Archive for econometrics

Cointegration, Dependency and Manufacturing (24-IV-09)

Posted in 04 - Abril, Año 2009 with tags , , , , , , , , , , , , , , , , , , , , , , , , , , on April 24, 2009 by Farid Matuk

Chile - USA (1981-2008)

Chile - USA (1981-2008)

Peru - USA (1981 - 2008)

Peru - USA (1981 - 2008)

These graphs show –for a naked eye- a similar cycle over time, besides differences on timing and amplitude, there is a similar number of boom and boost processes. A first question to analyze is the existence of cointegration between those series, and if the answer is affirmative to evaluate the dependency of some from one.

 

Cointegration concept comes from econometrics and it is related to time series which evolve over time in a similar pattern, cointegration does not imply causality between the variables analyzed, it implies a similar concept of parallel lines in geometry.

 

On the other side dependency theory in economics, implies the existence of a center and a periphery, equivalent to solar system in astronomy, the planets does not have exact orbits, but they are not comets drifting on the outer space. The dependency concept tells of an economy that is the center for periphery economies, which essentially are tied up to the evolution of the center.

 

This note founds that Chile and Peru manufacturing sector are periphery economic activities to the USA industrial sector on the long run, obviously in the short run a periphery sector may drift away, but sooner or later return to its orbit. A simulation is run from August 2006 up to December 2008, when Peru has a new presidential tenure in July 28th 2006, which shows a Peru industrial sector drifting-up, and then a forecast is made to evaluate how much economic contraction will face Peru to be back on track.

 

The monthly series are taken from International Monetary Fund’s International Financial Statistics Compact Disk disseminated March 2009. Only series from Chile and Peru are chosen from South America due lack of availability for other countries, only USA series will be taken from 24 advanced economies (IMF lingo), as center country. The series start in January 1979 because Peru is the constraint, until December 2008 because is most recent available data from USA. The codes are […66EY.ZF…] for Chile and Peru, and […66…ZF…] for USA; which is available here.

 

A first step is taking logarithm of each series, then to evaluate the existence of unit root for each one, which is accepted. A cointegration test between Chile, Peru and USA is rejected with zero lags, but a loop from 1 to 60 lags is run to find 12 lags (a calendar year) as appropriate to accept cointegration between the analyzed variables. The evaluation is constraint until July 2006, since Peru has a new presidential tenure since August 2006.

 

Two approaches were tried to model the dependency of Peru and Chile to USA. The unsuccessful one was an Error Correction Model (ECM) which shows a strong equilibrium relationship between Peru and Chile, but the equilibrium error component was nil for Chile equation and strong for Peru; but in any circumstance was possible to reject a null hypothesis for USA inclusion in the equilibrium relationship or in the equilibrium error.

 

The second and successful approach was a Vector Autoregressive (VAR) model with USA as exogenous component. The lag period was 12, since this length was found as adequate on the cointegration analysis described above. The computer code in RATS is here, and the output results are here.

 

The first null hypothesis tested for no relation between Chile and Peru is rejected for each equation and therefore the naked eye observation was correct. A second set of null hypothesis for each USA coefficient being zero in both equations is carried out, to find them rejected and to conclude that USA industrial sector has influence on Chile and Peru manufacturing sector, in the impact multipliers. A third set of null hypothesis for equilibrium multipliers of USA being zero is carried out, to find them accepted; this unexpected outcome is interpreted as neutrality on the long run of the level of USA industrial activity for Chile and Peru manufacturing sectors, only if USA variable become constant which never have been observed. A fourth set of null hypothesis for equilibrium unitary elasticity between Chile and Peru is carried out, to find them rejected; this outcome allows concluding that USA individual shocks in Chile and Peru become permanent for the level of manufacturing activity.

 

Those four sets of null hypothesis are re-run with a Seemly Unrelated Regression (SUR) model with similar specification in order to evaluate cross equation restrictions. The previous four null hypotheses are evaluated and similar conclusions are obtained. The fifth null hypothesis of USA impact coefficients with similar values vis-à-vis for Chile and Peru is carried out, to find them rejected; this outcome allows concluding differentiated short run impact between Chile and Peru, nevertheless for both countries the equilibrium multiplier for USA is zero. Finally, a sixth null hypothesis for null intercept in Chile and Peru is carried out and accepted; this outcome allows to conclude that long run average level of manufacturing in Chile and Peru is the long run multiplier of Peru and Chile –respectively- multiply by the average level of industrial activity in USA.

