Contemporaneous variables

What Are Contemporaneous Variables?

Contemporaneous variables refer to two or more variables that are observed or measured within the same time period and exhibit a statistical relationship or mutual influence. In the field of Econometrics and Time Series Analysis, these variables are crucial for understanding how different economic or financial factors interact concurrently. The concept highlights instances where cause and effect can operate simultaneously, making it challenging to untangle their individual impacts. When analyzing contemporaneous variables, researchers often seek to quantify the degree to which these variables move together at the same point in time.¹² Understanding the interplay between contemporaneous variables is fundamental for building accurate Economic Models and making informed decisions.

History and Origin

The rigorous study of contemporaneous relationships between economic variables gained significant traction with the development of simultaneous equation models in the mid-20th century. Pioneers in econometrics recognized that many economic phenomena involve variables that are jointly determined, meaning they influence each other within the same time frame. This realization led to a shift from simple, single-equation Regression Analysis to more complex systems of equations designed to capture these interdependencies.

A pivotal institution in this development was the Cowles Commission for Research in Economics, founded in 1932 by Alfred Cowles. The Cowles Commission, initially in Colorado Springs and later affiliated with the University of Chicago and then Yale University, played a crucial role in advancing econometric theory and the application of mathematical and statistical methods to economic problems.¹¹ Researchers associated with the Cowles Commission, including Nobel laureates, were instrumental in developing techniques to estimate parameters in models where variables exhibit contemporaneous relationships, addressing the biases that arise from such interdependence. Their work laid the foundation for understanding and modeling economic systems where variables affect each other simultaneously rather than sequentially.

Key Takeaways

• Contemporaneous variables are measured in the same time period and show a mutual relationship or influence.
• They are a core concept in econometrics, especially in the context of simultaneous equation models.
• Understanding contemporaneous variables is essential for accurately modeling complex economic systems where multiple factors interact concurrently.
• The statistical relationship between contemporaneous variables does not automatically imply Causation; further analysis is often required to establish causal links.¹⁰
• Proper analytical techniques are necessary to address the challenges posed by contemporaneous variables in statistical estimation.

Interpreting Contemporaneous Variables

Interpreting contemporaneous variables involves understanding that their observed relationship occurs within the same snapshot of time. For instance, if consumer spending and retail sales increase in the same month, they exhibit a contemporaneous relationship.⁹ This suggests a concurrent movement, but it doesn't immediately clarify which variable is driving the other or if a third, unobserved factor is influencing both.

In financial analysis, interpreting the relationship between contemporaneous variables requires careful consideration of underlying economic theory and market mechanisms. Analysts might observe that a sudden change in interest rates (a key Monetary Policy tool) and immediate shifts in bond prices are contemporaneous. While the policy change clearly influences bond prices, bond market reactions might also feed back into expectations that further influence the central bank's future actions. Accurately evaluating these relationships is critical for Forecasting and policy assessment, often requiring advanced statistical techniques beyond simple Correlation analysis to disentangle complex feedback loops.

Hypothetical Example

Consider a simplified economic model involving two contemporaneous variables: consumer confidence (C) and discretionary consumer spending (S). We hypothesize that higher consumer confidence leads to increased discretionary spending, and simultaneously, robust spending levels can bolster consumer confidence.

Let's assume we collect monthly data for a local economy. In a given month, we observe:

• Consumer Confidence Index (C) = 105 points
• Discretionary Consumer Spending (S) = $500 million

In the following month, we see:

• Consumer Confidence Index (C) = 108 points
• Discretionary Consumer Spending (S) = $520 million

Here, the increase in both C and S from one month to the next represents a contemporaneous relationship. The challenge in analyzing these contemporaneous variables is to determine the precise influence of one on the other within that same month, given their mutual dependence. A simple Regression Analysis treating one as purely a Dependent Variable and the other as a sole Independent Variable might produce biased results because each variable is also, in part, a cause of the other. Special econometric methods are needed to model such a system and accurately estimate the parameters of their concurrent interaction.

Practical Applications

Contemporaneous variables are fundamental in many areas of finance and economics, particularly where real-time interactions are crucial. They appear in:

• Macroeconomic Modeling: Central banks and government agencies use models with contemporaneous variables to understand the immediate impact of policy changes. For example, the Federal Reserve analyzes how current interest rate adjustments might concurrently affect inflation and employment figures. Organizations like the Federal Reserve Bank of Atlanta even publish "nowcasts" of key economic indicators like GDP, which leverage contemporaneous data to provide timely estimates before official releases.⁸
• Market Analysis: In financial markets, understanding how asset prices, trading volumes, and volatility interact in real-time is key. High-frequency trading models, for instance, must account for the contemporaneous influence of bid-ask spreads, order book depth, and trade execution speeds.
• Economic Forecasting: While lagged variables are often used for prediction, contemporaneous relationships help refine short-term forecasts and provide a more accurate picture of the current economic state. Policymakers and researchers, including those at institutions like the Brookings Institution, increasingly emphasize the importance of "real-time data" for effective decision-making.⁷ This real-time data captures contemporaneous movements and allows for more agile policy responses.
• Policy Evaluation: Governments and research institutions rely on contemporaneous data to assess the immediate effects of new regulations or fiscal policies, informing whether interventions are having their intended concurrent impact on economic activity.

