Do Stock Prices Impact Consumption and Interest Rate in South Africa? Evidence from a Time-varying Vector Autoregressive Model

Abstract

This article investigates the existence of spillovers from stock prices onto consumption and the interest rate for South Africa using a time-varying parameter vector autoregressive (TVP-VAR) model with stochastic volatility. In this regard, we estimate a three-variable TVP-VAR model comprising real consumption growth rate, the nominal three-months Treasury bill rate and the growth rate of real stock prices. We find that the impact of a real stock price shocks on consumption is in general positive, with large and significant effects observed at the one-quarter-ahead horizon. However, there is also evidence of significant negative spillovers from the stock market to consumption during the financial crisis, at both short and long horizons. The monetary policy response to stock price shocks has been persistent, and strong especially post the financial liberalisation in 1985, but became weaker during the financial crisis. Overall, we provide evidence of significant time-varying spillovers on consumption and interest rate from the stock market.

JEL Classification: C11, C15, C32, E31, E32, E44, E52

Keywords

Bayesian inference consumption stock price Markov chain Monte Carlo monetary policy structural vector autoregression stochastic volatility time-varying parameter

Introduction

The permanent income hypothesis postulated by Friedman (1957) asserts that real stock (asset) price inflation increases the expected lifetime wealth of households and hence their desired consumption. This is known as the wealth effect. In light of this, there exists wide international evidence suggesting that there are major spillovers from the stock market to consumption, in both advanced and emerging economies (see, for example, Afonso & Sousa 2011a; Apergis & Miller 2004, 2005a, 2005b, 2006; Bostic, Stuart & Painter 2009; Carroll, Otsuka & Slacalek 2011; Fratzscher & Straub 2009, 2010; Fratzscher, Juvenal & Sarno 2010; Koivu 2012; Lettau & Ludvigson 2001, 2004; Ludvigson, Steindal & Lettau 2002; Peltonen, Sousa & Vansteenkiste 2012; Rapach & Strauss 2006, 2007; Singh 2012; Singh & Pattanaik 2010; Sousa 2008a, 2008b, 2010a, 2010b, 2010c, 2010d; Zhou 2010 and references cited in these studies). As far as South Africa is concerned, to the best of our knowledge, there exists only one study by Das, Gupta and Kanda (2011), who, based on a single-equation error-correction model, indicate that real stock prices affect consumption significantly both in the short and long runs.¹ The literature relating to stock prices in South Africa has mainly dealt with the effect of monetary policy on stock prices, largely based on (structural) vector autoregressive (SVAR) and at times panel data approaches with South Africa as a country in the panel, with all the studies indicating a negative impact on stock prices (returns) following a contractionary monetary policy.² The lack of studies analysing the impact of stock prices on consumption is quite baffling in South Africa, especially when one accounts for the fact that financial wealth accounts for 49.95 per cent of household’s total assets and 61.59 per cent of household’s net worth (South African Reserve Bank, Quarterly Bulletin, 2012).

Besides the fact that stock market spillover could be inflationary if it significantly affects aggregate demand through consumption, the recent financial crisis has once again rekindled the debate on whether central banks should conduct monetary policy in a more active manner to prevent the development of bubbles that can be costly in terms of future output and financial stability (André, Gupta & Kanda 2011; Peretti, Gupta & Inglesi-Lotz, forthcoming). Further, given the fact that the South African Reserve Bank (SARB) has moved to an official inflation-targeting framework since the first quarter of 2000,³ there is clearly an added value in analysing this question for the country specifically. Recently, Naraidoo and Ndahiriwe (forthcoming) and Naraidoo and Raputsoane (2010) have developed financial conditions indices (FCI), which include stock prices amongst other financial variables, and have analysed the importance of the FCI using linear and non-linear Taylor (1993)-type rules in South Africa. These studies tend to show that the SARB has systematically reacted to the FCI, more so during the recent financial crisis. Darracq Pariès and Notarpietro (2008) and Finocchiaro and von Heideken (2009) suggest that trying to address the endogeneity problem in stand-alone monetary policy reaction functions using generalised method of moments (GMM) produces biased and dispersed estimates. Thus, there are concerns using single-equation Taylor (1993)-type models. Furthermore, the studies using an FCI, which is a composite of four or five asset-related variables, do not specifically indicate the role of stock prices in the monetary policy reaction functions. To the best of our knowledge, there are only two papers that specifically looks at the behaviour of the interest rate in response to stock price movements in South Africa: Bonga-Bonga (2011) and Muroyiwa (2011).⁴ Bonga-Bonga (2011) assessed the dynamic responses of stock prices on inflation, economic activity and monetary policy using a structural vector error-correction model, and concluded that there is a positive relationship between equity prices and interest rates in South Africa. Similar conclusions were also reached by Muroyiwa (2011) based on an SVAR where shocks were identified using a combination of both short-run and long-run restrictions.

