Macroeconomic Modelling and Bayesian Methods

A structural econometric model comprises a simultaneous equation system specifying causal relationships between the variables based (either formally or informally) on economic theory where all the variables are classified as endogenous or exogenous variables.

These models are generally estimated by ordinary least squares (OLS), two-stage least squares (2SLS), three-stage least squares (3SLS), limited information maximum likelihood (LIML), full information maximum likelihood (FIML) and seemingly unrelated regression equation (SURE) methods. Econometric models for the Indian economy include Krishnamurty et al. (2004; OLS), Krishnamurty (2002, 2008; OLS), Bhanumurthy and Kumawat 2009; OLS and ARDL), Sachdeva and Ghosh (2009; SURE), Narayana and Ghosh (2009; VAR/VEC), Kumar and Panda (2009; calibration and social accounting matrix (SAM)), Kar and Pradhan (2009; OLS), Parida and Bhide (2013); OLS), (Srivastava (2013); 2SLS and 3SLS) and Dua and Kapur (2017; 2SLS).

This resurrected the spectre of spurious regression as noted by Yule (1926), Champernowne (1960) and Granger and Newbold (1974).

See Pesaran and Shin (1999) and Pesaran et al. (2001).

See Kydland and Prescott (1982) and Long and Plosser (1983).

It noteworthy that the VAR specifications and time series models also have extensions which involve modelling second moments such as GARCH or stochastic volatility. See Dua and Suri (2016) and Dua and Tuteja (2016) for applications of VAR-multivariate GARCH BEKK and Dua and Tuteja (2016, 2017b) for applications of DCC-GARCH models. For instance, a BVAR with stochastic volatility has been estimated by Uhlig (1997), while Clark and Ravazzolo (2012) compared macroeconomic forecasting performance of AR models with alternative specifications of time-varying macroeconomic volatility. However, we do not discuss these here for the sake of brevity.

Thus, a VAR model is similar to a large-scale structural model and given the ‘correct’ restrictions on the parameters of the VAR model, they reflect mirror images of each other. As shown by Zellner and Palm (1974) and Zellner (1979), any linear structural model theoretically reduces to a VAR moving average (VARMA) model, whose coefficients combine the structural coefficients. Under some conditions, a VARMA model can be expressed as a VAR model and as a vector moving average (VMA) model. A VAR model can also approximate the reduced form of a simultaneous structural model.

The argument against differencing is that it discards crucial information related to co-movements amongst the variables such as cointegrating relationships.

See Bernanke (1986), Blanchard and Watson (1986) and Sims (1986).

However, this approach does not attempt to model the structure of the economy in the form of specific behavioural cause and effect relationships. These are relatively small sized models compared to structural macroeconometric models.

See Cogley and Sargent (2002) and Del Negro and Otrok (2008).

See Dua and Goel (2017) for an application of FAVAR to the Indian economy.

Thus, adding a few common factors to a macroeconomic VAR system controls for a variety of omitted variables within a typical low-dimensional VAR analysis.

These models are represented as augmented VAR models, denoted as VARX* and feature domestic variables and weighted cross-section averages of foreign variables, also referred to as “star variables”, which are treated as weakly exogenous (or long-run forcing).

The solution can be used for shock-scenario analysis and forecasting as is usually done with standard low-dimensional VAR models. See Pesaran et al. (2004) and Dees et al. (2007).

The alternative assumptions of the factor models include the strict factor models, approximate factor models and dynamic factor models.

The most popular estimation methods include the principal components approach (Breitung and Tenhofen 2011), ML-type estimators (Doz et al. 2011), time-domain approach (Stock and Watson 1989, 2002a, b) and the frequency-domain approach (Forni and Reichlin 1998; Forni et al. 2001, 2005). They have been widely used for various purposes such as to construct economic indicators, to forecast real and nominal economic variables and for instrumental variable estimation. Factor models have also been used for monetary policy analysis in combination with a vector autoregressive (VAR) system as in Bernanke et al. (2005). In many cases, only five to ten factors are constructed to capture more than a half of the total variation within a large data set of more than three hundred macroeconomic variables. Thus, adding a few common factors to a macroeconomic VAR system is supposed to control for a variety of omitted variables within a typical low-dimensional VAR analysis and circumvents the curse of dimensionality.

See Dua and Sharma (2017) for an application of spectral models to examine the synchronization of international growth rate cycles.

For example, Dua and Tuteja (2015, 2016, 2017a) and Dua and Sharma (2016) utilize MS-VAR models to study the common regimes across international economies and financial markets.

The New Keynesian DSGE framework was later proposed by Rotemberg and Woodford (1997).

Large-scale DSGE models with a sophisticated structure are being utilized by Central Banks as the papers by Smets and Wouters (2003, 2007) advanced evidence that these models fit the US macroeconomic data aptly.

Refer to Dua and Kapur (2016) and Dua and Suri (2016) for applications of panel VAR models.

In such a case, the MLE or the within estimator under the fixed-effects specification is no longer consistent with large N (number of cross-section units) and small T (number of time periods) due to the presence of incidental parameters problem. Thus, instrumental variables (IVs) and generalized methods of moments (GMM) estimation methods have been generally used to obtain consistent estimates.

However, in panel data models, the analysis of co-integration is further complicated in the presence of heterogeneity, unbalanced panels, cross-sectional dependence, and cross-unit co-integration. Further, the asymptotic theory is contingent on the sizes of N and T and lacks coherence.

See Bai and Ng (2004), Bai (2009), Moon and Perron (2004), Pesaran (2006) and Phillips and Sul (2003).

See the seminal work by Litterman (1981, 1982, 1986), Doan et al. (1984), Todd (1984), Blanchard and Quah (1989) and Spencer (1993).

According to UNCTAD (1999), “Portfolio investment involves transfer of financial assets by way of investment by resident individuals, enterprises and institutions in one country in securities of another country, either directly in the assets of the companies or indirectly through financial markets.”

Forecasting not the future but the present as well the near past is termed as ‘nowcast’.

See Marcellino and Schumacher (2008), Camacho et al. (2011, 2012), Angelini et al. (2011), and Giannone and Reichlin (2012).