The economic integration of Spain: a change in the inflation pattern

2.1 Disinflation and inflation convergence: evidence and lessons for Latin America

One geographic area that has long struggled to end high and chronic inflation is Latin America. Latin American countries have endured bouts of high inflation and hyperinflation in the recent past and some of them (mainly Venezuela and Argentina) are currently grappling with this scourge again. For the remaining countries, on a general basis inflation has come down from high numbers in the 70s, 80s and 90s to more moderate rates in the present decade. It is worth mentioning that, in addition to opening themselves up to trade, countries like Mexico, Chile, Peru, Colombia and Uruguay are known to have been quite successful in bringing to birth a full-fledged inflation-targeting regime.⁷ The inflation rates after the implementation of the new framework plummeted in all these economies.⁸ Additionally, to be sustainable, this monetary arrangement calls for the conduct of a more rigorous fiscal policy which may have also played some role in helping drive inflation down over time.⁹ It is important to mention that the evidence mostly points to the existence of a positive relation between the interplay of globalization and monetary policy, via the incentives that the former raises for central banks to behave prudently, and disinflation.

To our knowledge, the literature on the effects of the interaction of the aforementioned factors on inflation convergence within countries is fairly scant, especially in Latin America. Intuitively, a country’s regions, subject to the same monetary policy and roughly similar structural reforms and fiscal policies, should in principle experience long-run inflation convergence (Yilmazkuday 2013). Moreover, if, as a consequence of a further step taken toward a deeper economic and monetary integration, some of these joint policies are carried out at a supranational level, while others are influenced or restricted by common rules set at the same level, a stronger sub-national inflation convergence is likely to occur, at least throughout the initial stages of the process.

From a policy-oriented perspective, we view this analysis as relevant since non-negligible differences in real interest rates could arise within the country did regional inflation rates differ from each other, due for instance to distinct cyclical positions across these regions’ economies, thereby perpetuating diverging economic performances at regional level. Besides, persistent differences in inflation might reflect permanent structural rigidities that prevent the regions hardest hit by shocks from adjusting swiftly.

Let us now pick two countries, Mexico and Peru, among the “globalizers” we just chose because of data and empirical evidence availability. In the case of the former, to the best of our knowledge, only studies on regional (relative) price convergence can be found. Sonora (2005) tests whether the PPP hypothesis holds across Mexico’s main cities. His results show that there is relative price convergence in the long run. Furthermore, he also suggests that prices are relatively flexible, which runs counter to the slower long-run price convergence found for US and Canadian data. Gómez-Aguirre and Rodríguez-Chávez (2013a, b) also examine price convergence across the main Mexican cities by employing panel data unit root tests. Their findings in both papers coincide with Sonora’s: absolute price parity holds in the long run. As far as inflation convergence is concerned, a quick inspection of Mexican provincial inflation rate data (Instituto Nacional de Estadística y Geografía) provides a clue as to whether there has been regional/provincial inflation convergence over time. A simple sigma-convergence analysis leads us to think this has been the case. Mexico is a NAFTA member and is therefore relatively integrated by commercial and financial ties with the US and Canada, and with the rest of the world as well. This relevant economic integration, coupled with sound economic policies, in part due to the necessary consistency with the status of being a more open economy, may have contributed to this regional/local inflation convergence coming about over time.

On the Peruvian economy, Winkelried and Gutiérrez (2012) show that the central bank of Peru, by having targeted Lima’s inflation, has been in fact influencing the economy-wide inflation,¹⁰ which in the end constitutes an indication that regional inflation rates have converged over time. By means of a multivariate dynamic model of inflation comprising the main nine regions in the country, they conclude that the relative PPP holds among pairs of regional inflations. Again, Peru is an economy whose recent progress on the macroeconomic and institutional front has been remarkable. This virtuous cycle, in a way sparked by these aforementioned good policies,¹¹ has materialized itself in considerable economic growth rates and low inflation.¹² A steady convergence in regional inflation is an expected outcome given the policies put in place from the 90s onwards.

As may be seen, the Spanish case that we choose to analyze in this article can be generalized to other open economies, such as several in Latin America, to the extent that these latter economies share certain characteristics with the Spanish economy (degree of openness, central bank behavior, fiscal policy stance, etc.).

