Table of Neosustainable growth theory and MTF

Tableau 1a. Relation entre la croissance moyenne et la volatilité, avec les variables de contrôle de Levin-Renelt (voir figures etfichier de tables)

Les résultats de la régression sont présentés dans les tableaux 2a et 2b.

Dans cette spécification, les coefficients des régressions de la croissance moyenne sur la volatilité dans les deux échantillons présentent les mêmes signes négatifs, soit respectivement -0,618 et -0,295 pour le premier et le second échantillon, et sont statistiquement significatifs à un seuil supérieur à 1 %. L’introduction de variables de contrôle a renforcé la significativité de la relation entre la croissance moyenne et la volatilité, qui conservent désormais le même signe négatif. Ces variables ont consolidé la relation négative liant la croissance moyenne à la volatilité dans l’échantillon de l’OCDE et inversé son signe pour l’échantillon de 108 pays par rapport à la première spécification de base. La relation étudiée devient économiquement significative et traduit la théorie communément admise selon laquelle les pays présentant une volatilité annuelle plus élevée de leurs taux de croissance tendent à afficher des taux de croissance plus faibles.

Dans ce modèle, on constate que l’élasticité du commerce international après un déplacement de la frontière des possibilités de production (e _i) détermine le signe négatif de la relation entre croissance et volatilité (e _{_i -1} < 0). Voir les tableaux 2a (bis) et 2b (bis). L’élasticité du PIB global ou du commerce international (e_{_i}) est négativement corrélée à la tendance des déplacements de la FPP nationale définie par (gdppccp, inv, h_c, aapgr).

Bien que la principale variable de contrôle soit le PIB initial par habitant, j’observe que la part moyenne de l’investissement dans le PIB apparaît dans ce modèle avec un coefficient négatif dans les deux échantillons. Cependant, la relation redevient normale lorsque je régresse la croissance moyenne sur les variables de contrôle sans tenir compte de la variance de croissance (volatilité). Nous pouvons donc conclure que, contrairement à l’étude de Ramey et Ramey, la volatilité a un effet négatif sur la relation entre croissance et investissement. Ainsi, d’autres études montrent que la relation négative entre croissance moyenne et volatilité persiste même lorsque la part moyenne de l’investissement dans le PIB est omise, ce qui suggère qu’il n’y a pas d’effet systématique à contrôler l’investissement.

Si les États-Unis sont choisis comme pays de comparaison, les statistiques estimées indiquent qu’il existe une variation substantielle de la volatilité à travers le pays et que la relation étudiée est formellement négative.

5.1.1.1.2 – Tester la relation entre la variance de l’innovation et la croissance

Afin d’examiner l’incertitude liée à la relation entre croissance et volatilité, nous considérons le modèle ci-dessus et modifions le contenu des variables de contrôle. Ces variables sont de deux types : les mesures des variables au début de l’échantillon et les prévisions.

variables mesurées au début de l’échantillon

• Inv : La fraction de l’investissement dans le PIB de la première année de l’échantillon ;
• aapgr : taux de croissance de la population au cours des deux premières années de l’échantillon
• Variables de prévision :
• Two lags of log level of GDP per capita
• A time trend
• A time trend squared
• Four seasonal dummy variables (Q1_t, Q2_t, Q3 and DO_tt) whose role is to capture specific effects. When a country choice is suboptimal, its production possibilities frontier is in movement. Under these conditions, the seasonal dummy variables which are defined below and Arch/Garch method permit to link the movements of (PPF) and their interactions with international trade, growth rate and volatility.

Following Hendry’s method (1974), we use the combination of trend and seasonal dummy variables to model specific effects. In order to model these trend, seasonal and special effects, define new variables as follows:

Q1_t = {-1 for 1980-94, 0 otherwise

Q2_t = { 1 for 1994-2000, 0 otherwise

Q3_t = {-2 for 2000-2010, 0 otherwise

T = t = 1, 2, 3, …, 30

DT1_t = Q₁.T , DT2_t = Q2_t . T , DT3_t = Q3_t. T

DO_t={1 for 1987(1) and 1998(1) ; -1 for 1987 (2) and 1998(2) and 0 otherwise.

