Master Thesis in Economics, 30 credits
DYNAMICS OF U.S.
HOUSE PRICES
A VECM Approach
Marcus Ryhage
ACKNOWLEDGMENT
I would like to thank Giovanni Forchini at Umeå University, Department of Economics, for his guidance and expertise in the field of econometrics.
ABSTRACT
This paper aims to analyze the U.S. house price dynamics to estimate a long-term equilibrium price level for the U.S. housing market, using fundamental underlying macroeconomic factors.
For this, in line with the empirical literature, a vector error-correction model is employed. The results find a cointegrating relationship between the housing prices and its long-run driving factors: Residential Investment Ratio (RIR), Personal Disposable Income (PDI), and Construction Cost (CC), implying that these factors have a decisive role in determining equilibrium level of U.S. house prices. The estimated long-run equilibrium level suggests that the U.S. housing market is currently underpriced, which can bring some skepticism to our model. However, our model does manage to predict future house prices about one year in advance of the actual house price movement. Further, the slow rate of adjustment towards equilibrium testifies of a rigid housing market in the U.S.
Table of Contents
ABSTRACT ... 1
2 INTRODUCTION ... 1
2.1 BACKGROUND ... 2
2.2 PROBLEMDEFINITION ... 2
2.3 OBJECTIVEOFTHISSTUDY ... 3
2.4 LIMITATIONS ... 4
2.5 METHODDESCRIPTION ... 4
3 THEORETICAL FRAMEWORK ... 5
3.1 HOUSINGPRICEADJUSTMENTTOEQUILIBRIUMLEVEL ... 5
3.2 PREVIOUSSTUDIES ... 6
4 EMPIRICAL METHOD ... 8
4.1 COLLECTIONANDTREATMENTOFDATA ... 8
4.2 METHODOLOGYOVERVIEW ... 10
4.3 INFORMATIONCRITERION ... 11
4.4 AUGMENTEDDICKEY-FULLERTEST ... 12
4.5 JOHANSENCOINTEGRATIONTEST ... 13
4.6 VECTORERROR-CORRECTIONMODEL ... 15
4.7 GRANGER-WALDCAUSALITYTEST ... 17
4.8 IMPULSERESPONSEFUNCTION ... 18
4.9 LMTESTFORAUTOCORRELATION ... 18
4.10 JARQUE-BERASTATISTICTEST ... 19
5 RESULT ... 19
5.1 INFORMATIONCRITERION ... 19
5.2 AUGMENTEDDICKEY-FULLERTEST ... 20
5.3 JOHANSENCOINTEGRATIONTEST ... 21
5.4 VECTORERROR-CORRECTIONMODEL ... 22
5.4.1 LONG-RUN DYNAMICS - COINTEGRATED RELATIONSHIP ... 22
5.4.2 LONG-RUN DYNAMICS – ACTUAL VS. PREDICTED EQUILIBRIUM ... 24
5.4.3 SHORT-RUN DYNAMICS – ADJUSTMENT PARAMETERS ... 25
5.4.4 SHORT-RUN DYNAMICS – SHORT-RUN COEFFICIENTS ... 26
5.5 GRANGER-WALDCAUSALITYTEST ... 26
5.6 IMPULSERESPONSEFUNCTION ... 27
5.7 LMTESTFORAUTOCORRELATION ... 29
5.8 JARQUE-BERASTATISTICTEST ... 29
6 DISCUSSION ... 30
6.1 LONGRUNDYNAMICS ... 31
6.2 SHORT-RUNDYNAMICS ... 32
6.3 ACTUALVS.PREDICTEDEQUILIBRIUMHOUSEPRICE ... 33
7 CONCLUSION ... 34
8 REFERENCES ... 36
9 APPENDIX ... 39
1 INTRODUCTION
This section will include the purpose and problem definition to give the reader a clearer understanding of what implications that founded this study.
Owning our own home is something that most people desire or, in some cases, dream of. For most individuals who own their home, their housing investment is by far the most abundant element of their wealth. Therefore, a change in house prices has a significant direct effect on the total and net wealth of many households, who may react by adjusting their level of consumption. (Nakajima 2011).
Also, movements in house prices can affect the financial situation for both homeowners and non-homeowners in-directly. The best example of this is the financial crisis of 2008-2009, which spread to all parts of the world (Naifar 2011). During which, decreasing house prices are considered the main trigger of the severe amount of mortgage defaults and foreclosures, damaging the health of financial institutions linked to these mortgage loans. The declining health of these financial institutions was one of the main factors leading to the latest recession (Mian and Sufi 2009).
Consequently, housing prices have a tremendous direct and indirect effect on individuals, financial institutions, as well as the economy as a whole. Thus, understanding the fundamental drivers of housing prices is hugely beneficial for both policymakers and for people who want to make rational financial decisions (Miao et al. 2011).
Previous international studies, researched on different markets, like Gimeno and Martínez- Carrascal (2010), Gattini and Hiebert (2010) and Claussen (2013) have all agreed to consistent use of a specific set of fundamental macroeconomic drivers, determining the house prices. This paper takes a closer look at the long and short-run effects that these fundamental drivers have on house prices in the United States. By the use of a dynamic, multi equation model, we wish to analyze the fundamental macroeconomic drivers: short-run effects on house price, long-run relationship (equilibrium) with house price, and the adjustment sequence for house price in a potential disequilibrium market. All of these now referred to as house price dynamics.
1.1 BACKGROUND
It is now generally accepted that the downfall of the U.S. housing market was a significant cause of the most profound financial crisis in the U.S. since the Great Depression (Mian and Sufi 2009). Between the years 1975 and 2007, the average real house price in the U.S. rose about 1.5% per year. Up to the mid-1990s, real house prices did not change substantially. After this point, real house prices significantly increased until the end of 2007. Around this time, when the average real house price peaked before the 2008-2009 financial crisis, real house prices had risen over 60% from their level in the mid-1990s.
At this time, would it have been possible to prove that the housing market was in a disequilibrium (considered over-/underpriced) given the fundamental macroeconomic determinants? Exceedingly, since the U.S. is currently seeing a similar rate of increase in real house prices (as before the financial crisis), is the U.S. housing market currently considered fundamentally overpriced?
