Showing posts with label inflation. Show all posts
Showing posts with label inflation. Show all posts

9/30/12

Exploring Japan: on dismal perspectives of consumer prices

In this post, we continue to validate our predictions of the rate of consumer price inflation (CPI) in Japan by the estimate for 2011. The Japan Bureau of Statistics has estimated the rate of CPI inflation as -0.3%. Now we have an estimate of labour force for 2011 and are able to compare the observed and predicted  figures.  
We have been following inflation in Japan since 2005 when our first paper on the Japanese economy was published and covered the period through 2003. We have revisited inflation in Japan in 2010 and confirmed the predictions of deflation as expressed by the negative GDP deflator. In this blog, we also reported on deflation (both CPI and GDP deflator) several times.  
The case of Japan is the best illustration of our concept linking inflation to the change in labour force. (In a sense, all developed countries stay on the brink of deflation because of the threat of falling labour force.) Therefore we do not suggest the liquidity trap in Japan or any mistakes in monetary policy (inflation does not depend on monetary policy as our model shows.). The evolution of inflation is completely driven by the change in labour force. This is an unfortunate situation for Japan since the level of labour force can only fall in the long run due to the decreasing working age population.   
Previously, we carried out an estimation of empirical relationship between the change rate of labour force, dlnLF(t)/dt, and inflation, p(t).  
First, we test the existence of a link between inflation and labour force. Because of the structural (likely related to definition and measurement procedure) break in the 1980s, we have chosen the period after 1982 for linear regression. By varying the lag between the labour force and inflation one can obtain the best-fit coefficients for the prediction of CPI inflation, p(t),  according to the following relationship (updated with new data since 2009): 
p(t) = 1.39dlnLF(t-t0)/dt + 0.0004                                (1)
where the time lag t0=0 years; standard errors for both coefficients are shown in brackets.  Figure 1 (upper panel) depicts this best-fit case. (The period after 2003 is highlighted.) There is no time lag between the inflation series and the labour force change series in Japan. Free term in (1), defining the level of price inflation in the absence of labour force change, is statistically undistinguishable from zero.
A more precise and reliable method to compare observed and predicted inflation consists in the comparison of cumulative curves. Short-term oscillations and uncorrelated noise in data as induced by inaccurate measurements and the inevitable bias in all definitions should be smoothed out in cumulative curves. Any actual deviation between two cumulative curves persists in time if measured values are not matched by the defining relationship.
The predicted cumulative values shown in the lower panel of Figure 1 are very sensitive to the free term in (1). For Japan, the cumulative curves are characterized by complex shapes. There are periods of intensive inflation and a deflationary period. The labour force change, defining the predicted inflation curve, follows all the turns in the measured cumulative inflation.
One can conclude that relationship (1) is valid and the labour force change is the driving force of inflation. Statistically, the evolution of the overall level of consumer prices in Japan is fully defined by the change in labour force. Hence, no other variable or process can affect the change in price. Otherwise, the statistically reliable link would not exist.  
Having the projection of labour force borrowed from the National Institute of Population and Social Security Research, one can predict the future of CPI inflation in Japan. It will be decreasing to the level of -1% per year in 2050.  
Conclusion: invite immigrants and start a baby boom today! Otherwise, the level of consumer prices in 2050 will be a half of that of today.  
 
Figure 1. Measured inflation (CPI) and that predicted from the change rate of labour force. Upper panel:  Annual curves. Lower panel: Cumulative curves between 1982 and 2011. A good agreement between the cumulative curves illustrates the predictive power of our model.
 
Figure 2. Scatter plot: predicted vs. measured rate of CPI inflation.
Figure 3. Projection of the labour force evolution between 2005 and 2050.

Figure 4. The rate of CPI inflation in Japan through 2050.

