Revisiting the US money demand function: an application of the Lagrange multiplier structural break unit root test and the bounds test for a long-run relationship

In this article, we examine the issue of a levels relationship and stability of the US money demand function over the period 1959:01 to 2004:02. We use the Lagrange multiplier structural break unit root test and the bounds testing approach to a long-run relationship in levels of the variables, namely real money demand, nominal interest rate and real income. We find greater evidence for a long-run relationship in levels and stability of the US money demand function when we use M2 as a proxy for money demand. However, we find little evidence for a long-run relationship between M1 and M2 with their determinants for the recent period, spanning the last decade or so.

Are bilateral real exchange rates stationary? Evidence from Lagrange multiplier unit root tests for India

The paper examines the stationarity of India’s real exchange rate vis-a` -vis 16 of its major trading partner countries for the period 1960–2000. Application of the conventional ADF unit root test, the Lagrange multiplier (LM) unit root test with one structural break, and the LM unit root test with two structural breaks provides evidence that India’s exchange rate vis-a` -vis 15 out of 16 countries is stationary, implying support for purchasing power parity.

An alternative approach to understanding second-order conditions for constrained optimization - lagrange multipliers

This paper presents an alternative approach to solving a standard problem, frequently encountered in advanced microeconomics, using the technique of Lagrange multipliers. The objective is to enhance the understanding of students as to the derivation of the second-order conditions.

Comparing the small sample properties of two break Lagrange Multiplier unit root tests

In this note, we examine the size and power properties and the break date estimation accuracy of the Lee and Strazicich (LS, 2003) two break endogenous unit root test, based on two different break date selection methods: minimising the test statistic and minimising the sum of squared residuals (SSR). Our results show that the performance of both Models A and C of the LS test are superior when one uses the minimising SSR procedure.

Self adjusted security architecture for mobile ad hoc networks (MANETs)

In this work we present a novel security architecture for MANETs that merges the clustering and the threshold key management techniques. The proposed distributed authentication architecture reacts with the frequently changing topology of the network and enhances the process of assigning the node's public key. In the proposed architecture, the overall network is divided into clusters where the clusterheads (CH) are connected by virtual networks and share the private key of the Central Authority (CA) using Lagrange interpolation. Experimental results show that the proposed architecture reaches to almost 95.5% of all nodes within an ad-hoc network that are able to communicate securely, 9 times faster than other architectures, to attain the same results. Moreover, the solution is fully decentralized to operate in a large-scale mobile network.

Are oil shocks permanent or temporary? panel data evidence from crude oil and NGL production in 60 countries

This paper examines the unit root properties of crude oil production for 60 countries employing a range of panel data unit root tests for the period 1971 to 2003. The study first employs a number of panel data tests that do not accommodate structural breaks and then proceeds to apply the Lagrange Multiplier (LM) panel unit root test with one structural break. The results of the panel data tests without a structural break are inconclusive with at best mixed support for joint stationarity. The findings from the LM panel unit root test with a structural break, however, are conclusive, suggesting that for a world panel and smaller regional-based panels, crude oil and NGL production are jointly stationary.

Examining the behaviour of visitor arrivals to Australia from 28 different countries

Testing the integrational properties of visitor arrivals has important implications for policy, for if visitor arrivals are integrated of order one (nonstationary) then it implies that shocks to visitor arrivals are permanent. However, if visitor arrivals are found to be integrated or order zero (stationary) then this implies that shocks to visitor arrivals are temporary. In this paper we examine whether visitor arrivals to Australia are stationary or nonstationary, using the recently developed univariate and panel Lagrange multiplier tests, and the Im, Pesaran and Shin [Im, K.S., Pesaran, M.H., Shin, Y., 1997. Testing for Unit Roots in Heterogeneous Panels. Manuscript, Department of Applied Economics, University of Cambridge; Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics, 115, 53–74] panel t-test. Our exercise involves Australia’s 28 tourist source markets. Our main findings are: (1) that visitor arrivals to Australia from 28 tourist source markets are stationary, implying that any shock will have only a temporary effect and (2) the second structural break, which mainly coincides with the September 11 terrorist attacks and the Asian financial crisis, has slowed down the growth rate in visitor arrivals to Australia from 22 out of 28 (79%) of the tourism source markets.

