Empirical evidence of an S-curve in Croatia

The impact of currency depreciation on the trade balance is still an empirically unanswered question within international and financial economics. This paper is pointed towards partial clarification of that question as the author analyses trade perspectives in Croatia through the concept of an S-curve. The S-curve is an extension of the J-curve, for the impact of exchange rate depreciation wears out after a while and there is no further improvement when all impacts are realised, meaning that at the top of the curve the slope is zero or negative. By focusing on the relationship between the terms of trade (exchange rate) and trade balance the author is trying to provide some new insights into trade dynamics over a business cycle in Croatia. The main result is that both unconditional and conditional relations (conditional to technology’s role identified in the vector error correction model) are consistent with the empirical S-curve pattern of cross-correlations between the trade balance and the terms of trade (exchange rate). Nonetheless, the inability of the S-curve to depict the strength and/or the speed of the adjustment process before and after the terms of trade/exchange rate depreciation explains its limitation within policy recommendations for Croatia. ARTICLE HISTORY Received 30 October 2018 Accepted 25 February 2019


Introduction
Trade balance, terms of trade and the exchange rate are important indicators of macroeconomic stability and development policy perspectives. Trade balance absorbs net foreign exchange receipts, while the terms of trade (and the exchange rate) determine the purchasing power of a country's export and evaluated net trade gains. The point of understanding the international finance and trade dynamics is closely related to comprehension of the terms of trade (exchange rate)-trade balance nexus, i.e., what features of an economy determine whether an increase in the relative import prices is or will be associated with improvement or deterioration in the balance of trade. 1 The role of trade is important for economic growth as the exchange rate behaviour and terms of trade play crucial roles in transmitting external shocks to the domestic economy. Despite theoretical developments on the relationship between these variables, its dynamics remain fuzzy.
The uncertainty of the range in which economic policy in Croatia can influence these economic variables suggests it is desirable to analyse, test and reproduce regularities such as the J-or S-curve in order to evaluate dominant forces behind trade balance movements. Though the macroeconomic performance has improved since the first shock of the world economic crisis, the economy is still confronted with serious challenges, including persistent trade and budget deficits, indebtedness, lack of international competitiveness and latent economic policies, which have led to further macroeconomic instability. The European Union (E.U.) accession has not had the desired results so that trade with exports lagging behind imports has resulted in consistent trade deficits, all of which has important implications for economic growth. The average share of export to gross domestic product (GDP) since 2000 is around 45%, which indicates that the Croatian economy is an open economy (Tomi c, 2016a). However, this export share was insufficient in respect to demand and preferences towards import products (average share of import to GDP was around 55%), thereby generating a constant trade deficit (average share of the trade deficit to GDP was around 10%). Thus, in order to ensure macroeconomic stability and growth, some scholars and decision-makers saw a managed float exchange rate system as being vital for an improvement in productivity and export competitiveness, fiscal discipline and proper management of reserves. The Croatian central bank critically monitors exchange rate movements to ensure swift policy action to counteract any inflationary pressures from the external sector. In particular, the central bank is paying much attention to the events that could result in a large depreciation of the Croatian kuna (HRK), something that would lead to debt chaos due to the heavily indebted economy. Considering a plausible relationship between the exchange rates and the trade balance in Croatia, appreciation and depreciation episodes did not have a favourable impact on the trade balance. Namely, if we consider the J-curve behaviour, we could expect an initial worsening and later improvement of the trade balance following a term of trade depreciation. However, Croatia has a long history of a persistently widening trade deficit and a near-continual improvement in both barter and income terms of trade. A very limited number of papers on the J-curve phenomenon in Croatia leaves an opportunity to test the existence of an S-shaped curve, which could contribute to the debate on the international price adjustment processes vis-a-vis the large trade imbalance and macroeconomic instability in Croatia.
