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Exploramos la respuesta a esa pregunta en estos siete episodios. Grandes estrellas salieron de sus canteras, y sus hinchas eran conocidos en los estadios internacionales. Cuando una mujer se rebela contra las normas que la oprimen, cambia algo para todas. El movimiento empieza en una, pero las consecuencias son para todas. En diferentes momentos de su vida su aspecto la ha atormentado, inspirado, enfurecido, cerrado puertas y abierto otras. Sin lugar seguro Mariana vive sola en una casa en Tijuana y de vez en cuando le alquila habitaciones a turistas o viajeros. Toy Story A veces encuentras paz en los lugares menos esperados.

Moodle allows you to select some or all students and attach a single, common feedback file to their assignment feedback. This common feedback will appear to each student along with any other individual feedback files you have prepared for each.

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Usted quiere que ls estudiantes envien archivos en diferentes tiempos para un proyecto Set File submission to Yes, and use Maximum number of uploaded files to set the maximum number of separate files they can upload Advantage - all project files are in one assignment area for grading so they get a single grade.

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To download the original student submissions: In your course area, click the link to the Assignment whose submissions you want to download. Click the link to 'Download all submissions' and save the file. Sugerencias y Trucos Want to use an Assignment activity again in another Moodle site? Want to use an Assignment activity in another course you teach? Moodle will sometimes appear not to be uploading a resubmitted assignment - you seem to be downloading the original assignment.

The newer file will then appear. Assessing the order of integration of the variables Unit root tests are provided in Table 1. It can be seen that most variables display rather high first-order autocorrelation levels. It would not be surprising, then, to find unit- roots in the data.

In general, Dickey-Fuller tests suggest all variables are integrated of order one. On the other hand, Phillips-Perron tests do not reject non-stationarity in the cases of money balances and GDP. Finally, KPSS tests reject the null of stationarity in all cases. The contradictory picture emerging from unit-root tests on interest rates could be the result of the well-known low power of these tests when the true process is close to, but different than, a unit root see Cochrane, But, as discussed by Ghysels , Lee and Siklos , and Abeysinghe among others, it could also be that seasonal factors distort unit-root tests.

Lags were optimized according to marginal significance. The tests for non-seasonal unit roots tB suggest that all variables can be 1 adequately characterized as non-stationary in frequency zero that is, long-run non- stationary.

Moreover, HEGY tests found that most variables present unit roots at other frequencies. In particular, all variables present a unit-root at the semiannual tB and 2 quarterly frequencies tB , tB , with the only exception of the foreign interest rate. While in 1 4 most variables we are unable to reject the null hypothesis of non-stationarity according to B4, the evidence is mixed when considering tests on B3.

F tests of the joint hypothesis presented in the last column allow us to determine that unit-roots at the seasonal frequency are present in all variables except the foreign interest rate. As discussed above, DF, PP, and KPSS tests are sensitive to the presence of non stationarity in the residuals or to the incorrect pre-filtering of the series to remove seasonality. Moreover, since unit-root tests are sensitive to these problems, it is likely that cointegration tests applied in several studies of the demand for money in Chile may also be distorted.

Cointegration and Seasonal Cointegration We test for cointegration at the long run, semiannual, and quarterly frequencies using a two-stage strategy. An alternative procedure would be to follow the suggestion of Engle et al. Table 2 presents the results of estimating the trace statistics in each frequency. We use the critical values tabulated by Johansen and Schaumburg It can be seen that the data is consistent with only one hypothesized cointegrating vector in each frequency.

The presence of seasonal cointegrating vectors suggests that previously estimated models may be misspecified. In particular, there is no evidence of a second cointegrating vector at the zero frequency as claimed by Adam , which suggests the presence of spurious correlation problems in his paper.

An alternative strategy explored below is to estimate the non linear version single-step of the error correction-cointegration regression. Tests at frequency zero and semiannual include 5 lags. Quarterly frequency includes 2 lags. In the first row of table 3 we present the results for the long-run cointegration vector which, according to table 2, includes money balances, the scale variable GDP , and domestic and foreign interest rates.

Note that the scale elasticity is almost unitary, as found in other studies of the Chilean case, and the fit is quite high. Semi-elasticities for the interest rates are, as expected, negative and comparable in size to those found in previous studies. The disparate size of these parameters are, nevertheless, difficult to reconcile with the notion of asset substitutability. The second row in table 3 presents the result of testing for cointegration in the semiannual frequency.