2.2 Disinflation and inflation convergence within a European context

After the view of the processes of disinflation and convergence in inflation in Latin America, we are going to concentrate now on the Spanish case, logically placed within the euro area context. The process of Spanish disinflation in the past decades is well-known, and it has been widely studied using mainly the SVAR methodology—see the survey by Gómez and Usabiaga (2001).

As regards convergence, there exist several strands in the literature covering price level convergence, inflation convergence and inflation differentials. Although logically those literatures are closely related, each one of those research lines has some economic and econometric specific features. On the inflation rates and their convergence, main topic of our paper, there are more country-based case studies than region-based ones. For instance, there is a lot of literature on this topic for Western European countries. One can also find abundant literature on the euro area countries’ inflation differentials—see de Haan (2010) for a survey as well as several ECB publications.

Although with slight caveats, related to the price indices, the time periods, or the countries considered, in general, for the euro area countries inflation convergence has been reported—see for instance Montuenga-Gómez (2002), Busetti et al. (2007) and Beck et al. (2009)—, mainly before the mid-90s. However, there still exist significant and persistent inflation differentials in the euro area (de Haan 2010), which even allow classifying countries under different categories or clusters—see for instance Montuenga-Gómez (2002) and Busetti et al. (2007).

Beck et al. (2009, p. 153), with the euro zone in mind, present the following classification of the potential underlying factors in inflation differentials—de Haan (2010) uses a roughly similar classification—: (1) differences between the actual positions of the economies within their business cycles, asymmetric shocks, and asymmetric effects of area-wide impulses such as monetary impulses, exchange rate movements or oil price changes. (2) The Balassa–Samuelson effect. (3) Inappropriate domestic policies or other unwarranted domestic developments such as misaligned fiscal policies, immoderate wage evolution, or other production input factor price developments. (4) Nominal wage and price rigidities. Beck et al. (2009) point out that the most worrisome factors are those of the two last types.

There is no clear consensus on the specific underlying sources of the inflation differentials among the euro area countries, although there may be a consensus about the fact that they are rooted on structural or institutional factors—see for instance Jaumotte and Morsy (2012) and Beck et al. (2009). In this respect, Jaumotte and Morsy (2012), for a panel of 10 euro area countries (period 1983–2007), conclude that in order to reduce the persistent inflation differentials the following labor elements have to be reformed: high employment protection, intermediate coordination of collective bargaining and high union density. In this line, de Haan (2010) highlights that most empirical research suggests that EMU has not spurred labor market reform. However, Beck et al. (2009) do not emphasize the labor factors for the regional euro area inflation differentials. In their opinion, those differentials are mainly accounted for by the costs of the non-wage input factors, the degree of competition and the economic structure of the regions. In other words, the observed long-run differences are chiefly caused by inefficiencies in factor markets and region-specific structural characteristics. They also remark that there is considerable heterogeneity in the economic structure of euro area regions such that even symmetric impulses—such as a monetary policy shock—can have heterogeneous effects.

From the analysis of the regional inflation rates of the euro area countries, Beck et al. (2009) state that national factors matter. Thus, the dispersion is higher among the regions of all the European countries analyzed (Austria, Finland, Germany, Italy, Norway and Spain) than among the regions of each country. In addition, differences are substantially more pronounced across regions than across country averages. These authors assert that the strong influence of the national factor very likely stems both from nationally conducted fiscal policy and nationally determined labor market institutions. In comparison to US regional inflation rates, the euro area regional rates show a slightly higher degree of dispersion and persistence. Using a factor model, Beck et al. (2009) find that the variation in euro area regional inflation rates is explained following these proportions: area-wide factors 50 %, national factors 32 %, regional elements 18 % (Spain: national factors 26.8 %, regional factors 24.6 %). They come to the conclusion that the Spanish differential in this respect can probably be explained by the relatively high degree of independence that Spanish regions enjoy.

Several works highlight that the monetary policy followed by EMU could have generated convergence effects also at regional level, due to its effect on expectations and other factors. For instance, Beck et al. (2009) state that the area-wide monetary policy can considerably contribute to regional inflation stabilization even though it cannot take regional developments into account when making its decisions. Apart from Beck et al. (2009), other works also report regional inflation convergence. For instance, Busetti et al. (2006) conduct an analysis of the price level and the inflation rate for the monthly series of the CPI in 19 Italian regional capitals over the 1970–2003 period, concluding that the convergence process is stronger for the inflation rate. Gozgor (2013) also observes convergence in Turkish regional inflation rates (period 2004–2011).

