Are Microstates Necessarily Led by Their Bigger Neighbors’ Business Cycle? The Case of Liechtenstein and Switzerland

Abstract

This paper investigates Liechtenstein’s business cycle compared to its neighboring countries (Switzerland, Austria) and other countries with strong economic relations with Liechtenstein (Germany, Italy, France, USA). In contrast to the widespread notion of small countries “importing” the business cycle from bigger nations, it is shown that the real GDP of the microstate Liechtenstein is a leading indicator for the economy of its bigger neighbor Switzerland, regarding the growth rates as well as the output gap. This finding is based on cross correlation analyses and single- and multi-equation Granger causality tests, applying annual data from 1972 until 2014 or 2015. The significant GDP lead of one year is robust across all the various time frames and model specifications and seems to be driven by the goods exports. Also, Liechtenstein seems to react earlier to US business cycle fluctuations. This finding is not only interesting in the context of Liechtenstein and Switzerland but also encourages further research as it indicates the possibility that very small states are not only more exposed to foreign shocks, react more sensitively to international economic fluctuations, and are more volatile than their big “patron” nations—all stylized facts from small state economics literature—, but that their business cycles could be affected earlier.

Appendices

Appendix 1: Graphs and Tables

See Tables 6, 7 and 8 and Fig. 5.

Table 6 VAR(1) models with various country samples and deterministic regressors (emphasis on Switzerland as dependent variable, real GDP in dlogs)

Table 7 VAR(1) models with output gap

Table 8 Data sources

Fig. 5

The rolling regression model is an ARDL model of the following form, using 25-year windows from 2015 back to 1974 (the time dummies are skipped, as they do not fall into all of the time windows): $\Delta\log {[GDP{S_t}]} = \mu + \alpha \cdot\Delta\log {[GDP{S_{t-1}}]} + \beta \cdot \Delta\log {[GDP{S_{t-1}}]} + \gamma \cdot \Delta\log {[GDP{S_{t-1}}]} + \delta \cdot \Delta\log {[GDP{S_{t-1}}]}+{{\epsilon}_t}$. GDPS _t : Real GDP of Switzerland; GDPL _t : Real GDP of Liechtenstein; GDPA _t : Real GDP of Austria; GDPG _t : Real GDP of Germany. The rising p-values of Liechtenstein’s lagged variable (lead to Switzerland, 1975–1999 and 1974–1998) are explainable by the oil crisis’ impact. If the 1975 dummy is included, then the p-values are 0.0197 (1975–1999) and 0.0170 (1974–1998)

Liechtenstein’s one year lead, rolling regression (Coefficient and p value of $\Delta { \log }\left[ {\varvec{GDPL}_{{\varvec{t} - 1}} } \right])$.

Electronic supplementary Tables 9–15 and Figures 6–11 are shown in the web appendix that can be downloaded as PDF-file from http://andreas.brunhart.com/data.

Appendix 2: Additional Remarks

Liechtenstein’s GDP figures are internationally comparable as the national accounts follow the rules of the European System of Accounts (ESA). Yet, ESA 95 is still applied and the switch to ESA 2010 in December 2016 only affects GDP figures from 2013 on (no further backward estimates published). Thus, for all countries ESA 95 figures are used in this paper. The other countries’ GDP data was retrieved from the UN National Accounts Main Aggregate Data Base whose GDP figures rely on the OECD data base, which in turns compiles data from the national statistical offices. Note that some of the earlier GDP data originate from earlier ESA versions. For instance, Switzerland did not publish ESA 95 figures for the years before 1990. Instead, GDP growth from older ESA versions were used to account for the level shift effect caused by the introduction of ESA 95 and to provide a more consistent official GDP time series.

Liechtenstein’s nominal GDP figures from 1972 to 1997 are backward estimations published in the official Statistical Yearbook of Liechtenstein (see Amt für Statistik 2016a, p. 168). The figures originate from Brunhart (2012), where the methodology of the backward estimation procedure and its evaluation are outlined. The gross domestic product was compiled by using the generation of income account identity of Liechtenstein’s national accounting scheme: GDP = compensation of employees + taxes on production and imports + gross operating surplus − subsidies. The components could be well approximated by applying official figures, with the exception of the gross operating surplus which had to be estimated using a proxy. By compiling EBITDA figures of most of the biggest industrial and financial corporations in Liechtenstein a proxy for the retropolation of the gross operating surplus (operating profits) could be compiled.²³

