NiReMS: A regional model at household level combining spatial econometrics with dynamic microsimulation

ABSTRACT

The heterogeneous spatial and individual impacts of the Great Recession, Brexit and COVID-19 have generated an important challenge for macroeconomic and regional/spatial modellers to consider greater integration of their approaches. Focusing on agent heterogeneity at the ITL 1 level in the UK, we propose the National Institute Regional Modelling System (NiReMS) – a synthesis of dynamic microsimulation with a spatial regional macroeconometric model. The model gives regional macro projections while allowing for household level inference. To showcase the model, we explore the impact of discontinuing the uplift in Universal Credit (UC) before the end of the pandemic and show that it led to more households consuming less. Importantly, the proposed framework highlights the unequal distributional impact across regions of the UK.

KEYWORDS:

• microsimulation
• heterogenous agents
• universal credit
• spatial econometrics
• structural macroeconomic models

JEL:

• D15
• D31
• D6
• E65

1. INTRODUCTION

The onset of the COVID-19 pandemic brought about disruptive changes to the functioning of almost all economies and to the externalities within and between them. This includes the United Kingdom (UK) and its constituent nations (England, Wales, Scotland and Northern Ireland) and the associated subnational regions. Limits to labour mobility significantly affected production and its dynamics, while supply chain disruptions affected inter-regional and international trade. Mobility of factor inputs and trade are two of the most prominent channels through which shocks are transmitted and through which externalities between regions and countries are generated. While the pandemic severely restricted these standard interaction channels, the situation in the UK was exacerbated by Brexit which reduced international trade flows and also potentially enhanced linkages between Northern Ireland and the Republic of Ireland. The COVID shock underscores the need for new models and methods to understand regional macroeconomies and enable the design and delivery of regional and national policy.

National macroeconomic models still lack a robust spatial and distributional dimension. The collection of articles assembled by Vines and Wills (2018) sets out four major foci in the development of a template for rebuilding macroeconomic models to address major flaws and shortcomings exposed by the Great Recession.¹ However, the regional or spatial dimension was missing from consideration. The present paper outlines some first steps on a path to a more successful integration of spatial heterogeneity and spillovers in outcomes from macroeconomic models while at the same time providing insights into the combined heterogeneity of household agents mapped onto geographical locations. COVID-19, Brexit and the current cost of living crisis have highlighted the heterogeneous nature of the spatial impacts and the need to incorporate this aspect into modelling work.

Spurred by the need to understand the effects that aggregate shocks, such as COVID-19 and Brexit, have brought about for the UK economy and, specifically, impacts on the different regions in the UK, the National Institute of Economic and Social Research (NIESR) has been developing a new regional model – NiReMS (National Institute Regional Modelling System). Faced with the above disruptions, the conventional multi-regional generalised RAS approaches to update input-output tables is inadequate. Instead, NiReMS uses an approach based on aggregate national input-output tables and estimated latent spatial weights (Bhattacharjee & Holly, 2013). This spatial econometric approach highlights core interdependencies and channels of transmission of shocks between the regions of the UK. For each regional economy, the model includes the impact of both global shocks (at the economy-wide macroeconomic level) and local shocks (arising from the regional economies of each region).

Since the COVID-19 shock affected some households much more severely than others, thereby exacerbating extreme poverty and destitution, the regional analysis needs to pay greater attention to impacts at the household level. Carrascal-Incera and Hewings (2022) develop one way of doing this, building upon Miyazawa’s framework to endogenise the household sector and compute the so-called spatial income multipliers combining direct and indirect spatial effects. However, further enhancements were required to move beyond a representative agent model towards a collection (even a continuum) of heterogenous agents within each region and cohort by income, household demographics etc. This is commonly achieved in macroeconomic theory by considering heterogenous agents embedded in a new Keynesian model – the so-called HANK (Heterogenous Agent New Keynesian) models. In this paper we deviate from this approach and instead incorporate the heterogeneity among agents via dynamic microsimulation. Here, individuals and households drawn from an initial representative sample of the UK population are followed through time, through changes in household circumstances, births, education, work and finally death. Income/consumption and labour/leisure decisions are evaluated by dynamic optimisation of their utility functions through time. Furthermore, our microsimulation exercise is guided by the macroeconomic projections of key variables, in essence giving the simulated agents ‘macrofoundations’. Specifically, the circumstances each agent faces evolves over time in each region. While the analysis in this paper is centred at the International Territorial Level (ITL) 1 level,² there will probably be a high level of concordance between the region of origin and income and expenditures. With smaller spatial units (ITL 2 or local authority areas), this mapping is likely to be disrupted by daily/weekly commuting patterns and the propensity of households to exploit their love of variety by shopping for some goods and services in other spatial units.³

A key component of this integrated macro-micro model is a regional macroeconomic model (at the ITL 1 level) incorporating spatial interdependence modelled using an estimated spatial weights matrix. The common assumption of symmetric spatial weights inherent in geographical contiguity- or distance-based spatial weights or even in some estimates of spatial weights (Bailey et al., 2016; Bhattacharjee & Jensen-Butler, 2013) is not useful here because of likely core-periphery relations. A hierarchical tree structure is often useful when the network connections only run in one direction (Bhattacharjee & Holly, 2013). However, there are local deviations in parts of the network, which means that we need instrument validity tests to ensure that there are no strong causal cycles. This methodology is based on Bhattacharjee and Holly (2013) and discussed in further detail later in the paper.

An important feature of the model is that it tracks individuals through time in line with dynamics in their regional and national economies and can provide short-run projections of the impacts of regional (local) and national (global) shocks, as well as government policy. Here, we describe the model and methodology and illustrate its use in developing socio-economic projections for the UK regions. The combination of spatial econometrics and microsimulation, in line with structural macroeconomic models, provides a very useful tool for analysing consumption across groups and counterfactual policy exercises. We are able to quantify consumption loss due to COVID-19 and the cost-of-living crisis, and the impact of policy (for example, energy cost caps and benefit payments). However, an important characteristic should be the impact not just of national and regional shocks on consumption but also the feedback effects of that consumption on the paths of the regional economies. As Carrascal-Incera and Hewings (2022) demonstrate, beyond important spillover effects, the structure of the goods and services flows are also different from the income-generated flows. In addition, the proposed microsimulation exercise is more flexible since most models assume limited activity status options (employed, unemployed) while in this system, there are households with more than one earner (potentially in part-time employment) whose income may determine the labour force participation decision of the second member. Note, however, that the proposed framework is not a model with full micro-macro feedbacks since only the spatial-macroeconometric model informs the microsimulation model but not vice-versa.

The rest of the paper is organised as follows. Section 2 develops and describes our proposed model, focusing first on modelling the regional macroeconomies and their interconnections, and then heterogeneous household behaviour and outcomes. Section 3 presents some findings, focusing on a counterfactual policy experiment of extending a specific welfare scheme. Section 4 concludes and outlines some areas of potential further development.

2. METHODOLOGY

Macroeconomic models enable counterfactual structural policy analysis, but there are increasing concerns about what is overlooked. One issue is that they are often not able to adequately capture impacts of local shocks and regional/welfare policy, even models with spatial and regional interlinkages. To gain a better understanding of the distributional impacts of major shocks (like COVID-19) and progressive tax/benefits policy, a heterogenous agent framework is necessary. The recent literature has highlighted the importance of incorporating heterogeneity among agents, particularly following the Global Financial Crisis, as conventional economic models and analyses have been criticised for an excessive focus on a representative agent framework (Bunn et al., 2021; Challe, 2020; Golosov et al., 2021; Kaplan et al., 2018; Moll et al., 2022).

Microsimulation is a popular way to model households in their fullest heterogeneity by basing the simulated sample on some comprehensive survey data (Aaberge & Colombino, 2014; Bourguignon & Spadaro, 2006; Figari et al., 2015; NIESR, 2016; Orcutt et al., 1961; Sefton & van de Ven, 2004). For analysing policy outcomes, dynamic microsimulation has been a useful tool in the arsenal of policymakers (Li & O’Donoghue, 2012). As opposed to static microsimulation, dynamic microsimulation allows some aspects of household decisions to be based on rational expectations utility maximising behaviour using dynamic optimisation over a long-time horizon. This allows realistic modelling of heterogeneity together with close adherence to conventional macroeconomic principles. While building such models has become easier, particularly using tools such as the Simulator of Individual Dynamic Decisions (SIDD) (van de Ven, 2017b), the macroeconomic paths that these models generate do not necessarily match those implied by current generation macroeconometric models.⁴

Understanding the impacts of shocks and policy at the household level in a timely manner is a major challenge for evidence-based policy and research. Household surveys, on which microsimulation models often draw, take time to conduct. While models based on such surveys often provide the best picture of the impact of a macroeconomic shock (such as a recession or pandemic) or a specific policy, policymakers often do not have the privilege of waiting for the data and analyses to become available. Dynamic microsimulation provides a picture of households through time, but it does not factor in the ‘macrofoundations’ the economy imposes on the households, i.e., the microsimulation model is typically not linked to the macroeconomic situation faced by households. As such, faced with a macroeconomic shock, there is clearly a demand for methods that allow for real-time household level analysis before survey data become available.

