Many people seem to link high housing prices
with bubbles and immigration. This is an election year so more will be said as
the date of the election draws closer. Unfortunately, I have not seen any economic
analysis and measurements except from some graphs and some stories, here and
there.

I think that bivariate graphs are fine, but uninformative of a multivariate problem like this one. It is quite common to eyeball a strong graphical correlation, which disappears in regression analysis. Some stories, however, are reasonable. For example, expansionary (i.e., loose) monetary policy usually results in credit expansion, which leads to a higher demand for housing, and higher prices. I showed in a blog before that excess supply of money is also correlated with higher housing prices at a reasonable lag. Some dismiss money and talk about low interest rate instead. Fine too, because a lower interest rate increases the demand for money and credit and leads to higher asset prices. There is a general agreement that looser monetary policy also stimulates output (GDP) in the short run. It ends up opening a positive output gap whereby GDP exceeds its long-run potential over the business cycle. That must have an effect on the demand for housing, hence high housing price. These stories are fairly grounded in economic theory.

Housing supply issues are also widely acknowledged. Finally, the story that an increase in immigration could add a demand pressure on housing, why not? But where is the test? The graph shows cyclical variations in the housing price index and net immigration. There is a weak correlation (0.30), where immigration leads, but totally breaks down in 2008.

I think that bivariate graphs are fine, but uninformative of a multivariate problem like this one. It is quite common to eyeball a strong graphical correlation, which disappears in regression analysis. Some stories, however, are reasonable. For example, expansionary (i.e., loose) monetary policy usually results in credit expansion, which leads to a higher demand for housing, and higher prices. I showed in a blog before that excess supply of money is also correlated with higher housing prices at a reasonable lag. Some dismiss money and talk about low interest rate instead. Fine too, because a lower interest rate increases the demand for money and credit and leads to higher asset prices. There is a general agreement that looser monetary policy also stimulates output (GDP) in the short run. It ends up opening a positive output gap whereby GDP exceeds its long-run potential over the business cycle. That must have an effect on the demand for housing, hence high housing price. These stories are fairly grounded in economic theory.

Housing supply issues are also widely acknowledged. Finally, the story that an increase in immigration could add a demand pressure on housing, why not? But where is the test? The graph shows cyclical variations in the housing price index and net immigration. There is a weak correlation (0.30), where immigration leads, but totally breaks down in 2008.

Bubbles mean that the increase in housing prices is not justified
by the economic fundamentals. I think that there is no reliable statistical
test for bubbles and I have not seen a credible and convincing proof for
bubbles. However, when the supply of housing is fixed for whatever reason then shocks
that shift up the demand for housing (imagine a downward slopping curve
intersecting the vertical supply curve) will only result in ever higher housing
prices. This is quite easy to understand.

Here are some simple measurements. I estimate a simple equation for
housing prices in New Zealand, whereby the level of the house price index
(base=1000) depends on aggregate income (GDP), which reflects money and credit
markets, interest rate, fiscal policy factors….etc. (think about the goods and
money markets).[1]
It also depends on a measure of the supply of housings, which I approximate by
the ratio of the value of

*new*building consents / the value of the existing stock of housing. Finally, we have net immigration as an addition explanatory.[2]
Looking at the estimated long-run equilibrium of the model and the
actual housing price index shows no bubbles whatsoever. The housing price
fluctuates around the equilibrium closely. It was above equilibrium from 1996
to 2000; slightly overshot its equilibrium value in 2015; and less than or
equal to equilibrium during the rest of the period.

The coefficient of net immigration, conditional on demand and
supply factors, is 0.015 (with a standard deviation of 0.0055). So an increase
(decrease) of 50,000 people leads to an increase (decrease) in the housing
price index by 750 points, e.g., from 1000 to 1750. That is a growth
of 75 percent. GDP has a larger effect on housing prices. The coefficients is
0.059 (with standard error 0.0050). The supply factors have a coefficient of
-0.07 (standard error 0.0550). An increase in new building consents relative to
the stock of housing lowers the housing price index. This is a very large
coefficient. An increase of 100,000 new building consents lowers the housing
price index by 7000 points.

Unfortunately
I do not have data for Auckland and other regional housing markets so my
analysis is restricted to New Zealand as a whole. I hope that this is a useful
analysis. Someone may want to take it further, which could shed more light on
the matter. Panel data analysis could be done if regional data are available.

[1] We
cannot have credit in the model because it is highly correlated with GDP. The
same is true for money.

[2] The
equation is estimated over the period Mar 1996 to Dec 2016 using two-sided Dynamic-OLS
(Phillips-Loreatn, 1991). This is a most efficient estimator. It is equivalent
to a system of equations and accounts for endogeneity and serial correlation.
Housing price index is regressed on a constant term and the levels of GDP, the ratio
of new building consents / housing stock ratio, and net immigration; the growth
rates of these three variables; one lag and one lead of the growth rates (i.e.
the two-sidedness); and an error correction term. It assumes that the levels are
integrated of order 1, and cointegrated. Standard errors are consistent Newey-West.
The data are from the RBNZ website. Monthly new building consents are from Stat
NZ. It includes residential buildings, houses, apartments, townhouses, and
retirement village units. I ignored public building and constructions.