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Cointegration and Structure in Norwegian Wage–Price Dynamics^{ †}

^{1}

^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Wage Pattern Relationship

#### 2.1. Manufacturing Sector

#### 2.2. Private Service Sector and Public Sector

#### 2.3. Wage–Price Inflation

## 3. Data Set and VAR Formulation

- ${W}_{it}$: index for hourly wage in sector i = 1, 2, 3.
- ${P}_{t}$: consumer price index.
- ${Q}_{1t}$: price deflator of gross value added, manufacturing industry.
- ${Z}_{1t}$: labour productivity, output per hour in manufacturing.
- $P{I}_{t}$: price deflator of imports of goods and services.
- ${U}_{t}$: unemployment rate, in per cent, civilian unemployment.
- $I{M}_{t}$: immigration from EU/EFTA countries, North America, Australia and New Zealand and non-EU Eastern Europe, in per cent of the population aged 15–74.

## 4. Cointegration Analysis

## 5. Testing the Wage-Leading Hypothesis within a SEM

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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1. | The data set is available from the authors on request. |

2. | The co-editors’ observation. |

3. | |

4. | One internal inconsistency that arose was that the test of omission of the trend from the cointegrated system was significant. Dropping the trend, does however not damage the diagnostics, and it gives interpretable results. Keeping it in the cointegration space does not. |

5. | Additional results, based on a sample split in 2000(4), before both the change in monetary policy and the enlargement of the EU labour market, are available from the authors. |

**Figure 1.**Trends in manufacturing wage formation: hourly wage costs ${w}_{1t}$, average labour productivity ${z}_{1}$ and value-added deflator ${q}_{1}$. All three variables are measured in natural logarithms. The graphs have been scale adjusted for easier comparison.

**Figure 2.**Plot of the immigration flow ($IM$) measured as gross immigration in per cent of the working-age population and the natural logarithm of the unemployment rate (u). The graph for u has been scale adjusted for easier comparison.

${\mathit{w}}_{\mathbf{1}}$ | ${\mathit{w}}_{\mathbf{2}}$ | ${\mathit{w}}_{\mathbf{3}}$ | p | |
---|---|---|---|---|

${F}_{AR}$ | $1.49\left(0.21\right)$ | $1.61\left(0.17\right)$ | $1.53\left(0.19\right)$ | $1.46\left(0.21\right)$ |

${F}_{ARCH}$ | $0.56\left(0.21\right)$ | $0.55\left(0.70\right)$ | $0.17\left(0.95\right)$ | $0.46\left(0.76\right)$ |

${\chi}_{NORM}^{2}$ | $1.12\left(0.57\right)$ | $0.46\left(0.79\right)$ | $5.30\left(0.07\right)$ | $0.14\left(0.93\right)$ |

Eigenvalue | Trace Test | |||
---|---|---|---|---|

(${\mathit{\lambda}}_{\mathit{i}}$) | ${\mathit{H}}_{\mathbf{0}}$ | ${\mathit{H}}_{\mathbf{1}}$ | Test Statistics | Critical Values |

$0.49$ | $r=0$ | $r>0$ | 234.32 | $166.63$ |

$0.41$ | $r=1$ | $r>1$ | 139.80 | $121.65$ |

$0.29$ | $r=2$ | $r>2$ | 65.34 | $80.315$ |

$0.12$ | $r=3$ | $r>3$ | 17.26 | $41.97$ |

${w}_{1}=\underset{(.)}{1}{x}_{1}\underset{\left(0.11\right)}{-0.71}u\underset{\left(0.66\right)}{-1.91}IM\underset{\left(0.08\right)}{+0.07}{D}_{1}\underset{\left(0.15\right)}{+0.05}{D}_{2}$ |

${w}_{2}=\underset{(.)}{1}{w}_{1}\underset{\left(0.03\right)}{-0.17}u\underset{\left(0.18\right)}{-0.35}IM\underset{\left(0.03\right)}{+0.03}{D}_{1}\underset{\left(0.05\right)}{-0.03}{D}_{2}$ |