As a tool to approach the current empirical debate, this paper uses an adapted macroeconomic analysis related to international price adjustments and trade dynamics in order to put new and updated insights into the relationship between balance of trade, the terms of trade, and exchange rate developments in Croatia, because understanding the sources behind the rise of the Croatian external deficit is crucial for understanding whether the large deficit is sustainable and what policy measures are needed to ensure an orderly adjustment process. Hence, the goal of the paper is to test the validity of the so-called S-curve pattern in the Croatian economy. In a manner, this paper is a continuation of the work by Tomi c (2016a) on the topic of an Scurve. Besides unconditional cross-correlation functions, I calculated cross-correlation functions conditional on the technology impact from the vector error correction model (VECM) assuming that technology is the only factor that affects the long-run level of labour productivity, similar to Enders and M€ uller (2009). Analysis is carried out using the quarterly time series data for the period 2000-2018. The results confirm the existence of the S-curve behaviour of the variables, leading us to some indicative conclusions regarding the trade dynamics in Croatia. The rest of the paper is organised as follows. Section 2 provides the theoretical background of the topic and surveys the empirical literature. Section 3 gives a full perspective to the analytical part by describing the methodology and data and explaining the results. Section 4 provides some policy implications, and, finally, Section 5 offers concluding remarks.

Theoretical background and literature review
2.1. S-curve phenomenon: a conceptual background The relationship between the terms of trade and trade balance has been discussed thoroughly in the literature of international finance, and it is extended to include the exchange rate in the analysis of Rhee (2014), which elevated discussions on the Marshall-Lerner condition, J-curve phenomenon and more recently an asymmetric cross-correlations function that may resemble an S-curve pattern. The Marshall-Lerner condition states that currency depreciation improves the trade balance as long as the sum of import and export demand elasticity is at least equal to unity. However, empirical evidence suggests that there have been cases in which trade balance continued to deteriorate even though this condition was satisfied. This fact led researchers to focus on the short-run effect of the currency depreciation and on the post-depreciation/devaluation time path of the trade balance, which established grounds for a J-curve phenomenon (Akkay, 2015). Namely, the theory states that a country's trade deficit will worsen initially after the depreciation of its currency because higher prices on foreign imports will be greater than the reduced volume of imports. The effects of such change in the price of exports compared with imports will eventually induce an expansion of exports and a cut in imports, which, in turn, should improve the balance of payments. This is known as the J-curve effect since a graph of a trade surplus will resemble a J if this happens. Empirical evidence of the Jcurve phenomenon in the short and long run has been mixed, especially if the analyses are divided into those utilising aggregate data and those utilising bilateral data (Kimbugwe, 2006). Though there is a vast body of empirical literature dealing with the topic, the findings are still quite negative, i.e., there is little statistical evidence of a J-curve pattern in general, at least when we are considering a symmetric relationship. Most of the studies that tried to test J-curve existence have relied upon a reduced form trade balance model and regression analysis with not much support. Yet in some countries and in specific periods, the J-curve phenomenon has been recognised (for an extensive review of the literature see Akbostanci, 2004, Sim akov a, 2014, or Bahmani-Oskooee & Kutan, 2009. Considering frequent contrariety between these two concepts, we can conclude that the effects of exchange rate depreciations on exports, imports, and hence on trade balance are neither guaranteed nor instant. In 1994, a paper by Backus, Kehoe, and Kydland caught the attention by showing that the terms of trade (or alternatively exchange rate) tend to be positively correlated to future movements of the trade balance, but also tend to be negatively correlated with past movements, thus resulting in an S-shaped curve which was in fact an extension of the J-curve phenomenon. An S-curve is related to the J-curve in the sense that the impact of exchange rate depreciation wears out after a while and there is no further improvement when all impacts are realised. Though conceptually intertwined, these two concepts are methodologically different. Note that the S-curve, which is a description of unconditional cross-correlations between the two variables, is not the same concept as the J-curve, which describes the conditional dynamic response of one variable following a shock to the other. Thus, it is possible to depict an S-curve in the data, even without a detectable J-curve (Baxter, 1995). Bahmani-Oskooee and Hegerty (2010) and Ghosh (2012) accentuate that existing studies on the S-curve can be classified, and in that way differently evaluated under three categories: (1) aggregate level (one country against the rest of the world); (2) disaggregate level (to reduce aggregation bias considers bilateral relation); and (3) industry-level analyses (to further reduce aggregation bias considers trade flow on the bilateral level but disaggregated by commodities). An aggregate-level approach presents the line of logic we shall follow in assessing empirical relevance of the S-curve concept.

