Wage-price pass-through in Switzerland

55 min read Original article ↗

Abstract

We analyse the historical relationship between consumer prices and wages in Switzerland. Our results show that, between 1980 and 2019, the pass-through from prices to wages was substantial. At the same time, nominal wage increases only had a modest effect on prices. Other factors—such as imported inflation, inflation expectations and economic slack—clearly dominate wages in explaining price movements in Switzerland. Second-round effects of inflation, in turn, are mainly explained by inflation expectations. Our results suggest that the pass-through from wages to prices could be higher in an environment of elevated inflation. However, even in the 1980s and 1990s, the pass-through was only modest. It follows that periods of simultaneously high inflation and high wage growth were not the result of a wage-price spiral. Instead, the long-term comovement of the two variables can mostly be explained by common drivers (e.g. inflation expectations, economic slack) and by the gradual adjustment of wages to prices.

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1 Introduction

Driven by supply bottlenecks and a sharp rise in energy prices, consumer price inflation started increasing strongly in 2021 and 2022, quickly reaching levels not seen for decades. While inflation in Switzerland remained clearly below the rates observed in other advanced economies, it soon exceeded the Swiss National Bank’s range of price stability (0–2%) and the question of inflation persistence arose. Little surprising, the rise in inflation had led to calls for marked increases in nominal wages. And because labour costs represent an important cost factor for most firms, this, in turn, raised concerns also in Switzerland about substantial second-round effects of inflation (i.e. additional inflationary pressure following the initial increases in pricesFootnote 1) or even the emergence of a wage-price spiral. Over the course of 2023, it became evident that these fears would not materialise, with inflation quickly falling again and no signs of a wage-price spiral. Importantly, throughout this paper, we define a wage-price spiral as strong feedback effects between prices and labour costs, leading to a self-reinforcing process that causes persistently high inflation (see also, BIS, 2022).Footnote 2 Hence, a wage-price spiral is the result of strong causal relationships between wages and prices. Comovements between wage and price growth that are driven solely by common factors, such as inflation expectations or economic slack, are not included in this definition.

From a policy perspective, understanding the feedback effects between consumer prices and wages is crucial in understanding the role of wages in inflation persistence. In this paper, we study the historical link between the two variables in Switzerland. In a first step, we analyse whether prices contain information about future movements of wages and vice versa. This is done by testing for cointegration and Granger causality. In a second step, we estimate the magnitude of the respective pass-throughs. For this purpose, we set up a structural vector error correction model, which allows us to quantify the effect of a price or labour costs shock and explore the role of wages as a potential cause of persistently higher inflation.

Overall, the international empirical literature only finds modest effects of wage growth on price inflation.Footnote 3 For the USA, the effect is often even found to be non-existent. For example, Gordon (1988) and Knotek II and Zaman (2014) conclude that neither wages nor prices Granger-cause the other variable. Similarly, Hess and Schweitzer (2000) and Hu and Toussaint-Comeau (2010) find that wages do not Granger-cause prices and that the ability of wages to predict future inflation is limited. However, they provide evidence that prices are helpful in forecasting wage developments. Other studies have been more successful in identifying causal effects of wages on prices for the USA. However, significant findings are generally limited to periods of high inflation (Mehra, 2000) or to the periods before 1980 (Emery & Chang, 1996) or the early 2000s (Heise et al., 2022). Peneva and Rudd (2017) also document that the pass-through of labour cost growth to price inflation diminished markedly over the decades. Looking at data until 2018, Bobeica et al. (2021) attribute the decline in the wage-price pass-through in the USA over the three preceding decades to an improved anchoring in inflation expectations, the changing constellation of shocks hitting the economy, increased trade integration and rising firm market power. Similarly, Heise et al. (2022) attribute the decline to rising import competition and increasing market concentration in manufacturing.

For the euro area, the link from labour costs to prices is found to be somewhat stronger. For example, Bobeica et al. (2019) provide evidence that labour cost growth Granger-cause price inflation contains some forecasting power for price inflation. IMF (2018) and Ampudia et al. (2024) also find a statistically significant pass-through from labour cost growth to consumer price inflation and producer price inflation, respectively. Evidence further suggests that the wage-price pass-through is state-dependent. The analysis by Bobeica et al. (2019) suggests that the dynamics between wages and prices depend on the state of the economy and the type of shocks and that the wage-price pass-through is lower in a low inflation environment. Similarly, Gumiel and Hahn (2018) suggests that the wage-price pass-through is different for supply shocks than for demand shocks, and Hahn (2020) finds that the wage-price pass-through is smaller in recessions than in expansions.

In quantitative terms, the wage-price pass-through estimates in the literature range from 0 to slightly above 0.5.Footnote 4 For example, for euro area economies, IMF (2018) report a pass-through of 0.25, while Bobeica et al. (2019) find pass-throughs of 0.4 to 0.7. In the analysis of Ampudia et al. (2024), the estimated pass-through reaches, on average, 0.5 at the sectoral level. For the USA, Heise et al. (2022) report pass-throughs of 0 (manufacturing sector) to 0.5 (service sectors and with a labour share of one). Again, the estimates can be state-dependent, are typically higher for the euro area (as opposed to the USA) and for producer prices or value-added deflators as opposed to consumer prices.

With the rise in inflation after the pandemic, wage-price dynamics came back into focus. Ampudia et al. (2024) and Chin and Lin (2023) document an increase in the wage-price pass-through during the post-pandemic inflationary period. At the same time, Blanchard and Bernanke (2023) argue that there is no need to discard existing models of wage-price dynamics. They find that the tight labour market conditions accounted for only a small part of the surge in US inflation following the pandemic. Similarly, Shapiro (2023) finds that the increase in wages played a negligible role in the increase in the core PCE measure at the time. Applying Blanchard and Bernanke (2023)’s methodology, Arce et al. (2024) conclude that in the euro area as well, contributions of the tight labour market conditions to the higher inflation after the pandemic were small.

For Switzerland, the literature on the wage-price pass-through is scarce. The only relevant contribution is Zanetti (2007). He investigates the empirical link between wages and consumer price inflation by means of Granger causality tests. Zanetti provides evidence that prices influence wages, independently of the sample period. He also finds an effect of wages on prices, but, in line with the international literature, this effect seems to vanish in low inflation periods.

Our paper extends the analysis of Zanetti (2007) along several dimensions. First, our approach not only allows us to make qualitative statements but also quantifies the degree of the wage-price pass-through for Switzerland, using an extended sample that covers a longer time period and uses new and revised data. Second, we explicitly incorporate a measure of inflation expectations for the analysis. This refinement enhances the understanding of the transmission between prices and wages and proves crucial in capturing the dynamics of the pass-through. Third, our approach allows us to shed light on the relative importance of the wage and inflation expectations channels in the second-round effects of inflation. By switching off one of these channels at a time, we can disentangle to what extent additional inflationary pressure after an initial inflationary shock is the result of firms passing on higher wage costs and to what extent it is the result of increased inflation expectations.

