1/15/17

Recession may hit New Zealand in 2017, but at a five-year horizon real economic growth is about 2% per year

In 2010, we published a paper in the Journal of Applied Economic Sciences, which predicted real GDP per capita, rGDPpc, in several developed countries. Corresponding working paper was published in 2009 and covered the period before 2007. The evolution of rGDPpc in New Zealand was also presented in this blog in 2011.
Here, we revisit the 2010 model for New Zealand. It is important to stress that all defining parameters, which were estimated by the LSQ method from the data before 2008, are retained in the revisited model. Therefore, this is an out-of-sample test. The test result shows that our model accurately predicts the evolution of real GRP in New Zealand at an 8-year horizon. As predicted in 2009, in the next few years the growth rate will be increasing, except a deep fall in 2017, as we also expect in the USA.  Since the full prediction horizon is 14 years, we will be reporting on the model prediction in the future, but not often – the change in real economic growth is a slow process.
The original macroeconomic model for real GDP growth in developed countries was formulated in 2006 in the paper “GDP growth rate and population” published in the ECINEQ WPS. The model links the rate of growth in rGDPpc, g(t) = dln(rGDPpc)/dt, with the attained level of the rGDPpc and the rate of growth in population of a coutry-specific age.

g(t) = dln rGDPp(t)/dt  = A/rGDPpc(t) + 0.5dlnNs(t)/dt     (1)

 where empirical constant A and the specific age, Ns, are estimated from data. To obtain the model parameters, we used rGDPpc time series borrowed from the Total Economy Database.   The best fit annual increment value is A=$420 (notice that we used the EKS US$, as published by the Conference Board in 2016, while the GK 1990US$ were used before).  The term A/rGDPpc(t)  corresponds to inertial economic growth, which is observed when there is no change in the Ns.  The specific age population in New Zealand is 14 years, as in the previous versions. To describe the change in Ns, we used the age pyramid obtained in the 2006 census and extrapolated it in the past and in the future. The precision of Ns predictions decreases with the difference between the predicted year and 2006. We do not use fresher censuses because the goal of this study is to prove the model and to assess the accuracy of prediction at various time horizons. The largest time horizon for the 2006 census is 2021.
Figure 1 presents the observed and predicted GDP growth rates for New Zealand as obtained in 2008. Both curves are characterized by high-amplitude oscillations likely associated with measurement errors. Therefore, in Figure 2 we present both annual curves smoothed with MA(5) and MA(3), respectively. One can conclude that our prediction from 2008 was correct and real GDP per capita in New Zealand follows the predicted curve. This is the best validation of our model for NZ and the driving force of real economic growth in developed countries.

Figure 1. Observed and predicted growth rate of real GDP per capita in New Zealand between 1980 and 2015.  
Figure 2. The observed curve in Figure 1  is smoothed with a five-year moving average. The predicted rate is smoothed with MA(3). One can observe an outstanding accuracy of GDP prediction for 2009 and 2015 (between the smoothed curves).

1/14/17

GDP implicit price deflator in Germany will grow

In this blog, we introduced several models predicting inflation and unemployment in Germany in 2009 and 2010. These two posts presented a shorter version of our extended  paper published in 2007 on the dependence of the CPI, GDP deflator  (DGDP) and rate of unemployment, UE, on the change in labor force, LF. Two sources provide a complete description of our model and we are not going to repeat it in detail. Overall, the model says that one can describe inflation as a liner lagged function of the rate of labor force change, dLF/LF, and the rate of unemployment
DGDP(t) = adLF(t-6)/LF(t-6) + bUE(t-1) + c
where a, b, and c are empirical coefficients, t-6 means that dLF/LF leads inflation by 6 years, and t-1 means that UE leads DGDP by 1 year. Therefore, we have a one-year ahead natural prediction horizon. When we add new data, the empirical coefficients can change because the LSQ estimation procedure. But they should not change much.
Here, we revisit the DGDP prediction given 10 years ago using OECD data now available for the period between 2006 and 2016. Figure 1 compares the predicted and observed time series. Coefficients are as follows: a=0.3, b=-0.61, c=0.062, which are very close to the initial estimates in 2007. Overall, the observed curve is well matched by the predicted one, but the former has much larger variations. They disappear after smoothing with a four-year moving average, as shown in Figure 2. The fit is exciting. In Figure 3, we present the modelling error as the difference between the observed and predicted time series. This is an I(0) process, which is an important issue is the DGDP is a nonstationary process.
Conclusion: the GDP price deflator in Germany will be growing in the next years, despite the CPI inflation is close to zero. In 2016, DGDP was approximately 2%.