The question then is how macroeconometric models can be combined effectively with dynamic microsimulation models in a way that fulfils both objectives – credible macroeconomic (regional) projections and counterfactual analysis accounting for heterogeneities implied by real data. This paper offers an easy to implement method if one desires to analyse household impacts of macroeconomic shocks and policy given a macroeconomic path.⁵ In essence, our goal is to give the microsimulation model some ‘macrofoundations’.

The proposed framework has three building blocks: (1) a spatial model for regional macroeconomies and inter-regional connections; (2) a life-cycle model to optimise households’ labour and consumption choices; and (3) a dynamic microsimulation model addressing heterogenous households (and individuals) and tying the previous models together. Figure 1 shows how these three models are connected. Before microsimulation commences, we first create a representative sample of households: in our case, from round six of the UK Wealth and Assets Survey (WAS). Microsimulation requires some suitably large surveys that capture households (and individuals) in their fully representative heterogeneity – by observed socio-economic and demographic characteristics as well as latent preferences and tastes. These households are affected, through labour outcomes, by aggregate regional dynamics as captured in projections from the spatial model. In the spirit of heterogenous agent models, individual households react to these aggregate regional shocks in their full heterogeneity and this generates a profile of heterogenous behaviours in response to shocks and policy. In this manner the microsimulation model and its outcomes are tied in with short- and medium-run macroeconomic dynamics. Since microsimulation generates pseudo-panel data on a collection of households across time, it is important that the initial sample of households are representative of the UK economy. Discussion about the initial sample of households is included in Appendix A1 in the online supplemental data.

Figure 1. Flowchart of methodology.

The figure shows how the different building blocks integrate with the NiReMS model: Spatial models create a path for labour outcomes (wages and employment), the life-cycle dynamic microsimulation model is used to ensure that economic agents consumption and labour decisions are optimal, and static microsimulation is used to simulate households' non-structural decisions and outcomes.

After a representative sample of households is obtained, the microsimulation starts. In each simulated period, initially the household’s characteristics are modelled using simple transition probabilities and estimated reduced form models. These characteristics include (but are not limited to) the region where the household lives, the sectors the household members work in, childbearing, etc. Once these characteristics are simulated for the period, the households labour outcomes are guided by the regional macroeconomic model and the life-cycle model. In particular, regional employment and (average) regional wages follow the projected paths, while the life-cycle model ensures that household’s labour and consumption choices remain intertemporally optimal.

While microsimulation and macroeconomic models, such as life-cycle and overlapping generations models, have been combined in the literature before (see DeBacker et al., 2019; van de Ven, 2017b for example), these papers do not tie the simulation to a projected macroeconomic path. The key reason to guide the microsimulation with macroeconomic projections is that households outcomes are not just influenced by their microeconomic incentives, but also by the constraints the macroeconomy poses. In this paper, we let macroeconomic projections guide the households’ labour outcomes (employment and wage offers). Thus, households choose how many labour hours they wish to provide to market activities, but the macroeconomic projections guide how many households find such employment. As such households’ choices are ‘microfounded’, since the life-cycle model is rooted in the utility maximisation framework, as well as ‘macrofounded’, on account of macroeconomic projections imposing limits on labour outcomes. Note that the proposed method is flexible, and it is possible that other aspects of the model can be guided by macroeconomic projections.

To the extent that ‘macrofoundations’ are important to households’ economic outcomes, spatial macroeconomic projections are preferred rather than national projections: households are faced with different macroeconomic constraints depending on the region where they live. To this end we propose a spatial macroeconomic model to decompose the national macroeconomic trajectory into regional forecasts together with modelling of global and local shocks and their spillovers. This provides projections for each region of the economy. These projections are then used within a microsimulation model to simulate households’ consumption-saving and labour-leisure decisions. To showcase the model, we use UK data, where the base path of the UK macroeconomy is generated by forecasts from the National Institute Global Econometric Model (NiGEM) (NIESR, 2018). These forecasts represent national (global) shocks which our model decomposes into regional (local) paths of key macroeconomic variables by allowing heterogenous regional loadings within a factor model structure. Then, deviations of regional outcomes from these paths represent local shocks, which generate externalities upon other regions through a spatial lag model. This macro-spatial link is an important value-added feature of NiReMs, together with an extension of the representative agent regional macroeconomic model to heterogenous agents using dynamic microsimulation.

Next, we discuss the three building blocks in Figure 1. These descriptions are relatively high level, focusing more on the conceptual elements. Technical details are kept to a minimum so as to not detract from the main argument of the paper; see Appendix A.2 for further details.

2.1. Spatial regional macroeconometric model

The first step is to build a spatial macroeconometric model at the ITL 1 Government Office Region (GOR) level for the United Kingdom. There are twelve GORs, comprising nine English regions (NE: North East, NW: North West, YH: Yorkshire & The Humber, EM: East Midlands, WM: West Midlands, EA: East of England, LON: London, SE: South East, and SW: South West) and the three devolved nations of the UK (WA: Wales, SC: Scotland, and NI: Northern Ireland). There are two key questions that one has to tackle when estimating a spatial macroeconometric model. The first is how to describe the macroeconomy (which macroeconomic model to use, structural or reduced form, and choice of observed (state) and latent variables), and the second is how to model spatial interactions (choice of a spatial econometric model aligned to a suitable economic model for spillovers).

To choose variables that best describe the macroeconomy, we lean on the literature on Dynamic Stochastic General Equilibrium (DSGE) models (Gali et al., 2012; Smets & Wouters, 2007). From this wider collection of regional macroeconomic variables, we choose a smaller set of four state variables: real output (Gross Value Added, GVA), real consumption, employment, and real wages. As such we estimate a reduced form model using these variables. Beyond the DSGE literature, the choice of these state variables is also motivated by availability of quarterly data at the ITL 1 level of spatial granularity, together with adequate spatio-temporal variation. We use regional GVA data, by sector and region (Model-based early estimates of regional GVA in the regions of England, Wales, Scotland, and Northern Ireland), from the ONS (Office for National Statistics) and aggregate this across sectors. Regional consumption data are also available from the ONS (Regional Household Final Consumption Expenditure (Experimental statistics), by goods and services), which are then aggregated across all items and imputed to the quarterly level based on trends from aggregate data and output from NiGEM (NIESR, 2018). Similarly we impute regional wage data from ASHE (Annual Survey of Hours and Earnings), available at annual frequency, to quarterly using NiGEM aggregates. Employment data are available quarterly at the region level from LFS (Labour Force Survey). Regional data on prices and capital are also available; however, they do not show substantial regional variation in growth rates.

Open economy macroeconomic models are promising in the sense that they can model connections between economies through terms of trade. However, most models (such as Gali et al., 2012) focus on trade as the key driver of connections. In contrast, our application is focused on regions where trade is not the only channel by which the regions are connected. Mobility of factor inputs, technology spillovers, negation of arbitrage opportunities through convergence in prices of output (among others) all have an influence on the economic outcomes of all the regions. To this end, we closely follow the approach of Wasseja et al. (2022) which takes ideas from a classic technology spillover paper by Ertur and Koch (2007) and extends Gali and Monacelli (2005) to include potential multiple sources of interconnection. Note that the context of all the mentioned papers is multi-country, which is very different from our multi-region setting with harmonised monetary and fiscal policy and negligible terms of trade. As such, we include spatial lags of all the variables to capture the different sources of connectedness as well as national aggregates.

The spatial lag of consumption is included in the model to capture the effects of trade among the regions. Canonical macroeconomic models such as Gali and Monacelli (2005) have a composite consumption index combining a ‘home’ good and a ‘foreign’ good, where relative consumption is determined by relative prices or effective terms of trade. However, in our case, relative prices are (almost) the same across regions because trading constraints need to be negligible so that arbitrage opportunities are negated.⁶ Nevertheless, trading induces consumption across regional boundaries, whereby agents consume output produced across region boundaries. The terms of trade (or price differentials) determine the relative proportion of home and foreign goods consumed in each region, as well as the region from which these goods are ‘imported’. Then, spatial lag in relative prices implicit in terms of trade motivate a spatial lag model for regional consumption. Hence, trade between regions is captured by spatial lags of log-consumption, whereby a household in an index region can consume output produced in (neighbouring) regions.