Yilmazkuday (2013) tackles a more disaggregated analysis of regional inflation, in the line of the works related to the Balassa–Samuelson literature. He works with ten main CPI groups for each region, distinguishing between groups concentrated on tradable and non-tradable components (period 1994–2004). In this study a break in Turkish inflation is captured in 2002, and in 2001 for the cross-sectional standard deviation of regional inflation rates. This author distinguishes between a pre-inflation targeting period and an inflation targeting period (which coincides with a flexible exchange rate) starting from January 2002. As in our study, Pesaran (2007a)’s methodology is used, among other techniques—Arestis et al. (2014) also use that technique, but applied to countries’ inflation. As acknowledged by Yilmazkuday (2013), the results of this work require further study since during the inflation targeting period the CPI groups with relatively tradable components have diverged from each other, while the non-tradable groups have converged to each other. Caraballo and Usabiaga (2009c) share some elements of the disaggregated study of Yilmazkuday (2013) in their analysis of Spanish and Andalusian inflation. Finally, in the present study we can state that when we disaggregate provincial CPI-based inflation rates into province-level inflation rates of the 12 COICOP groups of goods and services over the 1994–2015 period, we are able to uncover some interesting patterns. With the exception of the Communications group involving mainly non-tradables, all the other groups of goods and services appear to exhibit a high degree of convergence among pairs of inflation rates across provinces. This indicates that convergence in provincial inflation rates is widespread across groups of goods and services, irrespective of the tradables/non-tradables distinction.

It is well accepted that the Balassa–Samuelson effect fails to account for the euro area inflation dynamics—see ECB (2005), Rogers (2007) and Beck et al. (2009). The Spanish economy is not an exception in this regard, maybe because some of its assumptions do not hold in that economy; for instance features like a rather centralized wage determination, a low labor mobility, etc. (Jimeno and Bentolila 1998), run counter to its central assumptions. Juselius and Ordóñez (2009) point out that the potential Balassa–Samuelson effect has more influence over the high unemployment than over prices. Rabanal (2009) concludes that the Balassa–Samuelson effect does not appear to be an important driver of the inflation differential Spain-EMU during the EMU period, although a gap in labor productivity between tradable and non-tradable sectors can be noted. In addition, Alberola and Marqués (2001) reject the Balassa–Samuelson hypothesis at Spanish regional level. Finally, in Beck et al. (2009) this theory is not supported for the Spanish regions. To sum up, there is overwhelming evidence against the relevance and explanatory power of that hypothesis for the Spanish economy. Our results do not support the Balassa–Samuelson hypothesis since there is not a significantly higher degree of convergence among pairs of provincial inflation rates for tradables, relative to non-tradables (of course bearing in mind the exception of the Communications sector). Likewise, our multivariate regression analysis provides evidence of a significantly negative impact of real GVA per capita growth on the inflation rate, which runs counter to the positive effect that would be predicted according to the Balassa–Samuelson hypothesis.

3.1 Determining the number of common factors

3.2 Analysis of the idiosyncratic component

We also employ the two Moon and Perron (2004) type pooled tests utilizing the PANIC residuals to estimate a bias-corrected pooled PANIC autoregressive estimator, and a panel version of the Sargan–Bhargava (1983) statistic using the sample moments of the residuals without the need to estimate the pooled autoregressive coefficients. A great advantage of the PANIC pooled statistics of Bai and Ng (2010) is that there is no need for least squares linear detrending that could give rise to a fall in statistical power.

3.3 Analysis of the common component

The corresponding ADF t-statistics are denoted by \( {\text{ADF}}_{{\hat{F}}}^{c} \) and \( {\text{ADF}}_{{\hat{F}}}^{\tau } \) and follow the limiting distribution of the Dickey and Fuller (1979) test for the specifications with only a constant, and a constant and a trend, respectively.