Overall, our results confirm the findings of Zanetti (2007) and are in line with the existing literature. Looking at the period from 1980 to 2019, we find that both wages and prices are informative about the future development of the other variable and that there are indeed some feedback effects. In particular, the estimated pass-through from prices to wages is substantial. The effect of labour cost increases on prices, on the other hand, is found to be modest (albeit significant), with an estimated pass-through of approximately one fourth. Other factors—such as imported inflation, inflation expectations and economic slack—clearly dominate wages in explaining price movements in Switzerland. Regarding second-round effects of inflationary shocks, we find that these propagate mostly via the inflation expectations channel, while the role of wages appears to be almost negligible. While our results suggest that the wage-price pass-through could be somewhat higher in an environment of elevated inflation, we only find a modest effect also in the 1980s and 1990s. Overall, our analysis implies that, in Switzerland, periods of simultaneously high inflation and high wage growth were not the result of a wage-price spiral. Instead, any long-term comovement of the two variables must have been mainly due to common drivers (e.g. inflation expectations, economic slack) and the gradual adjustment of labour costs to prices.

The structure of the paper is as follows. Section 2 sheds some light on the theoretical link between wages and prices. Section 3 takes a first look at the data. Section 4 covers the formal analysis of the relation between wages and prices, including some robustness tests. Finally, Sect. 5 concludes.

2 The basic links between wages and prices

According to economic theory, monopolistically competitive firms set their prices P as a mark-up \(\mu\) over marginal costs MC (see e.g. Dixit and Stiglitz, 1977):

$$\begin{aligned} P = MC \times (1 + \mu ) \end{aligned}$$

(1)

Marginal costs cover the costs of labour, capital and rents, as well as the expenses for raw materials and intermediate goods. The size of the mark-up typically depends on the degree of competition among firms and the state of the business cycle.

In the case of labour costs, marginal costs are given by nominal wages divided by the marginal productivity of labour. Under various standard assumptions (e.g. a Cobb-Douglas production function), marginal costs are equal to average costs and are thus given by the so-called unit labour costs (ULC). The latter are defined as labour costs per unit of output and are equal to nominal wages adjusted for labour productivity:

$$\begin{aligned} ULC = \underbrace{(W \times L)}_{\begin{array}{c} \text{total} \\ \text{labour} \\ \text{costs} \end{array}}/Y = W/\underbrace{(Y/L)}_{\begin{array}{c} \text{labour} \\ \text{produc-} \\ \text{tivity} \end{array}}, \end{aligned}$$

(2)

where W are nominal wages, L is labour and Y is real GDP. Importantly, an increase in nominal wages does not necessarily lead to higher cost pressures for firms. It is only when nominal wages grow in excess of real labour productivity—and thus unit labour costs increase—that cost pressures increase, which could force firms to increase sales prices to preserve their profit margins.

Price developments, in turn, affect nominal wages, or at least wage claims, as employees do not want to suffer a loss in real labour income. An increase in consumer prices will lead to calls for compensating wage increases. Similarly, expectations about higher prices in the future are likely to lead to higher wage claims already in advance. Thus, in addition to labour productivity (which is, according to standard economic theory, the main factor in the long-run determination of real wages), the price level is likely to be an important determinant of nominal wages:

$$\begin{aligned} W = (Y/L) \times P \times (1 + b) \end{aligned}$$

(3)

where b captures the bargaining power of workers, which typically depends on factors such as the workers’ outside options, firms’ profitability and labour market conditions (Layard et al., 2005). In Switzerland, the wage bargaining system is relatively decentralised compared to other European countries. According to OECD figures,Footnote 5 the share of employees who are members of a trade union has been steadily declining over the past 40 years, lying at 13% in 2023. At the same time, the share of employees covered by collective labour agreements was 50% in 2021. The collective agreements at the industry or sectoral level, however, usually only specify minimum standards for wages and working conditions, while individual firms often have the flexibility to negotiate wages directly with their employees or unions.Footnote 6

The price and wage setting considerations described above suggest that, in the long run, price developments are proportional to developments in nominal wages adjusted for productivity (i.e. unit labour costs):

$$\begin{aligned} P \propto ULC \end{aligned}$$

(4)

Note that the above relationship is consistent with a constant labour share and is valid only as long as there are no structural changes affecting, for example, the relative contribution of labour in the production process, workers’ bargaining power or firms’ mark-ups.

3 Some descriptive evidence

Looking at the data, Fig. 1, Panel 1, suggests that there is indeed a considerable comovement between prices and labour costs. It shows the year-over-year growth rates of the Swiss consumer price index (CPI) and unit labour costs, with unit labour costs calculated as nominal compensation of employees divided by real GDP. While growth in unit labour costs exhibits larger swings than CPI inflation, there seems to be a considerable comovement of the two series, especially in the first half of the sample. Importantly, this comovement does not necessarily imply that the periods of simultaneously high inflation and high wage growth were the result of a wage-price spiral, i.e. strong feedback effects between the two variables. They could equally have been the result of common drivers (e.g. inflation expectations, economic slack) or the fact that one of the two variables reacts to the other. Indeed, from simple visual inspection it appears that unit labour costs have a certain lag on price inflation.

On the other hand, Fig. 1, Panel 1, suggests that increases in wage growth were usually not followed by an increase in inflation. Considering the development of inflation during and after episodes of high ULC growth (e.g. in 1981/82, 1990/91 and 2000/01), these increases in ULC are, in most cases, not followed by an increase in inflation. On the contrary, inflation often declined. The only exception is the episode starting in 1986, where inflation increased after the rise in ULC growth. However, this increase could also have been driven by other factors, since the late 1980s were also characterised by high inflation abroad, a weakening Swiss franc and a highly positive output gap.

Looking at the data in levels, the CPI and ULC seem to have a common trend (see Fig. 1, Panel 2), suggesting that there is indeed a stable long-run relationship between the two variables (all series are seasonally adjusted). While there are periods of several years with diverging developments, the gaps tend to close again. Interestingly, the gaps between ULC and the CPI tend to be closed by adjustments in ULC rather than adjustments in the CPI. This conjecture is later confirmed in our estimation.

4 Empirical analysis

In this section, we examine the relationship between labour costs and prices in a more formal way. We first test whether there exists a long-term (cointegrating) relationship between prices and unit labour costs. Then, we use Granger causality tests to gain some first insights into the direction(s) of causation (for these first two steps, we follow Mehra, 1993). Finally, to explore the historical wage-price pass-through, we estimate a wage-price system in the form of a structural vector autoregression in error correction form.

Our baseline analysis covers the period from 1980Q1 to 2019Q4. We deliberately exclude the COVID-19 period from the sample as it led to some distortions in the data, which could potentially bias the results. In the robustness section, we discuss the COVID-19 period and the subsequent inflationary episode in more detail.

4.1 Cointegration analysis

The strong comovement of prices and unit labour costs that we observe in Fig. 1 suggests that there is a long-run relationship or cointegration among the two variables, namely, that their linear combination is stationary. Formally, we examine the long-run comovement of labour costs and prices using the Johansen test for cointegration (Johansen & Juselius, 1990). This test is a procedure to determine the number of cointegrating relationships among a set of time series, based on a vector autoregressive model (VAR). In our case, the starting point for this test is a VAR model for prices and unit labour costs:

$$\begin{aligned} Y_t = \nu + \varPsi _1 Y_{t-1} + ... + \varPsi _q Y_{t-q} + e_t \end{aligned}$$

(5)

\(Y_t\) is a vector containing the levels of prices \(p_t\) and unit labour costs \(ulc_t\) (lower-case letters denote logs). In our baseline specification, \(p_t\) is equal to the headline CPI, which is the price measure most relevant from a policy perspective. The two-by-two matrices \(\varPsi _i,i=1,...,q\) contain the coefficients.