5/28/12

Why price inflation in developed countries is systematically underestimated

Following several posts in this blog, I've compiled a paper (link to a complete pdf version):

 Why price inflation in developed countries is systematically underestimated

Abstract
There is an extensive historical dataset on real GDP per capita prepared by Angus Maddison. This dataset covers the period since 1870 with continuous annual estimates in developed countries. All time series for individual economies have a clear structural break between 1940 and 1950. The behavior before 1940 and after 1950 can be accurately (R2 from 0.7 to 0.99) approximated by linear time trends. The corresponding slopes of regressions lines before and after the break differ by a factor of 4 (Switzerland) to 19 (Spain). We have extrapolated the early trends into the second interval and obtained much lower estimates of real GDP per capita in 2011: from 2.4 (Switzerland) to 5.0 (Japan) times smaller than the current levels. When the current linear trends are extrapolated into the past, they intercept the zero line between 1908 (Switzerland) and 1944 (Japan). There is likely an internal conflict between the estimating procedures before 1940 and after 1950. A reasonable explanation of the discrepancy is that the GDP deflator in developed countries has been highly underestimated since 1950. In the USA, the GDP deflator is underestimated by a factor of 1.4. This is exactly the ratio of the interest rate controlled by the Federal Reserve and the rate of inflation. Hence, the Federal Reserve actually retains its interest rate at the level of true price inflation when corrected for the bias in the GDP deflator.

5/25/12

Real GDP per capita since 1870

We've just finished and published a working paper. The reader may want to download it from the MPRA: Real GDP per capita since 1870
Abstract
The growth rate of real GDP per capita in the biggest OECD countries is represented as a sum of two components – a steadily decreasing trend and fluctuations related to the change in some specific age population. The long term trend in the growth rate is modelled by an inverse function of real GDP per capita with a constant numerator. This numerator is equivalent to a constant annual increment of real GDP per capita. For the most advanced economies, the GDP estimates between 1950 and 2007 have shown very weak and statistically insignificant linear trends (both positive and negative) in the annual increment. The fluctuations around relevant mean increments are characterized by practically normal distribution. For many countries, there exist historical estimates of real GDP since 1870. These estimates extend the time span of our analysis together with a few new estimates from 2008 to 2011.  There are severe structural breaks in the corresponding time series between 1940 and 1950, with the slope of linear regression increasing by a factor of 4.0 (Switzerland) to 22.1 (Spain). Therefore, the GDP estimates before 1940 and after 1950 have been analysed separately. All findings of the original study are validated by the newly available data. The most important is that all slopes (except that for Australia after 1950)  of the regression lines obtained for the annual increments of real GDP per capita are small and statistically insignificant, i.e. one cannot reject the null hypothesis of a zero slope and thus constant increment. Hence the growth in real GDP per capita is a linear one since 1870 with a break in slope between 1940 and 1950.  

Key words: GDP, model, economic growth, inertia, trend, OECD

5/23/12

Time to buy SPY


A month ago, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. We also suggested buying the index when it is 1300.  Both are done by now. We are waiting the level 1500 in October 2013 to sell and fix profit. The explanation from April is fully repeated below. The red segment in Figure 2 is now black since the prediction is realized.

We also expect oil price to drop further and force deflation by the end of 2012.

This repeats our previous postSeveral days ago we predicted the current fall in the S&P 500 index. For this reason, we did not enter the stock market and instead invested in a defensive portfolio. We are waiting the level of 1350.  The reason is explained below.

Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007.  There are two deep troughs in 2002 and 2009 which are marked by red and green lines, respectively.  For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious – in the long run the market depends on the overall economic growth.

Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line).  When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360).  The black curve returned to the blue one in August/September 2011. A month ago, we observed a middle-size deviation of about 100 units and predicted that the index will have a negative correction down to the level of 1300 any time soon.  If the index will repeat the path of the previous rally one-to-one, one may expect the peak level of 1500 in the end of 2013.  In two to four weeks it might be a good time to invest for a 15% return cumulated to October 2013 (but not more than two months), when the negative correction is over. 

With the S&P 500 falling down to 1350, the prediction does not seem inappropriate. The next several weeks should decide on the new level. In Figure 2, we have drawn the fall we expect by the end of May 2012. We would wait by the end of April to decide on the following move in the S&P 500. If the current fall will reach 1300, it’s likely a good time to buy. Otherwise, the end of May is the horizon to wait the bottom.

Figure 1. The evolution of the S&P 500 market index between 1980 and 2012. 

Figure 2. The curve in Figure 1 peak is shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in Mach to 1300 in May.