The spatial lag of output, measured by GVA, models technology spillovers among the GORs. The motivation for this follows Ertur and Koch (2007) closely. Assuming a Cobb-Douglas production function one can capture technological progress by multifactor productivity, which has spatial lags induced by technology spillovers from neighbouring regions. Since productivity is not explicitly observed in our data, these spillovers the induce spatial lag dependence in log-output. Additionally, spatial Durbin effects will be induced by spatial correlation in factors of production.⁷ The key insight is that while technological progress might be exogenous, spillovers among the regions occur which helps the diffusion of technology. Crucially, due to the form of the production function we can capture the impact of technology spillovers by introducing spatial lags of output. Spatial lag dependence in log-employment is included to capture labour mobility across the UK regions. Further, the potential for labour mobility imply a degree of wage equalisation across regions to negate arbitrage, which induces a spatial lag in log-wages.

This system of four equations (Income, Consumption, wages, and Labour) in growth rates (logarithm of first differences) of the state variables, in our case, has a finite order VAR (vector autoregression model) representation of the so-called ABCD form (Fernández-Villaverde et al., 2007). The model can now be estimated using, for example, IV-SUR (instrumental variables seemingly unrelated regression) allowing for correlated errors; any cross-equation parameter restrictions as implied by theory can also be accommodated. This spatial model is the reduced-form VAR representation of the structural model of Gali and Monacelli (2005) and Gali et al. (2012). All the structural equations include respective budget constraints. As such, there is an aggregate economy-wide budget constraint in the NiGEM model, from which global shocks are obtained. Furthermore, the agents populating each region also have region specific budget constraints, following Gali et al. (2012). As a result, our reduced form VAR also implicitly includes region specific and national budget constraints; for more detail please refer to the papers cited, particularly Gali and Monacelli (2005), Smets and Wouters (2007) and Gali et al. (2012).

The inclusion of the spatial lags requires knowledge of the spatial weight matrix, W, that captures the structure of connection among the regions. In cross-country settings it is common to utilise trade data to construct W. However, we lack data on trade between regions at sufficient granularity. As such we estimate W using latent spatial weights approaches (Bhattacharjee & Holly, 2013; Bhattacharjee & Jensen-Butler, 2013). Since W is only partially identified, one needs to impose structural constraints, which in turn imply a sparse weights matrix, with strong spatial dependence induced by dense structures appropriately modelled by a factor structure (Pesaran & Tosetti, 2011). Following Bhattacharjee and Holly (2013), the network structure is estimated by repeated application of the Hansen-Sargan overidentifying restrictions test (Hansen, 1982). The key idea is that, for an index region, regions that are not its neighbours but are connected through the spatial network can act as instruments for the neighbours, which in themselves are endogenous. This property helps identify the weights matrix and avoids the endogeneity problem common when purely exogenous ‘classic’ (typically geographic) spatial weight matrices are not used. Note that symmetric (geographic) weights are untenable in our context because of potential core-periphery relationships.⁸

While the method of Bhattacharjee and Holly (2013) allows an unknown W to be estimated, it uses a sparse structure for identification. It can be argued that this structure is less realistic for certain variables which entails variable specific weight matrices. While we have a common, estimated and asymmetric W, our model estimates different spatial autoregressive parameters for the four variables, which helps alleviate concerns about the impact of a shared W.

Before estimating spatial weights, we also need to address (temporal) nonstationarity. Panel unit root tests reveal that all four variables (logarithm of: output/GVA (ln $Y$), labour/employment (ln $L$), consumption (ln $C$) and wages (ln $w$) are nonstationary and integrated of order 1, i.e., I(1). We also find two cointegrating relationships: between output and consumption (ln $Y$ and ln $C$); and between wages and labour productivity (ln $w$ and ln$(Y/L)$). This makes economic sense. Hence, rather than a VAR, we estimate a spatial panel VECM (vector error correction model) with potential partial adjustment to these two cointegrating relations. In line with economic intuition and practice, we also include inflation (at the national level) in the cointegrating relations. Further, we are conscious of potential spatial strong dependence (Pesaran & Tosetti, 2011), even if testing this is inadequate in small $N$ panel (Pesaran, 2015); as such national aggregates are included to the regression to account for the factor structure. This leads to a spatial VECM with spatially heterogenous slopes, as shown in (1): (1) $\begin{array}{rl}\mathrm{\Delta }{R}_{\mathrm{it}}& ={\alpha }_i+\mathbf{b}\mathbf{W}\mathrm{\Delta }{R}_{\mathrm{it}}+\mathrm{\Gamma }\left[\begin{array}{cc}\mathrm{\Delta }{R}_{i,t-1}& {\mathrm{\Delta }}_s{R}_{\mathrm{it}}\end{array}\right]-\mathrm{\Theta }\left[\begin{array}{cccc}-\gamma & 1& 0& 0\\ -\theta & 0& 1& \eta \end{array}\right]R_{i,t-1}\\ & +\mathrm{\Lambda }\left[\begin{array}{cc}\mathrm{\Delta }{R}_t^{\ast }& {\pi }_{t-1}\end{array}\right]+{ϵ}_{\mathrm{it}},\end{array}$(1) where $R_{\mathrm{it}}={\left[\begin{array}{cccc}\ln Y_{\mathrm{it}}& \ln C_{\mathrm{it}}& \ln w_{\mathrm{it}}& \ln L_{\mathrm{it}}\end{array}\right]}^{\mathrm{\prime }}$, $\mathrm{\Delta }$ and ${\mathrm{\Delta }}_s$ are the (temporal) first difference and seasonal (fourth) difference operators respectively, $R_t^{\ast }={\left[\begin{array}{cccc}\ln Y_t^{\ast }& \ln C_t^{\ast }& \ln w_t^{\ast }& \ln L_t^{\ast }\end{array}\right]}^{\mathrm{\prime }}$ is a vector of national aggregates to account for factor structure and potential strong dependence (Pesaran & Tosetti, 2011), and ${\pi }_{t-1}$ denotes lagged inflation (at the national level).

The above equation can be interpreted as a GVAR model for regions, combining the effect of two kinds of shocks – global and local. Our spatial econometric model is expressed in the GVAR (global VAR) framework (Elhorst et al., 2021). The effect of global shocks (like a pandemic) is captured in macroeconomic aggregates, in our case through UK-level income, consumption, wages, and employment. The spatial effects of this shock are expressed, in a factor model setting, through heterogenous loadings (elements of $\mathrm{\Lambda }$) upon the various regions.

In addition, there are local shocks affecting individual regions, and their spillovers are modelled in a standard spatial econometric tradition through a spatial weights matrix $\mathbf{W}$. We assume this spatial model to be a spatial lag model impacting upon each of the four regional macroeconomic variables included in our model – (1) regional output (GVA), (2) consumption, (3) wages and (4) employment – but with different spatial autoregressive parameters represented by the vector b. The error correction parameters $\mathrm{\Gamma }$ and $\mathrm{\Theta }$ capture heterogenous (temporal) short run dynamics and partial adjustments to the two equilibrium relationships, respectively.

This constitutes a very large GVAR type model with full heterogeneity across regions and about 1000 parameters. The partial adjustment parameter estimates for the consumption-income equilibrium average $-0.110$ across the regions, with a 95% CI$(-0.24,0.00)$; corresponding statistics for partial adjustment to the wage-productivity equilibrium are $-0.095$ and $(-0.19,-0.01)$ respectively.

Using the VECM model (1) the network between UK GORs identified is shown in the left panel of Figure 2. Next to this sparse structure we also show the map of the GORs with their respective populations in the right panel of the figure. The figure shows that while the position of London is central, it has only limited connections with regions across the country, particularly the devolved nations of Wales, Scotland and Northern Ireland. Finally, based on the above estimated neighbourhood structure, we estimate by IV-SUR spatial panel VECM models for all four variables. Motivated by the literature on GMM for dynamic panel data and spatial regression models, we use higher-order spatial and temporal lags as excluded instruments, validating instrument choice by overidentifying restrictions tests (Bhattacharjee & Holly, 2013). The model is estimated using data for twelve GORs (ITL 1 regions) over 84 quarters (1997Q1 to 2017Q4).⁹

Figure 2. UK: GORs (ITL 1 regions) and estimated spatial structure.

The identified sparse structure of the English regions and the devolved nations. There is a clear, core-periphery structure identified with London being the centre.

We take out-of-sample predicted output and employment from this model as inputs into our microsimulation exercise. Thus, our microsimulation is informed by macroeconomic aggregates (both for the UK and all its ITL 1 regions) but extends analysis to an heterogenous agent setting. By taking out-of-sample prediction from the spatial model we can also study the household impacts of counterfactual macroeconomic policies, utilising local projections for example Jordà (2005), enabling richer analysis of impacts of macroeconomic shocks. Note that while our regional model allows for region specific dynamics, it does not allow for structural change in the coefficients. As a result, the projected path of the regional model considers the COVID period as a short-term shock. Using microsimulation can help alleviate this weakness, as the heterogenous household-level impacts will have medium- to long-term effects. Nevertheless, these household level impacts are not taken into account when creating the projected paths which highlights the need for further research on fully integrated macro-micro models.

