RDP 2020-04: The Apartment Shortage Appendix E: Sensitivity Analysis

Some changes to our assumptions would change the results in obvious ways. For example, were we to assume that infrastructure charges or developer's margins were not a necessary cost of supply our estimates of the effect of building restrictions would increase substantially, other things equal. Were we to measure lower prices, the effect would be smaller. The following two subsections discuss variations that are less straightforward.

E.1 New versus Average Sale Prices

Glaeser et al (2005) note that construction costs for newly completed buildings should be compared with sale prices for new apartments, but consider adjusting for the depreciation of older units to be too difficult, so use prices for all dwellings. Kendall and Tulip (2018) followed this approach. We also face problems with data on building age, but believe these are surmountable. In particular, many sales are missing values for year of construction. However, there is very often an observation recorded for at least one apartment in a building. We assume that all apartments in a building are built at the same time and this can be estimated by the modal construction year of dwellings within that building. For Sydney, this increases the proportion of sales with year of construction data from 75 to 92 per cent.

We then exclude all sales more than five years after the estimated construction date. As shown in Table A1 this reduces our sample by 80 to 90 per cent. However, it has small effects on prices in 2016, raising them by 1 per cent in Sydney and 4 per cent in Brisbane, while lowering them 4 per cent in Melbourne. These effects are much smaller than earlier in the sample or the conditional estimates of depreciation from the hedonic regression in Appendix D. As noted earlier, our dataset contains substantially fewer new sales than completions at the end of our sample, raising concerns about the representativeness of the latest estimates. While our approach seems conceptually superior to others' assumption of zero depreciation, there is a chance that it may understate prices of new properties at the end of our sample.

An alternative approach would be to exclude sales of an apartment after the first sale, as is done by CoreLogic (reported in UDIA (2019, p 16)). However, for our dataset, which begins in 1997, this is impractical. It would involve assuming that almost all sales near the beginning of our sample are new sales.

Sales in the early part of our sample are more likely to be missing observations on building age. If we recalculate our historical estimates using average, rather than new, sale prices we find that the effect of building restrictions is still positive in all three cities over the past decade, and especially large for Sydney. However, when calculated this way, the effect of building restrictions in Melbourne and Brisbane is often negative prior to 2009. The effect remains positive in Sydney, but was relatively small in the late 1990s.

E.2 The Effect of Height

In Section 4.2 we estimate the effect of building up by regressing per unit construction costs on building height. In doing so, we weight observations by number of buildings, on the assumption that each building provides an independent observation on the cost–height relationship. Alternative approaches include using unweighted estimates, or weighting observations by the number of dwellings or gross floor area. Table E1 compares these alternative estimates with our baseline. In all cases, using a different weighting scheme would imply a flatter average cost curve than presented in the body of the paper. We argue that weighting by buildings both makes sense conceptually and provides a more conservative estimate of the slope coefficient and hence the ratio of marginal to average cost.

We also check the sensitivity of these results to outliers. A handful of observations – corresponding to very tall buildings – exert relatively high leverage. As a crosscheck, we exclude buildings above 50 storeys. This increases the slope coefficient by about 15 per cent, relative to the baseline. Base costs and the overall fit of the model are largely unchanged. We prefer to include the full sample since these differences are relatively modest and there is no obvious reason for disregarding the excluded observations. This exclusion result suggests that the slope of our cost curve might decline with height. However, most studies shown in Figure 3 show the opposite nonlinearity.