The Johansen test requires the variables to be difference stationary, i.e. to be integrated of order 1. In our case, both the CPI and ULC meet this requirement. The Augmented Dickey Fuller (ADF) test fails to reject the null hypothesis of a unit root for the levels, but clearly rejects it for the first differences (see Table 1). Given that the time series in \(Y_t\) are difference stationary, the system of equations in (5) can then be transformed into a vector error correction model (VECM) (\(\varDelta\) denotes the first difference):

$$\begin{aligned} \varDelta Y_t &= \nu + \varTheta _1 \varDelta Y_{t-1} +... + \varTheta _{q-1} \varDelta Y_{t-q+1} + \varPi Y_{t-1} + e_t, \nonumber \\ \text {with } \quad \varTheta _i& = - \varPsi _{i+1} -... - \varPsi _{q} \nonumber \\\quad \text { for } \quad i &= 1,..., q-1, \quad \text { and } \quad \varPi = \varPsi _1 +... + \varPsi _q - I \end{aligned}$$

(6)

The matrix \(\varPi\), associated with the first lag of the levels, contains information about the long-run properties of the model. In particular, its rank corresponds to the number of cointegrating relations among the variables. If the rank of this matrix is zero, the time series are not cointegrated, i.e. there is no long-run relationship between the levels of the time series. In this case, Equation (6) reduces to a VAR in first differences. However, if the rank of \(\varPi\) is equal to one, there exists a unique independent combination of the series in \(Y_t\) that is stationary. In other words, there is a long-run (cointegrating) relationship between the series.

Table 1 Unit root tests

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Johansen and Juselius (1990) proposed two test statistics for testing the existence of a cointegrating relationship. The “trace test” examines the rank of the \(\varPi\) matrix. It tests the null hypothesis that \(\text {rank}(\varPi ) \le r\), where r represents the number of cointegrating vectors. The “maximum eigenvalue test” evaluates the null hypothesis that the number of cointegrating vectors is equal to r against the alternative hypothesis of \(r + 1\) vectors.

Table 2 Cointegration tests

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The cointegration test results are displayed in Table 2. Both the trace and the maximum eigenvalue test statistics indicate that our time series are cointegrated: the null hypothesis of no cointegrating vector is rejected in all cases, suggesting that there is a long-run relationship between labour costs and the CPI. Although not reported, the results of alternative tests of cointegration, namely the Engle-Granger test, confirm the existence of a stationary linear combination of the two variables (at least at the 10% significance level).

While we use the Johansen procedure to determine the number of cointegration relations, as it is appropriate for identifying multiple cointegration vectors, we estimate and analyse the cointegration relationship between labour costs and prices using the dynamic OLS procedure suggested by Stock and Watson (1993). This method is chosen because it provides more efficient estimates and standard errors, especially in smaller samples where finite sample biases can be more pronounced. The dynamic OLS procedure is an extension of traditional OLS and accounts for autocorrelation in the data by including leads and lags of the changes in the explanatory variables. In our case, the regressions are as follows:

$$\begin{aligned} p_t&= a_0 + a_1 ulc_t + \sum ^{k}_{s=-k} a_{2k} \varDelta ulc_{t-s} + u_{1t}\end{aligned}$$

(7)

$$\begin{aligned} ulc_t&= b_0 + b_1 p_t + \sum ^{k}_{s=-k} b_{2k} \varDelta p_{t-s} + u_{2t}, \end{aligned}$$

(8)

The estimated slope coefficients are reported in Table 3. They are very close to unity, implying that, in the long term, consumer prices and ULC move almost perfectly in parallel. In view of this, for the remainder of the analysis, we fix \(\delta\) in

$$\begin{aligned} p_t= \delta ulc_t + u_t \end{aligned}$$

(9)

to one. In other words, we fix the cointegration vector, given by \([ 1, -\delta ]\), to \([ 1, -1]\), yielding the following cointegrating relation: \(p_t= ulc_t + u_t\). Because the slope coefficients are not statistically different from this value, this is a reasonable assumption to make.

Table 3 Cointegration relation

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4.2 Granger causality analysis

The analysis in the previous section confirmed the presence of a long-run relationship between labour costs and prices, indicating that at least one of the two variables adjusts whenever they substantially deviate from one another. To understand how this convergence takes place, we need to study the dynamics of the model in more detail. We can gain some first insights into the dynamic relationships at play by applying Granger causality tests to our system of equations. Given that we find evidence of cointegration between labour costs and prices, there must be Granger causation in at least one direction (Granger, 1988).

Besides applying the test directly to the basic system of equations (6), we also test for Granger causality in an augmented, more general system that controls for further potential drivers of wage and price dynamics. These drivers are taken as exogenous. They are summarised in the vector \(Z_t\). The augmented system is given by:

$$\begin{aligned} \varDelta Y_t = \nu +\varTheta _1 \varDelta Y_{t-1} + ... + \varTheta _{q-1} \varDelta Y_{t-q+1} + \varPi Y_{t-1} + \varLambda Z_t + e_t, \end{aligned}$$

(10)

Written out, we thus have the following system of equations:

$$\begin{aligned}\begin{bmatrix} \varDelta p_t \\ \varDelta ulc_t \end{bmatrix}& = \begin{pmatrix} \nu _{p} \\ \nu _{ulc} \end{pmatrix} + \begin{pmatrix} \theta _{p,p,1} & \theta _{p,ulc,1} \\ \theta _{ulc,p,1} & \theta _{ulc,ulc,1} \end{pmatrix} \begin{bmatrix} \varDelta p_{t-1} \\ \varDelta ulc_{t-1} \end{bmatrix}\\\quad & \quad+...+ \begin{pmatrix} \theta _{p,p,q-1} & \theta _{p,ulc,q-1} \\ \theta _{ulc,p,q-1} & \theta _{ulc,ulc,q-1} \end{pmatrix} \begin{bmatrix} \varDelta p_{t-q+1} \\ \varDelta ulc_{t-q+1} \end{bmatrix} \nonumber \\&\quad - \begin{pmatrix} \alpha _{p} & \\ \alpha _{ulc} \end{pmatrix} \begin{pmatrix} 1&-\delta \end{pmatrix} \begin{bmatrix} p_{t-1} \\ ulc_{t-1} \end{bmatrix} \\&\quad + \begin{pmatrix} \lambda _{p,\pi ^e} & \lambda _{p,gap} & \lambda _{p,\pi ^I} \\ \lambda _{ulc,\pi ^e} & \lambda _{ulc,gap} & \lambda _{ulc,\pi ^I} \end{pmatrix} \begin{bmatrix} \pi ^{e}_t \\ gap_{t-1} \\ \pi ^{I}_t \end{bmatrix} + \begin{bmatrix} e_{p,t} \\ e_{ulc,t} \end{bmatrix}, \nonumber \\&\quad \text {where } \begin{bmatrix}1&-\delta \end{bmatrix} \begin{bmatrix}p_{t-1}\\ ulc_{t-1} \end{bmatrix} \\\quad &= p_{t-1} - \delta ulc_{t-1} = cr_{t-1} \text { (cointegration residual)} \end{aligned}$$

The \(\alpha\) coefficients are the adjustment coefficients, capturing the reaction of \(p_{t}\) and \(ulc_{t}\) to deviations from their long-run relationship, captured by the cointegrating residual \(cr_{t-1}\) (recall that we fix \(\delta\) to one in our baseline specification).

