Re-examining the Fisher Effect: An Application of Small Sample Distributions of the Covariate Unit Root Test

Abstract

This article employs the covariate unit root test proposed by Elliott and Jansson to investigate the stationarity properties of real interest rates. Instead of blindly trusting the asymptotic distribution of the test, we extend Rudebusch's method to estimate its finite sample distributions under the null and alternative hypotheses. With these distributions, we can obtain the probabilities that the test statistic comes from the null and alternative hypotheses, and quantify the asymptotic size as well as the test power for each specific series. Our simulation experiments show that first, due to the higher power raised by the inclusion of covariates, the test can overwhelmingly reject the unit root null for the 16 industrialized countries; secondly, the Ng and Perron tests deliver lower powers in most countries, and thus lead to the false conclusion of non-stationary real interest rates. Finally, allowing for multiple endogenous breaks in the real interest rates provides only stationary evidence in half of the 16 countries.     

Mean Reversion in the Real Interest Rate and the Effects of Calculating Expected Inflation

We investigate the measured persistence in the real interest rate using a variety of methods to annualize inflation and calculate the real rate. Results from a battery of conventional unit root tests yield conflicting conclusions for the various real rates, adding to an existing confusion regarding mean reversion. Both long memory and exponential smooth‐transition autoregressive models (ESTAR) nonlinearity are considered as possible alternatives, and in contrast to the unit root test results, we find highly robust evidence against the unit root null. Based on the empirical results, Monte Carlo analysis is performed to study the disparate results obtained using fractional integration and unit root tests.     

The Unit Root Hypothesis for Aggregate Output May Not Hold after All: New Evidence from a Panel Stationarity Test with Multiple Breaks

This paper investigates the hypothesis of a unit root in output for four panels of real gross domestic product (GDP) and real GDP per capita series in the Organization for Economic Cooperation and Development (OECD). For that purpose, a panel stationarity test is employed that assumes a highly flexible trend function by incorporating an unknown number of breaks in level and slope. This analysis renders clear-cut evidence in favor of regime-wise trend stationarity in OECD output for the three data sets of annual data, while evidence of nonstationarity is found for the data set based on quarterly data, which is composed of only seven countries over the shortest time span. Overall, the results herein stand in stark contrast to previously published results that do not control for the existence of structural change in the trend function, but accord well with those that employ panel unit root tests that allow for a single homogeneous break in the trend function.     

Inflation in South Africa: An Assessment of Alternative Inflation Models

We consider the relative empirical performance of a range of inflation models for South Africa. Model coverage is of Phillips curve, New Keynesian Phillips curve, monetarist and structural models of inflation. Our core findings are that the single most robust covariate of inflation is unit labour cost. We further decompose unit labour cost into changes in the nominal wage and real labour productivity. The principal association is a strong positive relationship between inflation and nominal wages, while improvements in real labour productivity report only a relatively weak negative association with inflation. Supply‐side shocks also consistently report an association with inflation. As to demand‐side shocks, the output gap does not return a robust statistical association with inflation. Instead, it is growth in the money supply and government expenditure which return robust and theoretically consistent associations with inflationary pressure.     

Do Real Exchange Rates Follow a Nonlinear Mean Reverting Process in Developing Countries?

In an effort to fight relatively high inflation, many developing countries try to manage their nominal exchange rates through official intervention. In addition, developing countries tend to have high transportation costs, tariffs, and nontariff barriers. These factors are among the sources of generating nonlinearity in real exchange rates and hence some nonlinear adjustment toward purchasing power parity (PPP) in developing countries. In this paper, we employ monthly real effective exchange rate (REER) data of 88 developing countries and test the null of nonstationarity versus an alternative of linear stationarity by the means of a conventional unit root test and compare the results with those obtained from a new test in which the null is the same but the alternative hypothesis is nonlinear stationarity. The latter test supports the PPP theory in more developing countries compared with the former test, suggesting that nonlinear adjustment toward PPP in developing countries is an important phenomenon. Reported country characterizations indicate that reversion in REER occurs more often for high-inflation countries and for countries with high flexibility in their exchange rates.     

IS THERE AN ASYMMETRIC BEHAVIOUR IN AFRICAN INFLATION? A NON‐LINEAR APPROACH

In this paper we test the inflation persistence hypothesis as well as model the long‐run behaviour of inflation rates in a pool of African countries using a non‐linear framework. In order to do so, we rely on unit root tests applied to non‐linear models and fractional integration. The results show that the hypothesis of inflation persistence does not hold empirically for most of the countries. In addition, the estimated models (logistic smooth transition autoregressions) are stable in the sense that the variable tends to remain in the regime (low inflation or high inflation) once reached, and changes between regimes are only achieved after a shock. The results also indicate that the effects of the shocks on inflation tend to die out; exogenous factors, i.e. supply shocks and inertia may be causing this outcome, as they play a substantial role in the determination of the inflation rates for our selected African countries.     

