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Long and variable lags are the time it takes for changes in monetary policy to fully affect the economy. The central bank may implement a policy to control inflation or stimulate growth, but the effects of these actions might not be seen immediately. Due to these lags, policymakers may struggle to assess the effectiveness of their actions and adjustments in the short term. Moreover, if the lags are unpredictable, it becomes even harder to target specific outcomes using monetary policy.

Excess reserves are the additional reserves banks hold beyond the required reserve ratio set by the central bank. This means that banks have more liquidity available to lend out, potentially leading to a larger money supply in the economy. When these excess reserves are significant, it is more difficult for the central bank to use monetary policy tools effectively. For example, in times of economic contraction, the central bank may decide to lower interest rates, hoping to encourage lending and stimulate growth. However, if banks have a large amount of excess reserves already available, lowering interest rates may not lead to the intended increase in lending, and the desired effect on the economy might not be achieved.

Velocity refers to the rate at which money circulates in an economy, or the number of times a unit of currency is used to purchase goods and services within a specific time period. Movements in velocity can complicate the implementation of monetary policy because changes in velocity can alter the relationship between money supply and nominal GDP. If the velocity of money increases, it means that a smaller increase in the money supply can lead to a higher level of nominal GDP. Conversely, a decrease in velocity would imply that a larger money supply may be necessary to achieve a desired level of nominal GDP. Since it is difficult for central banks to predict or control changes in velocity, the implementation of monetary policy becomes more challenging and less predictable. In conclusion, long and variable lags, excess reserves, and movements in velocity all complicate the implementation of monetary policy, making it more difficult for central banks to accurately predict and control their desired effects on the economy.