smooth transition regression

As a next step, we look at short-run adjustments and in particular at the short-run relationship between exports and domestic demand, but take into account the long-run equilibrium we have estimated above. For this purpose, we apply an error-correction model. As already mentioned in section 2, in this context we are also taking into account the possibility of non-linearities. This allows us to investigate a non-linear adjustment process to a linear long-run equilibrium relationship depending on the state of the economy. A variable might e.g. react more sharply in a recession than during an economic expansion, or might hardly react to a small change in economic conditions, but the effect strongly increases for larger changes in conditions. This could be estimated in the context of a simple threshold model. However, for some processes such as an economy’s export performance where individual firm-level decisions are aggregated, it may not seem reasonable to assume that this threshold is a sudden and abrupt change which is identical for all firms and which is commonly known; the smooth-transition regression (STR) model thus allows for gradual regime change or for a change when the exact timing of the regime switch is not known with certainty. The error-correction model with non-linear short-run adjustment in STR form then looks like this:

Our paper thus makes use of a smooth transition regression (STR) econometric model to estimate threshold effects in the inflation-growth relationship for quarterly data collected for the post-inflation targeting era i.e. 2001:Q1 to 2016:Q4. To the best of our knowledge, this study becomes the first to use this framework to estimate inflation thresholds for South Africa as a singular country. We have chosen the STR model as preferential choice of empirical framework because of it’s superiority over other competing nonlinear econometric model. F or instance, STR models conduct their transition between regression regimes in a smooth manner thus rendering the model as being more theoretically appealing in comparison to other threshold models which impose abrupt change in the regime coefficients (Phiri, 2015). Moreover, the STR model is designed in a manner which encompasses other nonlinear econometric models such as the threshold autoregressive (TAR) model and the Markov- Switching (MS) models.

DOI: 10.4236/ojbm.2018.61005 64 Open Journal of Business and Management TMT and corporate innovation, ignoring the effect of equity structure between team member and innovation performance. Despite the paucity of empirical re- search, the literature indicates that shareholding proportion of the largest shareholder can significantly influence the relationship. At the same time, en- terprise decision-making and collaboration won’t show a fixed percentage or causal relationship, but it is usually characterized by a nonlinear feedback. And, the relationship between TMT heterogeneity and innovation performance will be a nonlinear relationship with the dynamic change of shareholding proportion of the largest shareholder. Moreover, the role of shareholding proportion of the largest shareholder has become an important research direction in the field of strategic management. Given the above observation, the empirical study makes use of a panel smooth transition regression model (PSTR) to investigate the nonlinear relationship between top management team (TMT) heterogeneity and corporate innovation performance in listed companies of household appliance industry.

The money supply process is assumed to be fixed in economic literature or at least there is a central bank trying to control the liquidity in the economy. On the other hand, the demand side is more volatile and more uncertain. This situation hinders the homogenous and symmetric information assumptions of the monetary models. The amount of money demanded is a dynamic process and changes depending on the transition variable in concern. The money demand increases in the boom periods of the economy but may diminish in the recessions gradually. Therefore the money demand function indicates an asymmetric behavior and nonlinearity. This paper estimates the money demand function by including the inflation uncertainty, that is assumed to be a transition variable for a small-open economy, Turkey by using the monthly data spanning from January, 1990 to May, 2012. The parameters of the money demand function are estimated by the Smooth Transition Regression (STR) models. While modelling the nonlinearity, an appropriate logistic function is determined. The dependent variables that are used to estimate the money function are gold, interest rate, inflation uncertainty, share prices, exchange rate and income. The inflation uncertainty data is gathered from the conditional variances of a specified EGARCH model. The results of the paper have several policy implications for the monetary authorities. First, the behavior of the money demand and its determinants are crucial at the times of adopting the inflation targeting regime. The stability of money demand is also related to the stability of inflation. So the results of the paper may be beneficial for the policy makers and monetary authorities during their decision making process.

Bessec and Fouquau [11] investigated the relationship between electricity de- mand and temperature in 15 European countries over the period from 1985 to 2000 using monthly data. They applied a panel smooth transition regression (PSTR) model to describe the relationship between electricity demand and tem- perature in those countries and find threshold temperatures for those countries. In addition, in order to estimate the pure effects of temperature on electricity demand, they also followed Moral-Carcedo and Vicéns-Otero [10], and used dummy variables to represent summer holidays and time trends to filter out oth- er source of electricity consumptions. Their results showed that the nonlinear pattern was more pronounced in the warm countries among the 15 European countries.