2.2. Life-cycle model

Microsimulation models critically depend on how behavioural decisions (such as consumption-savings and labour-leisure) are made. One can opt to model such decisions in reduced form, where typically an estimated regression model determines behavioural decisions. Alternatively, one can model such decisions more structurally, where either an overlapping generations (OLG) model or a life-cycle model helps impute the decision variables conditional on household characteristics. Our proposed microsimulation model is structural, utilising a life-cycle model to capture behavioural decisions. We consider a life-cycle model rather than an OLG as it simplifies computational burden. In particular, it allows us to create only one ‘grid’ for a representative agent, given household characteristics. Since our goal is analysing the short- and medium-term impact of macroeconomic shocks on households, this simplification should not have a large impact: the economic agent’s age is likely more important in making their consumption decisions, than their respective birth cohort.¹⁰ The baseline model is kept relatively simple to allow for flexibility in analysing a multitude of alternate counterfactual policies or shocks. Thus, the model can be expanded depending on what the researcher deems to be important in the short- and medium-run.

Our analysis is implemented at the household (benefit unit) level, where each household is defined as a single adult or a couple together with children (under 18 years of age); when persons reach the age of 18, they form their own benefit unit. This is done to align analysis to the way that the benefit system in the UK works. A household can have dual-earners, which needs to be accommodated in the life-cycle model. When interpreting the policy functions we refer to adult 1 in the household as the ‘reference’ adult, and adult 2 as the ‘spouse’. When determining who is a reference adult in a household, we simply designate the individual with the higher wage.

To compute the policy functions, the grid of decisions with given characteristics, we utilise the VFI toolkit for MATLAB which ensures that setting up such models is simple and computation times are reasonable (Kirkby, 2017, 2022). To create the grid of decisions, one only needs to specify the dynamic budget constraint and the utility function. The toolkit then creates a Bellman equation and employs value function iteration to create the policy functions. By creating the policy function first, computation resources are conserved, as the microsimulation model will only need to reference the computed policy function to impute specific consumption and labour choice values for the households.

2.2.1. Dynamic budget constraint

The first building block of the life-cycle model is the dynamic budget constraint. This constraint is modelled as: (2) $x_{t+1}=(1+r)x_t+E_t(y_{t+1})-C_t$(2) where $r$ is the interest rate, which is currently set at its long-term average of 5%, $x_t$ are household assets/wealth in period $t$, $C_t$ the consumption in period $t$, and $E_t(y_{t+1})$ is the expected household income in the next period. We restrict $C_t$ to be above 0 for all periods $t$. In our current implementation, a no-borrowing constraint is imposed, since the finance sector is not explicitly modelled and as such anyone with a loan request would be granted one. This would in turn lead to a situation where agents would take up as much loans as possible as long as the no-Ponzi condition ($x_T\ge 0$) binds. Due to the simplification of no borrowing, savings is simply the wedge between available assets and consumption at period $t$.¹¹

Incomes are an extremely important part of Equation (2). As such it is important to have an income process that mimics lifetime earnings profile. The first decision is in regards to pension age and lifetime age. To construct the policy function, we assume that agents can live up to a maximum age of 105 years. Such high ages are relatively common in microsimulation models (see for example NIESR, 2016) and ensure that consumption values can be imputed for every sampled (and simulated) agent.¹²

In the model we assume that agents work between ages 18 and the UK state-pension age of 68. During the working years, the income they earn is stochastic, but hump shaped over the agent’s lifetime. State pensions on the other hand are deterministic.¹³ While pensions are assumed constant over time (in real terms), that does not mean that all pensioners will have the same consumption profile: they can liquidate a fraction of their assets at any time without cost.

The income process is modelled as: (3) $y_t=\{\begin{array}{cc}{\kappa }_t{L}_{1t}\pi (z_t)w+{\mathbb{I}}_{n>1}{\kappa }_t{L}_{2t}\pi (z_t)0.95w& \mathrm{if}18\le t\le 68\\ \mathrm{Pen}& \mathrm{if}68<t\le 105\\ 0& \mathrm{otherwise}\end{array}$(3) where $\mathrm{Pen}$ is a deterministic pension, and ${\kappa }_t$ is a hump-shaped deterministic function reflecting earnings over the lifetime (calibrated to UK data), $L_{1t}$ and $L_{2t}$ are fractions of time spent on work by the first and second adult in the household respectively, $w$ is average labour income offered by firms in the market, and $n$ is the number of adults in the household. Note that ${\mathbb{I}}_n>1$ determines whether there are two wage earners in the household or only one. If $n=1$, then the second part of the wage equation drops out. Further, note that we multiply the second earners income in the household by 0.95. This was done simply because of how we designate reference adults – the individual with the higher wage in the household.¹⁴ Note that in this formulation $w$ denotes the wages offered to the agent, and not disposable income. Disposable income is determined by the agent’s age (through the ${\kappa }_t$ term), and labour choices (through the $L_i$ term). The deterministic $\kappa$ term and the labour choices (together with labour outcomes) ensure that agents will have heterogeneity in wages. At this point, labour choices are modelled continuously, i.e., households can freely choose how much hours they supply for market activities given the wages offered and their assets relative to average wages offered. This was done to ensure a continuous policy function for labour and consumption choices. In this way we can make a distinction between active ($L_i>0$) and inactive ($L_i=0$) individuals.¹⁵

Finally, on account of employment outcomes also being influenced by market conditions, we will model the risk of unemployment with $\pi (z_t)$, which is a 2-state Markov process determining whether the individual is employed in a specific period, given their employment status last period, where $U$ is a binary variable denoting unemployed or economically inactive: (4) $\pi (z_t)=\left[\begin{array}{cc}P(z_t=1-U|z_{t-1}=1-U)& P(z_t=1-U|z_{t-1}=U)\\ P(z_t=U|z_{t-1}=1-U)& P(z_t=U|z_{t-1}=U)\end{array}\right]$(4) Importantly, we normalise wage offers $w$ at 1. As such the policy grid is constructed relative to annual average wage offered for the household, subject to household socio-economic-demographic characteristics, including education, location, etc. To obtain average wage offers for the initial period we can simply use WAS to calculate the average labour income for any specific household. Using disposable income of a household where the household head is aged between 18 and 68 years, calibrated to round six of the UK WAS data, labour choices (full-time or part-time) from WAS, and the value of the deterministic $\kappa$, one can calculate the average wage offer. This yields approximately £30,000 per annum which is slightly higher than the average disposable income of £24,000 from the sample of households obtained from WAS.

Note that average wage offer will change through the simulation period. Growth rates can be modelled several ways. Our objective being rich inference at the household level with the combination of simple models, we opt to accommodate growth rates by interpreting the grids relative to average earnings of the given year.¹⁶ The advantage of this approach is that it is quick and requires no complex computations. In particular, this way the policy function generated can be used for each simulated period. The disadvantage is that the fit will deteriorate the more years we iterate forward, especially at parts of the grid where grid points are sparser, typically the higher wealth classes.

2.2.2. Utility and value function

The model uses a version of the nonseparable CES utility similar to NIESR (2016): (5) $\begin{array}{rl}u(C/m,L)=& {\displaystyle \frac{1}{1-\gamma }{[{({({\displaystyle \frac{C}{1+0.5n+0.3m})}}^{1-\frac{1}{ϵ}}+{\alpha }^{\frac{1}{ϵ}}[{(1-L_1)}^{1-\frac{1}{ϵ}}+{\mathbb{I}}_{n>1}{(1-L_2)}^{1-\frac{1}{ϵ}}])}^{\frac{1}{1-ϵ}}]}^{1-\gamma }}\\ & -{\mathbb{I}}_{n>1}{\mathbb{I}}_{L_2>0}{\mathbb{I}}_{{\displaystyle \frac{c}{1+0.5n+0.3m}>C_{\min }}}(2L_2)\end{array}$(5) where m is the number of dependent children in the household. To retain comparability by household composition, we equivalise the consumption of the household depending on the number of adults and children: we discount household consumption by 0.5 for an additional adult in the household, and 0.3 for each of the first three children in the household. The final term in the utility function is a cost to the labour hours of the second earner. Importantly, this cost only enters the equation if the consumption of the household is above some threshold C_min. We set $C_{\min }=0.8$, so that when equivalised consumption is above 80% of average labour income, there is a cost associated with the second earner taking on labour hours. The reason behind the inclusion of this term is that once a household has enough earnings to maintain a steady and comfortable living, it is not necessary for the second earner to enter the labour market. We think the inclusion of such a cost on the utility function is warranted as it covers the situation where the spouse in a dual-earner household supplies zero hours to the labour market.