The variables Q1_t, Q2_t and Q3_t are seasonal dummy variables. As the estimated model will include an intercept term and the joint presence of all four dummy variables and an intercept term would make the estimation procedure break down. The variable T is a time trend. The variables DT1_t, DT2_t, DT3_t allow for multiplicative seasonality where the absolute value of the seasonal effect changes over time depending on our estimations of PPF movements and their interactions with international trade. Thus international trade elasticity after a production possibilities frontier movement (e_i) should determine the sign of the relationship between growth and volatility. If e_i -1 < 0, the sign should be negative and positive if e_i – 1 > 0.

Thus the consecutive values of DT1_t are -1, 0, 0 ;  DT2_t are 0, 1, 0 ; DT3_t are 0, 0, -2

The equation to be estimated is:

The results of this regression are given in tables 3a and 3b.

In this new framework, it is clear that the relationship between the mean growth and innovation volatility is also negative, indicating that countries with higher innovation volatility will have lower mean growth rates.  Our results confirm the studies of Ramey and Ramey. Using two samples 24- OECD and 92-country sample from 1950 to 1988 and 1960 to 1985 respectively Ramey and Ramey growth rates on a group of explanatory variables in which we find the standard deviation of output growth. They find that the standard deviation of output growth has a significant negative effect on mean growth.

In this model we can see that international trade elasticity after a production possibilities frontier movement (e_i) determines the negative sign of the relationship between growth and volatility ( e_i -1 < 0). See table 2a (bis), table 3a(bis), table 3b(bis). Grgdp or international trade elasticity (e_i) is negatively correlated to the movements’ trend of national PPF defined by (gdppccp, inv, h_c, aapgr).

But, two problems remain pendant. The initial investment share of GDP and human capital, defined as the level of employment for 21 OECD-country samples and as the average years of schooling for individuals in the total population over age 25 for the first sample, are negatively correlated to the mean growth.  When I regress the same equation without volatility, the signs of these variables become positive and significant as we can see.

grgdp_it = 0 .0034053inv  + 0.0034703 aapgr+0 .9999967hc   -0.0021678   gdppccp+….

I conclude that high volatility is negatively associated with investment and human capital (unemployment increases) in 21-OECD sample and school dropouts in the first sample.

Testing the robustness of country-specific control for growth volatility

The question here is: does the inclusion of different country-specific control variables affect the nature of the relationships tested above? In order to investigate that, we are going to extract all the control variables which were statistically significant in volatility regression through time and countries (countries) and see the impact of these variables in new time and country-fixed effects models. This is done by the introduction of dummy variables for each country. At this end, we estimate the country-specific forecasting equations for government-spending growth as follows:

Govexp = f(two lags of the log level of GDP per capita, two lags of the log level of government spending per capita, a quadratic time  trend, four dummy variables and a constant term)

Then by testing the relationship between the variances of the innovations in the growth equations and the squared forecast residuals of the government spending equation, we will obtain the measure of volatility which depends on time and countries. It is therefore easy to be definitely fixed on the sign of the relation that links volatility to growth. 

The equations estimated are:

    (1a)

ε_it῀N(0, σ²_it)          vol²_it= a₀ + a₁ û²_it                 (1b)

grgdp_it: the growth rate of output, vol_it : the standard deviation of residuals, X; the vector of control variables and û²_it : the square of estimated residual for country i in period t from the government –spending forecasting equations.   

The regression results are presented in Tables 4a-4h.

