The Effect of Automatic Wage Indexation on the Inflation Rate Level: A
Panel Data Approach
Student: Max Gehrend Student number: 10603255
Master of Science in Economics Faculty of Business and Economics University of Amsterdam
Introduction
The aim of this paper is to investigate if automatic wage indexation has a positive effect on the inflation rate. The definition of wage indexation that we will adopt is taken from Aizenman (1987): “Wage indexation is a mechanism designed to adjust wages to information that cannot be foreseen when the wage contract is negotiated. A wage contract with indexation clauses will specify the wage base (i.e., the money wage applicable in the absence of new information), the indexation formula that will be used to update wages, and how often updating will occur.” Jadresic (2002) notes: “According to this definition, the mere adjustment of wages to reflect inflation does not qualify as wage indexation.” Indexation is special in the sense that it enables wages to automatically adjust to new information. This implies that if wages are increased due to contract renegotiations in the presence of a higher than expected inflation rate, then this cannot be considered as automatic wage indexation (Jadresic, 2002). We consider the latter practise as a form of informal indexation, whereas we are interested in the effects of automatic indexation on inflation. Concerning the structure of this paper, we will first discuss the theoretical predictions made by economic theory concerning the effects of wage indexation on inflation in order to determine which results can be expected and to be able to explain these findings. Thereafter, we will review the results of previous pertinent empirical studies and finally present and discuss our own findings for a panel of 25 European countries.
Theoretical overview Early macroeconomic models including wage indexation
In this section, the basic model by Gray (1976), which incorporates wage indexation in a macroeconomic framework and serves as benchmark for later research, is presented. This model assumes indexation of nominal wages to current inflation. Thereafter an extension by
Fischer (1977) where wages evolve conditional on lagged inflation is briefly discussed. Gray’s (1976) developed a simple neoclassical model augmented by uncertainty and
short-term wage rigidities. Stochastic shocks to the money supply and the production function generate the former, while the latter are due to a contracting scheme where nominal wages and an indexing parameter need to be fixed before these disturbances can be observed. Since the purpose of indexation is to protect against unanticipated price changes, expected changes to the productivity or the money supply are not of interest, as this information is available when wages and the indexing parameter are set. Hence shocks have zero mean and are symmetrically distributed. In the following, the different sectors included in the model will be
presented.
For simplicity, the capital stock is fixed and the economy is assumed to produce only one good. Aggregate output 𝑌𝑌𝑡𝑡 takes the following form:
𝑌𝑌𝑡𝑡= 𝛼𝛼𝑡𝑡𝐺𝐺(𝐿𝐿𝑡𝑡), 𝛼𝛼𝑡𝑡= 1 + 𝜇𝜇𝑡𝑡
𝐿𝐿𝑡𝑡 is labour, 𝜇𝜇𝑡𝑡 represents a zero-mean shock to productivity 𝛼𝛼𝑡𝑡 and 𝐺𝐺(𝐿𝐿𝑡𝑡) is homogenous of degree less than one.
The following stochastic process generates the nominal money supply: 𝑀𝑀𝑡𝑡𝑆𝑆 = 𝛽𝛽𝑡𝑡𝑀𝑀�, 𝛽𝛽𝑡𝑡= 1 + 𝜉𝜉𝑡𝑡
𝑀𝑀� is a constant and 𝜉𝜉𝑡𝑡 is a zero-mean shock to the money supply. 𝜇𝜇𝑡𝑡 and 𝜉𝜉𝑡𝑡 are uncorrelated. The nominal money demand is represented by a Cambridge equation:
𝑀𝑀𝑡𝑡𝐷𝐷 = 𝑘𝑘𝑃𝑃𝑡𝑡𝑌𝑌𝑡𝑡
Money demand depends on output and the price level 𝑃𝑃𝑡𝑡. In this form, 𝑘𝑘 is assumed to be constant. Thus, stochastic shocks to velocity are not considered. Prices are assumed to adjust immediately to changes in the money supply in order to equilibrate the money market (𝑀𝑀𝑡𝑡𝑆𝑆 = 𝑀𝑀𝑡𝑡𝐷𝐷).
The supply and demand functions for labour take the following typical forms: 𝐿𝐿𝑡𝑡𝑆𝑆 = 𝑔𝑔(𝑤𝑤𝑡𝑡), 𝑔𝑔𝑤𝑤 > 0
𝐿𝐿𝐷𝐷𝑡𝑡 = 𝑓𝑓 �𝑤𝑤𝑡𝑡𝛼𝛼
𝑡𝑡�, 𝑓𝑓𝑤𝑤/𝛼𝛼 < 0
The real wage is represented by 𝑤𝑤𝑡𝑡 and is equal to the nominal wage 𝑊𝑊𝑡𝑡 over 𝑃𝑃𝑡𝑡. Labour demand increases with productivity and decreases in real wages, while labour supply goes up with the real wage. As previously mentioned, the contracts in the labour market are fixed before shocks occur; at the end of period 𝑡𝑡 − 1, the nominal wage level for the period 𝑡𝑡 is determined so as to equilibrate the labour market. For reasons of simplicity, it is assumed that this always takes place subject to the constraint that the shocks will be equal to their means (𝜇𝜇𝑡𝑡 = 𝜉𝜉𝑡𝑡= 0) . Once this happened, the stochastic shocks are realised and productions decisions are made. Employment then becomes completely demand determined because labour supply is assumed to become perfectly elastic. The second decision made at the end of
depend inversely on prices. Thus, indexation is attractive if real wages that are irresponsive to price changes are desirable, which in turn depends on the type of disturbances the economy is subject to. In the following the effects of the two types of shocks investigated by Gray (1976) will be discussed in the light of full and no indexation.
First we consider a monetary shock. For example, an increase in the money supply requires money demand to go up as well; hence the price level needs to increase. If wages are fully indexed, then nominal wages increase proportionally to the general price level and the real wage stays constant. This leads to a constant labour input and in turn to a constant output. Thus, in the presence of indexation, monetary shocks have no real effect. Contrarily, a system with no indexation at all, and as previously assumed, fixed nominal wages responds with a decrease in real wages after a positive monetary disturbance. This results in higher employment and increased output. It can hence be concluded that full indexation completely stabilises real variables if an economy is only subject to monetary disturbances. However, it should be noted that in a system with indexation, the price level fully absorbs the monetary shock, whereas without indexation both output and prices fluctuate after the disturbance. As a result, the price level variability increases with indexation.
Nevertheless, the previous reasoning does not hold if the economy is subject to real shocks. On that account, we consider a positive shock to productivity. Given that the money supply is fixed, output will increase and hence the price level needs to decrease. Therefore, in the absence of indexation, the real wage goes up, effectively neutralising the positive effect of higher productivity on labour demand. Even though labour input itself remains constant, output increases since labour productivity is higher. With full indexation however, the real wage stays constant and does not neutralise the positive effect of a higher productivity on employment. Thus labour input increases, thereby amplifying the effect of the initial shock on output. Consequently, in the presence of real shocks, indexation leads to higher output and employment variability. Additionally, given a fixed money supply, it follows that with indexation the price level varies more than without since it has to neutralise the more intense output response.
Overall, it can be deduced that the optimal degree of indexation depends on the nature of the shocks that hit the economy. If it is assumed that economic agents only care about the variability of real variables, then more indexation is desirable with predominantly nominal disturbances whereas less indexation is desirable with real disturbances (Gray 1976). On the other hand, if economic agents also aim at reducing price variability, more indexation is
always detrimental for that purpose as it will be higher regardless of the type of shocks that occurs.
It should be pointed out that this early attempt to incorporate indexation in macroeconomic models has some important limitations. For instance, it assumes an immediate wage adjustment to inflation, whereas in reality indexation typically relies on past inflation to impose wage changes.
Fischer (1977) is the first author to incorporate indexation to lagged inflation instead of current inflation. In his setting, he found that indexation only stabilises output in case of persistent monetary shocks. If nominal disturbances are more transitory or if shocks in general are more of real nature, then indexation has a destabilising effect on output.
