Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations

Creedy, John; Gemmell, Norman; Scobie, Grant Working Paper Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations New Zealand Treasury Working Paper, No. 14/14 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Creedy, John; Gemmell, Norman; Scobie, Grant (2014) : Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations, New Zealand Treasury Working Paper, No. 14/14, ISBN 978-0-478-42194-1, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205669 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations John Creedy, Norman Gemmell and Grant Scobie New Zealand Treasury Working Paper 14/14 November 2014 DISCLAIMER The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government . The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate. NZ TREASURY Pensions, Savings and Housing: A Life-cycle Framework with WORKING PAPER Policy Simulations 14/14 MONTH/YEAR November 2014 AUTHORS John Creedy Visiting Professor/Principal Adviser Victoria University of Wellington/Treasury No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 917 6893 Norman Gemmell Professor of Public Finance Victoria University of Wellington Rutherford House 23 Lambton Quay Wellington New Zealand Email: [email protected] Telephone: ++64 +4 463 5843 Grant Scobie Treasury No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 917 6005 ISBN (ONLINE) 978-0-478-42194-1 URL Treasury website at November 2014: http://www.treasury.govt.nz/publications/research-policy/wp/ 2014/14-14/twp14-14.pdf We are grateful to Chris Ball, Peter Bushnell, Richard Disney, Adam Jaffe, Michael Reddell, Paul Rodway, Chung Tran, Mark Vink and Justin van de Ven for comments on earlier versions of this paper. We have also benefited from comments by participants at a Treasury seminar presentation. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email: [email protected] Telephone: +64 4 472 2733 Website: www.treasury.govt.nz ACKNOWLEDGEMENTS Persistent URL: http://purl.oclc.org/nzt/p-1688 Abstract The objective of the paper is to explore the saving and consumption responses of a representative household to a range of policy interventions such as changes in taxes and pension settings. To achieve this, it develops a two-period life-cycle model. The representative household maximises lifetime utility through its choice of optimal levels of consumption, housing and saving. A key feature of the approach is modelling the consumption of housing services as a separate good in retirement along with the implications for saving. Importantly, the model incorporates a government budget constraint involving a pay-as-you-go universal pension. In addition, the model allows for a compulsory private retirement savings scheme. Particular attention in the simulations is given to the potential impact on household saving rates of a range of policy changes. Typically the effect on saving rates is modest. In most instances, it would take very substantial changes in existing policy settings to induce significant increases in household saving rates. J.E.L. CLASSIFICATION D12; H24; H31; J26 KEYWORDS Savings; Housing; Retirement; Intertemporal elasticity of substitution; rate of interest; taxation. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations i Executive Summary Households make decisions about consumption, saving, housing and retirement income. These are highly interrelated and are influenced by the tax and expenditure policies of the government, while the latter are affected in turn by individuals’ behaviour. While abstracting from many complexities, this paper focusses on retirement savings decisions, mortgage borrowing for house purchase and consumption plans in the presence of both income and consumption taxes. Government expenditure is subject to a debt-neutral budget constraint. A two-period framework is constructed to explore household savings behaviour over the life cycle. The model is based on a representative household that chooses its optimal level of consumption, saving, retirement income and housing subject to its budget constraint. In addition a key feature of the model is the explicit treatment of taxation and expenditure and the constraints imposed by the government’s budget balance. The financial sector enters through the role of the interest rate and a mortgage loan-to-value ratio. The model is calibrated with benchmark values designed to mirror key features of the New Zealand economy. It is then used for an extensive series of policy simulations. These involve comparing the benchmark case with the values of the decision variables after introducing a specific policy change. These include, for example, changes in the rate of interest, the income tax rate, the consumption tax rate, contributions to a compulsory retirement scheme and a change in the rate of taxation on interest income. Particular attention is given to the response of savings, consumption and housing to changes in various tax rates, pension and savings policies, and demographic changes. In general the responses are typically modest. For example, a rise in the income tax rate of 1.5 percentage points reduces both financial saving and total household saving rates by 0.7 percentage points and implies a 1% fall in house prices. In view of the fact that New Zealand gives essentially no tax concessions on interest income, this issue was explored in some detail. The model was adjusted to eliminate all tax on interest income. In the first instance financial savings and total savings rise by 17% and 8% respectively. The household saving rate (expressed as a proportion of disposable income) rises by 1.4 percentage points. This is accompanied by a significant shift toward consumption in retirement and lower consumption of housing services, leading to a fall in house prices of some 2.5%. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations ii The loss of tax revenue involves a reduction of 1.7% in the public non-pension expenditure. However, as the extra savings over the working life are drawn down in retirement there is no net effect on aggregate household saving from such a policy. These results underscore the importance of including a government budget constraint and importantly of the mechanism by which a balanced budget is achieved after a policy intervention that alters the initial level of tax revenue or total expenditure. For example, for some comparisons, we impose a condition that non-pension expenditure per person increases by a set amount while the universal pension is held constant. Population ageing is expected to create additional fiscal pressures. One approach could be to introduce a compulsory retirement savings contribution and then reduce the universal pension such that total pension income remains constant. With a 10% decline in the ratio of workers to pensioners, this would involve a compulsory contribution rate of 6.5% accompanied by a 22% reduction in the universal pension. Consumption throughout the lifetime would be lower and voluntary savings would decline. All these results have been obtained as comparative static exercises. They do not allow for the time that adjustments to policy changes would take, or the time path of those adjustments. Furthermore, as the results are for a representative household they are silent on the distributional consequences of policy changes. Despite this, the model provides a rigorous and internally consistent framework for assessing the direction and magnitude of key responses in saving, consumption, housing and pensions to potential changes in a range of tax and retirement income policies. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations iii Contents Abstract i Executive Summary ii 1 Introduction 1 2 A Two-period Framework 3 2.1 The Basic Structure of the Model . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Treatment of Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 The Life-Cycle Model 6 3.1 Optimal Consumption and Saving . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 MortgageBorrowing............................... 8 3.3 A Compulsory SAYG Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 The Government’s Budget Constraint 10 5 Calibrating the Model 12 6 Simulating Policy Changes 14 6.1 Changes for which G is Constant . . . . . . . . . . . . . . . . . . . . . . . . 15 6.2 Changes in The Price of Housing . . . . . . . . . . . . . . . . . . . . . . . . 17 7 Tax and Expenditure Policy Changes 17 7.1 A Change in the Income Tax Rate . . . . . . . . . . . . . . . . . . . . . . . 18 7.2 A Change in the Consumption Tax Rate . . . . . . . . . . . . . . . . . . . . 18 7.3 A Reduction in the PAYG Public Pension . . . . . . . . . . . . . . . . . . . . 19 8 Impact of Other Policy Changes 20 8.1 A Change in the Loan-to-Value Ratio . . . . . . . . . . . . . . . . . . . . . . 20 8.2 A Change in the Compulsory Saving Rate . . . . . . . . . . . . . . . . . . . 21 8.3 A Change in the Tax Rate on Interest in the Compulsory Pension . . . . . . 22 8.4 A Change in the Interest Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.5 Eliminating Taxation of Interest Income . . . . . . . . . . . . . . . . . . . . . 22 9 Economy-wide and Demographic Changes 24 9.1 ARiseinIncome................................. 24 9.2 PopulationAgeing ................................ 25 9.3 Changes in the Preference for Housing . . . . . . . . . . . . . . . . . . . . 26 10 A Summary of the Policy Simulations 27 11 Conclusions 29 WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations iv List of Figures 1 Household and Government Components of the Model . . . . . . . . . . . 6 2 Two Policies Producing A Similar Change in G................ 16 3 Percentage Point Changes in Saving Rates . . . . . . . . . . . . . . . . . . 28 4 Percentage Changes in House Prices . . . . . . . . . . . . . . . . . . . . . 28 5 Variations in Housing Consumption with Rate of Interest . . . . . . . . . . . 40 6 Variations in Housing Savings with House Price Appreciation . . . . . . . . 40 List of Tables 1 BenchmarkValues................................ 13 2 Saving Rates for Income Deciles . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Summary of Policy Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Budget Contraints for Renters and Owners . . . . . . . . . . . . . . . . . . 33 5 Consumption Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations v Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations ”You can be young without money, but you can’t be old without it.” Tennessee Williams, Cat on a Hot Tin Roof (Act 1) 1 Introduction This paper uses a two-period framework to explore household savings behaviour over the life cycle. A primary objective is to explore the impact on the saving and housing decisions of a representative household, of policy interventions such as tax and retirement income policies. A distinction is drawn between two forms of savings. First, ‘financial savings’ are defined as interest-bearing savings made in the first (working) period of life in order to augment income in the second (retirement) period. Second, ‘housing savings’, also made in the first period, are augmented by a mortgage and used to purchase a house. The mortgage is the only form of debt allowed in the model. It is assumed that households maximise an intertemporal utility function subject to a lifetime budget constraint. Incomes are subject to an income tax. Consumption, other than housing, is subject to a broad-based goods and services tax. At any time the tax revenue from two overlapping generations of workers and pensioners is used to finance an unconditional (non-means-tested) retirement income, in addition to other non-transfer public expenditure per person. Furthermore, the implications of imposing a compulsory private superannuation system, where income obtained by the fund is taxed at a lower rate than other income, are investigated. Comparative static properties of the model are investigated in order to examine the implications for saving and consumption behaviour of a number of policy interventions and other exogenous changes. A key feature of the approach is modelling the consumption of housing services as a separate good in retirement along with the implications for saving. The present paper concentrates on microeconomic features of saving behaviour, while at the same time ensuring that the government budget constraint remains balanced, implying no change in the level of public debt. The results underscore the critical importance of the assumptions made as to how the government’s WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 1 c2=β0W{1 + r(1 −τ)} 1 + v(6) cH=γ0(1 + π)W(7) From (7), sH = cH/(1 + π) = γ0W does not depend on sH . 9 Financial savings are s1=y1(1 −τ)−c1(1 + v)−sH, so that: s1=y1(1 −τ)−(α0+γ0)W(8) Hence ∂s1 ∂r > 0and financial savings unambiguously increase as the rate of interest increases. 3.2 Mortgage Borrowing The previous results can easily be modified by the addition of a mortgage. If (as discussed in section 2) it is possible to borrow bfor a house purchase, then: cH= (1 + π) (sH+b)(9) and: sH=cH 1 + π−b(10) Housing savings required for a desired value of cH are thus reduced by the extent of the mortgage. In this type of model it is necessary to assume that the income tax system treats interest and debt symmetrically: that is, the same net-of-tax interest rate must be applied to interest receipts and payments. Different rates would imply a nonlinear inter-temporal budget constraint, giving rise to corner solutions. 10 Hence, it is required to assume that for tax purposes interest-income is deductible. On the assumption that the effective mortgage rate is thus r(1 −τ) , the interest paid on the mortgage is r(1 −τ)b . The investment of b yields b(1 + π) so that after the principal of b is repaid, and interest income is paid, there remains {π−r(1 −τ)}b. Hence, the budget constraint is now given by: (c1+c2) (1 + v) + cH=y1(1 −τ) + P+y2(1 −τ) +r(1 −τ)s1+πsH+{π−r(1 −τ)}b(11) Substitution for s1 and rearrangement of this constraint produces precisely the same form as in equation (3); all terms in bcancel.11 9Appendix C shows that this result is a special property of the Cobb-Douglas. 10 Complications arising from nonlinear constraints in two-period models, requiring the application of Kuhn-Tucker conditions, are examined in Creedy (1990). 11 If there is a difference between the mortgage rate and r , then b appears in a revised definition of W . If b were to be in the budget constraint, the only way to solve the model would be to set its value exogenously. Hence it would not be possible to obtain mortgage borrowing as an endogenous variable, arising from optimal lifetime choices. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 8 The value of b is determined by setting a borrowing constraint in the form of a loan-to-value ration (LRV), ξ=b/ (b+sH), so that: b=ξ 1−ξsH(12) Thus substituting in (9) gives sH = cH(1 −ξ)/(1 + π) and housing and financial savings are now given by: sH=γ0(1 −ξ)W(13) and: s1=y1(1 −τ)− {α0+γ0(1 −ξ)}W(14) Hence a minor modification is needed to the earlier results. Substitution of (13) into (12) gives b = γ0ξW , so that the use of a LVR constraint is equivalent to providing a mortgage that is also proportional to lifetime net worth. 