Inflation and unemployment in Switzerland: from 1970 to 2050

We have started writing a new monograph. As always, it’s an exciting process. This time we would like to collect all results on inflation and unemployment in OECD countries and to carry out a rigorous statistical analysis. We include only those OECD members who provide an extensive statistics on inflation, unemployment and labor force. As a result, some countries will not be modeled.

Switzerland was not fully modeled in our monograph on mechanomics. We have written a paper and submitted it to the MPRA. Now it is available via RePEc:


Inflation and unemployment in Switzerland: from 1970 to 2050
Abstract

An empirical model is presented linking inflation and unemployment rate to the change in the level of labour force in Switzerland. The involved variables are found to be cointegrated and we estimate lagged linear deterministic relationships using the method of cumulative curves, a simplified version of the 1D Boundary Elements Method. The model yields very accurate predictions of the inflation rate on a three year horizon. The results are coherent with the models estimated previously for the US, Japan, France and other developed countries and provide additional validation of our quantitative framework based solely on labour force. Finally, given the importance of inflation forecasts for the Swiss monetary policy, we present a prediction extended into 2050 based on official projections of the labour force level.

Theoretical and Practical Research in Economic Fields: Winter Issue

I am happy to inform all readers that the winter issue of the TPREF is now available.

Table of contents:

Macroeconomic Fundamentals and Stock Return Dynamics: International Evidence from the Global Finance Area

Ezzeddine Abaoub, University of 7 November at Carthage
Mongi Arfaoui,  University El Manar
Hammadi Sliti,  University El Manar ... 122

Financial Integration in the four Basins: A Quantitative Comparison
Sergio Alessandrini,  University of Modena and Reggio Emilia … 147

The Law of One Price: Survey of a Failure
Alessio Emanuele Biondo, University of Catania … 168
The Yield Curve and the Prediction on the Business Cycle: A VAR Analysis for the European Union
Giuseppe Cinquegrana ISTAT, Italy
Domenico Sarno, Department of Law and Economics Second University of Naples … 183

Neuroeconomics and Decision Making Process
Mădălina Constantinescu, Spiru Haret University … 210

Differential Games in Non–Renewable Resources Extraction
George E. Halkos, University of Thessaly
George Papageorgiou, University of Thessaly … 219

Consumption in Developed and Emerging Economies
Peter Kadish, Norvik Alternative Investments … 231

Intelligent Agent Approach for Business Process Management
Andy Ştefănescu, University of Craiova … 241

The Australian Phillips curve and more

This blog helps us to voice new ideas before they are formalized in an article or working paper. In many cases, original ideas are partially wrong and mathematics has to be changed severely. This was the case with labour force participation rate and productivity. As a rule, our initial ideas are good enough and do not suffer big changes.

In January 2011, we posted on inflation and unemployment in Australia. Meanwhile we prepared a formal working paper and submitted it to www.arXiv.org and MPRA. The major difference with the blog posts is a complete description of all models and thorough statistical assessment which includes successful tests for cointegration. However, it needs slight polish before we send it to a journal.

Now the paper on Australia is available:

Abstract

A quantitative model is presented linking the rate of inflation and unemployment to the change in the level of labor force. The link between the involved variables is a linear one with all coefficients of individual and generalized models obtained empirically. To achieve the best fit between measured and predicted time series cumulative curves are used as a simplified version of the 1-D boundary elements method. All models for Australia are similar to those obtained for the US, France, Japan and other developed countries and thus validate the concept and related quantitative model.

On real GDP growth in the US

The U.S. Bureau of Economic Analysis (http://www.bea.gov) has reported an estimate of real GDP in the fourth quarter of 2010. Accordingly, a new estimate of the growth rate in 2010 is available. It looks not so bad: +2.9% per year. Let’s ignore the rates of growth for a while and find out where the U.S. stays in terms of real GDP level. Below is a table with quarterly real (in billions of chained 2005 US dollars) GDP estimates since 2007:


2007q1 13,089.3
2007q2 13,194.1
2007q3 13,268.5
2007q4 13,363.5
2008q1 13,339.2
2008q2 13,359.0
2008q3 13,223.5
2008q4 12,993.7
2009q1 12,832.6
2009q2 12,810.0
2009q3 12,860.8
2009q4 13,019.0
2010q1 13,138.8
2010q2 13,194.9
2010q3 13,278.5
2010q4 13,382.6

Well, the US has finally overcome by a 19 billion margin the level of 2007q4. At a healthy pace of 2.5% per year, the rise since 2007 should be around 1 trillion. Moreover, approximately 1% of real economic growth in the U.S. is associated with the overall population increase by 1% per year. In the fourth quarter of 2007, real GDP per capita was $44.292 (civilian population in December 2007 - 301,710,949) and in the same quarter of 2010 - only $43.255. The overall decrease in real GDP per capita since 2007 is 2.3%.