Non-linear Co-integration between Nominal Interest Rates and Inflation: An Examination of the Fisher Hypothesis for Asian Countries

Abstract

This paper examines the long-run relationship between nominal interest rates and inflation for a group of Asian countries over the period February 1973–April 2007. We argue that the empirical failure to find evidence supporting the Fisher effect in previous studies may be attributed to the presence of non-linearities in the long-run relationship between nominal interest rates and inflation. We present evidence that the Fisher relation contains significant logistic smooth transition autoregression (LSTAR)-type non-linearity. This type of non-linearity is consistent with inflation targeting and the opportunistic behavior of policy-makers. Applying a non-linear unit root test to the residuals obtained from the Fisher relation decisively rejects the null hypothesis of a unit root against the alternative of non-linear but globally stationary in all the cases.     

Too Many Cooks? Committees in Monetary Policy

How many people should decide monetary policy? In this article, we take an empirical perspective on this issue and analyze the relationship between the number of monetary policy decision makers and monetary policy outcomes. Using a new data set that characterizes central bank monetary policy committees (MPCs) in more than 30 countries from 1960 through 2006, we find a U‐shaped relationship between MPC size and inflation; our results suggest that the lowest level of inflation is reached at MPCs with an intermediate size of about five to nine members. Similar results are obtained for inflation variability. Other MPC characteristics also matter for monetary policy outcomes, though to a smaller degree. For instance, the membership composition of the MPC as well as the frequency of MPC membership turnover appears to affect economic variables.     

Unit Root Tests,Persistence, and the Unemployment Rate of the U.S. States

In this paper, we investigate the existence of infrequent shocks and the degree of persistence of U.S. state unemployment over the period 1976-2004. We first apply individual Lagrange multiplier (LM) unit root tests and fail to reject the hysteresis hypothesis in forty states. When two changes in level are incorporated, we again fail to reject the hysteresis hypothesis in forty states. Since individual unit root tests normally lack power, we employ the recently developed panel LM unit root tests with up to two changes in level. Only in this case are we able to reject the joint unit root hypothesis in favor of regime stationarity. Computation of half-lives through impulse-response functions indicates the high degree of persistence of U.S. state unemployment. These results contrast with the common belief among scholars that U.S. state unemployment is closer to the natural rate paradigm than to the hysteresis paradigm.     

Are Real GDP Levels Stationary in African Countries?

In this study, we apply flexible Fourier stationary unit root test proposed by Enders and Lee (2012) to assess the non‐stationary properties of the per capita real gross domestic product (GDP) for 32 African countries. We find that Fourier stationary unit root test has higher power than linear method if the true data‐generating process of per capita real GDP is in fact a stationary nonlinear process of an unknown form with structural change using the low frequency components. We investigate the stationarity of per capita real GDP from the nonlinear point of view and provide robust evidence that clearly indicates that real output is well characterised by a nonlinear, mean‐reverting process, namely Benin, Botswana, Burundi, Cameroon, Senegal, Sierra Leone and South Africa. Our evidence points that these seven countries are nonlinear stationary, implying that per capita real GDP follows a steady rate of growth, and policy innovations then have temporary effects. These results have important policy implications for African countries.     

Mean Reversion of Real Exchange Rates in High-Inflation Countries

We test for mean reversion in real exchange rates using data from five countries, four of which have experienced episodes of high inflation. Using monthly data for Argentina, Brazil, Chile, Colombia, and Israel, we find that a stochastic unit root model is typically appropriate (Brazil is the exception). Kalman filter estimates of the stochastic unit roots show sharp deviations from unity associated with high inflation episodes. This suggests that stochastic unit root models are a more appropriate way to model mean reversion in real exchange rates for high inflation countries than models with fixed rates of mean reversion.     

REVISITING THE EFFICIENT MARKET HYPOTHESIS FOR AFRICAN COUNTRIES: PANEL SURKSS TEST WITH A FOURIER FUNCTION

This study applies the panel seeming unrelated regression of the Kapetanios‐Shin‐Snell (SURKSS) test with a Fourier function to investigate the time‐series properties of stock prices in five African countries (i.e. Egypt, Kenya, Morocco, South Africa and Tunisia) over the period of January 2000–April 2011. The empirical results from the univariate unit root and panel‐based unit root tests indicate that unit root hypothesis can not be rejected for these five countries under study. However, results from the panel SURKSS test with a Fourier function indicate that unit root hypothesis can be rejected for Egypt and Morocco, two countries under study. Our results indicate that the weak‐form efficient market hypothesis holds in the other three countries, namely, Kenya, South Africa and Tunisia.     

