The Effect of Macroeconomic Variables on
Stock Prices in the European Union
Yorick Reinders – S3162176
Supervisor: dr. J.V. Tinang Nzesseu
Abstract
This paper tries to determine the relationship between macroeconomic variables and stock prices in the European Union. Monthly data on short-term interest rates, long-term interest rates, money supply, inflation rates, industrial production, exchange rates, and oil prices are used for the period 1999:12 – 2019:12 to investigate their influence on the stock markets of France, Germany, Italy, the Netherlands, and Spain. In order to investigate this relationship, a vector error correction model (VECM) is used to study the short-run as well as the long-run relationship. Furthermore, Granger causality tests and innovation accounting analysis are used to analyse the dynamics. Findings show that in the short-run, the short-term interest is negatively related to stock prices. On average, a one unit, or 1%, increase in the short-term interest rate reduces the log of stock prices by 0.007 points. Further, in the long-run, the short-term interest rate, inflation rate, and oil price are negatively related to stock prices. On average, a one unit increase in the short-term interest rate reduces the log of stock prices by 0.014 points . Further, a one unit increase in the log of the inflation rate and oil price reduces the log of stock prices by 0.004 and 0.011 points respectively.
2 Acknowledgement
I would like to thank my supervisor dr. J.V. Tinang Nzesseu for his continued guidance and helpful comments throughout my research and the writing of this paper.
3 1. Introduction
Participants in financial markets pay close attention to all information which could potentially influence stock prices, with the goal of correctly determining the value of stocks. There are several different sources of information which have the potential to influence stock prices. Broadly speaking these sources can be divided into two subgroups: microeconomic information and macroeconomic information. While microeconomic information is concerned with company level information, macroeconomic information aggregates all this company level information and translates it to a government or country level.
Investors, economists, and policymakers all try to predict the direction of stock prices in order to make profits, or steer the economy in a certain direction. While on the first hand it might seem that investors are mainly interested in company fundamentals (such as earnings per share or profit margins) to search for worthwhile investments, the state of the overall economy is also highly relevant. The state of the economy can also heavily influence stock prices through its effects on companies’ fundamentals and investors might thus want to adjust their portfolios because of changes in the macro economy. While most investors focus on individual companies, economists are mainly concerned with predicting future stock prices for the overall economy, and hence they are interested in a model which could help them in predicting these prices. Policymakers on the other hand are more interested in deploying different tools in order to steer the market in a certain direction. With the tools they have at hand they can influence macroeconomic fundamentals and with a model which relates these fundamentals to stock prices they are able to more accurately predict policy implications.
Recently there has also been discussion about the apparent gap that has been developing between the macroeconomic variables and stock prices after the start of the Corona crisis. After the initial drop in stock prices the stock market recovered relatively quickly and in many countries has again risen to the highs set before the Corona crisis, even though the macro economy has clearly not fully recovered yet. This raises questions about the exact nature of the relationship between macroeconomic variables and stock prices.
With this in mind, this paper aims to study the relationship between some prominent macroeconomic fundamental variables and stock prices in the five largest European Union (EU) economies1 for the period 1999:12 – 2019:12. These macroeconomic variables include: the short-term interest rate, long-term interest rate, money supply, inflation, industrial production, exchange rate, and oil price. The EU countries which will be investigated in this paper are: France, Germany, Italy, the Netherlands, and Spain.
1
4 The relationship for these countries will be investigated using a VECM model, Granger causality tests, and innovation accounting analysis. These will be used to study the short-run as well as the long-run dynamics.
Most studies into the relationship between macroeconomic variables and stock prices have focused on emerging markets and large individual developed economies (Wongbangpo & Sharma (2002), Horobet & Dumitrescu (2009), and Humpe & Macmillan (2009)). Little research has been done on European countries, and the research that has been done has either focused on few variables, few countries, or has not been conducted recently (Nasseh & Strauss (2000), and Peiró (2016)). The contribution of this paper to the existing research will thus be twofold: First, this paper considers a large group of European countries which are part of one of the largest trade blocs in the world. Second, this paper uses a very recent dataset which can be used to compare findings with that of older papers to see if dynamics in the relationships between variables and stock prices have changed over time.
This paper will have the following outline: Section 2 presents the theory behind the macroeconomic effects on stock prices by using related literature, section 3 describes the dataset, section 4 describes the methodology used in this study, section 5 presents the obtained results, and section 6 concludes by summarizing the results, discussing limitations to this study and providing recommendations for future research.
2. Literature Review
5 According to these models, stock prices are determined by expected dividend payments, or cash flows, and the discount rate. Chen et. al (1986) suggest that several macroeconomic variables are expected to influence the dividend payments, cash flows, and the discount rate used in these valuation models. Hence, financial theory suggests that changes in macroeconomic variables are expected to have an impact on stock prices. Financial theory also provides guidance as to which variables may potentially influence stock prices, and the impact of the different variables can be broadly grouped as coming from three different sources: the money market, the goods market, and external sources.
The money market variables include the interest rates and the money supply. As discussed by Jammazi, Ferrer, Jareño & Hammoudeh (2017), finance theory suggests that interest rates influence stock prices through several different channels. They mention at least three different channels through which this effect might be present. First, changes in interest rates directly affect the discount rate used in equity valuation models, which impacts stock prices. Second, interest rate fluctuations affect the cost of capital of financing corporations. This effect is most clearly present for corporations with a large debt ratio. Through this channel the interest rate thus affects the expected future cash flows, which in turn affects stock prices. Third, interest rate fluctuations can lead to portfolio rebalancing. When yields on fixed-income securities change, stocks become more or less attractive to investors, which may either lead to a shift from fixed-income securities into stocks or vice versa. This in turn will affect the demand for stocks and hence their prices.
The authors elaborate further and suggest that there may also be a causal relationship from stock prices to interest rates. They for example suggest that when the forward-looking stock prices are expected to decrease sharply, this may signal pessimism about future economic prospects, and hence interest rates may be expected to decrease in order to stimulate the economy.
Theory suggests that short-term and long-term interest rates may influence stock prices differently. Nasseh & Strauss (2000) mention in their paper that short-term interest rates represent the effect of other macroeconomic activity, such as production, while long-term interest rates proxy for the discount rate. As a result, both types of interest rates can have different effects on stock prices. The authors mention that if the short-term interest rate can be used as a proxy for macroeconomic activity, then it is expected that it is positively related to stock prices. On the other hand, the long-term interest rate as a proxy for the discount rate is expected to negatively influence stock prices. The authors indeed found results in line with these expectations.
6 Money supply can also be linked to stock prices through several different mechanisms. First, Friedman (1969) describes how monetary policy affects the economy through the so called ”liquidity effect”. It is suggested that when the money supply increases, interest rates will decrease, and this is what is known as the liquidity effect. Hamilton (1997) measured the effect on the federal funds rate of an open-market operation and indeed concluded that this liquidity effect is real and leads to a decline in interest rates. As mentioned above, lower interest rates result in higher stock prices, hence the liquidity effect increases stock prices.
Second, as mentioned by Rogalski & Vinso (1977), research has shown that a relationship exists between changes in the money supply and changes in prices of other assets held in an investor’s portfolio. An unexpected change in the growth rate of money results in a change in the equilibrium position of money with respect to other assets in the portfolio. This results in investors trying to adjust the proportion of their portfolio represented by money. Equilibrium in the system is then re-established by changes in asset prices, of which common stock are an important component. Hence, it can be hypothesized that changes in the money supply cause changes in stock prices. As mentioned by Humpe & Macmillan (2009), expansionary monetary policy will lead to a portfolio shift from non-interest bearing money to financial assets such as equities, thus leading to an increase in stock prices.
Third, as mentioned previously, expansionary monetary policy leads to a decline in interest rates. Subsequently, lower interest rates boost economic growth, which in turn leads to an increase in the expected level of inflation. Fisher (1930) derived an equation which links the nominal interest rate, real interest rate, and inflation. The Fisher hypothesis states that the real interest rate is independent of the nominal interest rate and inflation rate, hence it should remain constant. Then, looking at the Fisher equation, an increase in the inflation rate will lead to an increase in the nominal interest rate. This results in lower stock prices, thus an increase in the money supply can also be linked with declining stock prices.