1/28/12

On wise monetary policy and the absence of liquidity trap in Japan


We have been following inflation in Japan since 2005 when our first paper on the Japanese economy was published. We have revisited inflation in Japan in 2010 and confirmed the predictions of deflation as expressed by the negative GDP deflator. In this blog, we also reported on deflation (both CPI and GDP deflator) several times. Here we validate our predictions of the rate of consumer price inflation (CPI) by the estimate for 2011. The Japan Bureau of Statistics has estimated the rate of CPI inflation as -0.3%.



The case of Japan is the best illustration of our concept linking inflation to the change in labour force. We assume that there was neither liquidity trap in Japan nor mistakes in monetary policy. The evolution of inflation is completely driven by the change in labour force. This is an unfortunate situation for Japan since the level of labour force can only fall in the long run due to the quickly decreasing working age population.   

Previously, we carried out an estimation of empirical relationship between the change rate of labour force, dLF(t)/LF(t), and inflation, p(t).  First, we test the existence of a link between inflation and labour force. Because of the structural (measurement related?) break in the 1980s, we have chosen the period after 1982 for linear regression. By varying the lag between the labour force and inflation one can obtain the best-fit coefficients for the prediction of CPI inflation, p(t),  according to the following relationship: 

p(t) = 1.43dLF(t-t0)/LF(t-t0) + 0.000         (1) 

where the time lag t0=0 years; standard errors for both coefficients are shown in brackets.  Figure 1 (upper panel) depicts this best-fit case. There is no time lag between the inflation series and the labour force change series in Japan. Free term in (1), defining the level of price inflation in the absence of labour force change, is practically undistinguishable from zero.

A more precise and reliable method to compare observed and predicted inflation consists in the comparison of cumulative curves. Short-term oscillations and uncorrelated noise in data as induced by inaccurate measurements and the inevitable bias in all definitions should be smoothed out in cumulative curves. Any actual deviation between two cumulative curves persists in time if measured values are not matched by the defining relationship.

The predicted cumulative values shown in the lower panel of Figure 1 are very sensitive to the free term in (1). For Japan, the cumulative curves are characterized by complex shapes. There are periods of intensive inflation and a deflationary period. The labour force change, defining the predicted inflation curve, follows all the turns in the measured cumulative inflation.

One can conclude that relationship (1) is valid and the labour force change is the driving force of inflation. Statistically, the evolution of the overall level of consumer prices in Japan is fully defined by the change in labour force. Even the annual curves have Rsq=0.73 with all fluctuations induced by the change in labor force. The cumulative curves are characterized by Rsq=0.99. Hence, no other variable or process can affect the change in price. Otherwise, the statistically reliable link would not exist. 
Effectively, this means that the Japanese monetary authorities can not create conditions for positive inflation and thus there is no liquidity trap.  The problem of deflation can be resolved only in the framework of increasing population and Figure 3 shows that the next forty years will be characterized by price deflation (both CPI adn GDP deflator) when population projections are used to extrapolated labour force.
 


Figure 1. Measured inflation (CPI) and that predicted from the change rate of labour force. Upper panel:  Annual curves. Lower panel: Cumulative curves between 1982 and 2009. A good agreement between the cumulative curves illustrates the predictive power of our model.


Figure 2. Scatter plot: predicted vs. measured rate of CPI inflation.



Figure 3. Inflation projection  for Japan: CPI and the GDP deflator

8/26/11

V- vs L-shaped recovery: Is CBO’s economic projection wrong?


CBO has recently published a new economic projection covering the period between 2011 and 2021. It explicitly defines the rate of real economic growth (GDP) and inflation for several segments: forecasts for 2011 and 2012, and projections for 2013 -2016 and 2017-2021. Overall, after two years of slow growth in 2011 and 2012, CBO expects a dramatic increase to the rate of 3.6% per year between 2013 and 2016 with the next five years of slow economy with the rate of 2.4% per year on average. Inflation is low over the entire period: the rate of PCE inflation varies between 2.4% and 1.3% per year and that of CPI inflation will be in the range 1.3% to 2.8% per year. Considering these figures one can conclude that CBO expects a slow version of a V-shaped recovery in the 2010s.  There is no double dip.   