In \(Z_t\), we include three control variables: i) a survey-based measure of inflation expectations, \(\pi ^{e}_t\), ii) an output gap measure, \(gap_{t-1}\), as indicator for the state of the economy, and iii) imported consumer price inflation, \(\pi ^{I}_t\), where each CPI product is weighted by its import share (published by the Swiss Federal Statistical Office, SFSO). Adding this measure of imported consumer price inflation to the regression model allows us to simultaneously capture the effect of foreign inflation and variations in both the oil price and the exchange rate while at the same time keeping the model parsimonious. Our measure of inflation expectations (\(\pi _t^e\)) is based on SECO’s household survey question on expected price changes.Footnote 7 As measure of slack, we use the output gap estimate based on the production function approach as published by the SNB. We take the first lag as this gives us the best fit. In addition, we can rule out endogeneity problems in this way.

Table 4 Granger causality tests

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The results of the Granger causality tests are displayed in Table 4. In rows (Ia) and (Ib), the short-run coefficients (\(\theta\)’s, associated with the first differences) and the long-run coefficient (\(\alpha\), associated with the cointegration residual) are tested jointly. The null hypothesis of no Granger causality is rejected for both directions and both specifications, i.e. both in the basic system without control variables (\(\varLambda =0\), where \(\varLambda\) is the coefficient matrix of the exogenous variables) as well as in the augmented system with control variables (\(\varLambda \ne 0\)). This suggests that prices help to predict productivity-adjusted wage changes while at the same time, ULC provide useful information on future CPI movements. Testing the short-run and long-run coefficients separately (see rows (II) and (III), respectively), we find that gaps in the long-run relationship between prices and ULC are closed by adjustments in ULC (see row (IIIb)). Prices, on the other hand, seem not to be affected by the cointegration residual (row (IIIa)). Looking at the specification that includes the control variables, which according to a Wald test on joint significance are highly relevant, it appears that for prices, only the most recent movements of ULC are informative, i.e. their first lag (see row (IIa)).

4.3 Structural VECM

The Granger causality tests in the previous section provided evidence that both prices and ULC contain information about future movements of the other variable. In addition to this qualitative finding, the crucial question for policymakers is the magnitude of the respective pass-throughs, especially of the pass-through from wage increases to prices. To address this question, we build a structural VECM, which allows us to quantify the effect of a price or labour costs shock:

$$\begin{aligned} B_0\varDelta Y_{t}=\mu +B_1\varDelta Y_{t-1} + ... + B_{q-1}\varDelta Y_{t-q+1} + \varPhi Y_{t-1}+\varGamma Z_{t}+\varepsilon _{t} \end{aligned}$$

(11)

Our structural VECM is an extension of the above VECM (Eq. 10). Unlike in the reduced-form VECM, we treat inflation expectations as endogenous in the identified system. This gives us more meaningful impulse response functions as it is well-known from the literature that short-term inflation expectations are likely to respond to recent price developments. With exogenous inflation expectations, inflation dynamics in the impulse response functions would be conditioned on the realised values for inflation expectations. Hence, inflation expectations \(\pi _t^e\) are now part of the vector \(\varDelta Y_t\). The cointegration relation, on the other hand, is left unchanged.Footnote 8 As control variables (\(Z_t\)), we again include the output gap and imported consumer price inflation.Footnote 9

Written out, our structural VECM is represented by the following three-equation system (here, the number of lags is set to one, which will turn out to be optimal):

$$\begin{aligned} & \left[ {\begin{array}{*{20}c} 1 & {- \eta _{{p,ulc}} } & {- \eta _{{p,\pi ^{e} }} } \\ 0 & {1} & {- \eta _{{ulc,\pi ^{e} }} } \\ 0 & {0} & {1} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\Delta p_{t} } \\ {\Delta ulc_{t} } \\ {\pi _{t}^{e} } \\ \end{array} } \right] \\ & = \left[ {\begin{array}{*{20}c} {\mu _{p} } \\ {\mu _{{ulc}} } \\ {\mu _{{\pi ^{e} }} } \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {\beta _{{p,p}} } & {\beta _{{p,ulc}} } & {\beta _{{p,\pi ^{e} }} } \\ {\beta _{{ulc,p}} } & {\beta _{{ulc,ulc}} } & {\beta _{{ulc,\pi ^{e} }} } \\ {\beta _{{\pi ^{e} ,p}} } & {0} & {\beta _{{\pi ^{e} ,\pi ^{e} }} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\Delta p_{{t - 1}} } \\ {\Delta ulc_{{t - 1}} } \\ {\pi _{{t - 1}}^{e} } \\ \end{array} } \right]\quad \\ & + \left[ {\begin{array}{*{20}c} {\phi _{p} } \\ {\phi _{{ulc}} } \\ 0 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} 1 & {- \delta } & {0} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {p_{{t - 1}} } \\ {ulc_{{t - 1}} } \\ {\tilde{p}_{{t - 1}}^{e} } \\ \end{array} } \right]\quad \\ & + \left[ {\begin{array}{*{20}c} {\gamma _{{p,gap}} } & {\gamma _{{p,\pi ^{I} }} } & {0} \\ {\gamma _{{ulc,gap}} } & {\gamma _{{ulc,\pi ^{I} }} } & {0} \\ {\gamma _{{\pi ^{e} ,gap}} } & {0} & {\gamma _{{\pi ^{e} ,d}} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {gap_{{t - 1}} } \\ {\pi _{t}^{I} } \\ {d_{t} } \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {\varepsilon _{{p,t}} } \\ {\varepsilon _{{ulc,t}} } \\ {\varepsilon _{{\pi ^{e} ,t}} } \\ \end{array} } \right], \\ \end{aligned}$$

$$\begin{aligned} \text {where } \begin{bmatrix}1&-\delta&0\end{bmatrix} \begin{bmatrix}p_{t-1}\\ ulc_{t-1}\\ \tilde{p}_{t-1}^{e} \end{bmatrix} = p_{t-1} - \delta ulc_{t-1} = cr_{t-1} \end{aligned}$$

The \(\varepsilon _{t}\) terms represent the structural shocks. Identification of the shocks is achieved through zero restrictions in the \(B_0\) matrix. In particular, shocks to inflation are assumed to have no contemporaneous effect on ULC growth.Footnote 10 In addition, shocks to inflation and ULC growth are assumed to have no contemporaneous effect on inflation expectations. Given that SECO’s household survey, on which our measure of inflation expectations is based, is conducted at the very beginning of each quarter (and, importantly, before the publication of the quarter’s first monthly inflation figure), this is a reasonable assumption.

