Data and Calibration | RDP 2025-04: HANK and the Transmission of Shocks to Demand and Supply

RDP 2025-04: HANK and the Transmission of Shocks to Demand and Supply 4. Data and Calibration

Karsten Chipeniuk, Gulnara Nolan and Matt Nolan

June 2025

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In a typical heterogeneous agent model, the income process is exogenously specified while the wealth distribution arises endogenously in general equilibrium. A key point of the calibration, then, is to use empirical sources to calibrate the distribution of income in such a way that the resulting wealth distribution is broadly similar to that found in the data. In this study, we follow the approach pioneered by Guvenen et al (2015) and Kaplan et al (2018).

Specifically, we use microdata from the Australian Taxation Office's (ATO) Taxation statistics, and in particular individual tax returns, to gather relevant information on earnings and income distributions. This dataset contains information on employed working age (18–65 year old) individuals, whether they work part-time or full-time. We focus on the gross earnings indicator series derived from individual income tax returns, which includes income from all sources in a given year. We construct changes in log earnings at one-year (2018–2019) and five-year (2014–2019) horizons, dropping individuals who leave the sample, for example, because they become unemployed or retire during the intervening years. We then construct moments of these changes, displayed in Table 1.

Table 1: Moments of Log Earnings Changes
	Observations	Mean	Standard deviation	Skewness	Kurtosis
2014–2019	8,162,462	0.189	0.981	−0.06	11.63
2018–2019	10,062,286	0.070	0.663	−0.08	21.11
Source: Australian Taxation Office.

We focus on the first four moments of log earnings changes. These include the mean, standard deviation (the width of the distribution), skewness (whether the distribution lies more to the right or left of the mean), and kurtosis (heaviness of the distribution tails). While these differ from the moments used in the cited literature,^[1] as we will see below, we are nonetheless able to capture several features of the Australian distribution of wealth in our model distribution.

Having estimated these moments in the data, we apply the method of simulated moments to choose the parameters for an income process such that the moments simulated from the process match those found in the data. In particular, we assume that the logarithm of individual productivity log(z_t) can be decomposed into two components,

\log (z_{t}) = z_{1, t} + z_{2, t}

where each component follows the stochastic specification

d z_{j, t} = - β z_{j, t} d t + d J_{j, t}, j = 1, 2

Here the first term represents a mean reversion (drift) element, while the second term reflects Poisson distributed jumps. That is, jumps occur such that the number in a given time interval are given by a Poisson random variable,

| {0 \leq t \leq T : d J_{j, t} \neq 0} | \sim Poisson (λ_{j} T), j = 1, 2

while the sizes of the jumps are normally distributed:

(d J_{j, t} | d J_{j, t} \neq 0) \sim Normal (0, σ_{j}), j = 1, 2

We then choose the parameters $β_{j}, λ_{j}, σ_{j}, j = 1, 2$ according to the following procedure, given the moments m_k, k = 1,...,4 in Table 1. First, we fix a simulation horizon T_h and guess values for the parameters. Given these parameter values, we simulate the above specification, drawing the number of jumps, the timing of the jumps, and the jump sizes dJ_j,t according to the appropriate Poisson, uniform, and normal distributions. We then set

(25)

z_{j, t} = z_{j . t}_{- Δ t} - β z_{j, t - Δ t} Δ t + d J_{j, t}

for each time t, where $Δ t$ is the size of the time step in the simulation. We then set $z_{t} = \exp (z_{1, t} + z_{2, t})$ and calculate the moments of z_t analogously to those found in Table 1. We then evaluate the sum of squared errors between model simulated moments and those found in the data, and update our parameter guess unless the sum of squared errors is sufficiently small.

While this procedure results in a jump diffusion process which matches dynamic moments of the income distribution, it is still not suitable for use in the HANK model. The reason being that, in contrast to the calibrated process, the exogenous process specified for the HANK model is a discrete state continuous time Markov process in which transitions between states are Poisson distributed. We therefore once again follow Kaplan et al (2018) and repeat the method of moments procedure to construct such a Markov process. In this context, the calibrated parameters $β_{j}$ and $σ_{j}$ are used to construct the transition matrices for the process, while the width and spacing of the income states are selected via the method of moments.

