importance of stochastic properties of economic variables for macroeconomic theories

Procedia - Social and Behavioral Sciences 109 ( 2014 ) 135 – 139

1877-0428 © 2014 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Organizing Committee of BEM 2013.doi: 10.1016/j.sbspro.2013.12.433

ScienceDirect

2nd World Conference On Business, Economics And Management - WCBEM 2013

Importance of stochastic properties of economic variables for macroeconomic theories

Korhan Gokmenoglua *

a Department of Economics, University of California, San Diego, CA 92093-0508, USA

Abstract

Stochastic properties are the basic determinants of behavior of economic variables. These properties are also important for construction of econometric models, interpretation of the findings and forecasting. So prior to any econometric study time series properties of variables have to be analyzed. Stochastic properties are also decisive for validity of many economic theories, including Fisher Hypothesis, Purchasing Power Parity, Consumption Based Asset Pricing Model, several monetary models and co-integration of international bond markets; those represent long run relationships between variables. This paper aims to put forward the importance of stochastic properties of economic variables for basic macroeconomic theories by giving special emphasis to real interest rates.

1. Introduction

Time series properties strongly affect the behavior of economic and financial variables. For non-stationary variables shocks have infinite effects, assumptions of asymptotic analysis are not valid and it is not possible to conduct hypothesis testing for estimated parameters. Integration properties of series might lead to problems such as spurious regression as well (Granger and Newbold, 1974). So, stochastic properties of variables need to be analyzed prior to econometric analysis (Gujarati, 2002).

On the other hand, time series properties of economic variables have important implications on basic assumptions of several macroeconomic theories. Especially for the last two decades, theoretical and applied studies on long run equilibrium of economy and short-term fluctuations from long-term equilibrium have given more importance to stochastic properties of variables.

This study briefly investigates importance of stochastic properties of economic variables on the basic assumptions of some macroeconomic theories.

* Corresponding Author: Korhan Gokmenoglu. Tel.: +1-480-359-9258 E-mail address: [email protected]

Keywords: Econometrics, macroeconomic models, interest rates;

Available online at www.sciencedirect.com

© 2014 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Organizing Committee of BEM 2013.

136 Korhan Gokmenoglu / Procedia - Social and Behavioral Sciences 109 ( 2014 ) 135 – 139

2. Co integration Relations

It is widely accepted that many economic-financial variables are non-stationary. This might be a problem for validity of macroeconomic theories, which based on the assumptions that there is long term and decisive relationships between certain variables (Gujarati, 2002).

Some non-stationary variables have co-movement in the long run as a result of some common macroeconomic factors. This implies that it is possible to expect a relationship even between non-stationary variables in the long run. If orders of integration of variables are same and OLS residuals are stationary, static regression between these variables will become long run equilibrium (Vogelvang, 2005). In other words, any misalignments, which can be observed in the short run between non-stationary variables, will disappear in the long run if these variables are co integrated (Engle and Granger, 1987). If this is the case, macroeconomic model those have non stationary ingredients will be valid at least in the long run.

Efficient market hypothesis claims that there are no permanent arbitrage opportunities in the markets that can be exploited. This idea will be true only if there is long-term relation between variables. If series are not co integrated, they have no common movement and these series can move apart from each other even in the long run.

2.1. Spot and Futures Market

Efficient Market Hypothesis expects that in an efficient market spot and futures prices have to have one to one relationship and there are no permanent arbitrage opportunities. Spot and futures prices represent the price of the same asset for different points in time, so it is reasonable to expect these series don't move apart from each other especially in the long run which means that they are co integrated.

Equilibrium relationship between spot and futures prices is known as ‘Cost of Carry Model’: The logarithm of this model shows that relationship between spot and futures prices have to be one to one. This equation implies that difference between spot and futures prices must be stationary. Otherwise, in contrast to

the expectations of the model, series move apart from each other and arbitrage opportunities emerge (Brooks, 2008). Using Nikkei Stock Average daily data Tse (1995) investigates the lead-lag relationship between the spot index

and futures price. Tse (1995) first finds that both series are non-stationary and then shows that these series are co integrated by employing two versions of error correction models. According to the study short-term adjustment in the spot index is affected by lagged changes in the futures price. Study also finds that error correction model produce better results for the post-sample forecasting the spot index in comparison to VAR model.

Brooks et al. (2001) conduct a similar research by employing a number of time series models. This paper examines the lead–lag relationship between FTSE 100 index and index futures price by analyzing 10 minutes observations for June 1996-1997 periods. It is expected that new information affect spot index and futures prices simultaneously. ADF (Dickey and Fuller, 1981) and Engle-Granger (1987) tests reveal that series are non-stationary and co integrated as expected. They claim that lagged changes in the futures prices could help to predict changes in the spot prices. Error correction is found as the best forecasting model. However, if transaction costs are taken into account this model cannot perform better than the benchmark, which means that it is practically not possible to make money by using this forecasting model.

2.2. Purchasing Power Parity (PPP)

PPP and deviations from this relation is one of the most investigated topics of macroeconomics. PPP basically relates exchange rates and relative price levels of two countries and estimates the amount of adjustment needed on the exchange rate.


Permanent deviations from this relation might result from demand or productivity shocks (Dornbusch, 1976) and international untradeable goods (Balassa, 1964; Samuelson, 1964). However, according to Hanck (2007) even these theoretical drawbacks are ignored, stochastic properties of the variables appearing in PPP equation may lead permanent deviations.

Studies investigate validity of PPP can be divided into 3 categories. First group ignores the possibility of non-stationary variables, second group employs unit root tests (Caporale et al., 2003) and third group employs co integration analysis (Froot and Rogoff, 1995).