Note that, besides the zero restrictions implemented for the identification of the shocks, we impose some further restrictions in the inflation expectations equation. First, following the reasoning on the exclusion of contemporaneous effects of inflation on inflation expectations, we assume that imported consumer price inflation also has no direct, that is contemporaneous, effect on inflation expectations.Footnote 11 In addition, we also set the coefficients on the cointegration residual and lagged ULC to zero. If not restricted, both turn out to be insignificant, with no noticeable effect on the results. Unlike in the other two equations, we include a time dummy \(d_t\) in the inflation expectations equation. It accounts for the fact that, over the past 25 years, average inflation has been, together with other nominal variables, significantly lower than in the 1980s and early 1990s.Footnote 12

Each equation of the VECM is estimated by ordinary least squares. Given the recursive structure of the model, this yields consistent coefficients. According to the AIC, one is the optimal number of lags to be included. Higher lags are mostly insignificant and have no noticeable impact on the results.

4.4 Results of the structural VECM

Table 5 Structural VECM

Full size table

In this section, we discuss the results of our baseline specification, with \(p_t\) equal to CPI inflation, the above-mentioned control variables and the estimation sample covering the whole sample period. Alternative specifications and results based on subsamples are presented in the next section.

The estimated regression coefficients are displayed in Table 5. While we cannot read the various pass-throughs from these coefficients directly, they still provide some interesting initial insights. Confirming the results of the previous section, the estimated adjustment coefficients (attached to the cointegration residual) suggest that it is mainly the ULC that respond to the cointegration residual, i.e. to deviations of prices and ULC from their cointegrating relationship. That is, wages tend to increase whenever the price level has increased by more than the level of labour costs. The adjustment coefficient in the ULC equation suggests that 16% or 1/6 of the gap is closed each year purely by changes in ULC.Footnote 13 The according coefficient in the inflation equation is much smaller in absolute terms and less significant than in the ULC equation. Looking at the relative size of the adjustment coefficients, a simple back-of-the-envelope calculation tells us that prices account for only approximately 15% of the adjustment, while ULC account for the remaining 85%. The movements in CPI inflation appear to be due more to the short-term dynamics of the other variables.Footnote 14

Regarding the control variables, the signs of the estimated coefficients in the inflation equation are in line with economic intuition. In the ULC equation, it is less clear what signs to expect in the first place. For example, an economic upturn usually comes along with a tightening of the labour market, i.e. upward pressure on wages and ULC, but also with higher labour productivity, which in turn dampens ULC. Our set-up does not allow us to differentiate between the various channels. Looking at the estimated coefficients, it appears that the output gap captures the effect of the labour market conditions, while the imported inflation, which is likely to be correlated with general demand conditions, may capture the labour productivity effect.

Fig. 2

Impulse responses to a 1% price shock

To assess the extent of the wage-price pass-through, we calculate the impulse responses of prices and unit labour costs, i.e. the cumulative responses of price inflation and unit labour cost growth to shocks to both variables.Footnote 15 Fig. 2 shows the responses of the CPI and ULC to a price shock. Our results suggest that, between 1980 and 2019, the pass-through of CPI increases to ULC was substantial. A price shock has a permanent effect on the CPI and leads to a gradual adjustment in ULC. A shock that, on impact, increases the CPI by 1% leads to an around 1.3% higher CPI in the long run. The long-run effect on ULC is of similar size, a result that is explained by the long-run relationship linking the two variables.

The fact that the final level of the CPI is higher than right after the initial shock suggests the presence of second-round effects. With the simultaneous acceleration in wage growth, one might be inclined to interpret this pattern as a wage-price spiral. However, even though inflation remains slightly elevated for extended period of time, it decreases very quickly after the initial shock (see Fig. 9 in Appendix); the increase is thus not “persistent”. In addition, and more importantly, these figures do not tell us to what extent the second-round effects on inflation are actually the result of the increase in wages. They could also be due to some persistence in inflation itself (e.g. due to the spread of price increases to goods and services not affected by the initial shock) or due to an increase in inflation expectations.

Fig. 3

Impulse responses to a 1% price shock: importance of different channels

To gauge the relative importance of the wage channel and the inflation expectations channel in the second-round effects of inflation, we compute two further versions of the price level response, with one of the channels being switched off in each version. To this end, we take again the coefficients of our baseline estimation, but set the coefficients related to the two channels to zero. Namely, to switch off the wage channel, we assume that neither changes in ULC nor their level have an effect on price inflation (i.e. \(\eta _{p,ulc}\), \(\beta _{p,ulc}\) and \(\phi _{p}\) are set to zero). To switch off the inflation expectations channel, we assume that inflation expectations have neither a direct nor indirect (via wages) effect on price inflation (i.e. \(\eta _{p,\pi ^{e}}\), \(\eta _{ulc,\pi ^{e}}\), \(\beta _{p,\pi ^{e}}\) and \(\beta _{ulc,\pi ^{e}}\) are set to zero). From Fig. 3, we can conclude that the wage channel plays an almost negligible role in the second-round effects of inflation. The inflation expectations channel, on the other hand, appears to be crucial: if switched off, the price level does not increase further after the initial shock (it even slightly falls as prices react to the cointegration residual), suggesting that second-round effects after an inflationary shock are mostly the result of increased inflation expectations.

The finding that wages have only a modest effect on prices is confirmed when we study the effects of a shock to ULC. Figure 4 shows that the cumulative response of the CPI to increases in unit labour costs is statistically significant but modest. While prices increase somewhat after an ULC shock, the total pass-through is limited. A shock that, on impact, increases ULC by 1% leads to an approximately 0.25% higher CPI in the long run, implying a pass-through of 0.25.Footnote 16 In line with a stable long-run relationship between the two variables, the effect of a shock to ULC on themselves is therefore mostly temporary. Right after the shock, the effect first becomes stronger but then starts to decline after two quarters, slowly converging towards a similar effect as on the CPI.Footnote 17 This result clearly suggests that any gap between unit labour costs and the price level is mostly closed by an adjustment in unit labour costs and not in the price level (as previously discussed).

Fig. 4

Impulse responses to a 1% ULC shock

The low wage-price pass-through in Switzerland may come as a surprise at first. Indeed, it suggests that Swiss firms accept, at least temporarily, a substantial squeeze in their mark-ups after a unit labour cost shock. However, at least in the medium term, the low pass-through does not necessarily need to be accompanied by lower firm mark-ups, even if the CPI response is lower than the response of ULC for an extended period of time. In fact, a low pass-through to the CPI seems plausible when taking into account a number of—partly Swiss-specific—factors. First, with Switzerland being a small open economy, a substantial share of goods entering the Swiss CPI is imported. According to the SFSO, the import share in the total CPI was approximately 25% on average over the past 40 years.Footnote 18 For imported goods, Swiss labour costs should only play a minor role in the final price. Indeed, we find a higher pass-through when replacing the total CPI by the domestic CPI (as will be discussed in the robustness section). Conversely, given that an important part of Swiss production is exported, a significant part of Swiss labour costs will be relevant for export prices rather than for domestic consumer prices. Second, regarding the domestic components of the CPI, labour costs have no direct effect on large parts of them. This holds especially for the two categories “rents” and “health”, which together account for almost 40% of the total CPI. While rents do not (or only marginally) depend on labour input, the prices of health services consist to a large part of administered prices with no direct link to labour costs. Third, for all other goods and services mainly produced in Switzerland, labour is only one of several production factors. Hence, as long as the prices of the other production factors remain unchanged, the increase in total costs and hence the justifiable increase in the final prices of domestic goods and services is smaller than the original increase in labour costs. The data strongly support this hypothesis. In a simple exercise, we replace the total CPI by the services CPI or the goods CPI, respectively. The results in Fig. 5, Panel 2, show a considerably higher pass-through of ULC increases to service prices (0.58 after 12 quarters) but no pass-through at all to goods prices, suggesting that the labour intensity behind CPI items is an important factor for the size of the wage-price pass-through.Footnote 19

Fig. 5

Impulse responses: services versus goods CPI

The only modest wage-price pass-through estimate suggests that, in Switzerland, episodes of simultaneously high inflation and high wage growth were not the result of a wage-price spiral. For a wage-price spiral to emerge, the pass-through would need to be substantial in both directions. With a pass-through clearly below one, an unanticipated increase in one of the two variables will be followed by second-round effects, but these effects will fade out relatively quickly and not lead to a lasting effect on the level of inflation (and wage growth). Given our modest estimate for the wage-price pass-through, any long-term comovement of the two variables must have been rather due to common drivers (e.g. inflation expectations,Footnote 20 economic slack) and the gradual adjustment of ULC to the CPI.

