A revisit on real interest rate parity hypothesis – simulation evidence from efficient unit root tests

A set of unit root tests are applied to test the existence of long-run real interest rate parity among the G-10 countries over the period 1971M1 to 2007M2. Rather than trusting the asymptotic distributions, this article uses simulation techniques to establish the small sample distributions of these tests, conditional on the stationary and nonstationary processes. The empirical results indicate that the tests have stable finite-sample sizes and higher size-adjusted powers such that the two estimated processes can be distinguished from each other. Thus, for six of the nine countries, their series are more likely to come from the estimated Autoregressive (AR) stationary process than from the nonstationary process. Noticeably, the testing results are rather different from those using the asymptotic distributions, in which only three countries support the real interest rate parity.     

Finnish GNP-series 1954/I–1990/IV: Small shock persistance or trend stationarity? Some evidence with variance ratio estimates

The “shock persistance” of Finnish adjusted quarterly real GNP series in logarithms from 1954/QI to 1990/QIV is analyzed using variance ratio estimators. The results indicate that the random walk component of the series is not big. The small sample properties of variance ratio estimators are studied using empirical distribution derived from simulations. The persistence measures calculated via the ARIMA modelling of the lnGNP_t series are biased upwards. The sampling properties show that the simple random walk model is not an alternative model for the lnGNP. A trend stationary alternative, an AR(2) process, gives almost the same “shock persistence” measures as the assumed unit root processes.     

Purchasing power parity with flexible Fourier stationary test for Central and Eastern European countries

This study applies stationary test with a Fourier function proposed by Enders and Lee (2004, 2009) to test the validity of long-run Purchasing Power Parity (PPP) to assess the nonstationary properties of the Real Exchange Rate (RER) for seven Central and Eastern European Countries (CEECs). We find that our approximation has higher power to detect U-shaped breaks and smooth breaks than linear method if the true data generating process of exchange rate is in fact a stationary nonlinear process. We examine the validity of PPP from the nonlinear point of view and provide robust evidence clearly indicating that the PPP holds true for all CEECs. Our findings point out their exchange rate adjustment is mean reversion towards PPP equilibrium values in a nonlinear way.     

Real interest rate parity with Flexible Fourier stationary test for Central and Eastern European countries

This study applies stationary test with a Fourier function proposed by Enders and Lee (2012) to test the validity of long-run real interest rate parity (RIRP) to assess the non-stationary properties of the real interest rate convergence for twelve Central and Eastern European (CEE) countries. We find that our approximation has higher power to detect U-shaped breaks and smooth breaks than linear method if the true data generating process of interest rate convergence is in fact a stationary non-linear process. We examine the validity of RIRP from the non-linear point of view and provide robust evidence clearly indicating that RIRP holds true for nine CEE countries. Our findings point out that their interest rate adjustment is mean reversion towards RIRP equilibrium values in a non-linear way.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

The time series behaviour of spot exchange rates in the German hyper-inflation period: (Was the process chaotic?)

A discrete time approximation to the continuous time hyper-inflation model of Sargent and Wallace (1993) in which the authorities finance a given budget deficit by printing money appears to admit the possibility of chaotic solutions. In this paper we investigate the time series properties of daily observations on the Pound Reichsmark spot exchange rate in the inter-war hyper-inflation period. Our empirical analysis is suggestive that spot rates were generated by a non-linear possibly chaotic process.     

The properties of some covariance matrix estimators in linear models with AR(1) errors

A Monte Carlo study is used to demonstrate how poor some traditional covariance matrix estimators can be in linear models with AR(1) errors. It is also shown that a second-order approximation suggested recently by Ullah et al. (1983) does not lead to a more accurate covariance matrix estimator.     

Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

We provide an asymptotic distribution theory for a class of generalized method of moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market. We allow for three sources of error: sampling error in estimating market shares, simulation error in approximating the shares predicted by the model, and the underlying model error. It is shown that the estimators are CAN provided the size of the consumer sample and the number of simulation draws grow at a large enough rate relative to the number of products. We consider the implications of the results for the Berry, Levinsohn and Pakes (1995) random coefficient logit model and the pure characteristics model analysed in Berry and Pakes (2002) . The required rates differ for these two frequently used demand models. A small Monte Carlo study shows that the differences in asymptotic properties of the two models are reflected, in quite a striking way, in the models' small sample properties. Moreover the limit distributions provide a good approximation to the actual Monte Carlo distribution of the parameter estimates. The results have important implications for the computational burden of the two models.     

