Under the Macroscope: An Empirical Model of the System of Norwegian Wage Formation

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Under the Macroscope:

An Empirical Model of the System of Norwegian Wage Formation

Simon Dalnoki

May 2019

Thesis for the Degree of

Master of Economic Theory and Econometrics

Department of Economics

University of Oslo

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Abstract

Several models of the Norwegian system of wage formation are estimated in this thesis. The point of departure is a single-equation error correction model (ECM) for manufacturing wages, while the final model is a simultaneous equation model (SEM) with eight endogenous variables. The estimation yields insight into both short-run and long-run dynamics of the system of wage formation. The results indicate that manufacturing wages error cor- rect with the manufacturing wage scope. Further, there are signs of pattern wage bargaining throughout the modeling, with manufacturing as the wage- leading sector. The estimation results indicate that inflation expectations significantly influence the manufacturing wage growth in the short-run. In- flation expectations affect wages in other sectors as well through the wage formation in the exporting sector. The estimation of the SEM shows similar results as for the recursive system. Finally, results from the estimation in this thesis indicate that a Phillips curve approach to modeling the system of Norwegian wage formation is not supported. However, principles from the Odd Aukrust’s Main Course framework seem to have empirical support throughout the estimation.

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Preface

Working with this thesis has been interesting, challenging and rewarding.

It has been a privilege to get the opportunity to do research of this kind.

Throughout the process, I have enjoyed excellent guidance from my super- visor Professor Ragnar Nymoen. Not only has he been more than generous with his time, but he has also shared with me his vast knowledge on the labor market and econometric modeling. His guidance has been invaluable and I want to thank him for this.

I also wish to extend my gratitude to Samfunnsøkonomisk analyse for sup- porting me in the process of writing my thesis. Finally, these last five years would not have been the same without my fellow students Eirik, Magnus, Ma- lin, and Mikkel. I appreciate our time together as students and our friendship throughout the years.

I am indebted to all of those above for their different contributions to this thesis. Any remaining errors or inaccuracies are mine and mine only.

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List of Tables

2.1 The aggregation of industries into the three sectors analyzed

in the thesis . . . 7

2.2 Unit-root test results . . . 10

4.1 Results from the re-estimation of models from “Norwegian wage curves” . . . 18

5.1 Results from the estimation of wages in three sectors . . . 24

5.2 Estimation results for the recursive system with four endogenous variables . . . 27

5.3 Diagnostics for the estimated recursive system with four endogenous variables . . . 29

5.4 Estimation results from the expanded system . . . 35

5.5 Diagnostics for the expanded system . . . 36

5.6 Testing error correction terms . . . 39

5.7 Results from 2SLS estimation of manufacturing wage growth with inflation expectations . . . 42

5.8 Estimation results for the simultaneous system . . . 44

5.9 Diagnostics for the simultaneous system . . . 45

A.1 Variable definitions and data sources . . . 55

B.1 Detailed sector division . . . 57

C.1 2SLS estimation of sheltered private sector wage growth with inflation expectations . . . 59

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C.2 2SLS estimation of public sector wage growth with inflation expectations . . . 60 C.3 Additional estimation results the simultaneous system . . . 61

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List of Figures

2.1 Plot of the three wage series . . . 9

4.1 M2* coefficient plots . . . 20

5.1 Plot of wages in sector 2 and 3 . . . 28

5.2 Simulated temporary shock to the recursive system . . . 31

5.3 Simulated permanent shock to the recursive system . . . 31

5.4 Coefficient plot from the estimation of ∆z1_t . . . 37

5.5 Coefficient plot from the estimation of ∆z2_t . . . 37

5.6 Simulated temporary shock to the simultaneous system . . . . 47

5.7 Simulated permanent shock to the simultaneous system . . . . 47

5.8 Combined plots of a simulated, temporary shock to two of the estimated models . . . 49

5.9 Combined plots of a simulated, permanent shock to two of the estimated models . . . 49

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Chapter 1 Introduction

In this thesis, I present an empirical econometric model of the national system of wage formation in Norway. The estimation aims to increase the understanding of the dynamics behind the development of wages in three sectors of the economy and how they are formed by distinctive, voluntary and coordinated negotiations between unions and employers’ organizations.

Furthermore, the role of inflation expectations is investigated in both single- equation models and multiple-equation models. This is done by building on existing work, but also by original contributions in terms of system estimation and abstraction from short-term dynamics, e.g., changing seasonal patterns, by using annual data. Despite being a central part of the “Nor- wegian Model”, a broadly defined term capturing characteristic traits of the organization of the Norwegian society, the wage formation as a system is arguably understudied. The two dominating theories of wage formation in Norway have, since several decades, been the Phillips curve theory and the Main Course framework. However, in recent years, the Phillips curve modeling of wage formation in macroeconomic models seems to have achieved almost total dominance in the field of modern macroeconomics. The Phillips curve model, either the “old” version or the “newer” versions (e.g., “New Keynesian Phillips Curves”), is used by a wide range of important institutions and dominates also the academic sphere. To a large extent, the Phillips curve theory has become such a prevailing theory that all models with wage

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change as a left-hand side (LHS) variable are called Phillips curves, even when they are actually not. In that way, researchers may overlook or fail to understand, the different theoretical implications of the Phillips curve theory versus those of the Main Course theory. Most recently, this misinterpretation happened in a Staff Memo written in Norges Bank, the central bank of Nor- way. Brubakk, Hagelund, and Husabø (2018) estimates what the authors call an “augmented Phillips curve”. However, the theoretical implications are partially lost in the memo as the authors interpret the estimated model as a Phillips curve model, despite the significant long-term dependence (error correction) between wages and the wage-scope. The dominance of the Phillips curve increases the required level of precision when interpreting the estimation results in this thesis. Below is a brief summary of the two above- mentioned contesting theories of wage formation, namely the Phillips curve and the Main Course theory.

According to Phillips curve theory, wages are determined by market conditions and individual wage negotiations (Phillips, 1958). Accordingly, as is Phillips’ main hypothesis, labor market institutions play a minor role in the wage formation, especially in the long-run. To capture the wage formation, the Phillips curve can be represented by wage growth as the left-hand side variable. Wage growth depends, in most modern applications of this theory, on inflation expectations and the output gap. Also, many interpretations of the Phillips curve theory imply a vertical long-run Phillips curve with a non-accelerating inflation rate of unemployment (“NAIRU”) as the “natural rate of unemployment”.

The Main Course Theory is a concretization of the Norwegian model of wage formation and formulated for the first time in English in 1977 as the Norwegian Model for Inflation, see Aukrust (1977). However, the first Nor- wegian mentioning of similar theory preceded the first English formulation by several years, see, e.g., Aukrust (1965). Also, it is likely that many of the features that characterize a relatively well functioning system with wage regulation by collective agreements had been in operation for several decades before Aukrust’s conceptualization of a Norwegian model.