3.4 Stationarity tests for the common and idiosyncratic components

As noted above, the stationarity test of Kwiatkowski et al. (1992, KPSS) is used and applied to both the common and idiosyncratic components following Bai and Ng (2004b). The univariate KPSS tests for the idiosyncratic components are denoted by \( S_{{\hat{e}}}^{c} (i) \) and \( S_{{\hat{e}_{0} }}^{\tau } (i) \) depending on whether trends appear or not in the specification, and the tests for the common factors are \( S_{{\hat{F}}}^{c} \) and \( S_{{\hat{F}}}^{\tau } \). The limiting distribution of \( S_{{\hat{F}}}^{c} \) and \( S_{{\hat{F}}}^{\tau } \) are those derived by KPSS for the cases of a constant, and a constant and a linear trend, respectively. However, the limiting distribution for testing \( \hat{e}_{it} \) depends on whether \( \hat{F}_{t} \) is I(0) or I(1). If all factors are I(0), \( S_{{\hat{e}_{0} }}^{c} (i) \) and \( S_{{\hat{e}_{0} }}^{\tau } (i) \) follow the distribution of the KPSS tests for the cases of a constant, and a constant and a trend, respectively. But if the factor is I(1), as it is our case, stationarity in the idiosyncratic component implies cointegration between the observed series and the I(1) common factor. In that case, we have to employ univariate cointegration tests denoted by \( S_{{\hat{e}_{1} }}^{c} (i) \) and \( S_{{\hat{e}_{1} }}^{\tau } (i) \), which have the limiting distribution of the cointegration test of Shin (1994).

With respect to the computation of pooled statistics, when the common factors are stationary, the p-values associated with the univariate KPSS tests for the idiosyncratic components can be used to compute the pooled tests of Maddala and Wu (1999) and Choi (2001). Otherwise, pooling is not valid since the non-stationarity of the common factors is transmitted to the residuals under the null hypothesis of stationarity because it does not fade away even asymptotically.¹⁸

4.1 Data description

The main data we deploy in this article are CPI data,¹⁹ spanning from 1955.1 until 2014.4 at a monthly frequency, and they are sourced from INE (Instituto Nacional de Estadística). We avail ourselves of year-on-year numbers so as to avoid the seasonality problem. The data correspond to provincial capitals (up to 1992) and to provinces themselves thereafter. Connecting both kinds of series, without manipulating them, proves unproblematic. We have only engaged in two very specific manipulations of our inflation series in order to correct for two anomalous figures related to the province of Zamora, in 1960.1 and 1961.1.²⁰ In spite of having access to previous years, we have decided to stick to 1955 as the first year of our study mainly for three reasons: (1) because we would not like to go too far back in time, since our analysis neither aims to adopt an economic history approach nor to deal with episodes too far back in history. (2) Because data might cease to be statistically trustworthy as we move backwards in time, this trust being a fundamental factor for the econometric analysis conducted. (3) Because for additional assessments we make use of some other series, in addition to inflation, which mostly start after 1955.

Our work’s basic data (inflation rate) is a panel made up of 50 (N, provinces) by 712 (T, months). Nevertheless, for our purposes, the aforesaid panel is split into two different sub-samples. Indeed, in what follows, our article attempts to clarify whether the behavior of the provincial inflation rate varies between sub-periods. But before turning to the PANIC analysis, we next try to determine through econometric techniques where the break is located, as a better alternative to exogenously imposing it.

4.2 Determination of the endogenous break in inflation

The unit root null hypothesis is given by \( \phi = 0 \) versus the alternative that \( \phi < 0 \), and the LM t-statistic is defined by \( \tilde{\tau } \) (t-statistic testing the null hypothesis that \( \phi = 0 \)). The minimum LM unit root t-statistic determines the endogenous location of the break (\( \lambda = T_{\text{B}} /T \)) by using a grid search over all possible break points such that \( {\text{LM}}_{\tau } = \mathop {\inf }\nolimits_{\lambda } \tilde{\tau }(\lambda ) \). To correct for serial correlation, we control for a sufficiently large number of augmentation terms (k) by employing the general to specific approach proposed by Ng and Perron (1995), setting k _max = 12.²³

For the crash model the mean shift is located at July 1978, whereas for the mixed change model the shift in mean and slope appears located at April 1979. Given the non-trending behavior exhibited by the inflation rate, we base our conclusions on the crash model which points to the existence of a mean shift at July 1978. The cross-province mean inflation rate for the first regime equals 9.4 %, whereas it equals 5.8 % for the post-break regime, implying a clear downward shift in the mean inflation rate after the break took place. In addition, it is interesting to point out that the value of the LM unit root test of LS for the crash and mixed change models is −2.155 and −2.795, respectively, both values well below (in absolute terms) the respective 10 % critical values (−3.504 and −4.989). This indicates the existence of a unit root in the common factor for the whole period after accounting for one structural break in the mean (and slope) of the series.