Limitations and Criticisms

While essential for understanding real-time interactions, contemporaneous variables present significant challenges, primarily related to Endogeneity and the resulting estimation biases. When two variables are contemporaneously determined, it becomes difficult to isolate the causal effect of one on the other using standard Ordinary Least Squares (OLS) regression. The core problem is that if an Independent Variable is also influenced by the Dependent Variable (or by the same unobserved factors affecting the dependent variable), it becomes correlated with the Error Term of the regression equation. This correlation violates a key assumption of OLS, leading to biased and inconsistent coefficient estimates.⁶

For example, if we try to model the relationship between money supply and inflation, both variables might influence each other simultaneously. An increase in money supply could lead to higher inflation, but rising inflation expectations might also prompt the central bank to adjust the money supply. Failing to account for this two-way Causation would yield unreliable results.

Addressing these limitations often requires more complex econometric techniques, such as Instrumental Variables (IV) estimation or two-stage least squares (2SLS). These methods attempt to identify exogenous sources of variation that affect only one of the contemporaneously related variables, thereby helping to isolate the true causal impact. However, finding valid and strong instrumental variables can be challenging in practice, and misspecification can introduce new biases.

Furthermore, economic data, especially that collected by statistical agencies like the U.S. Bureau of Economic Analysis (BEA), often undergoes revisions as more complete information becomes available. Initial "contemporaneous" releases of data are frequently updated, sometimes substantially, which means that analyses based on preliminary contemporaneous variables may need re-evaluation.⁵ This dynamic nature of economic data highlights the inherent difficulty in precisely capturing and interpreting contemporaneous relationships in real-time.

Contemporaneous Variables vs. Simultaneity Bias

The distinction between contemporaneous variables and Simultaneity Bias lies in their nature: contemporaneous variables are a characteristic of a system, while simultaneity bias is a problem that arises when analyzing such a system with inappropriate methods.

• Contemporaneous Variables: These are simply variables that interact or are determined within the same time period. Their simultaneous presence and mutual influence are a reality of many economic and financial systems, such as supply and demand curves determining price and quantity concurrently. It describes how variables are related in time.
• Simultaneity Bias: This is a specific type of Endogeneity that occurs in Regression Analysis when a Dependent Variable and one or more Independent Variables are jointly determined, leading to a bidirectional or circular causal relationship.⁴ If an ordinary least squares (OLS) model is used without accounting for this mutual influence, the estimated coefficients will be biased and inconsistent. The "bias" refers to the inaccuracy in the statistical estimates caused by this simultaneous determination when not properly modeled.³

In essence, contemporaneous variables exist in models where variables affect each other in the same period. Simultaneity bias is the statistical distortion that occurs when standard Ordinary Least Squares techniques are applied to estimate relationships among these contemporaneously determined variables without correction. It is the problem that needs to be resolved when working with contemporaneous variables.

FAQs

Q1: Can contemporaneous variables imply cause and effect?

No, the presence of a contemporaneous relationship between variables does not automatically imply Causation. It only indicates that they move together within the same time frame. Establishing causation requires further analysis, such as using advanced econometric techniques or controlled experiments, to rule out confounding factors or reverse causality.²

Q2: Why are contemporaneous variables challenging to analyze?

Contemporaneous variables are challenging because their mutual influence can create Simultaneity Bias in statistical models. This bias arises when an Independent Variable is not truly exogenous but is also influenced by the Dependent Variable or unobserved common factors within the same period. This violates assumptions of common regression methods like Ordinary Least Squares, leading to inaccurate estimates.

Q3: How do economists deal with contemporaneous variables in their models?

Economists employ specialized econometric techniques to handle contemporaneous variables. Methods such as Instrumental Variables (IV), two-stage least squares (2SLS), and full information maximum likelihood are used. These techniques aim to account for the simultaneous determination and endogeneity issues to obtain unbiased and consistent estimates of the relationships between variables.

Q4: Are contemporaneous variables common in real-world economic data?

Yes, contemporaneous variables are very common in real-world economic and financial data. Many economic phenomena involve simultaneous interactions, such as the interplay between supply and demand, interest rates and investment, or consumer confidence and spending.¹ Recognizing and correctly modeling these contemporaneous relationships is crucial for accurate economic analysis and Monetary Policy formulation.