Theory implies that real interest rate is stationary. So, stationary real interest rates can be taken as a proof for validity of PPP. Sufficient and necessary conditions for validity of PPP can be expresses as a co integration relation. If the series appearing in PPP equation are not co integrated, this situation implies arbitrage opportunities:

Chen (1995) examines long-run PPP for five European Monetary System countries, namely Germany, Italy,

France, Belgium and Holland. Chen uses monthly data for April 1973 and December 1990 periods to calculate ten bilateral nominal exchange rates. By employing Johanssens’ (1991) test he can reject null hypothesis of no cointegration for all country pairs. This study claims that PPP hypothesis is valid in the long run for the data investigated and this relationship is generally stable following dissolution of the Bretton-Woods system.

2.3. Co integration of International Bond Market

International portfolio diversification is an important risk management system. The success of diversification in the long run depends on co integration properties of international bond markets. Not highly interdependent bond market assumption is the basis of such diversification. The low correlation between bond returns in different markets offers that bond market can be used for international portfolio diversification. So in order to determine potential success of this strategy, stochastic properties, specifically integration and co integration, of variables have to be investigated.

Clare et al. (1995) employ ADF test to identify integration properties of five countries bond market data from January 1978 to April 1990 and find that all series are non-stationary. Then they use Engle and Granger (1987) methodology to examine long-run relationships between four major international government bond markets; US, UK, Germany and Japan and conclude that bond indices are not highly correlated. The paper suggests that during 1980s correlations are weak between these bond markets, which imply that diversification works and offers benefit especially to the investors with longer time horizon.

Mills and Mills (1991) reexamine long-run relationships between same four countries. Data set consists of 960 daily closing observations on the redemption yields from 1 April 1986 to 29 December 1989. DF unit root test reveals that all four series are non-stationary. To investigate co integration properties Johansen test (1991) is employed by considering all four series together but no evidence for co integration vector can be found. VAR analysis reveals that series move apart from and independently from each other. These findings imply that international diversification is beneficial for bond investor and has potential important implications on investment decisions.

2.4. Fisher Hypothesis

Fisher Hypothesis (1930) is based on basic M.V=P.q equation. Natural log form of this equation is expressed below.

Velocity of money cannot be observed and for empirical analysis it is expressed as a function of other economic

variables: In above equation e represents random error that arises because of proxy variable that replaces velocity. By using

these equations Fisher Hypothesis can be expressed like that.


This representation of Fisher Equation implies that there is a (1,1,-1,-1) co integration vector that combines four

left-hand-side variables into one 'e' series. So to test Fisher Hypothesis stochastic properties of variables can be used. Phillips (2005) finds that nominal interest rate is non-stationary but real interest rate and inflation are stationary.

These findings are not compatible with Fisher Equation. On the other hand it is contradictory with basic identity that defines real interest rate as difference of nominal interest rate and inflation.

Mishkin (1992) reexamines the puzzle of Fisher Effect, which is why a strong Fisher Effect occurs only for certain periods but not for others, by employing time-series techniques. Analysis of Mishkin is based on the relationship between inflation and interest rates and takes into account regime shifts. As a result of residual based co integration tests Mishkin concludes that even there are some problems with Fisher Effect in the short run, this hypothesis is valid in the long run. Inflation and interest rates trend together in the long run and there will be strong correlation between them, which is necessary for validity of Fisher Effect.

2.5. Capital Pricing Model

Variables appearing in Capital Pricing Model are often highly persistent and time series properties of these variables have important potential implications on this model. Canonical Consumption Based Asset Pricing Model (Lucas, 1976) can be defined with the equation below:

This equation relates conditional expectations of consumption growth per capita with real interest rates. For the

validity of this equation both series have to have same integration properties. It is almost certain that consumption growth is stationary. However, Rose (1988) asserts that real interest rates of several developed countries have unit root. This finding casts questions on validity of several macroeconomic theories including Capital Pricing Model.

This puzzle has reexamined by several researchers later on (among others, Neely and Rapach, 2008, Ozdemir et al., 2013). Those studies often find that real interest rates are highly persistent but mean reverting processes which imply that Canonical Consumption Based Asset Pricing Model will be valid at least in the long run.

2.6. Other Models

General Growth Model is based on an equation that is similar to Euler Equation of CBAPM. So, stochastic properties of real rates have implications on the validity of this model as well. Neoclassical Growth Model is based on steady-state real interest rate assumptions (Romer, 2006). This model can be represented with this equation:

. According to this equation permanent change in the exogenous rate of time preference, risk aversion, or long-run growth rate of technology will affect the steady-state real interest rate (Neely and Rapach, 2008).

Relationship between stock prices and dividends is similar to that of spot and futures prices. It is expected that stock prices and dividends have to be co integrated.

Intertemporal Permanent Income Hypothesis implies that if income has unit root, consumption has to do so and they have to be co integrated (Campbell, 1987). Hall (1978) claims that according to a simple version of Permanent Income Hypothesis consumption is a Martingale process.

Similarly, some versions of business cycle models claim that aggregate consumption; income and investment have to be co integrated. Some conventional business cycle models assume that demand shocks, which are main cause of economic fluctuations, are temporary, so in the long run economic growth rate reverts to natural rate. Non-mean reverting behavior of these series might lead to problems for the relevance of these theories (Cochrane, 1994).

3. Conclusion

This study aims to demonstrate importance of stochastic properties of economic variables on the relevance of several macroeconomic theories. Time series properties of the variables can be a plausible explanation for the


invalidity of several theories in the short run. This is an important research area for economists and has to be elaborated further.

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importance of stochastic properties of economic variables for macroeconomic theories

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