Fig. 6

Historical decomposition of CPI inflation

In line with the modest response of the CPI to a ULC shock, our results also suggest that variations in ULC play only a minor role in explaining past inflation dynamics in Switzerland. The historical decomposition in Fig. 6 shows the contributions of the different shocks and the exogenous variables to Swiss CPI inflation over the past 40 years.Footnote 21 The contributions of ULC (red bars) are only small. CPI movements are, to a large extent, explained by the imported CPI (light green bars), i.e. foreign inflation, the oil price and the exchange rate. Further substantial contributions come from the output gap (dark green bars) and from inflation expectations (yellow bars), whereby the contributions of the latter have decreased notably over the last 20 years.

4.5 Robustness

To test the stability of our results, we perform a wide range of robustness tests. Namely, we test the effect of the sample period on our results, and we run the model with alternative price and labour cost measures and other sets of controls.

Fig. 7

Impulse responses: sample split

While inflation was relatively stable at low levels between 2000 and 2019 (average: 0.5%; maximum: 2.4% in 2008), it was higher in the 1980s and 1990s (average: 2.8%; maximum: 6.5% in 1981). To test whether the magnitude of the wage-price pass-through in Switzerland changed over time, possibly with the inflation environment, we estimate our model for each of the two subsamples separately.Footnote 22 Fig. 7 indicates that the pass-through was somewhat higher in both directions in the earlier subsample, i.e. during the period of higher inflation. However, even in that period, the pass-through of ULC increases to prices was only modest (approximately 0.2 after ten quarters vs. approximately 0.1 in the more recent subperiod). Thus, overall, the pass-through estimates remain very close to the full-sample baseline estimates discussed above. However, owing to the relatively small number of observations in each subsample, the confidence intervals are much wider than for the full-sample estimates.

There are several possible explanations for the somewhat higher pass-throughs in the early subsample. In the case of the pass-through of CPI shocks to ULC (see Panel 1), employees might have had a greater incentive to push for wage increases in the 1980s and 1990s because of the more pronounced and more variable inflation at that time. In addition, wage indexation (i.e. the linking of wages to price developments) was more common during that period and union coverage was higher (see Fig. 10 in Appendix).

In the case of the pass-through from ULC to prices (see Panel 2), the very modest values in the short-term during the period between 2000 and 2019 may not come as a surprise given that there was little variation in both variables over that period. The finding that ULC changes had a significant effect on prices in the short-term in the 1980s and the 1990s suggests that the wage-price pass-through might be higher in an environment of elevated inflation, possibly because in an inflationary environment, it is easier for firms to enforce price increases. However, we cannot conclude from this simple exercise that the decrease in the pass-through after 2000 was a direct result of lower inflation. It might as well have been the result of structural changes, as discussed in Bobeica et al. (2021) for the USA, such as improved anchoring of inflation expectations, increased trade integration and rising market concentration. In Switzerland, the change in the monetary policy strategy in 2000 could also have played a role in reducing the pass-through.

Our finding regarding a wage-price pass-through that is clearly below one also holds for other measures of the price level or unit labour costs. Figure 11 provides an overview of the results for alternative price variables. As expected, the pass-through from ULC to prices of mainly domestic goods (domestic CPI, or similarly, CPI excluding oil-related products) is approximately 30% higher than the pass-through to the total CPI (0.27 vs. 0.20 after 12 quarters), which is well in line with the import share in the total CPI of one fourth. The estimated pass-through for the core measure is also slightly higher. The core CPI excludes oil-related products and food items, with oil-related products being little related to Swiss labour costs. Finally, we replace the CPI by the GDP deflator. As a measure of the price development of domestic value added, the GDP deflator is likely to have a closer link to Swiss production costs than consumer prices. Indeed, in the very short term and in the medium term, the reaction is somewhat higher than in the baseline specification. In Fig. 12, the Swiss wage index and the number of employed persons, both published by the SFSO, are used to calculate unit labour costs (instead of the national accounts data).Footnote 23 The medium-term pass-through is somewhat lower, as the estimated adjustment coefficient is small (with the wrong sign) and insignificant.

Our findings are also robust to the inclusion of different sets of control variables. One at a time, we replace the output gap by the labour gap (defined as an economy’s actual number of hours worked relative to its potential) and the unemployment gap (i.e. the difference between the actual unemployment rate and the natural rate of unemployment). Moreover, we replace imported consumer price inflation by the change in the import price indexFootnote 24 of the SFSO, the nominal effective exchange rate (NEER), the oil price and foreign inflation, or by the relative price change. The latter is used in Zanetti (2007), with relative prices defined as the ratio of imported CPI components over total CPI. Figure 13 provides an overview of the corresponding results. The estimated wage-price pass-through remains modest regardless of which control variables are used. However, our baseline specification shows the highest model fit.

Fig. 8

Out-of-sample exercise

Finally, an out-of-sample exercise suggests that our model is also able to capture the price dynamics of the recent years well. Covering the time span of 1980–2019, our estimation sample excludes the COVID-19 crisis and the subsequent inflationary episode. As a robustness test, we compute our baseline model’s forecast for CPI inflation and ULC growth for the period 2020Q1–2023Q4, taking the realisations of the exogenous variables as given. Figure 8 shows that the pseudo inflation forecast is somewhat lower than the actual CPI inflation. However, it is still close to it overall. Thus, our model is able to capture the price dynamics of this particular episode well, suggesting that there were no major changes in pass-through during this period.Footnote 25 Growth in unit labour costs, on the other hand, was higher than predicted by the model (possibly explaining some of the discrepancy between actual inflation and the model’s forecast). This is most likely because of the special features of the COVID-19 crisis. First, our measure of the output gap drops sharply during the pandemic, absorbing most of the decline in GDP. However, given that the extensive containment measures likely also affected the supply side and reduced potential output, our output gap measure may have been biased to the downside, signalling excessive downward pressure on prices and wages. Second, the partial shutdowns of the economy came along with significant labour hoarding by firms and thus a strong decline in labour productivity (GDP per worker). With wages being sticky and rigid to the downside, this prevented a pronounced fall in unit labour costs.