Table 1b. The sign of the link between growth and volatility with a sample 108 countries

Table 1c. The sign of the link between mean growth and volatility with a sample 108 countries

(endonnées de panel)

Table 1d. The sign of the link between growth and volatility with a sample 25 developed countries

2 step: introduction of  Levin and Renelt. control variables 

The models to test are in the following form:

grgdp_it = λvol_i + θX_it +ε_it (1a)

εit N(0, σ²_i) (1b)

i = 1, …,I t= 1, …, T

grgdpi average annual growth in GDP / head for country i and year t (obtained in taking the differences of logarithm).

σi: is the standard deviation of the residues, εit; εit is the standard deviation of growth obtained from predicted values based on Xit variables. Xit variables differ from one country to another

From one year to another. Xit: is the vector of the control variables Θ: is the vector of the coefficients common to the countries of the sample; λ denotes the relationship between growth and volatility and is the most important parameter in this specification. The vector of control variables, X proposed by R. Levine and R. Renelt (1992) are the most important variables for the analysis of the growth of the countries. These variables are defined as follows: 1) “inv” Share of average investment in GDP; 2) (gdppccp): the logarithmof the GNP / initial head (at the beginning of the period); 3) hc or hc-residue when hc is purged of the difference between observed and predicted values obtained using a partial regression of hc on other control variables; aapgr: average growth rate of the population. In the sample of 108 countries, human capital is the average number of years of schooling of individuals in the population aged 25 and over. But in OECD countries, human capital is the secondary enrollment rate as a percentage of the relevant age group. For regressions, we will use the maximum likelihood method on panel data. The number of observations for the sample at 108 countries is 3240 and 630 for the sample of 25 developed countries.

Table 2. Relationship between the mean growth and the volatility with Levin-Renelt control variables

Table 2a.The sample of 108 countries

Table 2b. The sample of 25 countries

Step 3: Test of the relationship between innovation variance and growth

In order to examine the stochastic part of the relationship between growth and investment, we take the above model while changing the content of the control variables. Thus, we have two types of variables: the measure of variables at the beginning of the period and the predictors X. The variables to be taken into account in this new specification are:

– Variables measured at the beginning of the period 1) Inv: the average share of investment in GDP at the beginning of the period; – aapgr: the average annual growth rate of the population at the beginning of the period.

– Predicted variables:

1) GDP per capita delayed by two periods

2) The trend of time

3) The trend of time squared

4) Four dummy seasonal variables (Q1t, Q2t, Q3t and DOt) whose role is to capture the specific effects. These variables are defined below.

Table 3a: Sample of 21 OECD panel data countries (see book (see Dynamics of trade and volatility)

Table 3b: The 108 country sample and panel data regression (see Dynamics of trade and volatility

Table 3: Relationship between average growth and volatility of innovations

Step 4: Test the robustness of country-specific control of growth volatility

The question here is: Does the introduction of different countries with specific effects affect the nature of the relationship tested here? In order to make this investigation, we will extract all the control variables that are statistically significant in the regression of volatility in terms of time and country and observe the impact of these variables on the new fixed-effects models in the time and space (country). This is done by introducing dummy variables for each country. To this end, we estimate country-specific equations for growth in government expenditures as follows:

Govexp = f (Log of GDP / head lagged by 2 periods, government expenditure log per capita

Delayed by 2 periods, a quadratic time trend, 4 dummy variables and a constant term)

The equations to be estimated have the following form:

grgdp_it = λvol_it + θX_it +ε_it (1a)

εit῀N(0, σ²_it) vol²_it= a₀ + a₁ u²_it (1b)

Table 3a. 21 OECD country- sample panel regression

Table 3b. 108-country sample psanel regression

Table 4a. Regression of governmental expensive on the the Levin-Renelt control variables (world technologye frontier) and dummy control variables

The estimation of the following relation vol²it= a0 + a1 û²it  gives:

Table 4b. Regression of the standard deviation of innovations on the square of standard deviation of residuals of the equation of the governmental expensive

Table 4c. Regression of the rate of governmental expensive (govexp) on the trend of resources (control variable contributing to WTF) and on the dummy variables and on 4 time trend variables and the LOG of GDP of 2 periods lag