Autodesk stock price to rise in 2011Q1

When modeling stock prices by decomposition into two CPI components and linear time trend we exercise two different  time periods: after January 1994 and after June 2003. The reason for this separation is simple – the difference between individual CPI components is usually characterized by the presence of several linear trends. When linear trend in the difference between two defining CPI components has a pivot point relevant stock model also has a break in all coefficients. Therefore, we usually prefer to avoid this type of bias and limit our modeling to the period after June 2003 when all turns in many CPI difference did happen after the 2001 recession. This shorter modeling period significantly influences the resolution of the model and we would prefer to use longer time series when possible.

The model for Autodesk (ADSK) is an excellent example of the possibility to extend the modeling period back to 1994. The resulting model has a deterministic character and predicts the share price evolution at a several month horizon. Our model for ADSK is stable over the past year and is defined by expected indices: the consumer price index of motor vehicle maintenance and repair (MVR) and the index of information technology, hardware and software (IT). The latter defining index definitely has tight relations to ADSK.

The MVR index leads the share price by 5 months and the IT one - by 8 months. Figure 1 depicts the overall evolution of the difference between the involved indices. As discussed above, no change in the trend has been observed since 1994. Hence, the final share price model for ADSK should not be biased by the change in the trend.

These two defining CPI components provide the best fit model between June 2010 and December 2010. The MVR coefficient is negative and thus the increasing price of motor vehicle maintenance and repair causes the share price to fall. The IT index has a positive coefficient but the long-term decrease in this index also causes the share to fall. The slope of time trend is positive revealing the price tendency to increase over time. The best-fit 2-C model for an ADSK(t) share price is as follows:

ADSK(t) = -3.97MVR(t-5) + 2.18IT(t-8) + 35.25(t-1990) + 265.90

where t is calendar time.

The predicted and observed curves are presented in Figure 2. The residual error is $4.75 for the period between January 1994 and December 2010. The model provides a relatively good prediction of the share price in the past. Currently, the predicted price shows a strong tendency to rise. One should expect the ADSK price to grow fast in the first quarter of 2011.

Figure 1. Evolution of the difference between MVR and IT. No change in the long-term sustainable linear trend is observed.

Figure 2. Observed and predicted ADSK share prices.

Unemployment in Australia

Following the previous post on inflation in Australia, we present a similar model for the rate of  unemployment .

It has been empirically revealed and statistically tested that the rate of unemployment, in developed countries is a linear function of the change in labor force. We expect the same relationship to be valid for Australia. A simple trial-and-error method applied to cumulative unemployment published by the Australian Bureau of Statistics at a monthly rate (see Figure 1) allows to accurately estimating both coefficient in the linear relation:

UE(t) = -2.1dLF(t)/LF(t) + 0.0977; t>1995

UE(t) = -2.1dLF(t)/LF(t) + 0.131; t<1996 (1)

Because of the change in monetary policy around 1995, we had to split the modeled period into two segments: before and after 1995. The above relationships show that only free term did change in 1996 from +0.131 to +0.099. The slope in the linear relationship is the same over the entire period. All in all, the agreement between the annual and cumulative curves is excellent. One can predict the rate of unemployment at any time horizon using labor force projections. We have failed to find any projection published by the Australian Bureau of Statistics except the one between 1999 and 2016. Unfortunately, this projection was all wrong and heavily underestimated the growth in labor force. It predicted the level of labor force in 2016 at 10,800,000. In December 2010, the level of labor force was 12,132,900. This is good news, however. According to (1), a higher rate of labor force results in a lower rate of unemployment.

Figure 1. Upper panel. Monthly estimates of the rate of unemployment in Australia and that obtained from labor force using (1). Due to high-amplitude fluctuations in the monthly estimates of dLF/LF, the predicted curve is smoothed by a twelve-month moving average, MA(12). Lower panel. Cumulative values of the observed and predicted curves in the upper panel. Notice excellent agreement between the cumulative curves.