For robustness purposes, we also applied the generalized least squares (GLS)-based unit root tests allowing for one break under both the null and alternative hypotheses proposed by Carrión-i-Silvestre et al. (2009). These tests include the class of modified tests (M tests), originally proposed by Stock (1999), and later extended by Perron and Ng (1996) and Ng and Perron (2001). The latter apply local-to-unity GLS detrending instead of ordinary least squares (OLS) when estimating the deterministic components of an ADF regression (see Elliot et al. 1996) so that important gains in statistical power can be achieved. More specifically, we employ the \( {\text{ADF}}^{\text{GLS}} \) test first proposed by Elliot et al. (1996), which is the t-statistic for testing the existence of a unit root with a specification where the underlying series is detrended with GLS prior to estimation by OLS. The \( M^{\text{GLS}} \)-class of tests includes \( {\text{MZ}}_{\alpha }^{\text{GLS}} \) and \( {\text{MZ}}_{t}^{\text{GLS}} \) which are modified versions of the \( Z_{\alpha } \) and \( Z_{t} \) Phillips and Perron (1988) tests, \( {\text{MSB}}^{\text{GLS}} \) which is a modified version of the Sargan and Bhargava (1983) test, the feasible point optimal test \( (P_{\text{T}}^{\text{GLS}} ) \) and the modified feasible point optimal test \( ( {\text{MP}}_{\text{T}}^{\text{GLS}} ) \).²⁴ In this case, the break is located at August 1977, which is very close to the break date identified with the LS procedure. Since a visual inspection of Fig. 1 appears to favor a major downward shift in mean inflation in the middle of 1978, we stick to the result obtained from the application of LS methods. Still, it is reassuring that both methods render fairly similar results. Not surprisingly either, none of the GLS-based unit root tests is able to reject the unit root null hypothesis at conventional significance levels,²⁵ thus supporting the non-stationarity of the common factor.

Our initial working hypothesis, which turns out to be confirmed throughout our analyses, is that from the break identified (1978.7) up to the present day a number of relevant economic, political and institutional changes, both at the national and international levels, have necessarily left their imprints on the inflation rate, among other variables. This changing pattern is intended to be captured, in a first step, via PANIC, and in a second step, via other convergence assessments.

The break identified can be largely thought of as a turning point in Spanish economic policy relative to Franco’s dictatorial regime, leading to a period of a high reformist vigor brought about by the new democratic period that encompassed almost every economic area, both within the country itself and further afield, spurred by the firm intention of Spain to access to the European core. As regards Spanish internal policy, which has been progressively constrained by the European integration process, after the Pactos de la Moncloa (1977)—a battery of urgent policy measures in response to the peak in inflation—, one of the first measures taken was the adoption of the medium-term economic program 1983–1986 (updated twice afterwards). In this program, on the one hand, some adjustment policies were put into place with the aim of correcting the main macroeconomic imbalances, and, on the other hand, several structural reforms were fostered in order to better articulate the productive fabric of the country and enhance the efficient functioning of the markets.²⁶ It is also indisputable that the initiatives in favor of the European integration, and the legislative alignment that ensued from that, were crucial during those years which ended with Spain entering the European Economic Community (EEC) on January the 1st 1986. Within this process, the Maastricht Treaty called for central banks’ independence of those countries aiming to join the Single Currency, which in the case of Spain led to the approval of the Law of Autonomy of the Bank of Spain (Law 13/1994). In the context of EMU, an inter-annual inflation target around 2 % was established.²⁷

In case the justification of the timing of the break, based on institutional, political and economic grounds, was deemed insufficient, Fig. 1 plots the evolution of the provincial inflation rates for both periods analyzed. Even at first glance, it is easily observable that the nature of the series appears to have undergone a transformation between periods. Apart from a lower average inflation in the second period,²⁸ even in those months in which inflation is at similar levels across both periods, a lower dispersion for the second one is perceived.

5.1 Analysis of cross-sectional dependence

5.2 PANIC analysis of the panel of CPI-based inflation rates for the Spanish provinces

5.3 Pairwise test of Pesaran

As can be observed in Table 5, we find evidence of a fraction of rejections close to 1 for both periods with the ADF and WS unit root tests, irrespective of the inclusion of a linear trend in the specification. This indicates that all provincial inflation rate pairs have converged to each other, thus confirming the pairwise convergence finding obtained with PANIC. However, according to the KPSS stationarity test, the null of convergence is rejected for a fraction higher than the nominal size, ranging from about 0.20 and 0.40. This would indicate the existence of a lower proportion (than 1) of inflation rate pairs converging to each other. Given the size distortions that the univariate KPSS test tends to exhibit, we base our conclusions on the basis of the ADF and WS unit root tests, which point to the existence of pairwise convergence in both periods.