3.3 A Compulsory SAYG Scheme In addition to the tax-financed PAYG pension, the model includes a compulsory saving scheme, which requires a proportion, δ , of the first period’s income to be placed into an individual retirement fund. The fund’s interest earnings are taxed at the lower rate τ0< τ . The pension from the fund, P0 , is not subject to income tax on withdrawal. The scheme corresponds to a system referred to by the letters TtE: contributions are fully taxed initially; earnings are partially taxed; final withdrawals from the fund are exempt from income tax. Of course, expenditures financed from the private pension and the PAYG pension are subject to GST. The public scheme continues to be universal and not subject to means-testing. The private pension, received in addition to the public pension, is therefore given by: P0=δy1{1 + r(1 −τ0)}(15) The individual’s budget constraint needs to be adjusted to allow for the compulsory contribution. In this case it can be shown that net worth, W0, is: W0=y1(1 −τ∗) + P+y2(1 −τ) 1 + r(1 −τ)(16) where: τ∗=τ−δr (τ−τ0) 1 + r(1 −τ)(17) If τ0 = τ , net worth is not affected, as τ∗ = τ . The tax advantage enjoyed by the compulsory fund therefore implies an effective reduction in the first period’s income tax rate. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 9 4 The Government’s Budget Constraint The government faces a budget constraint in financing both the PAYG pension and other expenditure. Holding debt constant, current expenditure must be financed from current tax revenue. The present treatment includes only income and consumption tax, which must finance the pension and additional expenditure of G per person. This non-pension expenditure does not enter the household’s utility function so that, for example, any benefits arising from public goods are ignored here. 12 The constraint applies to aggregates, and so the present section deals with distributions of different households from overlapping generations. Hence i subscripts are added to deal with different households and w (for worker) and p (for pensioner) subscripts are added to y and c to distinguish members from the two cohorts.13 Let the number of current pensioners and workers be denoted respectively by Np and Nw . Interest income tax is obtained from both the interest income on financial savings of the currently retired and their interest income on the compulsory fund. The latter is equal to rδτ0PNp i=1 yp,1,i . Setting total government expenditure equal to total income tax and GST revenue gives the required budget constraint as: NpP+ (Np+Nw)G=τ Nw X i=1 yw,1,i +τ Np X i=1 yp,2,i +τr Np X i=1 (yp,1,i (1 −τ−δ)−cp,1,i (1 + v)−sp,H,i) +v  Nw X i=1 cw,1,i + Np X i=1 cp,2,i  +rδτ0 Np X i=1 yp,1,i (18) The term on the left-hand side of (18) is total government expenditure, made up of the expenditure on the universal public pension, NpP , and per capita expenditure of all other non-pension payments of G , applied to all individuals, Np + Nw . On the right-hand side, the first line represents income tax from workers and pensioners; 12 This assumption is common even in standard optimal income tax models. If G enters utility additively, then it will not affect inter-temporal decisions directly. The present analysis is not concerned with optimal policy or with the allocation of expenditure among alternative uses. Models allowing for individuals’ preferences over public goods expenditure, along with transfer payments, are discussed by Creedy and Moslehi (2011). 13 Writing the constraint in terms of a distribution of y1 and other values means that it is possible to consider the case where, for example, yw,1,i is not equal to ¯yw,1 . However, in the majority of policy simulations below, the ‘representative’ individual is considered by setting variables equal to their mean values. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 10 the second line is interest income tax from the savings of pensioners; the third line represents GST revenue from the expenditure of workers and pensioners; the final line is the interest income tax obtained from interest on compulsory contributions to the SAYG. Growth of real incomes occurs at the rate, g, so that ¯yw,1= ¯yp,1(1 + g), where the ‘bar’ indicates arithmetic mean. Hence, each generation of workers receives an income during the working period that is 100 g per cent higher than that of the previous generation of workers. The appropriate averages, ¯cw,1,¯cp,2,¯cp,1 and ¯cp,H , can be obtained in terms of average net worth using the above results, on the assumption that all individuals have the same tastes. However, net worth includes the value of P , so the above expression does not directly give a reduced-form solution. First, define ¯ Wpas: ¯ Wp= ¯yp,1(1 −τ∗) + P+ ¯yp,2(1 −τ) 1 + r(1 −τ)(19) and ¯ Wwas: ¯ Ww= ¯yw,1(1 −τ∗) + P(1 + g0) + ¯yw,2(1 −τ) 1 + r(1 −τ)(20) Here P(1 + g0) is the pension that current workers can expect to receive when they retire. If pensions are adjusted fully in line with real incomes, then g0 = g , and if pensions are adjusted in line only with prices, then g0 = 0 and P is constant in real terms. Substituting gives: ¯cp,1(1 + v) + ¯sp,H = (α0+γ0(1 −ξ)) ¯ Wp(21) and: ¯cp,2v=v 1 + vβ0{1 + r(1 −τ)}¯ Wp(22) Furthermore: v¯cw,1=v 1 + vα0¯ Ww(23) Substituting into the government budget constraint and rearranging eventually gives the following form as the solution for G: 1 + Nw Np!G= Nw Np!τ¯yw,1 +τr¯yp,1[(1 −τ)−(α0+γ0(1 −ξ)) (1 −τ∗)] +τ¯yp,2"1−r(1 −τ) (α0+γ0(1 −ξ)) 1 + r(1 −τ)# +vβ0 1 + v[¯yp,1(1 −τ∗) (1 + r(1 −τ)) + ¯yp,2(1 −τ)] WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 11 +vα0 1 + v"¯yw,1(1 −τ∗) + ¯yw,2(1 −τ) 1 + r(1 −τ)#Nw Np −rδ (τ−τ0) ¯yp,1 −PΩ(24) where: Ω = 1 + τr (α0+γ0(1 −ξ)) 1 + r(1 −τ)−v 1 + v(β0+α0(1 + g0) 1 + r(1 −τ) Nw Np)(25) The approach here has been to solve for G in terms of exogenous variables. It can be seen that the alternative, of solving for the income tax rate, needed to achieve a given G , would require the solution to a quadratic equation. Hence it is more tractable in the present model to consider τ to be exogenous, and allow G to be determined endogenously. 5 Calibrating the Model Table 1 presents the values of the various parameters chosen to obtain a benchmark solution. Households from different cohorts are characterised by identical representative households, each with the appropriate arithmetic means corresponding to the cohort. In carrying out the calibration exercise, it is important to remember that in the present two-period model the unit of time is not simply a year. Furthermore, the artificial assumption – common to virtually all overlapping generations models – is that the time periods are of equal length, so that one generation of pensioners overlaps with one generation of workers, as in the government budget constraint discussed in the previous section. Thus it cannot be expected that precise calibration of this kind of model to empirical orders of magnitude can be achieved. Given the number of parameters, an extensive calibration exercise involving much trial and error is required. Clearly, absolute values of, for example, y1 , are largely arbitrary, but considerable effort has been taken to ensure that relative orders of magnitude of major endogenous variables are reasonable. Furthermore, as stressed earlier, the saving rates produced here relate only to savings over the working life. In considering appropriate values for the rate of interest, the relationship between an annual rate, ra , and the longer-period rate, given by 1 + r = (1 + ra)30 , was used. The value chosen for the interest rate of r = 1 . 1is consistent with an annual rate over thirty years of around 2.5%. In setting values of α and β , the former was normalised to 1, while in thinking about β it is useful to consider that β = 1 /(1 + ρ) , where ρ is the time preference rate. It is appropriate to impose a value of time preference in excess of the rate of interest: the value of ρwas set at 1.6. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 12 The value of 2.5 for Nw/Np is based roughly on the midpoint of the 2012 figure of 3.0 and the New Zealand Statistics projection for 2041 of 2.1. The benchmark value of the PAYG pension is set at 255, just under one quarter of the income in the working period. These values produce a value of endogenous non-transfer expenditure per person, G , of approximately 390. As discussed in section 4, at any time the value of G relates to the Nw + Np people currently alive, while of course the PAYG pension is received only by the Npnon-workers. Table 1: Benchmark Values Representative Individual Symbol Benchmark Taste parameters Exponent on consumption in first period α(α0) 1.0 (0.612) Exponent on consumption in second period β(β0) 0.385 (0.235) Exponent on housing consumption γ(γ0) 0.25 (0.153) Incomes Income in first period of life cycle y11000 Income in second period of life cycle y250 Economy characteristics Real rate of interest r1.1 Real growth rate of incomes g0.8 Rate of appreciation of housing π1.4 Elasticity of supply of housing εs0.5 Ratio of number of workers to pensioners Nw/Np2.5 Government policy Tax policy Income tax rate τ0.25 Tax rate applied to SAYG income τ00.20 GST rate v0.15 Expenditure policy PAYG pension P255 Rate of adjustment to PAYG pension g00.8 Other policies SAYG Contribution rate δ0.035 Mortgage loan to value ratio ξ0.5 In setting a suitable loan-to-value ratio, it is assumed that the representative individual is subject to an initial LV R when purchasing a housing asset in period 1. In period 2 the house is owned outright, having repaid the mortgage, such that LV R = 0 in period 2. Hence it is required to set ξ to capture the average LV R throughout the working period. For example, an initial LV R of 90%, which falls to 0 over a 30 year mortgage repayment period, could be represented as a 45% LV R on average (that is, half the initial LV R ) over the period of the loan. However, mortgage repayment schemes typically involve a fixed repayment per period, which is initially almost all interest on the loan. By the end of the repayment period it is WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 13 almost all capital repayment. Hence, the LV R falls non-linearly throughout the 30 years and the average annual value is greater than half the initial LV R . It can be shown that for each $1 borrowed over 30 years at 2.5% per annum (approximately the annual equivalent of the benchmark interest rate used here) with monthly repayments, a 90% initial LV R is equivalent to an LV R of 50% averaged over 360 months. An 80% initial LV R yields an equivalent average LV R of around 45%. 14 In the benchmark simulations below, ξ = 0 . 50 is therefore adopted, with a reduction simulated by setting it to 0 . 45. These can be thought of as approximately capturing the impact of setting initial LV R s of 90% and 80% respectively. The elasticity of housing supply, εs , of 0.5 is in line with the values reported by S ´ anchez and Johansson (2011). 6 Simulating Policy Changes The model can be used to examine the potential direction and magnitude of changes in key outcome variables as a result of specific changes in policies or economic conditions. For example, the impact on saving rates, consumption, investment in housing and retirement income of a reduction in the income tax rate can be examined, starting from a benchmark set of parameters and the associated solution. The types of change can be divided into three basic categories. The first category includes ‘tax and expenditure’ policies. These include changes in τ , v and P and, by implication, G . The latter is a policy variable but, as discussed earlier, it is endogenous because of the government budget constraint. For example, it may be desired to examine the effects of a change in the tax mix, from income tax to GST, by reducing τ and increasing v . Similarly, a shift in government expenditure towards non-transfer expenditure involves for example a reduction in the PAYG pension. In each case it is useful to ensure that changes involve similar changes in G . Subsection 6.1 explains how this is achieved, given that G is endogenously determined. The second category consists of ‘other policy changes’, such as changes in the loan-to-value ratio, ξ , the compulsory contributions rate in the SAYG pension, δ , and the rate of interest, r . The latter is an exogenous variable in the model. Associated with r is the issue of interest-income taxation: hence this second category includes the implications of exempting interest income from taxation. These policy changes would not normally be considered in the context of revenue switching or of revenue raising, although they clearly do have (in some cases small) 14 These average values rise to 56% and 50% respectively using a 5% annual interest rate. For a standard mortgage calculator, see: http://www.zyngrule.com/mortgage-calc.php. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 14 implications for revenue, and hence G . The approach taken when considering this type of change is thus to impose changes which are considered appropriate in the context of realistic policy changes and the calibration of the model. There is no reason here to impose policy changes which imply common changes in G.15 The third simulation category contains ‘economy-wide and demographic’ changes. These are changes over which the government would not be expected to have control, and include changes in the demographic ratio, Nw/Np , the level of income in the first period of life, y1 , and the preference for the housing good, γ . As with the second category, changes in these variables have varying implications for G , but this is just another endogenous variable that is of interest in comparing changes: there is no reason to impose common changes in G for all of the simulations in this group. 6.1 Changes for which G is Constant Suppose it is required to compare the effects on savings of alternative tax and expenditure policies. An initial indication is given by partial changes, such as ∂S/∂τ , ∂S/∂P and ∂S/∂v . These partial effects can be obtained numerically by imposing small changes in the policy variables and re-solving the model to obtain the corresponding changes in endogenous variables. The government budget constraint means that there is a loss of a degree of freedom in policy choices: the government cannot independently set, for example, the tax rate, τ , and the non-transfer government expenditure per person, G . Hence it is effectively not possible to change just one policy variable at a time, since a change in τ or v or P generates a change in G as well as changes in the endogenous variables that directly or indirectly affect utility. For this reason, partial changes in tax and expenditure variables are not directly comparable. Each partial change involves a different effect on G , and indeed G moves in different directions: it increases when τand vincrease, but falls when Pis increased. It is therefore desirable to adjust the partial changes so that comparisons are made for similar changes in G . Suppose it is required to compare all policy changes such that the associated change in G , denoted ∆ G , is the same for all changes. Suppose that, in a reasonable range around the benchmark solution, partial effects are linear, so that the partial changes, ∂S/∂τ and so on, are constant. For example, given the partial change, ∂G/∂τ = x , say, then the change in τ needed to achieve 15 Indeed, this would give rise to unrealistic changes, especially where the revenue implications are very small. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 15 a change in Gof ∆Gis given by: ∆τ= ∆G/x (26) Suppose, in addition, that the partial change in savings generated by a change in the tax rate is ∂S/∂τ = y . Then the change in S resulting from a change in τ of ∆τis given by: ∆S=y∆τ=y x∆G = ∂S/∂τ ∂G/∂τ !∆G(27) Similarly, the effect on savings of a change in v which produces the same effect on Gis given simply by replacing τin (27) with v. Figure 2: Two Policies Producing A Similar Change in G Comparisons are illustrated in Figure 2 for two policies. The left hand side of the diagram illustrates the effects on total savings, S , and expenditure, G , of changes in the exogenous PAYG pension, P , for a given tax rate, τ = τ∗ . The right hand side of the diagram shows variations in S and G for variations in the tax rate, τ , for a given pension, P = P∗ . Hence the points A, B, C and D represent the model’s solutions for τ∗ and P∗ . Each line through the points has a slope given by the respective partial derivative. Hence, from the right hand side of the diagram, a rise in τ which produces a change of ∆ G in government expenditure, with P held constant at P∗ , is associated with a reduction in savings measured by the length JK. To achieve an equivalent increase in non-transfer expenditure by a policy of WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 16 reducing P , with the tax rate held constant at τ∗ , it would be necessary to reduce P by LM, which yields an increase in total savings of JH. A similar approach can be extended to allow two policy variables to be combined in a comparable way. 6.2 Changes in The Price of Housing The model has so far been discussed in terms of the amount spent by the household on housing in period 1. This is the sum of savings sH and the mortgage, b , and is denoted by VH,1 . Let pH,1 and H1 denote the price and quantity of housing. Hence, when the house is purchased in period 1: VH,1=pH,1H1(28) In examining the comparative statics of the model, the assumption regarding the price elasticity of housing supply, εs = dH/H dpH/pH , allows the impact on pH,1 to be identified. First, dropping the time subscript, and differentiating (28) gives: dVH VH =dpH pH +dH H(29) and: dVH/VH dpH/pH = 1 + dH/H dpH/pH = 1 + εs(30) Hence: dpH,1/pH,1 dVH/VH =1 1 + εs (31) Hence, the proportional response of the house price in period 1 to a change in housing expenditure, VH , is positive unless supply is infinitely elastic, and is inversely related to the elasticity of housing supply. The effect of, for example, a change in the income tax rate, τ , on the price of housing can thus be obtained as: ηpH,τ =1 1 + εsηVH,τ (32) 7 Tax and Expenditure Policy Changes This section reports the comparative static results for a number of policy changes to the tax and expenditure structure. These include changes to the income tax rate, the tax rate on consumption, and the level of the public PAYG pension. The impact on different forms of saving and the housing market are reported. In order WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 17 than in the Cobb-Douglas case. This in turn would reduce the need for extra saving to support consumption in period 2. The implication is that the rise in saving rates can be regarded as an upper bound: see also Appendix C for discussion of the CES case. The increased saving rate following the elimination of the tax on interest income refers to financial saving during the working life (period 1 in the model). As those savings are made to support consumption in retirement. In the long run the net change in aggregate savings (in the cross section of overlapping generations) would be considerably reduced by the decumulation in retirement. The effect of eliminating the tax on interest income was also examined under the assumption of a 5% increase in non-pension expenditure per person, G . In this case the tax rate on labour income would need to rise from 0.25 to 0.27, while the overall saving rate increases by 1.3 percentage points. If G is held constant at its base level when the tax on interest income is removed then the labour tax rate needs to rise from 0.25 to 0.255, and the overall saving rate rises by 1.8 percentage points. 9 Economy-wide and Demographic Changes This section considers the third group of comparative static changes examined, which includes the non-policy changes. 9.1 A Rise in Income Consider the impact of a 10% increase in income during the working years, y1 . The higher value of Wimplies greater consumption of both housing and non-housing. At the same time the levels of both financial and housing savings increase by 23% and 8% respectively. Thus, while the financial saving rate rises, the saving rate for housing falls despite the absolute increase in the level. This apparent anomaly is simply due to the fact that following the rise in income of 10%, saving for housing rises less than 10%. This serves to underline the point that an increase in household savings during the working life is consistent with an apparent decline in the rate of saving. Greater income and the consequent rise in consumption spending means that both income tax and GST revenue rise. A balanced budget WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 24 is achieved by increasing Gby 11.5%. 9.2 Population Ageing The future fiscal challenges arising from population ageing and the associated decline in the ratio of workers to pensioners have been well rehearsed; for example, see Treasury (2013). It is important in practice to consider dependency ratios separately from population structure ratios, but in the present model all individuals work in the first period of the life cycle. A value of Nw/Np equal to 10% lower than the benchmark of 2.5 implies that, as a result of the decline in tax revenue, government non-pension spending per person falls by nearly 4%. However, reducing spending is only one possible way to achieve a balanced budget in the face of the decline in revenue associated with the falling share of workers in the economy. An alternative approach would be to hold spending constant and raise taxes. In this case, with both P and G held constant, the shortfall in revenue stemming from the ageing population could be meet by raising τ from 25.0% to 26.2% or raising the GST rate, v , from 15% to 17.4%.24 A further possible alternative for containing, at least partially, the rising costs of the PAYG pension, P , would be to change the way it is indexed. For example instead of being linked to average wage growth (which preserves its relativity with working-age incomes), it could be linked to a cost of living index (which would preserve its real value over time), or some average of the two.25 The benchmark case assumes that P grows at the same rate as labour incomes (that is, g0 = g ) thus maintaining a constant relation to average wage growth. Suppose instead that indexation of P is adjusted to maintain a balanced budget, with G held constant. The rate of growth of P , set at g0 = 0 . 