Against this background, the objective of this article is to analyse not only whether real stock price movements have significant spillover effects on consumption decisions in South Africa, but also whether stock price shocks result in a simultaneous response in the monetary policy instrument, or whether the response is a delayed one following inflationary pressures due to an increase in aggregate demand resulting, in particular, from the wealth effect of a positive shock in real stock prices. In addition, unlike the sparse literature in South Africa on these two issues, which essentially relies on constant parameter models, we use a time-varying parameter vector autoregressive (TVP-VAR) model with stochastic volatility. TVP-VARs are quite common in the analysis of macroeconomic issues and allow us to capture the time-varying nature of the underlying structure in the economy in a flexible and robust manner (Nakajima 2011). Therefore, this article makes the first attempt in the context of South Africa, to analyse the time-varying spillover effect of stock price shocks on consumption and interest-setting behaviour, with the time-varying framework allowing us not only to identify the general relationship between the variables of interest, but, more importantly, enables us to view how these relationships change depending on the underlying macroeconomic structure of the economy.

To the best of our knowledge, this is the first attempt, in the literature, to analyse the spillover effect of real stock prices on consumption and interest rate using a TVP-VAR model. The decision to use South Africa as our country of investigation simply emanates from our familiarity with major structural changes and shifts in monetary policy regimes in the economy over the period of the analysis, and their possible effects on the variables under consideration in the TVP-VAR model. The only other paper that is somewhat related to our study is the work by Baumeister, Durinck and Peersman (2008). However, the authors in this article is more interested in analysing how the dynamic effects of excess liquidity shocks on economic activity, asset prices and inflation differ over time. They show that the impact varies considerably over time and depends on the source of increased liquidity and the underlying state of the economy. The remainder of the article is organised as follows. The second section discusses the methodology of the TVP-VAR technique. The third section lays out the data used. The fourth section presents the results of a stock price shock on consumption and the monetary policy interest-setting behaviour. Finally, the fifth section concludes the research work.

Methodology

A vector autoregression (VAR), proposed by Sims (1980), has become a popular technique used in econometric analysis and is adaptable to a vast array of economic settings (Baltagi 2011). In this study, a TVP-VAR model with stochastic volatility is used. The TVP-VAR is common in the analysis of macroeconomic issues and allows us to capture the time-varying nature of the underlying structure in the economy in a flexible and robust manner (Nakajima 2011). The parameters in the VAR specification are assumed to follow a first-order random walk process, thereby incorporating both temporary and permanent changes to the parameters. The inclusion of stochastic volatility is an important aspect in this TVP-VAR model. In many situations, a data-generating process of economic variables seems to have drifting coefficients and shocks of stochastic volatility. In that case, the application of a TVP model but with constant volatility may result in biased estimations of the time-varying coefficients, since a possible variation of the volatility in disturbances is ignored. The TVP-VAR model with stochastic volatility avoids this misspecification. Although stochastic volatility makes the estimation difficult due to the intractability of the likelihood function, the model can be estimated using Markov chain Monte Carlo (MCMC) methods in the context of a Bayesian inference.

Following Nakajima (2011), this article estimates a TVP-VAR model with stochastic volatility of the form:

y_{t} = c_{t} + B_{1 t} y_{t - 1} + ... + B_{s t} y_{t - s} + e_{t}, e_{t} ~ N (0, Ω_{t}),