6.1 Multivariate regression analysis

The PANIC analysis we have performed shows that, mainly in the second period, there is convergence in the provincial inflation rates. Accordingly, digging deeper into the information about convergence, in the supplementary appendix we provide results on how much the coefficient of variation³⁶ changes (in terms of percentage of variation) from the start of each period up to its midpoint and from the beginning of each period up to its end, for an ample group of relevant variables that include the inflation rate and some of its potential determinants (the unemployment rate, two proxies for the real average wage, two proxies for the labor share in the GVA, nominal and real unit labor cost (ULC), real GVA per capita and real labor productivity).³⁷ A negative sign in the table means (sigma) convergence in the variable involved, and a positive one just the opposite. It is quite visible that widespread convergence in the variables occurs over time. It is also remarkable that this convergence process is stronger throughout the second period (the real GVA per capita being the only exception).³⁸ Overall, the broad pattern of convergence is illustrated in Fig. 2, particularly over the second period under scrutiny, thus confirming the results derived via PANIC analysis.

We next try to compare our study with that of Beck et al. (2009), an important reference in this field, which included the Spanish regions. However, the comparison can be only partial, due to some differences in the characteristics of our respective analyses. In our analysis, the dependent variable is the common factor obtained from the PANIC analysis of Spanish provincial inflation and we will use average national data as explanatory variables. Our series are expressed in time series form and they are generally long. In Beck et al. (2009) the dependent variable is regional inflation and they use the respective regional data as explanatory variables. Their analysis is in cross-section form and they only study a short period of time (1995–2004) for six European countries. They obtain their main conclusions from mean regional relations.

For this comparison, we have compiled several proxies trying to follow Beck et al. (2009)’s approach: (1) real ULC, as a way to capture the fact that different regional developments in the price of labor (i.e., wages), potentially caused by geographic labor market fragmentation, may lead to persistent inflation differentials. (2) Inter-annual growth in the COICOP index “Housing, water, electricity, gas and other fuels” (data source: Eurostat). It is a measure of costs of non-wage input factors, whose geographic differences may stem from supply and demand changes in segmented markets or structural inefficiencies in regulated markets (Beck et al. 2009). (3) Oil price inflation (dollars per barrel, data source: Reuters). It is also a measure of costs of non-wage input factors—this variable is not analyzed by Beck et al. (2009) but we consider its inclusion to be relevant for the Spanish case. (4) The unemployment rate that accounts for a region’s position in the business cycle and for the potential effect of labor market heterogeneity—caused by the geographic segmentation of labor markets—on inflation differentials. (5) Ratio: number of local units with three or more employees/population (in thousands). Data source: Directorio Central de Empresas (DIRCE) and population figures, both from INE. It is a measure of the market density in the manufacturing and wholesale sector (i.e., the number of suppliers), proxying for the competitive structure of a region, with a higher value implying a greater degree of competition. As pointed out by Beck et al. (2009), nominal rigidities are generally associated with imperfect competition in the goods and labor markets leading to a high degree of inflation persistence, which can be responsible for permanent inflation differentials. (6) Share of services in GVA at basic prices (data source: Contabilidad Nacional Trimestral de España, INE). It is one of the proxies used by Beck et al. (2009) to capture the economic structure, which can be the origin of asymmetric shocks and differences in the transmission of such shocks. Cross-regional differences in economic structure are conducive to asynchronous business cycle developments, which can at least have a transitory effect on inflation differentials. (7) The growth rate of real GVA per capita, as a way to capture the Balassa–Samuelson effect. Higher economic growth rates are generally associated with a higher price level for non-tradable goods, and in turn a higher overall price level. Hence, the price level will rise by a greater amount in fast-growing provinces relative to slow-growing ones, thus causing inflation differentials. In all, we have tried to follow as much as possible the spirit (and the specifications) of their exercise—see mainly Beck et al. (2009, pp. 161, 162).