What do empirics say?
A rich body of literature argues that trade flows respond to currency changes with some delays focusing both on J-and S-curve patterns and their short-and long-run relationship. The seminal paper by Backus, Kehoe, and Kydland (1994), in which they developed an international real business cycle model and found that the trade balance is countercyclical and the cross-correlation function of the trade balance and the terms of trade display an S-shape, focused on aggregate data for 11 developed O.E.C.D. countries. Roberts (1995) initially investigated the impact of exchange rate on trade balance in a dynamic model where import expenditure depends on wealth and found that besides the usual J-curve, a second independent one emerges. So, when two curves are considered in conjunction, an S-shaped curve is formed. In their empirical study, Marwah and Klein (1996) evaluated trade balance equations for the U.S. and Canada and also found an S-shaped pattern within the adjustment process in trade balances. Senhadji (1998) who also used the real business cycle model to show that, for most of the 30 less-developed nations, productivity shocks are a key factor in generating an S-curve. Parikh and Shibata (2004) analysed the relationship using annual data from 1970 to 1999 for 59 less-developed nations, all with mixed results. Using vector autoregressions on U.S. time series and an aggregate of industrialised countries, Enders and M€ uller (2009) found that technology shocks appreciate the terms of trade and lower the trade balance so they induce an S-shaped cross-correlation function for both variables. In addition, when calibrating a prototypical international business cycle model under complete and incomplete markets, they found that the underlying transmission mechanism of technology shocks is fundamentally different. Dmitriev and Roberts (2013) showed that a complete markets model with capital adjustment costs is consistent with the S-curve, while a model with investment adjustment costs is not. The specification of adjustment costs had little effect on the ability of the model to reproduce international co-movements.
Nadenichek (2012) introduced a basic general equilibrium model and found that both trade balance and terms of trade are driven by productivity shocks and that the subsequent behaviour generates an S-curve pattern, reminiscent of the J-curve. He concluded that the fact that productivity shocks generate a pattern similar to the J-curve underscores the importance of properly identifying the shocks generating movements in the trade balance in the broader J-curve literature. Rather heterogeneous results suggested that there could potentially exist the problem of 'aggregation bias'. The aggregation could smooth out the fluctuations observed in bilateral trade (Bahmani-Oskooee & Ratha, 2007b). This led to a number of papers dealing with disaggregate data re-examining the relationship between the terms and balance of trade on a bilateral basis (see Akkay 2015;Bahmani-Oskooee & Ratha, 2007a, 2007bGhosh, 2012;Ono & Baak 2014;Rhee, 2014). Most of the studies found support for the S-curve relationship; however, for most of the countries analysed this nexus was shown to be relatively weak. This again led to a further disaggregation, papers now focusing mainly on industry-level relations (see Bahmani-Oskooee & Ratha, 2008Bahmani-Oskooee & Xi, 2015, etc.). Since the focus of this paper is an aggregate-level type of the analysis, I shall not evaluate the literature on the other two approaches thoroughly (for a deeper literature review on this topic see Akkay, 2015). A comprehensive review of empirical investigations into the existence of both the J-curve and the S-curve can be also found in Bahmani-Oskooee and Hegerty (2010).