We have also projected the rate of inflation and real economic growth in this blog and academic papers. Our GDP (per capita) model is based on the change in demographic characteristics (the age pyramid). Another model describes price inflation as a function of the change rate of labor force. Skipping all mathematical details, we expect the rate of real economic growth (GDP per capita) to fall slightly below zero between 2012 and 2014 (recession) and hovering around 1%  per year after 2015. The rate of price inflation (the GDP deflator and CPI) in the 2010s has to be slightly negative on average with some years of formal deflation. All in all, we expect an L-shaped recovery, i.e. no actual recovery during the 2010s.

6/11/11

Krugman on the effect of quantitative easing in Japan

Paul Krugman shows in this post that the original quantitative easing (QE) in Japan did not help at all. Money supply did not react to an artificial increase in the monetary base. This observation raises a question on the effectiveness of a similar monetary policy in the U.S.

We have a simple explanation of the observed insensitivity of price inflation on QE:  inflation depends on the change in labor force, LF, not on monetary policy. The following models for the GDP deflator, DGDP, and CPI inflation, CPI, were obtained and presented in our previous posts:

DGDP(t) = 1.9d(lnLF(t))/dt – 0.0084      

CPI(t) = 1.3d(lnLF(t))/dt + 0.0004

Two figures below illustarte these models. There is no room for the BOJ to influence deflation after 1995.  

5/28/11

The New Keynesian Phillips Curve – methodological dead-end


Couple days ago we presented a Phillips curve for Germany.  When unemployment leads inflation (the GDP deflator) by one year in the model, one can explain about 80 per cent of the variability in the inflation time series. The model residual error can be explained by measurement errors and with increasing accuracy one could reach a much higher predictive power. This is a simple way of explanation which meets general requirements of scientific methodology. Economics and econometrics are likely to violate this methodology in order to fit own understanding of reality.
The new Keynesian Phillips curve (NKPC) and many other economic and econometric models are based on an assumption that the future inflation value must depend on its current and/or past values and additional variables related to economic activity. Among many others, it might be unemployment , output gap or marginal labor cost.  To define the input of the activity variable one has to apply an econometric model which is similar (but not equivalent) to linear regression and calculate relevant coefficients in the relationship:

P(t+1)=a0P(t) +a1P(t-1)+ ….anP(t-n) + b0U(t)+b1U(t-1) ….
where P(t) is the inflation time series and U(t) is the rate of unemployment.  Instead of using advanced VAR models we apply simple linear regression to the German inflation (Figure 1) and unemployment (Figure 2) time series. There is a series of models with increasing complexity. In model M1, the original time series is regressed against itself with lag 1. The slope of 0.86 and R2=0.744 in table 1 demonstrate a high level of correlation which is well expected. The inflation time series varies with a period larger than 1 year. A crucial characteristic of the model is its accuracy as expressed as RMSE=0.00955. Thus, the uncertainty of one year ahead forecast is 0.96% in Germany between 1973 and 2010. For a purely naïve model, which does not include the intercept in the regression, RMSE=0.0097.  
In model M2, we use lags 1 and 2. This model is even worse than model 1 with R2=0.738 and RMSE=0.00967. Therefore, lag=2 does not help much and we include U(t) in model 3. This new term dramatically change the model. Coefficient b0=-0.34 steals some input from a0, which is now only 0.57. It means that one can explain same variations in the DGDP time series using its lagged values or the unemployment series. In model 3, individual inputs are shared almost proportionally, as required for collinear parts of regressed time series. Is it a fair division of influence?  Let’s look closer.
The input of U(t) can be masked by  the influence of the lagged values of inflation. In order to estimate the true effect of unemployment on inflation one needs to exclude all past values of inflation.  Models 5 and 6 try the unemployment time series and its lagged version. We have expected the outcome since it was obtained previously and described in our post on the Phillips curve in Germany. Model M6 with unemployment lagged by one year has all merits: R2=0.80 and RMSE=0.0084. Why should one use the NKPC if it does not reach the predictive power of the original Phillips curve? The explanation is simple and sad. Economics and, in part, econometrics are the hostages of prejudice and unjustified assumptions (rational expectations and likes). 
Mathematically, any student knows that one must not decompose a function into any set of functions which are not orthogonal. Otherwise, the decomposition cannot be completely resolved, and thus, is unreliable.  The NKPC makes this school-level mistake and decomposes inflation into a set of non-orthogonal functions. This is a methodological dead-end. It will always mask real influence of true inflation drivers, such as unemployment as models M3 and M4 demonstrate. One can check that the VAR models with the same lags give almost the same coefficients as in table 1.