In the Main Course Model, a distinction is made between industries pro-

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ducing tradables and non-tradables. In addition, the model is characterized by the trait that manufacturing wage growth follows the wage scope in the same sector in the long-run. As the sheltered and exposed industries com- pete for labor power, high wages in one sector relative to the other steer the supply of labor in the direction of the sector with the higher productivity. This mechanism is a central motivation for the Norwegian system for wage formation hereby called the Wage-Leader Model (“Frontfagsmod- ellen”). The system builds on the principles formalized by Aukrust (1977), but Aukrust himself can of course not be accredited for creating the actual Wage-Leader-Follower Model. The Wage-Leader Model acknowledges the principles summarized in the Main Course theory and does as such use the manufacturing wage growth as a benchmark for the wage growth in other industries in the economy. The manufacturing wage growth is in turn re- stricted by the product of the manufacturing productivity and the prices on manufacturing goods, i.e., the wage scope. Wages in the other sectors of the economy grow, at least over time, at the same rate as the manufacturing wages do. Prices on domestic goods are as such endogenous to the system. To enable this wage-leader/follower dynamics, strong and overreaching unions and employers’ organizations are needed to enforce the sequential and coordinated bargaining necessary for the system to be upheld. This implies that the Main Course Model is best understood as a model where negotiations between unions and employers’ organizations, and not only between individuals and single firms, play a significant role in the system of national wage formation. Furthermore, it implies that there are several combinations of unemployment and inflation rates that are possible outcomes in the long- run as the unions and the employers’ organizations may accept compromises concerning combinations of wage-levels and unemployment rates.

The two contesting theories of wage formation, the Phillips curve and the Main Course Model, therefore differ both with respect to assumptions and with respect to implications about stabilizing and destabilizing dynamics. By putting all models of nominal wage change under the Phillips curve umbrella, many important insights are lost out of sight. Conversely, by specifying and estimating models capturing essential traits and dynamics of the Norwegian

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wage formation, further insight in regards to the empirical support for either theory can potentially be made. This thesis might, on the course of achieving the aims above, thus find results in support of the Main Course Model or the Phillips curve theory.

The thesis is organized as follows. In the following chapter there is a description of the data used in the estimation to come. Chapter 2 also contains tests of the time-series properties of some variables as well as some general notes on methodology. Chapter 3 refers to existing, relevant research on the topic of modeling the Norwegian wage formation. The results of the re-estimation of two existing models for manufacturing wages are presented in Chapter 4. In Chapter 5, the specification and estimation of wage equations for three sectors of the Norwegian economy are conducted. First, the equations are specified and estimated as separate relations. Second, a recursive system building on the sector equations is estimated. Third, the system is expanded and tests are conducted to discover potentially interesting long-term dynamics of selected relations. Finally, instrumental variable estimation is used to formulate and later estimate a simultaneous system for the wage formation across sectors of the Norwegian economy. In Section 5.5, there is a discussion of the differences in the dynamic properties of one of the recursive systems and the simultaneous system. Chapter 6 summarizes the thesis’ content and comments on the implications of the estimation results.

The data set and OxMetrics codes used for the estimation in this thesis are available upon request to the author. All numerical results were obtained by PcGive 14/15. For documentation, see Doornik and Hendry (2013a), Doornik and Hendry (2013b) and Doornik and Hendry (2018).

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Chapter 2 Data Description and Time Series Properties

To best capture the dynamics of the wage formation, it is a point to abstract from complicating short-term “noise” which can arise due to (potentially changing) seasonal patterns in several explanatory variables. Such interfering dynamics might not offer substantial insight into the topic in question. To avoid such “disturbances”, the estimation in this thesis is done using an annual data set. In addition, as the wage adjustments happen annually, using annual data is the natural choice in this context. No documented efforts at estimating wages for both manufacturing and other sectors using annual data are known to the author at the time of writing. However, as discussed in Chapter 3, there is an interesting literature on the modeling of manufacturing wages using annual data. This chapter contains some notes about the data and how the different sectors are defined within the data set. Furthermore, the times series properties of the variables are subject to tests and discussion before some general notes on modeling methodology are made.

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2.1 The data set

The data set used for the estimation in this thesis covers the years 1970 to 2018. The series are mainly aggregated, annual data from the National Accounts published by, or available upon request to, Statistics Norway.

The National Accounts is divided into industries. A challenge with using the National Accounts is that data is not available for clearly separated sectors such as the sheltered and the competitive sector (tradables). To cre- ate three sectors, which is necessary for the estimation in this thesis, several decisions have to be made regarding which sector each sub-industry belongs.

Table 2.1 shows how the industries have been divided into three groups to form the sectors which are referred to as the manufacturing sector, the sheltered private sector, and the public sector. In this thesis, the manufacturing sector refers to the sector particularly exposed to competition on the world market (sometimes also called exporting sector). Conversely, the two other sectors are regarded as sheltered from international competition. In addition, some industries were excluded from the data. These are primary industries (e.g., agriculture and commercial forestry), extraction of crude oil and natural gas (included related services), and international shipping (called “ocean transport” by Statistics Norway). These industries are not representative of the general wage formation in Norway for several reasons and are thus excluded. This is in line with established practice in research of similar nature, see, e.g., Langørgen (1993).

Economy-wide variables are also included in the data set, e.g., the total unemployment rate and CPI. Unemployment measured by the Labour Force Survey (“Arbeidskraftundersøkelsen”, AKU) is not available before 1972.

The series was, therefore, extended backward to 1970 by scaling registered unemployment (NAV unemployment) to match the AKU-level. Similarly, the manufacturing factor income deflator from the KVARTS-database, P Y F1, had to be extended to include 2018. This was done by using a deflator for value added in manufacturing calculated using National Accounts data. The variableH, representing the length of the normal working week, reflects both reductions due to legislation and changes in the main collective agreements

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Table 2.1: The aggregation of industries into the three sectors analyzed in the thesis.

Exposed Sheltered

Manufacturing Private Sector Public Sector

Mining and

quarrying Electricity, gas and steam Education Manufacturing Construction Health and social work

Wholesale and retail trade, repair of motor vehicles

Public administration and defence Transport activities excl.

ocean transport Postal and courier activities

Accommodation and food service activities

Information and communication Financial and insurance activities

Real estate activities Imputed rents of owner-occupied

dwellings

Professional, scientific and technical activities Administrative and support

services

Arts, entertainment and other services Transport via pipelines Water supply, sewage and waste

Note: See Appendix B for the SIC2007 classification codes for each industry.

that regulated the manufacturing industry most directly. For example, H takes the value 37.5 from 1987 even if the legislative length of the workweek is still 40 hours. In addition to the publicly available data from the National Accounts, some data is obtained from other sources such as the KVARTS- database. See Table A.1 for more detailed description of variables as well as listing of sources.

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2.2 Time series properties

As noted, the data set covers several decades. Some of the series grow over time, while others may fluctuate around a reasonably constant mean value.