There is a very limited number of papers dealing with the J-curve phenomenon 2 and just one (to the author's knowledge) that analysed the possibility of an S-shaped curve in Croatia. Tomi c (2016a) demonstrated the existence of an S-curve pattern for the Croatian economy (period 2000-2014) with a particular set of data (current account measure only for goods as a proxy for the balance of trade, income terms of trade for goods and real effective exchange rate) focusing only on goods and excluding services from the analysis. The logic behind that approach was that by using a broader measure of current account balance the author would be able to depict visible exports and imports (plus invisible exports/imports) contrary to trade balance that depicts only visible and really traded exports and imports. On the other hand, a similar analysis between various trade variables revealed the opposite conclusion, casting some doubt on the existence of the S-curve relation. The ambiguity of the results and general inconclusiveness in the literature offered enough research curiosity to investigate and provide new insights into the existence and relevance of an S-shaped curve for the Croatian economy.

Data
Quarterly data for the terms of trade, real exchange rate and trade balance (as well as other auxiliary variables; labour productivity, unit labour costs, national output) were collected from the Croatian National Bank (http://www.hnb.hr), Croatian Bureau of Statistics (http://www.dzs.hr) and Eurostat (https://ec.europa.eu/eurostat) for the period 2000:Q1-2018:Q1. First, all variables were seasonally adjusted using the Census X13 seasonal adjustment procedure and then transformed into their logarithmic form (except the balance of trade variable due to negative values) in order to model continuous outcomes. Second, instead of barter terms of trade we used the income terms of trade measure because Skare, Simurina, and Tomi c (2012) and Tomi c (2014Tomi c ( , 2016a found that this variable is more relevant in macroeconomic modelling for Croatia. Whereas the 'basic' barter terms of trade just measures variations in prices, the income terms of trade includes the effect of the changes in volume of quantities exported. This means that the terms of trade could decline even though income terms of trade improve since the quantities of export could grow at the larger scale. Income terms of trade measure reveals whether the country would end up with a net gain or net loss as a result of changes in terms of trade and export volume, which de facto depends on the elasticity of demand for its export or in broader terms on the Marshall-Lerner condition. Third, in order to evaluate labour productivity in the model that will enable us to extract cross-correlation functions conditional on the technology we introduced an approximated variable as we scaled national product by labour productivity, similar to Enders and M€ uller (2009).
Therefore, this analysis is based on these variables: lnITOTlog of income terms of trade (based on national accounts data on nominal and real exports and imports in HRK) is calculated by multiplying the basic terms of trade measure (the ratio of export deflator to import deflator) with the volume of exports; lnREERlog of the real effective exchange rate deflated with the consumer price index (2010 ¼ 100); and TBseasonally adjusted trade balance index (2010 ¼ 100). Other mediating variables are: lnYlog of labour productivity as real gross domestic product is scaled by real labour productivity per person employed (2010 ¼ 100); and lnLEFlog of unit labour costs in the economy (2010 ¼ 100). Since all the variables have changed over time, we had to test them for the presence of a unit root, and we used the augmented Dickey-Fuller test, Phillips-Perron test and Kwiatkowski-Phillips-Schmidt-Shin test. Using a battery of conventional unit root tests, we could not reject non-stationarity of variables over the sample period (available on request). Graphical displays of the observed variables also suggest that they are not stationary in levels. Based on the results obtained we concluded that all series are integrated of order I(1), i.e., they are stationary in their first differences. This assumption enabled us to consider a cointegration method and VECM analysis in estimating counterfactual time series for the estimation of conditional cross-correlation functions. To calculate adequate cross-correlation coefficients, we also detrended the data (using the Hodrick-Prescott filter with common smoothing parameter k of 1600 for quarterly data). 3

