Lucas' Law

Lucas' Law (or Lucas' Extension) was first proposed by Cambridge economist Spencer R Lucas (not to be confused with Robert Lucas Jr or the Lucas critique), and is an extension of the Exogenous growth model. The Exogenous Growth Model is structured around economic growth for a closed economy, yet has been used by many development economists to explain differentials between growth rates for countries in the real world, which are clearly open to some degree. Realising this, Lucas' adaptations make Solow's model more relevant, improving the level of significance in emperical econometric tests.

The Exogenous Growth Model

The Exogenous Growth Model May Be reduced to its core components, stating:
Δk = sf(k) - (δ + n + ς)k
Where Δk is the change in capital stock per effective worker, s the savings rate, f(k) the level of outuput per worker and δ, n & ς the depreciation rate, rate of population growth and rate of technological growth respectively.

The model may then be used to calculate the steady state level of growth, and also find the golden rule level of savings at which point consumption is maximised within the econonmy.

Extension of the Exogenous Growth Model

Lucas' Law simply incorporates some function of the marginal productivity of capital per effective worker (MPk);
Δk = sf(k) - (δ + n + ς)k + g(MPk)
The assumptions are simple: when the MPk for any given country is high, capital flows will increase and the term g(MPk) will be positive. Conversely, if MPk is relatively low, investment will flow abroad and the term g(MPk) will be negative.

It is important to note that this need not necessarily imply a higher steady state since, merely that it will be achieved at a faster rate. As k increases due to foreign investment, so will the value of g(MPk) fall. By a similar logic, a negative value for g(MPk) implies a fall in k and an eventual increase in g(MPk). Eventually, the marginal product of capital will be equal for all economies, and the only reason for differentials in output will be a result of the other economic variables in Lucas' Law, such as population growth or the savings rate.

Applications

From this, Lucas argues for reducing restrictions on capital flows so as to lower global economic inequality. Lucas argues little beyond this, stating that economic forces will act to bring about an optimum level for all other variables. However, alternative proposals take the Law further, arguing for synchronisation of cross-country savings rates so as to bring about a 'global golden rule steady state'. In practice, this would be highly problematic, and may only be possible where an Economic and monetary union already exists, such as the European Union