A further limitation of the Gray (1976) model is the absence of an explicit modelling of monetary policy. We will return to these points in subsequent paragraphs.
Wage Indexation and Inflation
After the works of Gray (1976) and Fischer (1977), several authors focused on the question of how indexation influences the inflation rate level. First indexation to current inflation in the tradition of Gray (1976) is discussed and subsequently the conclusions drawn there will be reconsidered in the context of indexation to lagged inflation.
The Case for Lower Inflation
Milesi-Ferretti (1994) departs from the Gray (1977) model in three basic ways:
(1) the market-clearing employment level is assumed to be below the socially optimal level, (2) monetary policy is modelled explicitly, and
(3) policymakers can choose the degree of wage indexation to prices.
The model follows a structure in the spirit of Barro and Gordon (1983) with discretionary policy and distortions that create a gap between the equilibrium and the socially optimal level of employment. The larger this wedge, the higher expected inflation, due to the increased incentive to reduce the former. Thus, an inflation bias arises. Specifically, policymakers try to keep employment above its natural level by creating surprise inflation. However, in equilibrium, economic agents anticipate this behaviour and render the policy unsuccessful, resulting in higher inflation without lower unemployment (Barro & Gordon, 1983).
monetary shocks on employment. Hence, there is no incentive to create surprise inflation in order to boost employment, since it is impossible to reduce the real wages that way. In that case expected and actual inflation will be equal to zero. Milesi-Ferretti (1994) presents four factors that increase the optimal indexation level:
(1) a lower variance of supply shocks,
(2) a larger gap between desired and market-clearing employment levels, (3) a more “inflationary” government, and
(4) a higher sensitivity of labour supply to the real wage.
(1) is similar to the standard Gray (1976) model. Real wage adjustments are required to minimise the effects of real shocks on employment and output. Since indexation prevents these adjustments, its optimal degree goes up if the variance of real shocks decreases.
(2) and (3) are, in fact, very similar. The larger the gap between equilibrium and desired employment level, or the higher the weight put on this gap, the higher the incentive for the government to produce surprise inflation. As a result, policymakers will be more willing to reduce this incentive through indexation. In this sense, wage indexation is a substitute for anti-inflationary preferences (Milesi-Ferretti, 1994). Crosby (1995) follows a similar argumentation. Policymakers might be better off by reducing the mean inflation they deliver. Especially if they are more left wing, wage indexation can help to reduce expected inflation and increase their re-election chances.
(4) is due to the fact that if labour supply reacts more to real wage changes, these changes become less attractive and the desirability of stable real wages increases.
In conclusion, indexation helps diminishing inflation by decreasing the incentive for monetary shocks. Particularly, policymakers that concern themselves relatively more with employment than with inflation benefit from introducing wage indexation because they get less exposed to the time-inconsistency problem. In other words, it helps them to gain credibility by tying their own hands (Milesi-Ferretti, 1994).
The Case for Higher Inflation
Ball and Cecchetti (1991) also investigate the effect of wage indexation on inflation in a Barro-Gordon framework with taxation causing labour market distortions. In line with Milesi-Ferretti (1994) and Crosby (1995), the authors recognise that indexation reduces the temptation of surprise inflation through a steeper Phillips curve. Nonetheless, they show that indexation might also reduce the cost of inflation, thereby being a source of it.
As previously mentioned, taxation causes the equilibrium wage to be higher and employment to be lower than their respective efficiency levels. Through a normalisation, the equilibrium real wage is equal to zero, while the efficient real wage is equal to the negative constant – 𝐾𝐾. Furthermore, the authors follow Taylor (1980) as they assume staggered wage-setting, meaning not all wage decisions in an economy are made simultaneously. More precisely, per time period half of the firms can sign new contracts and these are set to last for two periods. This is done after the money supply has been observed, but before employment is chosen. The welfare loss of a deviation of firm i’s real wage from the efficient level – 𝐾𝐾 is represented by:
𝐿𝐿𝑖𝑖 = (𝑤𝑤𝑖𝑖 − 𝑝𝑝 + 𝐾𝐾)2
Firm i’s loss function 𝐿𝐿𝑖𝑖 depends on the real wage (𝑤𝑤𝑖𝑖− 𝑝𝑝) and the efficient level – 𝐾𝐾. The central bank minimises this function averaged over all firms and time periods. However, contract signers set wages in order to minimise deviations of the real wage from the equilibrium value of zero, not from the efficient level. Thus, their loss function can be approximated by (𝑤𝑤𝑖𝑖 − 𝑝𝑝)2. Since the wage 𝑥𝑥𝑡𝑡 is fixed for two periods, the contractors choose the following wage-setting rule:
𝑥𝑥𝑡𝑡 =12(𝑝𝑝𝑡𝑡+ 𝐸𝐸𝑡𝑡𝑝𝑝𝑡𝑡+1)
Therefore, the aggregate social loss function at time 𝑡𝑡 can be written as: 𝐿𝐿(𝑡𝑡) =12(𝑥𝑥𝑡𝑡− 𝑝𝑝𝑡𝑡+ 𝐾𝐾)2+12(𝑥𝑥𝑡𝑡−1− 𝑝𝑝𝑡𝑡+ 𝐾𝐾)2
Under steady money growth 𝐸𝐸𝑡𝑡𝑝𝑝𝑡𝑡+1= 𝑝𝑝𝑡𝑡+1 holds and inflation is stable, meaning 𝑝𝑝𝑡𝑡= 𝜇𝜇𝑡𝑡, where 𝜇𝜇 is a constant. For the real wages at 𝑡𝑡, this yields:
𝑥𝑥𝑡𝑡− 𝑝𝑝𝑡𝑡 =12 𝜇𝜇 and 𝑥𝑥𝑡𝑡−1− 𝑝𝑝𝑡𝑡= −12 𝜇𝜇
Hence, it can be shown that:
𝐿𝐿(𝑡𝑡) =𝜇𝜇2 4 + 𝐾𝐾2
Indexation is able to reduce this cost of inflation since an indexing firm can set 𝑤𝑤 = 𝑝𝑝 every period, thereby reducing the private loss to zero. This can be achieved if the contractors set the wage equal to prices in the first period and specify full adjustment for the second period. Accordingly, a higher degree of indexation has the potential to reduce the resistance of the population against inflation. Consequently, on one hand, monetary shocks lose their effectiveness because of stabilised real wages, but on the other hand, the latter reduces the costs of inflation itself. The authors conclude that, in their model, wage indexation causes higher inflation since the positive effect of reduced costs outweighs the anti-inflationary effect of a steeper Phillips curve (Ball & Cecchetti, 1991). More detailed model derivations are provided in appendix A.
Indexation to Past Inflation
Jadresic (2002) reconsiders both views mentioned in the previous two subsections under the more realistic assumption of indexation to lagged inflation. He argues that it is relatively more likely that indexation will increase inflation. In the context of indexation to lagged inflation, Milesi-Ferretti (1994) and Crosby’s (1995) argument that the inflation bias would decrease because the real economy is insulated from nominal shocks weakens significantly. Indeed, if wages are indexed to past inflation, real wages first decrease when a positive nominal disturbance occurs, regardless of the degree of indexation. Jadresic (2002) finds that the response of output to monetary shocks is significantly less dampened and it can even be reinforced. Consequently, the incentive for surprise inflation is notably higher. Given that the cost of inflation is also reduced when wages are indexed to past inflation, it is more likely that inflation increases in such a scenario.
Table 1: Overview of theoretical predictions
Indexation Type
Current Inflation Past Inflation
Inflation Level Ambiguous Ambiguous, but increase re- (↓inflation bias vs. ↓cost of latively more likely inflation) (↑inflation bias rel. to current inflation indexation)
Expected result for the empirical study
The aforementioned competing theoretical predictions regarding the effect of wage indexation on the inflation rate do not allow for definite conclusions. Nevertheless, they are central in evaluating the empirical results presented later in this paper since they allow for a proper interpretation. Indeed, a positive effect on the inflation rate can be interpreted in the light of Ball and Cecchetti (1991), whereas a negative effect will make the case for Milesi-Ferretti’s (1994) and Crosby’s (1995) predictions. As we will discuss in the following paragraph, automatic wage indexation in practise consists of linking current nominal wages to past inflation rates. Therefore, it is more likely, following Jadresic (2002), that the inflationary pressures arising from indexation outweigh its anti-inflationary effects. Hence, we expect to find a positive effect.