According to seasonal unit roots, only money, income, and domestic interest rates should be included. It can be seen that residuals are stationary again cointegration DF tests apply as described in Engle et al, The inclusion of seasonal dummies is justified by the fact that, along with non-stationary seasonality, there can also be deterministic seasonal components.

The fit of these models is low especially when compared to the long-run cointegrating vector , thus suggesting that some of the determinants of intra-annual fluctuations have been omitted.

Determining which are those variables is an open area for further research. At the present time, we know that this is not caused by the exclusion of the foreign interest rate, which, as seen before, does not have a unit root in this frequency. The model cointegrates and there is no evidence of deterministic or stochastic seasonality in the residuals according to HEGY tests applied to the residuals.

The cointegrating seasonal vector adequately describes the seasonal aspects of the demand for money: since some seasonal dummies are significant in this model, seasonality is caused by both stochastic and deterministic factors.

Since the intuition behind the meaning of a cointegrating vector at the quarterly frequency may be hard to grasp, we provide a graphical description of what are these common seasonal trends. In figure 2 we present the seasonal component for the fourth quarter of real money balances and GDP. These components are obtained for each year by computing the actual value of each variable in the fourth quarter less the annual average.

It can be seen that these seasonal components fluctuate stochastically but tend to move together in the long run. Although in the short run they may deviate, it is likely that the seasonal components of series cointegrate. It is precisely this co-movement that is helpful when modeling the demand for money as it puts restrictions to seasonal fluctuations, allowing for more parsimonious and stable specifications.

The first alternative, suggested by Engle et al. In this case, one is implicitly disregarding the covariance between parameters in the cointegrating vector and those of the error-correction specification.

The second alternative is to estimate all parameters in a 23 nonlinear single-step error-correction model. The advantage of the former procedure is that it tends to be more robust to model mis-specification, while the latter provides consistent estimates.

The results of estimating both seasonal error correction models are presented in the first two columns of table 4.

As a benchmark of comparison, we estimated an error correction model using seasonally adjusted data with X methodology which we report in column three of the same table. The results can be summarized as follows. First, when comparing the results of the two models of seasonal cointegration, it can be seen that the fit to the data, the size of the parameters of the short-term variables, and the residuals are quite similar in both cases. The only notable exemption are the parameters of the foreign interest rate which are much bigger in the non-linear model.

In general, the similarity between the two models indicates that the nonlinear estimation does not yield a local maximum. The estimated loading factors " , nevertheless, bigger in the non-linear case. Both seasonal cointegration models produce stationary residuals at all frequencies. Moreover, cointegration is achieved avoiding the use of dummy variables and, as discussed below, our model is stable according to CUSUM tests see Figure 3.

The fit is very high above 0. The parameter of the foeign interest rate elasticity in the non-linear model The semiannual cointegrating parameters are very similar in both the nonlinear and two-step error correction model, with a scale elasticity statistically equal to one half, while the parameter of the domestic interest rate being one half of the long-run parameter.

When considering the quarterly frequency error-correction components, the results are mixed. For the second cointegrating vector, the estimated parameters differ significatively with to the two-step seasonal cointegration model.

The scale variable in the first quarterly cointegrating vector is, surprisingly, not significant at conventional levels in the case of the non-linear model. In fact, this result suggests that the adjustment is much faster than what previously believed, yielding new evidence on the speed at which the market operates. The adjustment towards equilibrium at semiannual frequencies is very fast 0.

On the contrary, at the quarterly frequency shocks dissipate slower than the semiannual frequency. Nevertheless, these estimated models have three important problems: 1 CUSUM and CUSUM of squares tests reveal models are unstable, 2 they present evidence of unit roots at the semiannual and quarterly frequency when the HEGY test is applied to the residuals of the cointegrating vector, 3 the fit of the error-correction model is markedly low.

Seasonal models suggest that the need to include dummies reflects only misspecification problems.

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The Stability of the Seasonal Error Correction Model The stability of these models can be graphically assessed by examining recursive tests on the linear error-correction specification non-linear models cannot be estimated recursively.

The results of estimating recursively the coefficients are displayed in Appendix Figure 1, while CUSUM tests are presented in figure 3. It can be seen that there is little evidence of structural instability in the estimated model. It can be seen the superiority of the nonlinear seasonal error-correction model with regards to standard dynamic models seasonally adjusted data, reflected in RMSE and MAE indicators that are significantly smaller than those of the linear models.