When estimating a dynamic model using time series, it is necessary to take into account the typical temporal properties of the different time series variables. The distinction between stationarity and non-stationarity is particularly important.

Wage, productivity, price indices, and similar variables are typically non- stationary series. Non-stationary series have a non-constant mean and vari- ance over time, which can arise from the presence of either a stochastic trend or a deterministic trend. However, in this thesis, it is assumed that non- stationarity in such series arises from the presence of a unit-root (stochastic trend).

Other variables, e.g., unemployment rate, might not have a sustained trend at all. Using the unemployment rate as an example, it is more reasonable to believe that the variable fluctuates around some mean than that it grows continuously over time. For such variables, the mean can, however, change in periods.

Table 2.2 shows Augmented Dickey-Fuller (ADF) t-statistics for key variables. The statistics are reported and used as unit-root tests for several variables. The column labeled X_t ∼ I(1) contains the test of a hypothesis that X_t is integrated of degree one, H₀ : X_t ∼ I(1). In the same way, column ∆X_t ∼ I(1) shows the test of H₀ : ∆X_t ∼ I(1), which is the same as X_t ∼ I(2). The reported tests must not be confused with Student’s t- statistics. Instead, critical values are taken from the ADF-distribution which varies depending on the specification of the ADF-test. In Table 2.2, the ADF-statistics come from testing for unit-roots when the ADF-regression contains a trend and a constant. Furthermore, all reported ADF-statistics are for the regression with one lagged differenced variable.

It is clear from the table that all three wage series can be assumed to be I(1). The tests show that H₀ :X_t ∼ I(1) cannot be rejected for any of the wage levels, while H₀ : ∆X_t ∼ I(1) can be rejected at the 5 percent level

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Figure 2.1: The natural logarithm of the three wage series plotted in three separate graphs.

and H₀ : ∆²X_t ∼ I(1) can be rejected at the 1 percent level for the wage series in all sectors. This fits well with the plotted series in Figure 2.1.

Productivity and the price indices are I(1) according to the results presented in Table 2.2. The test of non-stationarity of the level of the payroll tax rate is rejected at the 1 percent significance level.

For the manufacturing wage cost, wc1, the results indicate that neither the level nor the change is stationary at the 5 percent level, although the ADF-value of ∆wc1 is close to being significant. Further, the unit-root test for ∆²wc1_t ∼I(1) is rejected at the 1 percent level. Despite not being able to formally reject H₀ : ∆wc1_t ∼ I(1), wc1 will be treated as an I(1) series in this thesis. This is because manufacturing wage cost is calculated as w1 scaled up by an estimated payroll tax rate, i.e., wc1 = w1×(1 +t11). As t11 is I(0) andw1 is I(1), and degree of integration is a linear property, wc1 is also treated as an I(1) series in this thesis.

According to the ADF-test, the unemployment rate, uaku, is also I(1).

As the unemployment rate is not expected to grow over time, at least not

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indefinitely, one can, however, question the result that the series is I(1). One possibility is that the unemployment rate went up from remarkably low levels in the ’70s to a higher, but still low compared to international standards, level in the 2000s and onward. This could, therefore, mean that the unemployment rate is stationary after all, but that its mean has shifted. Due to the unlikely scenario of having a non-stationary unemployment rate, uaku is treated as an I(0) series in the estimation in this thesis. The possibility of having a shifting mean value of the unemployment rate is investigated in Chapter 5.

Lastly, scope1 is also assumed to be I(1) based on the unit-root tests.

Table 2.2: Unit-root test results for variables from 1970-2018

Variables X_t ∼I(1) ∆X_t∼I(1) ∆²X_t∼I(1)

w1 -2.592 -3.698* -6.032**

w2 -2.649 -3.601* -5.625**

w3 -2.524 -3.884* -6.084**

z1 -2.937 -5.297** -8.505**

z2 -1.986 -4.390** -7.204**

wc1 -2.725 -3.347 -6.081**

pyf1 -1.459 -5.104** -6.169**

pb -2.930 -4.135* -7.936**

cpi -2.571 -4.012* -6.668**

uaku -2.814 -5.956** -8.357**

t11 -4.468** -4.550** -5.877**

scope1 -1.821 -4.742** -7.435**

Each reported statistic is the ADF-statistics of a regression containing one lagged differenced variable, a constant and a trend. 5% and 1% critical values, constant+trend, are -3.51 and -4.17. * and ** denote significance at 5% and 1%

respectively.

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2.3 Notes on econometric modeling of non- stationary variables

As shown above, wage per hour, productivity, price indices, and similar series are typically non-stationary series. Non-stationarity can be solved by differencing the variables in question as long as the variables do not represent so-called explosive series. E.g., if a variable is integrated to degree d it can be made stationary by differencing itd times. However, when modeling wage formation it can be desirable to include lagged level-variables. It is precisely such variables that can indicate whether different economic theories have empirical support or not. Error correction models, which combine change- variables with lagged level-variables, are thus suited for modeling relations between non-stationary time series. Their ability to model both short-run and long-run dynamics is also a desirable trait when modeling wage formation. The long-run dynamics are captured by lagged level-variables, while differenced variables capture short-run dynamics. An ECM thus incorporates the part of the dynamics between the explained and the explanatory variables arising from a disequilibrium state.

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Chapter 3 Review of the Empirical Literature

In the paper “Norwegian wage curves” from 1995, Johansen used annual data for the manufacturing sector to estimate wage-curve models for the wage formation. “Norwegian wage curves” is a natural reference for this thesis both due to the use of annual data and due to the estimation of manufacturing wages. The paper found that the Phillips curve specification of manufacturing wages can be rejected. This is implied by the lack of empirical support for a unique equilibrium rate of unemployment depending only on parameters in the specified wage relation. Johansen continued to estimate an error correction model (ECM) for manufacturing wage which connects the long-term trend of the wage-cost level in the exporting sector to the value of the labor productivity. This can be regarded as an operationalization of the “Main Course Model” described briefly in Chapter 1.

Furthermore, Johansen found that the development in the cost of living (measured by the Consumer Price Index) affects manufacturing wage growth in the short-term, but does not have a long-term impact in the wage level.

This result, if it is robust, matters for the overall Norwegian wage formation as it reduces the risk of domestic wage-price spirals.

The curvature of the manufacturing wage curve is the main topic in Jo- hansen’s paper. The curvature has implications for how long-term unemploy-

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ment affects wages relative to the impact of short-term unemployment. It does as such imply how much wage dampening effect one can expect from high levels of unemployment. Johansen tested different functional specifications of the unemployment variable to find the best functional form. He concluded that the wage curve is strongly convex. This implies that unemployment need not reach a particularly high level before an additional increase neither affects the wage growth or the wage level. Such a wage curve can be tied to economic theory through its implications for the different impacts of short- term and long-term unemployment on wage formation. An example is the relatively small impact of the unemployed (“outsiders”) on the general wage formation. Aless convex wage curve could, on the other hand, be interpreted as an indication that the parties in the labor market have a wider perspective and manage both to dampen the wage growth at high unemployment levels and to avoid wage growth outside the “main course” in periods of low unemployment.