Wage Indexation in Practice Wage Indexation in Europe
After the Second World War, wage indexation was a widespread practise in many European countries. However, during the 1980s and early 1990s it was abolished in several countries including Denmark, France, Italy, the Netherlands, and Sweden in order to contain inflationary pressures (Calmfors & Joahnsson, 2006; Eurofound, 2010).
Belgium, Cyprus, Luxembourg, and Malta, however, still apply automatic indexation on a large scale (Eurofound, 2010). Furthermore, in Finland and Spain, indexation arrangements gained in importance after the instauration of the European Monetary Union (Calmfors & Johansson, 2006). Slovenia on the contrary abolished state imposed automatic wage indexation for the private sector during that same period (Du Caju, Gautier, Momferatou & Ward-Warmedinger, 2008).
Table 2 reports survey evidence on the importance of wage indexation for the 25 European countries included in our dataset.
Table 2: The importance of wage indexation in different countries
Automatic link to inflation at firm level (1)
Percentage of workers covered by indexation clauses (2)
Past Expected 1995 2006
Austria 8.6 1.3 0-25 0-25
Belgium 98.2 0.0 76-100 76-100
Bulgaria 7.9 2.5 / /
Czech Rep. 5.8 2.6 None None
Cyprus 38.7 2.1 51-75 51-75
Denmark / / None None
Estonia 2.6 1.3 None None
Finland / / 0-25 76-100
France 4.9 1.0 0-25 0-25
Germany / / None None
Greece 14.8 5.2 51-75 None
Hungary 7.2 4.2 None None
Ireland 2.4 2.8 None None
Italy 1.2 0.5 0-25 0-25
Latvia / / / /
Lithuania 7.3 3.7 / /
Luxembourg 100.0 0.0 76-100 76-100
Malta / / / /
Netherlands 0.0 0.0 None None
Poland 4.7 2.5 / 0-25
Portugal 2.7 6.5 None None
Slovakia 16.1 4.8 / /
Slovenia 20.3 2.7 76-100 26-50
Spain 38.3 16.2 51-75 76-100
UK / / / None
Notes: (1) Figures are in per cent. Firm-level policies, the figures are weighted by employment weights and
rescaled excluding non-responses of the survey. Data collected between mid 2007 and the beginning of 2008 (Sources: NBB (2012c) for Bulgaria, Cyprus, Luxembourg and Slovakia; Druant, Fabiani, Kezdi, Lamo, Martins and Sabbatici (2009) for the other countries). (2) Figures are in per cent. Data include workers in agriculture, industry, market services and non-market services sectors (Source: Du Caju et al., 2008).
Indexing countries
The results in table 2 indicate that six countries still apply or applied wage indexation on a larger scale between 1995 and 2008. These are Belgium, Cyprus, Finland, Luxembourg, Slovenia and Spain. Although survey evidence for Malta is not available, it can be considered as an indexing country as well (Eurofound, 2010). In the next subsection, the specific indexation mechanisms for these seven countries will be discussed in more detail. Information on indexation schemes in the remaining 18 countries is provided in appendix B.
Belgium
In Belgium, wages and social benefits are linked to the Health Index (CPI excluding tobacco, alcohol, and fuel prices) through an indexation scheme. It is mandatory for employers to adjust wages accordingly and while opt-out clauses exist, these are rarely used (Eurofound, 2010). In general, two groups can be distinguished. In the first group, which includes 40% of private sector employees, as well as public servants and social security beneficiaries, indexation takes place when the 4-month moving average of the Health Index exceeds a certain prefixed benchmark. For the remaining 60% of private sector employees, indexation takes place at fixed time intervals, mostly once a year (NBB, 2012a). In order to maintain the competitiveness of the Belgian economy, the government monitors the wage indexation process and tries to prevent upswings of relative labour costs. Currently, the forecasted increases in hourly labour costs in France, Germany, and the Netherlands are imposed as ceiling by the government for wage raises triggered by indexation (Eurofound, 2010). Du Caju et al. (2008) found that, in 1995 and 2006 respectively, 76-100 per cent of the workers in Belgium were covered by automatic wage indexation. Findings by Druant et al. (2009) support these results; for the period of mid 2007 to the beginning of 2008 98.2 per cent of the firms, weighted by employment, adjusted wages according to past inflation.
Cyprus
In Cyprus, wages of employees covered by collective agreements are automatically adjusted for CPI changes every six months. Even though, in theory, it only covers employees that are trade union members, in practice it applies to all of them (Eurofound, 2010). Du Caju et al. (2009) found that in 1995 and 2006 respectively, between 51 and 75 per cent of the workers
wage moderation was practised in the preceding years. In that context for example, in 2004 and 2005 wages were not increased in the semi-public sector (Eurofound, 2010).
Luxembourg
Luxembourg has an automatic indexation system imposed by the state. All wages and social benefits go up by 2.5 per cent when the 6-month moving average of the CPI increases by the same percentage, relative to its level when the previous indexation took place (Lünnemann & Wintr, 2009). The Tripartite Coordination Committee, a board consisting of four employer and four employee representatives, plus four government members, can suspend or postpone wage increases triggered by indexation. The committee assesses the economic situation of the country relative to Belgium, France, Germany, and the Netherlands and takes action if it seems necessary. This happened in 2006 for instance, when in order to slow down wage developments, indexation was suspended temporarily (Eurofound, 2010). Du Caju et al. (2008) strongly support the view of Luxembourg being a country that applies wage indexation on a large scale; in 1995 and 2006 the share of workers being subject to automatic indexation was between 76 and 100 per cent.
Malta
In Malta, wages and social benefits are adjusted on a yearly base with respect to Retail Price Index (RPI) changes. A board composed of a chairperson, the director of the National Statistics Office, two government officials, and two representatives of the industry and trade unions respectively, establishes this index. Indexation can be suspended with permission of the Ministry of Education, Employment and the Family if a company faces economic difficulties (Eurofound, 2010).
Spain
In contrast to the previously mentioned countries, legislation in Spain does not impose wage indexation. Nonetheless, most collective agreements include clauses that envisage indexation, but according to Eurofound (2010), with the difference that government forecast inflation instead of the past inflation rate is used to determine the magnitude of the pay raises (Eurofound, 2010). However, Druant et al. (2009) found that, for the period mid 2007-beginning 2008, 54.5 per cent of the firms, weighted by employment, applied automatic indexation, but mostly linked to past inflation (38.3% to past and 16.2% to expected inflation). This is the highest percentage of wages linked to the inflation forecast of all 15
countries that were included in Druant et al.’s (2009) study, but it still indicates that it is not the most common way to apply indexation in Spain. Eurofound (2010) points out that indexing wages to the government forecast has been introduced in order to reduce inflationary pressures. Furthermore, productivity increases and wage revision clauses in case of higher than expected inflation play a role in determining the magnitude of wage increases. It should be noted that if inflation falls short of the government forecast, this does not necessarily mean that pay raises decrease. For instance, in 2009 the forecast was 2 per cent, but actual inflation was -1 per cent. Consequently, some sectors increased wages by less than the formerly fixed 2 per cent. This lead to opposition from the trade unions and, in case the dispute went to the labour courts, it was often ruled in favour of the employees (Eurofound, 2010). As Calmfors and Johansson (2006) note, contracts containing indexation clauses have become especially widespread in Spain since the introduction of the Euro. Indeed, the share of workers covered by such contracts increased from 51-75 per cent in 1995 to over 75 per cent in 2006 (Du Caju et al., 2008).
Slovenia
According to Du Caju et al. (2008), Slovenia had a state imposed indexation system for the whole economy in 1995, but it has been abolished for the private sector by 2006. The ramifications of this measure becomes clear when comparing the percentage of workers covered by such clauses in the two years; while in 1995 more than 75 per cent of the wage contracts included an indexation clause, their share dropped to 26-50 per cent by 2006 (Du Caju et al., 2008).