1.2 PROBLEM DEFINITION
There are many studies investigating house price behavior on different markets worldwide, a substantial amount of these studies examines the effects of fundamental factors on housing price dynamics. However, these studies mainly focus on explaining the impact of specific fundamental factors on housing market dynamics, or the effectiveness of implementing various market regulations. This paper broadens the scope of the existing literature of studying the house price dynamics by including all fundamental drivers that have proven to explain housing prices in precedent studies best. As a result of the strong direct (and in-direct) link between housing markets and individuals, financial institutions/markets, and the economy in general (Miao et al. 2011), the study is performed on the U.S. housing market. A market, which financial condition act as a foundation for the global economy.
1.3 OBJECTIVE OF THIS STUDY
The goal of this study is to analyze the relationship between the U.S. fundamental macroeconomic drivers and the U.S. house price dynamics. Thus, it will tell us if the U.S.
housing market is in disequilibrium (over/underpriced) and demonstrate the potential adjustment sequence. The objective of this study is to answer:
- Is the U.S. housing market in disequilibrium (over/underpriced)?
- How does the U.S. housing market converge to the equilibrium level?
The research is based on data extending over a long time period (1975-2019), including many of the, according to previous studies, most vital fundamental drivers affecting house prices. The nationwide geographic area, long period of time, and the inclusion of numerous fundamental variables make this study differ from previous research on the U.S. housing market. Many earlier studies on the U.S. house market have been performed with specific research objectives, such as state-by-state comparisons, effects of recessions, and the effects of new tax implementations. The ambition of this thesis is to give the reader a broader perspective of the house price dynamics, enabling everyone from individual homebuyers to policymakers, to better evaluate the general house market situation in the U.S.
This study provides a new evaluation of Swedish house prices and covers an extensive period stretching from 1987q1 to 2019q4. This study also uses a more extended data series than previous studies on the Swedish housing market. Furthermore, this paper explicitly evaluates how house prices adjust to the long-run equilibrium prices, which is unique when comparing to other Swedish studies.
1.4 LIMITATIONS
The study will include nationwide (all states) data for the U.S., analyzing house price dynamics from quarter one of 1975 to quarter four of 2019 by the use of quarterly data. This time is chosen to maximize our sample data. There are limitations from selecting a more extended period, due to a lack of data available for earlier years. In addition, our data only captures general market behavior and not personal incentives from individuals or other small stakeholders. All changes in their behavior of preference, leading to an effect on house prices, will not be captured in this model.
1.5 METHOD DESCRIPTION
The error-correction framework has been widely used in the housing market literature for a considerable time. Many international studies where the error correction framework has been used, some mentioned below (Gattini and Hiebert 2010; Gimeno and Martínez-Carrascal 2010;
Berki and Szendrei 2017), found the vector error-correction model to have superior forecasting performance to naive time series models. The vector error-correction model simultaneously discloses short-run dynamics, error-correcting adjustment parameters, and long-run relationships between variables, all in a unified framework (Johansen 1995). This study will apply the vector error-correction model to analyze and assess U.S. house prices by looking at the fundamental, macroeconomic determinants.
2 THEORETICAL FRAMEWORK
In this section, we will explain the essential components of the study and analyze previous studies to get a better understanding of earlier results.
2.1 HOUSING PRICE ADJUSTMENT TO EQUILIBRIUM LEVEL
House prices have historically shown tendencies to move in cycles. An overpriced market in the short-run deviates from the long-run house market equilibrium level. This is followed by a sequence of convergence back to the equilibrium level. Relying on this history, changes in house prices follow an autoregressive pattern. In the short-run, positive autocorrelation increases house prices. While in the long-run, negative autocorrelation decreases house prices, making it converge back towards equilibrium level (Hort 1998).
However, the adjustment of housing prices to an exogenous shock takes time, even if the market functions well. With the assumption that the house market supply side is in-elastic (building new housing takes time), an example of a permanent shock to disposable income will have the following effect on the equilibrium of housing prices: (1) the higher demand for accommodation may increase the house prices. (2) If the increase in housing prices is expected to be permanent, like the shock in disposable income, the construction of new housing also increases. (3) The continuously expanding housing stock grows the supply side until the demand is met, decreasing the housing prices. (4) The decrease in house prices results in the fall of construction activities. The new long-term equilibrium housing prices will be higher than the original one, but overshooting is expected in the short run.
The above example might lead to the understanding that the house prices are very elastic, which is partly true if compared to the elasticity of the housing stock. However, the adjustment sequence of house prices, due to the change of fundamental macroeconomic drivers, is still hindered by several market frictions. These frictions are due to transaction costs such as sales/profit taxes, cost of realtors, costs of moving procedure, and costs associated with adjusting the new home to your personal preferences. Additional transaction costs may also arouse if you calculate the time spent on this process (Berki and Szendrei 2017).
The rental house market also contributes to the stickiness of housing prices. Since rental leases are often not subject to renewal/change in too short intervals of time, the price adjustment sequence for the rental housing market can also be considered quite slow. Since there has to exist a consistency between the buying and rental housing markets to deter arbitrage possibilities, the rental housing markets act as additional friction (or stability-control) of house market prices (Berki and Szendrei 2017).
2.2 PREVIOUS STUDIES
Gimeno and Martínez-Carrascal (2010) study the house price dynamics in Spain with quarterly data ranging from the first quarter in 1975 to the first quarter of 2009. With the use of a vector error-correction model, the author can determine the long- and short-run dynamics of the house prices, and this study also aims to provide some insight into the linkage between house prices and house credit availability. Their findings suggest that long-run house prices rely positively on labor income and house credit availability. The result of a positive long-run correlation between house prices and house credit availability leads to the conclusion of a negative long- run relationship between house prices and mortgage rates. The analysis of disequilibria adjustment shows that house prices adapt to a potential disequilibrium in house credit availability with a rate of 28% per year. However, no evidence can be found that house credit availability adjusts to a disequilibrium in house prices.
For the Swedish housing market, Claussen (2013) tries to explain the rapid increase in house prices since the mid-1990s to conclude if the Swedish house prices can be considered overpriced. For estimation, the author uses an error-correction model and a dynamic ordinary least squares regression model, also making it possible to distinguish between the long- and short-run equilibrium price. The estimations are based on quarterly data ranging from the first quarter of 1986 to the second quarter of 2011. The author arrives at a final, well-fitted model, including tax mortgage rate, disposable income, and net financial wealth as the only explanatory variables. The findings show that long-run house prices in Sweden rely positively on disposable income and net financial wealth and negatively with real mortgage rate. Further, increasing
disposable income and falling mortgage rates are stated as the main factors driving up house prices, but no evidence of overpricing is found.
