# Assessment of Policy Changes to Means-Tested Age Pension Using the Expected Utility Model: Implication for Decisions in Retirement

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## Abstract

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## 1. Introduction

## 2. Model

#### 2.1. Utility Functions

- Consumption preferences: It is assumed that utility comes from consumption exceeding the consumption floor, weighted with a time-dependent “health” status proxy6. The utility function for consumption is defined as:$${U}_{C}({C}_{t},{G}_{t},t)=\frac{1}{{\psi}^{t-{t}_{0}}{\gamma}_{d}}{\left(\right)}^{\frac{{C}_{t}-{\overline{c}}_{d}}{{\zeta}_{d}}}{\gamma}_{d}$$
- Bequest preferences: Utility is also received from luxury bequest, where the utility function for bequest is then defined as:$${U}_{B}({W}_{t},H)={\left(\right)}^{\frac{\theta}{1-\theta}}1-{\gamma}_{\mathrm{S}}.$$Note that the inclusion of housing in the bequest function simply adjusts the threshold for luxury bequest, as the allocation to housing is a one-off decision and remains constant after retirement. Because of this, if the retiree is a homeowner, then the marginal utility of bequest will be lower for a given liquid wealth; hence, additional consumption is preferred. The optimal consumption with respect to liquid wealth will have the same shape, although be slightly higher with higher house values. This justifies the simplification in Andreasson et al. (2017), where housing has been dropped from the bequest, as it is conceptually the same and avoids an extra state variables, while the impact on optimal control is marginal.
- Housing preferences: The utility from owning a home comes in the form of preferences over renting, but is approximated by the home value. The housing utility is defined as:$${U}_{H}(H,{G}_{t})=\frac{1}{{\gamma}_{\mathrm{H}}}{\left(\right)}^{\frac{{\lambda}_{d}H}{{\zeta}_{d}}}{\gamma}_{\mathrm{H}}$$

#### 2.2. Policies and Scenarios

- Policy 1, Pre-January 2015 (PRE2015): The first policy reflects the means-test and policy rules prior to 1 January 2015, which is what the majority of Australian retirees are being tested under. Any drawdown from the Allocated Pension account is counted towards the income-test, where minimum withdrawal rates impose a lower bound on optimal consumption (withdrawals from liquid wealth must be larger or equal to these rates).
- Policy 2, Post-January 2015 (POST2015): This policy focuses on the changes for the income-test of Allocated Pension accounts. The income-test now uses deemed income rather than drawdown; thus, the liquid wealth is used in both the asset and income-test. The retiree can therefore withdraw more liquid wealth without missing out on Age Pension payments.
- Policy 3, asset-test changes January 2017 (POST2017): On 1 January 2017, the thresholds of the asset-test were ‘rebalanced’, hence changed significantly. The thresholds for the asset-test increased, and the taper rate doubled. This effectively means that retirees will now receive full Age Pension for a higher level of wealth, but once the asset-test binds, the partial Age Pension will decrease twice as fast, causing them to receive no Age Pension at a lower level of wealth than before. No adjustments were made to the full Age Pension or income-test threshold.

#### 2.3. Age Pension

#### 2.3.1. Deemed Income

#### 2.3.2. Age Pension Function

#### 2.4. Parameters

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- A retiree is eligible for Age Pension at age $t=65$ and lives no longer than $T=100$.
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- The lower threshold for housing is set to $30,000. That is, a retiree with wealth below this level cannot be a homeowner, hence $H\in \{0,[$30,000$,\mathrm{W}\left]\right\}$.
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- A unisex survival probability is used to avoid separating the sexes, as it would add an extra state variable. The survival probabilities for a couple are assumed to be mutually exclusive, based on the oldest partner in the couple. The actual mortality probabilities are taken from Life Tables published by Australian Bureau of Statistics (2014).
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- The subjective discount rate $\beta $ is set in relation to the real interest rate so that $\beta ={e}^{-{\sum}_{i=t}^{{t}^{\prime}}{r}_{i}}$.