Finland
As in Spain, wage contracts with indexation clauses became more common in Finland after the instauration of the European Monetary Union (Calmfors & Johansson, 2006). Whereas less than 25 per cent of the workers had indexed wage contracts in 1995, they accounted for more than 75 per cent in 2006 (Du Caju et al., 2008).
Figure 1: Wage indexation coverage in 1995 (left) and 2006 (right)
Note: Red: 76-100%, orange: 51-75%, darker yellow: 26-50%, brighter yellow: 0-25%, white: none, grey: no
data. (Source: Du Caju et al., 2008)
Inflation in indexing and non-indexing countries
Table 3: Average inflation rate for selected countries (1998 Q1 – 2014 Q1)
Belgium* Luxembourg* Austria France Germany Netherlands
2.03 2.49 1.87 1.67 1.55 2.08
Cyprus* Malta* Spain* Greece Italy Portugal
2.27 2.42 2.56 2.73 2.17 2.29
Slovenia* Czech Republic Hungary Poland Slovakia
4.21 2.52 5.79 3.74 4.59
Finland* Denmark Norway Sweden
1.93 1.90 1.83 1.45
Notes: Figures are in per cent. Countries that applied widespread wage indexation at least over part of the
considered time period are denoted by *. (Source: Eurostat)
Table 3 depicts the average yearly inflation rate between the first quarter of 1998 and the first quarter of 2014. The first row regroups Western and Central European countries.
Luxembourg had a considerably higher average inflation rate than other countries of that group, while Belgium had a higher inflation rate than three out of four non-indexing countries. In the second row, Southern European countries are regrouped. Malta and Spain had a higher average inflation rate than Italy and Portugal. The inflation rate for Cyprus was higher than for Italy, and only slightly lower than for Portugal. Nevertheless the highest average inflation rate was registered for Greece, a country we consider as a non-indexing country over the time period in question. However, as explained in a later paragraph we consider Greece as part of that group until 1997 Q3 (see paragraph “Methodology: The indexation variable”, table 5), thus shortly before the period in question for table 3. In the third row, we compare Eastern European countries. Two countries experienced a higher and two a lower average inflation rate than Slovenia. For the Nordic countries regrouped in the fourth row, we observe a higher inflation rate on average in Finland than for the other three countries.
Overall, in Western and Central, in Southern, and in Northern Europe we assert a trend for higher average inflation in countries that apply wage indexation rules on a larger scale, whereas the figures for Eastern Europe show a mixed tendency.
Previous Empirical Studies Multivariate time series approach
Hujer and Rodrigues (2008) investigated the effects of wage indexation on inflation in five countries, namely Luxembourg, Germany, France, Belgium and Spain. To do so, they estimated a system of two equations containing the labour cost index and the CPI as endogenous, and labour productivity, the unemployment rate and an import price index as exogenous variables. The used data are quarterly and range from January 1995 to January 2007. Since the logarithms of all variables prove to be non-stationary and the labour cost index and CPI are found to be cointegrated, a vector error correction model (VECM) of the following form is estimated:
Δ𝑤𝑤𝑡𝑡 = 𝛽𝛽 + � 𝛽𝛽𝑤𝑤,𝑖𝑖Δ𝑤𝑤𝑡𝑡−𝑖𝑖 𝑘𝑘 𝑖𝑖=1 + � 𝛽𝛽𝑝𝑝,𝑖𝑖Δ𝑝𝑝𝑡𝑡−𝑖𝑖 𝑙𝑙 𝑖𝑖=1 + � 𝛽𝛽𝑢𝑢,𝑖𝑖∆𝑢𝑢𝑡𝑡−𝑖𝑖 𝑚𝑚 𝑖𝑖=0 + � 𝛽𝛽𝑧𝑧,𝑖𝑖∆𝑧𝑧𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=0 + � 𝛽𝛽𝐼𝐼𝐼𝐼,𝑖𝑖∆𝐼𝐼𝑀𝑀𝑡𝑡−𝑖𝑖 𝑜𝑜 𝑖𝑖=0 + 𝛿𝛿𝑤𝑤(𝑤𝑤𝑡𝑡−1− 𝜃𝜃𝑤𝑤𝑝𝑝𝑡𝑡−1) + 𝜀𝜀𝑤𝑤,𝑡𝑡
Δ𝑝𝑝𝑡𝑡 = 𝛾𝛾 + � 𝛾𝛾𝑤𝑤,𝑖𝑖Δ𝑤𝑤𝑡𝑡−𝑖𝑖 𝑘𝑘 𝑖𝑖=1 + � 𝛾𝛾𝑝𝑝,𝑖𝑖Δ𝑝𝑝𝑡𝑡−𝑖𝑖 𝑙𝑙 𝑖𝑖=1 + � 𝛾𝛾𝑢𝑢,𝑖𝑖∆𝑢𝑢𝑡𝑡−𝑖𝑖 𝑚𝑚 𝑖𝑖=0 + � 𝛾𝛾𝑧𝑧,𝑖𝑖∆𝑧𝑧𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=0 + � 𝛾𝛾𝐼𝐼𝐼𝐼,𝑖𝑖∆𝐼𝐼𝑀𝑀𝑡𝑡−𝑖𝑖 𝑜𝑜 𝑖𝑖=0 + 𝛿𝛿𝑝𝑝(𝑤𝑤𝑡𝑡−1− 𝜃𝜃𝑝𝑝𝑝𝑝𝑡𝑡−1) + 𝜀𝜀𝑝𝑝,𝑡𝑡
All variables are expressed in logarithms. The CPI is represented by 𝑝𝑝, the labour cost index by 𝑤𝑤, the unemployment rate by 𝑢𝑢, labour productivity by 𝑧𝑧 and the import price index by 𝐼𝐼𝑀𝑀. Thereafter, the authors tested if wages Granger-cause prices. For Luxembourg and Belgium, considered full-indexation countries, France where the minimum wage is indexed, and Spain where a significant part of labour contracts contain indexation clauses, the null hypothesis of no Granger-causality was rejected at a 1 per cent level. Thus, they provided evidence for a causal effect of wages on prices in these four countries. However, for Germany, a country without any indexation, a p-value of 0.34 was obtained, thereby suggesting no causal effect of wages on prices. Additionally, impulse response functions for a shock on wages were estimated for Luxembourg and Germany. For the former, a shock of this type permanently increases the price level; a one per cent increase in wages increases prices by 0.125 per cent. For Germany, the effect of such a shock is not significantly different from zero. Based on these results, the authors concluded that indexation probably affects the price level.
Furthermore, the effect of indexation on the prices of 12 broad, respectively 40 more specific groups of products in Luxembourg was investigated. As a proxy for indexation, they use the so-called cote d’application, a time series that has constant value until a wage increase through indexation takes place, then it increases by 2.5 per cent and remains constant again until the next indexation event. For each of the 12 product groups, a vector autoregressive model (VAR) of the following form was estimated:
𝐶𝐶𝐶𝐶𝑡𝑡= 𝛽𝛽 + 𝛽𝛽𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛽𝛽𝑝𝑝𝑝𝑝𝑡𝑡−1+ 𝜀𝜀𝐶𝐶𝐶𝐶,𝑡𝑡 𝑝𝑝𝑡𝑡= 𝛾𝛾 + 𝛾𝛾𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛾𝛾𝑝𝑝𝑝𝑝𝑡𝑡−1+ 𝜀𝜀𝑝𝑝,𝑡𝑡
𝐶𝐶𝐶𝐶 stands for cote d’application and 𝑝𝑝 for the price of a product category. The results of Granger-causality tests showed a significant relation between indexation and prices in 7 of the 12 groups.
Moreover, by decomposing the 12 product groups further into 40 subgroups and estimating similar VAR models, the authors found a significant positive effect of the cote d’application on prices in half of these more specific groups (Hujer & Rodrigues, 2008). Thus, considering
individual product categories, it seems unclear if indexation generally triggers price increases.