Gattini and Hiebert (2010) attempt to forecast and assess the euro-area house prices through the lens of key macroeconomic fundamentals. This paper presents a vector error-correction model based on quarterly data for the entire euro-area ranging from the first quarter of 1970 to the fourth quarter of 2009. The long-run cointegrating relationships suggest that the euro-zone house prices depend positively with disposable income and negatively with interest rate and residential investment. The short-run adjustment parameter (𝛼) of -0.013 implies that housing prices are assumed to converge towards the long-run equilibrium level with a rate of 1.3 percent per quarter.
3 EMPIRICAL METHOD
In this section, we will present the empirical method of choice, data collection, data treatment. Also, we will review the essential challenges and how we mitigate and correct for potential weaknesses.
3.1 COLLECTION AND TREATMENT OF DATA
The data is gathered in the time range from the 1st quarter of 1975 to the 4th quarter of 2019 (180 quarters/observations over 45 years) for the entire U.S. The sources for each dataset can be found under the individual description for each variable.
Variable descriptions:
- HP (House Price) - U.S. house price index for existing single-family houses. Real values are computed using the personal consumption expenditure (PCE) deflator. Seasonally adjusted over the entire sample period and then rebased to 1975Q1 = 1.
Source: Federal Reserve Bank of Dallas, Globalization Institute.
- PDR (Personal Debt Ratio) – U.S. total personal debt divided by U.S. total personal disposable income. Seasonally adjusted over the entire sample period.
Source: Federal Reserve Bank of St. Louis, Economic Research Division.
- PNW (Personal Net Wealth) – U.S. personal net wealth quoted in per capita terms using the working-age population. Real values are computed using the personal consumption expenditure (PCE) deflator. Seasonally adjusted over the entire sample period and then rebased to 1975Q1 = 1.
Source: Federal Reserve Bank of St. Louis, Economic Research Division.
- RMR (Real Mortgage Rate) – U.S. nominal 30-year mortgage rate minus annual nominal inflation. Seasonally adjusted over the entire sample period.
Source: Federal Reserve Bank of St. Louis, Economic Research Division.
- RIR (Residential Investment Ratio) – U.S. total private residential fixed investments (construction of single-family and multifamily structures, residential remodeling, production of manufactured homes) divided by U.S. total GDP. Seasonally adjusted over the entire sample period.
Source: Federal Reserve Bank of St. Louis, Economic Research Division.
- PDI (Personal Disposable Income) – U.S. personal disposable income quoted in per capita terms using the working-age population. Real values are computed using the personal consumption expenditure (PCE) deflator. Seasonally adjusted over the entire sample period and then rebased to 1975Q1 = 1.
Source: Federal Reserve Bank of Dallas, Globalization Institute.
- CC (Construction Cost) - U.S. construction cost index. Real values are computed using the personal consumption expenditure (PCE) deflator. Seasonally adjusted over the entire sample period and then rebased to 1975Q1 = 1.
Source: Federal Reserve Bank of St. Louis, Economic Research Division.
Table 1. Summary of data
Variable Type Interpretation Observations Mean Std. deviation Min Max
HP Index 1975 = 1 180 1.3831 0.2733 0.9919 1.9580
PDR Ratio e.g. 0.5 = 50% 180 0.9139 0.2106 0.5764 1.3359
PNW Index 1975 = 1 180 1.6534 0.4906 1 2.7352
RMR Rate e.g. 1.04 = 4% 180 1.0408 0.0259 0.9788 1.1095
RIR Ratio e.g. 0.5 = 50% 180 0.0435 0.0098 0.0239 0.0667
PDI Index 1975 = 1 180 1.5081 0.3280 1 2.1209
CC Index 1975 = 1 180 0.8453 0.0621 0.7614 1.0058
Note:The Real Mortgage Rate (RMR) is specified as (1 + RMR), where RMR is the real interest rate in basis points.
3.2 METHODOLOGY OVERVIEW
Our research will be based on the error-correction framework with the use of the vector error- correction model. All data are computed into logarithmic terms and coefficients presented in the results of the vector error-correction model can be interpreted as elasticities. Featured below is an overview of the empirical method carried out, consisting of necessary postestimations steps to confirm and specify the use of the vector error-correction model, estimation of the vector error-correction model, and postestimation procedures to investigate and confirm the results.
Preestimation:
1. Information Criterion: To check the optimal lag length for the dataset.
2. Augmented Dickey-Fuller Test: To check the order of integration (I(?)) for the dataset.
3. Johansen Cointegration Test: To check the number of cointegrated vectors in the dataset.
Estimation:
- Vector Error-Correction Model: To estimate the short-run and long-run relationship between the variables in the dataset.
Postestimation:
1. Granger Wald Causality Test: To check if our short-term coefficients in the estimation contain any joint predictive power.
2. Impulse-Response Function: To check the net effect of a shock in an impulse variable on a response variable.
3. LM Test for Autocorrelation: To check that the residuals in the estimation are not autocorrelated.
4. Jarque-Bera Statistic Test: To check that the errors in the estimation are normally distributed.
3.3 INFORMATION CRITERION
For a significant estimation result, selecting the optimal number of lags for our model is essential. If the lag of the model differs from the true lag-length, it can cause the model to become inconsistent (Braun and Mittnik, 1993). This can be assessed by using information criterions as well as economic theory. An information criterion is a quantitative analysis to examine errors of the model to reduce them to the smallest possible impact. Simply put, information criterions test the different number of lags and indicates the lag length, which best reduces the errors in our model.
There are several different information criterions, depending on the character of the data and the purpose, different information criterions are considered optimal (Ivanov and Kilian 2001).
The information criterions considered to be most commonly used are the Bayesian information criterion (BIC) and the Akaike information criterion (AIC), where the Akaike information criterion should be regarded as the most frequently used information criterion. In this study, the Akaike information criterion is used to find the optimal number of lags, which will be used for the following augmented Dickey-Fuller tests, Johansen cointegration test, and finally, the vector error-correction model. Please see the defined equation of Akaike information criterion in Equation 1 below:
Equation 1.
