it implies a feedback from income to the capital stocks. Consequently, the linear regression of the output on the public and private factors does not allow to directly identify the parameters of the production function. Several solutions have been proposed in the literature in order to take into account this problem of reverse causation. Canning (1999) and Canning and Bennathan (2000) argue that the use of panel estimates under various assumptions allows to identify the long run production function relationship. Another solution consists in estimating a system of simultaneous equations: one equation for the production function and another equation for the relationship between the public capital stock and the production (Demetriades and Mamuneas, 2000). Finally, the reverse causation problem can be tackled with an instrumental variable approach or a generalized method of moments. It is for instance the case in Finn (1993), HoltzEakin (1994), Baltagi and Pinnoi (1995), Ai and Cassou (1995), Otto and Voss (1998) and more recently in Calderon and Serven (2004). But the reverse causation issue can also be interpreted as the consequence of threshold e¤ects. For instance, let us assume that the true data generating process of the marginal productivity is a threshold model as suggested by Fernald (1999). The infrastructure investments enhance the output until the completion of the main networks, and once they are ...nished it is mainly the output which causes the changes in the infrastructure capital stocks. In this case, the use of a linear speci...cation leads to an estimated correlation which takes into account both the in‡uence of the infrastructures on the output in the ...rst period and the in‡uence of the output on the infrastructure stock in the second period. On the contrary, the use of a threshold model based on the value of the capital stock per capita for instance, makes it possible to identify the in‡uence of the infrastructures on the total factor productivity in the ...rst period.

The second major problem raised in the literature is the non stationarity and the non cointegration of the data used in the augmented production function (Tatom, 1991; Sturm and Haan, 1995; Crowder and Himarios, 1997). In time series, it is generally recognized that unit root tests based on linear speci...cations (ADF, KPSS etc.) are likely to conclude to the non stationarity of series when the true data generating model is a threshold model (SETAR, STAR etc.). Even if similar studies have not been done with panel unit root tests, it is obvious that the ...rst generation tests, as the Im, Pesaran and Shin’s test (2003) based on an average of individual ADF statistics, are likely to yield the same kind of results.

The last major problem, which is speci...c to the panel estimates, is the potential heterogeneity of the parameters of the production function and more particularly the heterogeneity of the elasticities of output with respect to infrastructure (or public capital) stocks. It is common, both in cross section and in panel data studies, to assume that the parameters are common across countries. However, this assumption may raise important problems when the countries of the panel are very di¤erent, as it is the case in our sample of developing countries. Consequently, the studies based on a production approach are generally based on speci...cations with ...xed or random individual e¤ects (Evans and Karras, 1994; Holtz-Eakin; 1994). But, to the best of our knowledge, few studies in the literature allow the other parameter of the augmented production function 4