The Effects of Monetary Policy in the US. The Vector Error Correction Model (VECM) compared to the Structural Autoregressive Model (SVAR)
Studienarbeit 2017 18 Seiten
3 The LSE approach
3.1 Vector error correction model
3.3 Coefficients instability
4 Structural VAR
4.1 Sign restrictions
4.2 Impulse response functions
Estimating and anticipating the effects of monetary policies on the economy has always been one of the main concerns in macroeconomics. Most of mone- tary policies are systematic; namely, dictated by rules. However, economists are primarily interested in non-systematic movements in monetary policy in order to estimate their causal effects on macroeconomic variables. For this purpose, deviations from the monetary rules are used to investigate the re- lation between monetary policy and the economy through the simulation of shocks or their structural identification (Ramey, 2016).
This paper investigates the effects of monetary policy in the US by com- paring a system of equations - estimated from a VECM (vector error cor- rection model) - to a SVAR (structural autoregressive) model. Vector error- correction models are used when there exist long-run equilibrium relation- ships between non-stationary data integrated of the same order. Those models imply that the stationary transformations of the variables adapt to disequilibria between the non-stationary variables in the model. In contrast, SVAR models focus on the contemporaneous interdependence between the variables (Pfaff, 2008). We apply these two methods on a model with a contractionary monetary policy which affects the short-term interest rate. Following Sims and Zha (2006) we use a shock to the Treasury Bill rate instead of a shock to the Federal Funds rate, this is also in line with Sims (1986) and Amico & King (2017).
The paper continues as follows. First, a description of the data is given. Sec- ondly, it presents a system of equations built from the LSE approach, aiming at macroeconomic simulations. Thirdly, it compares results obtained from the previous part to those obtained using SVAR impulse response functions (IRFs) identified with sign restrictions. The paper focuses on the impact of the simulated policies or monetary shocks on GDP and its growth rate.
The data was retrieved from the FRED database. The data set consists of the following monthly time series from July 1959 to March 2017.
- LY: log of real GDP, seasonally adjusted
- LRM 2: log of real M2, seasonally adjusted
- LRI: log of real gross private domestic investment, seasonally adjusted
- LP CE: log of real personal consumption expenditures, seasonally ad- justed
- π: Inflation, computed from Consumer Price Index, seasonally ad- justed
- R m: nominal own return on M2
- R b: interest rate on three-month Treasury Bills as a proxy for the Federal funds rate
- LT R: log of total reserves
- UNRATE: unemployment rate
- π commod: The inflation of the commodity price index for all commodi- ties.
The data for output and investment could only be found quarterly and were therefore interpolated linearly into monthly time series. Moreover, the two measures of inflation were computed as the growth rate of the consumer price index - or commodity price index - over one year, to be of the same scale as the interest rates.
According to augmented Dickey-Fuller (ADF) tests, all variables are in- tegrated of order 1, with the exceptions of π commod, which is stationary and unrate, which appears to behave as a long memory process. We will nonetheless consider the unemployment rate as stationary instead of taking a fractional difference, which would complicate the interpretation.
3 The LSE approach
For the creation of a system of equations, the LSE approach is used instead of the Cowles Commission (CC) approach. The CC methodology assumes that the structural form of the data generating process (DGP) is known qualitatively and the reduced form is then derived from it. The LSE ap- proach explains the failure of the CC approach; there is a lack of attention for the statistical model underlying the econometric structure adopted. The LSE approach recognises that economic theory suggests the general specifi- cation of the relevant form but the precise DGP is almost never known. The reduced form takes a central role within this approach in that it represents the crucial probabilistic structure of the data. The approach is thus turned backwards, the reduced form will lead to the structural one.
3.1 Vector error correction model
Various studies (e.g., Favero (2001)) have indicated cointegration - long- run equilibrium relationships - between the macroeconomic variables used here. Hence, to determine the potential number of cointegrating equations between the variables, we first estimated the number of lags to be included based on a VAR in levels, including lags of π commod and unrate, and a dummy representing the post-2008 crisis period as exogenous variables. The addition of commodity inflation will capture the effects of oil price crises or other significant commodity fluctuations that could have an effect on vari- ables in our model. Moreover, after the 2008 crisis, requirements for banks and monetary approaches have drastically changed, hence, the inclusion of the dummy will take that into account. Nonetheless, in the period 1979-1982 the monetary regime of the FED changed, from a strategy aimed at control- ling interest rates to a non-borrowed reserves targeting regime. The exis- tence of regime shifts and associated structural breaks is seen to undermine traditional forecasting procedures severely, hence, the sample was reduced to 1983-2017 (411 data points). Schwartz information criterion (BIC) advo- cates the use of two lags in levels, thus, only one lag for the first differences in the VECM. Consequently, the Johansen cointegration test was performed which suggested four cointegrating relationships. Various restrictions based on economic theory were imposed on the coefficients in the cointegrating equations and it appeared that only three of them were statistically differ- ent. This can be due to the relatively large number of variables included in the models as well as the exogenous ones that alter the critical values of the test. The three cointegrating relationships are presented in Table 1.
The first equation (ECM1) represents the long-run relationship between output and private consumption. Consumption depends positively on out- put since people tend to consume more when they have a higher income. The second equation (ECM2) is the long-run relationship of the interest on money with the market rate and inflation. An increase in inflation will, in the long-run, decrease the short-term interest rate since investors will be more willing to save than to invest, banks will therefore borrow less from the Fed as their minimum total reserves would be attained. Such a decrease in borrowing will thus decrease the ’price of money’, namely, the risk-free rate. On the other hand, an increase in market returns will increase invest- ments and consequently increase borrowing from investors. Banks will thus
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Table 1: Cointegrating equations
themselves need to borrow more from the Fed, leading to an increase of risk- free rate. The last equation (ECM3) is the long-run relationship between the total reserves with real M2 and short-term interest rate. As expected, if the amount of money available in the economy increases, the possibility for people to save expands as well, which in the long-run increases the to- tal reserves of banks. However, we would expect T bill 3 to have a positive effect on total reserves in the long-run since when it increases, people are more willing to save than to consume, intuitively leading to an increase in total reserves. However, as the money supply increases, market interest rate