INTRODUCTION

Can the U.S. Federal Reserve (FED) indefinitely maintain low interest rates to stimulate the economy? Is it possible to accurately predict when the FED could modify its monetary policy rate without adversely affecting the dynamics of the real economy? The answer to these questions is of substantial importance because it is highly likely that in 2016, the FED will gradually increase its monetary policy rate not only to fulfill its mandate to promote economic growth with price stability but also to recover its primary monetary policy instrument¹. The economic literature suggests that a central bank should set its monetary policy rate at a level at which its average short-term rate equals the neutral interest rate. The latter is the rate that is compatible with the potential output of the economy and the target inflation rate of a central bank. In theory, if a central bank seeks to maintain its monetary policy rate below the neutral rate for a long period, the aggregate demand will exceed productive capacity and generate inflation. Thus, the value of the neutral rate is an important parameter with respect to answering our two questions and to establishing the policy stance of the monetary authorities.

However, a fundamental problem is that the neutral interest rate is not observable and can change over time (^{Clarida, 2015}). Consequently, it is of crucial importance for central banks to possess empirical methods that enable them to project the neutral interest rate to determine with greater certainty when it is possible to withdraw the monetary stimulus without the fear of creating a new recession. In the international literature, various methods have been proposed to estimate this rate, from the use of simple time-series models to highly complex approaches, such as dynamic stochastic general equilibrium models (^{Giammarioli and Valla, 2004}; ^{Barsky, Justiniano, and Melosi, 2014}; ^{Cúrdia et al ., 2015}). However, often, the estimates obtained using these methods have been imprecise and prone to specification errors (^{Pescatori and Turunen, 2015}).

In this context, this article's objective is twofold. First, a multivariate method is proposed to approximate the long-term neutral interest rate based on a Cointegrated Vector Autoregressive (CVAR) model. Second, an estimate of the value of the neutral interest rate for the U.S. economy is made using this method, and a brief discussion is provided on the appropriateness of the FED gradually increasing its monetary policy interest rate in the coming months. We believe that the result of our estimation method is indicative of and complementary to the estimates obtained with other models. Similarly, the proposed method can be a useful reference in analyzing the positions of a central bank because it enables the determination of how expansive the monetary policy should be in a context such as the current one.

Specifically, to simulate the value of the long-term neutral interest rate, we propose a simple method that is based on the identification of an equation for the federal funds rate in the cointegrating space of a CVAR model, which contains the fundamental variables of the real monetary sector of an economy. Our results for the U.S. economy suggest that the nominal neutral rate in 2016 will be approximately 0.56% and that the neutral real rate will be -0.89%. If we compare our results with the nominal and real rates obtained with the Laubach-Williams method² (2003), we can observe that they are above the value of our estimates. In addition, based on our model's projections to 2021, we can suggest that there remains a place for a longer period of expansionary monetary policy in the U.S. Fundamentally, we conclude that the current position of an interest rate close to zero could be extended without problems until the last quarter of 2018. If the FED determines to gradually increase the rate starting in 2016, economic losses would be generated for the U.S. and countries whose economies are closely linked to that of the U.S., such as Mexico.

This paper is structured as follows. The second section presents the framework of monetary theory that serves as the basis according to which we determine our long-term neutral interest rate measurement. In the third section, the econometric method used to estimate the long-term neutral interest rate is described. The fourth section presents the model and the neutral interest rate. In the final section, possible implications for the U.S. economy are briefly discussed.

DETERMINATION OF THE NEUTRAL INTEREST RATE

The neutral interest rate (r_t*) is defined as the short-term interest rate that is consistent with full employment and the inflation target of a central bank. It has also been defined as that interest rate that would be established if there was no nominal rigidity (^{Galí, 2002}) in such a way that at any time the real equilibrium would be basically determined by the fundamentals of the economy. Therefore, knowing the accurate value of this rate is of substantial importance for decision making by the monetary authority. The problem is that the long-term neutral rate is a non-observable variable, which complicates its estimation. In theory, its value can be approximated from the estimate of a short-term interest rate equation that depends on the fundamental variables of the economy (^{Taylor, 1993}). Thus, to estimate this rate for the U.S., the parameters of the federal funds interest rate equation r _t can be identified and estimated as a function of the fluctuations in the inflation gap π-π¯ (i.e., the difference between observed inflation and the target inflation) and the output gap y-y¯ (i.e., the difference between potential output and observed output).

[1]

which can also be expressed as follows:

[1a]

If β₁ = β₂ and θ₁ = θ₂, equation [1a] is equivalent to equation [1]. This formulation suggests that the monetary policy rate r _t should increase when inflation and the output level of the economy are above the target inflation and the potential output, respectively, and it should decrease otherwise. There is an expanded form of the Taylor rule that incorporates inflation expectations: π^e _t+1. This model does not substantially differ from the original. The only difference is that the latter contains the neutral interest rate in real terms.

