Motor fuel price to fall in the near future

Our task is to estimate relative growth in a given price with time.  We use the ratio of price index, P(t), and GDP per capita in current prices, Y(t) (the idea borrowed from V.Kossov): 

Z(t)=P(t)/Y(t)

Figure 1 presents the evolution of the price index of motor fuel since 1935 (obtained from the BLS) and Figure 2 – nominal GDP per capita.   The share of motor fuel price in GDP per capita can be presented as a function of Y as well as time.  Figure 3 shows that there exist a long-term negative trend for Z(t) (notice the log-log scale) with two major fluctuations.  The trend looks sustainable and deviations seem to be of transient character.  Therefore, one can expect the fall in Z in the near future – motor fuel will be falling against GDP per capita. Oil price is likely to fall as well.  Figure 4 presents log(Z) as a function of time.

Figure 1. The consumer price index of motor fuel (not seasonally adjusted).

Figure 2. Nominal GDP per capita

Figure 3. LogZ vs. GDP per capita.

Figure 4. LogZ vs. time

Food is getting cheaper

Food is getting more and more expensive. Everybody knows that.  Figure 1 illustrates the evolution of the price index of food since 1913. At the same time, the US economy also grows including the growth in real GDP per capita which is shown in Figure since 1929 (chained, in 2005$).  One can easily estimate which of these two variables grows faster. Figure 3 depicts the ratio of CPI and GDP per capita relative to that in 1929. Overall, the food price falls relative to the GDP per capita, i.e. one has to pay a lower share of income (a fixed portion of GDP per capita)  for the same amount of food (we do not consider nomenclature and quality of food here).  Food is getting cheaper with time. It is interesting that the ratio in Figure 3 has not been falling much since 1975.

Figure 1.

Figure 2.

Figure 3.

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.

Real economic growth. The importance of being … small

Here, we compare real economic growth based on real GDP per capita, G. In developed countries, annual increment of GDP per capita is constant over time with all fluctuations caused by the change in the age pyramid. The average value of the annual increment of GDP per capita varies between countries, however. Among large economies, the USA grows with the highest annual increment.  In that sense, it is the most efficient economy.

Lately, we presented several posts showing the difference between real GDP per capita in the USA, Gusa,  and select countries, Gi:

dG = Gusa-Gi

When the difference dG has a positive trend, the gap with the USA increase with time. When dG has a negative trend, this country grows faster than the USA. There are not many economies outperforming the U.S. since 1990. Six developed countries deserve special consideration: Ireland, Norway, Luxembourg, Hong Kong, Singapore, and Trinidad and Tobago which joined recently.  Figure 1 demonstrates that these six economies all have negative trend in the dG time series. Ireland, the biggest among them, has been experiencing problems since 2006.

Hence, one can conclude that small countries have higher probability to grow fast. To be small is not enough, however!  

Figure 1. The differences between real GDP per capita in the USA and six select countries

Mark Thoma on the trend in real economic growth

Mark Thoma has published a long post on the evolution of real economy in the U.S. The question is -When will real GDP intercept its long-term trend? Or will it intercept at all? Mark also cited some related posts by Mankiw, Krugman, DeLong and own papers.

Before any discussion of real growth models one must replace real GDP with real GDP per capita in order to exclude the exponential working age population growth. This is a major source of confusion also missed by Mark. Then, one should compare other developed countries in order to reveal common features. Also, one has to test predictive power of all models.

My recent post on the growth model was based on observations in developed countries and showed that the growth rate of real GDP per capita has a trend decaying proportionally to the reciprocal value of the real GDP per capita. All fluctuations in the growth rate in developed countries, including the USA, return to this trend, at least since 1950 (no reliable data before).

Thus, the US economy will likely return to the decaying trend, not to the linear trend in the growth rate as borrowed from the Lucas lecture.

When discussing models one has to validate them by data. Otherwise this discussion is worthless.

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, u_t, and the rate of change of labour force, l_t=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:

u_t = -2.0l_t-3  + 0.09         (1)

Therefore, the lead of l_t 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.

The Phillips curve in Germany

In the posts on the USA and the UK, we mentioned the anti-Phillips curve in which unemployment lags behind inflation by several years. This contradicts the paradigm of the modern economic theory. There are cases, however, which comply with the theory. The Phillips curve in Germany is a good example where unemployment leads inflation by one year.

Figure 1 displays the observed rate of unemployment, u, and that predicted from inflation, which is represented by the GDP deflator, DGDP, according to the following relationship:

u(t-1) = -1.30[0.1]DGDP(t) + 0.105[0.005]              (1)

where u leads by one year. Standard deviation of the residual error is (s=) 0.013 for the period between 1971 (start of DGDP time series) and 2010. Both coefficients in (1) are reliable, and thus, there exists a linear and lagged relation between unemployment and inflation in Germany.

Figure 1. Unemployment and DGDP (both reported by the OECD) in Germany between 1971 and 2010. The lower panel shows the cumulative curves for the annual readings in the upper panel.

Both coefficients in (1) are determined from the cumulative curves with a higher accuracy when provided by linear regression. Figure 2 depicts the Phillips curve in a standard way. The slope of -0.645 instead of the linear coefficient -1.30 in (1) is highly underestimated due to the uncertainty in both time series. At the same time, the determination coefficient R²=0.83 is a strong evidence in favour of the Phillips curve in Germany.

 The existence of a conventional Phillips curve in Germany raises a question about the consistency of monetary policy of the Bundesbank. Does the bank conduct a monetary policy, which balances inflation and unemployment? Affirmative answer is counter-intuitive as in the past twenty five years show the unwillingness of the bank to reduce unemployment in exchange for higher inflation.

Figure 2. The Phillips curve for Germany. The unemployment readings are shifted by one year ahead to synchronize with the GDP deflator estimates.