(1)

for t = s + 1, . . . , n, where y_t is a (k × 1) vector of observed variables, B_1t, …., B_st are (k × k) matrices of time-varying coefficients and Ω_t is a (k × k) time-varying covariance matrix. A recursive identification scheme is assumed by the decomposition of $Ω_{t} = A_{t}^{- 1} Σ_{t} Σ_{t} A_{t}^{' - 1},$ where A_t is a lower triangle matrix with diagonal elements equal to one, and Σ_t = diag(σ_1t, . . ., σ_kt). Let us define β_t as the stacked row vector of B_1t, …., B_st; a_t is the stacked row vector of the free lower triangular elements of A_t; and h_t = (h_1t, …., h_kt), where $h_{j t} = \log σ_{j t}^{2} .$ The TVPs are assumed to follow a random walk process:

\begin{matrix} β_{t +1} = β_{t} + υ_{β t}, \\ a_{t +1} = a_{t} + υ_{a t}, \\ h_{t +1} = h_{t} + υ_{h t}, \end{matrix} (\begin{matrix} ε_{t} \\ υ_{β t} \\ υ_{a t} \\ υ_{h t} \end{matrix}) \sim N ((\begin{matrix} I & 0 & 0 & 0 \\ 0 & Σ_{β} & 0 & 0 \\ 0 & 0 & Σ_{a} & 0 \\ 0 & 0 & 0 & Σ_{h} \end{matrix})),

for t = s + 1, . . . , n, with $e_{t} = A_{t}^{- 1} Σ_{t} ε_{t},$ where Σ_a and Σ_h are diagonals, β_s+1 ~ N (μ_βo, Σ_βo), a_s+1 ~ N(μ_ao, Σ_ao), and h_s+₁ ~ N (μ_ho, Σ_ho).⁵

A Bayesian inference is used to estimate the TVP-VAR models via MCMC methods. The goal of MCMC methods is to assess the joint posterior distributions of the parameters of interest under certain prior probability densities that are set in advance. We assume the following priors, as in Nakajima (2011): Σ_β ~ IW (25, 0.01I), ${(Σ_{α})}_{i}^{- 2} ~ G (4, 0.02)$ ${(Σ_{h})}_{i}^{- 2} ~ G (4, 0.02)$ where ${(Σ_{α})}_{i}^{- 2}$ and ${(Σ_{h})}_{i}^{- 2}$ are the i-th diagonal elements in Σ_α and Σ_h, respectively. IW and G denotes the inverse Wishart and the gamma distributions, respectively. For the initial set of the TVP, flat priors are set such that: μ_β₀ = μ_a₀ = μ_h₀ = 0 and Σ_β0 = Σ_a0 = Σ_h0 = 10 × I.

Data

The data sample covers the quarterly period of 1960:1 until 2011:4. A three-variable TVP-VAR model is estimated, capturing the time-varying nature of the macroeconomic dynamics in the South African economy between real consumption, nominal interest rate and real stock prices. Seasonally adjusted real personal consumption expenditure data is obtained from the official website (www.resbank.co.za) of the SARB, while the three-month Treasury bill rate, the all-share stock index and consumer price index (CPI) data, used to convert nominal stock prices into its real counterpart, is derived from the International Financial Statistics of the International Monetary Fund. Based on all the standard unit root tests, namely, augmented Dickey–Fuller (ADF) (1981); Phillips–Perron (PP) (1988); Dickey–Fuller test with generalised least squares (DF-GLS) detrending; the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) (1992) test; the Elliot, Rothenberg and Stock (ERS) (1996) point optimal test; the Ng–Perron (2001) modified versions of the PP (NP-MZ_t) test; and the ERS point optimal (NP-MP_T) test, the real consumption expenditure and real stock prices were found to be non-stationary, so the variables were converted to their corresponding growth rates, and denoted as DC and DRSP. The nominal interest rate was found to be stationary at the 10 per cent level of significance using ADF, DF-GLS, ERS, NP-MZ_t and NP-MP_T tests, and hence was used in levels, and denoted as TBILL.⁶ The stable⁷ TVP-VAR is estimated based on two lags, as was unanimously suggested by all the popular lag-length tests, namely, the sequential modified likelihood ratio (LR) test statistic, the Akaike information criterion, the Schwarz information criterion, applied to a constant parameter VAR. Accounting for stationarity and lags, our effective sample period starts from 1960:4.