Table 1
model
a0
a1
b0
b1
Rsq.
RMSE
M1
0.86
0.744
0.00955
M2
0.81
0.05
0.738
0.00967
M3
0.57
-0.04
-0.34
0.821
0.00799
M4
0.43
-0.04
-0.1
-0.31
0.828
0.00783
M5
-0.66
0.691
0.01050
M6
-0.65
0.804
0.00840


 Figure 1. The GDP deflator in Germany between 1971 and 2010

Figure 2. The rate of unemployment in Germany.

5/25/11

New Zealand. Sad economic forecasts

Here we introduce a new model of unemployment in New Zealand.  It extends the set of models linking the rate of unemployment and the change in labour force.  The agreement between the measured and predicted unemployment estimates in New Zealand validates our concept which states that there exists a long-term equilibrium (causal) linear and lagged link between unemployment, ut, and the rate of change of labour force, lt=dLF/LFdt. For this purpose, we use data borrowed from the OECD.

The estimation method is standard – we seek for the best overall fit between observed and predicted curves by trial-and-error method. All in all, the best-fit equation is as follows:
ut = -2.0lt-3  + 0.09         (1)
Therefore, the lead of lt is three years. The intercept of 0.09 implies the rate of unemployment at the level of 9% when the labour force does not change. Hence, New Zealand needs increasing labour force in order to reduce unemployment.   
Figure 1 presents the observed unemployment curve and that predicted using the rate of labour force change 3 years before and equation (1). Since the estimates of labour force in New Zealand are very noisy we have smoothed both annual curves with MA(3). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1984.
Relationship (1) allows a relatively accurate prediction of the rate of unemployment at a three-year horizon. Figure 1 demonstrates that unemployment will likely grow to the level of 7% in 2012 from the current level of 6.5%.  Hence, the drop in the rate of real economic growth will be accompanied by an elevated unemployment.


Figure 1. Observed and predicted rate of unemployment in New Zealand. The lower panel shows the cumulative curves for the annual curves in the upper panel.

5/22/11

Inflation in the UK - no sign of deflation any time soon

There exists a long-term equilibrium link between price inflation, CPIt, unemployment, ut, and the rate of change of labour force, lt=dLF/LFdt, as was demonstrated in this blog for many countries. The UK is one of the world biggest economies with a relatively good statistics started chiefly from 1973.  It is a major challenge to model inflation in the UK using our approach.
We have to separate two periods to fit observations: before and after 1985:
CPIt = 1.0lt  + ut  - 0.046; t>1985
CPIt = -1.0lt -1.7 ut + .025; t<1985              (1)
For both periods, inflation does not lag behind unemployment and lt. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. The change from negative to positive linear coefficient in 1985 needs a special explanation. But such effects were observed in other developed countries as well.  A labour force projection could help to predict the future inflation. Since the inflow of new employees is still positive,  lt >0, and the rate of unemployment does not foresees any dramatic decline in the long run one can be sure that inflation will be positive in the near future.

Figure 1. The rate of CPI inflation in the UK, predicted and measured.

