1. Structural Approach Potential output - part II
Output Gap detection: all the different approaches Luxembourg, 8-10 June 2016
CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE EUROPEAN COMMISSION

2. Where are we heading to? 𝑌=𝑇𝐹𝑃∙ 𝐿 𝛼 𝐾 1−𝛼
Complete the application of the PF method
to measure potential output and output gap.
The missing element is potential labor, which EU Commission estimates based on three variables: NAIRU, labor force, average hours of work 𝐴𝑉𝐺𝐻𝑊= 𝐻 𝐿𝐹 .
𝐿= 1− 𝑢 ∗ ∙𝐿𝐹∙𝐴𝑉𝐺𝐻𝑊
We shall focus on the most problematic: the NAIRU.
Estimates will again be based on a bivariate KF. However, the most interesting part is how to get to the model to estimate. This will also help understanding cross-country differences.
𝑌=𝑇𝐹𝑃∙ 𝐿 𝛼 𝐾 1−𝛼

3. Plan of the lecture
To explain how the empirical model is constructed, we recall first principles on the Phillips curve construction and NAIRU.
In doing so, we add some more discussion to our 1st day of class. The aim is to clarify why some PC models fit EU data and some others work better in the US.
Finally, we shall discuss some further issues on measurement.

4. Modeling the NAIRU & NAWRU
The NAIRU is the unemployment rate consistent with stable inflation.
How did we determine it:
starting from a labor market model, based on 2 equations: the wage equation, and the price equation (labor demand);
derive the AS curve;
derive the expectation-augmented Phillips curve.
Hence, the NAIRU as an equilibrium rate corresponding to constant inflation.
We shall proceed slightly differently here, to work with the NAWRU.

5. Labor market
The wage equation (WS) is, 𝑊 𝑡 𝑃 𝑡 𝑒 =𝐹 𝑢 𝑡 , 𝑧 𝑡 written in logs, 𝒘 𝒕 − 𝒑 𝒕 𝒆 =−𝜶 𝒖 𝒕 + 𝒛 𝒕 The price equation (or wage-demand eq.) (PS) is, 𝑃 𝑡 =(1+𝜇) 𝑊 𝑡 𝜌 𝑡 𝒘 𝒕 − 𝒑 𝒕 = 𝒑𝒓 𝒕 − 𝒎 𝒕 𝑝𝑟 𝑡 = ln 𝜌 𝑡 , 𝑚 𝑡 = ln (1+ 𝜇 𝑡 ) The rhs is often taken as the difference btw. labor productivity net of profit-margins, and labor-demand disturbances/shocks.

6. Adding ingredients: z
In transforming the WS into an empirical model, we have to specify institutional factors affecting wage setting z.
This is particularly important to estimate the NAIRU of European economies (vs. US).
Institutional factors are essentially captured by the labor productivity and reservation wages.
From here we essentially follow the seminal paper by Blanchard and Katz (AER, 1999).

7. Adding ingredients: z
Why productivity affects wage determination?
There are several theories on labor productivity:
Efficiency wages: since labor productivity is not perfectly monitored by firms, employers tend to pay a wage above the reservation to avoid adverse selection and moral hazard. This increases in the workers’ outside options (e.g. informal market, home production)
Labor hoarding & firm-specific human capital: when workers have a firm-specific human capital and training is costly, firms try to lock in workers (hoarding). This also increases in the workers’ outside options (e.g. informal market, home production)
Contracting: in bargaining models, workers & employers bargain for the labor-matching surplus, which is also a function of labor-productivity.

8. Adding ingredients: z
z depends on reservation wage 𝑤 𝑅 which is a function of institutions, worker history & other individual characteristics:
unemployment benefits & other forms of income support if unemployed; institutionally, these benefits are usually linked with the worker’s wage history; hence, the reservation wage will also depend on past wages (AR component);
in much psychological research and fairness models of wage determination, 𝑤 𝑅 depends on workers’ wage aspirations in job search and bargaining; which are likely to depend on previous earnings (wage history);
the return from alternative “occupations”, including leisure and opportunities in the informal sector; it seams plausible that an increases in the worker productivity in the informal sect. and home production are closely related to those in the formal market economy;
non-labor income: returns from own savings (capital income, rents); returns from family assets.

