Time-series econometrics of growth-models: a guide for applied economists

Abstract

This article examines the use of specifications based on the endogenous and exogenous growth-models for country-specific growth policies. It is suggested that time-series models based on the Solow (1956) exogenous growth-model are useful and they can also be extended to capture the permanent growth-effects of some variables. Our empirical results, with data from Fiji, show that trade openness and human capital have significant and permanent growth-effects. However, these growth-effects are small and eventually converge over time.

Acknowledgements

I thank two referees of this journal and my colleagues Gyaneshwar Rao and Rup Singh for comments and suggestions. I alone take responsibility for the remaining errors.

Notes

¹Such applied works are plenty and it is not worth to make the reference list longer by citing them Kocherlakota and Mu Yi (1996) have found that in the USA, there is evidence only to support that nondefense structural investment expenditure has any permanent effect on output. Consequently, it is a bold assertion to state that defense expenditure has a permanent effect on the growth rates of some smaller countries like Fiji.

²See Rao (2007b) in which an endogenous growth framework has been used to show that learning by doing and trade openness have contributed significantly to the steady state growth rates in the newly industrialized Asian countries.

³The importance of the optimization framework, based on microeconomic foundations, can be explained as follows. It is not hard to imagine that the demand for a good depends on its price. Nevertheless, we need the constrained utility maximization framework not only to justify that price of a good is an important explanatory variable but also for insights into other important determinants of demand. Endogenous growth theory is important for this reason. In its absence, one can pick up, in an ad hoc manner, a handful of growth determinants to show that output growth depends on any set of arbitrary variables.

⁴There are some models, known as growth-models within the endogenous framework, which essentially use Solow (1956) but assume that TFP depends on, besides time, on externalities and learning by doing, etc. The main difference between this and endogenous growth-models is that improvements in TFP are manna from the heaven type, i.e. they do not need additional resources; See Rao (2007b).

⁵A referee suggested that we explain the methodology and techniques used in GETS. Since these are adequately explained elsewhere and also reviewed in Rao (2007a), the interested reader my refer to Rao (2007a) and the references suggested in the article.

⁶This criticism is also applicable to the cross-section studies where variables are averaged over shorter periods e.g. 4years because it is difficult to imagine that an economy reaches its steady state in 4 years. See for example Burnside and Dollar (2000) where 4-year growth rates are used to capture the effects of aid on growth. When Easterly et al. (2003) have used 8-year growth rates, the effect of aid on growth became insignificant. In some time-series studies, there is awareness about what is estimated is the long-run production function. However, often capital stock is proxied with the investment ratio. Feeny (2005), for example, in an elaborate study with 7 or 8 variables to analyse the effects of aid on the growth of output in Papua New Guinea, proxied capital and labour, respectively, with the investment ratio and a time trend, but their coefficients turned out to be negative. This is not to pillory this author and this study is cited because it is one of a few systematic studies of this type.

⁷A similar interest was shown by Senhadji (2000) in the determinants of the level of TFP, but not its growth rate. However, he has used cross-country data where the level of TFP relative to its level in the US was explained with initial conditions (ratio of initial level of TFP to the US level), external shocks, macroeconomic environment, the trade regime and political stability. Favourable external environment, good macroeconomic management, social harmony and political stability are all associated with higher levels of TFP.

⁸The variables are tested for unit roots with ADF and GLSADF. They are found to be I(1) in levels and I(0) in first differences. These results are not reported to conserve space but may be obtained by request.

⁹We have used the lagged values of the variables as instruments. In addition, an intercept and trend are also included.

¹⁰These growth accounting results in Rao et al. (2006).

¹¹The Sato closed form solution for the level of output in the Solow (1956) model is 

where Y is output s is investment ratio, A₀ is the stock of knowledge at the beginning of the period, L₀ is employment at the beginning of the period, a is the exponent of capital in the Cobb–Douglas production function with constant returns (Footnote 1), λ = (1 − α)(n + g + δ), n is growth of employment, g is growth rate of technical progress, s is the rate of depreciation of capital and t = 0 … t is time. Simulations with the closed form solutions are in Rao et al. (2006).

¹²The restriction could not be rejected by the Wald test. The computed test statistic with the p-value in the square brackets is χ²(1) = 0.0244 [0.876].

¹³When HKI is used instead of its log value, the constrained estimate of this equation where the coefficient of capital is set to its value in the unconstrained equation implied that these growth-effects of 0.004 taper off and converges to 0.009.

¹⁴This is computed as (0.0052823 + 0.0022624 × 1.6334) × 33 = 0.296.

¹⁵The equation based on the endogenous growth-model is re-estimated with ln PC replacing human capital and trade variables. However its adjusted R ²has declined to 0.620.

¹⁶Six other nonnested hypothesis test statistics viz. N, NT, W, J, JA and the encompassing tests rejected the endogenous growth based equation in column 5 of Table 1 against the exogenous growth based equation. However, these nonnested hypothesis tests are conducted by re-estimating these two equations with OLS and the adjusted R ²of both equations are close to their values with the NL2SLS-IV method.