${w}_{3}=\underset{(.)}{1}{w}_{2}\underset{\left(0.01\right)}{-0.03}{D}_{1}\underset{\left(0.01\right)}{+0.04}{D}_{2}$ |

${p}_{t}=\underset{\left(0.06\right)}{0.45}{w}_{2}-\underset{\left(0.14\right)}{0.09}{z}_{1}+\underset{\left(0.06\right)}{0.30}pi\underset{\left(0.02\right)}{+0.03}{D}_{1}\underset{\left(0.03\right)}{-0.07}{D}_{2}$ |

Test of over-identifying restrictions: ${\chi}^{2}\left(13\right)=19.45\left[0.11\right]$ |

**Table 4.**Wage–price simultaneous equations model (SEM). FIML estimates of the contemporaneous coefficient matrix ${\widehat{\mathbf{B}}}_{\mathbf{0}}$ (first four columns with estimates) and adjustment coefficients $\widehat{\mathbf{A}}$ (last four columns). Standard errors in brackets below the estimates. Sample period 1980(1)–2014(4).

$\mathsf{\Delta}{\mathit{w}}_{\mathbf{1}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{w}}_{\mathbf{2}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{w}}_{\mathbf{3}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{p}}_{\mathit{t}}$ | ${\widehat{\mathit{e}}}_{\mathbf{1}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{e}}}_{\mathbf{2}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{e}}}_{\mathbf{3}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{e}}}_{\mathbf{4}\mathit{t}-\mathbf{1}}$ | |
---|---|---|---|---|---|---|---|---|

$\Delta {w}_{1t}$ | $-1$ | $\underset{\left(0.20\right)}{-0.28}$ | $\underset{\left(0.13\right)}{-0.11}$ | $\underset{\left(0.21\right)}{0.44}$ | $\underset{\left(0.01\right)}{-0.03}$ | 0 | 0 | 0 |

$\Delta {w}_{2t}$ | $\underset{\left(0.06\right)}{0.21}$ | $-1$ | $\underset{\left(0.09\right)}{-0.19}$ | $\underset{\left(0.13\right)}{0.42}$ | 0 | $\underset{\left(0.06\right)}{-0.11}$ | 0 | 0 |

$\Delta {w}_{3t}$ | $\underset{\left(0.11\right)}{0.27}$ | $\underset{\left(0.16\right)}{-0.09}$ | $-1$ | $\underset{\left(0.22\right)}{1.10}$ | 0 | 0 | $\underset{\left(0.03\right)}{-0.20}$ | 0 |

$\Delta {p}_{t}$ | $\underset{\left(0.05\right)}{-0.05}$ | $\underset{\left(0.08\right)}{0.19}$ | $\underset{\left(0.06\right)}{0.07}$ | $-1$ | 0 | 0 | 0 | $\underset{\left(0.01\right)}{-0.10}$ |

${\chi}_{ENC-VAR}^{2}=74.48\left[0.06\right]$ |

**Table 5.**Likelihood-ratio tests of wage leader/follower restrictions on the model in Table 4.

Restrictions: | $\mathrm{Sec}\text{}1\nrightarrow $$\mathrm{Sec}\text{}2$ | $\mathrm{Sec}\text{}1\nrightarrow $$\mathrm{Sec}\text{}3$ | $\mathrm{Sec}1\nrightarrow \mathrm{Sec}\text{}2\text{}\mathrm{and}\text{}3$ |

${\chi}^{2}\left(1\right)=11.{91}^{**}$ | ${\chi}^{2}\left(1\right)=16.{78}^{**}$ | ${\chi}^{2}\left(2\right)=26.{23}^{**}$ | |