9. Adding ingredients: z WS empirical model (Blanchard & Katz, AER 1999).
We take,
𝑧 𝑡 =𝛾 𝑤 𝑡 𝑅 + 1−𝛾 𝑝𝑟 𝑡
𝑤 𝑡 𝑅 = 𝑤 0 𝑅 +𝜆 𝑤 𝑡−1 − 𝑝 𝑡−1 + 1−𝜆 𝑝𝑟 𝑡
and substitute into the WS,
𝒘 𝒕 − 𝒑 𝒕 𝒆 =𝜸 𝒘 𝟎 𝑹 +𝜸𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 + 𝟏−𝜸𝝀 𝐩𝐫 𝐭 −𝜶 𝒖 𝒕
From here we essentially follow the seminal paper by Blanchard and Katz (AER, 1999).

10. Toward an empirical model of WS
𝒘 𝒕 − 𝒑 𝒕 𝒆 =𝜸 𝒘 𝟎 𝑹 +𝜸𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 + 𝟏−𝜸𝝀 𝐩𝐫 𝐭 −𝜶 𝒖 𝒕
Adding and subtracting, 1−𝛾𝜆 𝑝𝑟 𝑡−1 & 𝑤 𝑡−1 − 𝑝 𝑡−1 :
𝚫𝒘 𝒕 =𝜸 𝒘 𝟎 𝑹 + 𝒑 𝒕 𝒆 − 𝒑 𝒕−𝟏 −(𝟏−𝜸𝝀) 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 − 𝒑𝒓 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝐩𝐫 𝐭 −𝜶 𝒖 𝒕
Wage inflation depends on expected inflation 𝝅 𝒕 𝒆 =𝒑 𝒕 𝒆 − 𝒑 𝒕−𝟏 , unemployment rate 𝒖 𝒕 and on a «correction term», with coefficient (𝟏−𝜸𝝀), defined as the difference between previous real wage 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 and the lagged productivity 𝒑 𝒓 𝒕−𝟏 .
This wage eq. has been estimated for various OECD countries in many studies: (1−𝛾𝜆)≈0.25 in EU and 0 in US.
In EU, 𝛾,𝜆<1. In US, 𝛾,𝜆≈1.

11. 𝒖 𝒕 = 𝜸 𝒘 𝟎 𝑹 + 𝟏−𝜸𝝀 𝒎 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝐩𝐫 𝐭 /𝜶
NAIRU & NAWRU
Determine the NAIRU: need to combine the last WS with the PS and compute an (equil.) sol’n., with stable prices, 𝚫𝒑=𝚫𝒘=𝟎, and correct expectations.
From the WS, with Δ𝑝=Δ𝑤=0 :
𝛾 𝑤 0 𝑅 − 1−𝛾𝜆 𝑤 𝑡−1 − 𝑝 𝑡−1 − 𝑝𝑟 𝑡−1 + 1−𝛾𝜆 Δ𝑝𝑟 t =𝛼 𝑢 𝑡
Using PS to substitute for the real wage rate,
𝛾 𝑤 0 𝑅 − 1−𝛾𝜆 𝑝𝑟 𝑡−1 − 𝑚 𝑡−1 − 𝑝𝑟 𝑡−1 + 1−𝛾𝜆 Δ𝑝𝑟 t =𝛼 𝑢 𝑡
𝒖 𝒕 = 𝜸 𝒘 𝟎 𝑹 + 𝟏−𝜸𝝀 𝒎 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝐩𝐫 𝐭 /𝜶
If, at a medium-run equil., 𝚫 𝒑𝒓 𝒕 =𝟎 and 𝒎 𝒕 has a trend component 𝒎 𝒕 ∗ , the NAIRU/NAWRU is:
𝒖 𝒕 ∗ = 𝜸 𝒘 𝟎 𝑹 + 𝟏−𝜸𝝀 𝒎 𝒕−𝟏 ∗ /𝜶