The remaining model parameters are shown in Table 2. On the household side, we choose the continuous time rate of preference such that utility one-quarter-ahead is discounted by a factor of 0.986. We set the coefficient of relative risk aversion and the reciprocal of the Frisch elasticity of labour supply to standard values of 2. We set the disutility weight on labour so that households on average spend a third of their unit time endowment working. We choose average individual productivity to have approximately a unit of output. The borrowing constraint is set to −0.25.

On the firm side, we choose price stickiness to give a slope of the Phillips curve equal to 0.1. We also set the elasticity of substitution between monopolistic goods to give a steady-state mark-up of 11 per cent.

Table 2: Model Parameters
Parameter	Value	Description	Target
Households
$ρ$	0.014	Discount rate	Quarterly factor 0.986
$σ$	2	Risk aversion	Standard value
$ψ$	24.3	Disutility weight	Hours ≈ 1/3
$φ$	2	Inverse Frisch elasticity	Standard value
z	3	Labor efficiency	Efficiency hours = 1
Intermediate goods
$θ$	100	Price stickiness	Phillips curve slope = 0.1
Final goods
$ε$	10	Goods elasticity of substitution	Steady-state mark-up = 11 per cent
Fiscal policy
$τ$	0.25	Income tax rate	Efficiency labour income tax rates
$γ_{T}$	0.06	Transfers/GDP	Ahn et al (2018)
$γ_{G}$	0.01	Government expenditure/GDP	Positive bond supply
$α_{F}$	1.5	Debt stability coefficient	Passive fiscal policy
Monetary policy
$α_{M}$	1.25	Taylor coefficient	Active monetary policy
Shocks
$ρ_{M}$	0.4	Monetary policy shock persistence
$σ_{M}$	0.0071	Monetary policy shock standard deviation	Christiano, Eichenbaum and Evans (1999)
$ρ_{F}$	0.8	Fiscal shock persistence
$σ_{F}$	0.005	Fiscal shock std dev
$ρ_{Z}$	0.9	Total factor productivity persistence
$σ_{Z}$	0.005	Total factor productivity std dev
$ρ_{G}$	0.8	Govt consumption shock persistence
$σ_{G}$	0.002	Govt consumption shock std dev
$ρ_{j}$	0.5	Other shock persistence
$σ_{j}$	0.006	Other shock std dev

On the policy side, we set the tax on labour income to 0.25, close to the average rate in Australia. Closing the model requires us to specify steady-state targets for lump sum transfers and government expenditures as a per cent of GDP. The first of these is set to 6 per cent following Ahn et al (2018). The latter is set to a relatively low value of 1 per cent, which ensures that the bonds are in positive net supply in the steady state. The Taylor coefficient is set to 1.25, while the government responds more than one-for-one to fluctuations of debt away from the steady state. Shock persistences and standard deviations are ad hoc, with the exception of the monetary policy shock whose standard deviation is taken from Christiano et al (1999).

Table 3 shows the fit of the endogenous model distribution of net worth to the empirical distribution in Australia. Broadly speaking, the model is able to fit a variety of characteristics of the wealth distribution. For interest, also included are statistics for New Zealand and the United States, from which we see that Australia's distribution is similar to New Zealand's, but quite different to that in the United States.^[2]

Table 3: Model Wealth Distribution Summary Statistics
Share held by quintile
Quintile	Australia		New Zealand		United States
Quintile	Data	Model	Data	Model	Data	Model
1	0.7	0.6	−0.1	0.6	−0.9	−0.4
2	4.8	4.8	2.7	3.8	0.8	0.4
3	11.3	13.2	8.7	11.6	4.4	3.5
4	20.5	26.6	18.7	24.4	13.0	14.8
5	62.8	54.7	69.9	60.0	82.7	81.7
Wealth Gini	0.61	0.54	0.68	0.60	0.77	0.76
Sources: Australian Bureau of Statistics; Krueger, Mitman and Perri (2016); Statistics New Zealand.

Footnotes

In particular, Kaplan et al (2018) use seven moments, namely the variances of log earnings, their one-year change, and their five-year change, the kurtosis of their one-year and five-year changes, as well as the fraction for which the one-year change was less than 10, 20, and 50 per cent. [1]

Results given for the United States use the productivity process estimated in Kaplan et al (2018), while those for New Zealand are taken from Chipeniuk and Nolan (2022). [2]