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Introduction
Generally, economy-wide forecasting models, at business cycle frequencies, are in the form of simultaneous-equations structural models. However, two problems often encountered with such models are as follows: (i) the correct number of variables needs to be excluded, for proper identification of individual equations in the system which are, however, often based on little theoretical justification (Cooley and LeRoy, 1985); and (ii) given that projected future values are required for the exogenous variables in the system, structural models are poorly suited to forecasting. The Vector Autoregression (VAR) model, though ’atheoretical’ is particularly useful for forecasting purposes. Moreover, as shown by Zellner (1979) and Zellner and Palm (1974) any structural linear model can be expressed as a VAR mov- ing average (VARMA) model, with the coefficients of the VARMA model being combinations of the structural coefficients. Under certain conditions, a VARMA model can be expressed as a VAR and a VMA model. Thus, a VAR model can be visualized as an approximation of the reduced-form simultaneous equation structural model. Though, both the large-scale econometric models and the VARs perform rea- sonably well as long as as there are no structural changes whether in or out of the sample.
Specifically, Lucas (1976) indicates that estimated functional forms obtained for macroeconomic models in the Keynesian tradition, as well as VARs, are not “deep” because these models do not correctly account for the depen- dence of private agents’ behavior on anticipated government policy rules, used for generating current and future values for government policy variables. Under such circumstances, while such models may be useful for forecasting future states of the economy conditional on a given government policy rule, they are fatally flawed when there are changes to government policy rules. Econometrically, this means that in a later time period, T + t, this problem would show up as an oc- currence of a “structural break” in the estimate for the parameters of the model at T. In other words, if the sampling period were broken up into two subsamples, one spanning periods prior to T, and one spanning periods after T, it would be seen that the “best-fit” estimates for the parameters of the model, over these two subsamples,are statistically different from each other. Furthermore, the standard econometric models, as well as the VARs, are linear and hence fail to take account of the nonlinearities in the economy. One and perhaps the best response to these objections has been the development of micro-founded DSGE models that are capable of handling both the possibilities of structural changes and the issues of nonlinearities, since DSGE models are able to identify that the actions of rational agents are not only dependent on government policy variables, but also on government policy rules. Since Kydland and Prescott (1982), a vast literature has evolved attempt- ing to model the business cycle, as an equilibrium outcome of the representative agents’ response to a productivity shock ( Hansen,1985; Hansen and Sargent, 1988; Christiano and Eichenbaum, 1992; King et al, 1988). Hansen and Prescott (1993) suggest the 1990-91 recession in the U.S. economy can be explained by a real business cycle model with technology shocks. However, the weakness of their analysis, with regard to forecasting, is that it cannot actually forecast the reces- sion since the measurements of technology shocks are ex post. Ingram and White- man (1994) show that forecasting with BVAR models, in which priors are gener- ated by real business cycle models, outperforms the one based on standard VAR models. Recently, based on the work done by Christiano, et al. (2003), Smets and Wouters (2003, 2004) develop micro-founded DSGE models with sticky prices and wages for the European economy.
By employing the Baysian techniques, the authors investigate the relative importance of the various frictions and shocks in explaining the European business cycle as well as its prediction performance. They find that the estimated DSGE model is able to outperform the unrestricted VAR and BVAR models in out-of-sample predictions. This result clearly suggests that the micro-founded DSGE models can be used as forecasting tools by central banks. The objectives of the thesis are twofold, with the primary objective being to develop alternative DSGE models for forecasting South African economy. It is worth noting that all the DSGE models used for forecasting discussed above suggest that productivity shock plays a leading role in all the models. This re- search starts off with a Real Business Cycle model but extends it to account for nominal shocks. This is extremely important in the case of the South African economy, given the structure and policy changes over time. Both calibrated and estimated versions of Real Business Cycle (RBC) and New Keynesian Macroeco- nomic (NKM) DSGE models have been employed to forecast the South African economy. The second objective is to evaluate the forecasting performances of the alter- native DSGE models by comparing them with both the Classical and Bayesian variants of VARs. This comparison study allows us to analyze the forecasting abilities of alternative models, and in turn help us to select a suitable model for predicting the economy. The thesis consists of three independent papers. The first paper develops a small-scale DSGE model based on Hansen’s (1985) indivisible labor RBC model. The calibrated model is used to forecast output and its main components, and a measure of the short-term interest rate (91 days Treasury Bill rate).£
The results suggest that, compared to the VARs and the BVARs, the DSGE model produces large out-of-sample forecast errors. In the basic RBC framework, business cycle fluctuations are purely driven by real technology shocks (Kydland and Prescott, 1982). This one-shock assumption makes the RBC models stochastically singular. As indicated by Rotemberg and Woodford (1995), output is unforecastable with only one state variable. In order to overcome the singularity problem in the RBC model developed in the first paper, the second paper develops a hybrid model (DSGE-VAR) model. In the hybrid model, the theoretical model is augmented with unobservable er- rors having a VAR representation. This allows one to combine the theoretical rigor of a micro-founded DSGE model with the flexibility of an atheoretical VAR model in the hybrid model. The model is estimated via maximum likelihood technique. The results suggest that the estimated hybrid DSGE (DSGE-VAR) model outperforms the Classical VAR, but not the Bayesian VARs. However, it does indicate that the forecast accuracy can be improved alarmingly by using the estimated version of the DSGE model. The third paper develops a micro-founded New-Keynesian DSGE (NKDSGE) model. The model consists of three equations, an expectational IS curve, a forward-looking version of the Phillips curve, and a Taylor-type monetary policy rule. Furthermore, the model is characterized by four shocks: a preference shock; a technology shock; a cost-push shock; and a monetary policy shock.