Figure 1. Predicted and measured DGDP in Germany


Figure 2. The observed time series is smoothed with 4-year moving average.

Figure 3. Modelling error is an I(0) process.

1/13/17

The French economy needs ”helicopter money” to boost labor force growth and avoid deflation



In 2013, we published a paper Does Banque de France control inflation and unemployment?” We demonstrated that the French economy would likely sink into a longer period of deflation or very low inflation rate after 2013. This is an excerpt from the paper discussing how Banque de France could boost labour force growth and inflation by flooding the French economy with money. Instead of this simple measure, there were several depressing years of contingency measures introduced by the ECB. This update uses data for the past three years and proves that austerity is a counterproductive approach. We just extend inflation prediction by 3 years ahead (to 2019) and put new measurement without change in the previous estimates. We have nothing to add. The text is still valid.

Here, we consider the rate of inflation, unemployment, and the change in labour force altogether. For France, the generalized relationship is obtained as a sum of (10) and (13), which results, with some marginal tuning of all coefficients in order to reduce the standard error of the model, in the following equation for the GDP deflator:

π(t) = 2.69l(t-5) - u(t-5) + 0.108;      1971≤t≤1995                                                                 
π(t) = 6.40l(t-5) - u(t-5) + 0.059;                t≥1996                                                     (14)
For the OECD CPI:
π(t) = 3.0l(t-5) - u(t-5) + 0.108;      1971≤t≤1995                                                                   
π(t) = 5.0l(t-5) - u(t-5) + 0.067;                 t≥1996                                                      (15)
where we model inflation since it lags by 5 years behind the change in labour force and unemployment. Formally, one can re-write both relationships for u(t). Notice that the change in the slopes and intercepts are much smaller than in individual relationships. The structural break is less prominent and thus its estimate is less reliable. 
The annual and cumulative curves for both cases are presented in Figure 12.  Linear regression of the observed inflation against that predicted according to (14) and (15) is characterized by outstanding for annual curves statistical properties: R2=0.87 and RMSFE=0.015 y-1, and R2=0.83 and RMSFE=0.017 y-1, respectively. For the cumulative curves, both R2 are larger than 0.99 and RMSFE~0.025 y-1, i.e. by 20% smaller than the naive ones (see Table 4). These estimates were obtained for the period between 1972 and 2012 with a five-year lag. These RMSFEs are the best obtained for France at a five year horizon so far. They explain the rate of price inflation to the extent beyond which measurement uncertainty should play the key role. Practically, there is no room for any further improvements in R2 given the accuracy of the current prediction.

Conclusion
We have successfully modelled unemployment and inflation in France. Their sensitivity to the change in labour force requires very accurate measurements for any quantitative modelling to be reliable. Unfortunately, the OECD labour force time series does not meet this requirement and poor statistical results are obtained for annual readings. The best prediction is obtained with the moving average technique applied to the change in labour force. For the period between 1970 and 2012, linear regression analysis provides R2 as high as 0.8 to 0.9 for the rate of unemployment and GDP deflator. The RMSFE for the best CPI model is 0.015 y-1 and 0.010 y-1 for the GDP deflator, both at a four year horizon. For the period after 1994, the best RMSFE=0.005 y-1 for both measures of inflation. In 1994, our models have structural breaks found by the OLS fit. For the VECM representation, the standard error for the GDP deflator is as low as 0.010 y-1 at a four year horizon and 0.005 y-1 for a two year horizon. The whole period and 0.004 y-1 for the period after 1994. All in all, we have obtained a very accurate description of unemployment and inflation in France during the past 40 years.   
Having discussed the technically solvable problems associated with the uncertainty in the labour force measurements, we start tackling the problem associated with the divergence of the observed and predicted curves starting around 1995.  An understanding of this discrepancy is a challenge for our concept. Potentially, these curves diverge due to the new monetary policy introduced by the Banque de France. We may claim that the policy of constrained money supply, if applied, could artificially disturb relationships (9), (10), and (13). We had to introduce a structural break and to estimate new coefficients after 1995 for unemployment and after 1994 for inflation, respectively. These coefficients are less reliable because the relevant time series are short and vary in narrow dynamic ranges, but they are definitely different from those before the breaks. One could conclude that Banque de France has created some new links between the unemployment, inflation, and labour force, shifting coefficients in the original long term equilibrium relations.