It is worth noting that, in comparison with bivariate analyses (common factor vs. each one of the aforementioned variables), the multivariate regression presents two main problems: (1) once you combine the different samples corresponding to the different variables involved, the joint time period of analysis is shortened—mainly due to the shorter samples of the additional variables following Beck et al. (2009)—, with the results corresponding only to a part of our second period of analysis. (2) The analysis faces severe potential multicollinearity problems—remember that in some cases we work with different proxies for the same type of variable and in other cases some of our variables embed or include other variables. Due to some problems with the data and the econometric methods already pointed out, Beck et al. (2009) only introduced a reduced group of variables in their multivariate analysis to explain inflation (for all the countries of their study): unemployment rate, real ULC, COICOP group index growth, competition proxy, percentage of services and real GVA per capita growth. Of those variables, only three resulted significant: COICOP group index growth (+), competition proxy (−), and percentage of services (−).

Concerning labor market variables, both the unemployment rate and the real ULC appear to explain the inflation rate. In the case of the unemployment rate, the negative sign of its coefficient appears to be consistent with the Phillips curve, which accounts for the negative relation between the inflation and unemployment rates.³⁹ The significantly positive coefficient on the real ULC indicates the existence of a positive relation between developments in the price of labor and persistent developments in inflation. All this suggests that labor market institutions can affect costs of production and in turn the inflation rate. The multivariate specification also offers consistent evidence of the positive impact that increases in non-wage input factor prices (measured either through the growth in the COICOP index “Housing, water, electricity, gas and other fuels” or the oil inflation rate) exert on the inflation rate, thus reducing the degree of competitiveness of the Spanish economy. In addition, market density, which proxies for the competitive structure of the Spanish economy, appears to be inversely related to the inflation rate. This indicates that the larger the number of suppliers and the higher the degree of competition, the lower the inflation rate. In line with Beck et al. (2009) findings, the services share in GVA is negatively associated with the inflation rate. This supports the fact that asymmetric shocks caused by sectoral specialization can exert a temporary effect on the inflation rate. Finally, the significant negative coefficient on the growth rate of real GVA per capita runs counter to the positive sign predicted by the Balassa–Samuelson hypothesis. This appears in line with other studies for European cities or regions like Rogers (2007) and Beck et al. (2009), and with previous evidence for Spain.

6.2 Analysis of weightings in the shopping basket

An alternative explanation of the acute convergence path found in the provincial inflation rates in the second time period could be ascribed to the fact that the composition of the shopping basket in the Spanish provinces has tended to become more homogeneous over time. This phenomenon can be approached by paying close attention to the provincial weightings attached to the different groups of goods and services the CPI comprises. In this particular analysis, we will thus heed the CPI breaking down into twelve groups of goods and services—the so-called COICOP—, although it could also be accomplished with a greater disaggregation—for the sub-groups, which are in effect more than thirty.⁴⁰

Unfortunately, lack of data availability prevents us from carrying out this examination for the first period. However, we can state something on that matter regarding the second period, as we are able to compare the figures of the years 1992 and 2014—chronologically speaking, they are the first year and the most recent one, respectively, for which there are CPI weightings data available.⁴¹

In short, during our second time period examined, it is shown that the Spanish provinces’ shopping basket tends to converge in a clear way, which could help to further account for the strong perceived convergence among the Spanish provincial inflation rates.

6.3 Testing the Balassa–Samuelson hypothesis using Pesaran’s (2007a) approach

As a final exercise aimed at more formally determining the extent of convergence in each of the 12 COICOP groups of goods and services across the 50 provinces forming Spain, we apply the pairwise convergence approach of Pesaran (2007a) to each of these groups of goods and services over the 1994.1–2015.11 period. This exercise, in line with that conducted by Yilmazkuday (2013), constitutes an indirect way to assess whether the Balassa–Samuelson hypothesis holds across the Spanish provinces over the period under scrutiny. If this hypothesis is to hold, convergence among pairs of provincial inflation rates should be more prevalent in those groups involving tradable goods, since cross-province trade would help eliminate inflation differentials. In contrast, for those groups mainly composed of non-tradable goods and services, a lower extent of convergence among provincial inflation pairs is expected. Hence, one would expect a higher degree of convergence for the following groups involving tradable goods and services: food and non-alcoholic beverages, alcoholic beverages and tobacco, clothing and footwear, and transport. A lower degree of convergence is expected in those groups involving a mix of tradables and non-tradables such as furnishings, household equipment and routine housing maintenance, and recreation and culture; and an even lower degree of convergence for those groups involving mainly non-tradables (in most cases services) such as housing, health, communications, education, restaurants, cafés and hotels, and miscellaneous goods and services.