#### 2.5. Numerical Implementation

## 3. Results

#### 3.1. Optimal Consumption

#### 3.2. Optimal Risky Asset Allocation

#### 3.3. Optimal Housing Allocation

#### 3.4. Limitations

## 4. Conclusions

^{st}of January 2015 and affect the treatment of income for the Age Pension income-test, which leads to different optimal decisions for consumption, investments and housing. In addition, we also evaluate the effect of the deeming rate levels in relation to portfolio returns.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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1 | Certain account types for retirement savings have a minimum withdrawal rate once the owner is retired. |

2 | The pension system in Australia is called ‘superannuation’. |

3 | The recommendations to introduce deeming was made in Henry (2009), where the fiscal sustainability is evaluated with the general equilibrium model ‘KPMG Econtech MM900’ (KPMG 2010). The model shows the estimation over a 10-year window; hence, we do not know the short-term or year-to-year estimates. In addition to this, the model includes additional suggested tax- and budget-related changes; hence, the effect of introducing deeming rates cannot be isolated. |

4 | As of 4 May 2017, the current three-month rate offered by Commonwealth Bank is 2.05% (https://www.commbank.com.au/personal/accounts/term-deposits/rates-fees.html, accessed on June 8, 2017). |

5 | By defining the model in real terms (adjusted for inflation), time-dependent variables do not have to include inflation, which otherwise would be an additional stochastic variable. |

6 | Note that the purpose is not to model health among the retirees, but rather to explain decreasing consumption with age. |

7 | The risk aversion is considered to be the same as consumption risk aversion for singles since a couple is expected to become a single household before bequeathing assets. |

8 | Because the marginal utility is constant for the bequest utility with zero wealth, in a model with perfect certainty and CRRA utility, the optimal solution will suggest consumption up to level a before it is optimal to save wealth for bequest (Lockwood 2014). |

9 | As of 1 July 2017, this increased to 65.5 years for people born after 1 July 1952, but for our dataset, the entitlement age was 65. Already retired Australians might have had earlier entitlement ages. |

10 | The current rates are at a historical low. In 2008, the deeming rates ${\varsigma}_{-}/{\varsigma}_{+}$ were as high as 4%/6%, but in March 2013, they were set to 2.5%/4% due to decreasing interest rates, then in November 2013 to 2%/3.5% and to the current levels of 1.75%/3.25% in March 2015. Note that despite the model being defined in real terms, it can be shown with simple algebra that the deeming rates shall not be adjusted to ‘real’ deeming rates. |

11 | It should be noted that the findings are for the account-based pension only, as other products that do not enforce the minimum withdrawal rates could incur additional savings for the government under the new rules. |

12 | A 401(k) is a defined-contribution retirement savings plan sponsored by the employer. |

**Figure 1.**Optimal drawdown and consumption for non-homeowner couple households for a given liquid wealth at the age t, under the three different policy scenarios in the case of low returns ($\mu $ = 0.0325).

**Figure 2.**Comparison of consumption, Age Pension and wealth over a retiree’s lifetime with the three different policy scenarios. The retiree starts with $1m liquid wealth, which grows with the low expected return each year ($\mu $ = 0.0325), and drawdown follows the optimal drawdown paths under each policy.

**Figure 3.**Comparison of consumption, Age Pension and wealth over a retiree’s lifetime with the three different policy scenarios. The retiree starts with $1m liquid wealth, which grows with the high expected return each year ($\mu $ = 0.06), and drawdown follows the optimal drawdown paths under each policy.

**Figure 4.**Comparison of the Age Pension function with the three policy scenarios, based on a single household aged 65–74 and where consumption is assumed to be the minimum withdrawal rate of 5%.

**Figure 5.**Optimal risky allocation for non-homeowner single and couple household, under each policy, given the low expected return ($\mu $ = 0.0325).

**Figure 6.**Optimal housing allocation given by total wealth $\mathsf{W}$ for single and couple households, under the three policy scenarios with the low return ($\mu $ = 0.0325).