𝐴𝐼𝐶(𝑝) = ln +𝑆𝑆𝑅(𝑝)
𝑇 / + (𝑝 + 1)(2 𝑇)
Where 𝑝 is the number of parameters, 𝑇 is the sample size, and 𝑆𝑆𝑅 is the sum of squares residual. The model identified with the lowest 𝐴𝐼𝐶(𝑝) is the preferred model. This implies that the inclusion of one more lag to the model needs to be justified by a decrease in 𝑆𝑆𝑅. In other words, the AIC indicates the optimal compromise between model fit and model complexity.
The AIC should help us prevent overfitting in our model (Stock and Watson 2015).
Previous studies (Gimeno and Martínez-Carrascal 2010; Oikarinen 2005) have found that the optimal number of lags to include are between 3-4 (3/4 of a year – 1 year).
3.4 AUGMENTED DICKEY-FULLER TEST
The Augmented Dickey-Fuller test (ADF-test) is used to confirm that the variables in the model are non-stationary in levels and to test the order of integration of our variables.
The order of integration of the variables in the model is tested through an augmented Dickey- Fuller test (ADF-test). It is one of the most reliable tests when testing the stationary properties of variables and the most commonly used in practice. Stationarity in a time series (𝑌!) is present if the probability distribution does not change over time. The variables need to be non-stationary (contain a unit-root) in levels and become stationary in differences to proceed with the cointegration analysis. Generally, a variable is said to be integrated of order (p) if it has to be differenced (p) times to achieve stationarity. The augmented Dickey-Fuller test checks the null hypothesis that the variable is non-stationary (contain a unit-root) against the alternative that it is stationary (Stock and Watson 2015). The augmented Dickey-Fuller test can be expressed as Equation 2 below.
Equation 2.
∆𝑦! = 𝛽"+ 𝑎!+ 𝛿𝑦!#$+ 𝛾$Δ𝑦!#$+ 𝛾%Δ𝑦!#%+ ⋯ 𝛾&Δ𝑦!#&+ 𝜀!
𝐻": 𝛿 = 0 (non-stationary)
𝐻': 𝛿 < 0 (stationary)
Where 𝛽" is the constant, 𝑎! is the time trend, 𝑗 is the number of lags, and 𝛾$,…, 𝛾& denote the parameters attached to the lags.
3.5 JOHANSEN COINTEGRATION TEST
To estimate the long-run relationship between our variables, determining the number of cointegrating equations in our vector error-correction model is essential. This is concluded by cointegration analysis. Cointegration occurs when two or more time series with stochastic trends share a common stochastic trend, in other words, that they move together closely over the long-run and appear to have the same trend component (Stock and Watson 2015). More formally, two non-stationary time-series that share the same stochastic trend are said to be cointegrated, if subtracting one time-series from the other makes the combination of the time series stationary (Hamilton 1994).
The initial framework for cointegration analysis was introduced by Granger (1983) and Engle and Granger (1987). However, The Engle and Granger method only tests for one single cointegrating equation (Drake, 1993). Johansen (1988) and Johansen and Julius (1990) later developed the framework for cointegration analysis that will be the method of use in this thesis.
With this theoretical framework, the number of cointegrating vectors can also be determined in a multivariate setting.
The Johansen cointegration test includes two tests to estimate the number of cointegrating equations, the trace test, and the max eigenvalue test. These tests are defined as Equation 3 and 4 below:
Equation 3. Trace test:
𝜆!()*+(𝑟∗) = −𝑇 E-
./((∗1$)
logH1 − 𝜆I.J
𝐻": 𝑟 ≤ 𝑟∗ (r* or fewer cointegrating vectors exists) 𝐻): 𝑟∗ < 𝑟 ≤ 𝐾 (more than r* cointegrated vectors exists)
Equation 4. Maximum eigenvalue test:
𝜆4)5(𝑟∗) = −𝑇 log(1 − 𝜆I(∗1$)
𝐻": 𝑟 ≤ 𝑟∗ (𝑟∗ or fewer cointegrating vectors exists) 𝐻): 𝑟 = 𝑟∗+ 1 (𝑟∗+ 1 cointegrated vectors exists)
Where 𝑟 is the number of cointegrated equations, 𝑟∗ is the hypothesized number of cointegrated equations for each test, T is the sample size, 𝜆I is the estimated eigenvalue, and 𝐾 is the number of variables included.
The two tests described above are likelihood ratio tests but does not have the usual chi-squared distributions. Instead, the appropriate distributions are multivariate extensions of the Dickey- Fuller distributions. As with the unit root tests, the percentiles of the distributions depend on a constant and time trend are included.
3.6 VECTOR ERROR-CORRECTION MODEL
Often when dealing with economic data, we find that the data cannot fulfill the requirement of stationarity. Cointegration analysis provides a framework for estimation and inference when the variables are non-stationary. One way of resolving the issue of non-stationary data is to compute first-difference (∆𝑌! instead of 𝑌!) on the non-stationary data, removing the stochastic trend and making it stationary. First-difference stationary processes are also known as being integrated of order 1, or I(1) while level stationary processes are I(0). Overall, a process whose x'th difference is stationary is an integrated process of order x, or I(x) (Johansen 1995).
If two non-stationary variables (𝑌! and 𝑋!) are cointegrated, a different approach to remove the stochastic trend is to compute 𝑌!− 𝜃𝑋!, where 𝜃 is selected to remove the common stochastic trend and leave us with the difference between the two time-series. As stated earlier, given that the time series are cointegrated, the computed difference (𝑌!− 𝜃𝑋!) between the variables is stationary and can be used in regression analysis (Stock and Watson 2015).
Modeling the stationary variables ∆𝑌! and ∆𝑋! using a standard vector autoregression (VAR) model and augmenting it by including 𝑌!#$− 𝜃𝑋!#$ as an additional regressor creates the combined vector error-correction model. The error correction term 𝑌!− 𝜃𝑋! will capture the short-run adjustment to the long-run equilibrium at periods when the current value exceeds or fall below the long-run equilibrium. In this model, past values of 𝑌!− 𝜃𝑋! helps to predict future values of ∆𝑌! and ∆𝑋! (Stock and Watson 2015).
The vector error-correction model accounts for multiple cointegrating relationships and models the stationary relationship between multiple time-series that individually contain unit-roots.
This will reveal the long-run relationship and short-run dynamics of the non-stationary time series. Based on the Johansen maximum likelihood framework, the vector error-correction model can be expressed as Equation 5 below (Johansen 1995):
Equation 5.