Kinematic modeling of a bio-inspired robotic fish

This paper proposes a kinematic modeling method for a bio-inspired robotic fish based on single joint. Lagrangian function of freely swimming robotic fish is built based on a simplified geometric model. In order to build the kinematic model, the fluid force acting on the robotic fish is divided into three parts: the pressure on links, the approach stream pressure and the frictional force. By solving Lagrange's equation of the second kind and the fluid force, the movement of robotic fish is obtained. The robotic fish's motion, such as propelling and turning are simulated, and experiments are taken to verify the model.

Are Australia's tourism markets converging?

In this paper we make an important contribution towards understanding Australia's tourism industry by examining whether or not Australia's tourism markets are converging. We define convergence as the reduction in tourist arrivals' differential, which is calculated as the difference between total visitor arrivals to a country and visitor arrivals from a particular tourist source market. We analyze Australia's thirteen major tourist source markets using monthly data over the period January 1991 to September 2003. To test for convergence, we use the univariate and panel Lagrange multiplier (LM) tests. Our main finding is that when we allow for two structural breaks in the data series, both univariate and panel LM tests provide strong evidence for convergence of Australia's tourism markets. This implies that policies aimed at attracting visitor arrivals from any one of Australia's thirteen tourist source markets will boost the volume of tourists coming into the country.

Are G7 per capita real GDP levels non-stationary, 1870–2001?

In this paper we examine whether or not G7 per capita income can be classified as a stationary process using data for over a century. The unit root null hypothesis is tested using the recently developed Lagrange multiplier test which allows for at most two structural breaks. We are able to reject the unit root null hypothesis for all the countries at the 5 percent level or better, except for Italy and Germany.

Are output fluctuations transitory? New evidence from twenty four Chinese provinces

The fact that an occurrence of a unit root in real output is inconsistent with the notion that business cycles are stationary fluctuations around a deterministic trend makes this an important topic for empirical investigation. We examine this issue for 24 Chinese provinces using the recently developed Lagrange multiplier panel unit root test which allows for a structural break. Our main finding is that real gross domestic product (GDP) and real GDP per capita for Chinese provinces are stationary fluctuations around a deterministic trend.

Structural breaks and unit roots in Australian macroeconomic time series

We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.

Evidence on PPP for selected Asian countries from a panel cointegration test with structural breaks

The goal of this article is to examine evidence for purchasing power parity (PPP) for a panel of Asian countries, namely Malaysia, Thailand, India, Pakistan, Sri Lanka and the Philippines. Our main contribution is that for the first time in this literature we use a panel cointegration test, developed by Westerlund (2006), which allows us to incorporate multiple structural breaks. We find that using Gregory and Hansen's (1996) residual-based test for cointegration and Pedroni's (1999) panel cointegration test without structural breaks provide weak evidence of cointegration between nominal exchange rates vis-à-vis the US dollar and relative prices. However, when we use the Lagrange multiplier panel structural break cointegration test we find strong evidence of panel cointegration, providing evidence for PPP.

Introduction to section 4

The nature and extent of the implementation of digital technology in mathematics curricula along with issues of access and equity were the issues considered by one working group of this ICMI study. A summary of the discussion conducted by the working group and the findings reported in the following chapters on this theme are presented. It is clear that widespread and sustained use of digital technology is not common and that where digital technology is used there are complex and confounding equity issues.

Gender and socio-economic issues in the use of digital technologies in mathematics

This paper has been prepared to address the issues and questions of the theme ‘access, equity and socio-cultural issues’. Findings from two studies are reported. In the first study gender issues in mathematical learning environments when computers were used were investigated. In the second effective practices for teaching disadvantaged or marginalised students with digital technology are canvassed. Teaching for equity and social justice in the digital age is complex. Teachers need to be aware that their beliefs and classroom practices may exacerbate gender and cultural inequalities in mathematics learning. Approaches that are consistent with social-constructivist and democratic theories need further investigation.