**Table 1.**Age Pension rates, thresholds and taper rates used in the means-test for each policy variation.

PRE2015 | POST2015 | POST2017 | |
---|---|---|---|

Full Age Pension singles (${P}_{\mathrm{max}}^{\mathrm{S}}$) | $22,721 | $22,721 | $22,721 |

Full Age Pension couples (${P}_{\mathrm{max}}^{\mathrm{C}}$) | $34,252 | $34,252 | $34,252 |

Income-Test | Drawdown | Deemed | Deemed |

Threshold singles (${L}_{\mathrm{I}}^{S}$) | $4264 | $4264 | $4264 |

Threshold couples (${L}_{\mathrm{I}}^{C}$) | $7592 | $7592 | $7592 |

Rate of reduction (${\varpi}_{\mathrm{I}}^{d}$) | $0.5 | $0.5 | $0.5 |

Deeming threshold singles (${\kappa}^{\mathrm{S}}$) | - | $49,200 | $49,200 |

Deeming threshold couples (${\kappa}^{\mathrm{C}}$) | - | $81,600 | $81,600 |

Deeming rate below ${\kappa}^{d}$ (${\varsigma}_{-}$) | - | 1.75% | 1.75% |

Deeming rate above ${\kappa}^{d}$ (${\varsigma}_{+}$) | - | 3.25% | 3.25% |

Asset-Test | |||

Threshold homeowners singles (${L}_{\mathrm{A}}^{S,h=1}$) | $209,000 | $209,000 | $250,000 |

Threshold homeowners couples (${L}_{\mathrm{A}}^{C,h=1}$) | $296,500 | $296,500 | $375,000 |

Threshold non-homeowners singles (${L}_{\mathrm{A}}^{S,h=0}$) | $360,500 | $360,500 | $450,000 |

Threshold non-homeowners couples (${L}_{\mathrm{A}}^{C,h=0}$) | $448,000 | $448,000 | $575,000 |

Rate of reduction (${\varpi}_{\mathrm{A}}^{d}$) | $0.039 | $0.039 | $0.078 |

${\mathbf{\gamma}}_{\mathit{d}}$ | ${\mathbf{\gamma}}_{\mathbf{H}}$ | $\mathbf{\theta}$ | a | ${\overline{\mathit{c}}}_{\mathit{d}}$ | $\mathbf{\psi}$ | $\mathbf{\lambda}$ | ${\mathbf{\zeta}}_{\mathit{d}}$ | |
---|---|---|---|---|---|---|---|---|

Single household | $-1.98$ | $-1.87$ | 0.96 | $27,200 | $13,284 | 1.18 | 0.044 | 1.0 |

Couples household | $-1.78$ | $-1.87$ | 0.96 | $27,200 | $20,607 | 1.18 | 0.044 | 1.3 |

**Table 3.**Minimum regulatory withdrawal rates for Allocated Pension accounts for the year 2017 and onwards (https://www.ato.gov.au/rates/key-superannuation-rates-and-thresholds/?page=10, accessed June 5, 2017).

Age | ≤64 | 65–74 | 75–79 | 80–84 | 85–89 | 90–94 | ≤95 |

Min. drawdown | 4% | 5% | 6% | 7% | 9% | 11% | 14% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Andréasson, J.G.; Shevchenko, P.V.
Assessment of Policy Changes to Means-Tested Age Pension Using the Expected Utility Model: Implication for Decisions in Retirement. *Risks* **2017**, *5*, 47.
https://doi.org/10.3390/risks5030047

**AMA Style**

Andréasson JG, Shevchenko PV.
Assessment of Policy Changes to Means-Tested Age Pension Using the Expected Utility Model: Implication for Decisions in Retirement. *Risks*. 2017; 5(3):47.
https://doi.org/10.3390/risks5030047

**Chicago/Turabian Style**

Andréasson, Johan G., and Pavel V. Shevchenko.
2017. "Assessment of Policy Changes to Means-Tested Age Pension Using the Expected Utility Model: Implication for Decisions in Retirement" *Risks* 5, no. 3: 47.
https://doi.org/10.3390/risks5030047