Figure 12. Comparison of the observed and predicted inflation in France - annual and cumulative inflation since 1972. The predicted inflation is a linear function of the labour force change and unemployment.

We think that the true money supply in excess of that related to real GDP growth should be completely controlled by the demand related to the growing labour force. This excessive money supply is accommodated in developed economies through employment growth, which then causes price inflation. The latter serves as a mechanism effectively returning the normalized personal income distribution to its original shape (Kitov and Kitov, 2013). The relative amount of money that the economy needs to accommodate through increasing employment, as a reaction on independently growing labour force, is constant through time but varies among developed countries. This amount has to be supplied to the economy by central bank.
The ESCB limits money supply to achieve price stability. For France, the growth in labour force was so intensive after 1995 that it requires a much larger money supply for creation of an appropriate number of new jobs. The 2% artificial constraint on inflation, and thus on the money supply, disturbs relationships (10) and (13). Due to lack of money in the French economy, the actual (and mainly exogenous) growth in labour force was only partially accommodated by 2% inflation. The lack of inflation resulted in increasing employment. In other words, instead of 2% unemployment, as one should expect according to the relationship before 1995, France had 9% unemployment. Those people who entered the labour force in France in excess of that allowed by the target inflation rate had no choice except to join unemployment in order to compensate the natural 7% rate of inflation, which was suppressed to 2%.
The lags and amplification factors (sensitivities) found for unemployment and inflation in France are quite different from those obtained for the USA and Austria (Kitov and Kitov, 2010). The latter country is characterized by the absence of time lags and low sensitivities. In the USA, inflation lags by two and unemployment by five years behind the change in labour force, with sensitivities much lower than those in France. Apparently, the variety of lags is the source of problems for the Phillips curve concept.
The causal link between inflation, unemployment, and labour force gives a unique opportunity to foresee future at extra long time horizons. The accuracy of such long-term unemployment and inflation forecasts is proportional to the accuracy of labour force projections. For example, central banks can use labour force projections as a proxy to “inflation expectation” in their NKPCs. Figures 8 and 12 imply that France will be enjoying a period of low inflation rate in the near future. Monetary policy of the ECB is also an important factor for these forecasts because of its influence on the partition of the labour force growth between inflation and unemployment. Moreover, this is the responsibility of the ECB and Banque de France to decide on the partition. “


As we predicted in 2010,a longer deflation period has started in Australia

Six years ago we wrote a paper on price inflation and unemployment in Australia. Here, we compare our predictions against measurements. Concluding this paper we made a projection into 2050:

“As a final remark on the evolution inflation (DGDP) and unemployment in Australia we present two predictions as based on the labour force projection provided by the Productivity Commission (2005) and the coefficients in (7) and (8) estimated for the period after 1994: a1=3.299, a2=-0.0259; b1=-2.08, b2=0.0979. We assume that there will be no change in the definitions of all involved macroeconomic variables through 2050 and these coefficients will hold.  Unfortunately, the accuracy of labour force projection has a poor historical record, taking into account the projection between 1999 and 2016. Nevertheless, it may be useful for assessment of the long-term evolution.  Figure 15 displays both predictions, with the period before 2010 represented by actual labour force measurements since the projected ones were not accurate. 