Abonouri and Teimouri (2013) analyze the effect of financial development on economic growth in selected member states of Organization of Economic Cooperation and Development (OECD) with upper middle income countries and compare them with each other. The results indicate that financial development has negative and significant effect on economic growth of selected countries. Since the OECD countries have a higher level of development, the impact of this effect for this class of countries is lower. Also, the effects of other variables such as government size, inflation rate, lag of real GDP per capita, investment and openness is based on theoretical expectation. Mohammadi (2016) studied the nonlinear effects of main socio-economic variables as well as the financial development index (measured by private credit to GDP ratio) on the environmental pollution. Specifically, the interaction of the socio-economic variables with financial development as a threshold variable in affecting CO2 emission is studied. In this respect the PSTR (Panel Smooth Transition Regression) technique is applied to a panel- data set for 16 middle income countries (including Iran) during the period 1970-2013.It is found that output level and energy use have positive significant effect on CO2 emission on the whole but their effects at higher levels of financial development decrease and increase respectively i.e. financial development has provided motivations for shifting to eco-friendly technologies on the whole but has not been effective for applying fuel efficient technologies . The effect of population on CO2 emission at higher levels of financial development, intensifies . As to the effect of financial development ,it has a positive significant effect on pollution with a threshold level of 34 percent for financial development index i.e. up to this point ,the effect of financial development on the increase of pollution, rises at an increasing rate.

Most empirical studies have examined the effect of fiscal policy on activity in general or in times of crisis are based on panel models or on SVAR models. However, these two models do not take into account the nonlinear character of fiscal policy. To overcome this limitation, it is necessary to use Panel Smooth Transition Regression (PSTR). This econometric model provides advantage to generate different dynamics depending on the phase of the cycle. Based on these results, we try to establish empirical studies that allow providing robust answers to show how emerging economies can face challenges to conduct countercyclical fiscal policies. The aim of this paper is to evaluate the effectiveness of fiscal policy in emerging countries in periods of crisis. However, we investigate the effect of fiscal policy on economic activity, distinguishing between periods of recession and normal periods or expansion. Thus, we hope to achieve two goals in this work: one is to contribute to the economic literature on the topic; and the other is to have a more reliable yardstick available in order to explore the nonlinear effect of fiscal policy in emerging countries on the activity during periods of crisis.

Mathew and Moore (2011) assess factors that explain state incapacity in the Bihar State of India. Using a Panel Corrected Standard Errors regression model, Mathew and Moore (2011) analyse the determinants of capacity to spend transfers from central government, the Centrally Sponsored Schemes, by the Bihar State in comparison to the spending capacity by states with comparable income levels. They specified capacity to spend as a function of capacity to collect taxes by the state government, deficit (the Gross Fiscal Deficit of the state government as a percentage of state GDP), percentage of the state’s rural poor, agriculture share (percentage contribution of the agricultural sector to state GDP), and election, which is a dummy variable to indicate whether a national parliament or general election to the state assembly had taken place in the year in question (Mathew & Moore, 2011). The results show that the capacity to collect taxes (as a measure of a state’s fiscal capacity) is positively related to spending capacity, while the percentage of poor people is negatively related to spending capacity (Mathew & Moore, 2011). According to Mathew and Moore (2011), the results indicate that richer states perform relatively better in terms of spending capacity.

event A occurs and 0 otherwise. In that case the PSTR model in equation (1) reduces to the two-regime panel threshold model of Hansen (1999). For m = 2, the transition function has its minimum at (c1 + c2)/2 and attains the value 1 both at low and high values of qit. When    , the model becomes a three- regime threshold model whose outer regimes are identical and different from the middle regime. In general, when m > 1 and    , the number of distinct regimes remains two, with the transition function switching back and forth between zero and one at c1, . . . , c m .

The aim of this paper is to assess the sign and magnitude of the nonlinear effects of main socio-economic variables as well as the financial development index (measured by private credit to GDP ratio) on environmental pollution. Specifically, the interaction of the socio-economic variables with financial development as a threshold variable in affecting CO2 emission is studied. In this respect the Panel Smooth Transition Regression (PSTR) technique is applied to a panel-data set for 16 middle income countries (including some countries of BRIC and Iran) during the period 1970-2013.It is found that the output level and energy use have a positive significant effect on CO2 emission although their effects at higher levels of financial development decrease and increase respectively i.e. financial development provides motivations for shifting to eco-friendly technologies but not being effective for applying fuel efficient technologies in energy consumption. Moreover, it is shown that as the economies reach higher levels of financial development, the effect of population on CO2 emission intensifies. As to the effect of financial development, it has a positive significant effect on pollution with a threshold level of 34 % for financial development index, i.e. up to this point, the effect of financial development on the pollution, rises at an increasing rate.

