Short-Run Dynamics

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might be positive. One possible explanation for this is that the long-run low interest rate enhances investors’ confidence in housing investment and consequently bolsters the housing prices as well as the bubble. The relationship between HL and the bubble is also significantly positive in all three countries.

2.5.2. Short-Run Dynamics

In the next step, the short-run dynamics between the variables in the models are analyzed. In the case of Portugal, the Johansen cointegration test indicates no cointegration relationship. Therefore, a VAR model in first differences as specified below is set up. 8_* is the 3×1 vector of the three variables included in the model. A_B is the 3×1 vector of intercept terms, A_C the 3×3 matrix of coefficients and ε the 3×1 vector of error terms.

∆8_* = A_B+ A_:∆8_*-:+ ⋯ + A_G∆8_*-G+ ε (6) In the case of Greece, Ireland and Spain, the same model is used for the Johansen cointegration test. The model includes a constant but no trend in the cointegration vector. This model removes the linear deterministic trend of the time series as it removes the unit roots so that the cointegration equation does not contain any trend.

This specification is close to the idea of the cointegrating equation defining an equilibrium relationship. The model is specified below where 8_* is the 3×1 vector of the variables included in the model, A_B is a 3×1 vector of constant terms, (@B+

@^HI_*-:) the cointegrating equation, J the speed of adjustment, A_C the 3×3 matrix of coefficients and ε the 3×1 vector of error terms.

∆8_* = A_B+ J(@_B+ @^H8_*-:) + A:∆8_*-:+ ⋯ + A_G-:∆8_*-GK:+ ε (7) The speed-of-adjustment coefficient indicates how the variables adjust to any discrepancies from the long-run equilibrium relationship. Given the positive value of the cointegrating equation, a positive coefficient indicates that the variable will go up

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and a negative coefficient indicates that the variable will decrease. The lower panel of Table 2.7 shows the estimates. In the short-run, the bubble in Ireland responds with an increase and the bubble in Greece with a decrease to a deviation from the long-run equilibrium; the implication is that in the short-run the bubble tends to depart from the long-run equilibrium in Ireland but tends to approach the long-run equilibrium in Greece. In the case of Spain, the speed-of-adjustment coefficient is not significant at the 5% level of significance.

Based on the VAR model for Portugal and the VEC model for the other three countries, the dynamic effects of innovations in the money market interest rate and lending for house purchase-to-GDP and the bubble are analyzed by computing orthogonalized impulse responses. Hereby the standard Choleski decomposition (C.

Sims, 1980) is used to derive the impulse responses. The ordering used is B-HL-IR and aligned to the specification used by Hofmann (2004) and Oikarinen (2009).

Following the ordering, it is assumed that the bubble does not respond instantly to innovations in lending for house purchase-to-GDP and the Euribor. The lending for house purchase does not respond instantly to a shock in the interest rate, and the interest rate is rather flexible because the ECB and the domestic banking system can respond immediately with an interest rate change to alterations of the former two variables. Thus, the bubble may be affected within a quarter by the other two variables. The chosen ordering of the variables is common in the literature on monetary policy transmission and reflects the assumption that interest rate changes are transmitted to the economy with a lag. The following figures (Figure 2.5, Figure 2.6, Figure 2.7, Figure 2.8) illustrate the impulse responses up to 20 quarters from the shock. As outlined above, differenced data is used in the case of Portugal and data in

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its levels for the other three countries. Therefore the results of the following analysis cannot be compared directly with the other three countries.

Figure 2.5 shows the response of the bubble in Portugal to an innovation in IR and HL.

The impulse response function of Portugal reveals that the response of the bubble to a positive innovation of the two variables is positive but very weak. The effect vanishes after 10 quarters.

Figure 2.5: Portugal’s Bubble Response to Cholesky One S.D. Innovations

As illustrated in Figure 2.6, the response of the bubble in Greece to a one standard deviation in IR is also positive, but relatively weak. The response to an innovation in HL becomes positive and relatively strong after a few lags.

Figure 2.6: Greece’s Bubble Response to Cholesky One S.D. Innovations

As shown in Figure 2.7 and Figure 2.8, a positive one standard deviation shock in IR has temporarily no effect in Ireland and a slightly positive effect in Spain before turning strongly negative. The initial positive response of Spain to a positive shock in

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IR can be explained by the effect of the WACC on the fundamental value and bubble.

An increase in the Euribor leads to an increase in the WACC. With an increase in the WACC, the fundamental value decreases, the gap to the market price widens and the bubble increases. The response of the bubble in Spain to a positive innovation in the IR turns strongly negative and is negative in Ireland because the investment demand

of real estate is affected by higher interest rates. One possible reason for the different response of Portugal and Greece to an unexpected innovation of the interest rate might be that the bubble in these countries reacts only to the effect of the WACC on the fundamental value but not to its effect on investment demand and thus the market price.

As for Ireland and Spain, in the case of a positive interest rate shock, mortgage borrowers become increasingly overwhelmed by the debt burden, and in the worst case default on their mortgage loans. Investors lose interest in real estate and start to switch to other assets where interest rates increase. This decreases the demand for property as well as the market price, thus resulting in a decreasing bubble.

Figure 2.7: Ireland’s Bubble Response to Cholesky One S.D. Innovations

Similar to the bubble in Portugal and Greece, the bubble in Ireland and Spain also respond positively to a positive shock in HL. However, unlike the bubble in Portugal the bubble in Greece, Ireland and Spain responds much stronger and with a lag to an innovation in HL.

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Figure 2.8: Spain’s Bubble Response to Cholesky One S.D. Innovations

The variance decomposition in Table 2.8 shows that almost no variance of Portugal’s bubble can be explained by the short-run dynamics of IR and HL. In Greece and Ireland, both, IR and HL account for a large proportion of the variance in the bubble.

For instance, at lag 10, IR explains around 20% of the bubble variance in Greece and around 31% in Ireland. At the same lag, HL accounts for around 21% of the variance of Greece’s and around 40% of Ireland’s bubble. In Spain, most of the variance in the bubble is primarily explained by IR. For example, at lag 10, around 16% in Spain’s bubble is explained by IR and only around 1% by HL. It is interesting to note that while the ECB’s monetary policy variables explain only a minor proportion in the bubble of Portugal, the variables explain a large proportion of the variance in the bubble of Greece, Ireland and Spain. Another interesting observation is that the explanatory power of IR and HL tends to increase with the number of lags. This illustrates the lagged effect of monetary policy on the formation of real estate bubbles.

Before moving on to the discussion part, the residual Portmanteau test for autocorrelations is applied to each model. The null hypothesis of this test is that the residuals exhibit no autocorrelations up to a specified lag. A maximum lag length of 20 is chosen and the test for the model of each country applied. The null hypothesis cannot be rejected at the 10% level of significance in Portugal and Spain meanwhile at the 5% level of significance in Ireland. In the case of Greece, however, the null

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cannot be rejected at several lags even at the 1% level of significance. Therefore, the empirical results of Greece should be interpreted with caution.

Table 2.8: Decomposition of Property Bubble Variance

Portugal Greece Ireland Spain

Period ∆IR ∆HL IR HL IR HL IR HL

Note: Since differenced data is used in the estimation of the VAR model of Portugal and level data is used in the estimation of the VEC models of Greece, Ireland and Spain above figures of Portugal cannot be compared directly with the other three countries.