Aggregation, Persistence and Volatility in a Macro Model

We introduce firm heterogeneity into the standard monopolistically competitive real business cycle (RBC) model. The fundamental equilibrium path is derived and the time–series properties of aggregate GDP are studied analytically. Although firms' productivities are subject to temporary shocks, the aggregate process displays a surprising novel form of nonlinearity and long memory which had not been built into the model at the outset. This aggregate GDP turns out to have very different properties from log–linear time–series models such as auto–regressive (AR) models and their extensions. It displays very strong persistence, which ends abruptly with a sudden change of tendency, giving its autocorrelation function (ACF) an S –shape. Although persistent, it is mean–reverting, unlike the everlasting memory of unit–root processes. Its volatility is of a greater order of magnitude than that of any of its components, so small micro–shocks can generate large macro fluctuations. It is also characterized by long, asymmetric cycles of random lengths. Increased monopoly power tends to reduce the amplitude and increase the persistence of business cycles. Strikingly, we find that the empirical ACFs constructed from GDP data for the U.K. and the U.S. display this characteristic S –shape.     

Is fiscal policy stationary in China? A regional study by local government

In this study, we apply a stationarity test with a flexible Fourier function proposed by Enders and Lee (2012) to test the stationarity of the deficit–GDP ratio in China. We find that our approximation has a higher power to detect U-shaped breaks and to smooth breaks than the linear method if the true data-generating process of the deficit–GDP ratio convergence is, in fact, a stationary non-linear process. The results show that the stationarity for fiscal policy varies across different regions and that the deficit–GDP ratio of half of the regions is stationary. The results related to the budget structural balance and the fiscal deficit indicate no expansion in the Eastern and Central regions. We find that China's provinces in these two regions meet the stability theory of fiscal policy in the current stage of development. The deficit–GDP ratio is not stationary in the Western and Northeastern regions. These results indicate that the fiscal deficits in these regions are expanding and cannot be controlled by automatic market adjustment, and the government should therefore avoid deficit expansion in favor of a balanced budget policy.     

Deficit model of exchange for continuous processes with external control

A method of constructing a deficit-having model of exchange based on the Markov chain theory for continuous processes with external control is developed, for which the results of the continuous and discrete models are identical. Continuous models allow us to study and predict exchange processes at any moment in time. The deficit model assumes that in the exchange process, when a stationary regime is achieved, those involved have a nonzero balance. The model allows us to determine the external force (control – the actions of the administration) for the realization processes of a specific exchange programme.     

On measuring average growth rate

This study investigates the difference in average growth rates obtained from two commonly used methods. It is analytically shown that the difference lies on the dichotomy of constant and time-varying growth that can be converted to the dichotomy of trend stationary (TS) and difference stationary (DS) processes. For TS processes the two methods would yield the same results whereas they differ in case of integrated processes. It is also proven that the OLS residuals of a log-linear trend model of an integrated series will be always a random walk, in which case the differenced model that yields the same result as geometric mean is appropriate. The findings are illustrated on the real GDPs of OECD countries.     

Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring its properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Markovian switching, and investigate the convergence of numerical approximation. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. A numerical example is provided to illustrate the theoretical results.     

Long memory in the volatility of China stock returns

In this paper, we empirically examine the volatility process of China's stock market returns using daily and weekly Shanghai and Shenzhen stock indices during January 1990 to August 2008. To investigate the property of the process, we used the FIGARCH (fractionally integrated GARCH) model including GARCH and IGARCH processes as special cases. Since the FIGARCH model allows fractional integration order, it can detect hyperbolically decaying volatility processes which cannot be explained by previous models with integer integration order. Our results show that the Shanghai and Shenzhen stock indices exhibit long-term dependencies. The long memory properties of the Shanghai and Shenzhen stock markets do not seem to be spuriously induced without exception.     