The agents in the model live for only finite time which leads to a nonstationary Bellman equation¹⁷ that the agents solve in each period $t$: (6) $\begin{array}{cccc}V(x_t,z_t,t)& =\underset{C_t,x_{t+1},L_t}{\max }u(C_t/m,L_t)+s_t\beta E_t[V(x_{t+1},z_{t+1},t+1)|z_t],& & \\ & 0\le L_t\le 1,C\ge 0,x_{t+1}\ge -B,x_T\ge 0& \\ & z_t=\pi (z_t)& & \end{array}$(6) Here, $L_t$ is potentially a vector when $n>1$. In this value function, we include a probability of survival $s_t$ to age $t+1$ which is age dependent. This ensures that when agents optimise their consumption and labour choices, they also factor in the probability of surviving to the next period. The $\beta$ in the equation is a discount factor needed to compute the present value of the next period’s expected value function given the employment transition matrix, $E_t[V(x_{t+1},z_{t+1},t+1)|z_t]$. The key to solving this set of equations is Bellman’s principle of optimality: if agents choose optimally between two adjacent periods, then one can solve for the lifetime utility, by sequentially solving each adjacent periods value function. Value function iteration is solving Equation (6) from the last period via backwards induction. This process yields a grid of consumption and labour choices.¹⁸

Note that while we do not implement a preference for leaving inheritance, agents will still leave assets behind due to the uncertainty of age at death. In the microsimulation model when an agent dies, their assets are distributed equally among surviving household members; otherwise, if they have no surviving household members, this just gets liquidated.

The parameters for the CES utility are taken from van de Ven (2017a) and reported in Table 1 for reference. Since van de Ven (2017a) fitted a similar utility function on the same survey, albeit an earlier round, we feel that the same parameter values can be retained. The one parameter that we change is the discount factor $\beta$ for couples for which we use 0.95 rather than 0.93. With this marginally higher discount factor, the second earner's labour force participation has no ‘islands’ on the grid. For more information on the parameters, please see van de Ven (2017a).

Table 1. Utility function parameters.

	Singles	Couples
Relative risk aversion, $\gamma$	1.55	1.55
Intertemporal elasticity, $ϵ$	0.6	0.6
Utility price of leisure, $\alpha$	2.2	1.034
Discount factor, $\beta$	0.97	0.95

2.3. Microsimulation

The behavioural decision to consume versus save is driven to a large extent by the desire to smooth consumption over time. The labour versus leisure choice on the other hand imposes a constraint on the degree to which this consumption smoothing is achieved. Due to the cost of working, as measured by the value of leisure, households will not change their labour choices freely in an effort to obtain a smooth consumption profile. While the behavioural side of the model is simple, we retain heterogeneity in agent characteristics and circumstances via microsimulation. An important innovation in our microsimulation model is that it is tied into projected economic growth (or contraction) over the short- and medium-run. This enables greater alignment of household income, wealth and consumption trajectories to reflect the effect of large economic shocks, for example, COVID-19 or the Global Financial Crisis, and of policy measures, such as the Universal Credit uplift of £20 per week for the poorest households.¹⁹ Sectoral growth rates are provided by a dynamic general equilibrium macroeconometric model – the National Institute Global Econometric Model (NiGEM) (NIESR, 2018) – together with an input-output based sectoral model NiSEM (National Institute Sectoral Economic Model) (Lenoël & Young, 2020).²⁰ Regional growth rates are provided by the model described in Section 2.1.

Note that since we take labour force participation from the life-cycle model, disposable income will be equivalent to the offered yearly wage, multiplied by the proportion of time spent working and the agent specific ${\kappa }_t$. This means that agents can choose exactly how much they want to work given their wage offer and assets. This can make computations cumbersome since small changes in labour participation influence disposable income that leads to changes in household assets which, in turn, influences agents’ optimal labour choices. As such, in our microsimulation model we therefore discretize labour decisions: (1) full-time employee if labour decision is above 0.3; (2) part-time employee if labour decision is above 0 but below 0.3; and (3) inactive if labour decision is zero.²¹ The cut-offs for the labour decisions were chosen so as to yield a split between full-time employees and part-time employees that closely matches the WAS data.²² Unemployed individuals have an optimal labour choice above zero, i.e., they are active, but they are not employed due to heterogenous personal circumstances.

The steps of the microsimulation model are described in Table 2. As highlighted in Figure 1, the microsimulation model has three key blocks: (1) Simulating non-structural outcomes; (2) Simulating labour outcomes; and (3) Imputing consumption. These three blocks are described next.

Table 2. Microsimulation algorithm.

Non-structural outcomes
	1.	Move period forward by a year
	2.	Multiply assets by interest rate $(1+r)$
	3.	Retirement
	4.	Death
	5.	Household Formation and Dissolution
	6.	Migration
	7.	Birth of children
	8.	Sectoral transition and growth rates
Labour outcomes
	9.	Match Microsimulations employment growth with regional models projected employment growth by firing/hiring agents
	10.	Match Microsimulations disposable income growth with regional models projected GVA growth by promoting/demoting agents (Note: employment match is rerun for each promotion/demotion as a change in household income can lead to new labour supply choices)
Impute Consumption
	11.	Use policy grid to impute consumption for each household

2.3.1. Non-structural outcomes

The microsimulation starts by simulating non-structural outcomes. These include birth, death, retirement, household formation (and dissolution), migration (between regions and immigration, but not emigration) and transitions between employment sectors. The first step in the microsimulation is to move forward every agent by 1 year followed by multiplying households’ assets by an interest rate, currently set exogenously at $(1+r)=1.05$.

The next step is to model retirement and death. Retirement is deterministic: once an agent becomes 69 years old, they move into retirement. Death is modelled by age and gender-specific death rates from life tables. Excess mortality from COVID-19 is explicitly modelled for the year 2020–21, but set to zero for later years.

Next household formation and dissolution is modelled. There are two ways a household can be formed: (1) a child turns 18 years old and is assigned their own benefit unit; or (2) cohabitation (finding a relationship match). For the first, the designation of a household in the model is based on the definition of benefit units in the UK tax and benefit systems. On reaching the age of 18, every individual forms their own benefit unit separately from their parents. This means that all households (actually benefit units) in the model comprise either a single adult or two adults in a relationship, potentially together with one or more children under the age of 18.

Cohabitation is based on UK WAS data. Single adult households are assigned a probability of looking for a match. Best matches are then attempted among the assigned individuals based on gender, age, location and wealth. Similar individuals are matched where possible. Nevertheless, not all individuals can find matches. In such cases, matches are attempted with all remaining singles in the sample. When matches are made, a reference adult, the individual with the higher wage offer, is assigned and everyone in the matched household moves to the location (region) of this individual.²³ Household dissolution is modelled in a simpler way. Couple households have a probability of divorcing every year. If a household dissolution occurs, assets are split in half and any children are assigned to the reference adult.

Migration between regions is next. Migration is determined by transition probabilities calculated from two rounds (round five and round six) of the UK WAS; currently, these transition probabilities are held fixed over time. As the economic circumstances differ across the different regions, migration allows households to change their ‘macrofoundations’. Immigration is modelled by adding an adequate small fraction of households each year, but currently there is no explicit emigration; this is retained for future work.

Childbirth is modelled by age-specific fertility rates, separately for single mothers and those in a relationship. Note that regional variation in fertility rates is currently not modeled.²⁴ The gender of the child is also allocated based on population statistics.

Before matching labour outcomes, sectoral growth rates and transitions are applied. NiSEM sectoral projections are used in this step to inflate wage offers of every individual by the sectoral growth rate. This induces some additional heterogeneity between households even if they inhabit the same region. The sectoral projections are also used to determine sectoral transitions. In our model, this is determined in two steps. First, the agent working in a specific sector in a given year has a probability of moving to a different sector the following year, where these transition probabilities are computed from the UK WAS data. The second step is to determine which sector the agent moves into. This is done by taking into account sectoral growth rates: the more a sector grows (relative to other sectors), the higher the probability that individuals will move into a job in that sector.²⁵

2.3.2. Labour outcomes

A key objective of the proposed method is to tie the microsimulation dynamics to the spatial/regional macroeconometric model projections. In essence, this introduces ‘macrofoundations’ to our model. In particular, we want regional employment growth in the microsimulation model to track regional employment projections of the macroeconometric model, and regional average wage growth to track growth of regional GVA. As such, after simulating non-structural outcomes of the households, we use the NiReMs growth rates to create projected employment and average wage projections for each region.

