Application of three non-linear econometric approaches to identify business cycles in Peru

I use three non-linear econometric models to identify and analyze business cycles in the Peruvian economy for the period 1980:1-2008:4. The models are the Smooth Transition Autoregressive (STAR) model suggested by Teräsvirta (1994), the extended version of the Markov-Switching model proposed by Hamilton (1989), and the plucking model of Friedman (1964, 1993). The results indicate strong rejection of the null hypothesis of linearity. The majority of models identify quarters concentrated around 1988-1989 and 1990-1991 as recession times. Other important events which happened in the Peruvian economy (natural disaster in 1983, e¤ects of the Asian and Russian crises in 1990s, terrorist activities in 1980s) are not selected except as atypical observations. Most of models also identify the period 1995:1-2008:4 as a very long and stable period of moderate-high growth rates. From the perspective of the Peruvian economic history and from a statistical point of view, the MSIAH(3) model is the preferred model.Nonlinearities, Asymmetries, STARModel, Markov-Switching Model, Plucking Model, Recession Times

Estimating Output Gap, Core Inflation, and the NAIRU for Peru

Following Doménech and Gómez (2006), and using quarterly Peruvian data for 1970:1-2007:4, I estimate a model that exploits the information contained in the inflation, unemployment and private investment rates in order to estimate non-observable variables as output gap, the NAIRU and the core inflation. The unknown parameters are esti- mated by maximun likelihood using a Kalman filter initialized with a partially difuse prior, and the unobserved components are estimated using a smoothing algorithm. The results suggest that only the infla- tion rate contains useful information in order to estimate the output gap. Estimates suggest poor performance for the unemployment and private investment rates. I explain this issue as related to the poor quality of the construction of these variables. In order to perform a sensitivity analysis, I estimate the output gap using other alternative methods. The correlations are very different and very far away from the estimates obtained in this paper. It is clear that estimates obtained from simple statistical filters give poor approximations.Potential Output, Core Inflation, NAIRU, Latent Variables, Investment

Using A Forward-Looking Phillips Curve to Estimate the Output Gap in Peru

This paper identifies the output gap using the theoretical definition of the gap within a Phillips curve. The results show that the output gap is large and persistent. Furthermore, the output gap is not correlated with the stochastic trend which is similar to the asumption used in the unobserved components model. The model is extended to include information coming from the unemployment rate. The results are very similar to those obtained without this variable indicating poor additional information in the unemployment rate to identify the output gap. Other estimations of the output gap are performed. I use the procedures of Hodrick and Prescott (1997), Baxter and King (1999), Beveridge and Nelson (1981), Morley, Nelson and Zivot (2003), the unobserved components model of Clark (1987) and a simple quadratic trend. The results show strong di¤erences between our measure of output gap and the other measures. The closer measure is the one obtained using the unobserved component model and the simple quadratic trend.Business Cycles, Phillips Curve, Output Gap, Inflation, Unemployment, Filters

Measuring polarization, inequality, welfare and poverty

This paper analyzes the relationship between polarization and inequality, welfare and poverty measures. First, the Wolfson polarization measure is generalized in terms of the between-groups and within-groups Gini components for income groups separated by any z income value. Second, it is shown that polarization is the difference between the welfare levels of rich and poor income groups when feelings of identification between individuals are based on their utility functions. Third, the proposed polarization measure is a function of the Sen poverty index, its extension due to Shorrocks (1995) and the normalized poverty deficit index when the z income value represents the poverty line. In addition, these results are linked to the Esteban and Ray (1994) and Esteban et al. (1999) polarization measures.polarization, inequality, welfare, poverty.

Measuring Bipolarization, Inequality, Welfare and Poverty

This paper analyzes the relationship between bipolarization and inequality, welfare and poverty measures. First, we clarify the similarities and differences between bipolarization and inequality measures. Second, it is shown that bipolarization is the difference between the welfare levels of the richer and poorer income groups when feelings of identification between individuals are based on their utility functions. In fact, bipolarization is interpreted as the welfare of the richer group that is wasted to compensate for income bipolarization. Third, a relationship between bipolarization measurement and the normalized poverty deficit index is established. These findings are applied to the polarization measures of Wolfson (1994), Esteban and Ray (1994) and Lasso de la Vega and Urrutia (2006).bipolarization, inequality, welfare, poverty.

Partial and complete equality-of-opportunity orderings

This paper proposes a partial equality-of-opportunity ordering based on the inequality-of-opportunity curve, a mechanism that gives preference to those who are worse in terms of opportunity. Moreover, it provides a complete ordering that depends on a sensitivity parameter representing the degree of priority in the equality-of-opportunity policy. The Moreno-Ternero approach is obtained as a particular case. This proposal is applied to a set of 11 countries to compare their degree of equality of opportunity. Results show the relevance for economic policy of observing inequality of opportunity over tranches. Denmark dominates, in terms of posttax income, all other economies.equality of opportunity, partial ordering, circumstances, responsibility.

The daily market for funds in Europe: Mathematical appendix

This paper includes the derivations of the main expressions in the paper ``The Daily Market for Funds in Europe: Has Something Changed With the EMU?'' by G. Pérez Quirós and H. Rodríguez Mendizábal.Overnight rates, reserve demand, martingale hypothesis

Is there a link between unemployment and criminality in the us economy? Further evidence

Using Markov-Switching models, this paper studies the existence of a relationship between the unemployment rate and four different types of crimes in the U.S. economy. After it, using the non-parametric Concordance Index of Harding and Pagan (2002, 2006), the correlation between the cycles of unemployment rate and crime variables is determined. Results confirm that there is no significant relationship between the unemployment rate, burglary and motor-vehicle theft. However, the unemployment rate has a significant relationship with robbery and larceny. The contemporaneous relationship is positive for robbery and negative for larceny. However, it turns to be positive between the lagged values of the unemployment rate and larceny.Markov-Switching Models, Cycles, Unemployment, Crime.

ESTIMATION OF A TIME VARYING NATURAL INTEREST RATE FOR PERU

Following the approach of MÈsonnier and Renne (2007), we estimate a Natural Rate of Interest (NRI) using quarterly Peruvian data for the period 1996:3-2008:3. The model has six equations and it is estimated using the Kalman Ölter with output gap and NRI as unobservable variables. Estimation results indicate a more stable NRI in period 2001:3-2008:3 than in period 1996:3-2001:2 and also more stable than the observed real interest rate. Real interest rate gap (di§erence between real and natural rates), which measures monetary policy stance, indicates a restrictive policy for 1996-2001. Results also show a negative interest rate gap onwards, suggesting a less restrictive policy.Interest Rate / Natural Interest Rate / Kalman Filter / Output Gap / Unobserved Components.

Estimation of a Time Varying Natural Interest Rate for Peru

Following the approach of Mésonnier and Renne (2007), we estimate a Natural Rate of Interest (NRI) using quarterly Peruvian data for the period 1996:3 - 2008:3. The model has six equations and it is estimated using the Kalman filter with output gap and NRI as unobservable variables. Estimation results indicate a more stable NRI in period 2001:3 - 2008:3 than in period 1996:3 - 2001:2 and also more stable than the observed real interest rate. Real interest rate gap (difference between real and natural rates), which measures monetary policy stance, indicates a restrictive policy for 1996-2001 and for 2003. Results also suggest a real interest rate greater than NRI for 2002 and for 2004-2008.Interest rate, natural interest rate, Kalman filter, output gap, unobservable components