[2]

Theoretically, if we can precisely estimate all of the components of equation [1], we can obtain the long-term nominal neutral interest rate through a simple algebraic manipulation as follows:

[3]

Based on this simple equation, we can define an empirical method to determine the value of the nominal neutral interest rate. To this end, the identification and estimation of equation [1] is proposed in a CVAR model, which provides the basis for the derivation of the value of the nominal neutral rate defined in equation [3]. In the following, we provided a more detailed explanation of the previously mentioned econometric method. In addition, we compare our results with a more traditional method, which estimates a neutral rate that changes over time, as has been popularized by Laubach and Williams for more than a decade.

ECONOMETRIC METHOD

In this section, we describe the econometric method used to empirically estimate the long-term nominal neutral interest rate in the U.S. economy. Fundamentally, the proposed procedure consists of identifying equation [1] in the error correction structure (long-term) of a CVAR model. Importantly, this procedure, which is based on a multivariate model, helps avoid problems of spuriousness when series are not stationary and the statistical biases that might arise from simultaneity problems, which are frequent in a single-equation estimate. Our model contains the fundamental variables proposed in equation [1], and its estimate enables us to infer not only the nominal neutral interest rate but also the neutral real rate.

In the presence of variables with unit roots, the estimation and identification of the long-term Taylor rule through a CVAR model can be performed in three steps. The first step involves specifying and estimating a VAR that is statistically appropriate for the set of variables that determine the monetary policy interest rate, r _t . That is, the nominal interest rate of the monetary policy, the real U.S. Gross Domestic Product (GDP), the potential GDP, inflation and inflation expectations are incorporated as the determinants of the rate. The estimate of this model involves choosing the order of lags of the VAR, the cointegration rank, the type of deterministic polynomial of the model and a sensitive specification of the space of cointegration (^{Johansen, 1995}, p. 74).

In the second step, the VAR model is transformed into a CVAR model to identify the long-term specific association between the nominal interest rate of the monetary policy and the inflation and output gaps. At this stage, the starting point is to estimate the CVAR model suggested in the following equation. Then, a series of restrictions are imposed on the model's long-term component:

[4]

That is, once model [4] has been estimated, restrictions are imposed on its error correction structure (αβ′z _t-1 ) to seek the identification of a cointegration relationship statistically significantly associated with equation [1], which can be estimated in the form of the following cointegrating vector:

[5]

where (y - y ^*) t -1 is the output gap; (π - π^*) t -1 is the inflation gap; e _t-1 is the error correction mechanism that represents policy rate, and r_t* is the non-observable long-term nominal neutral interest rate

Equation [1] must be exactly identified or over-identified in the CVAR, and the economic restrictions imposed in the long-term component must be validated by means of statistical evidence. Finally, the short- and medium-term validation of the CVAR model is performed using the traditional diagnostic tests (see Statistical ^Appendix) and a plausible modeling of the instantaneous correlations through the impulse response functions.

The third and final step in estimating the nominal neutral interest rate consists of using the estimated long-term equation [5] to estimate the rate based on the difference of the values of the monetary policy interest rate e _t-1 and the values predicted by the long-term equation, as suggested by equation [6]:

[6]

That is, the long-term signal of the non-observable neutral rate, r_t*, is extracted using the long-term equation identified and estimated by the CVAR model. This method is more appropriate than a single-equation model because it contains information on the dynamics and interactions between the involved variables.

EMPIRICAL RESULTS

For the econometric analysis, a statistically appropriate VAR model was estimated using variables from the U.S. monetary sector for the period 2000-2015. The data are released quarterly, and the output series is used in its logarithmic form. The remaining series that were used are the nominal interest rate of the monetary policy, the real U.S. GDP, the potential GDP estimated with the Hodrick-Prescott filter, inflation and expected inflation. The VAR model includes an unrestricted constant and three lags. The tests for unit root and for correct individual and joint specification of the model are shown in Tables 1a and 1b in the Statistical ^Appendix. The number of lags was selected based on the diagnostic of the general model. However, other tests were also used, such as the Schwarz information criterion, the Godfrey portmanteau test and the Likelihood Ratio (LR) test (see Tables 1c and 1d in the Statistical ^Appendix). First, the cointegration rank is analyzed based on Johansen's reduced-rank method. The trace statistics suggest that there are at least four cointegrating vectors, as shown Table 1 (^{Johansen, 1988, p. 235}).

To provide more evidence on the subject, Table 2 shows a sequential test, as described by Johansen (1995, chap. 11 and 12), for the joint determination of the cointegration rank and the polynomial trend³. Table 2 shows the testing for deterministic components with both the constant and the trend.

