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# Tobin’s Q

## 5. Comparative Empirical Analysis

### 5.3. Tobin’s Q

Figure 5.13

Source: SCB, 2015; Svensk Mäklarstatistik, 2017; OECD, 2006; Own calculations

From our results, we have observed that the Norwegian housing market is currently showing some bubble tendencies, in the sense that the real P/R ratio has for some time now been above the fundamental P/R ratio. Also, the trend of the housing price index compared to the CPI and rent prices is significant.

However, compared to its fellow Scandinavian country Sweden, the Norwegian market seems to be more stable. The Swedish housing market is showing an increasing rate of the real P/R ratio relative to its fundamental P/R ratio, which is unsettling. From this investigation, we would support the ERCB’s conclusion regarding the Swedish housing market.

Equation 5.9

𝑇𝑜𝑏𝑖𝑛𝑠 𝑄 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐶𝑜𝑠𝑡

This theory therefore states that housing prices and construction costs will converge in the long run.

With house prices being higher than construction costs, including the cost of construction and the cost of vacant land, developers would continue construction until prices equal each other and vice versa (Lerbs, 2012). The Q-theory is therefore useful in order to test whether market prices on housing have fundamental support from construction costs.

### 5.3.1. Marginal and Average Q

Since the Q described by Tobin is the ratio of one additional investment asset to its replacement cost, this is the marginal Q. The one used in empirical studies is however the average Q, as the marginal Q is not directly observable. Average Q is the ratio of the market value of existing capital to its replacement cost. Fumio Hayashi (1982) derives the relationship between them, and describes the specific scenario where average Q = marginal Q:

The suppliers in the market are price takers;

The market is characterized by perfect competition, so the individual supplier has no impact on prices, and adjust quantum according to demand. In a market with price-making suppliers, average Q would be higher than marginal Q, as the market value of an additional unit of capital would be higher than the value of an existing unit of capital.

Perfect capital markets;

Free flow of capital between borders is a necessary condition, as constraints on capital can limit firms from following their optimal investment strategies.

The production and installation function are linearly homogeneous with constant returns to scale:

This means that an increase in input variables will result in an equal increase in the output variables.

Investors are more willing to invest when the value of Q is high. As more and more investors start to invest, the value of the marginal Q will decrease. As long as Q > 1, rational investors will keep investing until marginal Q = 1. Therefore, the long run equilibrium for marginal Q is the same as the long run equilibrium for average Q: Q = 1.

Figure 5.14

MCC = Marginal Cost of Capital

MPK = Marginal Product of Capital

Q>1 then MPK>MCC, so it will be optimal to increase investment

Q<1 then MPK<MCC, so it will be optimal to decrease investment

Source: Own creation

### 5.3.2. Tobin’s Q and the Housing Market

The market price of housing is easily observable in the market. Comparing this to the replacement cost which is the total sum of all costs related to the construction of new housing gives us a Q-value that can help determine if there exists a bubble in the housing market. As housing varies greatly in size the market prices and replacement costs are usually measured in price per square meter.

For Q-values greater than 1, there is a profit to be made for investors with capital to invest. For the housing market, this means that home builders will be encouraged to turn uninstalled capital (lumber, nails, labor) into installed capital (Foote, 2010). Arguments can be made that a bubble exists if the market value greatly differs from the fundamental value, which is the same as market value being greater

than the cost of construction. Recalling that the long-term equilibrium is Q=1, we conclude that there are bubble tendencies if we see Q>1 for a longer period of time.

### 5.3.3. Limitations

Corgel (1997) raises several concerns about using Q-theory to analyze the housing market:

• The observed transaction prices might not be a good reflection of asset values.

• When the ratio is used to assess development opportunities, the ratio should be assembled from the value of newly constructed assets to development cost.

• The denominator should contain an adjustment to replacement cost for economic depreciation when the Q-ratio is used to evaluate price appreciation potential in the market. Newer housing will last longer and have a higher standard than old housing.

• Finally, the reported ratio yields little information about the intangible values of real estate and real estate firms.