12. Phillips curve revised
Adding and subtracting, 𝛼 𝒖 𝒕 ∗ = 𝜸 𝒘 𝟎 𝑹 + 𝟏−𝜸𝝀 𝒎 ∗ and letting 𝛽≡ 𝟏−𝜸𝝀 𝒎 ∗ , the WS becomes,
𝚫𝒘 𝒕 =𝜷+𝚫 𝒑 𝒕 𝒆 − 𝟏−𝜸𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 − 𝒑𝒓 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝒑𝒓 𝐭 −𝜶 (𝒖 𝒕 − 𝒖 𝒕 ∗ ) or
(𝒘 𝒕 − 𝒑 𝒕 𝒆 )=𝜷+( 𝒘 𝒕−𝟏 −𝒑 𝒕−𝟏 )− 𝟏−𝜸𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 − 𝒑𝒓 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝒑𝒓 𝐭 −𝜶 (𝒖 𝒕 − 𝒖 𝒕 ∗ )
This is a PC in the wage-rate of the popular form proposed by in Blanchard & Katz (AER, 1999).

13. Discussion
This PC formulation captures the relationship between wage-inflation and unemployment in Europe and US.
𝚫𝒘 𝒕 =𝜷+𝚫 𝒑 𝒕 𝒆 − 𝟏−𝜸𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 − 𝒑𝒓 𝒕−𝟏 + 𝟏−𝜸𝝀 𝚫𝒑𝒓 𝐭 +−𝜶 (𝒖 𝒕 − 𝒖 𝒕 ∗ ), 𝛽≡ 𝟏−𝜸𝝀 𝒎 ∗
Yet, estimated coefficients differ. 𝜸,𝝀≈𝟏 for the US, implying a «textbook» PC: assuming 𝑝 𝑡 𝑒 = 𝑝 𝑡−1 ,
𝚫(𝒘 𝒕 − 𝒑 𝒕 )=−𝜶 (𝒖 𝒕 − 𝒖 𝒕 ∗ )
Coefficient values also affect the natural rate; e.g. for the US:
𝒖 ∗ = 𝜸 𝒘 𝟎 𝑹 + 𝟏−𝜸𝝀 𝒎 ∗ 𝜶 ≈ 𝒘 𝟎 𝑹 𝜶

14. Discussion: interpreting 𝜸,𝝀
𝒘 𝒕 − 𝒑 𝒕 𝒆 =𝜸 𝒘 𝒕 𝑹 + 𝟏−𝜸 𝐩𝐫 𝐭 −𝜶 𝒖 𝒕
𝒘 𝒕 𝑹 = 𝒘 𝟎 𝑹 +𝝀 𝒘 𝒕−𝟏 − 𝒑 𝒕−𝟏 + 𝟏−𝝀 𝒑𝒓 𝒕
[𝜸=𝟏 no direct effect of labour productivity on wages – through z] In EU, the greater role of unions in wage-setting and more stringent hiring and firing regulations could increase workers bargaining power, making wages sensitive to productivity (𝛾<1) (Empirical evidence, Abowd et al.’s, 1998). Also labor hoarding/firm-specific capital can play a role.
[𝝀=𝟏 no indirect effect of productivity on wages –through 𝒘 𝑹 ]
In EU 𝜆<1 may be due to the stronger role of the underground/informal economy as an outside option (yet, no clear empirical evidence on this).