The results suggest there are at least four cointegrating vectors at the 95% confidence level. The Johansen maximum likelihood method also enables us to identify the cointegration space. One treatment used to solve the problem of identification is to adopt a set of a priori restrictions that are verifiable in the space of the long-term parameters (αβ′z _t-1 ). In this case, we normalize the first cointegrating vector as a long-term equation of the nominal interest rate of the monetary policy and then consider the hypothesis that the differences between the inflation and output gaps are stationary. That is, the coefficients of output and potential output are equal (β₁ = β₂) and the coefficients of inflation and expected inflation are equal (θ₁ = θ₂) in equation [1a]. The results shown in Table 3 suggest that these restrictions are statistically appropriate and enable a sensitive identification of the error-correction structure of the CVAR, as suggested by the over-identification test in the same table. That is, the data on the U.S. economy accept the restrictions associated with the Taylor rule. The normalized cointegrating vector is reported in the following as an equation of the federal funds rate.

Table 3 First normalized cointegrating vector as an equation of the federal funds interest rate 

Note: Over-identification test LR-CHISQR(2) = 0.514[0.473].

Source: Prepared by the authors based on the CVAR model.

The long-term relationship in Table 3 indicates that it is possible to identify a function according to which the policy interest rate should increase when there are increases in the output and inflation gaps, as indicated by the previous empirical models (^{Taylor, 1993}; ^{Clarida, 2015}). More concretely, it is confirmed that the gaps have a permanent effect and transmit macroeconomic information essential to the money market. The estimate of equation [1] using the CVAR model reveals a decrease in the coefficient of the output gap (0.26) and in the coefficient of the inflation gap (1.14) compared with the original coefficients of the Taylor rule (0.5 and 1.5, respectively) (^{Taylor, 1993}; ^{Clarida, 2015}). The preceding discussion suggests that the long-term neutral interest rate has probably decreased as a result of significant changes in the fundamentals of the U.S. economy in recent years.

DISCUSSION

In this section, we provide the estimate of the nominal neutral interest rate and the neutral real rate for the U.S. economy during the period 2000-2015 and their projections up to 2021. To this end, we use the cointegrating vector estimated through the CVAR in equation [7]. The neutral real rate is obtained by subtracting the inflation expectations that are obtained through an order-four autoregressive model of the inflation from the CVAR-projected nominal neutral rate. Table 4 shows our annual average projections of both rates and the estimate made by ^{Williams (2015)} to provide a reference parameter for the discussion of the relevance of the FED starting a new period of interest rate increase (^{Clarida, 2015}; ^{Clark and Kozicki, 2005}).

The neutral nominal rate estimated with our model reached a level of approximately 0.51 basis points (bps) in the period 2008-2015, whereas the neutral real rate was negative (approximately -1.033). If we compare this result with the neutral real rate results obtained with classical methods⁴, such as ^{Laubach and Williams (2003)}, we can observe that the results from our model coincide in direction but not in magnitude. In fact, our results are lower than the classical method results. The preceding suggests that according to our model the fundamentals of the U.S. economy in 2015 indicated that there was still a need to maintain an expansive policy. It is well known that in 2015, the FED decided for the first time in nearly seven years to increase this rate to a range of 0.25 to 0.50%. Our results and the most recent economic results seem to confirm that there is a full economic recovery and that the FED should defer a little longer the decision to increase its monetary policy rate. Thus, the CVAR estimates constitute a useful tool that can be used as reference to assess the positions of the central bank.

In addition, based on our model's projections for up to 2021, we can confirm that room remains for a longer period of expansive monetary policy in the U.S. (^{Pescatori and Turunen, 2015}). Fundamentally, we can conclude that the current position of an interest rate close to zero could be extended without problems until the last quarter of 2018 (see Graph 1).

Source: Prepared by the authors based on the prognosis of the CVAR model.

Graph 1 Projections of the nominal rate and neutral real rate for the U.S. economy: cvar model 

If the FED determines to gradually increase the rate starting in 2016, economic losses would be generated for the U.S. and countries whose economies are closely linked to the U.S. economy. In fact, according to our projections, the neutral real rate will remain negative until 2019, which means that the economy will continue to experience inflation below the 2% target and that unemployment will remain above the Non-Accelerating Inflation Rate of Unemployment (NAIRU) (^{Clarida, 2015}). In addition, the graph shows that despite the neutral nominal rate reaching a value between 2 and 3% after 2019, the rate would still be below the 4% estimated in the literature for the period prior to the 2008 crisis. This fact might indicate that the U.S. economy has undergone a structural change in its output potential and that the new neutral nominal rate associated with it is now substantially lower than the previously estimated 4%. Additionally, the neutral nominal rate is positive but very low in 2020, which indicates a need for the monetary stimulus not to be aggressively reduced because this action could result in a contraction with low inflation. Among other reasons for this outcome are that in the coming months, the GDP will likely be lower than the potential GDP and credit growth will also be very low (^{Bernanke, 2005}; ^{Clarida, 2004}; ^{Clarida, 2015}; ^{Hamilton et al. , 2015}).

