There is one multi-purpose “general” good, produced according to the production function:

where is the input of the latest version of intermediate good and is the productivity parameter associated with it.

The general good is used for consumption and as input to product and develop the intermediate goods. Since the general good is produced under perfect competition, the price of an intermediate good will be:

If in an intermediate sector, there is a successful innovation, the productivity of this sector will equal the productivity at the world technology frontier which grows with a positive constant rate. Therefore, the productivity of a sector evolve according:

In each intermediate sector, there some people who are able to produce a new version of intermediate good for a unit cost equal to. We assume that the market price of the last generation intermediate good will be. So the quantity demanded will be:

An unsuccessful innovator will earn nothing and the profit of a successful innovator will be:

where

For notational convenience, “average productivity” is defined as:

Let’s assume that at equilibrium the probability of innovation will be the same for all intermediate sector; so average productivity will be equal to:

The technology gap is defined as:. This ratio evolves according:

Therefore the production function (1) of the “general” good can expressed as:

where où

Under perfect competition, the wage rate will be:

Let’s define R&D investment function as:

where is the quantity of general good that must be invested. Thus an entrepreneur who has invested 𝑛 in R&D will innovate with probability equal to:

And his expected net payoff is given as:

For analytical convenience, it is assumed that banks operate at no cost and they don’t earn profit. Thus interest rates for lenders and borrows are the same and equal to.

For closed economy without government, we can write the GDP per capita as:

Therefore GDP per capita is a decreasing function of the development level of consumer credit market and an increasing function of the development level of investment credit market till that consumption and investment reach the optimum; and after that GDP per capita will grows with a constant rate the same as the technology frontier.

To test our theoretical model, we use a second-order Taylor expansion to approximate in the neighborhood of the technology frontier². Following Aghion, Howitt and Mayer Foulkes (2005) [13] , we omit pure quadratic terms and we assume that there is just one leader, labeled country 1.

Our theoretical model is approximated by the following growth regression:

²

where g denotes the growth rate of per-capita GDP, y the initial log of per-capita GDP, CC the log of consumer credit, CI the log of investment credit and X a set of control variables. Control variables used in our econometric investigation are GC the log of government consumption to GDP, INF inflation rate and Trade the log of the ratio of exports plus imports to GDP. Country 1 is the technology leader.

Given the specification of Equation (23), our regression is considered as a dynamic panel model. So, efficient estimators are given through the generalized method of moments. Arellano and Bover (1995) [14] and Blundel and Bond (1998) [15] shows that the system GMM estimator provide a more efficient estimator than the difference GMM estimator. The estimates were made by the one step and two step system GMM. In the one-step estimator, the error term is assumed to be independent and homoskedastic across countries and time. In the two-step estimator, the residuals of the first step are used to consistently estimate the variance-covariance matrix of the residuals, relaxing the homoskedasticity assumption. In the two-step System GMM, we adopt Windmeijer (2005) [16] small sample robust correction which makes a finite-sample adjustment for the two-step covariance matrix.

As a robustness check, we use data over five years instead of annual to prevent any biased estimates and to capture business cycle movements.

An important step that is relevant to the estimation of our model is to conduct M2 test, Sargan test, Hansen test and Kleibergen-Paap tests. The M2-test checks problem regarding the second-order serial autocorrelation of the error terms. The sargan test verifies that the instruments used are not correlated with the residuals. The Hansen test and the Kleibergen-Paap test provides statistics for weak instruments due to an over-identification and under-identification, respectively.

Our model is tested a balanced sample of 27 European’s countries³ over the period 1995-2012. Germany is considered as the leader of the 27 European’s countries in our sample. Disaggregated data on credit were extracted from Europeen Credit Research Institute Database. The WDI-World Bank database is the source for other macroeconomic variables. Table A1 and Table A2 in Appendix report respectively summary statistics and empirical correlations between variables.

The dataset shows that growth rate of GDP per capita is negatively correlated with consumer credit and positively correlated with investment credit. Macroeconomic indicators have the expected correlation sign with the economic growth: growth rate of GDP per capita is negatively correlated with government consumption as inflation and positively correlated with trade.

The results from estimating Equation (23) are reported in Table 1. System GMM regressions on annual data are reported in columns (1) and (2). These results confirms theoretical predictions and show that consumer credit has a significant negative effect on convergence to the leader growth rate and investment credit promotes positively the convergence at 5% significance level for the two specifications, one step and two step system GMM. In regression (3) and (4), we use data over five years instead of annual as a robustness check and to capture business cycle movements. Columns (3) and (4) confirm our main findings: consumer credit affects negatively and significantly the catch-up of technological frontier however investment credit has a positive effect.

Our findings give an explanation of the ambiguous credit-growth nexus in empirical literature since its uses aggregate credit to private sector as proxy of credit market development. Empirical studies must consider credit composition and study a distinctive effect of each market. In developed and developing countries, consumer credit market continues has an “explosive” trend while investment credit market show weak growth rate.

Theory provide evidence about the positive effect of investment credit on economic growth through capital accumulation, productivity growth and resource allocation but the effect of consumer credit on economic growth is ambiguous. Using a sample of 25 countries, Jappelli and Pagano (1994) [9] provide evidence that the development of consumer credit market has a negative effect on economic growth through reducing saving rate. Galor and Zeira (1993) [10] and De Gregorio (1996) [17] show that consumer credit affect positively economic growth only if it’s invested in human capital and/or microenterprises.

Furthermore, our findings provide also a clarification of theheterogeneity of credit-growth nexus across country. This can be explained by the disparity of the composition of credit across country and sample.

Our results shows that a negative relationship between relative growth rate and the initial GDP per capita relative to the leader. Thus the hypothesis of conditional convergence is validated. This concept assumes that each country converges to its own long-run equilibrium path and record a high growth rate when it’s far from the path.

T-Student are reported in parentheses. ^***, ^**, and ^* indicate significance levels at 1, 5, and 10 percent, respectively. For the M2 test for autocorrelation, the null hypothesis is that the errors in the first-difference regression exhibit no second-order serial correlation. For Sargan test, the null hypothesis is that the instruments used are not correlated with the residuals. For the Kleibergen-Paap test of under-identification, the null hypothesis is that the instruments used are potentially weak. For Wald Test, M2 test, Sargan Test, Hansen Test and the Kleibergen-Paap test the p-values are reported.

The control variables have the expected sign and are tightly estimated. The harmful effect of inflation rate on economic growth is confirmed by a negative and significant sign in the two specifications of the GMM estimator. Government consumption has a positive and significant effect on economic growth at least at 5% level in all specification. This finding proves that public consumptions in European countries are spending mainly in investment and infrastructure which improve economic growth (Kneller, Bleaney, and Gemmell, 1999 [18] ). The trade openness is positively correlated to economic growth. Trade openness boosts economic growth by facilitating the exchange of goods and services and by improving capital allocation efficiency.

Our results are robust: M2 confirms the absence of a second-order serial correlation of the residuals in the differenced regression. The Sargan test confirms no correlation between the used instruments and the residuals. Finally the Hansen and the Kleibergen-Paap test do not detect any problem of over-identifications and under- identifications restrictions and confirm the validity of variables in differences and in levels as instruments in system GMM.