This paper tries to verify the existence of the Armey curve, which states that there is an inverted U-shaped relationship between the government size and the economic growth. To that end, we use annual data over 1961-2008 to examine the existence of Armey curve in Greece. Instead of relying on a binomial model, which is very popular in the literature, we use a smooth transition regression (STR). STR models are very ‡exible and binomial models are considered as a special case of the STR models. The results show that there is a nonlinear connection, i.e., a threshold e¤ect, between the government spending and the growth rate in the Greek economy. However, since the relationship is positive in both regimes, i.e., before and after the threshold, we cannot con…rm the existence of Armey curve in the Greek economy.

Several researchers including Perron (1989, 1990), Rappoport and Rechlin (1989), Zivot and Andrews (1992), Lumsdaine and Papell, and Bai and Perron (1998) have recognized alternative trend specifications in testing for the unit root hypothesis. This strand of literature has focused on models with segmented line trends; and single or multiple breaks (Vougas, 2006). Yet, another strand of literature has developed unit root tests where the alternative hypothesis is that of stationarity around a smoothly changing trend. Leybourne, Newbold and Vougos (1996, 1998) (LNV, hereafter) and Sollis (2004) used logistic trend functions 3 that allow for a smooth break in the deterministic trend of the data. Bierens (1997) modeled nonlinear trend using Chebyshev polynomials, while Becker et al. (2006) used trigonometric functions (via means of Fourier transformations) to model possible gradual breaks in the data generating process. The use of either Chebyshev polynomials or trigonometric functions might be problematic, because there is no unique way of choosing the order of polynomials or the frequency components for the trigonometric functions. However, in the case of logistic trend functions the parameters of interest in the gradually changing trend function may be estimated using a convenient nonlinear estimation algorithm. By the same token, smooth transition regression (STR) models have also been proved to capture gradual structural breaks quite well (e.g., Granger and Teräsvirta, 1994; Lin and Teräsvirta, 1994; Greenaway et al. 1997). Moreover, the STR type trend modeling can incorporate broken or unbroken trend lines, thereby allowing for gradual as well as abrupt break (Vougas, 2006). Along these lines, the STR type of trend modeling can also be seen as a generalization of the first strand of trend modeling. Due

This paper investigates the relationship between industrial water withdrawal (IWW) and income in selected world countries. The issue is addressed by means of a smooth transition regression (STR) model on cross section data of 132 countries in 2006. The results confirm the nonlinearity of the link between IWW and income. According to the results, the income elasticity of IWW is a bell-shaped curve. Therefore, the policies and management processes in water sector including water allocation between activities and reigns should take into account the development degree and also fo- cus on income level, water scarcity and the economic, social and ecological structure in each country.

developed nonlinear econometric techniques to an updated version of the Friedman-Schwartz data set in order to model the demand for money in the US during the period 1869-1997. The results are encouraging on a number of fronts. We obtained a unique long-run money demand function relating real money, real income and the long-term interest rate, which displayed a plausible interest rate semi-elasticity of -0.058. Also, a dynamic evolution equation for the change in real money balances was obtained by estimating a nonlinear equilibrium correction in the form of an exponential smooth transition regression with the lagged long-run equilibrium error acting as the transition variable, implying faster adjustment towards equilibrium the greater the absolute size of the deviation from equilibrium.

However, we are not aware of any empirical study using a Multivariate Smooth Transition Regression framework or the Qu and Perron 2007 endogenous structural change approach to analyze th[r]

For Set 2, again we have a total of eight combinations to identify occurrence or non occurrence of events. It is evident that only those cases who observed the occur- rence of an event in Set 1 (i.e. made a transition) will be in Set 2 (i.e. can make a reverse transition). First two combinations observed an event (reverse transition) after observing a transition in Set 1 and coded as 1 for the event status column (Estatus) in Set 2. Hence these two combinations will be considered as an occurrence of an event for Set 2. Third to fifth combination in Set 2 did not observe any event after making a transition and will be considered as the non occurrence of an event for Set 2 and coded as 0 for the event status column (Estatus). Sixth and seventh combinations for Set 2 are also con- sidered as non occurrence of an event for this model due to missing observations after making a transition and are also coded as 0 for the event status column (Estatus). The covariate (X) value for Set 2 for first two combinations will be from follow-up 1 and follow-up two, respectively. The covariate (X) value for third to fifth combinations will be from fourth follow-up, since cases with these combinations did not change the state after making a transition. In case of missing data for outcome variable the covariate value for observation six to eight will be from second and third follow-up, respectively. The value of transition type (TranType) column is coded as 2 for all of the combinations corresponding to Set 2. Sequence number in (TranCode) column identifies the unique com-

