Sustainable Development and Institutions

Abstract

The World Bank now publishes estimates of adjusted savings for the world’s countries to keep track of sustainable development; the environment is seen as a gigantic capital asset. I explore these estimates for different countries. Dasgupta and Maler, who have worked on theoretical models of environmental accounting, initially used optimal control models but have shifted to modeling imperfect economies, in which institutions can affect resource allocation. Sneddon et al. suggest the importance of deliberative democracy for sustainable development, and Vatn describes the use of deliberative processes, which can build on structured information. Duflo and Pande statistically estimate that on average, dams in India increased poverty.

Appendices

Appendix A.1

I compare two models: DM2 (Dasgupta and Maler 2009) with DKM1 (Dasgupta et al. 1997); we can use mathematical techniques innovatively to frame an issue differently.

In both DM2 and DKM1, welfare over time is very similar. In DM2 welfare at time t is

$$ W_{t} = \int\limits_{t}^{\infty } {U\left( {C_{\tau } } \right)e^{{ - \left( {\tau - t} \right)}} d\tau } $$

where C is aggregate consumption. In DKM1 current social welfare, U is a function not only of C, but also of the environment and labour.

The key difference between DKM1 and DM2 is the use of α—a resource allocation mechanism—by DM2. The co-evolution of institutions and the state of the economy is reflected in α. This means that C, resource flows R, and capital stocks K, are functions of α. DM2 write the value function V can as

${\text{V}}\left( {{\text{K}}_{\text{t}} , \, \alpha ,_{\,{\text{t}}}} \right) \, = {\text{ W}}_{\text{t}} ,$ where W_t is given by the expression above. DM2 define sustainable development as a path where dV_t/dt ≥ 0. By using the value function directly, and assuming that α is autonomous, DM2 show that dVt/dt = Σp_it dK_it/dt = I ≥ 0 on a sustainable development path.

In contrast, DKM1 use optimal control theory to derive the adjustments that should be made to get net national product—this is common in theoretical models dealing with this issue—and the model is silent about institutions.

DM2 argue that sustainable development requires examining wealth and not GNP or even NNP; whereas DKM1 derive results for adjustments to NNP.

Appendix A.2

In this appendix I briefly discuss the statistical assumptions behind using instrumental variables.

Let our regression equation be

$$ {\text{Yi }} = {{\upbeta}}0 \, + {{\upbeta}}1{\text{ Xi }} + {\text{ ui}},{\text{ i}} = 1, \, \ldots ,{\text{ n}} $$

And let Xi be correlated with ui because of simultaneous causality (i.e. X and Y cause each other).

We could use an instrumental variable Z to estimate the effect β1 of X on Y.

The conditions for a valid instrument are: (1) instrument relevance: the correlation between Z and X should not be zero and should be high; and (2) instrument exogeneity: the correlation between Z and u should be zero.

We can test for instrument relevance statistically. Exogeneity is subtle—we need to use thinking and judgement. If we have more than one instrument, we can use a statistical test to aid our thinking and judgement, but it is ‘incumbent on both the empirical analyst and the critical reader to use their own understanding of the empirical application to evaluate whether this assumption is reasonable’ (Stock and Watson 2011, p. 454).