# RDP 2009-07: Estimating Marginal Propensities to Consume in Australia Using Micro Data 4. Methodology

In this section, we outline the models used to estimate the MPC out of tax cuts, the Baby Bonus and the Carer Bonus. Different methodologies are employed due to differences in the nature of the policy changes and data availability.

## 4.1 Tax Cuts

Following specifications used in previous studies (for example, Lusardi 1996 and Parker 1999), we estimate a standard version of a consumption Euler equation using a fixed-effects regression model. Given our data, the model is based on a balanced panel of households across three years; we also estimate a model in first-differences as a robustness check. These specifications have the advantage of allowing for unobserved household characteristics that are time-invariant. The model is:

where Expenditureit is the annual expenditure (on ‘non-durables’ or ‘strictly non-durables’) for household i at time t. The key variable Taxit is the measure of the value of tax paid by the household (as described in Section 3). β is the MPC out of the extra income associated with the tax cuts. The household fixed effect αi represents time-invariant unobserved heterogeneous characteristics such as household preferences. Variations in household characteristics over time are captured by the vector xit, which includes the number of adults and the number of children in the household,[13] the self-reported value of a home owner's dwelling (excluding home contents),[14] and a dummy for whether the household head possesses a credit card.[15] We also include time-specific effects, γt, which capture features of the macroeconomic environment that affect all households, such as interest rates, inflation and a general improvement in living standards. εit is the individual time-varying unobserved effect. Estimating the model using real variables (derived by using the private consumption deflator) does not materially change the results.

Consistent with the literature, current income is not included in the regression. One reason for this is that current income and consumption are likely to be endogenous, resulting in biased estimates (see Johnson et al 2006 for a discussion). This endogeniety arises because a household may consume more due to a higher income or might strive for higher income in order to be able to consume more. While we could instrument for current income, the better strategy is to utilise exogenous policy changes to identify the MPC. Another reason for excluding income is that it is potentially difficult to distinguish between temporary and persistent shocks to income – which theory suggests might have quite different effects on consumption. Again, this is a good reason to make use of the policy changes to identify shocks to income.[16]

In the sample, we exclude 401 multi-family households. We also exclude three extremely high-income households, although this makes little difference to our results. Due to missing expenditure data, we have around 5,600 households in our balanced panel, depending on the expenditure classification used (see Table 4 for precise details).

## 4.2 Lump-sum Transfers

Both lump-sum transfers – the Baby Bonus and the Carer Bonus – apply only to a small subset of the population. To accurately estimate the effects of receiving such a transfer on expenditure we ideally would compare the expenditure of those households that received a bonus with the amount those households would have spent had they not received a bonus. Obviously, the latter amount is not observed, so the next best option is to use the expenditure of households that are similar in almost every way to the households that received the bonus, except for the fact that they did not receive the bonus.

To get a suitable control group to estimate the MPC out of the Baby Bonus, we restrict our sample to those households that had a baby between October 2005 and March 2007, nine months either side of the approximately \$1,000 increase in the bonus in July 2006. Although all of these households would have received a bonus, the variation in the bonus payments across time, particularly the substantial change in July 2006, provides natural treatment and control groups. Since all households in this sub-sample had, or adopted, a baby around the same time, there is no reason to expect that there is some fundamental difference in the distribution of their characteristics; indeed, we find that the means of various characteristics for the two groups of households are not substantially different from each other. In contrast, the characteristics of households receiving the Baby Bonus are likely to be quite different to those that did not receive it, for example they are likely to be in a particular age group and have particular preferences. Combined with the additional costs of having a child, these differences imply that their expenditure patterns may be different from the rest of the population, and hence comparing the expenditure of households that received the bonus to that of the wider population would be inappropriate.