An unconditional S-curve
In order to analyse the dynamic relationship between terms of trade/exchange rate and trade balance, we first tested the phenomenon by evaluating an unconditional S-curve pattern. Accordingly, an S-curve depicts negative cross-correlations between past values of the trade balance (TB) and the income terms of trade (ITOT) or real effective exchange rates (REER), but positive cross-correlations between future values of the TB and the ITOT or REER. In order to test the validity of a possible S-curve pattern for the Croatian economy, we calculated cross-correlations for both terms of trade as well as real exchange rate. Cross-correlation coefficients (q k-ITOT , q k-REER ) are defined as in Rhee (2014): where marked values of the variables present the mean of all observations over a study period. By placing cross-correlation coefficients on the vertical axis and the different lags and leads (k) on the horizontal axis, we can graphically interpret and confirm the existence of the S-curve pattern. We shall display the cross-correlation function for the terms of trade/real exchange rate and the trade balance (t þ k) for k ranging from À8 to 8 quarters, i.e., lags and leads up to two years. First, the S-curve relation reflects the income terms of trade and trade balance nexus (straight line), whereas the second S-shaped curve displays the real effective exchange rate to trade balance relationship (dotted line), all at the aggregate level, respectively (see Figure 1). Both relations demonstrated that while the cross-correlation between the current values of lnITOT or lnREER and the future values of TB is positive, the same cross-correlation between the current values of the lnITOT or lnREER and past values of the TB is negative. When we plot cross-correlation functions against the lags and leads, relations resemble the letter S, meaning that we have found evidence of an asymmetric S-curve phenomenon in both cases (the function is typically negative for negative values of k, but turns positive for k between zero and eight, only the second S-curve turning into a negative value in k ¼ 8). Importantly, both curves hit the lowest and highest values in almost similar time points, suggesting the compliance of cyclicality in movements.

A conditional S-curve
Theoretical frameworks that feature the balance of trade led to a number of dynamic general equilibrium interpretations. International business cycle models have been largely used to analyse the international mechanism of technology shocks because they are directly related to short-term fluctuations in the trade balance and terms of trade. For example, in the standard transmission mechanism when a country experiences a positive technology shock domestic output expands and its terms of trade deteriorate. However, a surge of investment could induce a trade deficit, which will turn into a surplus once the domestic capital stock is built up. Empirical success of models based on such a transmission mechanism has provided mixed results (Enders & M€ uller, 2009). Unlike many authors, such as Gal ı (1999), Corsetti, Martin, and Pesenti (2007), Dedola and Neri (2007), Altig et al. (2011), and especially Enders and M€ uller (2009), our empirical strategy is not to replicate various theoretical business cycle models and/or vector autoregression approach (VAR) studies (that have tried to identify technology, monetary or fiscal shocks and their effects on trade balance) in the literature, but to extend the analysis by introducing VECM analysis which will allow us to debate on the role of productivity within a business cycle analysis. Hence the notion that productivity shocks are a key determinant of the joint dynamics of the terms of trade/exchange rate and trade balance at business cycle frequency. Theoretical models suggest, hence, that international transmission of technology shocks should deliver an S-curve. In that manner, we shall evaluate one such empirical model in order to test the existence of an S-curve pattern on that ground. The logic of our empirical analysis follows the work of Enders and M€ uller (2009).
