Model based economic analysis

Normetrics is an interface to research and consulting work based on econometric modelling, in particular to the development and use of the Norwegian Aggregate Model (NAM).

Sudden changes in economic activity, with and without lock-down

This comment, in the Norwegian journal Samfunnsøkonomen, discusses how a particular form of imbalance in capital markets (related to overdermination of the interest rate) can harbour quick and unexpected changes in macro economic actvity, with and without lock-down.

Mulighetene for brå endring i den økonomiske aktivitet, med og uten

See also the Covid-19 page

Posted 15 September 2020

Full circle: One year of CO2 forecasts

The September 2020 forecasts of atmospheric CO2 at Mauna Loa marks one full year of monthly forecasts posted on  The figure shows the actual CO2 level (green line graph) together with the new September 2020 forecast (blue) and the forecast form September 2019 (red).

Figure 1 Mauna Loa CO2 level (2008(9)-2020(8)) and forecasts from September 2019 and 2020.

The September 2020 forecast underestimated the steepness of the Co2 during the autumn of 2019 somewhat. The peak in the  April-June2020 was accurately forecasted though.

The difference between the two September forecasts is that 2020 is conditional on the CO2 level in August 2020, while the first forecast was conditional on August 2019.    Although it is not large, the still visible difference between the two line graphs for September-December 2020,  indicate that the difference in initial conditions had an impact on the forecasts.

The CO2 forecast page contains more details and data.

Posted 15 September 2020

New research articles on the modelling of pattern wage bagaining

Wage coordination plays an important role in macroeconomic stabilization. Pattern wage bargaining systems have been common in Europe, but in different forms, and with different degrees of success in terms of actual coordination reached. A recently published paper written by Marit Gjelsvik, Ragnar Nymoen and Victoria Sparrman focuses on wage formation in Norway, a small open economy, where it is custom to regard the manufacturing industry as the wage leader. The authors estimate a model of wage formation in manufacturing and in two other sectors. Deciding cointegration rank is an important step in the analysis, economically as well statistically. In combination with simultaneous equation modelling, the cointegration analysis provides evidence that collective wage negotiations in manufacturing have defined wage norms for the rest of the economy over the period 1980(1)–2014(4). 

The paper is titled “Cointegration and Structure in Norwegian Wage–Price Dynamics” and is published in Econometrics 20208(3), 29;

The article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen

Earlier this year, Simon Dalnoki published a research paper in the Norwegian Journal Samfunnsøkonomen: Empirisk modellering av systemet for norsk lønndannelse.

Posted 14 August 2020

Atmospheric CO2 forecast update: A small reduction in the growth rate

The monthly average of atmospheric CO2 for July was 414.4 ppm which was a lower than the forecast conditional on June information, but not significantly lower. 

The figure shows updated forecasts, conditional on data that includes July 2020. Panel a) in the figure shows the monthly rate of change. Interestingly, the point forecast for August (the middle of the fan) can be gauged to be a little lower than the rate of change one year earlier. However, since the level of CO2 has risen over the last year, the forecasted level (in log scale in panel b)) is higher for August 2020 than it was in August 2019.

The level of CO2 in the measured units of ppm is forecasts to continue its secular increase. The previous peak (417.07 ppm) form May 2020 is forecasted to be overtaken during the spring of 2021 with a new peak in May 2021 (418 ppm) and the next one in May 2022 (422 ppm).

Figure Rate of change ond level forecast, with forecast uncertainty fans.

The CO2 forecast page contains more details and data.

Posted 11 August 2020.

Labour market changes

New unemployment data from Statistics Norway (23 July 2020) showed that in the second quarter of 2020 the unemployment rate had increased to 4.6 per cent, up 1.2 percentage points from the seconf quarter of 2019. These numbers are from the labour force survey, which needs to be kept apart from the numbers for registered unemployment compiled by NAV.

As the figure shows, the usual pattern has been that the labour force measure of the unemployment rate is higher than the registered rate (and the gap has been consistently wider after 2010 than before).  But this changed in the first quarter of 2020, when the registered rate rose to 5.1 percent while the Labour force survey measure was almost unchanged at 3.6 percent.  