Foreign Capital Flows,Uncertainties of Exchange Rates and Central Bank Independence: Implications for Emerging Economies

Utilizing time series data for a panel of 22 emerging countries and applying Granger causality tests, this paper extends the relationship between central bank independence (CBI) and uncertainties of inflation by including the phenomena of exchange rates and foreign capital flows. There are two specific objectives of this investigation. The first objective is to see whether uncertainty of inflation induces volatility of exchange rates, and vice versa, under differing degrees of CBI. The second objective is to explore whether the dynamics of the former relationship influence foreign capital flows in turn and, if so, whether the extent of CBI plays any role in shaping that influence. The period of study spans the years 1968 through 2013. Conditional variances for inflation and exchange rates define proxies for uncertainties of inflation and exchange rates in the empirical analysis. Additionally, annual inflows of foreign direct investment (FDI) provide measures for foreign capital flows in the analysis. Results of causality tests for high and low CBI country subgroups show interesting differences. For the high CBI countries, uncertainty of inflation and uncertainty of exchange rates do not share any causal relationship whatsoever between them. However, a weak link runs from FDI to uncertainties of inflation in the long run. This may be indicative of the disciplined monetary policy and tamed inflation in these countries. Contrastingly, for the low CBI countries, there is strong evidence of causal links running from uncertainties of inflation to uncertainties of exchange rates on the one hand and to FDI flows on the other. In addition, there is indication of a bi-directional causal link between FDI flows and exchange rates for these countries.     

Did the underlying behaviour of inflation change in the 1980s? A study of 17 countries

Did the Underlying Behaviour of Inflation Change in the 1980s? A Study of 17 Countries. - Have the ERM member countries experienced a regime change to a lower degree of persistence for inflation in the 1980s compared to the 1970s? Some results give the impression that deflationary policies associated with ERM membership may have reduced the mean level of inflation, but did not reduce the persistence parameter over the last decade. However, other results show that the persistence parameter does decline for a majority of ERM members. Surprisingly, the results also show stronger evidence of a fall in inflation persistence for some non-ERM countries who adopted a strong anti-inflationary stance over the same period.     

Inflation and Structural Change in 50 Developing Countries

This study provides evidence on whether the inflation rate is stationary or nonstationary using quarterly inflation rate data from 50 developing countries. As Johansen [Johansen, Soren. “Testing Weak Exogeneity and Order of Cointegration in UK Money Demand Data,” Journal of Policy Modeling, 14, 3, June 1992, pp. 313–334] put it, “some time series such as the log of prices (P), have the property that even the inflation rate ΔP is nonstationary, whereas the second difference Δ²P is stationarity.” Results from fractional integration analyses provide evidence of long memory and confirm that the nonstationarity threshold of d³0.5 is satisfied in the majority of the cases. Results from recursive analyses indicate that, despite the finding that structural changes influence the behavior of the estimated integration parameters, evidence of long memory and nonstationarity can be found in each subsample as well as the full sample data.     

PURCHASING POWER PARITY IN AFRICAN COUNTRIES: EVIDENCE FROM PANEL SURADF TEST

This study reexamines the validity of long-run purchasing power parity (PPP) hypothesis using a battery of panel unit root tests for 11 developing countries in Africa over the period 1980-2007. Based on the conventional panel unit root tests, we found evidence that the monthly real exchange rates in these countries were mean reverting. By contrast, the series-specific unit root test proposed by Breuer et al. (SURADF) reveals that only six of the 11 RERs series were stationary using the US dollar as reference currency. Additionally, our results reveal that there is stronger evidence of the parity condition with the Rand-based rates than in the other currency-based rates like the US dollar or Euro. We conclude that PPP holds in some, but not all, of the African countries according to the SURADF tests.     

Is Delayed Disinflation More Costly?

An often-stated piece of monetary policy wisdom is that postponing disinflation raises the ultimate cost of disinflation. However, there is little empirical work that directly tests the validity of this view. This paper is a study of the relation between the duration of inflation and the cost of subsequent disinflation using 67 disinflation episodes in OECD countries from 1960 through 1993. The estimates indicate that delaying disinflation raises the output loss per unit of inflation reduction, although the effect is not statistically significant in all models. The largest marginal effects of delay occur soon after inflation is allowed to get under way, a finding consistent with a rapid decline in the credibility of the inflating central bank.     

Incremental State Higher Education Expenditures

Panel regressions are used to analyze various measures of state higher education expenditures for 45 states over a time period from 1986 through 2005. Results of panel stationarity tests indicate that each expenditures series contains a unit root. This finding is consistent with the incremental theory of public expenditures and implies that time series of these variables should be differenced if used as dependent variables in regression models. Regression results indicate that changes in state higher education expenditures are significantly procyclical. State higher education spending appears to fully adjust to population growth and over-adjust to CPI inflation. Larger state governments are associated with significantly larger annual adjustments to per capita real state higher education expenditures. No significant evidence is found that state Medicaid or elementary education expenditures crowd out higher education spending.

Purchasing Power Parity in Developing Countries: Multi-Period Evidence Under the Current Float

Using panel unit root tests, we examine purchasing power parity (PPP) for US dollar real exchange rates of developing countries during the current floating rate period. Since evidence of PPP may vary from period to period, we examine the data for moving 10-year periods from 1976–85 up to 1990–99. We organize panels based on country characteristics influencing the validity of PPP. Those characteristics include openness, inflation, and the level and growth rate of per capita GDP. Although we find stronger evidence of PPP after 1980, our examination of panel data over 15 10-year periods yields only limited support for PPP.