This study examines the validity of real interest rate parity by empirically analyzing developing economy's currencies versus the US dollar and the Euro. Using macroeconomic and financial data from five developing economies, we build a general theoretical framework to explore real interest rate parity theory. Contrary to popular opinion, our study finds evidence of deviations from the parity in developing economies in both cases of using the USA and Euro as numeri. The strong connection between the real interest rate differential and the three interaction terms(real exchange rate changes, nominal exchange rate changes, and the real interest rate-expected inflation rate differentials) confirms the non-trivial role played by the interaction terms. Furthermore, we support our findings by considering a currency risk factor and uncertainty as to the cause of the parity puzzle. We provide a new measure of uncertainty-the Exchange rate uncertainty index to provide empirical evidence of the deviations. We find that real interest rate parity is more likely to hold in low uncertain environments relative to high uncertainty ones. Therefore, we conclude that high economic uncertainty in developing economies that translates to high-risk premium explains why the parity does not hold.

Contents
1 Introduction…………………………………………………………………………………………… 1

2 The data…………………………………………………………………………………………………… 5

3 The Fundamental Models and Empirical Results……………………………………… 7
3.1 Uncovered interest rate parity………………………………………………… 7
3.2 Real Exchange Rate…………………………………………………………………… 7
3.3 Fisher's equation ……………………………………………………………………… 8
3.4 Deriving the model…………………………………………………………………… 9
3.5 Excess Returns………………………………………………………………………… 12

4 Exchange rate uncertainty index……………………………………………………………… 17

5 Conclusion……………………………………………………………………………………………… 21
6 References……………………………………………………………………………………………… 23

[1] Anthony, O., I. Onyinye and G.O.A. Emeka, 2013, \Does the Theory of Uncovered Interest Parity
Hold for Nigeria?" European Journal of Business and Management 5.
[2] Baker, S.R, N. Bloom and S.J. Davis, 2016, \Measuring economic policy uncertainty, " The quarterly
journal of economics 131, 1593-1636.
[3] Bekaert, G., M. Wei and Y. Xing, 2007, \Uncovered interest rate parity and the term structure,"
Journal of International Money and Finance 26, 1038-1069.
[4] Berg, K.A. and N.C. Mark, 2018,\Global macro risks in currency excess returns, " Journal of
Empirical Finance 45, 300-315.
[5] Berger, T., S. Grabert and B. Kempa, 2017,\Global macroeconomic uncertainty," Journal of Macroe-
conomics, 53, 42-56.
[6] Bilson, J.F., 1981 \Protability and stability in international currency markets, " NBER Working
paper, w0664.
[7] Bloom, N., 2009, \The impact of uncertainty shocks, " Econometrica 77, 623-685.
[8] Bui, A.T, 2010, \Tests of the Uncovered Interest Parity;Evidence from Australia and New Zealand,"
Higher Degree Research: book of abstracts, 17-18.
[9] Chang, M.-J. and C.-Y. Su, 2015,\Does real interest rate parity really hold? New evidence from G7
countries, " Economic Modeling 47, 299-306.
[10] Chang, M.-J., S. Chen and C.-C. Chien, 2019,\Real Interest Rate Parity in Practice: Evidence from
Asia-Pacic Economies.
[11] Chang, M.-J. and T.-H. Lee, 2020,\Monetary Policy Principle and Exchange Rate Dynamics in
Practice: An Application to Taiwan, " Working paper.
[12] Diebold, F.X., 2015,\Comparing predictive accuracy, twenty years later: A personal perspective on
the use and abuse of Diebold{Mariano tests," Journal of Business & Economic Statistics 33, 1-1.
[13] Engel, C., 1996.\The forward discount anomaly and the risk premium: A survey of recent evidence,"
Journal of empirical nance 3, 123-192.
[14] Engel,C., N.C. Mark and K.D. West, 2012, \Factor model forecasts of exchange rates," Working
Paper 18382, 1050 Massachusetts Avenue, MA 02138 Cambridge.
[15] Engel,C., 2016,\Exchange rates, interest rates, and the risk premium," American Economic Review
106, 436-74.
[16] Engel, C., D. Lee, C. Liu and S.P.Y. Wu, 2018, \The uncovered interest parity puzzle, exchange
rate forecasting, and Taylor rules," Journal of International Money & Finance, forthcoming.
[17] Engel, C., 2021,\A Reconsideration of the Failure of Uncovered Interest Parity for the US Dollar,"
National Bureau of Economic Research.
[18] Fama, E.F., 1984,\The information in the term structure, " Journal of nancial economics 13.4,
509-528.
[19] Hansen, L.P. and R. J. Hodrick, 1980, \Forward exchange rates as optimal predictors of future spot
rates: An econometric analysis, " Journal of political economy 88.5, 829-853.
[20] Jurado, K., S.C.Ludvigson and S.Ng, 2015, \Measuring uncertainty," American Economic Review,
105, 1177-1216.
[21] Karahan,  O. and O. C olak, 2012,\Does uncovered interest rate parity hold in Turkey?"
[22] McCracken, M. W., 2007,\Asymptotics for out of sample tests of Granger causality, " Journal of
econometrics 140.2, 719-752.
[23] Meredith, G. and M.D. Chinn, 1998, \Long-horizon uncovered interest rate parity, " National Bureau
of Economic Research, w6797.
[24] Nucera, F., 2017,\Unemployment
uctuations and the predictability of currency returns," Journal
of Banking & Finance 84, 88-106.
[25] Rossi, B. and T. Sekhposyan, 2015,\Macroeconomic uncertainty indices based on nowcast and forecast
error distributions," American Economic Review, 105, 650-55.
[26] Rossi, B. and A. Ismailov, 2017,\Uncertainty and deviations from uncovered interest rate parity, "
Journal of International Money and Finance 88, 242-259.
[27] Tanner, E., 1998,\Deviations from uncovered interest parity: a global guide to where the action is."
[28] Taylor, M.P., 1995, \The Economics of Exchange Rates," Journal of Economic Literature