The analytical results of Sects. 3 and 4 are independent of the fact that some of Liechtenstein’s GDP figures are backward estimates. The main arguments for the adequacy of the backwardly estimated GDP figures shall be summarized in the following: As mentioned, the applied backward estimation method is based on the structure of the official national account of Liechtenstein (generation of income account side). The cyclical pattern (timing and magnitude), the turning points and the growth trend are well confirmed by the historical national income series and other important economic time series of Liechtenstein. The comparison of the backward estimation method with the official figures for the years from 1998 until 2008 has revealed a convincingly good fit, with very high correlation coefficients (level 0.9974, growth rates 0.9608).²⁴ The methodology was also inspected by the national account department of the national Office of Statistics and the obtained GDP observations were integrated into the national Statistical Yearbook. Moreover and in relation to the lead of Liechtenstein to Switzerland, if Figs. 2 and 3 are inspected it becomes evident that also in the phase from 1998 on (after the official national accounts were introduced) several turning points were anticipated one year before Switzerland. A simple Granger test with the sample from 1998 till 2015 (therefore containing only official GDP data) also indicates a causal 1-year lead of Liechtenstein to Switzerland: The relevant coefficient has a positive sign and a p value of 0.0348 for real GDP growth rates or 0.0369 for the real GDP output gap (0.0220 and 0.0281 without degree of freedom adjustment). Hence, the lead is not just an artefact of the backward estimation method, which is additionally supported by the finding that also Liechtenstein’s quarterly goods exports and the industrial gross value added time series are Granger causally leading the Swiss counterpart.

Appendix 3: Model Variation and Robustness Checks

The regression models with variables in growth rates might involve the shortcoming that they neglect potential long-term relationships between the variables in levels (for example a connected long-run growth path). If such relationships exist then another way to cope with non-stationary data should be taken, namely the estimation of error correction models to capture both the short-run dynamics between the differences of the data and the long-term equilibria (cointegration) between the variables in levels. Cointegration tests of Johansen (1988 and 1992) including Switzerland, Liechtenstein, Austria and Germany have been carried out to check whether such equilibria exist. Additionally, single-equation tests following Engle and Granger (1987) and Phillips and Ouliaris (1990) including Switzerland and Liechtenstein have been conducted, additionally allowing for trend breaks in the cointegration relation. Yet, the generated test results do not indicate any cointegrating relationships. Thus, no error correction models are introduced.²⁵

As an alternative to the multi-equation setting, also single-equation Autoregressive Distributed Lag (ARDL) models are applied with special focus on Swiss GDP growth as dependent variable.²⁶ Doing so, the model fit compared to ordinary VAR settings can be improved, according to AIC_C of the equation with Swiss real GDP growth as dependent variable. Also, one additional observation can be applied in the ARDL-setting (as GDP data for Liechtenstein is only available until 2014, for all the other countries until 2015). Liechtenstein’s significant one year lead to Swiss real GDP growth also appears in the ARDL models and is robust across all settings, as shown in Electronic supplementary Table 11.

It turns out that the main conclusions of the leading property of Liechtenstein to Switzerland are insensitive to the selection and combination of the time dummies and also to the choice of lag lengths (see Tables 3, 4, 6, Electronic supplementary Tables 11 and 12). This also applies to the choice of intercept with or without linear time trend. The solid conclusion that Liechtenstein’s economy exhibits a highly significant Granger causal lead is also very robust across all the various time samples, as shown by recursive coefficient estimates and rolling regression windows (see Fig. 5 and Electronic supplementary Figure 8, Table 15 and their footnotes, and also the related discussion at the end of Sect. 4). Moreover, if heteroskedasticity robust standard error estimates by White (1980) or Newey and West (1987) are applied, then no notable changes occur: The p value of Liechtenstein’s lead remains low. Also the abandonment of the degree of freedom adjustment yields no changes in the results worth mentioning.

If output gaps instead of real GDP growth rates are applied, the highly significant lead of Liechtenstein versus Switzerland remains, regarding cross correlations and also all the applied VAR country samples (see Tables 7 and Electronic supplementary Table 10).²⁷

Unfortunately, more sophisticated models are not appropriate because of the small sample size. Otherwise, enhanced systems such as structural VAR or Seemingly Unrelated Regression (SUR) with imposed restrictions based on theoretical considerations could have been taken into account. However, it is questionable if a priori restrictions are advisable at all in the context of the analysis of the two countries in focus: Structural equation system modeling would probably have led to the decision to restrict the lead of Liechtenstein versus Switzerland to zero by the reasoning that Liechtenstein imports its business cycle. This justifies the non-theoretical application beyond the mere fact of the methodological constraints of the small sample size.