5 Conclusions

Our analysis indicates that, in Switzerland, both prices and labour costs are informative about future movements of the other variable. However, in quantitative terms, controlling for imported inflation, inflation expectations and economic slack, increases in unit labour costs have only had a modest impact on CPI inflation over the past 40 years. In line with international evidence, we find that the wage-price pass-through is clearly below one, although possibly higher in an environment of elevated inflation. However, even in the 1980s and 1990s, the wage-price pass-through was only modest. Regarding second-round effects of inflationary shocks, we find that these propagate mostly via the inflation expectations channel, whereas the role of wages appears to be almost negligible.

Overall, our analysis implies that, in Switzerland, periods of simultaneously high inflation and high wage growth were not the result of a wage-price spiral. Instead, any long-term comovement of the two variables was mainly due to common drivers (e.g. inflation expectations, economic slack) and the gradual adjustment of labour costs to prices. In line with this result, we find that a substantial part of past CPI dynamics in Switzerland can be explained by fluctuations in the prices of imports, caused by fluctuations in the oil price, foreign inflation and the exchange rate, as well as inflation expectations and economic slack.

Regarding potentially lasting effects on inflation, inflation expectations and economic slack play a more fundamental role than wages do. Both are important drivers of price and wage inflation and could push up inflation and nominal wage growth more permanently. Hence, in inflationary episodes, policymakers should closely monitor and react to changes in inflation, inflation expectations and macroeconomic conditions to prevent second-round effects from becoming more persistent.

Data availability

Data sources are given in the paper.

Notes

  1. Generally, second-round effects refer to additional, widespread inflationary pressure due to, for example, firms passing on increased input costs (such as the cost of raw materials or wages) or an increase in inflation expectations after an initial inflationary shock.

  2. In the international discussion, the term “wage-price spiral” is used in different ways. The public sometimes perceives an economy to be in a wage-price spiral when both price and wage inflation are high over an extended period of time. In its 2022 World Economic Outlook, the IMF (2022) also defines a wage-price spiral as an episode of several quarters characterised by accelerating wages and prices and abstracts from the role of causal effects. In most of the economic literature, however, the definition of a wage-price spiral entails feedback between wages and prices. From a policy perspective, understanding these feedback effects is crucial in understanding the role of wages as a potential cause of persistently higher inflation. Hence, in this paper, our use of the term “wage-price spiral” follows the definition of the BIS (2022).

  3. For a detailed discussion of the international empirical literature on wage-price dynamics up to 2018, see Bobeica et al. (2019).

  4. Note that the evidence suggests that even at the micro level, wage and price changes are not necessarily tightly linked. Relying on a large firm survey across a broad range of European countries, Druant et al. (2009) find that after an unexpected permanent increase in wages, “just” approximately 60% of firms would increase prices. Dogra et al. (2023) present similar findings for the USA, analysing a firm survey that suggests an average cost-price pass-through of approximately 60%, with significant heterogeneity across firms.

  5. See the OECD/AIAS ICTWSS Database.

  6. See Rosenblatt-Wisch and Scheufele (2015). We chose to work with inflation expectations of households instead of firms because we lack a long enough series of the latter. While a measure of firm inflation expectations might be even more suitable for the question we address, household inflation expectations influence wage claims and therefore also play a role in wage negotiations.

  7. This is mainly because the implied level variable \(\tilde{p}_{t}^{e} \equiv \tilde{p}_{t-1}^{e} + \pi _t^e\) does not correspond to the expected price level but is an artificial construct in our notation, formed from cumulative inflation expectations, whose level has no meaningful relation to the actual price level. Indeed, attempts to establish a cointegration relationship among cumulative inflation expectations, i.e. \(\tilde{p}_{t}^{e}\), the actual price level and ULC fail to reveal a stable relationship. The actual expected price level \(p_{t}^{e}\) (built, for example, from the current price level and expected inflation), on the other hand, cannot, by definition, deviate permanently from the actual price level. Therefore, relevant long-term dynamics cannot occur.

  8. According to basic economic theory, wage increases generate upward price pressure not only through firms’ production costs (cost-push channel) but also through higher demand by consumers (demand channel). By taking the output gap as exogenous, we shut down the demand channel in our set-up. However, a range of robustness tests suggests that treating the output gap as endogenous would not significantly alter our results. This is in line with Shapiro (2023), who finds that changes in labour costs affect prices mainly through the supply channel (i.e. the cost-push channel), while the role of the demand channel is negligible. Intuitively, the demand channel is likely to be weak in Switzerland because, among other things, private consumption tends to respond only sluggishly to changes in labour income, giving supply time to adjust, and because of the high import share of consumer goods.

  9. The results hardly change when imposing the opposite restriction, i.e. that ULC have no contemporaneous effect on inflation.

  10. Lifting this restriction has no noticeable effect on the results.

  11. While in the reduced-form VECM (Eq. 10), this was controlled for by the (exogenous) inflation expectations, we now account for it by including a time dummy in the inflation expectations equation. The breakpoint (1995 Q2) is determined by means of the Quandt-Andrews test on the basis of a univariate model for inflation expectations.

  12. Note that the dependent variables are in annualised percentage changes. Without this transformation, the reported adjustment coefficients would be 0.007 in the price equation and 0.040 in the ULC equation.

  13. As a robustness check, we conducted the Johansen-Juselius maximum likelihood (ML) cointegration estimation and compared the adjustment coefficients with those obtained from the two-step approach. The results show that the adjustment coefficients from the Johansen-Juselius estimation are very similar to those from the two-step method, with no statistically significant differences. Specifically, the adjustment coefficient for prices is slightly smaller, but not meaningfully different, while the coefficient for ULC remains essentially identical.

  14. For the derivation of the impulse response functions, see Sect. B in Appendix. For the construction of the confidence bands, we apply the residual-based bootstrap approach as described in Lütkepohl et al. (2020).

  15. Note that this value is very close to the estimated pass-through in IMF (2018) for euro area economies. Bobeica et al. (2019), on the other hand, report somewhat higher pass-through rates. However, they look at the value-added deflator (as opposed to consumer prices), which is presumably more closely linked firms’ cost pressures.

  16. Note that the medium-term decline in the ULC response does not imply that nominal wage growth is negative after a positive ULC shock (this would be highly implausible given the strong empirical evidence for downward nominal wage rigidity; see e.g. Funk and Kaufmann, 2022). It simply implies that ULC temporarily grow less strongly than they do on average, i.e. the excess growth of nominal wages relative to productivity is less strong than on average.

  17. While the import share in services (approximately 60% of the total CPI) has been relatively low, the import share in goods has been approximately 50% on average.

  18. Empirical evidence confirms that the labour intensity is—among other factors—a key component in explaining differences in the wage-price pass-through across sectors (see e.g. Heise et al., 2022, and Ampudia et al., 2024). Note, however, that our exercise is not a proper analysis of sectoral heterogeneity. This is mainly because we lack sectoral wage data for Switzerland covering a sufficiently long period and on the quarterly basis, so our analysis is limited to the effects of changes in aggregate ULC.

  19. For example, Abberger et al. (2024) find that changes in firms’ inflation expectations pass through to both their prices and wages, even though the pass-through is incomplete.

  20. The procedure we followed to calculate the various contributions is explained in Sect. C in Appendix.

  21. We tested for structural breaks using Quandt-Andrews and Bai-Perron methods. While there is some evidence of a single break (in 1995Q1 for inflation and 2008Q1 for ULC), neither break was statistically significant at the 1% level, and no evidence of a second break was found. Given the shift in the Swiss National Bank’s monetary policy strategy in 2000, which focused on a more explicit inflation-targeting framework, we believe the most appropriate year for splitting the sample is 2000.