Results

To compute the posterior estimates, we draw M = 50,000 samples after the initial 10,000 samples are discarded. Table 1 presents the estimates for the posterior means, standard deviations, 95 per cent credible intervals,⁸ the convergence diagnostics (CD) of Geweke (1992) and the inefficiency factors of selected parameters of the TVP-VAR, computed using the MCMC sample.⁹ Based on the CD statistics, the null hypothesis of the convergence to the posterior distribution in the estimated result is not rejected for the parameters at the 5 per cent level of significance. In addition, the efficiency factors are quite low in general. Finally, the 95 per cent confidence intervals include the estimated posterior mean for each of the parameters estimated. Therefore, the results show that the MCMC algorithm produces posterior draws efficiently. Figure A, in the appendix, presents the estimation results of the TVP-VAR model with stochastic volatility.

Table 1.

Estimation Results of Select Parameters in the TVP-VAR Model

Parameter	Mean	Std Dev.	95% Intervals	CD	Inefficiency
(Σ_β)₁	0.0040	0.0013	[0.0024, 0.0072]	0.645	69.72
(Σ_β)₂	0.0044	0.0017	[0.0024, 0.0091]	0.419	53.99
(Σ_a)₁	0.0056	0.0017	[0.0034, 0.0097]	0.925	67.45
(Σ_a)₂	0.0056	0.0016	[0.0034, 0.0097]	0.204	57.45
(Σ_h)₁	0.2515	0.0753	[0.1255, 0.4187]	0.565	90.1
(Σ_h)₂	0.5182	0.0967	[0.3510, 0.7288]	0.768	28.36

Source: Authors’ estimations.

Figure 1 reports the data of the three variables in our analysis (DC, TBILL and DRSP) in the top panel. The corresponding posterior estimates of stochastic volatility are plotted in the bottom panel. The time-series plots consist of the posterior draws on each date. The results show that stochastic volatility of consumption growth is highly volatile during the early period of our sample and peaks around 1985, followed by a general downward trend thereafter. This is intuitive as the financial liberalisation in 1985 following the recommendations of the De Kock Commission led to easy availability of credit which led to a consumption boom. The stochastic volatility of consumption remains low and stable from the 1990s. The low stochastic volatility towards the end of the sample period may reflect more certainty in consumption behaviour derived from a more stable economic and political environment in South Africa. The Treasury bill rate exhibits two major spikes in stochastic volatility during the financial liberalisation of 1985 and around 1999, just before the SARB formally introduced inflation targeting. A minor rise in volatility of the Treasury bill rate is also observed around the first oil price shock in 1973. Not surprisingly, the real stock returns are found to exhibit the most stochastic volatility, with a major peak around 2008, due to the decline in stock returns following the recent financial crisis. Smaller peaks are observed around the 1973 oil price crisis and the financial liberalisation. The significant posterior estimates of the stochastic volatility present in the variables of interest justify the use of a TVP-VAR model with stochastic volatility to avoid biased estimation.

Figure 1.

Source: Authors’ estimations.

Impulse responses are used as a tool to capture the macroeconomic dynamics in the estimated VAR system. For a standard constant parameter VAR model, the impulse responses are drawn for each set of two variables, whereas for a TVP-VAR model, the impulse responses can be drawn in an additional dimension, as the responses are computed at all points in time using the TVPs. There are several ways to simulate the impulse responses based on the parameter estimates of the TVP-VAR model. Following Nakajima (2011), we compute the impulse responses by fixing an initial shock size equal to the time-series average of stochastic volatility over the sample period, and using the simultaneous relations at each point in time, for considering the comparability over time. In the VAR, the variables are ordered in an attempt to identify the stock price shock using a recursive or Cholesky identification scheme, as obtained based on the lower triangular matrix A_t. We order the variables as follows: DC, TBILL and DRSP, following the literature analysing asset price shocks on measures of real economic activity and monetary policy behaviour. The ordering implies that consumption is not contemporaneously affected by interest rates and real stock prices. The interest rate is assumed to respond contemporaneously to consumption, but with a delay to real stock prices.¹⁰ Finally, stock prices react contemporaneously to an aggregate demand (consumption) shock and a monetary policy shock. To compute the recursive innovation of the variable, the estimated time-varying coefficients are used from the current date to future periods. Around the end of the sample period, the coefficients are set constant in future periods for convenience. Although a time series of impulse responses for selected horizons or impulse responses for selected periods is often exhibited in the literature, one could draw a three-dimensional plot for the time-varying impulse responses.

Figure 2 illustrates the time varying response trajectories at different horizons of one-quarter, four-quarters, eight-quarters and twelve-quarters ahead at each point of the sample, for the three variables of our concern following a shock to real stock price. In the figure, we report the mean of the posterior together with 16th and 84th percentiles.