Inflation in Australia

This is an earlier report on the quantitative model of  price inflation in Australia. We use our general approach well described in this blog.

Introduction

To create an inflation model for Australia we use our concept linking inflation solely to the change in labor force. As for other developed countries we use data obtained from various sources. Because of definitional and measuring problems data compatibility over time is not routinely provided by statistical agencies and one has to check for artificial breaks in data series. The OECD reports the following:

Series breaks: A new questionnaire was introduced in 2001 and employment and unemployment series were re-estimated from 1986. From April 1986, employment data include unpaid family workers having worked less than 15 hours in a family business or on a farm. Previously, such persons who worked 1 to 14 hours or who had such a job but were not at work, were defined as either unemployed or not in the labor force, depending on whether they were actively looking for work.

Many central banks shifted their monetary policy to inflation targeting around 1995. This can also introduce a break in underlying time series and the generalized dependence between three economic variables under study. This is the case for France.

The data

Here we introduce the estimates of all variables used in the study. There are two time series for inflation, unemployment and the level of labor force. Figures 1 and 2 introduce the overall behavior of all time series.

Figure 1. Upper panel: Comparison of CPI inflation and GDP deflator in Australia. Lower panel: Comparison of two estimates of unemployment according to US and OECD definitions.

Figure 2. Comparison of two estimates of the change rate of labor force level – according to the OECD and US definition (BLS).

The Phillips curve

Here we plot the rate of unemployment in Australia against reduced CPI inflation. The period between 1974 and 1994 shows a relatively good agreement, but then the curves diverge. This might be related to the new central bank monetary policy, as observed in France. All in all, the Phillips curve does not exist in Australia for the entire period between 1978 and 2009, i.e. for the period of accurate measurements presented by the Australian Bureau of Statistics.

Figure 3. Upper panel: Comparison of the measured unemployment (US definition) and that predicted from the CPI inflation according to the relationship obtained in the lower panel. The curves are close between 1974 and 1994. The following deviation might result from changes in monetary policy after 1994 and also be associated with revisions to corresponding definitions and measuring procedures. Lower panel: Scatter plot and linear regression of the CPI inflation and unemployment between 1974 and 1994.

Inflation as a linear function of the change in labor force

According to the change in definition of labor force in 1986, as described above, we have slit the period after 1978 (the start of reliable measurements (as reported by the Australian Bureaus of Statistics) into two segments and obtained the following models for inflation (GDP deflator) :

DGDP(t) = 4.2dLF(t)/LF(t) – 0.042; t>1985

DGDP(t) = 7.8dLF(t)/LF(t) – 0.024; t<1986 (1)

Figures 4 and 5 display the observed DGDP curve and that predicted according to (1).

Figure 4. Modeling of unemployment using the change rate of labor force level. Coefficients in the linear relationship are presented in the text and obtained by the trial-and-error method to fit the cumulative curves in Figure 5 between 1978 and 2009.

Figure 5. Modeling the cumulative GDP deflator as a function of the change rate of labor force level. The break in 1985 is explained by the changes in definition the labor force definition and corresponding measurement procedure.

Figure 6. Absolute and relative modeling error for the cumulative inflation in Figure 5. The curves converge in relative terms and one can replace the price deflator with the growth in labor force with the accuracy incrasing with time.

Generalized model for the link between labor force, inflation and unemployment

Because of breaks in the definition of labor force and unemployment/inflation relationship in 1995 (as shown in Figure 3) we spit the entire period of modeling into three segments:

CPI(t) = 3.9dLF(t)/LF(t) +0.88UE(t) - 0.1; t>1995

CPI(t) = 3.9dLF(t)/LF(t) +0.97UE(t) - 0.1; 1985

CPI(t) = 8.3dLF(t)/LF(t) +0.97UE(t) - 0.1; t<1986 (2)

Figure 7 presents the model.

Figure 7. Upper panel: Illustration of the generalized relation between inflation, unemployment and the change rate of labor force leveling Australia. The CPI inflation is modeled using the change rate of labor force level and unemployment. Lower panel: Cumulative curves use to estimate all coefficients in defining relationships (2).

Conclusion

Price inflation in Australia is a one-off function of the change in labor force. This conclusion validates earlier models for many developed countries: the US, Japan, Germany, France, Italy, Canada, the Netherlands, Sweden, Austria, and Switzerland.