As in Johansen (1995), Nymoen and Rødseth (2003) used annual data to estimate the wage formation. They used data for the four Nordic countries (Denmark, Finland, Norway, and Sweden) to explain features of the distinctively low unemployment in these countries in the 1980s and 1990s.

One for their results was that the wage relations for three of the countries included error correction terms, given the assumption of stationary wage share. Even without the assumption, error correction is indicated for the Norwegian wage formation while it is still significant for both Sweden and Finland. The paper also found empirical support for great similarities across the countries in reactions to changes in the explanatory variables. The similarities do not, however, apply to the constant terms. This implies similar reactions to changes, while the equilibrium rate of unemployment varies across the countries. One interpretation of the results may be that a “Scandina- vian model” can sum up some of the features in common for the countries.

This does as such point at similarities in the way the Nordic economies are organized.

Langørgen (1993) presents results from work on the wage relations in KVARTS. KVARTS is a macroeconomic model for the Norwegian economy.

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It is developed by Statistics Norway and used for, among other things, fore- casting and policy analysis (Boug & Dyvi, 2008). Langørgen (1993) estimated wages in three sectors of the Norwegian economy: the exporting sector (manufacturing), the sheltered private sector, and the public sector. The author highlighted three important results. Firstly, there is significant error correction in the wage relations for all of the sectors. Secondly, opportunity wage is a part of the long-run solutions of all relations. Finally, it is indicated that income tax is not important in explaining the long-term wage growth of manufacturing sector. The significant error correction implies that there are more long-run combinations of unemployment and inflation than implied by the theory of a “natural rate of unemployment”. Thus, Langørgen rejected the Phillips curve. It was further argued that the presence of opportunity wage in the wage relations contradicts the Main Course Theory. Besides, the variables CPI and income tax are significant in the long-run solutions of the wage relations for the public sector. This led to rejection of the Main Course Model in its “pure form”.

Attempts at multiple-equation modeling of wages with quarterly data have also been made. In Have Inflation Targeting and EU Labour Market Immigration Changed the System of Wage Formation in Norway?, Gjelsvik, Nymoen and Sparrman estimated a model for the wage formation in three sectors of the Norwegian economy. The authors identified and estimated a simultaneous, three-sector system of wages with the exporting sector as the

“wage-leader”. This was based on their expectations of cointegration between wages across sectors. More specifically, they estimated a cointegrated vector autoregressive model. The results support the conclusion that manufacturing takes the role of wage-leader for the two other sectors throughout the sample period. This means that the coordination in the wage formation follows so-called “pattern wage bargaining”, i.e., pattern wage bargaining in the meaning that the wage growth in one sector, in this case, manufacturing, works as a benchmark for the wage negotiations in the other sectors. In addition, the results show that there is no support for wage-wage effects, i.e., no feedback from wage formation in the sheltered sectors onto the exposed sector.

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The authors also tested whether the dynamics of the wage formation, more specifically the leader-follower dynamics, have been influenced by the transition to an inflation targeting monetary policy scheme as well as increased labor immigration from the European Union outside of Scandinavia.

They found no evidence for a structural change in the negotiation between unions and employers’ organizations due to the above-mentioned changes.

Interestingly, the role of inflation expectations had also not changed since the rise of the inflation targeting central bank. Results do however indicate that increased labor immigration has led to a lower long-run level of wages, due to increased labor supply, despite not fundamentally changing the leading sector’s (“frontfaget”) role in the wage negotiations (Gjelsvik, Nymoen,

& Sparrman, 2015). A later empirical study by Nymoen, Sparrman, Dapi, et al. (2019) argued further that although increased immigration might have decreased the parties’ bargaining power, it has not changed the pattern of the national wage formation.

Kruse (2015) is a different study than those mentioned above. In the paper, an econometric evaluation of the calibrated Phillips curve relation in Norges Bank’s macroeconomic model, NEMO, is carried out. Kruse’s results indicate that the econometric explanatory power of NEMO’s wage relation is rather limited. In a recent “Staff Memo” from Norges Bank, Brubakk et al.

(2018) found support for a significant wage share in an estimated expression for the wage formation. This has however not changed the way wage formation is modeled in NEMO.

As previously stated, and reflected by this review of literature, there is no documentation of a complete empirical model-representation of the wage formation using annual data. The closest contestant is the MODAG- documentation, see, e.g., Boug and Dyvi (2008), which is relatively old and

“stops” at equation-by-equation estimation. Consequently, this thesis makes, as the next chapters show, several original contributions to the modeling of the system of Norwegian wage formation.

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Chapter 4 Re-estimating an Existing

Model of Manufacturing Wage Setting

Johansen (1995) estimated several models for manufacturing wages in “Nor- wegian wage curves” using annual data. Despite the overall aim to model the system of wage formation, it is relevant to start modeling the manufacturing wage due to several reasons. First, manufacturing wage is an important component in the final system. Second, the literature covers the modeling of manufacturing wages more thoroughly than the modeling of other sectors’

wages. Therefore, it is interesting to re-estimate two of the models in “Nor- wegian wage curves” with a new and extended data set. Johansen used a sample spanning the years 1964-1990, while in this thesis, the time series covers the years 1970-2018.

Despite re-estimating the models with the same variables, it is not realis- tic to expect a near perfect replication of Johansen’s estimation results. The data set at hand is based on the National Accounts where the valuing prin- ciple is gross product basic value. Johansen, however, uses factor value in his paper from 1995. On the other hand, if the estimation does show similar results to a large degree, despite the differences in valuing principles, it will give support to the relevance and realism of such wage relations.

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The re-estimated models are called M2* and M4*. The models are identical to M2 and M4 in “Norwegian wage curves.” The re-estimated models only vary from each other with the functional specification of unemployment and whether contemporary unemployment is included or not. See Table 4.1 for complete overview of the estimation results from the reference study and the re-estimated models. Some differences in the data are worth mentioning. The factor income deflator, P Y F1, in M2* and M4* is likely different than that used in the estimation of M2 and M4. P Y F1 comes from the KVARTS-database and follows an implicit export price deflator, calculated using National Accounts data, closely. See Boug and Dyvi (2008) for more information on P Y F1. Other differences in data may have arisen as a result of data revisions, changes in measuring methods, or both. Lowercase variable names indicate the natural logarithm of the variable, e.g., a = ln(A).

Further, d times lagged variables are indicated by subscript “t-d”. E.g., a_t-1 indicates the first lag of the variable a_t. Registered unemployment is used in the re-estimation to be consistent with Johansen (1995).

The term (wc1−pyf1−z1)_t-1is the lagged difference between the natural logarithm of wage cost and the wage scope (“lønnsevne”) in manufacturing.