Hypothesis 2: The money supply is positively related to stock prices.
7 As discussed above, the Fisher equation can be used to conclude that an increase in the inflation rate leads to a subsequent increase in interest rates, which also negatively affects stock prices. Fama (1975) tested this hypothesis for the US and indeed observed this hypothesized relationship between nominal interest rates and rates of inflation. Thus, again increasing inflation rates lead to lower stock prices.
Hypothesis 3: The inflation rate is negatively related to stock prices.
Fama (1990) finds that growth rates of production, used to proxy for shocks to expected cash flows, explain 43% of the variance of annual NYSE value-weighted returns. Also, preliminary tests showed that industrial production explains as much, or even more, return variation as other variables that proxy for real economic activity. Here, industrial production is a measure of economic output and is described by the OECD as the output of industrial establishments, where it covers sectors such as mining, manufacturing, electricity, gas and steam, and air-conditioning.
Fama (1990) and Schwert (1990) further elaborate and suggest three reasons as to why there is a link between stock prices and real economic activity. First, information about future real activity may be reflected in stock prices well before it occurs. This implies that stock prices are a leading indicator for the well-being of the economy. Second, changes in discount rates may have the same effect on stock prices and real investments, however the output from real investment appears only some time after it is made. Again, stock prices can then be seen as a leading indicator. Third, changes in stock prices are equal to changes in wealth, which means that potentially the demand for consumption and investment goods may be affected.
Campbell and Ammer (1993) note that innovations to industrial production may be related to changes in stock prices for two different reasons. First, innovations in industrial production may reflect changing expectations of future cash flows. Second, interest rate innovations could be affecting both industrial production, through changes in investments, and stock prices, through changes in the discount rate. In that case there seems to be a relationship between industrial production and stock prices, while in reality interest rates are the driving factor. However, the authors also found that interest rates are not the main determinant for changes in stock prices.
8 To finalize, the two external sources considered in this paper are the exchange rate and the oil price. While stock prices are heavily influenced by factors from the money market and goods market, not all variability can be explained by looking at just these two markets. Some variability in stock prices will emerge from external sources which lie outside the control of the policymakers or which measure the degree of competitiveness of the domestic economy with respect to foreign economies.
The potential relationship between exchange rates and stock prices can be explained by the so-called ”portfolio balance approach”. This model assumes that assets in different countries are not perfect substitutes. It is assumed that an investor’s portfolio consists of local currency, local bonds, foreign currency, and foreign bonds. When demand for one of these assets changes, the investor rebalances the portfolio such that the desired balance is re-established. This rebalancing process in turn affects the exchange rate. For example, if the interest rate on local bonds increases with respect to foreign bonds, this would increase demand for these bonds. This in turn increases demand for local currency, leading to an appreciation of the local currency.
When a country’s local currency depreciates, its exported goods become cheaper to buy for foreign countries, which in turn increases demand for local goods. This is highly favourable for local companies, which can use this weakening of the local currency to export more goods and increase profits. This in turn increases expected future cash flows and subsequently stock prices.
Hypothesis 5: The exchange rate is negatively related to stock prices.
As explained by the European Central Bank (ECB) (2004), oil prices can impact stock prices through several channels. First, an increase in oil prices usually lowers the expected rate of economic growth and increases inflation expectations. The lower growth rate in turn lowers expected future cash flows, which lowers stock prices. Also, as explained before, increases in inflation expectations have a negative impact on stock prices. Second, increases in oil prices lead to increases in input prices for companies, which generally compresses profit margins, and this again lowers stock prices. Third, during periods of high oil prices, investors tend to become more uncertain about earnings outlooks, which may lead to higher equity risk premia, and lower stock prices.
9 Research has shown that the relationship between oil prices and stock prices mainly depends on the reason for the change in oil price. Kilian & Park (2009) found that the negative response of US real stock returns to oil price shocks is only found when the rise in oil price is caused by an oil-market specific demand shock such as an increase in precautionary demand, which could be driven by fears about future availability of oil. However, when increases in the oil price are the result of a global economic expansion, the authors found persistent positive effects on stock returns. Furthermore, they found that shocks to oil production have no significant effect on stock returns.
Also, Apergis & Miller (2009) found that different oil market structural shocks play a significant role in explaining stock market returns. The authors decomposed oil price changes into three components: oil supply shocks, global aggregate demand shocks, and global oil demand shocks. This last component refers to specific idiosyncratic features of the oil market, such as the precautionary demand mentioned earlier. They further found that these idiosyncratic demand shocks lead stock market returns, while no such relationship is found for the other two shocks.
Hypothesis 6: The oil price is negatively related to stock prices.
3. Data
10 Table 1. Variable Definitions
Variable Definition
Stock prices Real end-of-month-value of the national stock index RSP Short-term interest
rate
End-of-month 3-month money market rate STR
Long-term interest rate
End-of-month 10-year government bond yield LTR Money supply Average monthly seasonally adjusted narrowly defined money
supply (M1), expressed in USD
MON Inflation Average monthly seasonally adjusted Consumer Price Index (CPI) CPI Industrial production Average monthly seasonally adjusted Industrial Production Index
(IPI)
IPI Exchange rate Average monthly Real Effective Exchange Rate (REER) REER Oil price Real end-of-month WTI crude oil price, expressed in USD ROIL
For the money supply this paper uses the M1 as reported by the ECB, and not the M1 as reported by the individual countries’ central banks. This is done because the individual central banks in the EU hand over almost all power to the ECB, which sets the monetary policy for all EU countries. The M1 as reported by the ECB is simply an aggregate of the M1 as reported by all individual central banks in the EU. Also, it can be noted that the 3-month money market rate is the same for all countries because of similar reasoning. Further, the stock prices and oil prices are corrected for inflation using the CPI as reported by the country for which the specific variables need to be adjusted.
11 Table 2. Descriptive Statistics
12 From Table 2 a few things can be noted. First, the mean and median for all variables are relatively close to zero. This indicates that the average month-to-month change in the variables has been close to zero for the period under consideration. Second, the standard deviation and minimum and maximum vales show that for stock prices, money supply, and oil prices, the underlying month-to-month percentage changes could vary greatly, even though the average value is close to zero. This is an indication of volatility for these variables, especially for stock prices and the oil price. Third, looking at the skewness and kurtosis values, it can be noted that data across countries is distributed very differently and that quite some variables are clearly not normally distributed.
4. Methodology
This paper tries to model the short-run and long-run relationship between several macroeconomic variables and stock prices, and the ideal tool for this is cointegration analysis. Standard methods to analyse time series such as ordinary least squares (OLS) make the assumption that means and variances are constant over time. This cannot reasonably be assumed for the time series used in this paper. Cointegration analysis can be used to analyse non-stationary time series, which have time-varying means and variances. This paper will use the Johansen multivariate cointegration test to determine whether the macroeconomic variables are cointegrated with stock prices and to determine the potential long-run relationship. Then, after estimating the long-run model, the short-run relationship between the macroeconomic variables and stock prices will be examined.
Next, the Granger causality test will be used to determine the short-run and long-run causal relations between stock prices and the macroeconomic variables. The causal relations can be used in conjunction with the established relationships to draw conclusions. Here, the causality test results can help to indicate which macroeconomic variables affect stock prices, while the model results show the sign of the effect. Also, the short-run relations are used to order the variables for the innovation accounting analysis.
13 4.1 Long-run relationship
In order to test for the long-run relationship between the macroeconomic variables and stock prices this paper uses the Johansen multivariate cointegration test as proposed by Johansen (1991). This procedure is used for detecting cointegration and based on a vector error correction model (VECM). First, the stationarity of each time series is examined by using the augmented Dickey-Fuller (ADF) test. For this test two options are considered: the ADF test with an intercept, and the ADF test with an intercept and trend. This is done in order to take into account that some time series may be trending over time. Also, information criteria are used in order to correctly select the lag order for the ADF test. The highest suggested lag order will be chosen in order to be conservative in testing. These tests are used to determine the order of integration of the different time series. If these tests fail to reject the null hypothesis of the existence of a unit root in log levels, but reject this same null hypothesis in the log first difference of the time series, then the variable under consideration is integrated of order 1, or I(1) for short. This simply means that a single set of differences can transform the non-stationary variable into a stationary variable.