Since we want to evaluate short-run and, indirectly, long-run implications we shall evaluate the VAR. Engle and Granger (1987) indicated that a linear combination of two or more non-stationary series may be stationary. If so, these series are said to be cointegrated. This linear stationary combination shows the long-run relationship among the variables and is called a cointegrated equation. In order to test for cointegration, the methodology proposed by Johansen and Juselius (1990) and Johansen in 1991(Johansen, 2002 is used. Following that, the unrestricted VAR model is then defined: where y t is a k-vector of non-stationary I(1) variables, x t is a d-vector of deterministic variables, e t is a vector of independently normally distributed errors with mean zero and covariance matrix R, while A and B are matrices of parameters. Model (1) can be reformulated into a VECM: 4 Number of lags in the VAR model is determined using standard information criteria (AIC, HQ, SC, FPE, LogL and LR tests). 5 Although the criteria indicated roughly similar number of lags, the final model was estimated using two lags as suggested by SC and HQ tests. For determining the number of cointegrating vectors the Johansen's reduced rank procedure was introduced. Considering five different models, estimations were made by including constant and trend in the cointegration space following the results of the LR test. These models showed the best modelling properties. The operational form of equations, hence the long-run empirical models, are specified as follows: Long-run relationship models based on Equations (6) and (7) can be found in Table 1 with additional short-run analysis and diagnostic test in continuation. Longrun dynamics and VECM analysis exhibits expected theoretical relationships. Diagnostic tests implied that models are adequately estimated, i.e., that characteristics of the models are acceptable. 6 Estimations show almost no problem of heteroscedasticity, normality of residuals and of stability, which in fact enables stable conclusions.  (6)) Model II (Equation (7) The swings in the Croatian balance of trade, income terms of trade and real effective exchange rate have statistically significant and positive implications for the movement in labour productivity, both in the short and long term, however with different strength.
Since we are interested in finding the S-curve patterns, we focused mainly on the results from a mutual relationship between the variables trade, and income terms of trade/real effective exchange rate. To ensure that our analysis is not led by a plurality of candidates for structural impulse responses (from either monetary or fiscal policy), we did not impose any restrictions on the signs in the short-run analysis. Rather than a shortcoming, this is a potentially important advantage of our approach, for it did not have an impact on the degrees of freedom. With inconclusive impulse response results, our conclusion relied partially on variance decomposition identification (see the Appendix). Within Equation (6), variance decomposition results support the empirical findings because trade balance itself causes more than 70% of its variability on average, with a declining tendency so that after 12 quarters it explains around 62% of own variability. Income terms of trade shocks account for 20% of trade balance variance after 12 quarters. Variance decomposition results are consistent because the income terms of trade variable itself causes more than 60% of its variability through the whole period, with trade balance explaining over 26% of income terms of trade variance after 12 quarters. We also found consistency in the results from Equation (7). We see that trade balance explains over 86% of its own variability, with real effective exchange rate explaining around 7% of trade balance variance, on average. On the other hand, though the real effective exchange rate is responsible for most of its own variability, interestingly, trade balance shocks account for roughly 20% of exchange rate variability after 12 quarters. Variance decomposition analysis confirms the importance of the technology role within the international relationship for the joint dynamics of the trade balance and terms of trade/real effective exchange rate. In the next step, we focus on explaining that relationship on a business cycle frequency.
Given the estimated models, we computed in-sample counterfactual time series for variables of interest to us. 7 After we had filtered simulated time series, we calculated the cross-correlation functions for the relations trade balance vs. income terms of trade and trade balance vs. real effective exchange rate. The conditional cross-correlation functions (straight line) display a pattern that is similar to the unconditional cross-correlation functions (dotted line) for both relations. Similarity implied that unconditional cross-correlation functions, against the lags and leads for k ¼ 8, indeed resembled an S-curve behaviour. Overall, we concluded that technology, through the increase in labour productivity, has an important impact and implication for the existence of the unconditional S-curve pattern in the Croatian economy (Figures 2  and 3).
We employed two variables to test the S-curve hypothesis in order to answer the robustness requirements and came to the conclusion that there indeed exists an Scurve pattern in the Croatian data. We intentionally did not apply moving averages to smooth graphical presentation in order to utilise some diversity in movements between conditional and unconditional cross-correlation functions, especially between the balance of trade and income terms of trade. It is time to see what the results are telling us!