            The level of price inflation after 2015 will likely fall below zero and will remain at -1.5% per year through 2050. This lengthy period of deflation will be accompanied by an elevated rate of unemployment approaching 9% around 2030. The evolution of both variables is not fortunate for the Australian economy and is chiefly associated with the population ageing. The latter suppresses demographic growth and reduces the rate of participation in labour force. Australia will likely need a larger international migration to overcome deflation and high unemployment. This is the means to overcome deflation the U.S. has been using for many years, but even with a large positive migration the Australian economy will be on the brink of deflation during the next four decades. Without migration, Australia will soon join Japan having the same demographic problems and price deflation since the late 1990s.”

Here, we update our projections with three new readings for 2010 through 2016. As we predicted, the Australian economy is in the beginning of a long deflation period with an elevated unemployment. The reason behind these processes is the same as in Japan – falling labor force.




Figure. Same as in the above figure borrowed from our paper, but with updated  measurements for the period between 2010 and 2016.




1/11/17

In the long run, the rate of unemployment in Canada will be growing. A four year update.

Here, I continue presenting cases of accurate predictions based on the link between real GDP and unemployment, which is a modified Okun’s law in an integral form. This is a four-year update for Canada. The model prediction is getting better and better!

Canada provides an excellent set of macroeconomic data, which can be described by a few deterministic links with a high level of reliability and confidence. We have retrieved real GDP (GK per capita) data from the Total Economic Database and the rate of unemployment from the OECD. In 2012, we published a paper in the Journal of Theoretical and Practical Research in Economic Fields, where presented the first version of the modified Okun’s law for developed countries including Canada. The model was estimated till 2010 and used the data available in 2011.
The original model for Canada was also presented in this blog in 2011. It’s time to revisit the model and its predictions. It has to be mentioned that all coefficients below were estimated 6 years ago and we do not change them. Overall, the model is estimated using the LSQ technique to the integral version of Okun’s law:

u(t) = u(t0) + bln[G/G0] + a(t-t0) (1)

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients. For Canada, we estimated the model with a structural break allowed by data somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.28dlnG + 1.16,  t before1983
du =
-0.28dlnG + 0.30,  t after  1982 (2)

This model suggests no shift in the slope and a bigger change in the intercept around 1983. Figure 1 depicts the observed and predicted curves of the unemployment rate. Considering the accuracy of measurements for both involved variable the fit is excellent. The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.66% for the period between 1971 and 2016. The average rate of unemployment for the same period is 8.12% with a standard deviation of the annual increment of 0.92%.  Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.87.  


One can suggest that the rate of unemployment has been driven by real economic growth and there is no much room for other macroeconomic variable to intervene. Currently, Canada need approximately 1% per year increase in GDP per capita in order unemployment to fall. Otherwise, it will be growing as it was in 2015 and 2016. With decaying economic growth, as described in this post, the rate of unemployment will be growing in Canada.


Figure 1. The observed and predicted rate of unemployment in the Canada between 1970 and 2016.


Figure 2. The measured time series is regressed against the predicted one. R2=0.87 with both time series likely to be stationary.

The Okun's integral law for Australia revisited

Three and a half years ago, I reported that Australia gives the best example of accurate quantitative prediction of unemployment in developed countries and therefore I felt satisfaction. Historically, we published a paper on Okun's in developed countries in the Journal of Theoretical and Practical Research in Economic Fields in 2012. We presented the first version of the modified Okun’s law for developed countries including Australia. The model was estimated before 2010 and we used only data available in 2011. Briefly, the model is estimated by the LSQ technique applied to the integral version of Okun’s law:
u(t) = u(t0) + bln[G/G0] + a(t-t0)   (1)
where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients. Essentially, our model says that the current level of unemployment is the integral effect of the historical growth in GDP per capita. Then the change in unemployment, du, is proportional to the growth rate in GDP per capita, whcih can be expressed as dlnG. This is the differential (dynamic) form of the Okun's law.
For Australia, we estimated an integral model with one structural break allowed by data somewhere between 1980 and 2000. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) with the new data revision is as follows:
du = -0.69dlnG + 1.50, t before 1991
du = -0.45dlnG + 0.75, t after 1991 (2)

