Variable Costs

Before estimating the variable cost parameters, it is instructive to compare Figure 2.6, the map of average tract prices per square foot, with Figure 2.7, which shows the mean square footage of new houses in each tract. We should expect landowners to try to take advantage

of higher prices per square foot on the margin by building larger houses. This is more or less what appears to happen. For example, new houses built in the western suburbs, where prices per square foot are highest, tend to be larger than elsewhere. The goal of the structural estimation is thus to see whether, holding the marginal price constant, there are differences in the size of houses built that are correlated with zoning.

I modify Equation 2.4 in several ways to take account of the data. In one specification, I exclude lot size — which I have just shown is largely a function of the zoning regime — and include only the zoning variables. In the other, I include both lot size and the set of zoning variables to explore how much of zoning’s effect comes directly through the lot size. In this version, I incorporate whether the lot size is zero in addition to the actual reported lot size, as in the hedonic price and lot size regressions.

In both specifications, I include county (mc) and year (mt) fixed effects to account

for systematic variation in variable costs across time or space. In addition, I need to parametrize how the Pioneer Institute and MassGIS primary use code variables affect costs and therefore the size of new houses that are constructed. I do this simply by including them as linear terms in the model, with one coefficient for each variable. The variable cost estimating equation, including the lot size terms, is thus

Et−1

logP_j,tx =αxxˆj,t+αlj,tlj,t+αzlj,tF l

j,t+Zj,tαZ +mc+mt+ξj,t−1 (2.11)

whereZj,t is a matrix comprising all of the zoning variables as well as a constant term and

αZ is a vector of coefficients for these variables.18 The parameters represent the effect of

changing the covariates on the marginal cost of construction per square foot of house size. Intuitively, these parameters are identified by comparing the sales price per square foot of

18_{Note that only the primary use code terms actually vary by tract (j) and year (t). As shown in Table}

2.3, the constructed factors vary only by municipality, while the remainder of the Pioneer variables vary by municipality and year.

house size with the sizes of houses built; if zoning and regulation had no effect, the cost

per square foot would be identical across regimes andαZwould be a vector of zeros.

I estimate Equation 2.11 via GMM, with all the variables other thanxˆj,t — the depen-

dent variable — as instruments.19 The results are shown in Table 2.6. When the lot size

terms are included, in column (1), the costs per square foot are generally similar across the single-family residential codes, although they are somewhat lower in R3 and R2 (the omitted category) than in residential codes with larger or smaller minimum lots. These coefficients are only marginally above their standard errors, which range from $15 to $20.

The differences between single- and multifamily regimes is much more stark, with codes ML, MM and MU driving up costs by more than $100 per square foot relative to R2, with standard errors between $20 and $30. This estimates are quite large compared with the average sales price per square foot — which is also the average marginal cost, by assumption — of about $80. The costs imposed by other forms of regulation are estimated to be fairly minimal, although limitations on building permits (Growphase) seem to drive marginal costs up a bit, while inclusive zoning (Include) reduces them.

The most important effect in column (1), however, comes through the lot size. Each one acre increase in the size of the lot decreases the marginal cost per square foot by $44, with a standard error of $5, while having a lot size recorded as zero causes a level shift of more than $114, with a standard error of $10. These estimates indicate that it is much more costly to built large units when lots are small or the area is zoned for multifamily units, since landowners and builders do not build larger houses even holding constant the marginal price per square foot.

In column (2) I exclude the lot size terms to look at the overall effect of zoning and regulation. The coefficient on house size remains the same as in the first column, at 0.16,

19_{This gives the same parameter values as isolating xˆ}

j,t and estimating via least squares, but then the

which means that the cost per square foot rises by 16 cents for each square foot increase in size. This convexity is necessary for the marginal price, which is constant, to equal the marginal cost at exactly one point in the house size domain.

Unsurprisingly, the zoning cost estimates are now larger, and a nearly monotonic re- lationship appears in the primary use codes, with costs rising as the minimum lot zoning becomes more stringent, from R3 to R4 to R5 and into multifamily. Changing a tract from entirely R2, the baseline, to medium-density multifamily (MM) would increase the marginal cost per square foot by nearly $250, more than three times the average marginal price per square foot of $80. Since tracts are large enough that few consist entirely of a single use code, the effective differences across tracts are smaller than these coefficients suggest, but they are still very large. Taken together, these results indicate that the sizes of new houses in eastern Massachusetts are determined in large part by the zoning regime, particularly the primary use codes, rather than differences in marginal prices.