The NBB (2012b) followed a similar approach as the previously mentioned authors in assessing how the presence of a wage indexation system in Belgium affects prices and wages. They estimated a VAR model including the variables in question. In order to avoid problems with non-stationarity, the data were converted to logarithms and enter the model in first differences. However, the authors did not test for a possible cointegration relationship between the two variables, i.e. they did not use a VEC-model. The following system of two equations was estimated for Belgium, France, the Netherlands and Germany:
Δ𝑤𝑤𝑡𝑡 = 𝛽𝛽 + � 𝛽𝛽𝑤𝑤,𝑖𝑖Δ𝑤𝑤𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=1 + � 𝛽𝛽𝑝𝑝,𝑖𝑖Δ𝑝𝑝𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=1 + 𝜀𝜀𝑤𝑤,𝑡𝑡 Δ𝑝𝑝𝑡𝑡 = 𝛾𝛾 + � 𝛾𝛾𝑤𝑤,𝑖𝑖Δ𝑤𝑤𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=1 + � 𝛾𝛾𝑝𝑝,𝑖𝑖Δ𝑝𝑝𝑡𝑡−𝑖𝑖 𝑛𝑛 𝑖𝑖=1 + 𝜀𝜀𝑝𝑝,𝑡𝑡
The price level is represented by 𝑝𝑝 and the wages by 𝑤𝑤. Quarterly data from the first quarter 1996 to the second quarter 2011 were used. After the estimation, impulse response functions for the effects of a one standard error inflationary shock were generated.
Figure 2: Accumulated response of wages and prices after a one standard error shock to inflation (in per cent)
Source: NBB 2012b
Over the studied period, Belgium, as previously mentioned, indexed its wages to the Health Index (HI; CPI excluding tobacco, alcohol and fuel energy) and not to the harmonised CPI (HCPI). Thus, it is not surprising that the wage response is more intense after a shock to the HI than to the HCPI. Despite indexation, the reaction of wages to a price shock is relatively slow compared to the neighbouring countries. This might be due to the fact that wages are not immediately adjusted for inflation but rather after a fixed period or if a certain benchmark value is exceeded. Concerning the neighbouring countries, it should be noted that the wage response is stronger in the Netherlands, while the adjustment is very weak and not significantly different from zero in France. In Germany, wages do not response to a price change. Regarding the price level, it can be observed that, compared to the other countries, Belgium experiences a very intense response and a certain degree of overshooting in the first year after the shock. Nonetheless, the persistence of the general price level, relative to the initial one-standard error shock, is higher in the neighbouring countries than in Belgium. Unfortunately, the authors did not include a visualisation of the effects of normalised shocks.
Generally, the results seem to indicate that an increase in wages is not fully transmitted to prices and/or that the effect of foreign prices on domestic inflation is important.
Figure 3: Elasticity of the per-hour wage to the HI and HCPI for Belgium and the HCPI for the other countries
Source: NBB 2012b
From the wage elasticity with respect to changes in price indices, it can be concluded that a change in the HI in Belgium is nearly entirely transmitted to wages, whereas a change in the HCPI has a significantly weaker effect. Furthermore, the Netherlands seems to have some form of implicit indexation since a change in the HCPI is nearly fully absorbed by wages. In France the effect is very weak and in Germany it is completely absent.
Overall, the authors conclude that the wage indexation system in Belgium has not lead to systematically higher wage increases, compared to the neighbouring countries, and that inflation is not more persistent (NBB, 2012b).
suggest that France cannot be considered as an indexing country since the indexation coverage was below 25 per cent in 1995 and 2006. Druant et al. (2009) find similar results; only 5.9 per cent of employment-weighted firms applied such contracts in 2007-2008. Finally, even if the national guaranteed minimum wage (SMIC) is partially indexed to the cost of living developments, the law prohibits the indexation of wages to the SMIC in collective agreements (Eurofound, 2010). An alternative interpretation is possible when considering the specific characteristics of Germany. The IMF (2012) emphasises that Germany practised wage moderation after the reunification and especially during the 2000’s, while many other European countries experienced a steady increase in wages. Thus, one could also argue that wages Granger-cause prices in countries in general, except if wage moderation is practised on a large scale.
An additional drawback of the studies by Hujer and Rodrigues (2008) and by the NBB (2012b) is that they consider individual countries and not a large-scale panel. This makes it harder to determine if findings are really due to wage indexation or if they are the consequence of another underlying economic mechanism.
To correct for these limitations, we will introduce several innovations compared to the previous studies. First, we will use a significantly larger sample that includes 25 European countries, compared to 5 (Hujer and Rodrigues, 2008) and 4 (NBB, 2012b) respectively, over a similar time period than the one covered by the previous studies. Second, we will explicitly include a variable that accounts for the presence of wage indexation in a country. We use survey evidence on the effective coverage of wage indexation from Du Caju et al. (2008) and Druant et al. (2009) to categorise countries in non-indexing and indexing countries. Third, and linked to the second point, we will not evaluate each country individually but rather use a panel data approach. This makes it possible to draw more general conclusions on the effect of indexation on inflation by reducing the risk of explaining a higher inflation rate in a country through the presence of wage indexation, whereas it might also be due to other economic circumstances. Finally, we will use a larger set of control variables. The authors of the NBB (2012b) study did not use any control variables, while Hujer and Rodrigues (2008) controlled for labour productivity, the unemployment rate and an import price index. Compared to the latter study, we exclude the import price index due to a lack of available data, whereas we additionally control for the real GDP growth rate, the degree of openness of the economy, the adoption of the Euro as national currency and the debt-to-GDP and deficit-to-GDP ratios of the government.
Methodology The indexation variable
To capture the presence of automatic wage indexation in a country, we construct a dummy variable that takes the value of 1 in case a country applies such rules on a large scale, and 0 otherwise. We consider countries that have a percentage of workers covered by such clauses of 51 per cent or more in the Du Caju et al. (2008) dataset as being indexing countries. These countries also have the highest shares of employment weighted indexing firms in the data provided by Druant et al. (2009) and the NBB (2012c). According to this rule, it is clear that Belgium, Cyprus, Luxembourg and Spain will be considered indexing countries throughout the whole time period we consider. For Malta, data on the coverage is not available. Nevertheless, from the description of Eurofound (2010), Malta can be generally considered an indexing country as well.
When applying the above stated rule, three more countries become salient. Slovenia and Greece experienced a large drop in indexation coverage, as opposed to Finland where the opposite trend was observable. As it is not possible to determine when precisely these countries entered or exited the indexing group (51% or more coverage), we will apply a simple method that most likely provides a good approximation on the indexation coverage between 1995 and 2006. In the following, the underlying assumptions for the estimated group exit/entrance quarters are presented.
(i) The coverage data of Du Caju et al. (2008) were collected exactly in the middle of the two years, so between the second and the third quarter. Hence, there are 44 quarters (1995 Q3 to 2006 Q2) between the two survey events.
(ii) 76-100% is equivalent to 87.5%, 51-75% to 62.5%, 26-50% to 37.5%, 0-25% to 12.5% and none to 0%.
(iii) If countries are not in the same groups in 1995 and 2006, then they move from one group to another in a linear way. Hence, the step from 12.5 to 0% takes only half as long as the steps from 87.5 to 62.5%, from 62.5 to 37.5% and from 37.5 to 12.5% respectively, since it is only half the distance. Additionally the two data collection events are assumed to have taken place when a country has passed half of its time in that group.
Table 4: Periods of indexation for Greece, Slovenia and Finland Greece Group 62.5% 37.5% 12.5% 0% Periods 8 16 16 4 Quarters 95Q3 – 97Q2 97Q3 – 01Q2 01Q3 – 05Q2 05Q2 – 06Q2 Slovenia Group 87.5% 62.5% 37.5% Periods 11 22 11 Quarters 95Q3 – 98Q1 98Q2 – 03Q3 03Q4 – 06Q2 Finland Group 12.5% 37.5% 62.5% 87.5% Periods 7 15 15 7 Quarters 95Q3 – 97Q1 97Q2 – 00Q4 01Q1 – 04Q3 04Q4 – 06Q2
Sources: Du Caju et al. (2008) and own calculations
Based on this, it can be concluded that Greece belongs to the indexing group until the third quarter of 1997 (which is earlier than the beginning of our samples). Slovenia leaves the indexing group after the third quarter of 2003. Finland belongs to the indexing group from 2001 Q1 on.