See the Covid-19 page for more. Posted 28 July 2020.

Mauna Loa CO2 forecast update: Seasonal reduction

After the historical peak in May 2020, the atmospheric CO2 level became reduced in June. However, this represents a predictable seasonal reduction, as the figure illustrates.

Figure 1 Actual Co2 level at Mauna Loa and forecasts that condition on August 2019 information (labelled Forecast September 2019), and on June 2020 information (labelled Forecast July 2020)

Posted 18 July 2020

NAM and institutional forecasts for the Norwegian economy-summer 2020

In June, the two leading forecasting institutions, Statistics Norway (SSB) and Norges Bank (NB) published new forecasts for the macro economy.  Both institutions expect 2021 Mainland Norway GDP to be a little above the 2019 level in 2021. The number of person employed is also expected to get back to positive growth in 2021.

As the note on mid-year forecasts shows, a main difference between the two institutional forecasts and the NAM based forecast (for 2020Q2-2023q4) is that the NAM forecast for employment in 2021 is bleaker than in the two institutional forecasts.   

Posted on 10 July 2020

A predictable new world record: May 2020 CO2 level at Mauna Loa

A noted in last month’s update of the Mauna Loa CO2 forecast, the record level for April 2020 became  overtaken by May. Moreover, as noted, this peak was predictable on the basis of August 2019 information (the graph labelled September 2019 in the figure).

Figure 1: Acutal Co2 level at Mauna Loa and forecasts that condition on August 2019 information (labelled Forecast September 2019), and on May 2020 information (labelled Forecast June 2020)

The latest forecast, June 2020 in the figure, predicts that the summer months will be dominated by the usual seasonal pattern, bringing the CO2 level down to a low for 2020 in September and October, which will be significantly higher than the 2019 low, though.

Posted 8 June 2022. Go to CO2 forecast page for more details and data.

Update of NAM documentation (NAM 20.2)

An updated version of the NAM documentation (dated 25 May 2020) is available here.

Posted 27 May 2020.

New all time high C02 level in April

Data published by ESRL Global Monitoring Division shows that April 2002 became the month with the new CO2 record . This record has been correctly forecasted in this post since August 2019, as Figure 1 shows.  

Figure 1. Actual CO2 level (red graph) and the sequence of forecasts (in grey): The oldest forecast had September
2019 as the first forecasted month and was conditional on August 2019 information. The newest has
May 2020 as the first forecast period (and is conditional on April 2020 information).

April’s world record may however soon be taken over by May 2020, as shown on CO2 forecast page.

Posted 8 May 2020

Covid-19 extraplations for 16-30 April, evaluations.

The numbers from the second half of April are now available, and the extrapolations for that period can be evaluated.

The graphs in the figure show that over the period as a whole, the extrapolated series overestimated the number of cases in Norway in April. Hence, the average forecast error (actual minus forecast) is negative. However, considering the forecast confidence intervals, there are no cases of forecast failure (the actual numbers are always inside the interval).

Although not strictly monotonous, there is a tendency of increasing overestimation as the length of the forecast horizon is increased (away from the origin of the forecast). By 21 April the error had grown to 73 persons. For the following days the errors became smaller  (34 for 24 April for example). However, for the last days of April the errors increased again.  For 30 April, the actual number of Covid-19 positives was 138 fewer than the forecasted number (made half a month earlier).

More evaluation of forecasted new cases and hospital patients: Covid 19 Norwegian unemployment and income page.

Posted 1 May 2020.

Covid19 in Norway, extrapolations

The curve showing the accumulated number of Covid19 cases in Norway has been relatively flat, partly due to lockdown measures. Over the next weeks, there will be a gradual opening-up, which makes it relevant to extrapolate how the numbers evolve.

Forecasts of accumulated Covid 19 cases (shown below), new positives and the number of patients in hosptials are posted on: Covid 19 Norwegian unemployment and income page.