As pointed out by Corgel, newer housing will last longer and have a higher value than old housing. But including economic depreciation for old housing will be practically impossible. Buildings vary in age, standard and some have been refurbished recently while others can be virtually the same as they were decades ago. As an investor, the Q does not tell whether it is more profitable to build or buy, as it compares buying an old dwelling to the price of building a new one. Investors should compare the selling price they can get for a new dwelling to the cost of building a new if they are to use the Q-theory for investment decisions. The original Q-theory calculated the market price of a company by multiplying the number of outstanding shares with the market price of shares. This can be troublesome, as this market price contains a lot of expectations about the future. This is also true for housing prices, and therefore a variable that contains information about expectations for the future is included in later analyses. Because we add the site cost, our results might be skewed downwards. The site cost in the cities are much higher than the site cost in more remote areas in the north of Norway, thus pushing the average cost upwards.

This might give a lower average Q, telling investors not to invest even though it might be profitable in some areas. This also stems from the fact that we calculate using averages for the whole country, but Norway is as previously stated a country with huge local differences in prices, supply and demand.

Several market frictions that may imply a slow adjustment of real residential investment to house price and construction cost movements also makes the Q-theory a less good fit for the housing market (European Central Bank, 2013):

• Lack of transparency and land available for construction

• Time-consuming institutional procedures for granting building permits

• The time between starting and finishing a new building

This indicates that there exists a severe time-lag from planned to finished housing, thus the Q-theory might not be perfectly applicable to the housing market. Hence, observing a Q-value which is not at its equilibrium might be because of the delayed response from a change in prices or costs.

### 5.3.4. Data

The data used to estimate prices for Norwegian houses per square meter is collected from two different sources, as they together provide a longer time series. NEF, the Norwegian Real Estate Agents Association has published prices for 1985 – 2013, while SSB has published data from 2002-2016 (NEF, 2013) (SSB, 2017g). Using two different sources for house prices could lead to problems, but the average differences during the overlapping years is only about 1%, thus supporting our decision to use two different sources. NEF is no longer the publisher of the price data, as Eiendom Norge now is the main publisher of real-estate statistics and reports. This is however a subscription-only site, and as we do not have access to Eiendom Norge’s data, we will use a tool called WebArchive in order to access earlier versions of NEF’s site. This way, we can collect the data previously published by NEF. The price per square meter published by NEF is the average square meter price for the average Norwegian 100 square meter dwelling. For the data published by SSB, we use full-owner as a proxy for the average square meter price. This is justified by the fact that over 85% of all dwellings are full-owner dwellings.

The Norwegian State Housing Bank is the Norwegian state’s central organ for the government’s housing policy. Data on construction cost is found through annually published reports by Husbanken (Husbanken, 1985-2015). Their data is based on information from approved applications for mortgages and subsidies associated with projects related to construction, both new housing and repairs on existing

ones. As the data is gathered at the beginning of the construction period, the actual data might differ from the published data. Included in the data is both the cost and the size of land. The cost of construction includes both labor, materials, commission and construction loans. We are able to calculate construction cost per square meter both with and without the cost of land, as well as the isolated cost of land. Some years in the reports contain few observations, weakening the validity of the data. This needs to be taken into consideration while analyzing the data.

### 5.3.5. Empirical Testing

As stated earlier, the long-term equilibrium of Tobin’s Q is Q = 1. When Q is in equilibrium, the price per square meter for pre-owned housing is the same as the cost of construction per square meter, including the cost of land.

From figure 5.15 it is clear that for the data collected, it seems that Tobin’s Q for the Norwegian housing market actually does center around the equilibrium value, even though there are large and numerous deviations. The Q-value has fluctuated from 0.72 in the all-time low in 1992 to the all-time high in 2000 where Q equaled 1.19. Viewing these values in context with the historic development of Norwegian house prices, we see values below 1 during the Banking Crisis of the late 80’s and early 90’s, and the bursting bubble in 1987 is especially visible. The all-time low came in 1992, the same year as the real housing prices hit their lowest point. From 1988 until 1995 the housing market experienced a Q below 1, but from 1995 and onwards Q has been above equilibrium most of the time. There are however no clear indications of a bubble, as it fluctuates between 1.1 and 1 with an average of 1.04 the last 10 years, something that indicates that the increase in house prices are back by the fundamental construction cost.