Table 4d. Regression of the rate of per capita growth on the trend of resources (control variable contributing to WTF) and on the dummy variables and on the fixed effects of countries

Table 4e. Regression of the rate of governmental expensive (govexp) on the trend of resources (control variable contributing to WTF) and on the dummy variables with countries fixed effects

Table 4f: Regression of the rate of governmental expensive (govexp) on the trend of resources (control variable contributing to WTF)  and on the dummy variables with countries and time fixed effects

Table 4g. Regression of the rate per capita growth on the trend of resources (control variable contributing to WTF) and on the dummy variables with countries and time fixed effects

Table 4h Regression of the rate of governmental expensive (govexp) on the trend of resources (control variable contributing to WTF)  and on the dummy variables with countries and time fixed effects

This regression gives us the forecast residuals of government spending. Then by regressing the variances of the innovations in growth on the squared forecast residuals of the government-spending (i.e vol²_it= a₀ + a₁ û²_it), we will obtain the measure of volatility as a function of both time and countries if the relationship estimated is statistically significant. The next and final step is to test if we have a positive or negative relationship between growth and volatility by introducing in other regressions time and countries fixed effects.

The estimation of the following equation vol²_it= a₀ + a₁ û²_it gives:

We see that the relationship is negative but the coefficient is not strictly different from zero. If we consider that this relationship exists, we have the measure of volatility that depends on time and countries. Then our final regressions should show the panel variation in volatility.

These regressions in Tables 4c and 4d show that volatility is negatively linked to output growth and variances of the growth innovations are related to the squared innovations in government spending. But the relationship between government expenditures and the government volatility of output is positive.

These regressions confirm the previous negative relationship between growth and volatility with variables statistically significant. Thus, the presence of country or time fixed effects does not change the nature and the robustness of the relationship between the two key variables in this study (growth and volatility).

In this case, we can see that international trade elasticity after a production possibilities frontier movement (e_i) determines the positive sign of the relationship between growth and government expenditure volatility ( e_i -1 < 0). See Table 4a (bis). d2_gdppccp or international trade elasticity (e_i) is positively correlated to the movements’ trend of national PPF defined by ( inv, h_c, aapgr innovar).

3.2 Second Component: Intergenerational Trade Empirical Evidence

3.2.1 Test with a simple statistical data analysis

We have to apply the conclusions of the pure theory of international trade (presence of comparative advantages or proportions of factors, the international tradable goods levelling out of prices, trade earnings) to a model of intergenerational free trade.

3.2.2 Computing intergenerational levelling out of prices of goods and factors through Statistical Data Analysis

Let us consider 22 African and European countries and two kinds of variables (natural resources and unnatural resources). The natural resources variables are 1) Arable surface area (SUPTA).a Wooded surface area (SUPTB).3) Resources of renewable water. 4) Mineral resources (CRESMIN). Unnatural resources variables are represented by 1) GNP/capita (PIBRT). 2) Urbanization rate (TUR). 3) Green House Effect Emissions (INDICE SERR). 4) Pure water consumption (WATERCONSUMP). 5) Inhabitants number per physician (NH/M). 6) Life Expectancy at birth (ESPER). 7).The scientific diploma (ND). 8) A number of years of education (NAE). 9) Scientific and technicians number (NS).

3.3. Cross-Generation Volatility Evidence

For the second component (how changes in production factors supply affect intergenerational trade), I will first consider France through five generations of 50 years with 10 witness generations. In the second case, I mix France five generations with the remaining of 124 countries considered as current generations. For the results, see Table 5a and Table 5b. The relationship between growth and volatility, under overlapping generations hypothesis, is positive, confirming Mirman conclusion “ if there is a precautionary motive for saving, then higher volatility should lead to a higher saving rate, and hence a higher investment rate which is positively linked to growth”. But, in this case, generation PPF movements’ trend is indeterminate, because two control variables are positively linked to growth rate and two other control variables are negatively linked to the growth rate (Table 5a bis). It is possible that the relationship between growth and cross-generation volatility would be positive if I consider control variables with their weight (t-stat). In that case, we should expect to meet very often over-optimal growth than suboptimal growth because the first generations tend to mortgage the capacities of future generations (absence of intergenerational levelling out of prices of goods and factors).  

