مدل متغیر _ DSGE برای پیش بینی متغیرهای کلیدی اقتصاد کلان آفریقای جنوبی

The paper develops a Small Open Economy New Keynesian DSGE-VAR (SOENKDSGE-VAR) model of the South African economy, characterised by incomplete pass-through of exchange rate changes, external habit formation, partial indexation of domestic prices and wages to past inflation, and staggered price and wage setting. The model is estimated using Bayesian techniques on data from the period 1980Q1 to 2003Q2, and then used to forecast output, inflation and nominal short-term interest rate for one-to eight-quarters-ahead over an out-of sample horizon of 2003Q3 to 2010Q4. When the forecast performance of the SOENKDSGE-VAR model is compared with an independently estimated DSGE model, the classical VAR and six alternative BVAR models, we find that, barring the BVAR model based on the SSVS prior on both VAR coefficients and the error covariance, the SOENKDSGE-VAR model is found to perform competitively, if not, better than all the other VAR models.

Recent studies, namely, Liu and Gupta (2007), Liu et al., 2009 and Liu et al., 2010, Gupta and Kabundi, 2010 and Gupta and Kabundi, 2011 and Alpanda et al. (2011), have initiated a growing interest in forecasting macroeconomic variables in South Africa using Dynamic Stochastic General Equilibrium (DSGE) models.1 However, in general, the studies find it difficult to outperform the atheoretical Vector Autoregressive (VAR) models, especially its Bayesian variant (BVAR) based on the Minnesota prior. These studies tend to attribute the relatively poor performance of the DSGE models to the fact that the frameworks of these models are not sophisticated enough, in the sense, that they, perhaps, do not incorporate the real and nominal rigidities to an appropriate extent to correctly capture the true dynamics of the data characterising the South African economy.2 Against this backdrop, we develop a Small Open Economy New Keynesian DSGE-VAR (hereafter SOENKDSGE-VAR) model of the South African economy, characterised by incomplete pass-through of exchange rate changes, external habit formation, partial indexation of domestic prices and wages to past inflation, and staggered price and wage setting. This model makes use of the structural framework of the theoretical DSGE to alleviate concerns relating to potential in-sample overfitting, while retaining the flexibility of VAR models, which often produce improved out-of-sample forecasting results. In addition, by incorporating the theoretical structure of a DSGE model, which seeks to describe the theoretical time-invariant behaviour of economic agent, the SOENKDSGE-VAR model would not be subject to the Lucas critique (Lucas, 1976).3 Our decision to use a DSGE-VAR approach, over and above an independently estimated DSGE model, as done in the previous studies on South Africa, is motivated not only because of the fact that VAR models have tended to outperform DSGE model forecasts for the country, but also because of the available international evidence of DSGE-VAR models producing forecasts which are competitive, and at time substantially better, than the standard benchmark of VAR and BVAR models.4 The DSGE-VAR approach, as proposed by Del Negro and Schorfheide (2004), could be implemented by using a DSGE model to simulate time-series data, which is often used to populate parameter values in an unrestricted VAR model. In practice, the sample moments of the simulated data is replaced by the population moments computed from the DSGE model solution. Given that the DSGE model depends on unknown structural parameters, one uses a hierarchical prior, which involves placing a specific distribution on the DSGE models parameters. A tightness parameter (λ), which is estimated by maximising the joint density of the data and the parameters, controls the weight of the DSGE model prior relative to the weight of the actual sample, with the values of 0, ∞ and 1 implying an unrestricted VAR, an independently estimated DSGE model5 and a DSGE-VAR model with equal weight being given to the DSGE and the VAR.6 Finally, Markov Chain Monte Carlo (MCMC) methods are used to generate draws from the joint posterior distribution of the VAR and DSGE model parameters. The model is estimated using Bayesian techniques on data for South Africa and the United States (US) from the period 1980Q1 to 2003Q2, and then used to forecast output, inflation and a measure of nominal short-term interest rate for one- to eight-quarters-ahead over an out-of-sample horizon of 2003Q3 to 2010Q4. With South Africa moving to a flexible exchange rate regime in 1979, the starting point of the in-sample was obvious, while, the beginning of the out-of-sample horizon is chosen to correspond with the period when the inflation rate reverted back to the inflation targeting band of 3% to 6%. In February of 2000, the Minister of Finance, announced that the sole objective of the South African Reserve Bank (SARB) will be to achieve and maintain price stability.7 In this regard, the SARB would pursue a goal to ensure that the inflation is within the target band by the end of 2002. With the target band being achieved in 2003Q2, we decided to use 2003Q3 as the starting date of our out-of-sample forecasting exercise. Note that, the endpoint of the sample is purely driven by data availability at the time this paper was written. The forecast performance of the SOENKDSGE-VAR model is then compared with an independently estimated DSGE model, the classical VAR and BVAR models, with the latter being estimated based on six alternative priors, namely, Non-Informative and Informative Natural Conjugate priors, the Minnesota prior, Independent Normal–Wishart Prior, Stochastic Search Variable Selection (SSVS) prior on VAR coefficients and SSVS prior on both VAR coefficients and error covariance. After comparing the forecasts from the independently estimated DSGE and the DSGE-VAR models, we can determine exactly where the gains in the forecasting performance relative to standard benchmarks (if any), emanate from, i.e., whether it is because of the DSGE framework or due to estimation of the model based on the DSGE-VAR approach or both. To the best of our knowledge, this is the first attempt in forecasting key variables of the South African economy using a DSGE-VAR approach. In addition, we go beyond the convention in the forecasting literature of DSGE models, by incorporating BVAR models estimated under a wider set of prior assumptions (besides the Minnesota prior). The remainder of the paper is organised as follows: Respective sections under Section 2 lay out the estimation methodology of the DSGE-VAR model, a discussion on the DSGE framework, data, the priors imposed on the DSGE model parameters and the estimation results. Section 3 presents the basics of the alternative forecasting models, while, Section 4 compares the performance of the DSGE-VAR model relative to an independently estimated DSGE model, the classical VAR and the BVAR under six alternative prior assumptions. Finally, Section 5 concludes.

