where _r_ is the real interest rate, _g_ is the per capita growth of consumption, _σ_ is the inverse intertemporal elasticity of substitution for consumption, and _θ_ is the rate of time preference. Laubach and Williams (2003) link the natural rate, _rt_<sup>_∗_,to potential growth over time</sup><sup>_gt_,as well as</sup><sup>_zt_,which captures all other</sup> determinants of _rt_<sup>_∗_:</sup> This formulation has been the subject of some criticism including its importance in explaining the natural rate, the sensitivity of estimates to the statistical properties of _z_ , and it’s role in generating significantly different output gap estimates for the U.S., depending on its specification (Pescatori and Turunen, 2015; Beyer and Wieland, 2017). Despite this, the methodology continues to play a critical role in the literature and estimates of the neutral interest rate. This paper modifies the model to account for the open-economy nature of emerging markets and to exploit additional information in a multivariate setting. It links the Laubach-Williams approach to estimates of the output gap using an augmented set of variables as in World Bank (2018). The output gap equation is estimated as: where the output gap, _y_ ̃ _t_ , is the difference between real GDP and its potential (i.e. _y_ ̃ _t_ = _yt − yt_<sup>_∗_),</sup><sup>_ht−h_</sup> _t_<sup>_∗_</sup> is the gap between house prices and their trend, _ct − ct_<sup>_∗_is the gap between credit extension and its trend,</sup> _comt − comt_<sup>_∗_is the gap between real commodity prices and its trend,</sup><sup>_qt−q_</sup> _t_<sup>_∗_is the gap between the real</sup> exchange rate and its equilibrium, and _rt − rt_<sup>_∗_is the real interest rate from its equilibrium.7Trends for</sup> commodity prices, credit, house prices and the real exchange rate are the Hodrick-Prescott filter with a lambda of 1600. The model also includes capacity utilization and the unemployment rate–through Okun’s law–to further help identify the output gap (See the multivariate model in World Bank (2018) for more details).

To account for the fact that not all EMDEs have data available for all variables of interest, the model employs switches for certain variables that "switch off" the portion of the model when the data is not available. These switches are included for house prices, credit extension, commodity prices, the real exchange rate, capacity utilization, and the unemployment rate.

The Phillips curve is modified to reflect the inflation process in an EMDE: where _πt_ is consumer inflation, _πt_<sup>_∗_is the inflation target,</sup><sup>_y_ ̃</sup><sup>_t_is the output gap,</sup><sup>_q_ ̃</sup><sup>_t_is the real exchange rate</sup> gap, and _πt_<sup>_imp_</sup> is imported inflation.<sup>8</sup> Unlike Laubach and Williams (2003), the expectations-augmented

> 7House prices, credit extension, commodity prices, the exchange rate are modeled as autoregressive processes. Unlike Laubach and Williams (2003), only one autoregressive coefficient is used in the estimation step as it is more closely linked to the theoretical foundations of intertemporal optimization.

> 8The model does not include a time-varying standard deviation of the errors although evidence exists that this may be important in some EMDEs (Ha et al., 2019; Kabundi et al., 2019).

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