## Summary of the Article

“Macroeconomics and Reality” is an article written by Christopher Sims and published in the Econometrica journal in 1980. In the article, Sims begins by stating clearly that there is a difference between economic theory and reality. In many cases, what is proposed by theories is not exactly what we see in real-life situations.

He further states that statistical models should be valuable in reconciling the theories to the reality. He however points out that few statistical economic models are utilized within the context of the large macroeconomic models. Sims’ article is thus aimed at explaining this quagmire and offering suggestions on how it can be solved. The aim of this paper is to critically analyze Sims’ article.

One of the issues raised by Sims (1) is the problem related to one-equation-at-a-time specification of a large model. It is true that the demand or supply of any commodity is influenced by an array of factors. Consider for instance the demand for cars in a country. This demand is affected by the price of the car, the price of other models of cars, tastes and preferences of consumers among others.

Thus, a large macroeconomic model will constitute all these variables some of which are endogenously determined while others are exogenously determined. The one-equation-at-a-time specification will however consider the influence of each of the variables on the demand separately thus leading to a set of demand functions.

When this happens, problem arises from the placement of the variables on either side of the equation. Sims states that, “… any variable which appears on the right hand side of one of these equations belongs in principle on the right hand side of all of them,” (3).

Sims (1980) also raises the concept of dynamism of large macroeconomic models. Dynamic models assert that changes in one variable will bring about changes in other variables of the model. Thus, the market will not be in equilibrium.

Sims (3) however states that the concept of dynamic models does not present any problem as long as the condition that markets clear is not violated. After analyzing the conventional processes followed in identification of economic modeling, Sims (4) argued that the restrictions that originate from economic theory which are imposed on structural models are incredible and therefore cannot be taken seriously.

These restrictions are required for the achievement of identification. Sims disagreed with the arbitrary normalizations which take place when an equation is claimed to offer an explanation of the many endogenous variables it contains.

He also criticized the one-equation-at-a-time specification process of macroeconomic models in which restrictions which are suitable for partial equilibrium models are imposed, thus bringing about unattractive systems properties. In situations where equations are dynamic, the identification process is more complex.

Likewise, policy variables are often assumed to be externally determined but in real-life situations they are usually partly endogenous. Sims (5) therefore claimed that only strictly exogenous variables can aid the identification process, and thus many apparently identified models are not in fact identified.

Sims (6) also touched on the issue of expectations. He argued that the behavior of an economic agent relies heavily on the expected future values of variables and these can be affected by any information currently available. For instance, if the price of oil in one country goes up for some reason which only affects that particular country, oil suppliers in the neighboring countries are likely to hike their prices based on the information they have and on the expectations.

Sims therefore argues that any variable that enters into an equation in a large macroeconomic model can influence expectations, and this causes more with identification.

In order to rectify all these problems of large macroeconomic models, Sims (15) suggested that no restrictions should be imposed on the equations. In other words, we should model unrestricted reduced form equations. This would give us equations in which each of the endogenous variables is dependent on lagged values of all the variables present in the system. While this seems to make sense, Sims fails to explain how we should select the list of variables making up the system.

## Statistics used in the Article

### F tests and Chi-square tests

The article by Sims (19) makes use of various statistical techniques. In table 1 of the article, the author presents a couple of statistics. The first statistic is the F statistic. The author argues that the F tests in this table are used to show the corresponding single-equation test statistics.

The second statistic is the Chi-square statistics. The author argues that the Ch-square statistics are likelihood ratio test statistics conditioned on the initial observations. Table 1 and 2 show the price controls in the United States and compares them with price controls in Germany over different time periods.

The data presented in the table 1 shows that there is little difference between the time periods under investigation. The main source of difference between the time periods resulted from the commodity price boom of 1973 and 1974. Besides reporting the F-test and Chi-square statistics, Sims (20) also makes reference to significance levels for both the United States and Germany.

Sims (1980) also argues that with reference to the sample split at year 1958, the Chi-square statistic for the United States was significant at 0.0007 (equivalent to significance level of 0.007 percent). This implies that the researcher was 99.9993 confident of the results.

On the other hand, the Chi-square statistic for Germany was significant at 0.003 (equivalent to significance level of 0.3 percent). This implies that the researcher was 99.997 confident of the results. The F-test is normally used to test the equality of two population variances. It is also used to test the joint significance of more than one coefficient, that is, it is used in multiple regression analysis and is equivalent to the t-test in a simple regression analysis.

In a multiple regression analysis, the F-test is used to test if the explanatory variables jointly explain the dependent variable. But in the article by Sims (19), the F-test is used to test the equality or differences in the variances of two populations. Specifically, the populations under study include the United States and Germany.

Sims also argues that the F tests used in his article do not have the normal F distribution because of the presence of lagged dependent variables in his model.

The Chi-square statistic on the other hand is used to test the goodness of fit of data. That is, the Chi-square tests whether the data originated from a population that has a particular distribution (Leedy & Ormrod, 25). The null hypothesis is that the data follows a specific distribution whereas the alternative hypothesis is that the data does not follow the specific distribution.

Sims (20) argues that the Chi-square statistics used in his article are likelihood ratio test statistics that are based on the original observations. In computing the statistics, the author used an unrestricted model in which a different parameter was introduced to explain each of the variables in the each of the periods under study.

## Standard errors

Table 5 of the article by Sims (25) makes use of standard errors. Standard errors are often confused with standard deviations (Leedy & Ormrod, 47). Standard errors are important in any statistical analysis involving a sample because they show how much a sample has deviated from the true population.

Standard errors are associated with the size of a sample: if the sample size is large, the standard error will be small but if the sample size is small, the standard error will be big. The standard errors reported in Sims (1980) are for data on the United States and West Germany.

The standard errors are generally small and range between 0.03 and 0.158. This implies that the samples chosen do not deviate so much from the populations.

## Conclusion

In sum, the article by Sims (1980) presents some interesting and thought-provoking arguments. In addition, Sims makes reference to several works previously done by authoritative figures in the field thus increasing the credibility of the article.

On the negative side, the article is full of jargons and words that are difficult to understand. Many of the models in the article are also difficult to understand. All these make the article unreadable especially to a layman and require repetitive reading in order to grasp the article’s context.

## Works Cited

Leedy, Paul and Jeanne Ormrod. *Practical research: Planning and design* (8^{th} ed.). Upper Saddle River: Pearson, 2005.

Sims, Christopher. “Macroeconomics and Reality.” *Econometrica* 48.1 (1980): 1-48.