Data and models
We use quarterly data for 25 European countries from 1998 Q1 to 2014 Q1. The countries are Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain and the United Kingdom. All time series except debt and deficit ratios are seasonally adjusted (cf. end of this subsection). Moreover, it should be noted that the panel is unbalanced. All data are drawn from Eurostat, except for the UK inflation rates which originate from the OECD.
We will estimate an equation with the inflation rate as dependent variable and one with labour cost growth as dependent variable. Since we are interested in the effect of indexation on prices, it makes sense to not only estimate how wages influence prices but the inverse effect as well. Indeed indexation operates through the linking of wage developments to inflation.
The estimated dynamic panel data models (DPD models) with the inflation rate as dependent variable take the following form:
∆𝑝𝑝𝑖𝑖𝑡𝑡 = � 𝛼𝛼𝑝𝑝,𝑗𝑗 ∆𝑝𝑝𝑖𝑖𝑡𝑡−𝑗𝑗 8 𝑗𝑗=1 + � 𝛽𝛽𝑝𝑝,𝑘𝑘 ∆𝑤𝑤𝑖𝑖𝑡𝑡−𝑘𝑘 4 𝑘𝑘=1 + 𝛾𝛾𝑝𝑝 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡+ � 𝛿𝛿𝑝𝑝,𝑙𝑙 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡× ∆𝑤𝑤𝑖𝑖𝑡𝑡−𝑙𝑙 4 𝑙𝑙=1 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝,𝑖𝑖𝑡𝑡+ 𝜇𝜇𝑝𝑝,𝑖𝑖+ 𝜆𝜆𝑝𝑝,𝑡𝑡 + 𝜀𝜀𝑝𝑝,𝑖𝑖𝑡𝑡
The DPD models with labour cost growth as dependent variable take the analogue form:
∆𝑤𝑤𝑖𝑖𝑡𝑡 = � 𝛼𝛼𝑤𝑤,𝑗𝑗 ∆𝑤𝑤𝑖𝑖𝑡𝑡−𝑗𝑗 8 𝑗𝑗=1 + � 𝛽𝛽𝑤𝑤,𝑘𝑘 ∆𝑝𝑝𝑖𝑖𝑡𝑡−𝑘𝑘 4 𝑘𝑘=1 + 𝛾𝛾𝑤𝑤 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡+ � 𝛿𝛿𝑤𝑤,𝑙𝑙 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−𝑙𝑙 4 𝑙𝑙=1 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑤𝑤,𝑖𝑖𝑡𝑡+ 𝜇𝜇𝑤𝑤,𝑖𝑖+ 𝜆𝜆𝑤𝑤,𝑡𝑡+ 𝜀𝜀𝑤𝑤,𝑖𝑖𝑡𝑡
We omit contemporary values for variables that might suffer from simultaneous causality problems. ∆𝑝𝑝𝑖𝑖𝑡𝑡 captures country 𝑖𝑖’s inflation rate at time 𝑡𝑡 and is measured as the quarterly percentage change of the Harmonised Index of Consumer Prices (HICP). ∆𝑤𝑤𝑖𝑖𝑡𝑡 stands for the labour cost growth rate and is measured as Labour Cost Index (LCI) growth. Since the Eurostat LCI composition changed in 2000, we have two sub-samples. The first one runs from 1998 to 2008 and excludes labour costs in the public administration, while the second runs from 2000 to 2013 (except for Germany: 1996-2013) and includes these in the LCI. 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡 is a dummy variable that captures the presence of wage indexation in a country. 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝑡𝑡 contains variables that are likely to influence inflation and labour cost growth. In the following, we explain which variables are exactly in included as controls. Starting at 𝑡𝑡 − 1, the growth rate of labour productivity ∆𝐶𝐶𝑝𝑝𝑖𝑖𝑡𝑡, measured as real GDP per employed person, the unemployment rate 𝑈𝑈𝑈𝑈𝑖𝑖𝑡𝑡 and real GDP growth ∆𝑔𝑔𝑔𝑔𝑝𝑝𝑖𝑖𝑡𝑡 will be included. Additionally variables that are unaffected by inflation and for which we include only the contemporary values are also included, as the degree of openness of the economy 𝑂𝑂𝑝𝑝𝑂𝑂𝐶𝐶𝑖𝑖𝑡𝑡, measured by the ratio of exports plus imports to GDP and a dummy variable 𝐸𝐸𝑢𝑢𝐶𝐶𝐶𝐶𝑖𝑖𝑡𝑡 for being member of the EMU. Finally, the yearly average government debt 𝐼𝐼𝑂𝑂𝐷𝐷𝑡𝑡𝑖𝑖𝑡𝑡 and deficit 𝐼𝐼𝑂𝑂𝑓𝑓𝑖𝑖𝐷𝐷𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡 as a percentage of nominal GDP are included in the model. Including the contemporary values should not be a problem in terms of simultaneous causality since the effect of inflation on the denominator of both ratios is negligible for one year. We do not include seasonally adjusted values for the deficit because fluctuations are too intense to perform a reasonable adjustment.
non-indexing countries. Country-fixed effects are captured by 𝜇𝜇𝑖𝑖 and time-fixed effects by 𝜆𝜆𝑡𝑡 (one dummy variable per country and one per time period).
Estimation methodology
The standard approach to estimate panel data models is to use the Least Squares Dummy Variables (LSDV) method. It consists of adding a dummy variable for every entity and possibly for every time period as well to the equation of interest and perform the estimations using OLS. However, with DPD models, it is more complicated to decide which estimator is best suited and it strongly depends on the characteristics of the data in question. Judson and Owen (1999) pointed out that the Least Squares Dummy Variable (LSDV) for DPD models generates biased estimates if the number of observed time periods is small (typical for micro data). However, macro data normally has a higher time (higher T) and a lower cross-sectional dimension (lower N). This is of interest because the bias goes to zero as T goes to infinity. The authors gave a recommendation on which estimator to use for different N and T by comparing the OLS (without fixed effect dummy variables), the LSDV, a bias-corrected LSDV, the Anderson-Hsiao and two GMM estimators. They concluded that for the highest time dimension they investigate (T=30), the corrected LSDV estimator should be used. However, as this estimator might not be easily applicable to unbalanced panels in practice, the LSDV estimator would be the second choice. The recommendation was based on the bias comparison of the coefficient on the lagged dependent variable (𝛼𝛼’s in our case). This is the only criterion used since the bias for the exogenous regressor coefficients “are relatively small and cannot be used to distinguish between these estimators” (Judson & Owen, 1999). Given that our T is larger than 30 (on average 40 per country), that our panel is unbalanced, and that the coefficients of interest are mostly not on the lags of the dependent variable (𝛼𝛼’s), we will use the LSDV estimator.
To decide how many lags of each variable to include, we will use a general-to-specific approach; we will start by including 4 lags per variable (except for the dependent variable lags, see next paragraph), compare the lags that date back the longest for every variable and step-by-step delete the statistically least significant one. We will stop deleting dynamic terms of a variable when:
(i) a lag is significant at a 10% level, (ii) we arrive at the 𝑡𝑡 − 1 lag, or
(iii) when the coefficient on ∆𝑝𝑝𝑡𝑡−𝑖𝑖/∆𝑤𝑤𝑡𝑡−𝑖𝑖 is insignificant, but the coefficient on the corresponding interaction term is significant.
After we obtained the final model, an F-test is performed in order to guarantee that all dropped lags are jointly insignificant.