This is an update with new data for the years between 2012 and 2016 obtained from:  real GDP (GK per capita)  from the Total Economic Database, and the rate of unemployment from the OECD

Figure 1 depicts the observed and predicted curves of the unemployment rate. Statistically, the agreement is better than three years ago, when it was excellent. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.88 (0.86 in 2013 and 0.84 in 2011).  The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.7% for the period between 1975 and 2016. The average rate of unemployment for the same period is 7.0% with a standard deviation of the annual increment of 1.4%.  This is an extremely accurate prediction considering the accuracy of GDP (~1% per year) and unemployment (0.3% to 0.4%) estimates. The whole discrepancy is related to the measurement errors and thus the residual error shown in Figure 3 is an I(0) random process. 
The rate of unemployment depends on the cumulative change in real GDP per capita, as relationship (1) implies. To reduce the rate of unemployment in Australia, the rate of GDP (real per capita) growth must be above 1.7% per year.

I have to repeat it again and again. The beauty of science is the accuracy of prediction. It is difficult to express the feelings of a researcher than new observations fit his predictions based on a simple concept.  It is especially exiting when this concept is different from the mainstream one. 


Figure 1. The observed and predicted rate of unemployment in Australia between 1975 and 2015. The regression line is red.





Figure 2. The measured time series is regressed against the predicted one. R2=0.88 with both time series likely to be stationary.
  

Figure 3. The residual error of the unemployment model. 

1/10/17

In 2008, we accurately predicted the evolution of unemployment rate in Italy!


In this blog, three and a half years ago we revisited our prediction of the rate of unemployment in Italy, which had been made in our 2008 paper.  Five years after this publication, we found that the accuracy of prediction was excellent. We decided that our  model works well. Since the model has a natural 11-year horizon, in this post we check our original (2008!) prediction for 2013 and 2016 (preliminary) using new estimates.  According to the OECD, the unemployment rate in 2015 is 12.0%. For 2016, the rate is 11.6%.  There is no doubt; these values again fully validate our model of unemployment as a function of the change in labour force. Moreover, our model has predicted two pivot points in the unemployment rate – in 2008 and 2014. There was a peak observed in 2014 and currently the rate of unemployment is falling.  

We introduced the model of unemployment in Italy in 2008 with data available only for 2006. The rate of unemployment was near its bottom at the level of 6%. The model predicted a long-term growth in the rate unemployment to the level of 11% in 2013-2014.

The overall agreement between the measured and predicted unemployment estimates in Italy validates our concept, which states that there exists a long-term equilibrium link between unemployment, ut, and the rate of change of labour force, lt=dLF/LFdt. Italy is a unique economy to validate this link because the time lag of unemployment behind lt  is eleven (!) years. 

The estimation method is standard – we seek for the best overall fit between observed and predicted curves by the LSQR method. All in all, the best-fit equation is as follows:

ut = 5.0lt-11  + 0.07        (1)

As mentioned above, the lead of lt is eleven years. This defines the rate of unemployment many years ahead of the current change in labour force.

Figure 1 presents the observed unemployment curve and that predicted using the rate of labour force change 11 years ago and equation (1). Since the estimates of labour force in Italy are very noisy we have smoothed the annual predicted curve with MA(5). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1988. The period between 2006 and 2016 was predicted almost exactly. (If anybody knows a better prediction in 2008 of the 2016 unemployment rate, please give us the link.)  

The fit between predictions and observations is the best validation of any quantitative model. No other macroeconomic model is capable to describe such dramatic turns many years ahead. The evolution of the rate of unemployment in Italy is completely defined ten year ahead.  Since the linear coefficient in (1) is positive one needs to reduce the growth in labour force in order to reduce unemployment in the second half of the 2020s. For the 2010s everything is predefined already and the rate of unemployment will be high, i.e.  above 9%.





Figure 1. Observed and predicted rate of unemployment in Italy.