Impulse Response Function

Through the impulse responds function, the analysis observed the impulse of specific variables to other variables. The impulse responds functions could be divided into impulse responds function decomposed by Cholesky and general impulse function. The former needed to set up the order of influences based on the degree of influence of variables, while the latter, proposed by Pesaran and Shin(1988), could be used to analyze results of impulse responses without order, which could prevent the possible distortion of causality caused by preconceptions. The study conducted the analysis based on general impulse responds function.

The definition of the function was as below:

GIRF(𝑥

- E

, (4)

In this function, Ω_!!! was the information set in t-1 period; 𝜎_!,! represented the variance in the j equation in the ith variable-diagonal elements of covariance matrix; n was the length of forecast period. Which measures the effect of one standard error shock to the jth equation at time t on expected values of x at time t+n. Through the observation on differences between two expected values, the possible trend in the future could be projected. The empirical result was shown in Figure 6-8 as below:

Figure 6-a Response of GDP to GDP Figure 6-b Response of GDP to HPI

Figure 6-c Response of GDP to SPI Figure 6-d Response of GDP to IR

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  Figure 6-e Response of GDP to INCOME Figure 6-d Response of GDP to CPI

Figure 6 Impulse Response Function - GDP

Figure 7-a Response of CS to CS Figure 7-b Response of CS to HPI

Figure 7-c Response of CS to SPI Figure 7-d Response of CS to IR

Figure 7-e Response of CS to INCOME Figure 7-f Response of CS to CPI Figure 7 Impulse Response Function - CS

Figure 8-a Response of HPI to HPI Figure 8-b Response of HPI to GDP

Figure 8-c Response of HPI to SPI Figure 8-d Response of HPI to IR

Figure 8-e Response of HPI to INCOME Figure 8-f Response of HPI to CPI Figure 8 Impulse Response Function – HPI

First, under the macroeconomic environment in Taiwan, as shown in Figure 6, a positive standard deviation impulse of INCOME, and GDP had a long-term consistent and positive influence on GDP, with about 2%~4% positive and steady growth. The increase of SPI had a positive influence on GDP; in case of per capita national income, although there did not had a positive influence on GDP under the direct effect. While include indirect effects in the model, INCOME has continuous 4% positive responses in GDP after 1 year, consistency with the consumption theory proposed by Friedman. The expected increase of income would indirectly affect consumption and domestic investment and thus create the economic prosperity.

A positive standard deviation impulse of HPI caused not significant increase of short-term economic growth to 2%, though HPI has crowing-out effect on consumption, the increase of house prices represented the increase of total investment in terms of direct effects. However, in

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terms of overall long-term average, increasing of house prices is not significant influence on economic growth.

A positive standard deviation impulse of IR had a slightly discontinuous negative influence on economy. As a tool used in the monetary policy of Central Bank, the interest was adjusted upward to inhibit the demand for real estate investment and reduce the price of real estate as well as reduce the mortgage burden rate and make consumption return to positive growth. Interest rate also affect the investment in the financial market and exchange rate on the import and export. In terms of overall long-term average, the increase of interest had a slightly negative influence on economy.

In the analysis of impulse responses of variables to consumption as shown in Figure 7, a positive standard deviation impulse of SPI, INCOME, and CS had a long-term consistent and positive influence on consumer spending, with 2%~4% positive influence. The increase of lag consumption had a positive direct effect on the current consumption, the vicious cycle of deflation would occur if consumption had a negative growth for a long time, resulting in the continuous decline of economic growth, increase of unemployment, and reduction of income.

Thus, concerning impulse responses of other indirect effects, once again emphasized the important of consumer spending (accounted for 60% of GDP). Besides, the INCOME and CS had a positive influence on CS, which was consistent with the consumption theory of Friedman and Fisher equation.

Based on the influence of changes of prices of two assets on consumer spending, the SPI and HPI were selected in the study to explore their degree of wealth effects. For a positive standard deviation impulse of SPI had a positive influence with a short-term 2%-3% influence and long-term 2% growth on average. In terms of HPI, the nearly zero not significant positive influence in the short run. Which showed that the wealth effect existed in the stock market in Taiwan and could promote the growth of consumption. A positive standard deviation impulse of HPI had slightly less than 1% effect in CS, the wealth effect is not significant. If the growth of real estate market could not had significant contribution to economy, the great amount of money invested in the real estate would crowd out industrial structural development and consumer spending. However, in terms of analysis of crowding-out effect based on impulse responses, the negative volatility was still insignificant. The number of vacant housing¹⁰ was 1,560,000, which accounted for 19.25% of housing in Taiwan. In terms of number of self-owned houses¹¹, under most of people are occupier-owner, owners havingmore than two houses accounted for 3.6% of total homeowners in Taiwan. Given the increase of house prices, the wealth effect maybe still existed among these owners (3.6%). However, in case of more than 60% of people who did not own real estates, the annual growth of consumption decreased

10  ^“Vacant housing” referred to houses which no people resided in frequently or were not provided for other purposes, including houses to be rented, houses to be sold, sold or rented houses, and houses which no people resided in currently, more than two houses which no people resided in frequently, or houses which no people resided in frequently due to work in other places.  

11  The number of houses owned by taxpayers of house tax collected by Ministry of Finance in 2012: 1 house: 7,240,000; 2 houses: 680,000;

and 3 houses and more: 180.000. Based on the percentage of homeowners to the total population on average in Taiwan: 0 house: 65.4%; 1 house: 30.9%; and 2 houses and more: 3.6%.  

since 2010; based on the impulse responses, crowding-out effect still not significant.

A positive standard deviation impulse of CPI had instant negative influence on CS. It reached 3% negative influence one and half years later, which indicate under the growth of

“real income” was nearly zero, increasing CPI will cause negative influence on consumption.

In contrast, a negative standard deviation impulse of IR had no significant 1% negative effect on CS. It pointed out that when interest rate decline, does not improve the strength of consumption, the lack of consumer confidence will facing deflation environment such as Japan.

So constructed the model on predict the changes of consumption are important for Taiwan.

In the analysis of impulse responses of variables to HPI as shown in Figure 8, a positive standard deviation impulse of HPI had a long-term consistent and positive influence on itself;

among them, the impulse of HPI was the most immediate and significant, which had 4%

positive response in Q1 and had about 5%-6% steadily positive growth one and half year later.

It showed that the continuous unexpected increase of house prices caused the continuous increase of demand for real estate investment, and a great amount of money was invested for the realization of capital gains.

A positive standard deviation impulse of SPI had a short-term 2% positive influence on HPI, which gradually became zero and had 3% negative response after one and half year.

Indicate that stock market has a positive impact on short-term and negative effect on long-term.

The possible reason might be short-term stock market profits of funds will spillover to the real estate market. In the long run, two markets are attracting investment capital, when SPI rising will cause real estate funds transferred to the stock market.

A positive standard deviation impulse of IR had about 1% positive influence in a short-run.

However, the effect continued decreasing and had a negative influence on HPI one year after.

The magnitude of such effect increased as time went by and had about 8% negative response four years after, showing that under the high loan-to-value and low interest rate, the increase of interest rate represented the increase of cost for house purchase, and the investment risk increased as the interest rate increased. When investors could not afford high principal and interest, they had no choices but to sell and auction houses, which directly impacted on the real estate market. It also showed that the low interest rate caused by the easing monetary policy carried out in recent years was one of main reasons for continuous increase of house prices.

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