It seems that although a massive monetary policy intervention to boost the economy in the manner of the 2008 intervention is not required (^{Summers, 2014}), the conditions do not exist for an aggressive increase in the FED bonds interest rate because the estimated figures suggest that the monetary stimulus should continue for at least three years if the economy is to resume sustained growth with an inflation within goal. However, as noted by ^{Clarida (2015)}, it is likely that the FED will start an aggressive program of monetary contraction once the economy achieves the NAIRU. However, too much anticipation could result in a contraction in the U.S. and closely linked economies, such as that of Mexico.

CONCLUSIONS

This article proposed a multivariate method to approximate the value of the long-term neutral interest rate based on a CVAR model. The results of our estimation method are only indicative. However, they may serve as a useful reference in assessing the positions of a central bank because they offer evidence of how expansive the monetary policy should be over time based on projections of the neutral nominal and neutral real rates. Our model projects a negative neutral real interest rate until the last quarter of 2018, which is substantially lower than the estimates reported in recent documents. The preceding discussion suggests that the U.S. economy will experience below-target inflation with an unemployment rate above the NAIRU for at least two more years. Thus, there is a need for the FED not to increase its reference interest rate in the coming months to avoid creating an economic contraction with low inflation. Generally, our empirical evidence suggests that a low neutral rate (approximately 2%) will continue until 2021, which means that this rate will not return to pre-crisis levels for a long time. In fact, it seems that the neutral rate has permanently changed to a lower level associated with the new fundamentals of the U.S. economy.

IMPORTANCIA DE LA TASA DE INTERÉS NEUTRAL Y HALLAZGOS DEL DOCUMENTO COMENTADO

De manera general, la tasa de interés neutral se define como aquella tasa de interés de corto plazo que prevalecería en la economía si esta se encontrara operando en su nivel potencial. De aquí que comparar el nivel de ésta con el nivel de la tasa de referencia establecida por un banco central sea fundamental para identificar la postura de política monetaria. Así, por un lado, si la tasa de referencia se encuentra por encima del nivel neutral, la política monetaria es restrictiva, ya que los distintos canales del mecanismo de transmisión de la política monetaria operan en el sentido de restringir el ritmo de crecimiento de la demanda agregada (con el fin de mitigar las presiones inflacionarias). Por otro lado, si la tasa de referencia se encuentra por debajo de dicho nivel, la postura de política monetaria es acomodaticia y, a su vez, el mecanismo de transmisión monetario estimula la demanda agregada.

No obstante su relevancia, la tasa neutral es un concepto predominantemente teórico y, por ende, no observable -su determinación requiere, en principio, conocer el estado de la economía en su nivel potencial en cada momento del tiempo-, lo que hace de su estimación una tarea difícil. Una complejidad adicional para su determinación es que la tasa neutral no es constante, sino que puede variar debido a cambios en factores económicos, que pueden ser poco o muy persistentes, o incluso permanentes.

En este contexto, y dado el proceso de normalización de la política monetaria que la Reserva Federal de Estados Unidos ha comenzado a llevar a cabo, luego de que a raíz de la crisis financiera global de 2008-2009 ésta redujera su tasa de referencia hasta alcanzar niveles de prácticamente cero por ciento -nivel en el cual permaneció durante siete años-, el análisis presentado en "Should the U.S. Federal Reserve increase the federal funds rate in 2016? An assessment based on the neutral interest rate", de Armando Sánchez-Vargas, resulta oportuno y relevante.

A grandes rasgos, el artículo puede dividirse en dos partes. En la primera, el autor propone un método empírico para estimar la tasa neutral de la economía estadounidense. Con base en los resultados de esta estimación, en la segunda parte realiza un diagnóstico sobre la conveniencia de que la Reserva Federal incremente la tasa de Fondos Federales, i.e. su tasa de referencia, en los próximos años.