Accumulated number of persons tested positive on Covid19 test. Actuals and forecasts (with 90 % fan) for 16 -30 April 2020. Forecast produced on 16 April 2020. Source. Verdens Gang, Normetrics.

Posted 16 April 2020.

CO2 forecast update: April 2020

Data published by ESRL Global Monitoring Division shows that the CO2 level measured in the athmosphere above Mauna Loa was 414.50 ppm in March 2020. This is lower than the 415.2 ppm forecasted in the previous posting (6 March 2020). The over-prediction is marginally significant, as the lower bound of the 95 % forecast interval for March was 414.55 ppm.

The new forecast nevertheless indicates that the secular rise in the CO2 level in the athmosphere is continuing, and that April 2020 is likely to become the month with highest recorded level of CO2 in history, cf. the figure below.

Forecasts for 2020(4)-2020(12) with 95% forecast intervals (dashed lines), togheter with the actuals for 2019 (thinner black line graph) for comparison. The actual measurements for the two first months of 2020 are also included (the short line graph).

The CO2 forecast page contains more details and earlier forecasts.

Posted on 7 March 2020

Unemployment during the ongoing Covid 19 crisis, and after

In the second week after the “lock-down” of the Norwegian economy as part of the fight against Covid 19, the rate of registered unemployment continued to increase dramatically to approximately ten percent of the workforce. The phenomenon of collective lay-offs is the all-dominating cause of the increase in registered unemployment.

If the laid-off wage earners return to their jobs over the next weeks and months, the unemployment level can start finding back towards the level from earlier this year. However, as a huge Covid 19 caused international downturn now seems unavoidable, such a scenario does not seem to be likely.

Both the registered unemployment rate (UR) and the labour force survey measure (UAKU), are endogenous variables in Norwegian Aggregate Model (NAM).  The figur shows forecasts for the two measures of the unemployment rate for the three first quarters of 2020, conditional on the lay-offs seen in March, as well as on some of the other dimensions of the crisis, i.e., contraction of private domestic demand, plummeting international trade, but also monetary policy stimulus. 

Labour force survey (right) and registered (right) unemployment percentages, actuals and forecasts for the peridod 2020q1-2020q3. Source. NAM, NAV, Statistics Norway

More about this on the Covid 19 Norwegian unemployment and income page.

International economic crisis as well as measures taken to fight-off Covid 19 takes its toll on Norwegian jobs

The number of lay-offs per day is increasing in a way hitherto unseen in Norway. New statistics from NAV imply that the number of workers who applied for unemployment benefits on Tuesday 17 March amounted to more than 2 percent of the workforce. The total number of new UB applicants was 63680.  Most of these (59930) were collective temporary lay-offs, see graph.

Unemployment benefits (UB) applictations per day due to collective lay offs (blue line graph), together with ordinary new claimants
(green line) and new sick absentees due to Covid 19 virus. In percent of labour force (fourth quarter 2019)
Source: NAV and Statistics Norway

Though temporary, most of the new daily UB applications are certain to enter the stock of unemployed workers, which is therefore believed to increase swiftly to very high levels by Norwegian standards.

On the same day, 17 March, the number of  new workers being away from work due to Covid 19 (suspected as well as diagnosed after testing)  was 0.09 percent of the workforce. Increasing from previous days though.  

CO2 forecast update: March 2020

The longest time series for atmospheric CO2 is for the Pacific island of Mauna Loa. Based on this time series, the development of the CO2 level can be forecasted on a monthly basis.

The updated forecast supports our earlier forecasts saying that the CO2 level may reach a new all-time high already in March 2020, and that the level is likely to increase to more than 417 ppm in May 2020, significantly higher than the highest level recorded so far, which was for May 2019 (cf. the figure below.)

