Capital and investment dynamics (Outdated)

Capital dynamic

Capital invested in a given region is a bundle obtained using the same CES nesting structure as for intermediate consumption. However, the product composition of both bundles differs according to the data, while the composition by geographical origin for each product is unique.

Installed capital is assumed to be immobile. This confers investment an important role, as the only adjustment device for capital stock. This “putty-clay” hypothesis is important because it implies that capital stock adjusts gradually. The sectoral allocation of capital can thus be sub-optimal, and the corresponding loss is interpreted as an adjustment cost for the economy. In addition, these assumptions imply that the rate of return to capital varies across sectors after the initial year.

Foreign direct investment

FDI modeling in MIRAGE

Regarding trade policies, investment is also important through its cross-border component, that is FDI. In a standard framework, international financial flows result from the assumptions of perfect capital mobility across countries and sectors. This modeling is micro-founded, but it considerably overestimates cross-border capital flows. On the other hand, directly using the results of econometric estimates for parametrizing an ad-hoc relationship would give more realistic results, but it would lack theoretical consistency.

In MIRAGE, the modeling of FDI combines empirical realism and theoretical consistency. The latter objective requires, in particular, that domestic investment’s setting be consistent with FDI’s and that savings allocation behavior be rational. In this context, the rate of return to capital is a natural determinant of investment sharing across sectors and countries. Notably, this rate of return incorporates the influence of many FDI determinants identified in the empirical literature (see, for example, Chakrabarti 2001 for a recent survey), such as market size, growth rate, or market potential. As a consequence, these determinants need not be taken into account over and above the sectoral rate of return to capital.

In the present model version, some of the issues related to FDI are left aside, though, as some mechanisms would be better addressed by a model of the multinational firm (see, for instance, Markusen and Venables 2000).

Formal specification

A single generic formalisation is used for setting both domestic and foreign investment. It stems from allocating savings across sectors and regions as a function of the initial savings pattern, of the present capital stock, and of the sectoral rate of return to capital, with an elasticity \(\alpha\): \[\frac{P^K_s I_{i,r,s}}{S_r}=\frac{A_{i,r,s} P^K_s K_{i,s} \mathrm{e}^{\alpha W^K_{i,s}}}{\sum\limits_{i,s'} A_{i,r,s'} P^K_{s'} K_{i,s'} \mathrm{e}^{\alpha W^K_{i,s'}}},\] where \(P_s^K\) stands for the price of capital good in region s, \(S_r\) for country r savings, \(I_{i,r,s}\) for country r representative agent’s investment in the sector i of country s, \(K_{i,s}\) for installed capital stock, \(A_{i,r,s}\) for a calibrated parameter, \(W_{i,s}^K\) for the capital remuneration rate in sector i of country s. Parameter \(\alpha\) sets the adjustment speed of capital stock. The capital good used in a given region is the same whatever the investing country.

Introducing an endogenous variable \(B_r\) as: \[ B_r= \frac{S_r}{\sum\limits_{i,s} A_{i,r,s} P^K_{s} K_{i,s} \mathrm{e}^{\alpha W^K_{i,s}}}\] allows the problem to be rewritten as follows: \[I_{i,r,s}= B_r A_{i,r,s} K_{i,s} \mathrm{e}^{\alpha W^K_{i,s}}\] \[\sum\limits_{i,s}P^K_s I_{i,r,s} = S_r\]

Since \(\alpha\) cannot be calibrated, two static models were built, corresponding to a short-run and a long-run version of MIRAGE. We applied the same shocks to both of them and chose \(\alpha\) so that half the adjustment of capital stocks towards the long run would be made in around 4 years, for a variety of small commercial shocks. It led to the value: \(\alpha\) = 40.

Elements of discussion

Foreign-owned firms are treated as domestic firms in all respects. The only difference is that the capital revenue goes back to the source country. By changing the number of firms, FDI may have an influence on productive efficiency. Nevertheless, it is worth emphasizing that FDI is not assumed to originate any technological spillover here. Although some empirical studies have shown that such spillovers may arise, they are neither systematic nor robust enough to be considered in a model aimed at studying a large scope of trade policy shocks.

It is noteworthy, in addition, that product quality is assumed to depend only on the region of production. This contrasts, for example, with Petri (1997), who assumes that foreign affiliates produce the same quality as their parent company. In this framework, also adopted by Hanslow (2000), and Lee and Mensbrugghe (2001), FDI liberalisation induces quality upgrading in developing countries, originating significant gains. Though interesting, this mechanism is not supported by robust enough empirical results.

FDI database

A reconciliated database providing flows and stocks of FDI for most countries and 35 sectors was developed at CEPII in 2008. It can be used to calibrate the model for the reference year independently from the aggregation.


Chakrabarti, Avik. 2001. “The Determinants of Foreign Direct Investment: Sensitivity Analyses of Cross-Country Regressions.” Kyklos 54 (1): 89–113.
Hanslow, Kevin. 2000. “The Structure of the FTAP Model.” Purdue University.
Lee, Hiro, and Dominique van der Mensbrugghe. 2001. “Interactions Between Direct Investment and Trade in the Asia-Pacific Region.” Purdue University.
Markusen, James R., and Anthony J. Venables. 2000. “The Theory of Endowment, Intra-Industry and Multi-National Trade.” Journal of International Economics 52 (2): 209–34.
Petri, Peter A. 1997. “Foreign Direct Investment in a Computable General Equilibrium Framework.” Tokyo: Keio University.