In many instances, the forecasting performance of theoretical DSGE models are unable to consistently outperform certain VAR or BVAR models, when applied to South African macroeconomic data. Against this backdrop, we develop a SOENKDSGE-VAR model of the South African economy, characterised by incomplete pass-through of exchange rate changes, external habit formation, partial indexation of domestic prices and wages to past inflation, and staggered price and wage setting. The model is estimated using Bayesian techniques on data for South Africa and the US from the period 1980Q1 to 2003Q2, and then used to forecast output growth, inflation and a measure of nominal short-term interest rate for one- to eight-quarters-ahead over an out-of-sample horizon of 2003Q3 to 2010Q4. The forecast performance of the SOENKDSGE-VAR model is then compared with an independently estimated DSGE model, the classical VAR and BVAR models, with the latter being estimated based on six alternative priors, namely, Non-Informative and Informative Natural Conjugate priors, the Minnesota prior, Independent Normal–Wishart Prior, SSVS prior on VAR coefficients and SSVS prior on both VAR coefficients and error covariance. Overall, for the three variables, we can make following important observations: First, as far as out-of-sample is concerned, barring the BVAR model based on the SSVS prior on both VAR coefficients and the error covariance, the SOENKDSGE-VAR model is found to perform competitively, if not better than all the other VAR models for most of the one- to eight-quarters-ahead forecasts. Second, there is no significant gain in forecasting performance by moving to a DSGE-VAR framework when compared to an independently estimated SOENKDSGE model, both within and out-of-sample. Combining the two observations made above, we can conclude that the DSGE framework, developed in this paper, is in itself quite competent, and, does not require a combined approach involving the DSGE and VAR models, whereby macroeconomic theory of the DSGE model is utilised to provide priors to an otherwise completely atheoretical VAR model. Third, when we analyse the role played by the seven different rigidities in the forecasting power of the SOENKDSGE-VAR model, we find that though all the rigidities seem to matter for the three variables, but the Calvo (1983)-type staggered domestic price setting behaviour adds the most to the forecasting power of the SOENKDSGE-VAR model. Finally, based on the out-of-sample forecasting exercise, there is quite strong evidence that the BVAR model based on the SSVS prior on both VAR coefficients and the error covariance, is the best-suited model in forecasting the three variables of interest.