For the households that have had children in the 18-month period from October 2005 to March 2007, we use fixed effects to estimate a model of household expenditure across three waves of the HILDA Survey, as follows:

where: Expenditureit is annual household expenditure (on ‘non-durables’ or ‘strictly non-durables’); Bonusit is the size of the Baby Bonus in the time period that the household receives it; xit is a vector of household characteristics that vary across time; αiis a constant unobserved household fixed effect; and εit is the individual time-varying unobserved effect. The household characteristics we control for are a dummy variable for whether or not the baby is the household's first, the number of adults (people aged 15 years and over) in the household, and the self-reported value of a home owner's dwelling (excluding home contents). We also include time-specific effects, γt, which capture features of the macroeconomic environment that affect all households. These time effects are highly correlated with the policy variable, Bonusit. Consequently we also include a variant of the model that excludes time effects, although this makes the results more difficult to interpret. As with the model for tax cuts, estimating the model using real variables did not greatly affect the results.

In the HILDA Survey, 247 households had, or adopted, a baby between October 2005 and March 2007.[17] Of these, 80 households have some missing or inconsistent expenditure data and so are dropped from the sample.[18] We further restrict the sample by dropping those very few households that had two babies during the sample period. The final sub-sample for the Baby Bonus regressions consists of 161 households, 106 households that received the pre-July 2006 rate and 55 that received approximately \$1,000 more.

Like the Baby Bonus, households that receive the Carer Bonus are likely to be noticeably different from other households. At least one person in these households provides care to another person in a private dwelling. These households are also likely to have other inherent differences to non-carer households, which makes it difficult to find suitable households for comparison in order to predict how carer households were likely to have behaved had they not received the bonus.

Given that there was no change in the Carer Bonus over our sample period, we use one-to-one matching techniques to find a suitable control group. If we can find suitable ‘matches’, then these techniques assume that there are no important differences between the two households, other than the fact that one received the bonus and one did not. Our preferred matching method is nearest-neighbour propensity score matching. The propensity score is the estimated probability that a household received the transfer, and this method matches each recipient household to the non-recipient household with the closest propensity score. The propensity score is estimated using household characteristics that simultaneously affect the participation decision (to receive the transfer) and household expenditure to ensure that recipient households are matched to an appropriate control. The propensity score is estimated for each household using a logit model:

where: Di is one if the household is in the treatment group and zero otherwise, and xi is a vector of household characteristics. Household characteristics must satisfy the condition that they simultaneously influence household expenditure and eligibility for the bonus. We include a number of variables to control for: the number of children under 15 years of age; the number of adults; the share of adults working full-time; the highest level of education in the household; income; the value of assets in Wave 6; [19] whether the household has a mortgage; the number of household members reported to have a long-term health condition, disability or impairment; and a variable that indicates whether someone in the household is a carer of a person who is not a resident in that household. Once a suitable control sample has been formed we compare the difference in the (weighted) conditional means of expenditure of the treatment and control groups to get an estimate of the MPC.

## Footnotes

Children are defined as being under 15 years of age. The time variation in these variables is generated from respondents moving into, or out of, households and household members ageing and thus changing groups. [13]

Ideally we would like to have included a more comprehensive measure of wealth. However, other wealth measures are only available in Wave 6. The property value variable thus proxies for changes in household wealth over time. Given that 42 per cent of household wealth is held in housing assets, this is probably a reasonable assumption (Australian Bureau of Statistics 2004). There is variation in this variable for 60 per cent of households. However, it should be interpreted with care as this is a self-reported measure and variation could be due to arbitrary reporting differences across time. [14]

This accounts for the possibility that households who obtain a credit card may do so in order to fund greater consumption. Since this is a fixed-effects model, this variable is identified by comparing households that change status with those that do not. We do not account for the effect that servicing any credit card debt will have on consumption. [15]

We tried including lagged income (which by construction is highly correlated with our estimate for taxes) as a control in the regression. As discussed, any interpretation of the coefficient on income is problematic. However, it is important to note that the key results including the MPC estimates are robust to the inclusion of income. Results are available from the authors upon request. [16]

We restrict our sample to two-parent or single-parent households. Group households and multi-family households were excluded. [17]

Households were only dropped from the sample if data were missing in the year immediately before and after the baby was born or adopted. [18]

The value of assets is available in Wave 6 and is assumed to be constant over the three waves. [19]