The wage scope is represented by the hourly labor productivity times the factor income deflator. The product of these variables should indicate how much the manufacturing sector is able to pay a worker by the hour (on average). dumJ ohansen is set to one in 1979 and 1988, 0.5 in 1989 and zero otherwise. This is to capture income policy measurements made in the mentioned years. The dummy is defined in the same way as in Johansen (1995). For more detailed description of the variables, see Chapter 5 and appendix A.

Results from the estimation show that most of the coefficients in M2 and M2*, and M4 and M4* are of similar magnitude. The exceptions are the constant terms and the coefficients of the change in the payroll tax rate (“ar- beidsgiveravgift”), ∆(1 +t11)t. The constant terms reflect different averages in the variables in the two data sets and, thus, require no deeper analysis at this point. The change in the payroll tax rate has coefficients that deviate substantially from the models in “Norwegian wage curves.” The signs are,

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Table 4.1: Reported estimation results from “Norwegian wage curves” and output from the re-estimated models.

Dependent variable: ∆wc1 Dependent variable: ∆w1

1964-1990 1971-2018

Johansen (1995) Re-estimation

Variables M2 M4 M2* M4*

(wc1-pyf1-z1)_t-1 -0.25 -0.21 -0.23 -0.20

(7.03) (7.30) (-4.55) (-3.53)

∆pyf1_t 0.34 0.31 0.30 0.25

(8.21) (8.50) (4.63) (3.63)

∆cpit-1 0.42 0.46 0.59 0.62

(7.49) (9.52) (6.24) (6.48)

∆(1-t11)_t 0.77 0.52 -0.79 -0.86

(3.27) (2.42) (-2.29) (-2.36)

∆h_t -0.54 -0.60 -0.50 -0.60

(5.89) (7.80) (-2.99) (-3.47)

ut-1 -0.08 — -0.02 —

(4.97) (-2.82)

U_t⁻² — 0.007 — 3.43e-006

(1.92) (2.29)

Ut-1−2 — 0.015 — -4.03e-007

(4.59) (-0.32)

dumJohansent -0.06 -0.05 -0.05 -0.04

(10.15) (10.32) (-4.46) (-3.39)

Constant -0.00 -0.02 -0.12 -0.06

(0.40) (2.25) (-5.50) (-2.57)

Diagnostics

σ 0.0072 0.0060 0.0137 0.0139

DW 1.63 1.99 1.16 1.15

AR(1) 0.57 (0.46) 0.00 (0.93) 13.12 (0.00) 10.64 (0.00) AR(2) 0.39 (0.68) 0.12 (0.89) 6.51 (0.00) 5.46 (0.01) ARCH(2) 0.09 (0.91) 0.46 (0.64) 0.49 (0.61) 0.62 (0.54) NORM 0.21 (0.90) 0.16 (0.92) 0.21 (0.90) 1.66 (0.44) t-values in parentheses to keep in line with output from article. For the diagnostics, p-values are reported in parentheses. The mis-specifaction tests regarding M2 and M4 are reported in Johansen (1995). The tests for M2* and M4* are the standard tests reported by PcGive 14 as well as the DW-statistics (which is available in the test menu): DW is the Durbin-Watson statistic. AR(j) test, j=1, 2, is the LM-test for error autocorrelation, F-form, see Harvey (1981). ARCH(2) is the 2nd order LM-test of ARCH heteroskedasticity, see Engle (1982). NORM is the Chi-square- test of normality, see Jarque and Bera (1980).

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however, as expected as the left-hand side variable in M2* and M4* is wage, while the left-hand side variable in the reference paper is wage cost. The t-values’ magnitudes are across the board lower for the re-estimated models than for M2 and M4. In addition, reported t-values can be somewhat inflated due to the positive autocorrelation in the residuals (AR 1-2 tests). Equivalent diagnostics for M2 and M4 do however show few signs of autocorrelation.

As with the original models, the estimation of M2* and M4* shows that there is significant error correction between manufacturing wages and the wage scope. This gives support to upholding the conclusion in “Norwegian wage curves,” namely that the Phillips curve model excludes important long- term mechanisms characteristic of Norwegian wage formation. To sum up, the significant results in Johansen (1995) still hold despite extending the data set with more than 25 years beyond 1990. This could, in turn, indicate that there have not been structural changes in the manufacturing wage formation since at least 1964 (the start of Johansen’s sample).

Another result is that the functional specification of the unemployment rate is not robust. The more convex specification leads to a non-significant coefficient of contemporaneous unemployment and a close to zero coefficient of lagged unemployment¹. In M2*, unemployment is included as the natural logarithm of the unemployment rate, i.e.,ln(U) oru. With this specification, the coefficient of lagged unemployment is negative and significantly different from zero. The models’ standard deviations are lower for M2 and M4 than for M2* and M4*.

Figure 4.1 shows the recursive estimation of the coefficients of M2*. The estimates are quite stable over time when assessed in the interval of ±2 estimated standard errors.

1In the estimation of M4*, unemployment was included first as a rate and then as percentage. The result was almost identical for both specifications

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Figure 4.1: Plots of the recursively estimated coefficients of the variables in M2*. The dashed bands are the respective approximate 95 percent confidence intervals of the coefficients.

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Chapter 5 Empirical Modeling of the System of Wage Formation

In this chapter, empirical models of the national system of wage formation in a macro perspective are presented. The different models represent systems which determine the wage growth in three sectors of mainland Norway:

manufacturing, sheltered private sector and the public sector. First, separate equations for the three sectors are estimated. The manufacturing equation is recognized from the previous chapter. Second, the equations are estimated as a recursive system. The system is then expanded. The final part of the chapter presents a simultaneous equations model (SEM) which incorporates inflation expectations as an explanatory variable.

5.1 Sector-by-sector equations

M2* is the point of departure for the model for manufacturing wages. How- ever, some changes are made. Firstly, unemployment measured by the Labour Force Survey is used in the following, while registered unemployment was used in the previous estimation. Secondly, the dummy for income policies is altered somewhat. It is now defined as dumST OP which takes the value of one in 1978, 1979, 1988 and 1989, zero otherwise. This specification is in line with relevant literature, see, e.g., Langørgen (1993). Finally, scope1

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is used as the name for the wage scope of the manufacturing sector, earlier (pyf1 +z1). Which sector variables belong to is indicated by numbers 1-3 at the end of the variable names. E.g., w1 is the natural logarithm of the hourly wage of sector 1 (manufacturing), while w2 is the equivalent for sector 2 (sheltered private sector) and w3 the same for sector 3 (public sector).

The three modeled variables in this section are wage growth in the above- mentioned sectors, namely ∆w1, ∆w2 and ∆w3. See Table 5.1 for estimation results and diagnostic tests.

The estimated model for the wage in the sheltered private sector clearly shows error correction of deviations from manufacturing wages. According to the estimation result, 27 percent of a gap between wages in manufacturing and sheltered private sector would, all else equal, be “corrected” in one period. In addition, manufacturing wage growth enters the estimated equation significantly. This implies that one percent higher wage growth in the manufacturing sector would, isolated, lead to a 0.75 percent higher wage growth in the sheltered private sector.