3.3.1      The model: Evidence on Multidimensional Suboptimal Trade and the Sign of the Link between Growth and Volatility

In order to study the relationship between growth and volatility in the context of multidimensional trade, I will follow three steps: 1) In the first case, I consider France through five generations of 50 years with 10 witness generations; 2) In the second case I mix France five generations with the remaining of 124 countries; 3) I will mix France five generations with the remaining of 124 countries and observe the sign of the relationship between growth rate and growth volatility and with control variables.

1st step

Table 5a. Mean growth and growth volatility with a sample of 8 France generations (1800-2000)

Table 5b. Mean growth and growth volatility with a sample of 8 France generations (1800-2000) with Levin-Renelt control variables

Table 5c. Test of Mean growth and growth volatility with a sample of 108 countries and its  generations (multidimensional trade)

Table 5d. Test of Mean growth and growth volatility with a sample of 8 generations of France trading with all the generations of the 2 samples

THE TEST: Step 1

We test this relationship on two samples. A sample of 25 OECD countries and a sample of 108 developing countries. The study period is 1980 to 2010.

Table 1a: Relationship between average growth and growth fluctuation With a sample of 108 countries

These two groups of countries and the period are chosen because of the relative homogeneity of production technologies within the groups. All statistics come from the World Development indicators.

1. i) Testing the spatial relationship between growth and volatility. At this first stage, it is important to examine the basic nature of the spatial relationship between growth and growth volatility. To this end, we calculate the average growth and standard deviation of growth rates by country and over a given period (1980- 2011). The results of the regression of average growth (grgdp) on growth volatility (vol), for the sample of 108 countries and over the period 1980 to 2010 :

F(1, 106) = 0,48

R- squared = 0.0204 AdjR- squared=0.0222 Log

Table 1b: Relationship between average growth and growth fluctuation With a sample of 108

Table 1c: Relationship between average growth and growth fluctuation With a sample of 25 countries

Table 2:Sample of 21 countries

likelihood=4493.291

2nd step: introduction of Levin and Renelt control variables. The models to be tested are of the form :

grgdpit = _λvolivoli + θXitXit _+εitit (1a) εitit

N(0, _σ2i) (1b) i = 1, …,I t= 1, …, T grgdpi average annual growth in GDP/head for country i and year t (obtained by taking log differences). σi : is the standard deviation of residuals, _εitit ; _εitit is the standard deviation of growth obtained from predicted values based on Xit variables. _Xit variables differ from country to country from one year to the next. _Xit: is the vector of control variables Θ: is the vector of coefficients common to the countries in the sample; λvoli denotes the relationship between growth and volatility and represents the most important parameter in this specification. The vector of control variables, X proposed by R. Levine and R. Renelt (1992) are the most important variables for the analysis of country growth. These variables are defined as follows: 1) ≪ inv ≫ Share of average investment in GDP; 2)

(gdppccp): logarithm of initial GNP/head (at start of period); 3)hc or hc-residual when hc is purged the difference between observed and predicted values obtained using a partial regression of hc on other control variables; aapgr: average population growth rate. In the sample of 108 countries, human capital is the average number of years of schooling of individuals in the population aged 25 and over. But in OECD countries, human capital is the secondary school enrolment rate as a percentage of the relevant age group. For the regressions, we use the maximum likelihood method on panel data. The number of observations for the 108-country sample is 3240, and 630 for the second sample, which becomes a 21country sample in this new specification. The regression results are presented in the tables below:

Table 2: Relationship between average growth and volatility with Levin-Renelt control variables.