 

The third and sixth null hypotheses are imposed in a new estimation on the SUR model in order to produce a forecast outside the boundaries of the estimation, which are January 1979 and July 2006. The forecast values are plotted in graphs for Chile and Peru showing an interesting feature which differentiates Chile and Peru; while Chile forecast values are close to observed values, Peru forecast values are systematically below observed values.

 

A first econometric conclusion is the existence of cointegration between Chile, Peru, and USA. A second econometric conclusion is the dependency of Chile and Peru with USA which is coherent with the economic dependency theory. A third conclusion is Chile manufacturing sector is on track, and its contraction will mirror USA industrial contraction. A fourth conclusion is Peru manufacturing sector is off track, and its contraction will be more than proportional to USA industrial contraction.

 

 

Chile Forecast (August 2006 - December 2008)

Chile Forecast (August 2006 - December 2008)

Peru Forecast (August 2006 - December 2008)

Peru Forecast (August 2006 - December 2008)

Chile and Peru gap between observed and forecast values

Chile and Peru gap between observed and forecast values

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Growth, Inflation & Poverty (24-III-09)

Posted in 03 - Marzo, Año 2009 with tags , , , , , , , , , , , , , , , , , , , , , , , on March 24, 2009 by Farid Matuk

The most common approach to lowering poverty rates is to have high economic growth, but recent evidence from Peru disputes this result, pointing out that high growth rates could be canceled out by high inflation rates, with as a consequence high growth rates and higher poverty rates.

Measuring poverty has many tools from the most elemental to the most sophisticated; data available speaks of the degree of statistical development of each county, as well the willingness of each government to finance surveys that expose the painful reality of the poor.

The simplest method consists of a poverty line in US dollars, being US$ 2 per day a popular threshold. The conventional problem with this value is different purchasing power of US$ 2 in different countries, the World Bank has tried to solve this problem with a successful world-wide effort to measure PPP (purchasing power parity) for each country and therefore now it is possible to have US$ 2 PPP for each country. But a large limitation of this approach is that rural areas – where the poor live- have been excluded because the PPP was build with domestic CPI (consumer price index), which by definition excludes rural areas.

A second approach, also pioneered by the World Bank, is a poverty survey, well known as Living Standard Measurement Survey (LSMS). A medium size survey (around 5,000 households) is applied in urban and rural areas of any country, with a strong emphasis in food and beverage consumption (as source of calories), plus expenses in other major items of any consumption basket. The main result of this approach is to obtain a poverty line in domestic currency for any given country.

The main pitfall of this approach is the lack of transparency of the assumptions taken for producing a poverty line. Almost every country produces data tabulates; most of them data base access; and almost none computer code applied. The computer code written is essential to identify is a systematic bias have been applied for the published poverty line, as well to learn all arbitrary decision taken on the steps described below.

Step 1: How to define an average poor household? Usually the average is in the half poor of the sample, but there is no international standard to identify it. If the mean poor household is closer to the median household, the final poverty line will be high compare to a mean poor household who is far from the median household.

Step 2: How to define a vicinity of the average poor? After a mean poor household was identified, vicinity must be defined. This could be one tenth, one fifth, one fourth or one third of the sample, and again there is no international standard. For a larger vicinity, a lower poverty line is found, and vice versa.

Step 3: How to define a basket of food and beverages for the extreme poverty line? After steps 1 and 2 are done, the researcher must choose which goods will be taken in account for valorizing the extreme poverty line, which is made setting a price for each product chosen. The exclusion criterion is arbitrary and may produce biases in any direction, according the price of the excluded products.

Step 4: How to deflate prices spatially? Since the survey is applied nation-wide, there are areas were food and beverages are non-market items, because the households in rural areas have an economy of subsistence, where they are producers and consumers at the same time. Theoretically there is many options to imputed prices, but since computer code is not public, a source of bias could be easily masked.

