Academic Research on Parity

• The purchasing power parity puzzle, Rogoff, K. (1996). Journal of Economic literature, 34(2), 647-668. The authors utilize a compositional multinomial logit model to study the effect of the introduction of the euro on currency invoicing, by using sample data of Norwegian imports from OECD countries for the period 1996-2006. They conclude that the introduction of the euro has resulted in Eurozone countries that have trade relations with Norway drastically increasing their share of home currency invoicing. Furthermore, Norwegian imports have been increasingly using the euro as a vehicle currency in lieu of the U.S. dollar.
• The purchasing-power parity doctrine: a reappraisal, Balassa, B. (1964). Journal of political Economy, 72(6), 584-596. The author adopts a novel approach to perusing the concept of purchasing-power parity. He introduces two different interpretations of this concept that he calls the absolute and the relative interpretations. Absolute interpretation: This interpretation states that the delineation of purchasing-power parities as a ratio of consumer goods prices for any two countries favors the approximation of the equilibrium exchange rates. Relative interpretation: This interpretation states that changes in relative prices indicate requisite exchange rate adjustments.
• Low-density parity check codes over GF (q), Davey, M. C., & MacKay, D. (1998). . IEEE Communications Letters, 2(6), 165-167. This paper scrutinizes the performance of binary low density parity check (LDPC) codes and concludes that when decoded by employing a probabilistic decoding algorithm, LDPC codes demonstrate performances nearing the Shannon limit. The authors employ the analogous codes over GF(q) for q>2, with binary symmetric channels and binary Gaussian channels. The results display significant improvements over the performance of the binary codes, including a rate 1/4 code with bit error probability <10/sup -5/ at E/sub b//N/sub 0/=0.2 dB.
• The myth of parity, Neuborne, B. (1976). Harv. L. Rev., 90, 1105. The author strongly contends that federal and state trial courts are not equally competent in enforcing federal constitutional rights. He cites the presence of numerous institutional dissimilarities between federal and state trial courts to conclude that constitutional litigators have always favored trials in federal courts to have their constitutional claims arbitrated. 
• The capacity of low-density parity-check codes under message-passing decoding, Richardson, T. J., & Urbanke, R. L. (2001). IEEE Transactions on information theory, 47(2), 599-618. The authors outline a procedure for measuring the capacity of low-density parity-check (LDPC) codes under message-passing decoding. The procedure involves decoding binary-input memoryless channels with discrete or continuous output alphabets. Any rate of transmission that is below the LDPC capacity will result in a randomly small target probability of error. Conversely, any rate of transmission above the LDPC capacity will cause the probability of error to bound away from zero by a strictly positive constant. 
• The overvaluation of purchasing power parity, O'Connell, P. G. (1998). Journal of international economics, 44(1), 1-19. The author states that recent studies of purchasing power parity have shown that mean-reversion exists in real exchange rates. Nevertheless, these studies have ignored cross-sectional dependence in the data, on occasions inflating the significance level of tests with a nominal size of 5 percent to an incredible 50 percent. The paper goes further to state that when controlled for cross-sectional dependence, panels did not display evidence against the random walk null. 
• The purchasing power parity debate, Taylor, A. M., & Taylor, M. P. (2004). Journal of economic perspectives, 18(4), 135-158. The paper traces the origins of the concept of purchasing power parity (PPP) and studies its utilities in both the short and the long terms. Towards the beginning of the 21st century, PPP estimates showed significant improvements owing to the usage of larger sets of data as well as nonlinear economic methods. 
• Parity time synthetic photonic lattices, Regensburger, A., Bersch, C., Miri, M. A., Onishchukov, G., Christodoulides, D. N., & Peschel, U. (2012). Nature, 488(7410), 167. The design of new artificial optical structures has, thus far, been exploiting their refractive index properties. However, newer methodologies incorporating paritytime symmetry have suggested the simultaneous usage of both gain and loss in order to achieve newer levels of optical behavior. This study observes the travel of light in large-scale temporal lattices that are paritytime symmetric. Additionally, the authors assert that operating periodic structures near their exceptional points will will make them function as unidirectional invisible media. 
• Purchasing power parity in the long run, Abuaf, N., & Jorion, P. (1990). The Journal of Finance, 45(1), 157-174. The authors scrutinize the long-term effects of purchasing power parity (PPP). The paper seeks to disprove the theory that the real exchange rate follows a random walk. The authors apply powerful techniques of estimation to a multilateral framework and conclude that while deviations from purchasing power parity are sizeable in the short term, they still require a period of roughly three years to be reduced in half.
• Purchasing power parity tests in cointegrated panels, Pedroni, P. (2001). Review of Economics and Statistics, 83(4), 727-731. Pedroni scrutinizes the strong version of purchasing power parity for a panel of post Bretton Woods data and compares outcomes by employing fully modified and dynamic OLS approaches. Based on these outcomes, Pedroni is able to disprove the hypothesis and introduce a new between-dimension dynamic OLS estimator. He concludes that the between-dimension FMOLS and DOLS approximations of the long term deviation from PPP are larger than the corresponding within-dimension approximations. The interest rate parity theorem: A reinterpretation, Aliber, R. Z. (1973).Journal of Political Economy, 81(6), 1451-1459. Aliber samples 163 central banks and evaluates their indices of central bank autonomy (CBA). He also evaluates comparable indices for a subgroup of 68 banks within the sample. Aliber concludes that economic and political CBA indices have shown significant improvements within the span of a couple of decades. However, he contends that it is only through further improvements that central banks in emerging economies can hope to attain satisfactory political autonomy.