Table 2a:Sample of 108 countries

Step 3: Test the relationship between innovation variance and growth

In order to examine the stochastic part of the relationship between growth and investment, we repeat the above model but change the content of the control variables. Thus, we have two types of variables: the measurement of variables at the beginning of the period and the predicted variables X. The variables to be taken into account in this new specification are :

• Variables measured at start of period 1) Inv: average share of investment in GDP at start of period; – aapgr: average annual population growth rate at start of period.
• Predicted variables:
• GDP per capita delayed by two periods
• The weather trend
• Time trend squared
• Four dummy seasonal variables (_Q1t, _Q2t, _Q3t and _DOt) to capture specific effects. These variables are defined below.

Table 3a: The 21-country OECD sample based on panel data (see our publication “Dynamics of trade and volatility)

Table 3b: The 108-country sample and panel data regression (see our book “Dynamics of trade and volatility”)

Table 3: Relationship between average growth and innovation volatility

Step 4: Test the robustness of country-specific control of growth volatility The question here is:

Does the introduction of different country-specific effects affect growth volatility?

What is the nature of the relationship being tested here? In order to carry out this investigation, we will extract all the control variables that are statistically significant in the volatility regression in terms of time and country, and observe the impact of these variables on the new fixed-effect models in time and space (country). This is done by introducing dummy variables for each country. To this end, we estimate country-specific equations for government spending growth as follows:

Govexp = f(Log of GDP/head lagged 2 periods, log of government spending per head lagged 2 periods, a quadratic time trend, 4 dummy variables and a constant term The equations to be estimated have the following form:

grgdpit = λvolivolit + θXitXit +εitit (1a)

εitit ῀NN(0, _σ2it) vol2it= _a0 + _{a1 u2it} (1b) _grgdpit: the growth rate of per capita product, _volit: the standard deviation of the residuals; X is the vector of control variables and _u2it: is the square of the residuals estimated for each country i in period t from the government expenditure equations.The results of the equations are presented in the tables below:

Table 3 : Relationship between mean growth and innovation volatility

Table 3a: 21 OECD country- sample panel regression

 Table 4: Effects of government spending and induced fluctuations

Table 4a: Regression of government spending on Levin-Renelt explanatory variables (Global Technological Frontier) and dummy explanatory variables.

Intercept

Log

likelihood=1517,92 Estimation of the following relationship vol²it= _a0 + _{a1 û²it} gives: Table 4b: Regression of innovation variances on the squared residuals estimated from the government expenditure equation.

Variable Definition Coefficient T-Stats Std. Dev. [95%Conf.Interval] [95%Conf.Interval]m min

                       Vol2                      Standard deviation 0.000045

                                                        of innovations                                      -1.31                                                 0.000034                                       -0.00001        0.00002

                        Residu2 Square of residues 3 .2829              2.14                                  1.5342                               0.275                 6.289

equation of government spending

Random- effect GLS regression R-sq :

0.0026

Table 4c: Regression of the growth rate of per capita product (grgdp) on the explanatory variables forming the MTF and on the dummy variables, 4 trend variables and the LOG DU PNB lagged by 2 periods

Log

likelihood=-

775.99 Log likelihood=Prob>chi2= 775,99

0.000                    Prob>chi2=

0,000

Table 4d: Regression of the government spending rate (govexp) on the explanatory variables forming the MTF and on the dummy variables, 4 trend variables and the LOG OF GNP lagged by 2 periods

Log likelihood=- 1824,3

Prob>chi2=

0.000

Table 4e: Regression of per capita product growth rate on explanatory variables forming the

MTF and on dummy variables with country fixed effects

Log likelihood=- 739.27

Prob>chi2=

0.000

Table 4f: Regression of government spending rate on explanatory variables forming the MTF and on dummy variables with country fixed effects

Log likelihood=- 1465.637

Prob>chi2=

0,000

Table 4g: Regression of government spending rate on explanatory variables forming the MTF and on dummy variables with country fixed effects

Log likelihood=- 1465.637

Prob>chi2=

0.000