In the expression for the public sector, error correction is non-significant if wage growth in the sheltered private sector is included. However, error correction between sector 2 and 3 is significant if the wage growth in sector 2 is not included in the expression. One interpretation of this result is that sheltered private and public sector wages follow each other so closely that it is not possible to single out both a level-term and a growth-term. The final specification of the model of public sector wage thus includes wage growth in sector 2 and not an error correction term to the same sector. See Section 5.2 for further discussion of how closely the series follow each other. The dummydum2003 is included in ∆w3 to capture an unusually large difference in negotiated nominal adjustments in the public sector from 2003 to 2004.

The differences can probably be explained by relatively high nominal wage adjustments for employees in the public sector, especially in health services, while the adjustments were substantially lower in 2004 (probably partially due to low inflation, 0.4 percent)¹. The dummy equals one in 2003 and zero

1https://frifagbevegelse.no/skjult-artikkel/lonnsoppgjorene-1990--2014-6.158.75663.

57907ee781 (downloaded 05.02.2019)

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otherwise. The misspecification tests vary in terms of significance with most of the issues arising from the manufacturing wage growth equations. Table 5.1 reports misspecification test statistics and the statistics’ p-values in the diagnostics section.

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Table 5.1: Results from the estimation of wages in the three sectors. Sample period: 1970-2018.

Dependent Variables

Variables ∆w1 ∆w2 ∆w3

uakut-1 -0.032*** -0.012** —

(0.01) (0.00)

(wc1-scope1)t-1 -0.210*** — —

(0.05)

(w2-w1)t-1 — -0.273*** —

(0.08)

(w3-w2)_t-1 — — 0.012

(0.03)

∆w1_t — 0.745*** —

(0.07)

∆w2t — — 0.869***

(0.04)

∆w2t-1 — 0.071 —

(0.07)

∆w3t-1 — — -0.060

(0.05)

∆cpit-1 0.506*** — 0.086*

(0.10) (0.05)

∆(1+t11)t -0.869** — —

(0.34)

∆h_t -0.521*** 0.016 —

(0.16) (0.09)

∆pyf1_t 0.217*** — —

(0.06)

dumSTOP_t -0.031*** -0.008 -0.012***

(0.01) (0.00) (0.00)

dum2003t — — 0.027***

(0.00) Constant -0.158*** -0.030** 0.007**

(0.02) (0.01) (0.00)

Diagnostics

σ 0.0136 0.0070 0.0049

AR 1-2 5.29 (0.009) 0.61 (0.55) 1.38 (0.26) ARCH (1) 0.06 (0.81) 0.12 (0.73) 8.56 (0.01) NORM 0.87 (0.65) 0.35 (0.84) 2.40 (0.30) HETERO 2.40 (0.02) 1.15 (0.35) 1.99 (0.07) Estimated coefficients with standard errors in the parentheses. Regarding the diagnostics, p-values are reported in the parentheses. *, **, *** denote significance at 10%, 5% and 1% respectively. σis the equation standard error. The misspecification tests are the standard tests reported by PcGive 14, see Table 4.1 for sources.

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5.2 Recursive system

The sector-equations yield insight into the determinants of wages in three sectors of the Norwegian economy. However, as the results show, it is likely that the wage formation has system qualities. Estimating the equations as a recursive system can capture some intuition behind the sequential nature of how wage negotiations are carried out. This estimation means that the main principles of the Wage-Leader Model (“frontfagsmodellen”) are taken as given, and the pattern wage bargaining system is modeled as “strictly”

recursive. This thesis has not carried out econometric testing of the causal relations, e.g., of whether manufacturing actually serves as wage-leader for the other sectors or not. That would entail more comprehensive investigation, but econometric tests on quarterly data give a reasonably clear indication of stability in the systemic relations, especially from the mid-1990s and onward, see Gjelsvik et al. (2015). The recursive estimation in this section leads to the results reported in Table 5.2, while Table 5.3 reports related diagnostics.

To “close off” the system, an equation for inflation measured by the growth in the Consumer Price Index, ∆cpi_t, is included as an endogenous variable. This is done to account for the cost of living as a primary factor in the wage formation, also in the leading industry, and that inflation, in turn, depends on wage growth, not necessarily simultaneously but at least over time. It is important to mention that the specified inflation-equation does not aspire to be a full-fledged model of the inflation, but rather to represent a simple relation with those strengths and weaknesses it entails. The estimated CPI-equation aims to capture, in broad strokes, the connection between wage costs and CPI-growth. Estimation showed that prices on imported goods accounted for a share of the inflation, while sheltered sector unit labor cost, w2−z2, also matters. As a consequence, it is interesting to test whether there is a long-term relationship between CPI-development and the mentioned variables weighted by the terms’ contribution to total CPI.

In line with B˚ardsen, Jansen, and Nymoen (2003), the import price index is weighted by a factor of 0.4. The corresponding weight on the unit labor cost in the error correction term is consequently 0.6. The long-term relationship

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to be tested is thus cpi−0.6×(w2−z2)−0.4×pb, wherepb is an estimated import price deflator based on data from the national accounts.

The system in Table 5.2 is estimated using one stage least squares (1SLS).

It is in total four endogenous variables. All of the error correction terms are defined as identities under the estimation.

The estimated manufacturing wage equation shows that unemployment in one year significantly affects the wage growth in manufacturing the following year. Furthermore, a particularly significant relationship between manufacturing wage growth and the difference between wage costs and wage scope (“lønnsevne”) is observed. This entails, all else equal, that the expected wage growth is positive if the wage costs in the previous period were lower than what the exposed industry could bear in the that period, i.e., if the employers had lower wage costs than the value of what the workers produced. In the opposite case, it means that the exporting sector cannot sustain higher wage costs than the sector can bear, namely the wage scope, over time. One interpretation of this is that the manufacturing industry is subject competition on the world market and cannot have “run-away” wages separated from the world market prices of what they produce if they wish to stay competitive. The significant error correction term indicates that the Norwegian manufacturing sector has over time pinned its hourly wage level to factors which contribute to the sector’s “survival”.

For the sheltered private sector, ∆w2, the wage formation is obviously tied to the manufacturing sector, both in the short-run and in the long- run. Firstly, the contemporaneous change in manufacturing wages has a coefficient of approximately 0.8 in the estimated equation. This is a clear example of the short-run relation. Secondly, there is an evident long-run dynamic between the sectors. Around 24 percent of a deviation between wages in the two sectors is, all else equal, corrected from one period to the next. This indicates that also the level of the wages follow each other over time.

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Table 5.2: Results from the estimation of the recursive system with four endogenous variables. Sample period:

1970-2018.

