Panel unit root tests under cross-sectional dependence

In this paper alternative approaches for testing the unit root hypothesis in panel data are considered. First, a robust version of the Dickey-Fuller t -statistic under contemporaneous correlated errors is suggested. Second, the GLS t -statistic is considered, which is based on the t -statistic of the transformed model. The asymptotic power of both tests is compared against a sequence of local alternatives. To adjust for short-run serial correlation of the errors, we propose a pre-whitening procedure that yields a test statistic with a standard normal limiting distribution as N and T tends to infinity. The test procedure is further generalized to accommodate individual specific intercepts or linear time trends. From our Monte Carlo simulations it turns out that the robust OLS t -statistic performs well with respect to size and power, whereas the GLS t -statistic may suffer from severe size distortions in small and moderate sample sizes. The tests are applied to test for a unit root in real exchange rates.     

Reinvestigating the Nature of Persistence of Shocks in the Macroeconomic Variables Relating to the Indian Economy with Special Reference to Structural Changes and Seasonality

Over the last two decades, there is a substantial debate on the persistence of shocks, in terms of their transitory and permanent nature, caused to the macroeconomic aggregates. Macroeconomic variables with transitory shocks will revert back to the long-run deterministic path eventually, whereas variables with permanent shocks will move according to random walk having no fixed predetermined path. These two series known as Trend Stationary (TS) and Difference Stationary (DS), respectively, have their significance in the specification of the regression equation and testing competing economic theories. Consequently there are a good amount of studies to classify the macroeconomic aggregates as TS vs. DS. In this context, relatively new developments of seasonal integration and presence of structural breaks in the macro variables has aroused a need to reinvestigate these hypotheses afresh. This paper makes an attempt to examine some of these issues by making use of the Indian data.

     

Regional convergence of growth,inequality and poverty in India—An empirical study

The paper attempts to examine whether there is regional convergence of per capita consumption, inequality and poverty across various states in India. Using panel unit root tests that are robust to cross-sectional dependence, we find that inequality and poverty indicators converge at both rural and urban levels. Further, per capita consumption converges at urban level but not at rural level. Based on factor analysis, we find two groups of states for rural sectors, viz., low-growth and high-growth states, for each of which per capita consumption converges. We also attempt at identifying the responsible entities — central or state governments or both in cases where convergence is not achieved.     

Coherent forecasting for count time series using Box–Jenkins's AR(p) model

During the last three decades, integer‐valued autoregressive process of order p [or INAR(p)] based on different operators have been proposed as a natural, intuitive and maybe efficient model for integer‐valued time‐series data. However, this literature is surprisingly mute on the usefulness of the standard AR(p) process, which is otherwise meant for continuous‐valued time‐series data. In this paper, we attempt to explore the usefulness of the standard AR(p) model for obtaining coherent forecasting from integer‐valued time series. First, some advantages of this standard Box–Jenkins's type AR(p) process are discussed. We then carry out our some simulation experiments, which show the adequacy of the proposed method over the available alternatives. Our simulation results indicate that even when samples are generated from INAR(p) process, Box–Jenkins's model performs as good as the INAR(p) processes especially with respect to mean forecast. Two real data sets have been employed to study the expediency of the standard AR(p) model for integer‐valued time‐series data.     

Price convergence across regions in India

The paper attempts to examine whether there is price convergence across various regions in India. Using panel unit root tests that are robust to cross-sectional dependence, it is found that relative price levels among various regions in India are mean-reverting. Further, we decompose each series into a set of common factors and idiosyncratic components. The decomposition enables us to test stationarity and estimate half-lives of the common factors and the idiosyncratic components separately. Both these components are found to be stationary. Idiosyncratic price shocks, however, are found to be more persistent as compared to the common factor. Results also indicate that transportation cost proxied by distance can explain a part of the variation in prices between two locations in India. The authors would like to thank Dibyendu Bhaumik for arranging the data for this study. Views expresed in the paper are personal and do not reflect the views of the organizations.     

Modelling money,price and output in India: a vector autoregressive and moving average (VARMA) approach

This article studies director additions and removals for S&;P 500 firms during the period 2000 to 2003. It finds that firms with smaller board size than estimated efficient levels add more and remove fewer directors than firms with larger board size. It also finds that firms with lower board independence than estimated efficient levels add more and remove fewer independent directors, and add fewer and remove more nonindependent directors than firms with higher board independence. These findings suggest that firms add and remove directors to adjust board structure in a manner consistent with economic efficiency.     

Change-point analysis through integer-valued autoregressive process with application to some COVID-19 data

In this article, we consider the problem of change-point analysis for the count time series data through an integer-valued autoregressive process of order 1 (INAR(1)) with time-varying covariates. These types of features we observe in many real-life scenarios especially in the COVID-19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time-varying smoothing covariate. By using such model, we can model both the components in the active cases at time-point t namely, (i) number of nonrecovery cases from the previous time-point and (ii) number of new cases at time-point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID-19 data sets and compare our proposed model with another PINAR(1) process which has time-varying covariate but no change-point, to demonstrate the overall performance of our proposed model.     

Causal ordering and inference on acyclic networks

This paper develops a new identification result for the causal ordering of observation units in a recursive network or directed acyclic graph. Inferences are developed for an unknown spatial weights matrix in a spatial lag model under the assumption of recursive ordering. The performance of the methods in finite sample settings is very good. Application to data on portfolio returns produces interesting new evidences on the contemporaneous lead–lag relationships between the portfolios and generates superior predictions.     

Inventory of differential items selling from two shops under a single management with periodically increasing demand over a finite time-horizon

Inventories of differential items including the defective ones purchased/produced in a lot and sold from two shops (primary and secondary shops) under a single management are considered here over a finite time-horizon. A primary shop receives the differential units in a lot but sells only the non-defective ones whose demand periodically increases with time and decreases during the shortage period in such a way that it comes back to the initial value at the beginning of the next cycle. Hence in this shop, shortages are allowed and fully backlogged. Moreover, at the beginning of the next cycle, the retailer purchases purely non-defective units at a higher price to meet up the shortage amount along with the usual lot of differential units for regular sale. The defective units identified at the time of selling at the primary shop are continuously transferred to the adjacent secondary shop from which the defective ones are sold at a reduced price after some rework. Normally, the price of a defective item is fixed depending upon the quantum of its defect and people go for these items if they are cheap. Hence, demand for these units is dependent on the selling price, which is again inversely proportional to the rate of defectiveness. There may be five scenarios for dealing with defective units depending upon the coincidence of the time periods at two shops. For all scenarios, problems have been mathematically formulated and solved by the use of both parametric study and a gradient-based non-linear optimisation method. The models are illustrated with the help of numerical examples.