In order to account for the dynamics and nonlinear path of that relationship, this paper adopts the framework of modeling the growth and fiscal adjustments nexus using transfer functions.<sup>16</sup> As an alternative to structural models, transfer functions combine regression and time series analysis, and are particularly suitable for modeling nonlinear functional relationships [Chiogna et al. (2008)]. In particular, they allow the inclusion of lagged response and lagged explanatory variables, and other contemporaneous variables in the specification of the response.

This flexibility can help integrate the dynamics of growth during fiscal adjustments in a model that goes beyond the restriction to a single input, counterfactually assessing the growth effects under an alternative expansionary fiscal policy.<sup>17</sup> In their reduced form, these models can be represented by equation (3) in terms of a structural and time series component as follows: where the variable<sup>_Y_</sup> _t_<sup>is the real GDP per capita income at time</sup><sup>_t_. Throughout the paper, the real</sup> GDP per capital is the response variable.<sup>18</sup> The second component of the right-hand side ( <sup></sup> 1( _B_ )  ( _B_ )  _t_ ) provides the time series representation of the combined model.  ( _B_ ) and  ( _B_ ) are lagged polynomials, and  _t_ is a normally distributed error term which has a small variance [Chiogna et al. (2008)].<sup>19</sup> The first component of this transfer function provides the _k_ structural representation ( _f_ ( _x_ )   _i_<sup>_x_</sup> _i_ , _t_ ). _i_  0 In order to account for the multiplicity of growth determinants, the initial set of variables considered for inclusion in the structural component of the model are government revenues (<sup>_R_</sup> _tg_ ) , aggregated government expenditures ( _Gtx_ ) , private capital ( _K t_ ) and labor supply (<sup>_L_</sup> _t_ ) .<sup>20</sup> This specification is consistent with the model developed by Kneller et al. (1999). However, variables in the proposed framework also include lagged response as well as lagged and contemporaneous explanatory variables to account for the initial conditions and resilience effects. Hence, an expanded form of (3), taking into account that dual formulation can be represented by equation (4) as follows:

> 16 Transfer functions are also known as multivariate autoregressive-moving average models (MARMA).

> 17 Transfer functions are very popular in the field of engineering where they are used to estimate the magnitude of impulse responses. These models relate specific inputs and outputs, and their application has been extended to economics in settings. For further details, see Box, Jenkins and Reinsel (1994).

> 18 Estimating the effects of fiscal adjustments on growth in the USA, Fu et al. (2001) use unemployment rates which are sensitive to the business cycle as the response variable. However, most countries in Sub-Saharan Africa do not have accurate time series data on unemployment rates.

19 The smaller variance is embedded in the modeling specification, which produces relatively stable parameter estimates (see Pindyck and Rubinfeld for further details).

20 Real GDP per capita, public and private investment as well as human development variables are taken from the World Bank World Development Indicator data base, the data on public finance is taken from Government Financial Statistics (GFS) and World Economic Outlook (WEO) Economic Trends in Africa (WETA).

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