The model derivation in the remainder of this sub-section is obtained using the Stata13 Manual (2013). First, consider a general vector autoregressive (VAR) model with p lags. This can be expressed as follows:
𝑌𝑡 = 𝑣 + 𝐴1𝑌𝑡−1+ 𝐴2𝑌𝑡−2+ ⋯ + 𝐴𝑝𝑌𝑡−𝑝 + 𝜀𝑡 (1) This equation can be defined as follows:
- 𝑌𝑡: K x 1 vector of variables.
- 𝑣: K x 1 vector of constants, serving as the model intercept. - 𝐴𝑝: K x K matrix of parameters.
- 𝜀𝑡: K x 1 vector of error terms.
This general VAR(p) model can be rewritten to represent a VECM. The general VAR(p) model containing n endogenous variables written in the error correction form and allowing for deterministic trends can be represented as follows:
14 This equation can be defined as follows:
- 𝑌𝑡: K x 1 vector of variables.
- 𝑣: K x 1 vector of constants, serving as the model intercept and allowing for deterministic drift.
- 𝛿: K x 1 vector of parameters, allowing for a time trend component.
- ∏: K x K matrix containing the cointegration relationships and capturing the adjustments towards the long-run equilibrium.
- Г𝑖: K x K matrix describing the short-run impact and capturing short-run deviations from the
equilibrium.
- 𝜀𝑡: K x 1 vector of error terms.
Furthermore, ∏ and Г𝑖 can be expressed as follows:
∏ = ∑𝑗=𝑝𝑗=1𝐴𝑗− 𝐼𝑘 (3)
Г𝑖 = − ∑𝑗=𝑝𝑗=𝑖+1𝐴𝑗 (4)
These expressions are defined as follows: - 𝐴𝑗: K x K matrix of parameters.
- 𝐼𝑘: K x K identity matrix.
Then, Engle & Granger (1987) show that if all variables 𝑌𝑡 are I(1), the matrix ∏ has rank 0 ≤ r < K, where r is the number of linearly independent cointegrating vectors. If the variables are cointegrated, a VAR in first difference is misspecified, since it omits ∏𝑌𝑡−1, the
error correction term (ECT). Then three different cases have to be considered:
1. r = 0: There is no cointegration among the variables and a VAR in first differences is the appropriate model to use.
2. r = K: All variables are stationary, or I(0), and a VAR in levels is the appropriate model to use.
3. 0 < r < K: There are r cointegrating relationships among the variables, and the matrix ∏ can be decomposed into two different matrices such that:
∏ = α𝛽′ (5)
In this equation:
15 Using this expression, equation (2) can be rewritten as follows:
∆𝑌𝑡 = α𝛽′𝑌𝑡−1+ ∑𝑝−1𝑖=1 Г𝑖∆𝑌𝑡−𝑖+ 𝑣 + 𝛿𝑡 + 𝜀𝑡 (6)
Here, 𝑣 implies a linear trend in the undifferenced data, while 𝛿𝑡 implies a quadratic time trend in the undifferenced data. Also, because α is a K x r rank matrix, the deterministic components in equation (6) can be rewritten as:
𝑣 = 𝛼𝜇 + 𝛾 (7)
𝛿𝑡 = 𝛼𝜌𝑡 + 𝜏𝑡 (8)
In equations (7) and (8), the variables are expressed as follows: - 𝜇 & 𝜌: r x 1 vector of parameters.
- 𝛾 & 𝜏: K x 1 vector of parameters.
Then, equations (7) and (8) can be used to rewrite equation (6) as:
∆𝑌𝑡= α(𝛽′𝑌
𝑡−1+ 𝜇 + 𝜌𝑡) + ∑𝑝−1𝑖=1 Г𝑖∆𝑌𝑡−𝑖+ 𝛾 + 𝜏𝑡 + 𝜀𝑡 (9)
This equation forms the basis for testing for deterministic components in the VECM. Johansen (1992) proposes a systematic test procedure to determine the VEC model specification. Using this procedure the deterministic component of the cointegrating system can be determined. This test specifies three models to test, where Model 1 is the most restrictive, and Model 3 is the least restrictive out of the three. These three models are specified in equations (10)-(12) in Appendix B. The procedure involves going from Model 1 to Model 3 and at each stage comparing the λtrace to its critical value. The deterministic
component is then determined where the null hypothesis is not rejected for the first time. The model specification first has to be determined before testing for the number of cointegrating equations.
Then, Johansen developed two likelihood ratio tests to test for the number of cointegrating vectors r: the trace test and the maximum eigenvalue test. The trace statistic (λtrace) tests the null hypothesis of r = 0 against the alternative hypothesis that r > 0, while the
maximum eigenvalue (λmax) statistic tests the null hypothesis of r cointegrating vectors against
16 4.2 Short-run relationship
From equation (2) can be seen that the estimated model consists of two parts, namely a long-run estimate and a short-run estimate. The ∏ matrix contains the coefficients used to determine the long-run relationship, while the Г𝑖 matrix contains the coefficients used to determine the short-run relationship. The long-run estimates are obtained from a VECM in levels, while the short-run estimates are obtained from a VAR model in first differences.
4.3 Granger causality test
Granger (1988) suggests that in a cointegrated set of variables the causal relations between these variables should be examined within the framework of the VECM. The dynamic causal link between a macroeconomic variable (X) and stock prices (Y) can be modelled as follows:
∆𝑌𝑡 = 𝛼1+ 𝛽1𝐸𝐶𝑡−1+ ∑𝑘𝑖=1𝛾1𝑖∆𝑌𝑡−𝑖+ ∑𝑖=1𝑘 𝛷1𝑖∆𝑋𝑡−𝑖+ 𝜀𝑡𝑌 (13)
In this paper, for stock prices this relationship can be expressed as:
∆ln (𝑅𝑆𝑃)𝑡 = 𝛼1+ 𝛽1𝐸𝐶𝑡−1 + ∑𝑘𝑖=1𝛾1𝑖∆ln (𝑅𝑆𝑃)𝑡−𝑖+ ∑𝑖=1𝑘 𝛷1𝑖∆𝑆𝑇𝑅𝑡−𝑖+ ∑𝑘𝑖=1𝜌1𝑖∆𝐿𝑇𝑅𝑡−𝑖 + ∑𝑘𝑖=1𝜔1𝑖∆ln(𝑀𝑂𝑁)𝑡−𝑖+ ∑𝑖=1𝑘 𝜏1𝑖∆ln (𝐶𝑃𝐼)𝑡−𝑖+ ∑𝑖=1𝑘 𝜉1𝑖∆ln(𝐼𝑃𝐼)𝑡−𝑖+
∑𝑘𝑖=1𝛿1𝑖∆ln (𝑅𝐸𝐸𝑅)𝑡−𝑖+ ∑𝑘𝑖=1𝜑1𝑖∆ln (𝑅𝑂𝐼𝐿)𝑡−𝑖+ 𝜀𝑡𝑙𝑛𝑅𝑆𝑃 (14)
This equation can be defined as follows:
- 𝐸𝐶𝑡−1: Error correction term obtained from the first cointegrating vector. - k: Lag length.
- 𝛽 , 𝛾, 𝛷, 𝜌, 𝜔, 𝜏, 𝜉, 𝛿 & 𝜑: Parameters to be estimated.
- 𝜀𝑡𝑅𝑆𝑃: Stationary random processes with zero mean and constant variance.
17 This procedure is followed for every variable to test for Granger causality. F-statistics are used to test the joint significance of the lags of each separate variable, and t-statistics are used to test the significance of the lagged error correction term coefficient. When a variable is found to Granger cause stock prices, it can be concluded that past values of this variable are useful in predicting future stock prices.