Δ𝑦! = 𝛼𝛽6𝑦!#$+ E Γ.Δ𝑦!#.+ 𝑣 + 𝛿!+ 𝜖!
7#$
./$
- 𝑦!: 𝐾 𝑥 1 vector of all I(1) variables.
- 𝑝: Lag length.
- 𝛽: 𝑟 𝑥 𝐾 matrix with rank 𝑟 of cointegrating vector parameters. Each column in the matrix is a vector that specifies a long-run relationship.
- 𝛼: 𝑟 𝑥 𝐾 matrix with rank 𝑟 of the adjustment parameters. The adjustment parameters capture the speed of adjustment to the equilibrium level.
- Γ.: 𝐾 𝑥 𝐾 matrix of the short-run parameters.
- 𝑣: Linear trend term in the levels of the data.
- 𝛿!: Quadratic trend term in the levels of the data.
- 𝜖!: Vector of independent and identically distributed errors.
A vector error-correction model with 𝑟 cointegrating vectors requires at least 𝑟% imposed restrictions. Johansen's identification scheme is a normalization method that restricts 𝑟% parameters in the cointegrating equations and thereby defines an exactly identified model.
In the presence of three cointegrating vectors, the Johansen normalization method restricts one of the 𝛽 parameters in each equation to be normalized to one, and two of the 𝛽 parameters in each vector to be zero. The zero restrictions could be numerical rather than exactly zero.
(Johansen, 1995). The normalization method has become widely used by researches to identify the cointegrating vectors when economic theory is not sufficient. Also, it is possible to impose further restrictions, creating an overidentified model. Both exactly identified and overidentified models are considered super consistent (Johansen 1995).
To correctly specify the vector error-correction model and identify the deterministic components, restrictions can also be placed on the trend terms 𝑣 and 𝛿!. Analysis of the dataset in this thesis suggests the presence of a linear and non-quadratic trend in the levels of our data.
Therefore, applying an unrestricted constant (𝛿! = 0) excludes the possibility of a quadratic trend while maintaining the linear trend in the levels of the data and restricts the cointegrating equations to be stationary around constant means (Johansen 1995). Previous studies also support the use and application of an unrestricted constant.
3.7 GRANGER-WALD CAUSALITY TEST
To examine if our data contain any predictive information, the Granger causality test is applied.
The basis of the Granger test is to indicate if an X variable causes a Y variable and also in the opposite direction (Y causes X). The Granger test does this by checking if all the coefficients, within the lag set, are different from zero. The test is based on the aforementioned vector error- correction model and its specifications.
The Granger causality test is based on the null-hypotheses - that the coefficients for all lagged values of one of the variables are zero. If the null hypothesis cannot be rejected, the data does not contain any predictive power.
However, the Granger causality test has been criticized since it fails to distinguish causality from predictability. The definition of causality is that one event causes another, for example, winter causes an increase in house fires (due to more lighted candles). Predictability can occur without any causality between the events. For instance, winter also causes car crashes to increase. This means that maybe house fires can predict car crashes even though there is no causality between the events (Stock and Watson 2015).
The vector error-correction model does not produce a regular Granger causality test based on the F-statistic, the analysis is instead performed through a chi-square (X2) distribution test. This test is called a Granger Wald causality test (Pala 2013). In this thesis, the Granger Wald causality tests will be performed to investigate whether our short-term coefficients contain any joint predictive power.
3.8 IMPULSE RESPONSE FUNCTION
The results from the aforementioned Granger causality tests can tell us if there is any predictive power in our data. However, we still need to check what kind of predictive power is present.
With impulse response functions, we simulate a shock in an impulse variable to see the net effects on a response variable, all other variables in our model held constant. For example, if a shock (increase) of Personal Disposable Income (PDI) would hit the economy, how would House Price (HP) react? The impulse response function would then graph the response from House Price over time with a baseline from historical data. In the vector autoregressive framework, stationary data characteristics suggest a time-invariant mean and variance. The responses from the simulated shocks are transitory and oscillate back to its mean. However, in the vector error-correction framework with cointegrating equations based on first-difference stationary data (I(1)), shocks from the impulse variables can result in more permanent responses. (Lütkepohl 2007; Pesaran and Shin 1998). This needs to be considered when examining the results in Section 4.6, since it may explain responses that are not in compliance with economic theory.
3.9 LM TEST FOR AUTOCORRELATION
The vector error-correction model estimation, inference, and postestimation analysis are predicated on the assumption that the errors are not being autocorrelated. We implement a Lagrange multiplier (LM) test for autocorrelation in the residuals of the vector error-correction model. The test is performed at lags j = 1, . . . , n. For each j, the null hypothesis of the test is that there is no autocorrelation at lag j (Johansen 1995).
3.10 JARQUE-BERA STATISTIC TEST
The vector error-correction model log-likelihood is derived based on another assumption, that the errors are independently and identically distributed (i.i.d.). The Jarque-Bera statistic tests kurtosis and skewness jointly using the results from the vector error-correction model. The test produces statistics to indicate if we can reject the null hypothesis that the disturbances in the vector error-correction model are normally distributed. Rejection of the null hypothesis suggests model misspecification. However, a great deal of researchers agrees that many of the asymptotic properties can still be derived under the weaker assumption that the errors are merely i.i.d. (Johansen 1995).
4 RESULT
In this section, we will present the results of the thesis and summarize essential information from our empirical models. The tables and plots will be displayed in the text with additional information available in Appendixndix.
4.1 INFORMATION CRITERION
The Akaike information criterion suggests the optimal lag length for the model to be three lags (quarters), which is what below preestimation and estimation results will be based on. The use of the Akaike information criterion and its indication of an optimal number of three lags are both in line with economic theory. Please see Table A1 in Appendixndix for detailed results.
4.2 AUGMENTED DICKEY-FULLER TEST
The augmented Dickey-Fuller test is used to check the order of integration of the variables. The test is specified with three lags, as motivated earlier in this study. The critical values used to determine the order of integration are the linearly interpolated values of Fuller (1996). The null hypothesis of non-stationarity cannot be rejected for any of our variables in levels. However, when variables are computed into first-difference, we can reject the null hypothesis on all variables on a 1 percent significance level, except for Personal Debt Ratio (PDR), which can reject the null hypothesis on a 5 percent significance level. This indicates that all variables in the dataset are integrated of order one (I(1)), validating us to proceed with the cointegration analysis.