Primero, el autor estima la tasa de interés neutral de Estados Unidos mediante el método de vectores autorregresivos cointegrados (CVAR en inglés), que consiste en establecer una relación de largo plazo entre la tasa de interés neutral respecto a la tasa de interés nominal, la brecha de la inflación y la brecha del producto. Para ello, se realiza la estimación en tres pasos: 1) se estima un VAR de orden tres para el conjunto de variables que determinan la política monetaria (inflación, expectativas de inflación, producto, producto potencial y la tasa de Fondos Federales); 2) el VAR se transforma en un CVAR, es decir, se imponen ciertas restricciones en la relación de largo plazo respecto a la brecha de inflación y la brecha del producto de tal forma que su estructura se asimila a una regla de Taylor y, de esta forma, obtener un vector de corrección de error, y 3) se estima la tasa de interés neutral de largo plazo utilizando el vector de corrección de error. De la estimación del CVAR, el autor encuentra que los coeficientes de la brecha de inflación y del producto disminuyeron en comparación con aquellos de la regla de Taylor (^{Taylor, 1993}), lo que lleva al autor a concluir que hubo un cambio significativo en los fundamentales de la economía estadounidense en años recientes, traduciéndose esto en una disminución de la tasa de interés neutral.

Posteriormente, utilizando el vector de corrección de error estimado mediante el CVAR descrito anteriormente, el autor proyecta la tasa de interés neutral hasta 2021. Los resultados de este ejercicio apuntan a que tanto la tasa de interés neutral real como la nominal se incrementarán gradualmente (lo que, implícitamente, supone que la inflación se acercará paulatinamente a su objetivo de 2%). En particular, la tasa de interés neutral real permanecerá negativa hasta 2017, para luego incrementarse hasta 0.34% en 2021; en tanto que su contraparte nominal aumentará de 0.56% en 2016 a 2.12% en 2021.

Los resultados anteriores llevan al autor a concluir que el hecho de que la tasa neutral nominal sea positiva pero muy baja "indica la necesidad de que el estímulo monetario [prevaleciente en la economía estadounidense] no sea reducido agresivamente, dado que esta acción podría resultar en una contracción [económica] con baja inflación".¹ Asimismo, el autor señala que existe evidencia para suponer que la tasa neutral de interés no regresará al nivel que tenía antes de la crisis por un periodo largo de tiempo y que, incluso, parecería que su nivel ha cambiado permanentemente a uno menor.

DISCUSIÓN

Como ya se mencionó, el tema de este documento resulta oportuno y relevante, a tal grado que, recientemente, la propia Reserva Federal ha divulgado los resultados de sus propios estudios sobre el tema en diversas publicaciones.² Por ello, es de suma importancia que el autor realice un esfuerzo adicional para comunicar de manera clara y detallada los principales puntos de su análisis y los argumentos que lo llevan a las conclusiones que plantea. En este sentido, a continuación se mencionan algunas recomendaciones que podrían ser de utilidad.

THE WICKSELLIAN CONNECTION AND THE THEORY OF THE NATURAL INTEREST RATE

The neutral interest rate is the cornerstone of Armando Sánchez's paper. Knut Wicksell, who pioneered the theory of the rate of interest "which is neutral in respect to commodity prices, and tends neither to raise nor to lower them", explained it as "the current value of the natural rate of interest on capital " (1965 [1898], p. 102; author's emphasis). Wicksell's interest-rate mechanism establishes the connection between the endogenous money supply and the supply and demand for credit, as well as the coordination of saving and investment.

It has been argued that the monetary system of various economies currently bear a strong resemblance to the Wicksellian mechanism of interest rates (see ^{Woodford, 2003}). While in Wicksell's model of a "pure credit economy" the capital rate is the centre of gravity of both prices and market interest rates, he envisaged basic information and coordination troubles with regard the determinants of the natural or neutral rate of interest on capital. Coordination failures of interest rates and saving and investment give rise to cumulative effects (inflationary effects when the market rate is lower than the capital rate and contractionary ones in the reverse case). Furthermore, it is important to bear in mind that Wicksell thought of his pure credit economy as an abstract construct or, to use David Laidler's expression, as an analytic fiction, one in which the natural or neutral rate is determined by real factors alone. Wicksell hardly treated his pure credit economy as a mirror image of a real-world monetary economy; nor he treats it as Woodford's moneyless economy in which the supply and demand for money plays no role whatsoever in the transmission mechanism of monetary policy. Moreover, even today's U.S. monetary system hardly works as Wicksell would have it in his theoretical abstraction.

Today's U.S. economy's neutral rate, Armando Sánchez maintains, has permanently declined (about 2%), and "will not return to pre-crisis levels for a long time". Such self-assured avowal, I surmise, suitably derived from Armando's CVAR model, begs the question of the causes which determine the neutral or natural rate of interest (cf. ^{Wicksell, 1965} [1898]), a puzzle that the Swedish highbrow economist painstakingly endeavoured to unravel theoretically in his notable piece of excavation Interest and Prices: keeping the average level of money prices constant "is to be regarded as the fundamental problem of monetary science" (^{Wicksell, 1907}, p. 219). Yet, Wicksell's solution to the natural rate conundrum hinges upon a number of convoluted assumptions. Since Armando Sánchez's paper is meant for the present journal's section called "for the scientific debate", some theoretical discussion of the precedent issue would have been appropriate to supplement Armando Sánchez's original empirical analysis of an economy -i.e. , that of the United States- facing a liquidity trap, stagnation, the zero lower bound, risks of (Wicksellian) cumulative effects and, most importantly, the imperative challenge of a return to normalcy.