4.4 Innovation accounting analysis
Innovation accounting analysis can be used to analyse the short-term dynamics among variables and to interpret the results obtained from VAR models more easily. The analyses considered in this paper include impulse response functions (IRFs) and forecast error variance decompositions (FEVDs). An impulse response analysis can be conducted to analyse the response of stock prices to a one standard deviation shock to the macroeconomic variables.
The intuition behind IRFs can be explained using the Stata13 Manual (2013). First, consider again a VAR(p) model as described in equation (1):
𝑌𝑡 = 𝑣 + 𝐴1𝑌𝑡−1+ 𝐴2𝑌𝑡−2+ ⋯ + 𝐴𝑝𝑌𝑡−𝑝 + 𝜀𝑡 (1)
If this VAR is stable, it can be rewritten in moving average form as follows:
𝑌𝑡 = 𝜇 + ∑∞𝑖=0𝛷𝑖𝜀𝑡−𝑖 (15)
This equation is defined as follows: - 𝜇: K x 1 time-invariant mean of 𝑌𝑡.
- 𝛷𝑖: 𝐼𝑘 if i = 0, ∑𝑖𝑗=1𝛷𝑖−𝑗𝐴𝑗 if i = 1, 2, … - 𝜀𝑡−𝑖: K x 1 vector of error terms.
In the above equation, the 𝛷𝑖 can be interpreted as the simple IRFs at horizon i. These
IRFs give the effect of a one-time unit increase in one of the elements of 𝜀𝑡 (shock) on 𝑌𝑡 after
i periods, holding all else constant. This is equivalent to measuring the effect of a one-time
18 This can be overcome by rewriting equation (15) in terms of mutually uncorrelated innovations. In equation (1) it is assumed that the 𝜀𝑡 are white noise, and hence E(𝜀𝑡𝜀𝑡′) = Σ, where Σ is the covariance matrix of shocks. The vector of shocks, 𝜀𝑡, can be orthogonalized by 𝑃−1, if a matrix 𝑃 can be found with the following properties:
Σ = 𝑃𝑃−1 (16)
𝑃−1𝛴𝑃′−1= 𝐼𝑘 (17)
Then, equation (15) can be rewritten as follows:
𝑌𝑡 = 𝜇 + ∑ 𝛷𝑖𝑃𝑃−1𝜀 𝑡−𝑖 ∞ 𝑖=0 = 𝜇 + ∑∞𝑖=0𝛩𝑖𝑃−1𝜀𝑡−𝑖 = 𝜇 + ∑∞𝑖=0𝛩𝑖𝑤𝑡−𝑖 (18) In this equation: - 𝛩𝑖 = 𝛷𝑖𝑃 - 𝑤𝑡−𝑖 = 𝑃−1𝜀 𝑡−𝑖
Now, the shocks are mutually orthogonal, which means that no information will be lost if all else is held constant. Hence, the 𝛩𝑖 are the orthogonalized IRFs that can be used for
causal interpretation.
Sims (1980) suggests that 𝑃 should be the Cholesky decomposition of Σ. The VAR model can be considered as a reduced form of a dynamic structural equation (DSE) model. Choosing 𝑃 as the Cholesky decomposition of Σ is the same as imposing a recursive structure on the corresponding DSE model. The ordering of this structure is the same as the one imposed in the Cholesky decomposition. As explained by Zivot (2005), consider the following recursive causal ordering:
𝑌1 𝑌2 𝑌3
19 A cointegrating VAR model (VECM) can also be written in a moving-average form as in equation (15), however the cointegrating VAR model is not stable. This makes the
derivation much more complicated and less intuitive, however the derivation above for a general VAR model can still be used to understand the workings of the IRFs. The main difference between a stationary VAR model and a cointegrating VAR model is that for the stationary model all eigenvalues of A have moduli strictly less than one, which means that the IRFs revert back to zero. In contrast, in the cointegrating model some eigenvalues of A are imposed to be 1, which has as a result that some IRFs will not revert back to zero as in the stationary case. This implies that in a cointegrating VAR model some shocks may be
transitory (revert back to zero over time), while other shocks can have a permanent effect (do not revert back to zero over time).
Then, FEVDs can be used to determine how important each shock is in explaining the variation in stock prices. The derivation below is again obtained using the Stata13 Manual (2013) and can also be extended to the cointegrating VAR model.
The FEVD can be used to measure the fraction of the error in forecasting stock prices after h periods that is attributable to the orthogonalized shocks in the macroeconomic variables. Lütkepohl (2005) shows that the h-step forecast error can be written as an adaptation of equation (15):
𝑌𝑡+ℎ − 𝑌̂𝑡(ℎ) = ∑ℎ−1𝑖=0 𝛷𝑖𝜀𝑡+ℎ−𝑖 (19)
In this equation:
- 𝑌𝑡+ℎ: Value observed at time t + h.
- 𝑌̂𝑡(ℎ): h-step-ahead predicted value of 𝑌𝑡+ℎ made at time t.
Again, like with the IRFs, the 𝜀𝑡 are contemporaneously correlated, which means that the distinct contributions of the shocks cannot be observed. Hence, using the same reasoning as earlier, the 𝜀𝑡 are orthogonalized, and the relative contribution of the distinct shocks can be
determined. Equation (19) can be written in a similar fashion as equation (18) to obtain the following:
𝑌𝑡+ℎ − 𝑌̂𝑡(ℎ) = ∑ℎ−1𝑖=0 𝛷𝑖𝑃𝑃−1𝜀𝑡+ℎ−𝑖
20 5. Results
5.1 Long-run relationship
5.1.1 Variable stationarity
First, the stationarity of the time series is examined using the ADF tests. The results of these tests are presented in Table 3.
Table 3. Augmented Dickey-Fuller Test Results
Variable France Germany Italy
Constant Constant & Trend
Constant Constant & Trend
Constant Constant & Trend ln(RSP) -2.232 -1.963 -1.075 -2.778 -2.205 -2.208 STR -1.619 -2.775 -1.619 -2.775 -1.619 -2.775 LTR -0.708 -2.881 -0.821 -3.063 -1.382 -2.219 ln(MON) -1.572 -1.379 -1.572 -1.379 -1.572 -1.379 ln(CPI) -2.335 -1.286 -1.329 -1.719 -3.243** -0.537 ln(IPI) -1.814 -2.425 -1.922 -3.022 -1.585 -2.885 ln(REER) -1.114 -1.989 -1.375 -2.228 -1.551 -2.018 ln(ROIL) -2.372 -2.361 -2.358 -2.330 -2.417 -2.407 Δln(RSP) -14.580*** -14.660*** -14.478*** -14.535*** -6.355*** -6.448*** ΔSTR -5.341*** -5.327*** -5.341*** -5.327*** -5.341*** -5.327*** ΔLTR -8.215*** -8.200*** -9.941*** -9.918*** -9.881*** -9.862*** Δln(MON) -15.092*** -15.152*** -15.092*** -15.152*** -15.092*** -15.152*** Δln(CPI) -9.521*** -9.825*** -9.002*** -9.081*** -3.957*** -4.945*** Δln(IPI) -13.005*** 12.977*** -5.358*** -5.362*** -5.037*** -5.025*** Δln(REER) -10.327*** -10.349*** -8.842*** -8.841*** -10.222*** -10.319*** Δln(ROIL) -8.981*** -8.976*** -8.969*** -8.967*** -8.986*** -8.979*** Netherlands Spain
Constant Constant & Trend
Constant Constant & Trend ln(RSP) -2.310 -1.946 -2.366 -2.405 STR -1.619 -2.775 -1.619 -2.775 LTR -0.731 -2.696 -0.591 -1.443 ln(MON) -1.572 -1.379 -1.572 -1.379 ln(CPI) -2.797* -3.446** -3.566*** -0.965 ln(IPI) -2.916** -3.219* -1.049 -1.321 ln(REER) -2.271 -2.418 -2.077 -1.737 ln(ROIL) -2.347 -2.320 -2.458 -2.446 Δln(RSP) -14.416*** -14.540*** -15.292*** -15.272*** ΔSTR -5.341*** -5.327*** -5.341*** -5.327*** ΔLTR -10.285*** -10.262*** -10.673*** -10.673*** Δln(MON) -15.092*** -15.152*** -15.092*** -15.152*** Δln(CPI) -3.129** -3.155* -8.710*** -9.544*** Δln(IPI) -9.803*** -9.803*** -7.308*** -7.298*** Δln(REER) -10.141*** -10.180*** -10.108*** -10.316*** Δln(ROIL) -8.922*** -8.917*** -9.000*** -8.991***
21 From the table can be seen that the ADF tests indicate that some variables are potentially already stationary. These variables are tested again using the Dickey-Fuller GLS (DF-GLS) test and the Phillips-Perron (PP) test, and their time series plots are examined. The results of this can be found in Table A3 and Figures A1-A4 in Appendix A. From this can be concluded that the variable ”ln(IPI)” for the Netherlands is I(0), while all other variables are I(1). Hence, ”ln(IPI)” is excluded from the model, since it is not possible to find a long-run relationship with I(0) variables.