Table 2. Augmented Dickey-Fuller Test
Variable (c, t, L) T-value (levels) T-value (Difference) I(k)
lnHP (c, 0, 3) 0.352 -2.658*** I(1)
lnPDR (c, 0, 3) -1.826 -3.116** I(1)
lnPNW (c, 0, 3) 1.614 -4.314*** I(1)
lnRMR (c, 0, 3) -0.883 -5.415*** I(1)
lnRIR (c, 0, 3) -0.074 -4.966*** I(1)
lnPDI (c, 0, 3) 3.239 -3.960*** I(1)
lnCC (c, 0, 3) -0.09 -4.957*** I(1)
Note: *, ** and *** indicates that the null hypothesis can be rejected at a 10%, 5%, and 1% significance level. Critical values are the linearly interpolated values of Fuller (1996).
4.3 JOHANSEN COINTEGRATION TEST
The Johansen test for cointegration is used to determine the number of cointegrating vectors in our dataset. The test is specified with three lags and an unrestricted constant, as motivated earlier in this study. The critical values of Osterwald-Lenum (1992) are used to determine the number of cointegrating equations. The null hypothesis of 𝑟∗ (maximum rank in Table 3 below) or less cointegrating vectors can be rejected by both the Trace and the Maximum statistic for the maximum ranks of 0, 1, and 2 at a 1% significance level. Johansen (1995) states that 𝑟 should be chosen at the smallest value at which we fail to reject the null hypothesis, thereby indicating (at least) 3 cointegrating vectors in our dataset (Johansen 1995). See Table 3 below for detailed results.
Table 3. Johansen cointegration test
Maximum rank Parameters Trace statistic 5% critic. value 1% critic. value
0 105 208.4411*** 124.24 133.57
1 118 132.6742*** 94.15 103.18
2 129 85.3532*** 68.52 76.07
3 138 41.3877 47.21 54.46
4 145 19.4026 29.68 35.65
5 150 6.0157 15.41 20.04
6 153 0.0819 3.76 6.65
7 154 . . .
Maximum rank Parameters Max statistic 5% critic. value 1% critic. value
0 105 75.7668*** 45.28 51.57
1 118 47.3210*** 39.37 45.10
2 129 43.9655*** 33.46 38.77
3 138 21.9851 27.07 32.24
4 145 13.3869 20.97 25.52
5 150 5.9338 14.07 18.63
6 153 0.0819 3.76 6.65
7 154 . . .
Note: *, ** and *** indicates that the null hypothesis can be rejected at a 10%, 5%, and 1% significance level. Critical values are the values of Osterwald-Lenum (1992).
4.4 VECTOR ERROR-CORRECTION MODEL
After the establishment of the lag order, order of integration, and the number of cointegrated vectors, the vector error-correction model can be specified. This will enable us to analyze the long- and short-term dynamics of the US house prices in a unified framework. The model is defined with three lags, an unrestricted constant and three cointegrated vectors, as motivated earlier in this study.
4.4.1 LONG-RUN DYNAMICS - COINTEGRATED RELATIONSHIP
To identify the cointegrated vectors in the vector error-correction model, the Johansen normalization method imposes restrictions on 𝛽 in all three cointegrated vectors. For the purpose of investigating the housing price dynamics, the analysis will be performed on the integrated vector that is normalized on the coefficient of House Price (HP), with zero- coefficient restrictions imposed on Personal Debt Ratio (PDR) and Personal Net Wealth (PNW). The estimates of the cointegrating coefficients (normalized to House Prices (HP) = 1) in this vector, can be expressed as Equation 6 below:
Equation 6.
𝑙𝑛𝐻𝑃 = 2,816 + 0.494𝑙𝑛𝑅𝑀𝑅 + 0,881𝑙𝑛𝑅𝐼𝑅 + 1,179𝑙𝑛𝑃𝐷𝐼 + 0,842𝑙𝑛𝐶𝐶 + 𝜖!
Results indicate a negative and significant adjustment parameter (𝛼) for the House Price (HP) equation, this is corresponding to earlier time-series studies performed under similar time- periods and is considered a key-requirement for interpretation of long- and short-term effects of housing price dynamics. More theoretically, this confirms a long-run relationship between House Price (HP) and the included determinants, indicating that this relationship is stationary in the long run, even though all the variables individually are considered non-stationary.
The coefficients for the long-term cointegrated equation normalized on the coefficient of House Price (HP), indicates a positive long-term relationship between House Price (HP) and the included determinants: Real Mortgage Rate (RMR), Residential Investment Ratio (RIR), Personal Disposable Income (PDI) and Construction Cost (CC). All coefficients for the included house price determinants are significant at a 1% significance level except for Real Mortgage Rate (RMR).
Turning to the coefficients of in the cointegrating equation, the coefficient of Personal Disposable Income (PDI) is around 1.18 and appears to be the variable with the most substantial impact on House Price (HP). The coefficients of Residential Investment Ratio (RIR) and Construction Cost (CC) is around 0.86 and indicates that they both have a very similar relation in terms of the elasticity towards of House Price (HP). Both the coefficient values and signs of all the coefficients are in accordance with the expected values and signs derived from previous studies, with the exception of the insignificant and positive Real Mortgage Rate (RMR).
More generally, the values and signs of the included variables indicate that, in the long run, an increase of House Price (HP) is associated with a rise in Residential Investment Ratio (RIR), Personal Disposable Income (PDI) and Construction Cost (CC). At the same time, we cannot distinguish the effect on/from Real Mortgage Rate (RMR). See Table 4 below for detailed results. Additionally, the coefficients for cointegrating equation two and three can be found in Table A2 in the Appendix.
Table 4. Long-run cointegrating relationship (cointegrating equation 1)
Beta (ce1) Coefficient Std. error Prob > z
lnHP 1 . .
lnPDR 0 . .
lnPNW 0 . .
lnRMR -0.4944 0.5323 0.353
lnRIR -0.8813*** 0.0803 0.000
lnPDI -1.1791*** 0.0662 0.000
lnCC -0.8421*** 0.1734 0.000
cons -2.8164 . .
Note: *, ** and *** indicates significance at a 1%, 5% and 10% significance level. The coefficients should be interpreted with reversed signs.