  22. In our set-up, the relevant wage cost measure is unit labour costs. Some studies look at nominal wages without adjusting them for changes in labour productivity (see e.g. Knotek II and Zaman, 2014, Shapiro, 2023, Chin and Lin, 2023, or Ampudia et al., 2024). Their estimated effects on prices are similar to those based on ULC.

  23. The basket of the import price index also includes intermediate goods. Hence, its link to consumer goods prices is relatively weak. Its correlation with total CPI inflation is only about half of the correlation between imported CPI inflation and total CPI inflation.

  24. In another exercise, we estimate the model using data from 1980 to 2023. The estimated pass-through values are very similar to our baseline results.

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Acknowledgements

We thank Christian Hepenstrick, Carlos Lenz, Matthias Lutz, Inske Pirschel and Yannic Stucki, the participants of the SNB brown bag seminar and the Annual Congress of the Swiss Society of Economics and Statistics, and an anonymous referee for valuable comments and suggestions. The views, opinions, findings and conclusions or recommendations expressed in this paper are strictly those of the authors. They do not necessarily reflect the views of the Swiss National Bank (SNB). The SNB takes no responsibility for any errors or omissions in, or for the correctness of, the information contained in this paper.

Funding

This research did not receive funding.

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Authors and Affiliations

  1. Forecast and Analysis Switzerland Unit, Swiss National Bank, P.O. Box, 8022, Zurich, Switzerland

    Jessica Leutert & Rolf Scheufele

  2. Department of Management, Technology, and Economics, ETH Zurich, 8092, Zurich, Switzerland

    Selina Schön

Authors

  1. Jessica Leutert
  2. Rolf Scheufele
  3. Selina Schön

Contributions

J.L. and R.S. wrote the main manuscript text, and S.S. provided the code for the econometric analysis and prepared tables and figures. J.L. and R.S. reviewed the code and the regression output. All authors reviewed the manuscript.

Corresponding author

Correspondence to Jessica Leutert.

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Appendices

Appendix

See Figures 9, 10, 11, 12 and 13.

A Additional Figures

Fig. 9

Impulse responses to a 1% price shock

Fig. 10

Wage indexation and unionisation

Fig. 11

Impulse responses: alternative price variables

Fig. 12

Impulse responses: alternative wage variables

Fig. 13

Impulse responses: alternative control variables

B Derivation of IRFs

We estimate the following structural VECM (with one being the optimal number of lags):

$$\begin{aligned} B_0\varDelta Y_{t}=\mu +B_1\varDelta Y_{t-1}+\varPhi Y_{t-1}+\varGamma Z_{t}+\varepsilon _{t} \end{aligned}$$

(12)

To derive the effect of a shock \(\varepsilon _{t}\) on \(Y_{t+\tau }\), we express equation 12 in levels as follows:

$$\begin{aligned} B_0 (Y_{t} - Y_{t-1})=\mu +B_1(Y_{t-1}-Y_{t-2})+\varPhi Y_{t-1}+\varGamma Z_{t}+\varepsilon _{t} \end{aligned}$$

$$\begin{aligned} \Leftrightarrow Y_{t}=B_0^{-1}\mu +\underbrace{B_0^{-1}(B_0+B_1+\varPhi )}_{K}Y_{t-1}\underbrace{-B_0^{-1}B_1}_{\varXi }Y_{t-2}+B_0^{-1}\varGamma Z_{t}+B_0^{-1}\varepsilon _{t} \end{aligned}$$

$$\begin{aligned} \Rightarrow Y_{t}=B_0^{-1}\mu +K Y_{t-1} +\varXi Y_{t-2}+B_0^{-1}\varGamma Z_{t}+B_0^{-1}\varepsilon _{t} \end{aligned}$$

(13)

Hence, the effect of a shock \(\varepsilon _{t}\) on \(Y_t\) is given by:

$$\begin{aligned} \frac{\partial Y_{t}}{\partial \varepsilon _{t}}=B_0^{-1} \end{aligned}$$

(14)

For the effect at \(t+1\), equation 13 for \(Y_{t+1}\) is written as follows:

$$\begin{aligned} Y_{t+1}&=B_0^{-1}\mu +K Y_{t}+\varXi Y_{t-1}+B_0^{-1}\varGamma Z_{t+1}+B_0^{-1}\varepsilon _{t+1}, \end{aligned}$$

(15)

which gives us:

$$\begin{aligned} \frac{\partial Y_{t+1}}{\partial \varepsilon _{t}}=K\frac{\partial Y_{t}}{\partial \varepsilon _{t}}=K B_0^{-1} \end{aligned}$$

(16)

The same procedure for deriving the response at \(t+2\) is used as follows:

$$\begin{aligned} Y_{t+2}=B_0^{-1}\mu +K Y_{t+1}+\varXi Y_{t}+B_0^{-1}\varGamma Z_{t+2}+B_0^{-1}\varepsilon _{t+2}, \end{aligned}$$

(17)

which implies that:

$$\begin{aligned} \frac{\partial Y_{t+2}}{\partial \varepsilon _{t}}=K\frac{\partial Y_{t+1}}{\partial \varepsilon _{t}}+\varXi \frac{\partial Y_{t}}{\partial \varepsilon _{t}}=K^{2}B_0^{-1}+\varXi B_0^{-1} \end{aligned}$$

(18)

More generally, for all \(\tau \ge 2\), the effect of a shock \(\varepsilon _{t}\) on \(Y_{t+\tau }\) is given by:

$$\begin{aligned} \frac{\partial Y_{t+\tau }}{\partial \varepsilon _{t}}=K\frac{\partial Y_{t+\tau -1}}{\partial \varepsilon _{t}}+\varXi \frac{\partial Y_{t+\tau -2}}{\partial \varepsilon _{t}} \end{aligned}$$

(19)

Hence, once we have calculated \(\frac{\partial Y_{t}}{\partial \varepsilon _{t}}\) and \(\frac{\partial Y_{t+1}}{\partial \varepsilon _{t}}\), we can iterate further to calculate the full impulse response functions.

C Historical decomposition

The historical decomposition was derived using the following steps.

  1. 1.

    First, the residuals resulting from the fitted model are saved, representing the shocks to the three endogenous variables.

  2. 2.

    Then, a model is defined with the estimated coefficients, and the saved residuals are included as additional variables with a coefficient of 1.

  3. 3.

    Next, a forecast is made for all three endogenous variables, starting from \(t=2\). The values of the endogenous variables are taken as given for the first two periods (\(t=0\), \(t=1\)).

    • The baseline forecast corresponds to the actual realisations.

    • To determine the contribution of the exogenous variables \(Z_t\), the according variables are set to zero, one at a time, and the difference from the baseline is calculated.

    • Similarly, to determine the contribution of the endogenous variables, the corresponding shocks are set to zero, again one at a time, and the difference from the baseline is calculated.

    • Finally, the residual represents the contribution of the constants, the dummy and the initial values.

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Leutert, J., Scheufele, R. & Schön, S. Wage-price pass-through in Switzerland. Swiss J Economics Statistics 162, 2 (2026). https://doi.org/10.1186/s41937-026-00148-x

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