Furthermore, we use heteroskedasticity consistent standard errors. In order to prevent that we obtain autocorrelated error terms, we include 8 instead of 4 lags of the dependent variable as regressors. To test for possible autocorrelation, we apply a test developed by Wooldridge (2002). It is designed to test for AR(1) autocorrelation in panel models estimated with OLS and is operationalized the following way:
(i) Estimate 𝑦𝑦𝑡𝑡 = 𝑥𝑥𝑡𝑡𝛽𝛽 + 𝜀𝜀𝑡𝑡,
(ii) retain the obtained residuals 𝜀𝜀̂𝑡𝑡, (iii) estimate 𝑦𝑦𝑡𝑡 = 𝑥𝑥𝑡𝑡𝛽𝛽 + 𝜌𝜌𝜀𝜀̂𝑡𝑡−1+ 𝑂𝑂𝑡𝑡, (iv) perform a standard t-test on 𝜌𝜌�.
If we cannot reject the null hypothesis that the coefficient on 𝜀𝜀̂𝑡𝑡−1 is equal to zero, we can assume that autocorrelation does not pose a serious threat. It is worth noting that the obtained t-statistic is even valid if the regressors are not strictly exogenous (Wooldridge, 2002). We will report the test results at the end of every table.
Finally, it should be clear from the design of the 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥 variable that there is necessarily a high degree of imperfect multicollinearity since we also include country-fixed effect dummy variables (there is no perfect multicollinearity since Finland and Slovenia change from one group to another during the considered periods). As Stock and Watson (2012) point out, the OLS estimator will not be biased in the presence of imperfect multicollinearity if the standard assumptions hold, but the variances of the coefficients in question will be higher. Hence, it is possible that we falsely conclude that the coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥 is insignificant because of an inflated variance. Therefore, if we find for the LSDV estimation that the coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥 is insignificant, we will provide the results for the within-estimator in appendix C. For the latter method, the country average is subtracted from every observation, thereby removing the fixed-effect dummy variables from the estimated equations and thus eliminating the threat of a high degree of imperfect multicollinearity between the indexation and the country-fixed effect dummy variables. This will not alter the estimation of the coefficients; it will only
turn out that we do not fail to reject a null hypothesis of an insignificant coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥 because of collinearity (cf. appendix C).
Results
Tables 5 to 8 report an overview of the results most relevant for investigating the effects of wage indexation. The complete estimates including all control variables, the results for autocorrelation tests, F-test results for joint insignificance of the dropped lags, as well as information on the minimum, average and maximum numbers of observations per country, are provided in appendix D.
In column (1) the indexation dummy variable and interaction terms are excluded, in (2) the indexation dummy variable is included and the interaction terms excluded, in (3) the indexation dummy variable is excluded and the interaction terms included, and in (4) both the indexation dummy variable and the interaction terms are included.
Table 5: Labour cost growth (LCI data excluding public administration, 1998-2008)
Dependent variable: ∆𝑤𝑤𝑖𝑖𝑡𝑡 (1) (2) (3) (4) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 -0.1190 (0.5769) -0.5846 (0.6170) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−1 0.1983 (0.1790) 0.3241* (0.1750) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−2 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−3 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−4 ∆𝑝𝑝𝑖𝑖𝑡𝑡−1 0.1466 (0.0964) 0.1492 (0.0984) 0.1038 (0.1095) 0.0894 (0.1084) ∆𝑝𝑝𝑖𝑖𝑡𝑡−2 0.2788*** (0.1039) 0.2808*** (0.1051) 0.2832*** (0.1035) 0.2959*** (0.1047) ∆𝑝𝑝𝑖𝑖𝑡𝑡−3 0.0809 (0.1103) 0.0823 (0.1111) 0.0726 (0.1092) 0.0743 (0.1087)
∆𝑝𝑝𝑖𝑖𝑡𝑡−4 0.3016*** (0.1040) 0.3033*** (0.1046) 0.3033*** (0.1038) 0.3126*** (0.1039) 𝑈𝑈2 0.4064 0.4064 0.4076 0.4087 Number of observations 882 882 882 882
Notes: (i) Variables are expressed in per cent (except 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡). (ii) All estimates are obtained through the
LSDV method (OLS with one dummy variable per time period and one per country). (iii) Standard errors are reported in parentheses and are robust to heteroskedasticity. This makes it not possible to compute the adjusted 𝑈𝑈2; hence we report the standard version. (iv) We apply an autocorrelation test developed by Wooldridge (2002). We find no evidence for autocorrelation in any equation (see appendix D). (v) F-test results for joint insignificance of dropped lags are included in appendix D. (vi) Significance at the 10, 5 and 1% level is denoted by *, ** and *** respectively.
For the dataset excluding public administration from the LCI composition, we find that the inflation rates two quarters and four quarters back have a significantly positive effect on labour cost growth. Both have a positive effect on current labour cost growth of around 0.3 per cent for 1 per cent of inflation during that quarter, which corresponds to a positive effect of roughly 1.2 per cent over a year. However, we do not find a significant coefficient on the variable 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 in the equations (2) and (4). All other variables being equal to zero, there is no evidence that labour cost growth for the private sector is higher in indexing countries. Furthermore, we cannot find conclusive evidence that past inflation rates have a stronger effect in indexing countries. The coefficient on the interaction term in equation (3) is not significant while the one in equation (4) is only significant at a 10 per cent level. This might be due to the strong but insignificant negative effect of 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 in (4) that is counterbalanced by the positive effect of the interaction term. Overall, there seems to be no compelling evidence for a higher labour cost growth in the private sector in indexing countries.
Table 6: Labour cost growth (LCI data including public administration, 2000-2013)
Dependent variable: ∆𝑤𝑤𝑖𝑖𝑡𝑡 (1) (2) (3) (4) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 0.3263 (0.7241) -0.0305 (0.8185) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 -0.1759 -0.1739
𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−3 0.4638*** (0.1315) 0.4659*** (0.1308) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑝𝑝𝑖𝑖𝑡𝑡−4 ∆𝑝𝑝𝑖𝑖𝑡𝑡−1 0.1264 (0.0782) 0.1210 (0.0786) 0.1538 (0.0856) 0.1539* (0.0857) ∆𝑝𝑝𝑖𝑖𝑡𝑡−2 0.1528** (0.0774) 0.1472* (0.0779) 0.1681* (0.0887) 0.1682* (0.0888) ∆𝑝𝑝𝑖𝑖𝑡𝑡−3 -0.0352 (0.0904) -0.0351 (0.0904) ∆𝑝𝑝𝑖𝑖𝑡𝑡−4 𝑈𝑈2 0.4580 0.4582 0.4641 0.4641 Number of observations 974 974 974 974
Notes: (i) Variables are expressed in per cent (except 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡). (ii) All estimates are obtained through the
LSDV method (OLS with one dummy variable per time period and one per country). (iii) Standard errors are reported in parentheses and are robust to heteroskedasticity. This makes it not possible to compute the adjusted 𝑈𝑈2; hence we report the standard version. (iv) We apply an autocorrelation test developed by Wooldridge (2002). We find no evidence for autocorrelation in any equation (see appendix D). (v) F-test results for joint insignificance of dropped lags are included in appendix D. (vi) Significance at the 10, 5 and 1% level is denoted by *, ** and *** respectively.
When including public administration data in the LCI, we find that past inflation rates do not play such an important role than if the public administration is excluded. Indeed, the coefficients on inflation four quarters ago are highly insignificant in equations (1) to (4), while the coefficients on the inflation rate two quarters ago are only significant at a 10 per cent level in (2) to (4) and are only half as large as in table 5. The coefficients on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 in (2) and (4) are also not significant, suggesting that labour cost growth is not higher in indexing countries if all other variables are assumed to be zero. However, we find strong evidence that the inflation rate three quarters ago has a positive effect in indexing countries, compared to non-indexing countries. The coefficients on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡× ∆𝑝𝑝𝑖𝑖𝑡𝑡−3 are significant at a 1 per cent level in (3) and (4) and they are of the order of 0.5 per cent per quarter. Hence, a 1-percentage point increase in the inflation rate three quarters back increases labour cost growth by 0.5 percentage points in the current quarter in indexing countries, while it seems to have no significant effect in non-indexing countries.
Overall, we find that indexation does not affect labour cost growth in the private sector. Past inflation plays a similarly important role for indexing as for non-indexing countries in the development of labour costs. There seems to be some form of informal indexation in the private sector for the considered European countries.
