Essays on macroeconomics and household heterogeneity
Keywords: Household Consumption
Heterogeneous Households
Leverage
Housing Demand

The goal of this thesis is to explore how household heterogeneity propagates and amplifies macroeconomic shocks within the economy using both economic theory and empirical data.
The assumption of a single "representative" household has been a mainstay of macroeconomic research over the past half-century. However recent work suggests that not only is there a considerable degree of heterogeneity among households, but that these differences have a significant impact on a range of macroeconomic issues such as the e?ectiveness of fiscal stimulus (Kaplan et al., 2014; Broda and Parker, 2014), monetary policy (Auclert, 2017; Kaplan et al., 2016), the housing market (Attanasio et al., 2012; Blundell et al., 2008; Guerrieri and Iacoviello, 2017; Ngai et al., 2016; Mian et al., 2013), consumption (Ahn et al., 2017a; Blundell and Preston, 1998; Campbell and Cocco, 2007; Engelhardt, 1996) and employment (Ravn and Sterk, 2016; McKay and Reis, 2016; Abo-Zaid, 2013a) among many others. This literature has highlighted how households respond differently to aggregate shocks or changes in policy and how simply aggregating or averaging across them can obscure important truths about the economy.
However, relaxing this assumption poses several challenges. The first is choosing the degree and manner in which households di?er. While in reality households can differ along many dimensions, in practice it is only feasible to include a small number of these in any given model. Thus one must choose the most salient dimensions along which households differ and the structural reasons behind such differences. For example, when examining the dynamics behind the housing market is it important to model differences in income, wealth, age, tastes or composition? No single model will be able to incorporate all these differences and so it is incumbent on researchers to proritise and justify their choices. In this thesis I will show why household heterogeneity in the housing and labour markets is both empirically relevant and an important consideration when considering the problem of optimal policy.
The second challenge is a computational one. While models can be structured such that differentiated households make identical decisions, in general these differences will cause choices, and thus outcomes, across households to diverge. This produces a non-degenerate distribution of households across their specific state variables. This raises the problem of how this potentially infinite-dimension distribution is incorporated within the model. Previous literature has developed a range of options for handling this problem including approximating the distribution with a small handful of moments (Krusell and Smith, 1998) and approximating it with projection and perturbation methods (Reiter, 2009). In this thesis I will outline two different methods for dealing with this computational problem. The first, set out in Chapter 1, shows how market clearing prices can be feasibly calculated by aggregating over the distribution of households. The second approach involves simulating the model with aggregate uncertainty using numerical derivatives based on impulse response functions.
The first chapter of this thesis will examine how heterogeneity in wealth and income affects households' decision to purchase housing and the implications for their consumption of non-durable goods. It constructs an Aiyagari-Bewley-Huggett model in which households are subject to an idiosyncratic income shock and thus hold different amounts of liquid wealth and illiquid housing. I then evaluate how the anticipated changes in household debt associated with the leveraged purchase of housing affect the consumption of non-durable goods. I show that the differences in income and wealth lead to significant variance in marginal propensities to consume among households. I show that households that are saving for a house deposit can have negative marginal propensities to consume as they lower their consumption in anticipation of being credit constrained as the probability that they will buy a house increases. This result has important implications for the design of fiscal policy, as it shows that payments to first time home buyers, which was a common policy response to the Global Financial Crisis, can lead to falls in aggregate consumption rather than stimulating growth.
The second and third chapters examine how the combination of heterogeneity in workers' wages and downward nominal wage rigidity affects the transmission and design of different aspects of monetary policy. In Chapter 2 I show that in this environment there is a trade-off between a higher rate of inflation which gives workers more flexibility when setting real wages, at the cost of greater price dispersion in the goods market. After outlining a numerical algorithm to solve the model I use micro-data on the distribution of workers' change in wages to calibrate the nominal wage rigidity. I show that downward nominal wage rigidities bend the Phillips curve constraining the inflation rate from falling in times of low demand. This indicates that an inflation rate that is only moderately below its target can mask large falls in the output gap. Finally, I find that the monetary policy rule can be implemented by placing a higher weight on wage inflation, relative to a symmetric nominal wage rigidity. In Chapter 3 I discuss how downwardly rigid wages can amplify or mitigate the welfare loss caused by the zero lower bound on nominal interest rates and how this varies with the parameterisation of the model. I find that the optimal rate of inflation is increased by the presence of both nominal interest rate and wage rigidities, when modeled either separately or in tandem, and is 3 per cent in the baseline calibration of the model.