TO HIKE OR NOT TO HIKE RATES?

Armando Sánchez's purpose, in this paper, is to empirically gauge, with the aid of a multivariate method, the long-term value of the Fed's neutral interest rate which is consistent with full employment and price stability. His results, derived from a cointegrated vector autoregressive model, lead him to delve into the rather complex question whether it would be reasonable for the U.S. Fed to increase its policy rate (the ^if ) any time during 2016-2018.

Some commentators have argued that the Federal Reserve is fuelling the next inflation (cf. ^{Meltzer, 2014}), and would like to see drastic rate hikes, and, for that matter, the Fed going back to a monetary policy system akin to that of the Great Moderation period, when inflation declined faster than both the ^if and the 10-year bond yield, except for the sub-period 2002-2005 in the case of the ^if when the Fed eased monetary policy to fight the dot-com recession (see Figure 2). However, clearly the long-run bond rate outgrew the federal funds rate for most of the Great Moderation period, until they converged on the eve of the outbreak of the Great Recession in 2007.

Source: FRED Economic Data, Federal Reserve Bank of St. Louis. Available through: < https://research.stlouisfed.org/>.

Figure 2 Interest rates and inflation during the great moderation, 1983-2007 (percentages) 

It seems that Armando Sánchez's empirical analysis does not support such a U-haul which would imply a return to the Great moderation era. In this regard, his most amazing findings are: (i ) a seemingly permanent lower long-term neutral interest rate, compared to the pre-Great Recession level; (ii ) a lower nominal neutral rate in 2016 (and even beyond 2020), also compared to the 4% level observed before the crisis; (iii ) a negative neutral real interest rate between 2016 (-0.899) and the beginning of 2018 (0.054), along with inflation rates below the inflation target (2%) and high unemployment rates; (iv ) all these empirical results are indicative of the U.S. economy undergoing deep changes in its fundamentals in the last decades. Therefore, Armando Sánchez concludes, there is policy space for monetary stimulus consistent with price stability, and the Fed should keep its current policy stance "for at least three [more] years if the economy is to resume sustained growth with inflation within goal". Thus, it turns out that the Fed should stand still on the ^if , otherwise deflation with output contraction would ensue. As it were, our author here appears to advocate a continuance of the zero interest rate policy (ZIRP), which makes an interest rate scenario similar to that of the post-Great Recession or quantitative easing period (see Figure 3), where the Fed systematically has kept ^if below the inflation rate target to support economic recovery.

Source: FRED Economic Data, Federal Reserve Bank of St. Louis. Available through: <https://research.stlouisfed.org/>.

Figure 3 Interest rates and inflation during the quantitative easing era, 2008-2016 (percentages). 

Other authors from different theoretical persuasions have also recommended the Fed should not engage in rate hikes for the time being (see ^{Borg, 2015}). Moreover, it seems -at least to the present commentator- that Armando Sánchez's main tenet of a permanent lower long-term neutral interest rate implies the Fed should adopt unconventional monetary policy as the new normal, a suggestion already made in another context by ^{Posen (2013)}, ^{Krugman (2015)} and ^{Summers (2015)}, among other New Keynesian analysts. Yet, this standstill position raises the questions of the potential risks, tradeoffs and costs associated with a zero lower bound and negative interest rates.

On the whole, what seems to be out of the question is that the policy normalization of the Fed will not entertain a return to a state of affairs of volatile interest rates and rampant inflation similar to the pre-Volcker era (see Figure 4), where, for reasons opposite to the ZIRP scenario, the Fed lost control of its policy tool.

Source: FRED Economic Data, Federal Reserve Bank of St. Louis. Available through: <https://research.stlouisfed.org/>.

Figure 4 Interest rates and inflation during the stagflation crisis, 1970-1979 (percentages) 

THE PATH TO NORMALIZATION

Armando Sánchez's paper raises two important queries (whether the Fed can indefinitely carry on its zero interest rate policy and whether the appropriate time for a benign "litoff" can be predicted). These inquiries belong to a Wicksellian tradition dealing with the influence of the rate of interest on prices and business fluctuations (see ^{Wicksell, 1965} [1898]; ^{Lindhal, 1930}; ^{Woodford, 2003}).