4.4.2 LONG-RUN DYNAMICS – ACTUAL VS. PREDICTED EQUILIBRIUM
Using the 𝛽-vector displayed in Equation 6, consisting of the fundamental variables cointegrating coefficients, the long-run equilibrium of house prices can be predicted. By graphing this long-run equilibrium together with the actual house prices, we can determine if and when our model considers the house prices to be in disequilibrium (fundamentally over/underpriced). At first glance, we can quickly determine that our predicted equilibrium price for the housing market projects similar trends as the actual house prices; however, with a more volatile movement. In addition, the predicted equilibrium prices seem to have a time- predictive capability of foreseeing future swings in house prices since the movements of our predicted prices generally appear 3-6 quarters in advance of the actual house prices.
According to our model, actual housing prices are more often than not considered to be under the predicted house price equilibrium. Only three short, but still significant, periods are observed where the market is deemed to be overpriced.
Figure 1. Actual house prices vs. Predicted long-run equilibrium house prices
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1
1975 1976 1978 1980 1982 1983 1985 1987 1989 1990 1992 1994 1996 1997 1999 2001 2003 2004 2006 2008 2010 2011 2013 2015 2017 2018
US house prices - Actual vs. Predicted
ACTUAL PREDICTED
4.4.3 SHORT-RUN DYNAMICS – ADJUSTMENT PARAMETERS
The short-run adjustment parameters of the vector error-correction model aim to explain the adjustment sequence towards the estimated long-run equilibrium value and the rate of adjustment variables in the short-run. Thus, the short-run dynamics also play an important part in determining the long-run housing price equilibrium.
The significant House Price (HP) adjustment parameter estimated in the cointegrated house price equation is 0.072. This result suggests that if house prices are in disequilibrium, and other fundamental variables are held constant, housing prices will converge towards the long-run equilibrium level with a rate of 7.2% in the next quarter. This means that the disequilibrium gap between current house prices and equilibrium of house prices will be reduced by approximately 28% over the next year.
The Real Mortgage Rate (RMR) and Residential Investment Ratio (RIR) adjustment parameters (𝛼) estimated in our house price equation is 0.055 and 0.095 and are significant at a 1% and 5%
significance level respectively. Meanwhile, the negative Construction Cost (CC) adjustment parameter (𝛼) estimated in our house price equation is -0,034 and significant at a 5%
significance level. All other adjustment parameters (𝛼) estimated in our house price equation are insignificant and thus not interpreted. Please see Table 5 below for detailed results.
Table 5. Short-run adjustment parameters
Alpha (ce1) Coefficient Std. error Prob > z
D_lnHP -0.0721*** 0.0122 0.000
D_lnPDR -0.0203 0.0138 0.141
D_lnPNW 0.0011 0.0246 0.962
D_lnRMR 0.0547*** 0.0136 0.000
D_lnRIR 0.0945** 0.0479 0.048
D_lnPDI -0.0047 0.0121 0.697
D_lnCC -0.0336** 0.0136 0.014
Note: *, ** and *** indicates significance at a 1%, 5% and 10% significance level.
Given the scenario of current House Price (HP) exceeding the equilibrium level, results imply that the disequilibrium gap will be corrected by a reduction in House Prices (HP) and Construction Cost (CC) while Real Mortgage Rate (RMR) and Residential Investment Ratio (RIR) are expected to increase.
4.4.4 SHORT-RUN DYNAMICS – SHORT-RUN COEFFICIENTS
The short-run coefficients are associated with the lagged values of 𝑦! in the vector error- correction model. From the results, we can see that Real Mortgage Rate (RMR) and Residential Investment Ratio (RIR) have a positive and significant short-run effect on House Price (HP).
Further, results suggest that Personal Debt Ratio (PDR), Personal Disposable Income (PDI), and Construction Cost (CC) have a negative and significant short-run effect on House Price (HP). All significant positive/negative coefficients are associated with the first lagged value of each variable, except for Construction Cost (CC), where the significant value is associated with the second lagged value. Please see Table A3 in Appendixndix for detailed results. Further evaluation of short-run effects follows in Sections 4.5 and 4.6 below, together with Granger- Wald causality tests and impulse response functions.
4.5 GRANGER-WALD CAUSALITY TEST
Given the conclusion of a cointegrated relationship, long-run causality has already been confirmed. With the Granger-Wald test, tests are performed to check for the presence of jointly significant estimators in the off-diagonal short-run coefficients. The Granger-Wald causality tests are performed jointly on the short-run coefficients for each variable to establish if they contain any predictive power on house prices in the short-run. The test is based on the aforementioned vector error-correction model and its specifications. Firstly, we check which variables are suggested to contain direct joint predictive power on house prices in the short run.
Secondly, we check if the variables that contain no direct joint predictive power on house prices in the short-run can affect house prices by channeling through the variables with direct joint predictive power on house prices.
Results show that the variables Residential Investment Ratio (RIR), Personal Disposable Income (PDI), and Construction Cost (CC) all contain direct joint predictive power towards house prices at a 1% significance level, with Real Mortgage Rate (RMR) at a 5% significance level.
Looking at the variables with no direct joint predictive power towards House Price (HP), we see that Personal Debt Ratio (PDR) contains joint predictive power towards Real Mortgage Rate (RMR) and Personal Disposable Income (PDI) at 5% and 10% significance level respectively. Further, we can see that Net Personal Wealth (NPW) contains joint predictive power on Residential Investment Ratio (RIR) at a 5% significance level. Please see Table A4 in Appendixndix for detailed results.
4.6 IMPULSE RESPONSE FUNCTION
Impulse response functions are performed to simulate a shock in the fundamental house price determinants to see the net effects on a House Price (HP). The test is based on the aforementioned vector error-correction model and its specifications. Figures 2-7 below display the net effects that one standard deviation shock in the fundamental house price drivers (variables), while ceteris paribus, has on House Price (HP). The impulse response functions also account for the bidirectional causality, to define the net effects on our response variable House Prices (HP). All impulse response functions simulate the House Price (HP) response over a 32-month (8 years) time-period.
From the results, we can see that a standard deviation shock in all variables seems to have a fairly permanent effect on House Price (HP), except for Personal Disposable Income (PDI), which oscillates back to 0 within the 32-month time-window displayed. Since the impulse- response functions are performed in a vector error-correction framework, with first-difference stationary data (I(1)), the results of more permanent effects are expected. Further, we can see that a shock in all impulse variables gives the expected sign/effect except for Personal Disposable Income and Real Mortgage Rate (RMR), which both display effects that contradict previous studies and economic theory. The impulse variable that has the most substantial effect on House Prices (HP) is Residential Investment Ratio (RIR). A standard deviation shock in all impulse variables, except for Real Mortgage Rate (RMR) and Construction Cost (CC), displays the maximum net effect on House Prices (HP) after 12-16 months. Please see Figure 2-7 below for detailed results.