8, the equivalent of 2% per year in the benchmark case, would need to be reduced by one percentage point. In other words the PAYG pension would grow in real terms at half the growth rate of average wages. The overall effect is to reduce lifetime wealth, W . Hence, consumption in both periods falls slightly, the financial and total saving 24 As discussed above, the GST option is expected to have less effect on savings. Experiments with the Treasury’s Long Term Fiscal Model (LTFM), for comparable degrees of population ageing, were found to produce very similar tax rate increases in order to maintain NZS and other expenditures at constant real levels. We are grateful to Matthew Bell for obtaining results using the LTFM. 25 For an analysis over time of the impact on household saving of changing the method of indexation, see Law (2013). WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 25 rates increase slightly, and the housing saving rate falls slightly.26 An alternative policy response to population ageing is to maintain constant total pension income from the PAYG and compulsory SAYG schemes combined, along with G , without raising taxes. This can be done by increasing the compulsory saving rate and simultaneously reducing P . The problem then is to find a compulsory rate of savings and a corresponding reduction in P such that the total retirement income from P combined with the private pension remains constant, as does the level of public expenditure per capita, G . The solution, which can be found by a process of trial-and-error, is to raise the compulsory contribution, δ , from 3.5% to 6.5% of gross income in period 1, and reduce P by 22%. The reduced value of P implies a lower value of W , and hence lower values of consumption in both periods: both fall by 3.3%. Total savings (financial and housing) decline by 7.3%. This decline together with that of P closely matches the rise in private compulsory saving. 9.3 Changes in the Preference for Housing In the benchmark case, the parameter describing relative housing preferences, γ0 , is 0.153. A 10% rise in γ raises γ0 to 0.166 and results in a significant shift in the demand for housing at every price level. Consumption is reallocated from nonhousing to housing consumption in both periods, with a result that GST revenue falls, leading through fiscal adjustments to a decline on non-pension expenditure in order to achieve a balanced budget. Not surprisingly, there is a marked rise in saving for housing, and the overall saving rate rises. House prices increase by 7.8% and the value of housing rises by 11.6% (on the assumption that the elasticity of supply of housing is 0.5). With the shift from the consumption of non-housing goods toward housing, the amount of mortgage borrowing increases, and with it financial savings, as these are in part dedicated to the repayment of a larger mortgage. It is commonly argued that the apparent preference New Zealanders have for housing means other forms of saving are reduced. In fact these results demonstrate that for given incomes and a given structure of taxation, a shift in preferences toward housing is associated with a rise in household saving rates, given the LV R constraint. 26 It could be argued that the PAYG pension involves an implicit saving rate, despite being financed by intergenerational transfers. The question arises of whether total savings, allowing for this fall in the implicit component as a result of the lower indexation, remain unchanged. Calculations show that the rise in total savings does not quite match the fall in implicit savings. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 26 10 A Summary of the Policy Simulations Table 3 provides a summary of the comparative static effects of policy changes examined in Sections 7 to 9. It focuses on saving and the housing market, two of the central themes of this study and, in each case, the value of the PAYG pension, P , is held constant. Alternatively, Figures 3 and 4 provide a graphical summary of the changes. As discussed above, comparisons among a range of policy changes are difficult: there is a danger of comparing policies which have very different scales. For example, in the present context the value of G is adjusted to keep the government budget constraint in balance (debt neutral changes are examined). While, by assumption, this does not affect the behaviour of the representative household, it is obviously an important variable in evaluating policy changes. Table 3: Summary of Policy Effects Percentage point change in: Percentage change in: Policy Change Financial Housing Total Stock of Price of saving saving saving rate Housing Housing A. Tax and Expenditure Policies:producing an increase in Gof 5% Tax on labour income -0.57 -0.11 -0.68 -0.54 -1.07 Tax on consumption 0 0 0 0 0 Public PAYG pension 2.95 -0.33 2.62 -1.62 -3.13 B. Other Policy Changes: 10% increases,except for removal of interest income tax Loan to value ratio -0.70 0.70 0 0 0 Contrib rate to private pension -0.36 0.00 -0.36 0.00 0.01 Tax on private pension earnings 0.03 0.00 0.03 -0.02 -0.03 Interest rate 0.47 -0.05 0.42 -0.25 -0.50 Remove interest income tax 1.52 -0.17 1.35 0 -2.42 C. Economy-wide and demographic changes Period 1 income: 10% increase 1.00 -0.11 0.89 2.60 5.49 Ratio NW/NP: 10% reduction 0 0 0 -1.13 -2.22 Housing pref: 10% increase in γ0.26 0.58 0.84 2.63 5.56 Part A of Table 3 refers to the tax and expenditure policies whose impacts were estimated assuming the same change in non-pension expenditure (an increase of 5%); in this way they are directly comparable. Raising the tax rate on labour and interest income reduces the saving rates and lowers demand in the housing market. In contrast, a rise in the rate of GST lowers consumption but, because it does not affect intertemporal price ratios, leaves saving and the housing market unaffected. The increase in G requires a large reduction in the PAYG pension, of over 30%, and not surprisingly this stimulates a relatively large increase in financial savings. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 27 Figure 3: Percentage Point Changes in Saving Rates Figure 4: Percentage Changes in House Prices WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 28 Of the other policy changes shown in Part B, all relevant policy variables are increased by 10% except for the policy of removing the tax on interest income which is clearly a very much larger change (the relevant tax rate falls from 25% to zero). Care must therefore be taken interpreting the larger increase in savings reported by this policy change. Furthermore, the increase is modified when the income tax rate is simultaneously raised in order to keep G constant. 27 This is the main change which affects the intertemporal effective price ratio between present and future consumption, so the reduction in the price of consumption in period 2 leads to more saving. The direction of change is unambiguous in the case of Cobb-Douglas utility assumed here, with a high elasticity of substitution.28 The results here represent an upper bound on the increased saving rate for several reasons. First, in reality any policy change would probably be less than the total removal of the tax. Second, higher savings over the working life would be matched by decumulation in retirement, leading to no change in aggregate. Third, the Cobb-Douglas form of the utility function leads to greater substitution towards savings than with an intertemporal elasticity of substitution less than 1. 11 Conclusions This paper has examined the inter-related choices made by a representative household regarding saving, consumption, housing and retirement income. It has developed a two-period life-cycle model in which the optimal values of these variables are all outcomes of utility maximising behaviour of a representative household, subject to a budget constraint. In addition, an important element of the model is the incorporation of a government budget constraint, in which government pension and all other expenditures are financed on a pay-as-you-go basis. This ensures that any policy changes do not result in budget imbalances and associated changes in public debt levels. Furthermore, there are critical feedbacks from the government to the household sector via taxes, pensions and non-transfer expenditures. The model incorporates income taxation, including interest-income taxation, as well as a broad-based consumption tax in the form of a GST. It has a universal (non-taxable) public pension and accommodates both private pension savings and a compulsory 27 In the present model this has a relatively small effect because a small amount of revenue is raised by interest-income taxation. In reality, most interest-income tax is raised at higher marginal tax rates, and the tax forms about 6% of total personal tax revenue. 