To match the employment projections of the microsimulation model to that of the spatial model, we first set regional employment numbers by multiplying the employment numbers per region in our sample with the predicted growth rates from our spatial model. Then, we allow firms to hire and fire individuals to calibrate microsimulation employment numbers to match employment numbers implied by the spatial model. To determine who gets fired and hired we take into account an agent’s continuous labour market choices. As such, an individual’s $L$ can be thought of as determining the probability of being hired and $\max (L_{\mathrm{Region}})\times L_{\mathrm{Discrete}}-L$ as probability of being fired.²⁶ As such, we treat $L$ not only as a measure of the fraction of time spent working, but also as a measure of job search intensity when the individual is unemployed. When an individual is hired, their ‘offered wage’ $w$ is determined by a reduced form Mincer-type model based on region, sector, and individual/household characteristics.²⁷ Note that this is the wage offered to the economic agent but not necessarily their disposable income.²⁸

For sectoral assignment of new hires, we consult NiSEM sectoral projections. In essence, sectors within a region with higher growth have a higher probability of hiring individuals. The same rule is used for firing individuals: sectors that grow less relative to the other sectors are more likely to fire individuals. If the pool of individuals to hire from is empty, which happens when the number of sampled households is low, the microsimulation uses a copy of one of the households working in the given sector.

While it is feasible to ensure that employment numbers in the microsimulation match projected employment of the spatial macroeconometric model, matching average wage growth is more challenging. This is because as wages are adjusted, households re-optimise their labour decisions which influences the average wage of the region. For this reason, we need to allow for some discrepancy between the two: ${\epsilon }_w$. Formally we want the difference between wage growth in the two models to be: (7) $\mathrm{\Delta }{\hat{w}}_{i,t}=\left|{\displaystyle \frac{{\sum }_{n=1}^{N_t}{\hat{w}}_{i,t,n}}{N_t}-{\displaystyle \frac{1}{f}\sum _{\tilde{t}=t}^f\left({\displaystyle \frac{\mathrm{GV}{A}_{i,\tilde{t}}-\mathrm{GV}{A}_{i,\tilde{t}-f}}{\mathrm{GV}{A}_{i,\tilde{t}-4}}}\right)\times {\displaystyle \frac{{\sum }_{n=1}^{N_0}{\hat{w}}_{i,0,n}}{N_0}}}}\right|<{\epsilon }_w$(7) where, $N_t$ represents the number of employed individuals in time $t$, with $t=0$ being the reference period taken from WAS. The time period of the simulated data is indexed by $t$, while the time period of the spatial models projected paths are indexed by $\tilde{t}$. Finally $f$ denotes the number of additional periods in the regional model on account of frequency difference. This is needed because temporal frequency of regional projections and the microsimulation’s frequency do not need to match. In our application, the macroeconometric model is at quarterly frequency and the microsimulation at annual frequency. In essence, the above equation takes the dynamics as described by the regional model, and projects it to the initial sample of households obtained from WAS. This projected path is then used as a guide for the microsimulation.

Importantly, these differences are region specific, which allows the spatial regional macroeconometric model projections to guide the microsimulation in the labour outcomes of the agents. The goal is to adjust households’ labour force status and wages in such a way as to move as close to the projected paths as possible. In particular, we want the absolute value of the difference to be below ${\epsilon }_w$. To achieve this goal, we demote or promote individuals until the two paths match.

We model decisions on promotion and demotion using the ${\kappa }_j$ parameter. Recall that in the life-cycle model the agent’s disposable income was ${\hat{w}}_{i,t}={\kappa }_j{L}_{i,t}{w}_{i,t}$. While the changes in ${\kappa }_j$ with an individual’s age are deterministic, the wage offered by their firm, $w_{i,t}$ is not. Instead, when the agent is employed, they are assigned ${\hat{\kappa }}_j={\kappa }_j$. This ${\hat{\kappa }}_j$ is not automatically updated every year which means that as the microsimulation progresses through time, differences between the two $\kappa$ terms start to emerge. Upon promotion/demotion, the agents ${\hat{\kappa }}_j$ is pushed up/down. Promotion/demotion probability is determined by ${\kappa }_j-{\hat{\kappa }}_j$: As this term becomes more positive, the agent is more likely to be promoted, as it becomes more negative, the agent is more likely to be demoted.

After every promotion/demotion step the household re-optimises their labour choices. It might happen that due to a promotion, one of the adults in the household opts to drop out of the labour market. Due to this, we also need to readjust the employment path with every promotion/demotion decision.

The advantage of using the ${\kappa }_j$ term to adjust average wage path is that this ensures the offered wage is unchanged. Because labour and consumption choices are optimised using the offered wages, we can adjust the path of each region sequentially, which speeds up computation time.

To ensure that ${\kappa }_j$ does not become unreasonably high, we limit $\kappa \in [0,2.5]$. Further, to preempt a situation where every individual in the region gets its ${\kappa }_j$ value updated to the maximum, we introduce a check: if the region takes too long to optimise, we reset every individuals ${\kappa }_j$ and inflate/deflate the wage offers of everyone in the region by $5\text{\%}$, and start promoting/demoting again. In our experience, this wage offer inflation is only needed when the number of households sampled is low.²⁹

2.3.3. Consumption

The final block of the microsimulation is to impute consumption values for every household. The amount of money a household can contribute to consumption is the sum of assets they had last period with interest $((1+r)x_{t-1})$, the household’s disposable income $({\hat{\kappa }}_{1,j}{L}_{1,t}{w}_{1,t}+{\mathbb{I}}_{n>1}{\hat{\kappa }}_{2,j}{L}_{2,t}{w}_{2,t})$, pensions and benefit payments.³⁰ Together, these terms give the assets available to the household to make consumption decisions. The policy function also needs the reference adult’s age and the household’s composition (number of adults and children) to impute consumption.

While the policy function used comes from a simple life-cycle model which uses representative agent framework, we model heterogeneity in circumstance with microsimulation. As such the consumption profiles of households over time become richer: they are driven by macroeconomic changes modelled by the spatial model, as well as micro-level changes modelled by transition probabilities. This enriches the potential to assess the impact of welfare policies on a household’s consumption and labour choices.

The proposed methodology comes at a cost: the model does not explain behavioural differences or changes. As opposed to more popular heterogeneous agent modelling frameworks (such as occasionally binding constraints in DSGE models), the proposed method does not explain behavioural differences in consumption. Instead, it relies on the heterogeneity in household circumstances to drive differences in consumption profiles. As such, the macro guided microsimulation framework is useful for policy work, where the analysis is focused on household consumption against changing macroeconomic and tax/welfare policy environment, but it lacks the capacity to provide behavioural explanations. This also highlights an avenue where the model can be further improved: by allowing for heterogeneity in behaviours as well. Nevertheless, the key benefit of the proposed methodology is that it allows for household level analysis of the impact of macroeconomic shocks.

Agent-based models (ABM) provide an alternative, but closely related, approach to obtain consumption profiles (Richiardi, 2014). ABM accounts for network externalities between agents by explicitly modelling them, but dynamic microsimulation also accounts for them via triangulation across different characteristics through representative random sampling from the population. As such, the distinction between ABM and dynamic microsimulation is better thought of along the lines of practical implementation. In this model we rely on UK WAS to provide a representative sample of households, which yields a credible random sample of the population.³¹

3. APPLICATION TO UK DATA AND CONTEXT

To showcase the model, we draw a random sample of 5000 UK households and project their outcomes through the COVID-19 shock. When the COVID-19 pandemic hit economies and societies around the world, it exacerbated inequalities particularly in regions, demographies and communities that were already ‘left behind’. This made it important to design appropriate policies in order to address the distributional consequences of the COVID-19 shock, which a microsimulation model like ours is intended to deliver.

In an effort to restore the economies back to pre-pandemic dynamics, policymakers have focused heavily on aggregate macroeconomic outcomes. This has been inadequate, as evident in the United Kingdom (UK) government agenda focus shift to ‘building back better’ and ‘levelling up’. While the economy’s aggregate recovery is no doubt important, an exclusive focus on the aggregate can obscure some impacts of the COVID-19 crisis and policy responses to it. In essence, households in different regions and with different levels of wealth were not affected to the same degree by the COVID-19 shock. This meant that some households were able to weather the adjustments imposed by the COVID-19 economy without major problems, while other households needed to liquidate part of their wealth to maintain consumption or even ended up sliding into destitution (Bhattacharjee & Lisauskaite, 2020). As such, ‘COVID-19 was never the great leveller’ (Pabst, 2020) – it has exacerbated economic inequalities in the UK in a way that can be missed by exclusively focusing on aggregate outcomes.

Nevertheless, the policymakers had an impossible task: household level information was not available to them during the pandemic. This is where our proposed methodology can aid policymakers in uncertain times: using the macroeconomic projections, the model is able to simulate heterogenous households facing these macroeconomic circumstances. We apply our proposed model to the UK to better understand the impacts of the COVID-19 shock and policy responses upon regions and society. At the start of 2020, the UK government introduced temporarily increased welfare payments (the Universal Credit uplift) for very poor households.³² Together with an employment protection scheme (UK Coronavirus Job Retention Scheme, commonly known as the ‘furlough scheme’), enhanced Universal Credit (UC) payments³³ helped shield extremely poor households from the most adverse effects of the pandemic. Note that the furlough scheme is already accommodated in the regional macroeconomic and microsimulation models by inducing a temporary (time-contingent) disjuncture between productivity and wages. The UC uplift was discontinued in September 2021, and the central counterfactual exercise we report are the distributional and regional implications of continuing this payment beyond the period it was implemented. It is also useful to compare outcomes in the factual relative to a counterfactual where the economy was not hit by the COVID-19 pandemic shock.