5.1.2 Lag selection
Prior to performing the Johansen tests, the optimal lag length of the underlying VAR model has to be determined. Ivanov & Killian (2001) conclude that for monthly VAR models, the Akaike Information Criterion (AIC) produces the most accurate structural and semi-structural impulse response estimates for realistic sample sizes. Hence, the optimal lag length for the models under consideration in this paper is determined using the AIC. The AIC suggests to use lag lengths of 2 for all five countries.
5.1.3 Model specification
Testing for the model specification gives the results as presented in Table 4 below.
Table 4. Deterministic Components Test Results
France Germany
Model 1 Model 2 Model 3 Model 1 Model 2 Model 3
r=0 330.17* 204.20* 228.21* 337.12* 192.27* 225.67* r=1 170.37* 141.04* 164.13* 176.39* 134.67* 157.27* r=2 115.95* 88.63 107.58 199.92* 85.08 102.43 r=3 76.01 57.06 73.90 77.09* 56.03 73.26 r=4 45.08 31.68 48.33 48.05 36.83 46.70 r=5 25.42 19.49 26.25 29.66 21.67 27.67 Italy Netherlands
Model 1 Model 2 Model 3 Model 1 Model 2 Model 3
r=0 363.78* 262.53* 284.65* 368.46* 174.13* 208.46* r=1 168.06* 138.36* 159.69* 225.67* 109.75* 137.28* r=2 114.68* 89.30 106.62 137.80* 60.10 81.63 r=3 69.58 58.63 70.94 92.35* 33.39 50.89 r=4 48.88 38.05 48.69 51.48 19.20 28.32 r=5 31.44 22.96 30.79 25.20 8.67 14.94 Spain
Model 1 Model 2 Model 3
r=0 330.62* 240.48* 260.46* r=1 211.70* 160.26* 178.76* r=2 137.94* 98.41* 116.58* r=3 83.36* 62.72 80.46 r=4 54.78* 36.06 53.38 r=5 28.38 21.07 32.05
22 From these results can be concluded that for all countries Model 2 is appropriate, where the model contains an unrestricted constant, where cointegrating equations are stationary around a constant mean, and there is a linear trend in the undifferenced data.
5.1.4 Cointegrating vectors
The λtrace and λmax statistics used to test for the number of cointegrating vectors are
presented in Table 5 below.
Table 5. Number of Cointegrating Vectors Test Results
France Germany Italy
λtrace λmax λtrace λmax λtrace λmax
r=0 204.20* 63.17* 192.27* 57.61* 262.53* 124.17* r=1 141.04* 52.41* 134.67* 49.59* 138.36* 49.07* r=2 88.63 31.57 85.08 29.05 89.30 30.66 r=3 57.06 25.38 56.03 19.20 58.63 20.58 r=4 31.68 12.19 36.83 15.17 38.05 15.09 r=5 19.49 9.78 21.67 10.96 22.96 11.49 Netherlands Spain
λtrace λmax λtrace λmax
r=0 174.13* 64.38* 240.48* 80.22* r=1 109.75* 49.65* 160.26* 61.85* r=2 60.10 26.71 98.41* 35.69 r=3 33.39 14.19 62.72 26.66 r=4 19.20 10.53 36.06 14.99 r=5 8.67 6.13 21.07 13.26
Note: * = rejection of the null hypothesis at the 5% level.
Johansen and Julius (1990) emphasize that when there is a conflict between the two test statistics, the λtrace should be used. Furthermore, Kasa (1992) mentions that the λtrace
statistic takes into account all (n – r) of the smallest eigenvalues, so it tends to have more power. Hence, from these results can be concluded that there are 2 cointegrating vectors for France, Germany, Italy, and the Netherlands, while there are 3 cointegrating vectors for Spain.
5.1.5 Long-run relationship estimation
Johansen and Julius (1990) note that the first cointegrating vector corresponding to the largest eigenvalue is the most correlated with the stationary part of the model, and thus is most useful. After normalizing the coefficients of stock prices to one, the restricted long-term relationship between stock prices and the macroeconomic variables can be found. This relationship can be expressed as follows:
ln (𝑅𝑆𝑃) = 𝜇 + 𝛽1𝑆𝑇𝑅 + 𝛽2𝐿𝑇𝑅 + 𝛽3ln(𝑀𝑂𝑁) + 𝛽4ln(𝐶𝑃𝐼) + 𝛽5ln(𝐼𝑃𝐼) +
23 Table 6 shows the estimation of this relationship for all countries.
Table 6. Long-Run Relationship Estimation Results
Variable France Germany Italy Netherlands Spain
μ -291.566 -23.701 23.733 -1.638 7.310 STR 8.916*** 0.315*** 0.035 0.225*** 0.288*** (1.704) (0.078) (0.032) (0.029) (0.036) LTR -8.456*** -0.084 -0.018 -0.002 -0.019 (2.712) (0.125) (0.027) (0.058) (0.032) ln(MON) -73.338*** -1.553** 0.735*** -0.248 1.609*** (18.418) (0.649) (0.278) (0.255) (0.410) ln(CPI) 499.141*** 13.766*** -6.215*** 4.530*** -5.105*** (138.210) (4.102) (1.583) (1.566) (1.626) ln(IPI) -255.061*** 2.580* 3.808*** N/A -0.922 (38.166) (1.502) (0.581) (0.608) ln(REER) 306.167*** 0.644 -5.746*** -0.981 -4.261*** (61.462) (2.352) (0.828) (0.817) (1.141) ln(ROIL) -13.226*** -0.077 0.524*** -0.424*** 0.422*** (5.095) (0.166) (0.104) (0.094) (0.132)
Note: * = significant at 10% level; ** = significant at 5% level; *** = significant at 1% level; Numbers in parenthesis indicate Johansen corrected standard errors.
The results show significant evidence for a long-run relationship between macroeconomic variables and stock prices in all five countries. These results are combined with the results from Table 10 to draw conclusions on the long-run relationship. In general, the following conclusions can be drawn:
1. All macroeconomic variables, except for the long-term interest rate and oil price, are found to Granger cause stock prices in the long-run.
2. Short-term interest rates are positively related to stock prices in the long-run.
3. Long-term interest rates and exchange rates are negatively related to stock prices in the long-run.
4. The effect of the money supply, inflation rate, industrial production and oil price on stock prices in the long-run is mixed across the five countries.