The results of the seasonal cointegrating models are similar to those obtained in previous studies with linear specifications, with the important difference that no dummies were included in the forecasting exercise.

A more important advantage, though, is that the model does not show the deterioration of its forecasting abilities during turmoil that characterizes the performance of standard error-correction models. Additional testing is provided by out-of-sample forecasts. The models were estimated in the period and a dynamic, out of sample forecast errors we computed for the period. This period comprises one of the most peculiar phenomenon in money markets. Agents began to increase their monetary holdings by the end of in precaution of potential computing problems in the financial sector derived from the change in the millenium the so called Y2K effect.

Monetary balances increased by 7. Since Y2K problems in Chile were non existent, money balances adjusted quickly downwards in the first quarter of The results are presented in Figure 4. It can be seen that in all models Y2K is a completely unanticipated event. The seasonal ECM is always closer to the real value of money balances than the traditional ECM models, although it overestimates money demand throughout Figure 4 Out of Sample Forecasts: Conclusions A stable money demand function is of paramount importance not only to monetary policy, but also for economic theory.

The empirical estimation of money demand functions in the Chilean case has been, as in many countries, a popular topic in applied econometrics. Likewise, it is not unusual to observe out-of-sample forecasts that over predict actual levels and are not useful to make recommendations for monetary policy based on monetary aggregates, a fact that has led most central banks to adopt interest rates as their instruments.

This study finds an empirical specification for money demand in the case of Chile, which solves many of the unstability and lack of robustness found on previous estimations. The methodology relies in a largely ignored issue, the information contained in the seasonal components of the determinants of money demand.

Evidence shows that money and its determinants have non-stationary seasonal processes. This made the use of seasonal dummies or filters inadequate. The use of incorrect seasonal adjustment leads to spurious correlations and unstable parameters in traditional estimations. A two-stage procedure reveals the existence of cointegrating vectors in all seasonal frequencies.

When these vectors are used to estimate money demand, the existence of common seasonal processes acts as an additional restriction that provides a better modeling of the behavior of money balances in the long run. As this allows to distinguish with more 31 clarity temporary and permanent shocks, a stable empirical estimation of money demand is found for the period , without using ad-hoc dummies.

The estimated function remains stable even through the crisis. Finally, the forecasting abilities of the seasonal cointegration models are way beyond those of traditional ECMs. With data for the period , the seasonal ECM has the lower prediction error, even accounting for the Y2K effect, an unexpected shock for all money demand specifications. The estimated demand is a valuable instrument to guide monetary policy, even if uses the interest rate —instead of monetary aggregates- as instrument.

In the future, this type of models should be upgraded, and extended to monthly data. Then, the convenience of alternative instruments in the conduction of monetary policy should be evaluated, comparing the volatility and forecasting power of money demand models with the growth and inflation models associated with interest rates policy.

References Abeysinghe T. Deterministic seasonal models and spurious regressions, Journal of Econometrics, 61, Adam, C. Apt, J.

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Quiroz Una Demanda de Dinero Mensual para Chile, Bohl, M.. Nonstationary stochastic seasonality and the German M2 money demand function, European Economic Review, 44, Canova, F. Hansen Are seasonal patterns constant over time? A test for seasonal stability, Journal of Business and Economic Statistics, 13, Chumacero, R. Testing for Unit Roots Using Macroeconomics. Central Bank of Chile. Clower, R.

A Reconsideration of the Microfoundations of Monetart Theory. Western Economic Journal , 6, Cochrane, J. Dickey, D. Fuller Testing for unit roots in seasonal time series, Journal of the American Statistical Association, 79, Engle, R. Granger Co-Integration and Error-Correction.

Representation, Estimation, and Testing, Econometrica, 35, Engle, R; C. Granger; S. Hylleberg; and H. Lee Seasonal Cointegration. Fair, R. Franses Ph. Unit-root tests and the statistical pitfalls of seasonal adjustment. Goldfeld, S. Sichel Friedman and F. Hargreaves, C. Hargreaves, editor, Oxford University Press.

Herrera, L. Vergara Herwartz, H. Reimers Hylleberg, S. Tests for seasonal unit roots. General to specific or specific to general? Journal of Econometrics, 69, Hylleberg, S.

Engle, C.