15. Kalman methodology
Measurement equation: is the PC, as a function of observables. In a matrix format:
𝒛 𝒕 =𝑫+ 𝑭 𝟏 𝒙 𝒕 + 𝑭 𝟐 𝒉 𝒕 + 𝝋 𝒕 , (𝒛 𝒕 ,𝒙 𝒕 )=(𝚫 𝒘 𝒕 , 𝒖 𝒕 ∗ )
𝐹 1 and 𝐹 2 are vectors of parameters, h is a vector of observed exogenous variables (actual u, lagged inflation,..).
Transition equation: 𝑥 𝑡+1 = 𝑥 𝑡 + 𝜖 𝑡 ⇔𝑢 𝑡 ∗ = 𝑢 𝑡−1 ∗ + 𝜖 𝑡
𝝋 𝑡 , 𝜖 𝑡 are iid, normal distributed with mean 0 and constant variances.
References:
Turner et al., OECD 2001, Econ.Studies n.33
EU-Commission. Econ.Papers n.420, 2010 & n.535, 2014

16. Recent results: real GDP growth
Source: OECD calculations based on OECD Economic Outlook (database),

17. EU methodological changed
The PC used up to 2014 was a New Keynesian one (NKPC), assuming that the wage growth rate would depend on expected current and future changes of wages.
«Too much rationality» tends to produce a NAWRU which is too procyclical.
In 2014 an «hybrid» NKPC has been adopted, along with a new measure of labor cost (unit real labor cost).
Revisions have changed figures.

18. Recent results: EU NAWRU
GDP weighted average of euro-area countries for which long series are available for the alternative NAWRUs (i.e. AT, BE, DE, EL, ES, FI, FR, IE, IT, NL and PT) Source: DG ECFIN calculations based on Eurostat data

20. Methods revisions: some implications
Table 1
provides details regarding the impact of the methodological change on the key affected variables.
The main determinant of this impact is the change in the labor cost indicator (the wage rate) resulting from the difference in the theory underlying the two model specifications.
Spain is the most significantly affected country, with a downward revision in its NAWRU of 4.8pp in Downward revisions to the NAWRU are also noticeable, albeit to a lesser extent, for Ireland, Croatia, Cyprus and Portugal. A small number of countries also witness some upward revisions, in particular Estonia (in 2015) and Poland (in 2013).
All these revisions reflect the reduced pro-cyclicality of the NAWRU estimates according to the NKP model compared to the previous estimates based on the TKP model. Furthermore, as the NAWRU is a component of the production function approach which is used to compute output gaps, revisions to the NAWRU translate into revisions of the output gap estimates. On average, a 1.0 pp change in the NAWRU translates into a 0.65 pp change in the output gap. Revisions for the output gap are also shown in Table 1.
In turn, a revision to the output gap affects the structural balance estimates, with a 1 pp revision leading, on average, to a 0.4 p.p. revision to the structural balance. Revisions for this variable are also reported in the table.
Importantly, despite the fact that the structural balance figures are revised for some countries, the implications for the excessive deficit procedures (EDPs) under the fiscal surveillance framework are limited.

21. “Hybrid” NKPC
This allows for a combination of backward and forward-looking behavior: 𝜔 𝑡 ≡ 𝑤 𝑡 − 𝑝 𝑡 −𝑝 𝑟 𝑡
Δ 𝜔 𝑡 =𝑎 𝑠Δ 𝜔 𝑡+1 𝑒 + 1−𝑠 𝜔 𝑡−1 − 𝛼 1 𝑢 𝑡 − 𝑢 𝑡 ∗ + 𝛼 2 𝑢 𝑡−1 − 𝑢 𝑡−1 ∗ , 𝑎≤1,0≤𝑠≤1
Δ 𝜔 𝑡+1 𝑒 ≡ 𝜔 𝑡+1 𝑒 − 𝜔 𝑡
s = the fraction of forward looking wage setters. The timing implies that wage setters can use current period information for wage negotiations to avoid future discrepancies btw w-p and pr.
An AR(2) is used for the unemployment-gap to smooth variations.

22. Recent results: output gap (% gdp)
See European Econ. Forecasts, Spring 2016 (table 14) for the latest forcasts.
European Econ. Forecasts, Spring 2015