Figure 2.

Source: Authors’ estimations.

Following a shock to real stock price, the effect on stock price itself is mostly positive, especially for one-quarter- and four-quarters-ahead horizons. The effect is significant over the entire sample period for the one-quarter-ahead horizon, while the significance for the four-steps-ahead impulse responses lasts till the mid-1980s. Though the effect on stock price is positive for majority of the sample at longer horizons, the effect is not significant at any point of time. Following a positive shock to real stock price, consumption in general responds positively, with the effect becoming negative when stock prices become negative. The effect on consumption is primarily significant at the one-quarter-ahead horizon, barring the period of mid-1980 till the late 1990, when the effect was insignificantly negative even when real stock prices were significantly positive. Interestingly, at the one-year horizon following the stock price shock, the effect on consumption is hardly significant for the entire period. Negative significant effects on consumption are seen in the latter part of the sample, mainly during the financial crisis, for eight-quarters-ahead and twelve-quarters-ahead impulse responses, when the stock price in itself was negative, though not significantly. Note that based on the scales of the graphs, the size of the effect on consumption following an increase in real stock prices diminished at longer horizons.

The behaviour of the interest rate following a real stock price increase is quite interesting. For the one-quarter-ahead impulse responses, the effect is positive in general, barring a short period in mid- to late 1970s, but the effect is only significant post financial liberalisation, until the financial crisis. For the one-year-ahead horizon, the impulse responses are initially positive, and then become negative, though insignificant, until shortly after financial liberalisation. A positive and significant response is observed from there on until the end of the sample, though the effect weakened during the financial crisis. A similar pattern, to the four-quarters-ahead horizon, is observed for the eight-quarters-ahead and twelve-quarters-ahead horizons. It seems that the monetary authority started to respond positively to stock price movements more seriously after financial liberalisation, with its response reaching a peak just before the financial crisis. The results tend to suggest that for a prolonged period after the first oil price shock till financial liberalisation, the SARB was quite happy to allow the stock markets to grow, by lowering interest rate following a positive shock to stock prices. Further, there seems to be quite a bit of persistence in the effect of interest rate movement to stock price behaviour, since the interest rates were positive and significant at longer horizons (eight and twelve) even when the effect on stock price following a shock on itself had become negative. This could possibly be indicating the SARB’s attempt to keep inflation in check that could have originated from the wealth effect of real stock price increases on consumption. In addition, based on the scales of impulse responses, the effects are bigger at longer horizons than immediately following the shock on stock prices.¹¹

The results suggest that there is a high degree of variability in the behaviour of both consumption and interest rates to a stock price shock during different periods and trajectories. The behaviour of stock price following a shock to itself also exhibits different responses depending on the trajectory analysed. All this variability in the behaviour of the variables of our concern justifies the use of a TVP-VAR with stochastic volatility.

Conclusion

This article uses a three-variable (growth rate of real consumption, nominal three-months Treasury bill rate and real stock price growth rate) TVP-VAR model with stochastic volatility to analyse the impact of a house price shock on consumption levels and monetary policy for South Africa over the quarterly period of 1966:4–2011:4. We find that the impact of a real stock price shocks on consumption is in general positive, with large and significant effects observed at the one-quarter-ahead horizon. However, there is also evidence of significant negative spillovers from the stock market to consumption during the financial crisis, at both short and long horizons. Monetary policy response to stock price shocks has been persistent and strong, especially post financial liberalisation, but became weaker during the financial crisis. Overall, we not only provide evidence of significant spillovers on consumption and interest rate from the stock market, but also, more importantly, highlight the fact that these effects have significantly varied over time, which we would not have been able to capture without the usage of a time-varying model. Given that the recent papers by Afonso and Sousa (2011b), Agnello and Sousa (2011b), Agnello, Castro and Sousa (forthcoming) and Castro and Sousa (2012) have analysed the impact of fiscal policy on asset prices and also the possible feedback of asset prices on setting of fiscal policy, it would be interesting to carry out such analyses for South Africa using a TVP-VAR approach in the future, since this would allow us to account for not only possible non-linearity amongst the variables of interest but also how the relationship has evolved over time.

Footnotes

Acknowledgements

We would like to thank Jouchi Nakajima for many helpful comments. The usual disclaimer applies.

Appendix

Notes

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