Limited information minimal state variable learning in a medium-scale multi-country model

Rational expectations has been the dominant way to model expectations, but the literature has quickly moved to a more realistic assumption of boundedly rational learning where agents are assumed to use only a limited set of information to form their expectations. A standard assumption is that agents form expectations by using the correctly specified reduced form model of the economy, the minimal state variable solution (MSV), but they do not know the parameters. However, with medium-sized and large models the closed-form MSV solutions are difficult to attain given the large number of variables that could be included. Therefore, agents base expectations on a misspecified MSV solution. In contrast, we assume that agents know the deep parameters of their own optimising frameworks. However, they are not assumed to know the structure nor the parameterisation of the rest of the economy, nor do they know the stochastic processes generating shocks hitting the economy. In addition, agents are assumed to know that the changes (or the growth rates) of fundament variables can be modelled as stationary ARMA(p,q) processes, the exact form of which is not, however, known by agents. This approach avoids the complexities of dealing with a potential vast multitude of alternative misspecified MSVs.Using a new multi-country euro area model with boundedly estimated rationality we show that this approach is compatible with the same limited information assumption that was used in deriving and estimating the behavioural equations of different optimising agents. We find that there are strong differences in the adjustment path to the shocks to the economy when agents form expectations using our learning approach compared to expectations formed under the assumption of strong rationality. Furthermore, we find some variation in expansionary fiscal policy in periods of downturns compared to boom periods.     

Indeterminacy of equilibrium in stochastic OLG models

Summary. This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods, and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either autarchy or the stochastic analogue of the Golden Rule. Received: November 19, 2001; revised version: March 22, 2002 RID="*" ID="*" We are grateful for the stimulating environment and research support provided by the Cowles Foundation at Yale University during the Fall 2000 when this paper was first conceived. We are also grateful to the participants of the SITE Workshop at Stanford University and the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001 for helpful discussions. Correspondence to: M. Magill     

The balance between size and power in testing for linear association for two stationary AR(1) processes

The classical statistical procedure in testing the null hypothesis of zero correlation for two independent stationary AR(1) processes produces spurious correlations, contrast to the alternative testing approach that has been proposed by Agiakloglou and Tsimpanos (2012). This study examines the trade-offs between size distortions and power using both testing techniques, including the case where the true values of the autoregressive parameters are replaced by their estimates.     

An Evolutionary Approach to Financial Innovation

The purpose of this paper is to explain why some markets for financial products take off while others vanish as soon as they have emerged. To this end, we model an infinite sequence of CAPM-economies in which financial products can be used for insurance purposes. Agents' participation in these financial products, however, is restricted. Consecutive stage economies are linked by a mapping ('transition function") which determines the next period's participation structure from the preceding period's participation. The transition function generates a dynamic process of market participation which is driven by the percentage of informed traders and the rate at which a new asset is adopted. We then analyse the evolutionary stability of stationary equilibria. In accordance with the empirical literature on financial innovation, it is obtained that the success of a financial innovation, a mutation, depends on a sufficiently high trading volume, marketing, and new and differentiated hedging opportunities. In particular, a set of complete markets forming a stationary equilibrium is robust with respect to any further financial innovation while this is not necessarily true for a set of incomplete markets.
"There is no generally accepted theory of financial innovation, but some broad generalizations of the innovation process are possible. What matters is not the invention of a financial product or process (which is often obscure) but its diffusion through the market environment".
Ted Padolski (1987) in: The New Palgrave on Money and Finance: Financial
Innovation and Money Supply (p. 68)     

Crude oil price volatility dynamics and the great recession

Using a very simple econometric framework, we identify two major changes in the dynamics of crude oil price volatility based on data from 1997 to 2017. More precisely, we model weekly West Texas Intermediate (WTI) crude oil price realized volatility in a two-regime setting, one where realized volatility evolves as a plain autoregressive (AR) process (static), and the other where the level, persistence and innovation volatility of the AR process are subject to changes (dynamic). We use a Markov chain to model the probability that the process is in the static regime. The post Great Recession period sees a longer duration of the dynamic regime as well as smaller changes in the level and conditional volatility of realized volatility when switching actually occurs. Crude oil volatility also responds more aggressively to changes in economic variables, such as the t-bill rate and equity market volatility in the dynamic regime.     

A Two-Sector Model of Endogenous Growth with Leisure

This paper analyses the equilibrium dynamics of an endogenous growth model with physical and human capital in which leisure enters the utility function. The inclusion of leisure introduces a potential source of non-convexities in our optimization problem and leads to the possible existence of multiple balanced growth paths. This multiplicity of optimal stationary solutions is linked to the assumption that education has no effect on the quality of leisure, and hence a relatively more educated economy may choose to grow faster, and devote more time to income-directed activities. To characterize the set of optimal solutions in our non-concave optimization framework we develop a new method of analysis that should be of interest in related applications.