Dependent Variables

Variables ∆w1 ∆w2 ∆w3 ∆cpi

uakut-1 -0.032*** -0.009* -0.008** 0.003 (0.01) (0.00) (0.00) (0.00)

(wc1-scope1)t-1 -0.231*** — — —

(0.05)

(w2-w1)t-1 — -0.237*** — —

(0.08)

(w3-w2)_t-1 — — -0.033 —

(0.03)

∆w1_t — 0.804*** — —

(0.05)

∆w2t — — 0.803*** —

(0.05)

∆w2t-1 — 0.033 — —

(0.06)

∆(w2-z2)t — — — 0.371***

(0.09)

∆cpit-1 0.546*** — 0.065 0.243**

(0.10) (0.04) (0.10)

∆(1+t11)t -0.690* — — —

(0.36)

∆h_t -0.500*** — — —

(0.16)

∆pb_t — — — 0.117***

(0.04)

∆pyf1_t 0.197*** — — —

(0.06) (cpi-0.6×(w2-z2)

-0.4×pb)t-1

— — — -0.167***

(0.04) dumSTOPt -0.031*** — -0.016*** -0.006

(0.01) (0.00) (0.01)

dum2003t — — 0.025*** —

(0.00)

Constant -0.166*** -0.025* -0.019 0.822***

(0.02) (0.01) (0.01) (0.22) Standard errors are reported in the parentheses. *, **, *** denote significance at 10%, 5% and 1% respectively.

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For the modeling and estimation of the recursive system, the lagged unemployment rate was added to the public sector wage equation, ∆w3t. As the potential significance of the coefficient of the unemployment rate has important theoretical implications, it is interesting to include the unemployment rate as an explanatory variable in the system estimation. As in the single- equation estimation, see the previous section, the public sector appears to be connected to the industry not directly, but through its relationship with the sheltered private sector. The error correction term between sector 2 and 3 is also here non-significant when including wage growth in the sheltered private sector in ∆w3. It is worth point out that while, as seen in Table 5.2, the error correction term is not significant, the magnitude of the coefficient’s t-value has increased a lot after estimating the equations as a recursive system. Fig- ure 5.1 shows how closely the series follow each other and, as commented on in the previous section, illustrate how that can make it difficult to separate both long-run and short-run dynamics concerning sector 2 in this case. Fur- ther, it is clear that the dummies for the income policies in the late ’70s and

’80s,dumST OP, and the difference in nominal compensation in 2003 relative to 2004 are significant in the estimated equation for public wage growth.

Figure 5.1: The upper panel shows the natural logarithm of wage in sector 2 and 3 from 1970-2018, while the lower panel shows the difference in the same variables in the same period.

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The results for the growth in the CPI show that there is error correction between growth in consumer prices and the unit labor costs, (w2−z2), and

“imported” inflation, pb. While unit labor costs dominate in the expression, the almost equally large weight on the import price index reflects the fact that Norway is a small open economy. The weights should however not be taken too seriously as modeling CPI is not the main aim of this thesis. Notice how the change in w2−z2 and pb have coefficients which are both positive and significant. This implies that changes in wage growth, productivity, and import prices also affects domestic CPI-inflation in the short-run. It is also interesting to point out that the unemployment rate does not have a significant coefficient in the CPI-equation. The effect of changes in the unemployment rate on the CPI “path” is thus mostly indirect, through wage growth.

Table 5.3 shows the single-equation diagnostics for the equations in the system. As with the sector equations previously estimated separately, the autocorrelation tests yield the lowest p-values. However, single-equation tests should not be given too much attention in a system like this.

Table 5.3: Single-equation diagnostics for the estimated recursive system with four endogenous variables. Sample period: 1970-2018.

Dependent Variables

Diagnostics ∆w1 ∆w2 ∆w3 ∆cpi

σ 0.0131 0.0071 0.0047 0.0096 AR 1-2 5.47*** 8.53*** 8.68*** 7.67***

(0.01) (0.00) (0.00) (0.00)

ARCH 1-1 0.02 4.35** 0.95 0.54

(0.88) (0.04) (0.34) (0.47)

NORM 0.43 2.09 3.76 0.61

(0.81) (0.35) (0.15) (0.73) HETERO 2.01* 3.05*** 3.86*** 0.87

(0.05) (0.00) (0.00) (0.63) p-values in parentheses. *, **, *** denote significance at 10%, 5% and 1% respectively. σis the equation standard error. The misspecification tests are the standard tests reported by PcGive 14, see Table 4.1 for sources.

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5.2.1 Simulation

The model above can be classified as being dynamic in the sense that time plays an essential role. It is thus interesting to assess the dynamics of the estimated model by simulating exogenous shocks to one or more of the system equations. Such shocks, or impulses, can either be temporary or permanent.

In the following, two shocks are given to the system in turn.

The first shock is a temporary, unit shock to ∆pyf1t, i.e., the change in the manufacturing factor income deflator. As seen in Table 5.2, ∆pyf1_t is a part of the equation for manufacturing wage growth with a coefficient of 0.197. Therefore, the shock to ∆pyf1_t will hit the system through ∆w1_t with a magnitude of 0.197. Figure 5.2 illustrates the dynamics, or the impulse response, of the three wage equations for 20 periods after the shock hits. Interestingly, the impulse response dies out relatively quickly. The wage equations behave quite similarly with an initial increase followed by a downward trend until the impulse slowly phases out. There is little reason to believe that wages in the three sectors have reached a higher level.

Figure 5.3 illustrates the impulse response of a permanent unit shock to ∆pyf1_t. Again, this hits the system with a force of 0.197 to ∆w1_t. For manufacturing and sheltered private sector, the change yields a higher growth in wages for around 20 periods. For the public sector wage growth, the shock has a relatively smaller initial effect but the impulse response lasts, in return, somewhat longer. The implication is that wage growth increases in all sectors as a response to the increase in the wage scope in the manufacturing sector. The wage growth is positive for several periods, but eventually returns to zero when the wages have adjusted to the new and higher level of the manufacturing wage scope.

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Figure 5.2: Plotted impulse response (dynamic multiplier) over 20 periods of the three estimated wage equations to a temporary unit shock in ∆pyf1.

Figure 5.3: The accumulated impulse response (accumulated multiplier) over 20 periods of the three estimated wage equations to a unit shock in ∆pyf1.

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5.3 Modifying and expanding the recursive system

The recursive system in Section 5.2 can be regarded as a baseline model.

While CPI was included to close off the system, there are still several variables which can be regarded as potentially important in the dynamics of the equations for wage formation. To account for such dynamics, it is desirable to endogenize more variables. In this section, the system is expanded by including unemployment, productivity in manufacturing and sheltered private sector and the manufacturing factor income deflator as endogenous variables in the system. This is done without expanding the data set. Furthermore, the significance of the error correction terms in the wage and CPI equations is tested when the terms are included as lagged explanatory variables in the formulated equations for uaku_t, ∆z1_t, ∆z2_t and ∆pyf1_t.