5.1.6 Short-run relationship estimation
The short-run relationship can expressed as follows:
Δln(𝑅𝑆𝑃)𝑡 = 𝛾 + Г1Δln(𝑅𝑆𝑃)𝑡−1+ Г2Δ𝑆𝑇𝑅𝑡−1+ Г3Δ𝐿𝑇𝑅𝑡−1+ Г4Δln (𝑀𝑂𝑁)𝑡−1+
24 Table 7 shows the estimation of this relationship for all countries.
Table 7. Short-Run Relationship Estimation Results
Variable France Germany Italy Netherlands Spain
γ -0.000 0.008 -0.003 0.007 0.001 (0.005) (0.005) (0.006) (0.005) (0.005) Δln(RSP)t-1 0.027 0.003 -0.033 0.031 -0.060 (0.069) (0.072) (0.074) (0.070) (0.072) ΔSTRt-1 0.019 -0.014 0.004 -0.019 -0.029 (0.030) (0.031) (0.030) (0.031) (0.027) ΔLTRt-1 0.005 -0.006 0.019 -0.016 0.002 (0.022) (0.028) (0.018) (0.025) (0.019) Δln(MON)t-1 0.092 0.035 0.300* -0.073 0.238 (0.157) (0.177) (0.182) (0.163) (0.171) Δln(CPI)t-1 -1.314 -1.068 -1.316 -5.429*** 0.672 (2.362) (2.146) (3.308) (2.111) (1.602) Δln(IPI)t-1 0.229 -0.269 0.453* N/A 0.278 (0.250) (0.292) (0.272) (0.391) Δln(REER)t-1 -0.480 -0.241 -1.141* 0.142 -0.930 (0.588) (0.571) (0.642) (0.609) (0.756) Δln(ROIL)t-1 0.024 0.025 -0.002 0.046 0.013 (0.046) (0.053) (0.050) (0.049) (0.050) αt-1 -0.001 0.033** 0.027 0.025 0.034* (0.000) (0.013) (0.018) (0.020) (0.020)
Note: * = significant at 10% level; ** = significant at 5% level; *** = significant at 1% level; Numbers in parenthesis indicate standard errors.
Since the VECM for the Netherlands does not contain the ”ln(IPI)” variable, the short-run relationship does not take into account this variable. As a robustness check, the short-short-run relationship is also estimated using a VAR with all variables expressed in first differences, except for ”ln(IPI)”, which is expressed in levels. The results however do not change significantly, and also the ”ln(IPI)” variable is found to be not statistically significant.
25 5.1.6 Post-estimation tests
Standard post-estimation tests used to test for misspecification of the VEC model include testing for serial correlation in the residuals, normality of the residuals, and model stability. The Lagrange Multiplier, or LM(k) test is used to test the null hypothesis of no serial correlation in the residuals up to lag k. Further, the Jarque-Bera (JB) test is used to test the assumption of normally distributed residuals. Also, model stability is tested by ensuring the eigenvalues do not exceed unity. The results of these tests are presented in Table 8 below.
Table 8. Post-Estimation Test Results
Country LM(12) Jarque-Bera Stability
Chi-square P-value Chi-square P-value
France 63.489 0.495 2924.639 0.0000 Stable
Germany 88.687 0.022 4261.305 0.0000 Stable
Italy 75.522 0.154 5249.763 0.0000 Stable
Netherlands 60.376 0.128 2246.838 0.0000 Stable
Spain 76.753 0.132 2881.422 0.0000 Stable
As can be seen from the results, there is no significant sign of autocorrelation in the residuals. For Germany, there is some evidence for autocorrelation at lag 12, which could point to seasonality issues in the data since this study uses monthly data. However, when inspecting lags 24 and 36, no evidence for seasonality issues is found. The JB test for normally distributed residuals indicates that the residuals are not normally distributed. However, this result is often found for sample sizes which are relatively small. In order to assess the distribution of the residuals, a QQ-plot and histogram are inspected to see if it is reasonable to assume that the residuals are normally distributed. The results of this can be found in Figures C1-C5 in Appendix C. For all five countries the residuals are approximately normally distributed, but with slightly heavier tails. Hence, the obtained results have to be interpreted with some caution. Finally, model stability is assessed. The results can be found in Figure C6-C10 in Appendix C, and for all countries can be concluded that all the eigenvalues lie on or within the unit root circle. Hence, all models are found to be stable.
26 5.2 Granger causality
5.2.1 Long-run Granger causality
The results of the t-tests to detect long-run Granger causality for each country can be found in Table 9 below. The results are then qualitatively summarized in Table 10. Significant t-statistics for the lagged error correction term indicate that past values of the variable are useful in predicting stock prices in the long-run.
Table 9. Results t-test Lagged Error Correction Term
Variable France Germany Italy Netherlands Spain
ΔSTR 4.51*** 4.79*** 0.31 7.31*** 3.13*** ΔLTR 0.01 0.38 -0.28 0.28 1.10 Δln(MON) 1.76* -0.49 -2.17** -2.16** 1.62 Δln(CPI) 4.70*** -1.19 -9.60*** 2.01** -2.80*** Δln(IPI) -1.47 5.99*** 3.85*** N/A 6.97*** Δln(REER) 2.29** -1.99** -3.83*** -1.85* -0.76 Δln(ROIL) 0.34 2.09** 1.06 -0.37 2.09**
Note: * = significant at 10% level; ** = significant at 5% level; *** = significant at 1% level; Numbers represent t-statistics.
Table 10. Long-Run Granger Causality Test Results Country STR RSP LTR RSP MON RSP CPI RSP IPI RSP REER RSP ROIL RSP
France Yes No Yes Yes No Yes No
Germany Yes No No No Yes Yes Yes
Italy No No Yes Yes Yes Yes No
Netherlands Yes No Yes Yes N/A Yes No
Spain Yes No No Yes Yes No Yes
5.2.2 Short-run Granger causality
The results of the F-tests to detect short-run Granger causality for each country can be found in Table 11 below. Here, ”Δln(RSP)” is used as the dependent variable to analyse which macroeconomic variables Granger cause stock prices in the short-run. The results are then qualitatively summarized in Table 12. Significant F-statistics for the lagged variables indicate that past values of the variable are useful in predicting stock prices in the short-run.
Table 11. Results F-test Lagged Variables
Variable France Germany Italy Netherlands Spain
ΔSTR 0.43 0.22 0.02 0.36 1.18 ΔLTR 0.04 0.05 1.20 0.43 0.01 Δln(MON) 0.34 0.04 2.72* 0.20 1.94 Δln(CPI) 0.31 0.25 0.16 6.61** 0.18 Δln(IPI) 0.84 0.84 2.78* N/A 0.51 Δln(REER) 0.67 0.18 3.16* 0.05 1.52 Δln(ROIL) 0.26 0.23 0.00 0.88 0.07
27 Table 12. Short-Run Granger Causality Test Results
Country STR RSP LTR RSP MON RSP CPI RSP IPI RSP REER RSP ROIL RSP France No No No No No No No Germany No No No No No No No
Italy No No Yes No Yes Yes No
Netherlands No No No Yes N/A No No
Spain No No No No No No No
5.2.3 Variable Ordering
The results of the short-run Granger causality tests for all variables from the five countries can be found in Tables D1-D5 in Appendix D. Using these results and economic theory, the ordering of the variables used for the innovation accounting analysis can be found in Table 13 below. Looking at the table and the explanation in section 4.4, the interpretation is as follows: Variables to the left of the arrow are assumed to affect all variables to the right of the arrow, but not vice versa. Also, since stock prices are the primary variable to be studied in this paper, this variable is placed first.
Table 13. Variable Ordering
France RSP MON ROIL STR CPI LTR REER IPI
Germany RSP MON ROIL CPI STR LTR REER IPI
Italy RSP ROIL STR CPI MON LTR REER IPI
Netherlands RSP MON ROIL CPI STR LTR REER
Spain RSP MON ROIL STR LTR CPI REER IPI
It has to be noted that different orderings of the variables did not significantly affect the outcome of the innovation accounting analysis.