Armando's treatment of such queries makes the case for the policy space on hand to postpone the litoff decision until monetary accommodation will no longer be needed (about 2019, according to his econometric projections). What is also out of the question is that the day of reckoning, as it were, will come sooner or later, and the litoff shall take place in the realm of a quite substantial stock of excess reserves in the hands of the financial sector³. Yet, the paper under consideration bypasses another puzzling key aspect of the transition to normalcy, i.e. , the reduction of the Fed's balance sheet to a range commensurate with, say, that of the pre-Great Recession balance sheet size, and this is a not too easy trouble to deal with. For such a reduction will be slow and protracted; and what is more, given that the Fed's accommodative stance has to bear with long-term problems such as risks of financial instability, secular stagnation, slow productivity growth, "savings glut", debt overhangs and the like, the liftoff decision -occurring along with or without a balance sheet reduction- involves costs. But the no-liftoff option is not cost-free either: for instance, the ZIRP seems to hamper arbitrage in the federal funds market, and the costs a substantial balance sheet involves hinder interest rate margins (^{Williamson, 2015}). Therefore, and to wrap up, whatever decision is to be taken on the best timing for a liftoff should also include a hint of the best way for the Fed to exit QE in its path to normalcy.

COMENTARIOS SOBRE LAS RECOMENDACIONES PARA EL EJERCICIO ECONOMÉTRICO

La estimación del modelo CVAR utiliza las variables descritas en la regla de Taylor, en la ecuación [1] del documento original, pero la prueba de cointegración arroja la existencia de cuatro relaciones de cointegración porque se descomponen las brechas del producto y de la inflación en sus componentes, es decir en el PIB real y potencial, y en la inflación observada y la meta de inflación de la Reserva Federal. Como el objetivo del artículo es determinar una ecuación de la tasa de interés de corto plazo, sólo se lleva a cabo el proceso de identificación econométrica de dicho vector de cointegración. Sin embargo, como lo afirman los comentaristas, es completamente posible identificar una ecuación de producto, de inflación o alguna otra de acuerdo a la teoría económica. Sin duda, una completa identificación del espacio de cointegración del CVAR podría ofrecer una mayor precisión estadística. Este objetivo nos permitimos plantearlo como una tarea para futuras investigaciones sobre el tema.

Cabe destacar que la tasa de inflación en el CVAR es la tasa de crecimiento del índice de precios de los gastos de consumo personal excluyendo alimentos y energía, que es la misma que utilizan ^{Laubach y Williams (2003)} en el artículo donde estiman la tasa de interés neutral para Estados Unidos. Los métodos utilizados para estimar los valores históricos del producto potencial y la inflación de largo plazo son el filtro de Hodrick-Prescott y un modelo AR(4) respectivamente, lo que es muy común en la literatura previa.

Para verificar la robustez de nuestras estimaciones se estimó el mismo modelo CVAR pero usando el PIB potencial reportado por el CBO y la inflación tendencial que resulta de un VAR bayesiano (^{Primiceri, 2005}). Específicamente, se utilizó un VAR conocido como Time Varying Structural Vector Autoregressions (TVP-VAR) con volatilidad estocástica para estimar la inflación de equilibrio. A continuación se comparan dichas variables con las del modelo original (véanse las gráfica 1 y gráfica 2).

Fuente: elaboración propia con datos de la FRED Economic Data, Federal Reserve Bank of St. Louis. Disponible a través de: <https://research.stlouisfed.org/>.

Gráfica 1 Comparación de la inflación de equilibrio de un modelo AR(4) y de un TVP-VAR (porcentajes). 

Fuente: elaboración propia con datos de la FRED Economic Data, Federal Reserve Bank of St. Louis, disponible a través de: <https://research.stlouisfed.org/>, y del Congressional Budget Office, disponible a través de: <https://www.cbo.gov/>.

Gráfica 2 Comparación del pib potencial con Hodrick-Prescott y de la cbo (porcentajes). 

En principio, las series estimadas para la inflación de equilibrio con el TPV- VAR es bastante similar a la estimada con un modelo AR(4) como lo muestra la gráfica 1. Cabe destacar que la serie que tiene una mayor discrepancia cuando se usan diferentes métodos (Hodrick-Prescott versus CBO) es la del PIB potencial. No obstante, las tendencias de las series con diferentes métodos son bastantes similares, lo que nos lleva a pensar que no debería haber cambios muy drásticos en las estimaciones del nuevo CVAR.

Para verificar lo anterior, se estimó y proyectó la tasa de interés neutral siguiendo exactamente la misma metodología propuesta en el artículo pero usando el PIB potencial del CBO y la inflación de equilibrio del TVP-VAR. Los resultados de las proyecciones se reportan en el cuadro 1.