Implications of the research
Empirical evidence reveals that there is a regularity or systematic pattern between the cyclical movements in income terms of trade/real effective exchange rate and the balance of trade. Accordingly, trade positions will be improved systematically via depreciation of an income terms of trade or a real effective exchange rate for an S-curve effect to take place, ultimately improving trade balance and international competitiveness. Competitiveness is still one of the key elements of the performance assessment of the economy and a 'mirror' of the success of a country on a global level (Kisel ' akov a et al., 2018). Of course, the question of efficiency and effectiveness of sound public spending is also of utmost importance ( Zi zka et al., 2018). Our results indicate that income terms of trade movements could provide insurance against negative movements in the balance of trade if they lead to an increase in  domestic output relative to foreign output due to the technological improvement. Terms of trade deteriorate as the price of domestically produced products falls relative to foreign products, which initially leads to a wealth transfer outside the economy. From the short-run analysis in our model, we see that the balance of trade initially worsens for both income terms of trade and real effective exchange rate depreciation. However, as both unconditional and conditional S-curve relations suggest, the cross-correlation between the current values of income terms of trade or real effective exchange rate and the future values of the current account is positive. We trace an almost immediate positive effect after three quarters for the income terms of trade variable and just one quarter for the real effective exchange variable. Therefore, the positive change in relative prices should lead to a positive wealth effect through the trade balance improvement. Similarity in movements (percentage change in income terms of trade and real effective exchange rate vs. trade balance; see the Appendix), especially after a volatile period of economic crisis, implies that an S-curve pattern could indeed exist.
Also, we found evidence of an S-curve pattern between the income terms of trade for goods and trade balance. We additionally checked the cross-correlation functions between the income terms of trade and the volume of exports/import, and found both to be positive. When we observed a graphical display of the relationship between the real effective exchange rate and the volume of exports/imports we found an allusion to the S-curve pattern in the data, which is in conformity with our previous conclusions.
The finding of an S-curve pattern does not necessarily mean we confirmed the Jcurve pattern, thus it is possible to depict an S-curve in the analysis without finding any evidence of the J-curve. Our conclusions should be affiliated in that manner. In addition, the inability of an S-curve to depict the strength and/or the speed of the adjustment process before and after the exchange rate/terms of trade depreciation explains its limitation within policy recommendations. Though we trace an S-curve pattern in the data (unconditional relation) and model (conditional relation), there are many reasons which are, au contraire, a large deviation in the form of depreciation. Characteristics of the Croatian economy, such as high indebtedness across all sectors (private and public), underlying uncompetitiveness of an export sector, persistent trade deficit, exogeneity of the terms of trade, the havoc that can be caused by the complete pass-through effect, stability of a monetary system as a cornerstone of policy by the Croatian central bank counteracting any inflationary pressures, inefficient public finance and public debt management, appeasement to Maastricht criteria, and so on, raise some doubts on the possible depreciation as a foreign exchange policy recommendation. 8 Nonetheless, complemented with other types of research (correlations between other trade variables, exchange rate misalignment -Marshall-Lerner conditions -J-curve pattern, pass-through effectterms of trade dynamics and its causal relation to trade balance or output, analysis on disaggregated level, etc.), the S-curve confirmation could be of great help in achieving long-term policy goals, suggesting that there indeed exists a nexus of some kind between the terms of trade/exchange rate and the balance of trade. Further research on this topic should be aimed at developing a business cycle model for a small open economy with similar characteristics to Croatia which would test theoretical international transmission of different shocks such as technology shocks, terms of trade shocks, and monetary or fiscal shocks that would confront the standard business cycle model parameters with real time series evidence.