28 Elasticities of substitution below unity imply smaller responses, and for low elasticities the income effect can in fact outweigh the substitution effect of a price change. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 29 saving scheme. The model is calibrated to a stylised version of the New Zealand economy. It is then used to simulate the responses of the representative household to a change in policies and other exogenous shifts. Particular attention is given to the response of savings, consumption and housing to changes in various tax rates, pension and savings policies, and demographic changes. In general the responses are typically modest. For example, a 6% rise in the average income tax rate reduces both financial saving and total saving rates by 0.7 percentage points. In view of the fact that New Zealand gives essentially no tax concessions on interest income, this issue was explored in some detail. The model was adjusted to eliminate all tax on interest income. In the first instance financial savings and total saving rates rise by 17% and 8% respectively. Overall household saving rates would rise by 1.4 percentage points. This is accompanied by a significant shift toward consumption in retirement and weaker consumption of housing services leading to a fall in house prices of some 2.5%. The loss of tax revenue is compensated by a reduction of some 1.7% in the public non-pension expenditure, while holding unchanged the real value of the universal pension. In contrast, if the non-pension expenditures were to be also held constant, then tax rates elsewhere would need to be increased. These results underscore the importance of including a government budget constraint and, in particular, the mechanism by which a balanced budget is achieved after a policy intervention that alters the initial level of tax revenue or total expenditure. Were the public pension to be indexed to a mix of wages and prices such that it grew in real terms at 1.0% rather than 2% (in annual terms), the overall effect would be to reduce lifetime wealth following the fall in the real value of the public pension. Hence, consumption in both periods falls very slightly, the financial and total saving rates increases slightly, and the housing saving rate falls modestly. Raising the rate of compulsory saving by 10% from its base of 3.5% of gross income leads to offsetting declines in other financial savings; in fact on average households would fully offset the effect of a compulsory savings scheme by a commensurate reduction in their voluntary private savings. A 10% decrease in the loan-to-value ratio from its benchmark of 0.5 results in a shift of savings from financial savings toward housing, but with little overall impact on total savings. The housing market is unaffected with no long run changes predicted in either prices or the stock of housing. All these results have been obtained as comparative static exercises. They do WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 30 not allow for either the time that adjustments to policy changes would take, or the time path of those adjustments. Despite the strong assumptions of the model, it provides a rigorous and internally consistent framework for assessing the direction and magnitude of key long term responses in saving, consumption, housing and pensions to potential changes in tax and retirement income policies. Particular attention in the simulations was given to the potential impact on household saving rates of a range of policy changes. Typically the effect on saving rates was found to be modest. In most instances, it would take very substantial changes in existing policy settings to induce significant increases in household saving rates. The main options that would increase household saving rates by more than one percentage point are reductions in the level of the PAYG pension or a substantial cut in the taxation of interest income. In both cases house prices would decline by 2 to 3%. However there are different fiscal implications. While a reduction in the pension would allow for tax cuts or increases in other expenditures, the loss of revenue from reducing taxes on interest income would mean higher taxes or reduced expenditure on non-pension items. Higher average incomes over the working life would result in higher rates of household saving, increased consumption and higher retirement incomes. However some of the increased demand stemming from higher incomes would affect the housing market. In the long run the stock of housing would increase, but in the short run some of the demand would be reflected in higher house prices. Any potential policy changes which are explicitly designed to raise saving rates should recognise that the long run impact is likely to be modest. An analytical framework such as that developed here can help to understand the complex interactions and provide some guidance on the likely magnitude of policy responses. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 31 Appendix A: Renting versus Ownership In the two period model of this paper, the assumption was made that the representative individual does not purchase a house in the second (retirement) period of the life cycle. The aim of this appendix is to examine the conditions under which it would be optimal to purchase a house in period 2, while renting in period 1, rather than purchase in period 1. The assumption underlying the above analysis is strengthened if it turns out that very strong conditions are required for purchase in period 2 to be optimal. Given this objective, in what follows there is no need to consider the option of renting in both periods. Furthermore, to simplify the analysis, this appendix abstracts from income and consumption taxation, and transfer payments (such as a tax-financed pension). In addition, no mortgage borrowing is allowed. The representative consumer must choose optimal values of consumption of nonhousing and housing in both periods [C1, C2, CH1, CH2] . The fundamental choice considered here is to be a renter (typeR ) in period 1 and buy a house in which to live in period 2; or to be an owner (typeO ) in period 1 and live in the house in both periods. The ‘renter’ must accumulate financial savings in period 1 to fund both house purchase and retirement income in period 2, as well as paying rent in period 1. The ‘owner’ saves in period 1 to fund only retirement income in period 2. Housing consumption, CH1 and CH2 , can be thought of as being measured in ‘quality units’. For a house owner, consumption is equal to the imputed rent. For a renter, consumption is somewhat below the equivalent imputed rental: there are benefits merely from the fact of ownership which are not appropriated by a renter. One approach to this problem would be to set up the complete optimisation problem involving the range of discrete choices available. However, progress can be made using a simplified approach to obtain an indication of the condition required for option R to be preferred to option O , as follows. Let superscripts R and Orepresent consumption in the respective cases. Table 4 gives expressions for C1, C2, CH1 and CH2 , for the R and O cases, in terms of the corresponding savings, and informed by the relevant budget constraint. Consumption of non-housing by renters in period 1, CR 1 , is equal to exogenous income, y1 , less