Restrictions: | $\mathrm{Sec}\text{}2\nrightarrow $$\mathrm{Sec}\text{}1$ | $\mathrm{Sec}\text{}3\nrightarrow $$\mathrm{Sec}\text{}1$ | $\mathrm{Sec}\text{}2\text{}\mathrm{or}\text{}3\nrightarrow $ Sec 1 |

${\chi}^{2}\left(1\right)=2.04$ | ${\chi}^{2}\left(1\right)=0.62$ | ${\chi}^{2}\left(2\right)=2.75$ | |

Restrictions: | $\mathrm{Sec}\text{}2\nrightarrow $$\mathrm{Sec}\text{}3$ | $\mathrm{Sec}\text{}3\nrightarrow $$\mathrm{Sec}\text{}2$ | $\mathrm{Sec}\text{}2\text{}{\text{}}_{\nleftarrow}^{\nrightarrow}$$\mathrm{Sec}\text{}3$ |

${\chi}^{2}\left(1\right)=0.32$ | ${\chi}^{2}\left(1\right)=4.{41}^{*}$ | ${\chi}^{2}\left(2\right)=5.90$ |

**Table 6.**Wage–price SEM with wage leader-follower restrictions imposed. FIML estimates of ${\widehat{\mathbf{B}}}_{\mathbf{0}}$ and $\widehat{\mathbf{A}}$ in Equation (7) with standard errors in brackets below the estimates. Sample period 1980(1)–2014(4).

$\mathsf{\Delta}{\mathit{w}}_{\mathbf{1}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{w}}_{\mathbf{2}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{w}}_{\mathbf{3}\mathit{t}}$ | $\mathsf{\Delta}{\mathit{p}}_{\mathit{t}}$ | ${\widehat{\mathit{ec}}}_{\mathbf{1}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{ec}}}_{\mathbf{2}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{ec}}}_{\mathbf{3}\mathit{t}-\mathbf{1}}$ | ${\widehat{\mathit{ec}}}_{\mathbf{4}\mathit{t}-\mathbf{1}}$ | |
---|---|---|---|---|---|---|---|---|

$\Delta {w}_{1t}$ | $-1$ | 0 | 0 | $\underset{\left(0.16\right)}{0.30}$ | $\underset{\left(0.005\right)}{-0.02}$ | 0 | 0 | 0 |

$\Delta {w}_{2t}$ | $\underset{\left(0.06\right)}{0.17}$ | $-1$ | 0 | $\underset{\left(0.11\right)}{0.33}$ | 0 | $\underset{\left(0.02\right)}{-0.14}$ | 0 | 0 |

$\Delta {w}_{3t}$ | $\underset{\left(0.08\right)}{0.20}$ | 0 | $-1$ | $\underset{\left(0.24\right)}{1.19}$ | 0 | 0 | $\underset{\left(0.07\right)}{-0.26}$ | 0 |

$\Delta {p}_{t}$ | 0 | $\underset{\left(0.05\right)}{0.14}$ | 0 | $-1$ | 0 | 0 | 0 | $\underset{\left(0.01\right)}{-0.10}$ |

${\chi}_{ENC-VAR}^{2}=86.42\left[0.03\right]$ |

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**MDPI and ACS Style**

Gjelsvik, M.; Nymoen, R.; Sparrman, V. Cointegration and Structure in Norwegian Wage–Price Dynamics. *Econometrics* **2020**, *8*, 29.
https://doi.org/10.3390/econometrics8030029

**AMA Style**

Gjelsvik M, Nymoen R, Sparrman V. Cointegration and Structure in Norwegian Wage–Price Dynamics. *Econometrics*. 2020; 8(3):29.
https://doi.org/10.3390/econometrics8030029

**Chicago/Turabian Style**

Gjelsvik, Marit, Ragnar Nymoen, and Victoria Sparrman. 2020. "Cointegration and Structure in Norwegian Wage–Price Dynamics" *Econometrics* 8, no. 3: 29.
https://doi.org/10.3390/econometrics8030029