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = PDR | Response = HP Figure 2. Accumulated response of HP to
one st. dev. PDR shock
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = PNW | Response = HP Figure 3. Accumulated response of HP to
one st. dev. PNW shock
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = RMR | Response = HP Figure 4. Accumulated response of HP to
one st. dev. RMR shock
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = RIR | Response = HP Figure 5. Accumulated response of HP to
one st. dev. RIR shock
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = PDI | Response = HP Figure 6. Accumulated response of HP to
one st. dev. PDI shock
-0,02 -0,01 0 0,01 0,02 0,03
0 4 8 12 16 20 24 28 32
Impulse = CC | Response = HP Figure 7. Accumulated response of HP to
one st. dev. CC shock
4.7 LM TEST FOR AUTOCORRELATION
The Lagrange multiplier (LM) test for autocorrelation is performed to check that there is no autocorrelation in the residuals of our model, thereby partly validating our model. The test is based on the aforementioned vector error-correction model and its specifications (three lags).
The results conclude that we cannot reject the null hypothesis of no autocorrelation for all lags (1 and 3-8) except for lag two, which contain autocorrelation. Tests on re-specified vector error- correction models with more lags were performed. However, this did not solve the issue of autocorrelation but instead made the model more complex and with fewer degrees of freedom.
The study proceeds with the use of three lags, with autocorrelation present in the second lag.
Please see Table A5 in Appendixndix for detailed results.
4.8 JARQUE-BERA STATISTIC TEST
The Jarque-Bera statistic test checks for normally distributed disturbances in our equations. The test is based on the aforementioned vector error-correction model and its specifications. Results show that we reject the null hypothesis of independently and identically distributed errors when our first differenced equations are tested jointly or individually. The only exception is the first differenced equation of Housing Price (HP) on which we cannot reject the null hypothesis of independently and identically distributed errors.
As mentioned previously, the rejection of the null hypothesis indicates model misspecification and non-efficient parameter estimates. However, the parameter estimates are still considered consistent, and many of the asymptotic properties can still be derived under the weaker assumption that the errors are merely i.i.d. (Jarque and Bera 1987). Please see Table A6 in Appendixndix for detailed results.
5 DISCUSSION
In this section, we will discuss and compare the reported results with regards to previous studies, economic theory, the problem definition, and our hypotheses. We will also discuss the strengths and weaknesses of the model.
From the results previously presented, we can conclude the existence of a cointegrating relationship between House Prices (HP) and the fundamental macro drivers. Presented below in Table 6 are the significant long-run cointegrated coefficients and adjustment parameter estimated in this study, compared to previous relevant studies. The relevant studies chosen for this comparison are all based on the error-correction framework and, therefore, also exhibit long-run cointegrated coefficients (normalized on House Price (HP) = 1) and adjustment parameters. However, all fundamental macro determinants included in this study are not consistently present in all of the chosen reference studies. This, in combination with differences in definitions for the included variables, can cause the questioning of how reliable conclusions can be drawn from this comparison. With this in mind, it can still serve as a reference point for discussion and maybe even slightly increase the validity of this study.
Table 6. Comparison – Cointegrated coefficients and adjustment parameters
Previous study Region Coef. - RMR Coef. - RIR Coef. - PDI Coef. - CC Alpha - HP
Gimeno (2010) Spain -3.20 . 1.02 . -0.069
Claussen (2013) Sweden -6.00 . 1.31 1.55 -0.081
IMF (2005) EU zone -1.00 to -2.00 . 0.65 . -0.12 to -0.13
Gattini (2010) EU zone -6,87 -2.21 3.07 . -0.013
McCarthy (2002) USA -2.91 2.86 3.43 4.54 -0.049
Berki (2017) Hungary . . 1.27 . -0.141
Oikarinnen (2005) Finland -3.00 to -3.70 . 0.80 to 1.32 1.10 to 2.27 -0.10 to -0.15
Current study USA . 0.88 1.18 0.84 -0.072
Note: All reported values are significant at a 10% significance level (or lower). The fundamental variables (RMR, RIR, PDI, and CC) may vary in definition between studies.
5.1 LONG RUN DYNAMICS
A quick look at long-run cointegrating coefficients in Table 6 indicates that the fundamental determinants most consistently used are Real Mortgage Rate (RMR) and Personal Disposable Income (PDI), included in almost all previous studies chosen for comparison. Whereas, Residential Investment Ratio (RIR) and Construction Cost (CC) are only included in slightly less than half of the previous studies chosen. Further, we can see that the long-run cointegrating coefficients and signs for all fundamental variables in this study are in line with the expected signs and estimates from previous studies, except for the low coefficient of Construction Cost (CC). However, Claussen (2013) argues that the high Construction Cost (CC) elasticity of 1.55 with regards to House Prices (HP) on the Swedish market is improbable. If Construction Cost (CC) is exogenous, and there is a working market competition in the construction industry, Construction Cost (CC) elasticity should fall below 1. The high elasticity may, therefore, be due to limited competition in the Swedish construction industry. In other words, the elasticity shown in our model of 0.84 can be considered reasonable and may rather indicate that there exists a stronger competition in the U.S. construction industry.
The cointegrating coefficient for Real Mortgage Rate (RMR) is not significant and therefore excluded from the comparison in Table 6. Real Mortgage Rate (RMR), consisting partly of inflation, which similarly to housing price dynamics, shows a mean-reverting pattern. Meaning that forward-looking households with long planning periods could defer from changes in Real Mortgage Rate (RMR) in the long run (Oikarinen 2012).
Summarizing the results from our significant long-run cointegrating coefficients, we can determine that U.S. House Prices (HP) depend positively on Personal Disposable Income (PDI), Residential Investment Ratio (RIR), and Construction Cost (CC). The elasticity of House Prices (HP) with respect to Personal Disposable Income is close to 1.2 and is higher than the House Price (HP) elasticity with regards to Residential Investment Ratio (RIR) and Construction Cost (CC) which exhibit elasticities of around 0.85.