Figure 3 shows the projected wage dynamics of the macroeconometric model and the microsimulation model. The figure shows two types of microsimulated wage dynamics: one where the ${\epsilon }_w$ is set to a low number to ensure the wage dynamics follow the macroeconometric model more closely, and one where ${\epsilon }_w$ is set to $\mathrm{\infty }$ (i.e., only employment dynamics are made to match). The figure reveals that it is not enough to only match employment outcomes, one has to also match regional wages, otherwise the microsimulated sample’s wages deviate from the macroeconometric projected wage path too much. The figure shows that using small ${\epsilon }_w$ values can help guide the microsimulation model obtain dynamics which align with macroeconometric models. The ‘loose’ microsimulation also shows that with less stringent guidance, the model would require far more time to recover after the COVID-19 shock. In fact, the ‘loose’ model projects far stronger adverse impacts of macroeconomic shocks. From this we infer that heterogeneity exacerbates the impacts of global shocks in a way that a representative agent’s rational expectations model would not. This is because rational agents would anticipate a reversal of shocks (in expectation), and hence their behavioural responses would be moderated (Kaplan et al., 2018; Moll et al., 2022). Given this, it is not surprising that all the regions are below the projected path even for the ‘tight’ microsimulation in 2024. Note that if the differences in the projected paths between the ‘tight’ microsimulation and the macroeconometric model were simply on account of sampling, we would expect some of the regions to be above the macro path. This highlights that the distributional impacts of such adverse shocks have medium- to long-term effects, pulling the average wage dynamics lower for all the regions.³⁴

Figure 3. Wage dynamics.

The average wages of the different regions over the simulated time-frame for the macroeconometric model and 2 microsimulated samples. The ‘loose’ microsimulation gives consistently lower wage dynamics. The ‘tight’ microsimulation is closer to the macroeconometric projection, but even there the simulated path is below the macroeconometric model in the medium-run.

As opposed to the macroeconometric model, the microsimulation model allows one to look at the consumption and labour choice distribution of households over time. We examine the consumption distribution of the tight microsimulation from Figure 3 and compare it with a microsimulation (with the same ${\epsilon }_w$ settings and same initial sample of households) where the uplift in universal credit was cut earlier. In particular, we are interested in the distribution of consumption and labour choices for young adults (ages 25 and below) with low assets (less than £20,000, which is fewer assets than the median household disposable income). We note that these distributions are for the year 2021–2022, i.e., the fiscal year the COVID-19 uplift in Universal Credit was withdrawn.

In Figure 4, we plot kernel densities of consumption distribution for poor households (in terms of wealth) by region. The central conclusion is that without extended UC we find more individuals at the lower end of the consumption spectrum. Importantly, an added insight that our regional macroeconometric model provides is to highlight that not all regions were affected equally. Our analysis shows that low asset households in the North East, Yorkshire and the Humber, Wales, and Northern Ireland were hit particularly hard, with significantly more households pushed into consumption of £5000 per annum or less as the UC uplift is not extended. Additionally, London and Scotland also exhibit notable differences in consumption behaviour compared to the other regions. In particular, London features more low asset households ‘bunching’ around £10,000 in consumption and fewer households consuming less, when the UC uptick is maintained. The consumption behaviour difference in London is particularly insightful, seeing how it is identified as the central node in the UK network (Bhattacharjee & Holly, 2013). Scotland shows a different consumption behaviour, with its low asset young household consumption distribution being smoother when the UC uplift is maintained. This is likely on account of Scotland’s employment figures rebounding quicker than the other UK devolved nations and English regions (Bhattacharjee et al., 2022). The figure reveals how even with the ‘tight’ microsimulation, there are significant regional differences in consumption behaviour. As such without maintaining the UC uptick, there are likely two types of low asset young households: ones who were able to obtain new employment after the COVID-19 recession, and ones that were unable to do so. In this regard, maintaining the UC uplift would have meant a more equitable recovery from COVID-19 in Scotland. From a policy maker perspective these differences are important as they not only highlight how a change in national welfare policy can have very distinct regional consequences, but also provide an estimate about how much the different households in the different regions are affected.

Figure 4. Consumption densities for low asset households per region (consumption £’000s).

Consumption densities for the different regions show that the impact of no UC benefit uplift extension has a non-uniform impact on the regions: low asset households in the North East, Yorkshire and the Humber, Wales, and Northern Ireland were hit particularly hard, with significantly more households pushed into consumption of £5000 per annum or less.

Figures 3 and 4, showcase how the two building blocks (spatial modelling and microsimulation) yield the potential for rich inference. The spatial model informs the researcher about heterogeneity in ‘macrofoundations’ while the microsimulation captures (and models) heterogeneity of household characteristics. Accounting for both types of heterogeneity yields a model that is capable of giving answers pertaining to household level distribution. Without tying the life-cycle model to the spatial dynamics with microsimulation, the consumption differences revealed in Figure 4 would have been missed.

The finding in Figure 4 that the impact of the COVID-19 shock is not uniform across the regions entails that regional consumption distribution is heterogenous. This has significant implications for the new economic geography literature, where products are more accessible to core regions. In essence, our findings suggest that such disparities have widened during the COVID-19 crisis. This further exacerbates low-asset households’ consumption.

Our microsimulation model allows individuals to make consumption-saving as well as labour-leisure decisions. This allows us to examine individuals’ labour decisions. To this end we present the proportion of time spent on the labour market in Figure 5. The x axis of the figure shows the proportion of time spent on labour market activities,³⁵ while the y axis measures the proportion of households (with low assets) who choose the given amount of labour hours. Ideally, it is in the best interests of society that young adults go through education so that their lifetime income profiles improve, i.e., young adults ideally spend a lower proportion of time working. However, the figure shows that without the additional welfare support in maintaining the UC uptick, young adults’ labour hours shift upwards dramatically across all regions, highlighting that they are more likely to be pushed into full-time work. Note, however, that choice for educational attainment is not modelled explicitly in the current microsimulation. Importantly, the difference between the counterfactuals in labour choices is even starker than consumption which is not surprising given that the utility function is set up in a way that encourages households to smooth consumption over time.

Figure 5. Labour choice histogram for low asset young adults per region (proportion of time compared to highest Labour hour).

Labour choice histograms for the different regions show that without the additional welfare support in maintaining the UC uplift, young adults’ labour hours shift upwards dramatically across all regions, highlighting that they are more likely to be pushed into full-time work.

4. CONCLUSION

In this paper, we propose and present a new model, NiReMS (National Institute Regional Modelling System), as a synthesis of a spatial regional macroeconometric model and dynamic microsimulation to account for heterogenous agents. Using this model, we can create counterfactual scenarios to analyse distributional and regional impacts of aggregate (global) and local shocks together with a menu of policy measures to mitigate against such shocks. We consider an application where the microsimulation exercise creates one longitudinal pseudo-panel dataset for each scenario modelled, namely the factual (where the economy has been hit by the pandemic shock and enhanced Universal Credit (UC) is withdrawn in September 2021); and a counterfactual where enhanced UC is not withdrawn.

Unsurprisingly, aggregate consumption is lower for the case when the UC benefit uptick is not maintained. Importantly, looking at the low asset households, we can see clearly that the early termination of the COVID-related uplift in UC benefits has led to more households that are consuming less. Furthermore, the impact is not uniform across the regions, with the North East, Wales and Northern Ireland seeing significantly more households pushed into consumption of £5000 per annum or less. Additionally, London, Yorkshire and Humber, and Scotland (along with the aforementioned regions) see comparatively more households consume less than £10,000 per annum when the UC benefit uplift is not maintained. This highlights the way microsimulation, informed by a spatial regional macroeconometric model, is capable of imputing household consumption in a manner that inherently incorporates heterogenous agents.

As noted earlier, this is an initial step towards the more complete integration of a national macroeconomic model with a regional modelling system that addresses both spatial and agent heterogeneity. As several other analysts have noted, there is a parallel need to incorporate firm heterogeneity. This can be accomplished, in part, by the development and integration of interregional input-output tables with the spatial econometric system that has been used in this paper. One important methodological advance would be the exploration of the way that feedback effects that are derived from the input-output system can be harnessed into the spatial econometric system. An initial exploration was provided by Kim and Hewings (2012a, 2012b), integrating a metropolitan-wide econometric input-output model with a spatial econometric model at the community level in which a system of equations links aggregate population and employment with formal consideration of the spatial spillover effects.