Step 5: How to measure an Engel coefficient for the extreme poverty line? After the extreme poverty line is obtained, it is necessary to produce a total poverty line, which must include non-calorie goods and services. While again, there is a large literature on this subject, without the computer code is impossible to analyze if the poverty line has a bias that overestimates or underestimates real poverty.

Besides these limitations, a poverty line is measured with a survey, and a poverty basket is designed to monitor poverty evolution. All problems of a conventional Laspeyres index are valid, but certainly a national poverty line is better than a US$ 2 PPP line because this measurement includes rural areas, where most of the poor used to live.

The UN MDG (United Nations Millennium Development Goals) has several goals, where Goal 1 is “Eradicate extreme poverty and hunger”, Target 1.C is “Halve, between 1990 and 2015, the proportion of people who suffer from hunger”, Indicator 1.8 is “Prevalence of underweight children under five years of age” and Indicator 1.9 is “Proportion of population below minimum level of dietary energy consumption”.

While Target 1.A and Target 1.B for Goal 1 are related to economic conditions of the poor, Target 1.C is related to biological and anthropometric characteristics of the poor. The main advantage of indicators for Target 1.C is that fewer assumptions are required for its measurement, therefore less built-in steps for biases.

For Indicator 1.8, the most common statistical device is the Demographic and Health Survey (DHS) which is funded by United States International Development Agency (USAID) around the world. The traditional design is a large scale sample around 20,000, which allows to measure demographic and heath variables, applied in intervals of 5 years. A new approach, which has Peru as pilot country started in 2004, sampling every year 6,000 households in a five year plan; this new design is able to produce statistical results for key variables with low variance, and for other variables in 5-year average.

For Indicator 1.9, a World Bank’s LSMS could be used in order to measure caloric intake and caloric needs for each household and from both figures the percentage of population below minimum intake could be obtained.

The graphs below are for Peru where Indicator 1.9 is plotted with inflation in the first and with growth in the second.

Poverty & Inflation (2004 - 2008)

Poverty & Inflation (2004 - 2008)

Poverty & Growth (2004 - 2008)

Poverty & Growth (2004 - 2008)

Starting May 2003, Peru was applying a LSMS in monthly basis with an annual target of 20,000 households. This new approach has sampling difficulties that were solve through a technical cooperation program with Statistics Canada, who did the sampling for the first year, and subsequent years were done by Peru’s statistical agency.

For monetary poverty results, an annual sample is cumulated and then a poverty line in domestic currency is obtained as described above. The first result was measured for May 2003 – April 2004, and subsequent results have been published for calendar years.

But the main advantage of this design is to obtain quarterly results for caloric poverty as defined by UN MDG Indicator 1.9. In the graphs above, the bars are annual moving average for caloric poverty, as well economic growth and consumer inflation. The spreadsheet to redo the graphs is available here and was obtained from official sources as described below.

The quarterly results are available in PDF on the web site of Peru’s Statistical Agency, first step is to click in “Boletines” on the left side panel, then to click on “Condiciones de Vida” also on the left side panel, and download the PDF files for each calendar quarter since 2007, and for each moving quarter since 2003.

The other two variables, economic growth and consumer inflation are taken from the web site of Peru’s Central Bank, economic growth is obtained from real quarterly national accounts, with the rate of growth of the moving average of four quarters compared with previous fourth quarters of Gross Domestic Product (GDP). Consumer Inflation have been built from the implicit deflator for private consumption; in order to obtain this index, the private consumption in the nominal quarterly national accounts, is divided by the private consumption in the real quarterly national accounts. The rate of growth follows same procedure for economic growth.

An examination of both graphs offers a clear example that GDP growth by itself will not reduce poverty, and that the inflation level is a more critical tool for fighting poverty. Therefore low growth with low inflation reduces poverty at a steady rate, while high growth with high inflation increases poverty at a steady rate.

  • Econometric Analysis

Besides this graphical analysis, an econometric one is feasible and some results are presented below. In first place, the sampling period for the analysis is the whole period for available quarterly measurement of caloric poverty; this is from 2003 Q3 to 2008 Q4, with a total of 22 observations. Data for economic growth and consumer inflation is available quarterly since 1980.