5.3.1 Specification of marginal equations

Expanding the system requires specification of equations for the variables to be endogenized in the system. It also requires some assessment of which variables to consider as exogenous to the system.

Firstly, it is assumed that the import price index, pb, is exogenous to the system. As Norway is a small open economy, it is reasonable to assume that consumers of imported goods are price takers with respect to those goods.

Secondly, the length of the workweek, H, is also considered exogenous.

Unemployment is a clear candidate when searching for variables to include as endogenous. In Chapter 2, it was assumed that the unemployment rate,uaku, is stationary. However, the tests indicated that the series could be I(1). As briefly commented, one reason for the non-significant I(1) test could be due to a shift in the variable’s mean. Therefore, when trying to express the unemployment rate as an endogenous variable, automatic break detection was used to detect potential location shifts of the mean value. Also, outlier detection was used to capture other potentially meaningful events.

Both outlier and break detection is a part of the PcGive package in OxMet-

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rics, more specifically the function Autometrics. For outlier detection, the program uses Impulse Indicator Saturation while Step-Indicator Saturation is used for detecting structural breaks (i.e., location shifts of the mean value).

These methods are well documented, see e.g., Castle, Doornik, and Hendry (2012) and Castle, Doornik, Hendry, and Pretis (2015).

The process revealed two one-period dummies and one structural break.

The dummies dum1973 and dum1976 are highly significant and do, most likely, capture the volatile conditions of the 1970s. They take the value 1 in 1973 and 1976 respectively, zero otherwise. The structural break, B : 1986, represents an increase in the mean unemployment rate from 1987 and onwards. The dummy takes the value 1 from 1970-1986, and zero otherwise.

One possible reason for the increase in the unemployment rate might be the de-regulation of the financial markets in the 1980s which, coupled with oil price drops, global economic slowdown and tightening monetary policy, lead to a recession from 1987-1990². This supports the assumption in Chapter 2, namely that the unemployment rate indeed is I(0) and that the location shift of the mean affected the unit-root tests. Unemployment is thus, in this simplified setting, considered to follow an AR(2) process with a constant term, dum1973_t, dum1976_t and B : 1986_t.

Productivity might also improve the modeled dynamics of the system.

The recursive system in Chapter 4 contains z1 and z2, both assumed to be I(1) in Chapter 2. Due to the non-stationarity of the level-variables, equations for ∆z1 and ∆z2 are specified. Both variables are assumed to follow a simple AR(1) process (with a constant term). With the available data set, this seemed to give the best representation of the growth in productivity.

The factor income deflator, pyf1, was also assumed to be I(1) following the unit-root tests. Consequently, ∆pyf1 is modeled as a simple AR(1) process (with a constant term).

2https://www.ssb.no/bank-og-finansmarked/artikler-og-publikasjoner/bankkrisen (downloaded 11.03.2019)

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The final equations to be included in the expanded system are:

uaku_t =α₀+α₁uaku_t-1+α₂uaku_t-2+α₃dum1973_t +α₄dum1976_t+α₅B : 1986_t+_uaku

∆z1t =β0+β1∆z1t-1+z1

∆z2_t =θ₀+θ₁∆z2_t-1+_z2

∆pyf1t =γ0+γ1∆pyf1t-1+pyf1

5.3.2 Estimating the expanded system

Including four variables as endogenous of the system affects the misspecification tests of all the estimated equations in the system. However, as the system is recursive, the coefficients and t-values of the previously estimated equations do change. Hence Table 5.4 only reports the estimation results of the new variables, while Table 5.5 reports the single-equation diagnostics for the whole system.

It is clear from Table 5.4 that the coefficients of included explanatory variables in the expression for the unemployment rate are significantly different from zero. Regarding productivity in the manufacturing sector, it seems as if the growth is random around some mean as the coefficient of the lagged variable is not significant. The misspecification tests are all insignificant for

∆z1_t. As ∆z1_t = ln_Z^Z^1t

1t-1 = 0.019 and thus _Z^Z^1t

1t-1 = exp (0.019) ≈ 1.02, it means that the average annual growth in productivity in the manufacturing sector is 2 percent. Figure 5.4 illustrates how the constant goes towards the value of 0.02 as the estimation sample grows. The plot does not clearly indicate that productivity growth has seen a mean shift, but it does not rule it out either.

Productivity growth in the sheltered private sector appears to be an AR(1) process. None of the misspecification tests are significant except from the normality test which barely made the 10 percent significance level mark.

See Figure 5.5 for the coefficient plots of the estimated productivity growth in sector 2. Similarly, the growth in the factor income deflator also appears

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Table 5.4: Estimation results for the added endogenous variables to the recursive system. Sample period: 1970- 2018.

Dependent Variables

Variables uaku_t ∆z1_t ∆z2_t ∆pyf1_t

uaku_t-1 1.180*** — — —

(0.12)

uakut-2 -0.603*** — — —

(0.12)

∆z1_t-1 — 0.045 — —

(0.15)

∆z2_t-1 — — 0.425*** —

(0.14)

∆pyf1t-1 — — — 0.339**

(0.15)

dum1973_t -0.415*** — — —

(0.14)

dum1976_t -0.501*** — — —

(0.14)

B:1986t -0.233*** — — —

(0.06)

Constant -1.369*** 0.019*** 0.010*** 0.027***

(0.23) (0.005) (0.00) (0.01)

Standard errors in parenthesis. *, **, *** denote significance at 10%, 5% and 1% respectively.

to follow an AR(1) process. None of the misspecification tests regarding

∆pyf1_t in Table 5.5 are significant.

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Table 5.5: Misspecification tests for the expanded recursive system in Table 5.4.

Diagnostics Dependent

variables σ AR (1-2) ARCH(1-1) NORM HETERO

∆w1t 0.013 7.58*** 2.17 3.70 3.25***

(0.00) (0.15) (0.16) (0.00)

∆w2_t 0.007 11.09*** 0.61 1.48 1.37

(0.00) (0.44) (0.48) (0.22)

∆w3t 0.005 9.16*** 0.09 1.61 1.24

(0.00) (0.77) (0.45) (0.30)

∆cpit 0.009 8.21*** 0.17 0.44 3.37***

(0.00) (0.69) (0.80) (0.00)

uaku_t 0.126 0.95 0.07 0.46 0.45

(0.40) (0.79) (0.79) (0.81)

∆z1t 0.028 1.08 0.81 0.20 0.59

(0.34) (0.37) (0.90) (0.56)

∆z2t 0.014 1.10 0.01 4.92* 1.30

(0.34) (0.92) (0.09) (0.28)

∆pyf1_t 0.040 0.90 0.25 0.03 1.29

(0.41) (0.62) (0.98) (0.29) p-values in parentheses. *, **, *** denote significance at 10%, 5% and 1%

respectively. σ is the equation standard error. The misspecification tests are the standard tests reported by PcGive 14, see Table 4.1 for sources.

Under the Macroscope: An Empirical Model of the System of Norwegian Wage Formation