Introduction

Research on the geographic diversity of macroeconomic categories is currently one of the most important issues of empirical macroeconomics. Precise determination of the economic diversity of different areas of the country provides more opportunities for analysing and understanding a given phenomenon. Research on the nature of fluctuations in economic activity includes analyses of spatial diversification, focusing on income, wages, and other variables. The results from this stream of research may be crucial in assessing the impact on fiscal policy (e.g., Hallett, 2017; Carniti et al., 2018), monetary policy (e.g., Anagnostou & Gajewski, 2018; Lea, 2018), and macroprudential policy (Rubio, 2014).

Spatial and temporal disaggregation methods for the time series of basic macroeconomic variables have been intensively studied for over a half-century. Disaggregation was one of the first fields of economic research where missing data analysis was employed. In time, the search for methods enabling accurate spatial and temporal estimation of macroeconomic variables developed into a separate field of econometrics, because of their fundamental importance for the statistical analysis of national accounts.

The first articles where annual data were converted into quarterly estimates were written by Lisman and Sandee (1964), Boot, Feibes, and Lisman (1967), Denton (1971). They presented a general approach and some specific procedures involving constrained minimisation of a quadratic form in the differences between revised and unrevised series. Unfortunately, empirical applications are omitted in these initial proposals.

Based on Autoregressive Integrated Moving Average (ARIMA) models (Wei & Stram, 1986, 1990; Guerrero & Martinez, 1995) and factor models (Angelini et al. 2006; Marcellino, 2007), the preliminary approaches were developed into a dynamic method where higher frequency of the selected time series of economic variables could be obtained based on sets of additional variables and validating the numerical results estimated in practice.

Chow and Lin (1971) presented methods that utilise a generalized linear regression model with a set of explanatory variables of the same frequency as the studied one. Their approach served as a basis for the most popular data interpolation approach that was often modified into a range of related methods. For example, Rossi (1982) added the condition of equal units and a sum of the lower frequency data. Fernandez (1981) and Littermann (1983) considered a complex stochastic structure assuming a temporal relationship between the random components. A generalization of Chow and Lin’s estimator was presented by DiFonzo (1990), who developed an estimation procedure relying on higher frequency regional data. DiFonzo’s (1990) approach is particularly applicable to the case when lower frequency regional data and higher frequency explanatory variables are available. The modifications of DiFonzo’s estimator for some special cases of Aitken’s estimator for the linear regression model take account of the number of estimated parameters, the dynamic nature of data series, and spatial correlations between residuals and their autocorrelation (see Salazar et al., 1997; Santos-Silva & Cardoso, 2001; Pavia-Miralles & Carber-Borrasa, 2007).

One of the most recent modifications of Chow and Lin’s method was proposed by Polasek et al. (2010), who used Spanish regions’ Gross Domestic Product (GDP) data at the NUTS-2 level to derive GDP estimates for NUTS-3 regions. Regression was performed with socio-economic and spatial information on NUTS-3 regions.

The main advantage of the Polasek et al. (2010) study is the use of the Bayesian approach to estimate spatial regression parameters and to present information about the statistical uncertainty of the estimates of regional GDPs. In the Bayesian approach, elicitation of the prior distribution allows researchers to exploit their knowledge of the parameters of the model. Also, consistency between the estimates of regional macroeconomic indicators and their inherent values is ensured by definition. The approach was modified by Polasek (2013).

Pavia-Miralles (2010) made an extensive review of the literature on disaggregation methods, and Chen (2007) presented the comparative analysis methods in an article juxtaposing the results of five disaggregation methods applied to 60 variables derived from national accounts. Marcellino (1998) discussed methods based on numerical interpolations.

Proietti, Marczak, and Mazzi (2017) prepared a density estimate of monthly GDP for the Euro area. They performed analyses based on output (value added in branches and taxes minus subsidies) and expenditure (final consumption, gross capital formation, government spending, and net export), components of GDP, and dynamic factor models. Proietti, Marczak, and Mazzi (2017) reported not only point estimates of monthly GDP but also the uncertainty associated with the estimation method and the modelled data. Higher uncertainty is associated with the expenditure approach, but the point GDP forecast (the median of the distribution) is almost in line with the realized GDP growth rates.

The structure of this monograph is the following. In Chapter 2, we review the problem of relevance and usefulness of regional data for setting and assessing the effectiveness of the regional policy objectives. We stress the necessity of forecasting regional data since this has been recently emphasised in economic research. A review of the literature identified crucial problems encountered by researchers when selecting indicators and methods for estimating regional data.

In Chapter 3, we put an exhaustive overview of official statistics of economic conditions that are available at the regional level. Because the empirical examples are based on the Polish economy, the statistics concern only Poland. However, many economies, especially European ones, have similar official regional statistics. In addition to presenting the available data, this chapter also shows the regional variations in GDP levels and the business cycle measures.

Chapter 4 presents methodological issues related to the properties of the Seemingly Unrelated Regressions Equations (SURE) model. We summarise the procedures for estimating and testing a simple linear regression model. We also state the assumptions and show variants of the SURE model.

Chapters 5 and 6 cover empirical examples of the application of the SURE model to modelling and disaggregating regional GDP. Chapter 5 presents the results of estimating the parameters of a model describing regional GDP (level or its rate of change), a function of the current economic situation of the whole economy, and economic interdependencies with other regions. We discuss estimates of the regional GDP measures as well as the associated statistical uncertainty represented by the bands of the confidence intervals. In Chapter 6, we present the results of applying the SURE model built upon a broader set of regional explanatory variables to estimate regional labour productivity levels. In this chapter, we discuss the results obtained based on the SURE model with a diagonal variance matrix, as well as the model with an unconstrained variance matrix. We discuss the estimates of regional economic indicators and statistical uncertainty. Chapter 7 presents the conclusions.

To our knowledge, this monograph is the first to address the value of the SURE model for disaggregating and forecasting regional data. It provides a set of econometric methods suitable for the spatial and temporal disaggregation of basic macroeconomic variables. We provide insight into the statistical uncertainty of the outcomes of disaggregation, which we believe are just as important as the estimates themselves. The book contains advanced but intuitive methods and tools that may serve as a framework to disaggregate observed macroeconomic variables.

The results presented in this monograph were obtained under the research project supported by the National Science Centre, Poland (decision DEC-20 16/21 /B/HS4/01565).