However, when the public sector is included in the LCI, past inflation seems to have a strong effect on labour cost growth only in indexing countries. The general effect of past inflation becomes less statistically and economically significant. This suggests that the effect of automatic wage indexation on labour cost growth is particularly strong in the public sector.
Table 7: Inflation rate (LCI data excluding public administration, 1998-2008)
Dependent variable: ∆𝑝𝑝𝑖𝑖𝑡𝑡 (1) (2) (3) (4) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 0.4257*** (0.1465) 0.4310*** (0.1626) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−1 0.0279 (0.0290) -0.0030 (0.0305) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−2 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−3 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−4 ∆𝑤𝑤𝑖𝑖𝑡𝑡−1 0.0432*** (0.0156) 0.0426*** (0.0153) 0.0376** (0.0168) 0.0432** (0.0170) ∆𝑤𝑤𝑖𝑖𝑡𝑡−2 0.0433** (0.0175) 0.0449*** (0.0173) 0.0446*** (0.0176) 0.0448*** (0.0174) ∆𝑤𝑤𝑖𝑖𝑡𝑡−3 0.0370** (0.0167) 0.0384** (0.0167) 0.0379** (0.0166) 0.0383** (0.0166) ∆𝑤𝑤𝑖𝑖𝑡𝑡−4 0.0425** (0.0185) 0.0442** (0.0184) 0.0429** (0.0185) 0.0441** (0.0183)
Notes: (i) Variables are expressed in per cent (except 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡). (ii) All estimates are obtained through the LSDV method (OLS with one dummy variable per time period and one per country). (iii) Standard errors are reported in parentheses and are robust to heteroskedasticity. This makes it not possible to compute the adjusted 𝑈𝑈2; hence we report the standard version. (iv) We apply an autocorrelation test developed by Wooldridge (2002). We find no evidence for autocorrelation in any equation (see appendix D). (v) F-test results for joint insignificance of dropped lags are included in appendix D. (vi) Significance at the 10, 5 and 1% level is denoted by *, ** and *** respectively.
For the dataset excluding the public administration in the LCI, we find that labour cost growth one to four quarters ago has a positive effect on current inflation, while the coefficients on these variables are significant at least at a 5 per cent level. However, a 1-percentage point increase in the labour cost growth rate in one of the four quarters leads to an increase in the inflation rate of approximately 0.04 percentage points in the current quarter. This suggests that labour cost increases are only slowly passed through to the price level. Moreover, we cannot find evidence that labour cost growth has a stronger effect on the inflation rate in indexing countries since the coefficients on the interaction terms in (3) and (4) are not significant. Nevertheless, indexation has a strong positive effect since the coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 is significant in equations (2) and (4) and it is of the order of more than 0.4 per cent per quarter, or more than 1.7 per cent over a year.
Table 8: Inflation rate (LCI data including public administration, 2000-2013)
Dependent variable: ∆pit
(1) (2) (3) (4) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 0.6232*** (0.1656) 0.9657*** (0.2248) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−1 0.0094 (0.0335) -0.0227 (0.0351) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−2 -0.0765** (0.0311) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−3 -0.0597* (0.0317) 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 × ∆𝑤𝑤𝑖𝑖𝑡𝑡−4 ∆𝑤𝑤𝑖𝑖𝑡𝑡−1 0.0206 (0.0136) 0.0216 (0.0136) 0.0229 (0.0145) 0.0221 (0.0148) ∆𝑤𝑤𝑖𝑖𝑡𝑡−2 0.0429*** 0.0442*** 0.0386*** 0.0500***
(0.0125) (0.0123) (0.0134) (0.0131) ∆𝑤𝑤𝑖𝑖𝑡𝑡−3 0.0480*** (0.0142) 0.0494*** (0.0142) 0.0445*** (0.0152) 0.0535*** (0.0155) ∆𝑤𝑤𝑖𝑖𝑡𝑡−4 𝑈𝑈2 0.5260 0.5304 0.5261 0.5337 Number of observations 1090 1090 1090 1090
Notes: (i) Variables are expressed in per cent (except 𝐼𝐼𝐼𝐼𝐼𝐼𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡). (ii) All estimates are obtained through the
LSDV method (OLS with one dummy variable per time period and one per country). (iii) Standard errors are reported in parentheses and are robust to heteroskedasticity. This makes it not possible to compute the adjusted 𝑈𝑈2; hence we report the standard version. (iv) We apply an autocorrelation test developed by Wooldridge (2002). We find no evidence for autocorrelation in any equation (see appendix D). (v) F-test results for joint insignificance of dropped lags are included in appendix D. (vi) Significance at the 10, 5 and 1% level is denoted by *, ** and *** respectively.
In the dataset with public administration included in the LCI, the coefficients on labour cost growth one and four quarters back are not significant anymore, whereas the ones dating two and three quarters back are slightly higher than in table 7. In equation (2), the coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 is significant at a 1 per cent level and it is even higher than in table 7 with a value of around 0.6 per cent per quarter, or approximately 2.4 per cent per year. The interaction term coefficients are not significant in equation (3). However, the lagged interaction terms reaching two and three quarters back turn significant at a 5 and 10 per cent level respectively when 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 is added to the equation, as done in (4). Furthermore, they appear to be negative whereas the coefficient on 𝐼𝐼𝐶𝐶𝑔𝑔𝑂𝑂𝑥𝑥𝑖𝑖𝑡𝑡 becomes extremely high, suggesting an inflation rate that is one per cent higher per quarter in indexing countries if lagged labour cost growth rates are equal to zero and everything else is equal. The interaction term coefficients more or less neutralise the positive coefficients on lagged labour cost growth rates in indexing countries. Thus equation (4) suggests that labour cost developments are relatively less important in indexing countries when trying to explain inflation, while the latter is higher in general.
Overall, we do not find conclusive evidence that labour cost developments have a stronger effect on inflation in indexing countries. According to the results in table 8, equation (4) the opposite is even true. However, the results unambiguously point in the direction that
Discussion
As can be seen in tables 5 and 6, our findings suggest that indexing countries do not have a systematically higher labour cost growth. Furthermore, the results indicate that informal indexation is practised in the private sector in non-indexing countries since past inflation rates have a positive effect on current labour cost growth in general. This effect does not seem to be more pronounced in indexing countries. This is a very striking result, since it goes against the expectation that automatic indexation would, through its underlying mechanism, naturally influence labour cost growth more than in the case where it is absent. The underlying cause is probably a widespread practice of informal indexation. This might represent the fact that, according to the Du Caju et al. (2008) survey, prices are the most important determining factor entering wage negotiations.
However, when the public administration sector is included in the LCI composition, we find that in indexing countries past inflation affects present labour cost growth more positively than in non-indexing countries, where the effect greatly diminishes. From the aforementioned results, we can deduce that labour costs in the public administration are positively influenced by past inflation mainly in indexing countries. Automatic wage indexation seems to play a central role for the evolution of labour costs in the public administration, and not so much in the private sector. One explanation might be the more rigorous enforcement of indexation rules in the public sector, possibly due to a higher degree of centralisation. As previously mentioned, the inflation rate approximately 9 months ago seems to greatly influence labour cost growth when the public sector is considered as well. This approximately matches the functioning of indexation rules in practice; indeed wages are for example adjusted every 6 months in Cyprus, every 12 months in Malta (Eurofound, 2010) or when the 4-month moving average of the Health Index exceeds a certain benchmark for the Belgian public sector (NBB, 2012a). Overall, there is no evidence for a systematically higher labour cost growth in indexing countries and some evidence that past inflation has a stronger effect on labour costs, even though it seems to be mainly the case in the public sector. However, it should be noted that for a given higher inflation rate in indexing than non-indexing countries, labour cost growth will then also be higher in the those, even if the effect of the same inflation rate level is not different in both types of countries.
Concerning the effect of wage indexation on inflation, the results in tables 7 and 8 endorse more definite conclusions. From table 7, we can conclude that, ceteris paribus, the inflation rate is more than 0.4 per cent per quarter (or 1.7 per cent per year) higher in indexing countries than in non-indexing countries. From table 8, equation (2) we can draw a similar
