N is large relative to the number of time periods T available for estimation. This problem is even accentuated in the case of emerging economies (including CIS countries and China), which are often characterized by the scarcity and poor quality of data, in many cases also featuring significant structural changes during the relatively short time periods for which data are available. Moreover, an essential point of interest in these kinds of studies is often the examination of complex and interdependent transmission channels of global, international, or country-specific shocks in other countries, taking into account the potential heterogeneity in the responses of the individual countries. This further strengthens

the curse of dimensionality and requires the empirical setup to allow for cross-sectional dependence and heterogeneous coefficients.

Due to these features that have to be taken into account, a choice also has to be made about the restrictions or data shrinkage process to be applied in the estimation.

There are several alternatives: explicit restrictions derived from economic theory, Bayesian approaches, other restrictions on the influence channels (e.g., spatial models), and factor models. Also at this point, we have chosen a more data-oriented approach using factor modeling and minimal restrictions based on the data, as discussed below.

1.2.1.1 Single-equation approach

In the first essay of this work, we use a single-equation approach for examining the pass-through of certain global shocks and exchange rate movements to consumer prices in several CIS countries. The single-equation approach allows us to take into account a wider set of explanatory variables more flexibly despite the relatively short time series available. In addition, in the single-equation setup, it is quite straightforward to also examine non-linearities and structural breaks, which allows us to account for asymmetrical effects more easily than in the multi-equation framework (Aron et al. 2014).

On the other hand, in the single-equation setup, challenges often arise especially with the endogeneity of variables. Furthermore, in single-equation panel models, endogeneity can arise due to both serial correlation and correlation between the explanatory variables. A widely used solution is to apply general method of moments (GMM) estimation methods. When examining the international propagation of shocks, however, cross-sectional dependence is often present in the data, as noted above. Moreover, in many cases it is plausible to allow for heterogeneity in the coefficients among units of the panel (typically countries), but these features may invalidate the use of GMM estimators.

For datasets with a large number of cross-sectional units N relative to the time dimension T and cross-sectional dependence, the most common solutions for estimation strategy are spatial or factor models (Sarafidis & Wansbeek 2012). Spatial models represent a parameter shrinkage process so that restrictions are posed on the nature of the cross-sectional dependence (e.g., neighboring units showing higher cross-sectional dependence than more distant units). However, in many macroeconomic applications, it might be difficult to formulate the restrictions, or the dependencies might be more general.

In our case, we indeed find it difficult to determine plausible spatial parameter restrictions. An alternative approach is to opt for data shrinkage instead by applying a factor model. Factor models are based on the idea that the comovements present in a large dataset may be driven by a small number of latent variables. There are also several possibilities for applying the factor approach, but we have chosen to use an augmented mean group estimator introduced by Eberhardt and Teal (2010). This estimator is suitable for dynamic, cross-sectional dependent panels with heterogeneous coefficients and allows for cointegration. In addition, common factors are not considered as just a nuisance to be accounted for but are treated as observed common factors and taken into account explicitly as separate explanatory variables. In order to address the possible endogeneity between variables, we provide a robustness check, applying the dynamic CCE (MG)-GMM estimator of Neal (2015) for the estimations, and receive largely similar results.

1.2.1.2 Multi-equation models

In the multi-equation framework, various vector auto regression (VAR) models are a popular approach for examining the transmission and spillover effects of international shocks. In VAR models, all variables are typically treated as endogenous and interdependent, although it is possible to also include exogenous variables. The dependent variable is regressed on its own lagged values as well as contemporaneous and lagged values of certain other variables, which alleviates the endogeneity problem. The VAR models provide a very general representation and allow the capturing of complex data relationships as they attempt to capture the relationships present in the data with a minimal set of ex ante restrictions (Canova & Ciccarelli 2013).

On the other hand, the high level of generality also causes drawbacks to the VAR models. They have been criticized for a lack of theoretical foundations and for problems with structural interpretation. But, as Canova and Ciccarelli (2013) argue, it is possible to generate VAR models from standard intertemporal optimization problems under constraints, and vast literature already exists on structural identification in the VAR framework (Canova & Ciccarelli 2013; Chudik & Pesaran 2016). The high level of generality also limits the number of variables that can be included in the model, which potentially causes an omitted variable bias.

The curse of dimensionality is an essential problem in VAR models, but there are several alternative approaches presented in the literature to address the issue.

Structural VARs can be used when focusing only on a small set of countries or

aggregated regions so that the degrees of freedom are preserved by reducing the number of regressors (Bayuomi & Swiston 2007). With large-scale VARs, a common factor approach is again an option for data shrinkage. Cross-country comovements of several variables are collapsed into common factors, and vectors of domestic variables are then augmented with these estimated factors to form small-scale models (Cimadomo & Benassy-Quere 2012). Another approach is the Bayesian VAR, which uses priors about the cross-country correlation patterns that are subsequently updated with the data (Banbura et al. 2010). Finally, global VAR models address the dimensionality problem by decomposing the large unconditional model into smaller conditional models that are linked through cross-sectional averages (Chudik &

Pesaran 2016).

In the second essay, we turn to the multi-equation approach and opt for the global VAR (GVAR) approach to examine the impact of various country-specific output shocks and oil price shocks on several CIS economies. Although requiring a priori assumptions on the interlinkages between countries, GVAR models offer an intuitively appealing framework in the context of international shock transmission.

GVAR models have gained popularity in various macroeconometric applications after the seminal contribution by Pesaran et al. in 2004 as they impose an intuitive structure on cross-country interlinkages, but no restrictions are imposed on the dynamics of the individual sub-models (Chudik & Pesaran 2016).

The GVAR model is composed of several small-scale country-specific models that are first estimated conditional on the rest of the world. The country-specific models include domestic variables and weakly exogenous foreign variables that are weighted cross-sectional averages as well as global variables. Following the previous literature, we utilize trade and financial shares as weights. Moreover, we use time-varying weights in order to take into account the significant changes in the international relations of the countries under examination and to evaluate if the transmission of shocks has changed correspondingly. As a global variable we have oil price, which is common in the literature, and we model it as a dominant unit variable, as in Chudik and Pesaran (2013), to allow for endogenous relationships between domestic and global variables within the VAR models. Then, the country-specific models are stacked and estimated simultaneously as one large global VAR model. The resulting GVAR model can be used for scenario analysis and forecasting in a similar way to the traditional simple VAR models, and we calculate generalized response functions to assess the effects of various output and oil price shocks.