In addition, agent heterogeneity also has an important activity analysis dimension; following the initial work of Batey and Madden (1981), the microsimulation model used here can be expanded to capture alternative participation in the labour market – e.g., the increasing cohort of retirees accounting for an estimated 20% of the total population by 2030. Also important in this context is modelling breaks from employment for retraining – an increasingly critical element of achieving better jobs-skills matches – aligned to local needs and the diversity of individuals/households. In addition, access to the WAS will also provide an indication of the speed of recovery by households of different income and asset levels, enriching the quality of forecast of the trajectory of the macroeconomy.

There is a further opportunity, once the macro-spatial integration has been completed, to explore the impacts of addressing spatial heterogeneity on macroeconomic outcomes. As Kim and Hewings (2012a, 2012b) found, admittedly for a two-level system with fewer than 10 million inhabitants, limitations at the lower (community) level on the ability to house the expected population increase generated by a macroeconomic model created a difference of greater than 5% in the forecast population beyond 2040. In the UK context, regional variations in recovery could generate an important impact on macroeconomic outcomes.

One important and exciting aspect of ongoing and future research is the integration of spatial econometric and interregional input-output analysis to provide micro-macro feedbacks. Following insights from inter-sectoral context, this has the potential to capture consumption variation in macroeconomic models much more accurately as well as amplified effects of aggregate shocks. Finally, while our spatial weights here are freely estimated, one could well use trade estimates from the SEIM system (Carrascal-Incera & Hewings, 2022) at the ITL 2 level and aggregate to the higher level. This might provide us with some quasi-robustness checks of spatial econometric estimates versus input-output derived estimates and provide a better integration of the two approaches.

Note that, since the number of spatial units is small (twelve regions), our current work did not require an explicit RAS or Miyazawa type approach (Carrascal-Incera & Hewings, 2022; Haddad et al., 2021). Future work will proceed towards greater spatial granularity going down to ITL 2 and ITL 3 levels. All of these developments will enhance the understanding of spatial and individual inequality in the UK and provide a much richer set of analytical tools on which to base national and regional policy initiatives.

ACKNOWLEDGEMENT

The authors would like to thank Robert Kirkby for helping understand the nuances of the VFI toolkit, and Jagjit Chadha, Elena Lisauskaite and Max Mosley for assistance and collaboration on aspects of the work. Special thanks are due to Monojit Chatterji, Luisa Corrado, Nicolas Debarsy, Huw Dixon, Paul Elhorst, Etienne Farvaque, Jan Fidrmuc, Hande Küçük, Mark Schaffer, two anonymous referees and the audience at Laboratoire de Recherche LEM (Lille) and Université d’Évry Val-d’Essonne for comments and suggestions at different stages of this work. The authors would like to thank the National Institute of Economic and Social Research (NIESR, UK) for its encouragement to trial early findings of the research as part of the NIESR’s quarterly Economic Outlook. UK Data Service provided kind access to the UK Wealth and Assets Survey (WAS) data. The work is part of NIESR’s NiReMS (National Institute Regional Modelling System). The usual disclaimers apply.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s). The findings and conclusions in this publication are those of the author(s) and should not be construed to represent any official USDA or U.S. Government determination or policy.

Additional information

Funding

Tibor Szendrei is grateful to the Economic and Social Research Council (ESRC, UK) for awarding him a PhD studentship and, together with Heriot-Watt University and the National Institute of Economic and Social Research (NIESR, UK), for facilitating internship/secondment at NIESR under whose auspices this research was conducted.

Notes

1 Donaghy (2021) has provided a valuable contribution that explores the implications of the Rebuilding Macroeconomic Theory Project for regional science research.

2 ITL is the geocode standard for referencing regions within the United Kingdom. Currently, it aligns exactly with the previous NUTS (nomenclature of units for territorial statistics) subdivisions.

3 Hewings and Parr (2007) provide an example of the complexity of flows of goods and services, journey to work, income and consumption flows within a metropolitan region.

4 This is not surprising since the objective of dynamic microsimulation is often to analyse the lifetime impacts of policies rather than to provide medium-run macroeconomic forecasts.

5 Since our policy focus here lies on understanding the impact of welfare policy on individuals and households, we model heterogenous individuals and households. However, the approach itself is more general and can accommodate firm-level heterogeneities. This will be important in understanding the impacts of an industrial or job-skills policy. This is retained for future work.

6 We note that price differentials will always be small as one goes down to finer spatial scales.

7 Note that since we do not explicitly model capital, the spatial correlation of capital formation remains in the spatial error terms. For more information, see Appendix A.2.

8 Spatial weights based on the gravity model is a potential alternative. However, given the complex nature of spatial interactions implied by our regional macroeconomic model, we prefer an estimated spatial weights matrix.

9 We have further periods of data, all the way to 2021Q4, that are not used in the estimation. They are used to verify out-of-sample performance of the estimated model. The reason we use data until 2017Q4 is because our microsimulation exercise is based on survey data for the financial year 2017–18 – April 2017 to March 2018. We make a simplifying assumption that the same spatial weights matrix applies to all the four regional macroeconomic variables, but with different spatial autoregressive parameters.

10 Note that it is possible to swap the life-cycle model to an OLG model. We leave for future research to tie ‘macrofoundations’ to an OLG framework based microsimulation model.

11 Note that borrowing potential can be accommodated in the model by simply allowing for negative assets.

12 Note that agents have only a very small chance of living up to age 105 as there is a probability of survival built into the utility function as described in Section 2.2.2,

13 Pensions are currently set at UK average as estimated from WAS. Modelling heterogeneity in pensions is retained for future work.

14 This does not affect findings much and, if one wishes to define reference adults in a different way, this parameter can be set to 1.

15 We will later discuss how we discretise the active and employed workers into full-time and part-time workers.

16 This is similar to multiplying the policy grid with the growth rates akin to Gourinchas and Parker (2002).

17 Note that the equation is a contraction mapping when$\beta <1$, which means that the simulation gets closer to stationary as the years alive increases.

18 Some of the policy functions generated by the life-cycle model are presented in Appendix A.3.

19 An important motivation of developing this new microsimulation model was to enable the study of the impact of the COVID-19 shock and corresponding welfare measures. The NIESR has a previous microsimulation model LINDA (lifetime income distributional analysis) (NIESR, 2016; van de Ven, 2017a) which did not allow such alignment to short- and medium-run macroeconomic projections.

20 NiSEM projects growth rates for nine sectors while WAS has 10 sectors where employed persons work. We match the nine NiSEM sectors to the closest corresponding WAS sector and take the average growth rate for the remaining WAS sector. While this is not a perfect match, it is adequate to capture sectoral differences experienced by households.

21 Households also potentially receive benefit payments from the state, the value of which are means tested, and depend on household income and demographic composition. This includes unemployment and child benefits determined by current UK government provisions.

22 However, one can choose alternate cut-off points, for example, to match aggregate unemployment dynamics. This modelling choice has only marginal impact on our empirical findings.

23 The above matching model is restrictive but is adopted without prejudice or ascribing value. Alternate, more liberal matching models based on fuzzy matches can and should likely be used in future work.

24 This can be done following Zhang et al. (2021). We leave this extension for future research.

25 One can make the sector decision more elaborate incorporating it into a reduced form discrete choice model of sectoral choice, subject to education, household characteristics, age, location and other determinants. In future developments, we plan to include occupational or skills information or characteristics since these attributes may enhance or dampen mobility between sectors and regions.

26 Multiplying the maximum continuous $L$ with the discretised $L_{\mathrm{Discrete}}$ is necessary otherwise part-time workers would always be fired.

27 It is possible to make this Mincer-type wage determination equation as elaborate as desired, but one has to make sure that determinants are also simulated in the microsimulation.

28 We retain introducing wage-curves akin to Blanchflower and Oswald (1995) for future work.

29 One can speed up wage dynamics matching by first inflating wage offers of each region by the deviation from the macro-model projections. This will lead to each household re-optimising its labour choices, and promotion/demotion will commence to ensure the projected paths remain close. If one is interested in setting a low ${\epsilon }_w$, then it is advised to do this step before promotion/demotion.

30 Benefits are calculated according to current UK rates.

31 Further discussion about sample choice is included in Appendix A.1.

32 Means-tested additional welfare payments of £20 per week for households (benefit units) whose weekly (household composition adjusted) income fell below a minimum subsistence threshold (Bhattacharjee & Lisauskaite, 2020).

33 See https://lordslibrary.parliament.uk/universal-credit-an-end-to-the-uplift/

34 This also motivates further research in this area, where the distributional effects of the microsimulation inform the macroeconomic model, to obtain more refined medium- to long-term forecasts.

35 Relative to the highest labour hour observed. This is to ensure that all regions are on a scale of 0 to 1.