Los resultados de las columnas 3 y 5 son bastante similares a los de las columnas 2 y 4; solamente se observan cambios no muy grandes en magnitud, pero no en la dirección, lo que sugiere que hay evidencia de robustez no sólo ante cambios en las variables utilizadas, sino también ante cambios en los métodos de estimación de las variables no observables. Cabe destacar que habría que probar otros métodos y variables alternativas para aumentar la certidumbre sobre la robustez de las estimaciones que ofrece nuestra metodología.

Ahora bien, la estimación y proyección de la tasa neutral, como bien lo sugieren los comentaristas, es un ejercicio sujeto a una gran incertidumbre porque, por ejemplo, para estimar la brecha de producto se requiere una estimación del producto potencial que no es observable. Esto es, las estimaciones dependen de la precisión de los pronósticos de las brechas de producto y de inflación. Así, los resultados siempre estarán sujetos a los supuestos sobre los fundamentos y la evolución futura de la economía norteamericana. Por ello, para dimensionar adecuadamente la posible utilidad de nuestra metodología y la veracidad de sus resultados es importante aclarar que los pronósticos de la tasa neutral se realizaron tomando como base los pronósticos dinámicos del propio CVAR. Esto es, los insumos externos (inflación de equilibrio y PIB potencial) sólo se usaron para la parte histórica de la base de datos, y los pronósticos de la tasa neutral se realizaron tomando como base los pronósticos dinámicos del propio CVAR. Por lo tanto, una correcta especificación del CVAR es de crucial importancia en esta metodología. Es importante mencionar que también se podría incluir insumos externos de los pronósticos de las brechas y comparar resultados.

Con la finalidad de ofrecer más certidumbre a los lectores sobre nuestros resultados, a continuación se contrastan las trayectorias futuras de la tasa de crecimiento del PIB real, del PIB potencial y de la inflación que se derivan del CVAR con los pronósticos para las mismas variables publicados por la Reserva Federal y el CBO.

Las cifras del cuadro 2 sugieren que existe cierta similitud entre los pronósticos de las variables no observables del CVAR con los de la Reserva Federal y el CBO. No parece haber enormes discrepancias ni en las proyecciones de los insumos externos ni en los resultados derivados de nuestro método de análisis en el cuadro 2. Así, se confirma que los supuestos sobre las variables a futuro no son extremadamente diferentes a los utilizados por la Reserva Federal y los del CBO.

RECOMENDACIONES PARA LA INTERPRETACIÓN DE LOS RESULTADOS

En esta sección coincidimos con los comentaristas en que no se puede identificar la postura de política monetaria a través del nivel de la tasa neutral o de la tasa de referencia en aislamiento; se necesita de ambas tasas. En este caso, para juzgar si la política monetaria debería ser expansiva o restrictiva en el futuro, sería necesario evaluar la diferencia entre la tasa de interés de referencia pronosticada (una meta proyectada por el banco en el futuro) respecto al nivel pronosticado de la tasa neutral. En el cuadro 3 comparamos la trayectoria futura de la tasa de Fondos Federales según las proyecciones de la Reserva Federal (2016-208) con la trayectoria futura de la tasa neutral estimada mediante el modelo CVAR:

Estas cifras sugieren que la posición de política monetaria que implican las proyecciones de la tasa de corto plazo de la Reserva Federal seria restrictiva si las comparamos con las tasas neutrales derivadas del CVAR. Cabe mencionar que la anterior conclusión puede cambiar si comparamos contra tasas neutrales de un modelo de otra naturaleza.

Por ejemplo, en 2018 la Reserva Federal espera una tasa de interés objetivo de alrededor de 3 cuando nuestro modelo sugiere que debe ser de alrededor de 1.65. En consecuencia, con base en nuestras proyecciones de la tasa neutral y comparadas con las previsiones de la tasa de fondos federales de la Reserva Federal podríamos sugerir que la postura de política de ésta debería mantenerse mucho más moderada y que hay espacio para una política monetaria acomodaticia por al menos tres años más.

Como bien nos hacen notar nuestros comentaristas, si asumimos que nuestra metodología basada en el CVAR es robusta estadísticamente hablando, entonces el cuadro anterior ofrece cierta evidencia de que la política monetaria que podría seguir la Reserva Federal sería contractiva en los años venideros y que, aunque la tasa neutral muestra señales de recuperación, no alcanzaría a crecer más rápidamente que las proyecciones de la de corto plazo que publica en su prospectiva oficial. Así, la economía estadounidense experimentaría costos debido a una postura monetaria restrictiva. Si nuestras estimaciones son apropiadas, la orientación de la política monetaria debería ser aún más acomodaticia de lo que sugieren sus prospectivas.

Finalmente, se considera que la referencia a ^{Clarida (2015)}, sobre la previsión de que la Reserva Federal iniciará un programa de contracción monetaria agresiva una vez que la economía alcance la NAIRU, fue una cita colocada en un lugar inapropiado.