Conclusion
Our results provide a new perspective on the cyclical links between the trade and economic activity in a pre-and post-economic crisis period, a crisis whose magnitude and resilience had severe consequences on the E.U. and Croatian economy. Croatia's high volume of external debt and import dependency can increase the speed and dimension of transmission of any adverse external (oil, financial, exchange rate, etc.) shock in the future, meaning that research of this kind can help in either the narrowing of recommendations for economic policy (relevance of the quasi-fixed exchange rate and possible depreciation of Croatian kuna, loss of competitiveness, further deterioration the trade balance, business process management; see, e.g., Zemguliene & Valukonis, 2018) or increased cost of financing the current account deficit. By employing two variables (income terms of trade and real effective exchange rate) within two distinct approaches (unconditional cross-correlation functions against modelled computed in-sample counterfactual cross-correlation functions conditional on the role of technology), we found evidence of the so-called S-curve phenomenon but immediately cast some doubt on its relevance for the Croatian economy considering the immense internal and external problems this country faces. Access to the large E.U. market did not provide the desired economic effects for Croatia, hence it accentuated the importance of raising its competitiveness (rather than manipulation of the exchange rate), which could generate both opportunities and challenges for any government. There are two major shortcomings of this paper that a reader can detect. First is the relatively short time series and second is the generalisability of some conclusions. Both can impose scant economic reasoning; however, we find this argument an incentive for further research that might include more complex methods of analysis (for example, by introducing a general equilibrium business cycle model) and international comparison (especially with E.U. countries).
How well a country can balance its international trade engagements over international price changes, composition of exports and imports, terms of trade shocks, exchange rate flexibility and adjustments, competitiveness aspirations, and so on, is of great importance, especially for small, open, indebted and import-dependent country such as Croatia. The relevance of external trade position should be a cause of concern for economic policy-makers in Croatia, especially now within the aftermath of an economic crisis when net export is expected to become a driver of new economic growth.

Notes
1. There are many other factors that influence the balance of trade, such as: the cost and availability of raw materials, intermediate goods, i.e., thus the factor endowments, the cost of production between an importing vs. exporting country, trade policies related to the restriction on trade plus taxes and incentives, prices in the domestic country (inflation) and exchange rate dynamics, foreign currency reserves, etc. World income in a broader sense also has a huge influence on trade dynamics. Similar factors tend to cause the change in the terms of trade in the short and long run, making the nexus between the trade balance and terms of trade even more interrelated. 2. The first to find evidence of the J-shaped curve for Croatia was Stu cka (2004) (Tica & Nazifovski, 2012), changes in international prices (Tomi c, 2012, 2016b), terms of trade volatility ( Skare, Simurina, & Tomi c, 2012), etc. This is especially true if we know that the Croatian economy inherently suffers from a lack of international competitiveness and internal structural problems (Benazi c & Tomi c, 2014). 3. For this purpose we again tested the presence of a unit root with the same three tests (available on request). Generally, all tests confirmed the absence of a unit root for all the variables (graphical displays of the variables also suggest that they are stationary in levels). In conclusion, variables reveal a stationary behaviour after the trend has been removed. Stationarity of a variable within a business cycle analysis is an important property, otherwise a spurious cycle (if the data are difference stationary) might lead to artificial conclusions. 4. Granger's representation theorem asserts that if the coefficient matrix P has reduced rank r < k, then there exist k Â r matrices a and b each with rank r such that P ¼ ab and by t is I(0). r is the number of cointegrating relations (the cointegrating rank) and each column of b is the cointegrating vector. The elements of a are known as the adjustment parameters in the VECM and p is the number of lags. 5. AIC: Akaike information criterion; FPE: final prediction error; HQ: Hannan-Quinn information criterion; SC: Schwarz information criterion; LogL: log likelihood criterion; LR: likelihood ratio criterion. In both cases (income terms of trade and real effective exchange rate) we evaluated VAR(2), which showed adequate properties for proceeding to the next step (results available on request). 6. Model I: Portmanteau test (4) ¼ 42.02 (p-value ¼ 0.95 ÃÃÃ ), LM autocorrelation test (4) ¼ 11.79 (p-value ¼ 0.76 ÃÃÃ ), normality joint test v 2 (4) ¼ 11.70 (p-value ¼ 0.50 ÃÃÃ ).

Disclosure statement
No potential conflict of interest was reported by the author.