Caloric poverty (CALP) is the percentage of population who lacks the minimum calorie intake; economic growth (GDP) is the difference of logarithm of real GDP in any quarter to similar in previous year; and consumer inflation has same mathematical transformation with the deflator of private consumption (DPC).

The model to be estimated is quite simple, with a perturbation component that fulfill classical assumption for error term of normal distribution, serial independence, and homocedasticty:

CALP{t} = BETA0 + BETA1*DPC{t} + BETA2*GDP{t-1} + U{t}

The data could be found here, the RATS source code could be found here, and the RATS output file could be found here.

An initial regression was tried with GDP impact in same period, but GDP lagged one period showed a better result. Therefore changes in inflation have a faster impact on poverty than growth rate, which is not surprising that a nominal variable has faster impact than a real variable.

The best result provides BETA1 and BETA2 coefficients with null hypothesis of zero value rejected at 99% confidence, when the first observation of the sample is excluded, having as result a total of 20 observations for the analysis.

Another important result also showed in the output file is that null hypothesis of BETA1 and BETA2 having similar value with opposite sign is always accepted, with several sampling periods. This allows conclude that lowing inflation has the same impact that increasing growth rate.

Finally, the econometric evidence reaffirms what was intuitive on the graphs. Not only economic growth matters for fighting poverty, also matters low inflation in equal degree.

Sat Apr 5, 2003 10:11 pm

Posted in 2003-04 Abril with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , on January 28, 2009 by Farid Matuk

Activos y Flujos

Hoy tenemos en La República “… ¿nuestras exportaciones no
tradicionales (que son las que importan) podrán seguir creciendo con
una moneda nacional que se revalúa día a día? …” y “Sea lo que
fuere, es difícil pensar en un crecimiento sostenido de las
exportaciones no tradicionales si se mantiene o profundiza la
apreciación de nuestra moneda (precio relativo desfavorable). ¿Qué
es lo que viene sucediendo?”

Primero quisiera recordar un libro de Fair, quien es uno de los
pocos con un algoritmo propio para máxima verosimilitud, donde tiene
dos modelos simples para explicar valor agregado. Uno basado en
flujos donde el PBI depende de un componente de demanda exógeno, que
sería clasificado popularmente como keynesiano, y otro basado en
activos donde el PBI depende de un activo cualquiera, que sería
clasificado popularmente como monetarista.

En el pico de la hiperinflación, se discutía sobre las causas de
ésta, y básicamente había la de exceso de demanda interna (flujos) y
la de escasez de divisas (activos). Creo que similar enfoque se
puede aplicar al presente. O necesitamos un tipo de cambio real que
permita crecer via exportaciones no tradicionales (flujos) o
necesitamos un tipo de cambio real que permita crecer via
acumulación (activos).

La impresión que tengo esta sustentada en un mundo de activos,
donde la brecha entre las tasas de interés de soles y las tasas de
interés de dólares reflejan la devaluación esperada, pero
parafraseando a Beckett en “Esperando a Godot” la espera desespera y
la devaluación nunca llega, mientras el deseo que llegue se torna
desesperación.

Con un poco de tiempo y con la información detallada de la SBS,
se podría hacer el cálculo de la desesperación en 2002, es decir
cuanto fue la pérdida implícita de aquellos que ahorraron en dolares
y los que prestaron en dólares, versus la minoria que hizo las
mismas operaciones de activos en soles.

Un tema final sobre el tipo de cambio real, está en la
complejidad de construir los deflatores del comercio exterior de
bienes, ya que de servicios es sumamente dificultoso. Para
exportaciones suele ser mas fácil ya que estan mas concentradas pero
para un país con un fuerte componente de exportaciones primarias,
deflatar las exportaciones no primarias es titánico. Pero
importaciones tambien suele ser un problema ya que se tienen dos
soluciones básicas, o se deflata con algún índice de precios del
socio comercial o se se enfrenta la díficil tarea de construir un
índice de volumen de las importaciones.

Farid Matuk 

http://groups.yahoo.com/group/MacroPeru/message/2747