financial savings in period 1, SR 1 , less housing rent paid in period 1, R1 . As mentioned above, the payment of rent gives rise to ‘quality units’ of consumption of CR H1 = φR , with φ < 1. Consumption of non-housing in period WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 32 Table 4: Budget Contraints for Renters and Owners Renters Owner-Occupier CR 1=y1−SR 1−R1CO 1=y1−SO 1−SO H CR 2=y2+θSR 1(1 + r)CO 2=y2+SO 1(1 + r) CR H1=φR1=φλSO HCO H1=λSO H CR H2= (1 −θ)SR 1(1 + r)CO H2= (1 −λ+π)SO H Table 5: Consumption Differences (1) CO 1−CR 1=SR 1−SO 1−(1 −λ)SO H (2) CO 2−CR 2= (1 + r)(SO 1−θSR 1) (3) CO H1−CR H1= (1 −φ)λSO H (4) CO H2−CR H2= (1 −λ+π)SO H−(1 −θ)SR 1(1 + r) 2, CR 2 , is equal to y2 + θSR 1 (1 + r )where θ is the fraction of the total return to financial saving, SR 1 (1 + r ), that is allocated to period 2’s non-housing consumption. Hence a fraction, 1 −θ , is allocated to house purchase in period 2. This delivers CR H2 = (1 −θ ) SR 1 (1 + r )of housing consumption, as shown in the final line of Table 4). The right-hand column in Table 4 shows the corresponding expressions for consumption in the O case. Here, CO 1 is income, y1 , less housing equity in period 1, SO H , less financial savings, SO 1 . The housing asset, SO H , delivers housing consumption in both periods. Let a fraction λ , be delivered in period 1, with 1 −λ in period 2. Housing consumption in the later period also benefits from the appreciation of the asset at rate π . A possible value for λ would be around 0.67 where the working life (period 1) is approximately twice the length of the retirement period 2. Using the expressions in Table 4, the differences between the four consumption values are given in Table 5. The expressions in the table do not of course represent solutions for the differences between consumption levels: the various values of forms of savings are endogenous. Nevertheless, further insights can be obtained by making the assumption that, for optimal solutions, the period 2 consumption values are the same for R and O -types, so that CO 2−CR 2 = 0 and CO H2−CR H2 = 0. By assumption, R is a home owner in the second period, so that both types enjoy WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 33 Figure 5: Variations in Housing Consumption with Rate of Interest Figure 6: Variations in Housing Savings with House Price Appreciation WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 40 while the latter are more relevant for many of the comparative static comparisons. More appropriate comparisons of elasticities would be for values of α , β and γ which give similar ‘benchmark’ values of the major endogenous variables of interest. However, calculations show that the term, EW,r , is a relatively large component of the various elasticities derived in this appendix. Yet it has been seen that the role of the budget constraint, involving an endogenous change in P , is to leave Wvirtually unchanged when the rate of interest changes. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 41 References Attanasio, O.P. and Brugiavini, A. (2003) Social security and households’ saving. Quarterly Journal of Economics, 118, pp. 1075-1119. Attanasio, O.P. and Rohwedder, S. (2003) Pension wealth and household saving: evidence from reforms in the United Kingdom. American Economic Review, 93, pp. 1499-1521. Aura, S., Diamond, P. and Geankoplos, J. (2002) Savings and portfolio choice in a two-period two-asset model. American Economic Review, 92, 1185-1191. Bernheim, B.D. (1992) Is the baby boom generation preparing adequately for retirement? Merrill Lynch Technical Report (Princeton, NJ). Chetty, R. and Szeidl, A. (2012) The effect of housing on portfolio choice. (Unpublished paper, Harvard University). Coleman, A. (2010) Squeezed in and squeezed out: The effects of population ageing on the demand for housing. Motu Economic and Public Policy Research Working Paper, No. 10-01. Creedy, J. (1997) The Statics and Dynamics of Income Distribution in New Zealand. Wellington: Institute of Policy Studies. Creedy, J. (1990) Modelling wealth in a simple two-period model. Journal of Econometrics, 43, pp. 167-177. Creedy, J. and Moslehi, S. (2011) Modelling the Composition of Government Expenditure. Cheltenham: Edward Elgar. de Freitas, N. E-M. and Martins, J.O. (2013) Health, pension benefits and longevity: How they affect household savings? Network for Studies on Pensions, Aging and Retirement Discussion Paper DP10/2013-046. Diamond, P.A. (1977) A Framework for Social Security Analysis. Journal of Public Economics, 8, 275-98. Disney, R. (2005) Household saving rates and the design of social security programmes. CESifo Working Paper, No. 1541. Disney, R. (2006) Household saving rates and the design of public pension programmes. National Institute Economic Review, 198, 61-74. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 42 Guest, R., Bryant, J. and Scobie, G. (2003) Population ageing in New Zealand: the impact on living standards and the optimal rate of saving with a flexible real exchange rate. New Zealand Treasury Working Paper 03/34. Gunning, T.S., Diamond, J. and Zodrow, G.W. (2008) Selecting parameter values for general equilibrium model simulations. The James A. Baker III Institute for Public Policy, Rice University, March. Havr ´ anek, T. (2013) Publication bias in measuring intertemporal substitution. IES Working Paper, WP 15/2013. Hayashi, F., Ito, T. and Slemrod, J. (1988) Housing finance imperfections, taxation and private saving: a comparative simulation analysis of the United States and Japan. Journal of the Japanese and International Economies, 2, 215-238. Henry (2010) Australia’s Future Tax System. Accessed at: http://taxreview.treasury.gov.au/Content/Content.aspx?doc=html/home.htm. Hurd, M. Michaud, P-C. and Rohwedder, S. (2012) The displacement effect of public pensions on the accumulation of financial assets. Fiscal Studies, 33, 107-128. Kuttner, K.N. and Shim, I. (2013) Can non-interest rate policies stabilise housing markets? Evidence from a panel of 57 countries. Bank for International Settlements Working Paper No.433. Law, D. (2013) Retirement income policy and national savings. New Zealand Treasury Working Paper, no. WP 13/28. Lindbeck, A. and Persson, M. (2003) The gains from pension reform. Journal of Economic Literature, XLI, 74-112. Moore, J.F. Mitchell, O.S. (1997) Projected retirement wealth and savings adequacy in the health and retirement study. National Bureau of Economic Research Working Paper, no. 6240. Retirement Policy Research Centre (2010) Household wealth in Australia and New Zealand. Pensions Briefing 2010-05. Accessed at: www.docs.buiness.auckland.nz/doc/pensionbriefing-2010-5-household-wealthin-australia-and-new-zealand-revised.pdf S ´ anchez, A.C. and Johansson, ˚ A. (2011) The price responsiveness of housing supply in OECD countries. OECD Economics Department Working Paper, no. 837. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 43 Savings Working Group (2011) Saving New Zealand: Reducing Vulnerability and Barriers to Growth and Prosperity. Final Report to the Minister of Finance, Wellington. Accessed at: www.Treasury.govt.nz/publications/reviewsconsultation/savingsworkinggroup. Scobie, G.M., Gibson, J. and Le, T. (2004) Saving for retirement: new evidence for New Zealand. New Zealand Treasury Working Paper, 04/12. The Treasury (2013) Affording Our Future: Statement of New Zealand’s Long Term Fiscal Position. Wellington: New Zealand Treasury. Venti, S.F and Wise, D.A. (2001) Ageing and housing: another look. In Perspectives on the Economics of Ageing (edited by D.A. Wise). Chicago: University of Chicago Press. WP14/14 Pensions, Savings and Housing: A Life-cycle Framework with Policy Simulations 44