Essentially, by incorporating four shocks, that generally tends to affect a macroeconomy, the paper attempts to model the empirical stochastics and dynamics in the data bet- ter, and hence, improve the predictions. The results indicate that, besides the usual usage for policy analysis, a small-scale NKDSGE model has a future for forecasting. The NKDSGE model outperforms both the Classical and Bayesian variants of the VARs in forecasting inflation, but not for output growth and the nominal short-term interest rate. However, the differences of the forecasts errors are minor. The indicated success of the NKDSGE model for predicting inflation is important, especially in the context of South Africa — an economy targeting inflation. The main contribution of the thesis lies in its ability to show that economet- rically estimated models which have strong theoretical foundations can be used for forecasting key macroeconomic variables. Moreover, a theoretically sound framework, well-suited for forecasting, has the simultaneous advantage of being used for policy analysis at business cycle frequencies. This thesis, using South Africa as a case study, hence, attempts to bridge the gap between Econometri- cians and the Business Cycle Theorists. The thesis shows that, when compared with the atheoretical econometric models, the theoretically well equipped models have worthwhile future in carrying out economy-wide predictions.
A Small-Scale DSGE Model for Forecasting the South African Economy
This paper develops a small-scale Real Business Cycle Dynamic Stochastic General Equilibrium (DSGE) model for the South African economy, and forecasts real Gross National Product (GNP), consumption, investment, employment, and a measure of short-term interest rate (91 days Treasury Bill rate), over the pe- riod of 1970Q1-2000Q4. The out-of-sample forecasts from the DSGE model is then compared with the forecasts based on an unrestricted Vector Autoregression (VAR) and Bayesian VAR (BVAR) models for the period 2001Q1-2005Q4. Generally, economy-wide forecasting models, at business cycle frequencies, are in the form of simultaneous-equations structural models. However, two problems often encountered with such models are as follows: (i) the correct number of variables needs to be excludes, for proper identification of individual equations in the system which are, however, often based on little theoretical justification (Cooley and LeRoy, 1985); and (ii) given that projected future values are required for the exogenous variables in the system, structural models are poorly suited to forecasting.
The Vector Autoregression (VAR) model, though ’atheoretical’ is particularly useful for forecasting purposes. Moreover, as shown by Zellner (1979) and Zellner and Palm (1974) any structural linear model can be expressed as a VAR mov- ing average (VARMA) model, with the coefficients of the VARMA model being combinations of the structural coefficients. Under certain conditions, a VARMA model can be expressed as a VAR and a VMA model. Thus, a VAR model can be visualized as an approximation of the reduced-form simultaneous equation structural model. Though, both the large-scale econometric models and the VARs perform rea- sonably well as long as as there are no structural changes whether in or out of the sample. Specifically, Lucas (1976) indicates that estimated functional forms obtained for macroeconomic models in the Keynesian tradition, as well as VARs, are not “deep” because these models do not correctly account for the depen- dence of private agents’ behavior on anticipated government policy rules, used for generating current and future values for government policy variables.
Under such circumstances, while such models may be useful for forecasting future states of the economy conditional on a given government policy rule, they are fatally flawed when there are changes to government policy rules. Econometrically, this means that in a later time period, T + t, this problem would show up as an oc- currence of a “structural break” in the estimate for the parameters of the model at T. In other words, if the sampling period were broken up into two subsamples, one spanning periods prior to T, and one spanning periods after T, it would be seen that the “best-fit” estimates for the parameters of the model, over these two subsamples,are statistically different from each other.1 Furthermore, the standard econometric models, as well as the VARs, are linear and hence fail to take account of the nonlinearities in the economy. One and perhaps the best response to these objections has been the development of micro-founded DSGE models that are capable of handling both the possibilities of structural changes and the issues of nonlinearities, since DSGE models are able to identify that the actions of rational agents are not only dependent on government policy variables, but also on government policy rules. Since Kydland and Prescott (1982), a vast literature has evolved attempting to model the business cycle, as an equilibrium outcome of the representative agents’ response to a productivity shock ( Hansen,1985; Hansen and Sargent, 1988; Chris- tiano and Eichenbaum, 1992; King et al, 1988)2 .
TABLE OF CONTENTS :
- Chapter 1: Introduction
- Chapter 2: A Small-Scale DSGE Model for Forecasting the South African Economy
- 2.1 Introduction
- 2.2 The Model Economy
- 2.3 Calibration
- 2.4 Empirical Performance of the Model
- 2.4.1 Data moments and cross-correlation
- 2.4.2 Impulse response analysis
- 2.4.3 Forecast accuracy
- 2.4.3.1 Classical and Bayesian VARs
- 2.4.3.2 DSGE vs. VARs
- 2.5 Conclusion
- Appendix
- Chapter 3: Forecasting the South African Economy: A DSGE-VAR Approach
- 3.1 Introduction
- 3.2 The Model Economy
- 3.3 The Hybrid Model: A DSGE-VAR Approach
- 3.4 Results
- 3.4.1 Classical and Bayesian VARs
- 3.4.2 Forecast accuracy
- 3.5 Conclusion
- Appendix
- Chapter 4: A New-Keynesian DSGE Model for Forecasting the South African Economy
- 4.1 Introduction
- 4.2 The Model
- 4.2.1 The Representative Household
- 4.2.2 Final-Goods Production
- 4.2.3 Intermediate-Goods Production
- 4.2.4 The Monetary Authority
- 4.3 Solution of the Model
- 4.4 Results
- 4.4.1 Classical and Bayesian VARs
- 4.4.2 Forecast accuracy
- 4.5 Conclusion
- Appendix
- Chapter 5: Conclusions
- Bibliography