5/21/11

Low inflation in Germany

There exists a long-term equilibrium link between price inflation, CPIt, and the rate of change of labour force, lt=dLF/LFdt, as was shown in this blog for many countries. Germany is a crucial economy to validate this link.  It had a major change in the latest history associated with the reunification. What was the effect of the merge? Here, we model the change in inflation dependence on labour force in 1989. Quantitatively, inflation became less sensitive to the change in labour force by a factor of 4: sensitivity has fallen from -2.2 to - 0.6.  
The estimation method is enhanced relative to our previous studies – the best overall fit is sought by the least squares method as applied to the cumulative curves. In addition to the formal LSQ minimization of the model error we have introduced a varying break year in the model. We allow such a break within 3 years around 1990. By definition, the break year has to provide the lowermost RMS residual. All in all, the best- fit equations for the period before and after 1990 are as follows:
CPIt = -2.2lt-6  + 0.046; t<1990
CPIt = -0.6lt-6 + 0.018; t>1990           (1)
For both periods, the lead of lt is six years. This defines the rate of inflation six years ahead of the current change in labour force. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. Because the big lag between the change in labour force and inflation one can foresee the change in prices many years ahead. In Germany, one should not expect high price inflation since the level of labour force has not been growing fast.
The coefficient in (1) obtained for the period after 1990 is not well constrained because the change in inflation is small and statistical estimates are not reliable. The future evolution of the overall CPI in Germany will help to resolve the model better. The previous model published in this blog, was obtained for the whole period and did not include the reunification. Corresponding coefficients were -1.71 and 0.041, which are close to those for the period before 1990.

Figure 1. The rate of CPI inflation in Germany, predicted and measured. The lower panel shows the cumulative curves.

4/18/11

Why inflation will be low in 2011

Three months ago we reported that the price index of housing had been decreasing since the end of 2008 relative to the overall CPI. This is a sustainable negative trend in a CPI subcategory with the highest input in the overall CPI. The housing index comprises approximately a half of the headline CPI.

Figure 1 displays the difference between the CPI and the housing index (both not seasonally adjusted) as reported by the BLS on April 14, 2011. The current trend is positive (the CPI grows faster than the index of housing) and the difference has been growing at a rate of +0.4 per month. Between 1996 and 2007, the slope was -0.06 per month.

FBR’s Vice Chair Yellen discussed the evolution of commodity and consumer prices over the past year and found that

Turning now to the outlook for U.S. consumer prices, I anticipate that the recent surge in commodity prices will cause headline inflation to remain elevated over the next few months. However, I expect that consumer inflation will subsequently revert to an underlying trend that remains subdued, so long as increases in commodity prices moderate and longer run inflation expectations remain reasonably well-anchored …

This statement does not contradict the long term trend in Figure 1. In several months, the current surge in energy prices will die and they likely return to the level of 2010. Then one will see a very low price inflation rate for 2011, as we predicted in 2005.

The decrease in the housing index (relative to the CPI)  will be accompanied by an effective stop in the food price growth and the fall in the transportation index relative to the CPI. All these effects will bring an extended period of deflation into the U.S. economy in 2012.

Figure 1. The change in the trend started in 2009. The current trend is positive (the CPI grows faster than the index of housing) and the difference has been growing at a rate of +0.4 per month. Between 1996 and 2007, the slope is -0.06 per month.

3/31/11

A win-win monetary policy in Canada

We have published a working paper on structural breaks related to the introduction of  inflation targeting in Canada. The intuition behind the Lucas (1976) crituque is correct. The reader may enjoy the beauty, i.e. the simplicity and clearness,  of the integral approach. 

The paper is available on arXiv::

A win-win monetary policy in Canada

Abstract
The Lucas critique has exposed the problem of the trade-off between changes  in monetary policy and structural breaks in economic time series. The search for and characterisation of such breaks has been a major econometric task ever since. We have developed an integral technique similar to CUSUM using an
empirical model quantitatively linking the rate of inflation and unemployment to the change in the level of labour force in Canada. Inherently, our model belongs to the class of Phillips curve models, and the link between the involved variables is a linear one with all coefficients of individual and generalized models obtained by empirical calibration. To achieve the best LSQ fit between measured and predicted time series cumulative curves are used as a simplified version of the 1-D boundary elements (integral) method. The distance between the cumulative curves (in L2 metrics) is very sensitive to structural breaks since it accumulates true differences and suppresses uncorrelated noise and systematic errors. Our previous model of inflation and unemployment in Canada is enhanced by the introduction of structural breaks and is validated by new data in the past and future. The most exiting finding is that the introduction of inflation targeting as a new monetary policy in 1991 resulted in a structural break manifested in a lowered rate of price inflation accompanied by a substantial fall in the rate of unemployment. Therefore, the new monetary policy in Canada is a win-win one.

Drang nach Osten — «натиск на Восток»

ИИ гугла написал « Drang nach Osten — «натиск на Восток») — это исторический термин, обозначающий германскую экспансию на славянские и восто...