Forecasts for 2020(3)-2020(12) with 95% forecast intervals (dashed lines), togheter with the actuals for 2019 for comparison (thinner black line graph). The actual measurements for the two first months of 2020 are also included (the short line graph)

See the CO2 forecast page for more details. Posted on 6 March 2020

A plague of interest rate setters

At the end of 2019, the rate of CPIAET inflation in Norway was right on the 2 percent inflation target (see graph).  However, forecasts that take into account that the effect of the weakening of the international value of the krone may indicate that inflation will be moving up and away from the target.  The graph in the upper panel of the figure shows one such forecast. 

In the course of the winter, signals have also been strengthened about a weakening performance of the Norwegian real economy.  For example, forecasts have shown, for some time already that an increase in the rate of unemployment in 2020 is plausible.

In such circumstances, Norges Bank’s projected interest rate for the future reflects the balancing of partly conflicting policy goals.  The second graph in the figure shows the interest rate path from the last monetary policy report in 2019, as replicated by simulation of Norwegian Aggregate Model (NAM).   Given the likelihood of higher inflation, an inflation targeting central bank might be expected to signal a higher interest rate level in the future.  However, Norges Banks is not particularly inflation targeting in practice. Especially with the negative economic consequences of the new coronavirus now above the short-run policy horizon, the interest rate is more likely to be lowered, in Norway as elsewhere.

At the same time, the mechanisms behind the possible disruptive effects of coronavirus disease are in many respects different from the scenarios where interest rate reductions are believed to be  effective.  Reduced man-hours in production due to illness and quarantine, and resulting reduced trade with intermediary goods, are consequences that are not fixed by lowering the interest rate.  Parts of aggregate demand, in particular tourisms and travel, entertainment and education, seem to be acutely impacted by virus fright, but also by health policy measures needed take down the risk of pandemic developments.  Interest rate cuts will do little to raise aggregate demand as long as such factors are dominating the picture. (4 March 2022)

Norwegian Aggregate Model version 20.1

A new version of the NAM documentation is available here. It documents new model features and revisions of existing ones.

CO2 forecast update: February 2020

The longest time series for atmospheric CO2 is for the Pacific island of Mauna Loa. Based on this time series, the development of the CO2 level can be forecasted on a monthly basis.

The atmospheric level of CO2 measured in January 2020 was 413.4 pp (average for the month). The latest forecast for January was 413.12 ppm. The updated forecast predicts that the CO2 level may reach a new all-time high in March 2020, and that the level might increase to 417.548 ppm in May 2020, which is significantly higher than the highest level recorded so far, which was for May 2019.

These predictions are illustrated in the figure below, which shows the forecasts for 2020(2)-2020(12) in the same figure as the actuals for 2019(1)-2020(1) (the dotted line). The vertical distance between the dashed lines indicate 95 percent forecast intervals.

Dette bildet mangler alt-tekst; dets filnavn er 12month-1024x433.png
Forecasts for 2020(2)-2020(12), with 95 % forecast intervals (dashed lines) and the actuals f
or 2019 (thin dashed line).

See the CO2 forecast page for more details.

Posted on 7 February 2020


The day inflation targeting died

Norway’s monetary policy regime formally changed to inflation targeting in March 2001. In the following years, Norges Banks’s practicing of the new policy regime impacted significantly on the interest rate level. However, soon after the coming of the international financial crisis, the footprints of inflation targeting became more difficult to follow in the data, and they soon disappeared altogether.

The figure below tracks this development by showing an estimated “Taylor-coefficient” which measures by how much the policy interest rate can be expected to increase when the inflation gap changes by one unit.

In the heyday of inflation targeting, an increase in the inflation gap could be expected to lead to an even larger increase in the policy rate. However, soon after the financial crisis the estimated Taylor coefficient plunged down zero.  On the face of it, the epoch of inflation targeting was over almost as soon as the regime had installed itself.   

Norges Bank cut policy interest rate three times in the autumn of 2009. However, on exact which day, 15 October, 20 October or 17 December, inflation targeting became defunct may better be left is for the monetary policy historians to find out.      

Figure : Evolution of estimated Taylor coefficient with 95 % confidence interval indicated by dashed lines

Posted 8 January 2020. pdf-version