5.3 Innovation accounting analysis 5.3.1 Impulse response functions
28 Table 14. IRF Analysis Results
Country Steps ln(RSP) STR LTR ln(MON) ln(CPI) ln(IPI) ln(REER) ln(ROIL)
France 6 0.0525 0.0055 -0.0024 -0.0024 -0.0003 -0.0036 0.0013 -0.0003 12 0.0503 0.0053 -0.0038 -0.0030 0.0006 -0.0065 0.0032 -0.0025 24 0.0484 0.0049 -0.0049 -0.0035 0.0014 -0.0089 0.0049 -0.0046 36 0.0477 0.0048 -0.0053 -0.0037 0.0016 -0.0097 0.0054 -0.0052 48 0.0475 0.0047 -0.0054 -0.0037 0.0017 -0.0099 0.0056 -0.0054 Germany 6 0.0667 -0.0173 0.0020 0.0058 -0.0078 -0.0062 -0.0007 -0.0053 12 0.0682 -0.0258 0.0031 0.0082 -0.0103 -0.0075 -0.0005 -0.0089 24 0.0688 -0.0289 0.0035 0.0089 -0.0110 -0.0079 -0.0003 -0.0103 36 0.0687 -0.0288 0.0035 0.0088 -0.0110 -0.0079 -0.0003 -0.0103 48 0.0687 -0.0288 0.0035 0.0088 -0.0110 -0.0079 -0.0003 -0.0103 Italy 6 0.0656 -0.0004 0.0054 0.0011 0.0002 -0.0022 -0.0005 -0.0076 12 0.0673 -0.0083 0.0062 0.0028 -0.0002 -0.0073 0.0037 -0.0186 24 0.0682 -0.0175 0.0067 0.0044 -0.0008 -0.0125 0.0080 -0.0302 36 0.0684 -0.0209 0.0069 0.0050 -0.0010 -0.0142 0.0095 -0.0343 48 0.0685 -0.0220 0.0069 0.0052 -0.0010 -0.0148 0.0100 -0.0357 Netherlands 6 0.0627 -0.0041 -0.0024 0.0022 -0.0120 N/A 0.0005 0.0004 12 0.0649 -0.0052 -0.0024 0.0030 -0.0126 N/A 0.0006 0.0011 24 0.0665 -0.0060 -0.0024 0.0037 -0.0130 N/A 0.0007 0.0017 36 0.0669 -0.0062 -0.0024 0.0038 -0.0131 N/A 0.0007 0.0018 48 0.0670 -0.0062 -0.0024 0.0038 -0.0132 N/A 0.0008 0.0018 Spain 6 0.0600 -0.0162 0.0009 -0.0005 0.0021 0.0019 -0.0002 -0.0075 12 0.0607 -0.0235 0.0007 -0.0009 0.0018 0.0011 0.0011 -0.0129 24 0.0603 -0.0251 0.0005 -0.0008 0.0014 0.0008 0.0013 -0.0141 36 0.0602 -0.0248 0.0005 -0.0008 0.0013 0.0008 0.0012 -0.0139 48 0.0603 -0.0248 0.0005 -0.0008 0.0014 0.0008 0.0012 -0.0139 These results can be used to draw some general conclusions regarding the effect of the
variables on stock prices in the short-run and the long-run. Then, the results can be compared to the findings earlier in this paper. First, looking at the short-run (0-6 months) results, and assuming shocks are positive, the following general conclusions can be drawn:
1. Shocks in stock prices are positively related to stock prices in the short-run.
2. Shocks to the short-term interest rate are negatively related to stock prices in the short-run (H1a is rejected).
3. The significance of the effect of shocks to the inflation rate and oil price on stock prices in the short-run is mixed, but in general these are negatively related to stock prices (H3 & H6 are confirmed).
29 Then, looking at the long-run (6-48 months) results, and assuming shocks are positive, the following general conclusions can be drawn:
1. Shocks in stock prices are positively related to stock prices in the long-run.
2. Shocks to the short-term interest rate and oil price are negatively related to stock prices in the long-run (H1a is rejected & H6 is confirmed).
3. The significance of the effect of shocks to the money supply on stock prices in the long-run is mixed, but in general shocks to the money supply have a small positive effect on stock prices (H2 is confirmed).
4. The significance of the effect of shocks to the inflation rate on stock prices in the long-run is mixed, but in general the inflation rate is negatively related to stock prices (H3 is confirmed).
5. The significance of the effect of shocks to industrial production on stock prices in the long-run is mixed, but in general shocks to industrial production have a small negative effect on stock prices (H4 is rejected).
6. The significance of the effect of shocks to the exchange rate on stock prices in the long-run is mixed, but in general shocks to the exchange rate have a small positive effect on stock prices (H5 is rejected).
7. Shocks to the term interest rate have no significant effect on stock prices in the long-run (H1b is rejected).
When comparing the short-run results to the short-run relationship estimation, it can be seen that indeed few macroeconomic variables significantly affect stock prices in the short-run. When looking at the long-run results, they are slightly different compared to the results from the long-run relationship estimation. Indeed, most macroeconomic variables have some form of impact on stock prices in the long-run, and it is confirmed that the long-term interest rate does not have any significant impact. However, the oil price is found to significantly impact stock prices. Also, short-term interest rates have a negative effect on stock prices, not a positive effect as found earlier. Further, the mixed effects of the money supply, inflation rate, and exchange rate are confirmed.
The negative effect of the short-term interest rate indicates that it is not regarded as a proxy for macroeconomic activity as suggested by Nasseh & Strauss (2000), but affects the stock prices negatively through its effects on the discount rate, cost of capital, and expected future cash flows, as explained by Jammazi et al. (2017).
30 The negative impact of the inflation rate on stock prices is supported by findings from Fama (1975) and Friedman (1977) who explain this negative relationship with stock prices by emphasizing the result an increase in the inflation rate has on uncertainty about the future inflation rate and interest rates.
The mixed effects of the money supply on stock prices can be explained using two different views. On the one hand, Friedman (1969) and Humpe & Macmillan (2009) emphasize the positive relationship between the money supply and stock prices through the effect that an increase in the money supply has on interest rates and the demand for equities. On the other hand, Fisher’s (1930) results can be used to hypothesize a negative relationship through the effect than an increase in the money supply has on inflation expectations. The response of stock prices through an increase in the money supply thus depends on which effect dominates.
The mixed effects of industrial production on stock prices is not expected, since theory suggests a positive relationship between industrial production and stock prices. Campbell & Anner (1993) explain this relationship through the effect of industrial production on expected future cash flows. However, evidence has also been found which suggests that the effect of industrial production is ambiguous. For example, Young (2006) and Bhuiyan & Chowdhury (2020) find that the positive relationship is no longer present in the US. Bhuiyan & Chowdhury (2020) explain that this might be the case because the economy has switched from being manufacturing-based to being service-based.
The mixed effects of the exchange rate on stock prices can be explained by looking at the relative importance of imports and exports. Theory suggests a negative relationship between the exchange rate and stock prices. When the exchange rate depreciates, exported goods become cheaper, and demand for local goods increases. However, a positive relationship can be explained if a country’s economy depends more heavily on imports rather than exports, since the reverse holds in this case.
5.3.2 Forecast error variance decomposition
31 Table 15. FEVD Analysis Results
Country Steps ln(RSP) STR LTR ln(MON) ln(CPI) ln(IPI) ln(REER) ln(ROIL)
France 6 99.05 0.62 0.06 0.08 0.04 0.10 0.02 0.02 12 98.10 0.85 0.20 0.17 0.02 0.50 0.11 0.05 24 96.22 0.92 0.47 0.29 0.03 1.41 0.38 0.28 36 94.85 0.93 0.65 0.36 0.05 2.07 0.60 0.50 48 93.94 0.92 0.77 0.41 0.07 2.50 0.75 0.65 Germany 6 96.51 2.05 0.02 0.24 0.58 0.45 0.02 0.13 12 90.96 5.89 0.08 0.63 1.13 0.70 0.01 0.60 24 85.19 9.99 0.14 0.99 1.61 0.88 0.01 1.19 36 83.17 11.43 0.16 1.11 1.76 0.94 0.00 1.41 48 82.23 12.11 0.17 1.16 1.84 0.97 0.00 1.52 Italy 6 98.84 0.07 0.46 0.04 0.00 0.11 0.26 0.21 12 96.58 0.26 0.60 0.06 0.00 0.32 0.16 2.02 24 88.29 1.96 0.68 0.17 0.00 1.20 0.46 7.25 36 82.13 3.49 0.70 0.24 0.01 1.83 0.76 10.85 48 78.39 4.47 0.70 0.28 0.01 2.21 0.95 12.99 Netherlands 6 96.81 0.26 0.12 0.05 2.75 N/A 0.01 0.00 12 96.18 0.39 0.13 0.11 3.18 N/A 0.01 0.01 24 95.67 0.56 0.12 0.19 3.42 N/A 0.01 0.03 36 95.45 0.65 0.12 0.23 3.50 N/A 0.01 0.04 48 95.33 0.69 0.12 0.25 3.55 N/A 0.01 0.05 Spain 6 96.96 2.37 0.02 0.04 0.08 0.14 0.10 0.29 12 91.79 6.38 0.02 0.02 0.09 0.09 0.05 1.55 24 86.40 10.35 0.01 0.02 0.07 0.05 0.04 3.05 36 84.71 11.60 0.01 0.02 0.06 0.04 0.04 3.52 48 83.94 12.17 0.01 0.02 0.05 0.03 0.04 3.74
Note: Numbers represent percentages.