The established conditions to the smooth-transitions may generate impossible patterns (in terms of the topological spatial relations that can actually exist). This impossible patterns need to be identified and eliminated from the set of valid ones (possible conceptual neighbors). One simple validation can be done by checking if the identified conceptual neighbor does match with one of the intersections matrices that are the possible topological spatial relations [1, 2]. If not, certainly that represents an impossible pattern. Although this simple validation, Egenhofer and Mark [7] defined two consistency constraints that are here adopted and extended in order to consider the specific case of the topological spatial relations that can exist between a CSEP (P) and a line (L). These constraints limit the possible transitions that can occur following conditions I to IV in order to guarantee that the identified patterns are valid. In that sense, these constraints are equivalent to some of the conditions used in the identification of the topological spatial relations that can exist between a CSEP and line [1, 2].

tested for countries as a whole, ignoring the urban/rural divide, as is usually done by other analysts. For our test- ing, the baseline date was chosen two years prior to the time at which the onset of the stall was proposed, since published estimates of TFR calculated over three years apply to the fertility level 1.5 years before the survey, on average. Among the seven countries investigated, none exhibited a significant stall during the proposed period when using the complete yearly data sets [See Table 3.] In Benin, Cameroon, and Mozambique, there were no significant changes in the slope of fertility declines since the previous surveys (2001 in Benin, 1998 in Cameroon, and 1997 in Mozambique), although the difference in slope was borderline when using the logistic regression in Mozambique. In Ethiopia and Uganda, the fertility decline accelerated during the second period (assumed to be a fertility stall), after 1999 in Ethiopia and after 1993 in Uganda. In Côte d’Ivoire and Zimbabwe, the speed of fertility decline was reduced significantly during the second period (1997-2005 and 1999-2006, respec- tively), but remained negative and far from a fertility stall defined by a slope equal to or above zero. In con- clusion, none of these hypothesized stalls was found to be statistically significant, whether using a linear regres- sion model or a logistic regression model.

A number of additional factors may limit the transfer- ability of the Avahan transition management lessons. First, Avahan addressed prevention needs of HRGs in a concentrated epidemic, rather than for a generalized epi- demic: a generalized epidemic would warrant a larger scale of activities, but government may find it easier to meet the general population’s needs compared to HRGs’ needs. Second, there has been substantial growth in the Indian government’s budget for HIV/AIDS since 2004, which means that there were adequate financial resources to support transitioned programs. Third, the NACP III provided a policy framework for HIV/AIDS prevention among HRGs in India, which closely matched the prin- ciples of the Avahan program [31]. Finally, there are relatively high levels of bureaucratic capacity across the Indian government’s HIV/AIDS administration. Despite these somewhat distinctive features of the Avahan tran- sition, we believe that many of the management lessons are transferable.

A further transmission channel for international spillovers stems from the fact that central banks no longer decide on policy rates in an independent way (Taylor, 2013). While interest rates have been set according to national conditions up to the turn of the century, policy reactions have been increasingly affected by the international environment since then. Hence, the deviations might indicate a substantial shift in the monetary policy regime. Among others, Kim (2000) demonstrated that US monetary policy shocks can affect other countries. Belke and Gros (2005) provided evidence that the ECB followed the Fed in its interest rate decisions. In fact, low US interest rates can increase risk-taking in other countries, and one option to react is to lower interest rates, see Bruno and Shin (2012). In addition, central banks tend to resist large exchange rate appreciations, and adjust their interest rates according to the behaviour of other central banks. Most importantly, the actions of the Federal Reserve Bank have been magnified due to the mimicking responses of other central banks (Gray, 2012). Overall, deviations from a Taylor rule can amplify due to international spillovers (Taylor, 2013). Deviations can also occur due to asymmetric behaviour by the central banks. For example, interest rate reaction functions can be different in expansionary and restrictive periods of monetary policy. This distinction may hold independently of an impact of international spillovers. Asymmetric responses lead to nonlinear Taylor rules as recently proposed by Riedl and Brüggemann (2011), among others. Such explanations might be better able to capture the evolution of policy rates. Expansionary and contractionary monetary decisions might be based on a different set of determinants. In this vein, Alcidi et al. (2009) show that linear Taylor rules fail to detect policy decisions driven by policy-makers' judgment while smooth transition models are well-suited to improve linear Taylor reaction functions.