Figure 5.15 indicates that the housing market has been more balanced in terms of construction prices compared to house prices for the past 10 years than for the period from 1985 until 2006. There is less volatility in the Q-measure the past 10 years.

Figure 5.15

Source: NEF; SSB 2017g; Husbanken 1985-2015; Own calculations

One of the arguments against using the Q-theory to analyze the housing market, is that the housing market is inelastic in the short-run, and that it takes time for suppliers to adjust to changes in demand.

This can be some of the reason for the constant change in Q, and that it does not stay in the theoretical long-term equilibrium. Building dwellings is a time-consuming process, and this has caused a surplus in housing demand. In big cities, the lack of supply is intensified by the scarcity of vacant land.

The Q-value is determined by the price, cost and by the cost of land. Only analyzing the value of Q will not tell us what is driving the development in Q. To analyze whether prices or costs are the biggest driver behind the changes, they are both displayed in figure 5.16:

0,6 0,7 0,8 0,9 1 1,1 1,2 1,3

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

### Tobin's Q for Norway

Figure 5.16

Source: NEF; SSB 2017g; Husbanken 1985-2015; Own calculations

Comparing prices and costs, it is clear that it was the fall in housing prices that caused the value of Q to be consistently low from 1987 and until 1992. The Banking Crisis made housing prices drop, and a rapidly decreasing oil price further intensified the economic downturn of this period. Costs were at the same time relatively stable, and from figure 5.16 it seems like costs follow prices with a short time lag.

An increase in housing prices is shortly followed by an increase in construction costs, and a decrease in housing prices is shortly followed by a decrease in construction cost. This highlights the lag between supply and demand and that a delayed reaction to a change in one of the variables could be one of the reasons for Q never staying at its long-term equilibrium. Throughout the last half of the 90’s, housing prices increased rapidly while construction costs took some time to catch up. The caused an artificially high Q-value that led to the drop in Q when costs started increasing following the initial increase in housing prices.

### 5.3.6. Comparison - Denmark

It proved more challenging to find data for Denmark than for Norway. Using the construction cost index and the housing price index from DST, we compute a Q-value based on index numbers, something that only tells us the development and not the actual level of Q (DST, 2016) (DST, 2017). This makes

0 5000 10000 15000 20000 25000 30000 35000

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

### House prices and construction cost, nominal per m2

Nominal prices Nominal costs

comparisons with the Q calculated for Norway less relevant, but differences in development are still possible to detect. Because of limitations in the time series published by DST, we had to limit our analysis to 2003-2015. Still, this period incorporates the boom seen in the years before the Financial Crisis and the large downturn which followed. The Q-value for the Danish market is presented below in figure 5.17:

Figure 5.17

Source: DST (2016;2017); Own calculations

The development does not seem to be as volatile as for the Norwegian market, though we are analyzing a shorter period. We also see a negative trend in Q from 2006 all the way until 2012. This indicates that the rise in building cost has been bigger than the rise in housing prices, which is also backed by an article published by Cembrit, a Danish manufacturing firm (Cembrit, 2015). The development was quite different than what was seen in Norway during that same period. In Norway, prices exceeded costs for most of the period. Like Norway, housing prices increased prior to the Financial Crisis, resulting in Q >

1 in Norway and a rising Q for Denmark in the years leading up to the crisis. When it started, the Financial Crisis hit Denmark’s housing market hard and this is clearly reflected in the figure. Prices on housing first started to recover in 2012, which is also shown in the figure. The base year here is 2015, so naturally Q is in equilibrium in 2015. However, this does not mean that the actual value of Q is in equilibrium due to the use of indexes.

0 0,2 0,4 0,6 0,8 1 1,2 1,4

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

### Index Q, Denmark

Outline

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