32 In the long-run, still a large part of the variance in stock prices can be attributed to stock prices themselves. For example, in Italy, after 48 months still about 78% of stock price variance can be attributed to innovations in stock prices itself. Also, a significant impact on stock prices comes from short-term interest rates in Germany and Spain, and oil prices in Italy. Innovations in these variables explain about 12% of FEV in stock prices. Further, some smaller long-run impacts can be found to come from the short-term interest rate in Italy, the inflation rate in Germany and the Netherlands, industrial production in France and Italy, and oil prices in Spain. Here, innovations in these variables explain about 2-4% of FEV in stock prices.
5.4 Country comparison
The results obtained from the different countries can be compared to learn more about the drivers behind the effects of the macroeconomic variables on the stock prices. Below, the results from each macroeconomic variable, except for the long-term interest rate (since there is no significant effect), will be compared across countries using the results from the innovation accounting analysis and Granger causality tests, and economic theory.
5.4.1 Short-term interest rate
Looking at Table 14, it can be noted that the negative effect of short-term interest rates on stock prices is negative in Germany, Italy, the Netherlands, and Spain. Then, looking at Tables D1-D5, the main driver behind short-term interest rates in these countries are the inflation rate and oil prices. However, in France, where the effect of the short-term interest rate on stock prices is positive, the short-term interest rate is also driven by stock prices, hence there is bi-directional causality. Studies such as Rigobon & Sack (2003) have shown that stock market movements have a significant impact on short-term interest rates, driving them in the same direction as changes in stock prices. Hence, the bi-directional causality between the short-term interest rate and stock prices might be the cause of the positive relationship between the two in France.
5.4.2 Money supply
33 5.4.3 Inflation rate
Looking at Table 14, the inflation rate has a negative impact on stock prices in Germany and the Netherlands, while the effect in France, Italy, and Spain is negligible. When looking at Tables D1-D5, it can be noted that in the countries where the effect of the inflation rate on stock prices is negligible, one of the drivers of the inflation rate is in fact the stock price, while this is not the case for Germany and the Netherlands. Hence, it can be hypothesized that when stock prices are drivers of the inflation rate, the effect of the inflation rate on stock prices will be negligible.
5.4.4 Industrial production
Looking at Table 15, it can be noted that industrial production is not a highly relevant factor in explaining variation in stock prices. The effect of industrial production on stock prices is negative in France, Germany, and Italy, and negligible in Spain, as can be seen from Table 14. Although this negative effect is not expected, its significance is relatively small and as mentioned before this is mainly due to the fact that all economies studied in this paper are service-based economies and not manufacturing-based economies. Hence, industrial production plays a relatively small role in determining stock prices in these economies.
5.4.5 Exchange rate
Looking at Table 14, the exchange rate is positively related to stock prices in France and Italy, while its effect on stock prices in Germany, the Netherlands, and Spain are negligible. Looking at Table 15, the exchange rate does not seem to be a very important driver of stock prices. When looking at data from the CIA World Factbook (2020), in recent years France was a net importer of goods and services, which may explain the positive relationship between the exchange rate and stock prices. However, the effect remains relatively small.
5.4.6 Oil price
34 6. Conclusion
This paper has investigated the short-run and long-run impact of the short-term interest rate, long-term interest rate, money supply, inflation rate, industrial production, exchange rate, and oil price on stock prices in the five largest EU countries for the period 1999:12 – 2019:12. In the short-run, the short-term interest rate is found to be negatively related to stock prices, while the other macroeconomic variables generally have no significant effect.
In the long-run, the short-term interest rate, inflation rate, and oil price are found to be negatively related to stock prices. Further, the effect of the money supply, industrial production, and exchange rate on stock prices is mixed, while the long-term interest rate again has no significant effect.
These findings can be used to make predictions about the future direction of stock prices. It is evident that for policymakers the most important tool to influence the economy is the short-term interest rate, which can help boost stock prices in the short-run and the long-run. Also, policies can be used to aim at a low and stable inflation rate. Further, keeping a close look at the oil price might be beneficial to make predictions about where the economy is heading in the long-run.
35 Appendix A: Data and Stationarity Tests
Table A1. Data Sources
Variable Data Source
Stock prices Thomson Reuters Eikon & Yahoo! Finance Short-term interest rate Federal Reserve Economic Data (FRED) Long-term interest rate Federal Reserve Economic Data (FRED)
Money supply European Central Bank (ECB) Statistical Data Warehouse Inflation International Monetary Fund (IMF) Data
Industrial production International Monetary Fund (IMF) Data Exchange rate International Monetary Fund (IMF) Data Oil price Federal Reserve Economic Data (FRED) Table A2. Dickey-Fuller GLS Test Results
Lags ln(CPI) – Italy ln(CPI) – Netherlands
Trend No trend Trend No trend
1 0.738 3.922 -0.680 6.030 2 0.157 2.355 -0.783 4.529 3 -0.022 1.918 -0.858 3.703 4 -0.175 1.569 -0.844 3.380 5 -0.266 1.378 -0.956 2.894 6 -0.374 1.182 -1.012 2.646 7 -0.517 0.980 -1.218 2.315 8 -0.506 0.950 -1.432 2.065 9 -0.484 0.934 -1.580 1.957 10 -0.418 0.958 -1.675 1.904 11 -0.555 0.803 -1.692 1.881 12 -0.361 0.957 -1.753 1.847 13 -0.358 0.909 -1.621 1.880 14 -0.409 0.793 -1.571 1.881
ln(IPI) – Netherlands ln(CPI) – Spain
Trend No trend Trend No trend
1 -3.411** -1.496 0.052 2.946 2 -2.700* -1.121 0.093 2.780 3 -2.400 -0.950 0.097 2.560 4 -2.330 -0.902 -0.060 2.087 5 -2.251 -0.851 -0.243 1.655 6 -1.989 -0.709 -0.277 1.530 7 -1.859 -0.632 -0.297 1.422 8 -1.748 -0.565 -0.328 1.323 9 -1.785 -0.581 -0.392 1.191 10 -2.098 -0.748 -0.482 1.055 11 -1.918 -0.638 -0.407 1.100 12 -1.932 -0.637 -0.373 1.098 13 -1.772 -0.540 -0.396 1.019 14 -1.651 -0.465 -0.387 0.986
36 Table A3. Phillips-Perron Test Results
ln(CPI) – Italy ln(CPI) – Netherlands Constant Constant & Trend Constant Constant & Trend
Z(t) -4.589*** -0.126 -2.304 -2.787
ln(IPI) – Netherlands ln(CPI) – Spain
Constant Constant & Trend Constant Constant & Trend
Z(t) -4.310*** -5.206*** -4.170*** -0.975
Note: *** = significant at 1% level; Similarly to the ADF test, two separate tests are conducted in order to take into account that some time series may include a trend over time.
Figure A1. Time-Series Plot ”ln(CPI) – Italy”
37 Figure A3. Time-Series Plot ”ln(IPI) – Netherlands”
